A Second-Order Phase Transition as a Limit of the First-Order Phase Transitions —Coherent Anomalies and Critical Phenomena in the Potts Models—

NASA Astrophysics Data System (ADS)

Katori, Makoto

1988-12-01

A new scheme of the coherent-anomaly method (CAM) is proposed to study critical phenomena in the models for which a mean-field description gives spurious first-order phase transition. A canonical series of mean-field-type approximations are constructed so that the spurious discontinuity should vanish asymptotically as the approximate critical temperature approachs the true value. The true value of the critical exponents β and γ are related to the coherent-anomaly exponents defined among the classical approximations. The formulation is demonstrated in the two-dimensional q-state Potts models for q{=}3 and 4. The result shows that the present method enables us to estimate the critical exponents with high accuracy by using the date of the cluster-mean-field approximations.

Scaling in the vicinity of the four-state Potts fixed point

NASA Astrophysics Data System (ADS)

Blöte, H. W. J.; Guo, Wenan; Nightingale, M. P.

2017-08-01

We study a self-dual generalization of the Baxter-Wu model, employing results obtained by transfer matrix calculations of the magnetic scaling dimension and the free energy. While the pure critical Baxter-Wu model displays the critical behavior of the four-state Potts fixed point in two dimensions, in the sense that logarithmic corrections are absent, the introduction of different couplings in the up- and down triangles moves the model away from this fixed point, so that logarithmic corrections appear. Real couplings move the model into the first-order range, away from the behavior displayed by the nearest-neighbor, four-state Potts model. We also use complex couplings, which bring the model in the opposite direction characterized by the same type of logarithmic corrections as present in the four-state Potts model. Our finite-size analysis confirms in detail the existing renormalization theory describing the immediate vicinity of the four-state Potts fixed point.

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.

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

PubMed

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.

A thermodynamic counterpart of the Axelrod model of social influence: The one-dimensional case

NASA Astrophysics Data System (ADS)

Gandica, Y.; Medina, E.; Bonalde, I.

2013-12-01

We propose a thermodynamic version of the Axelrod model of social influence. In one-dimensional (1D) lattices, the thermodynamic model becomes a coupled Potts model with a bonding interaction that increases with the site matching traits. We analytically calculate thermodynamic and critical properties for a 1D system and show that an order-disorder phase transition only occurs at T=0 independent of the number of cultural traits q and features F. The 1D thermodynamic Axelrod model belongs to the same universality class of the Ising and Potts models, notwithstanding the increase of the internal dimension of the local degree of freedom and the state-dependent bonding interaction. We suggest a unifying proposal to compare exponents across different discrete 1D models. The comparison with our Hamiltonian description reveals that in the thermodynamic limit the original out-of-equilibrium 1D Axelrod model with noise behaves like an ordinary thermodynamic 1D interacting particle system.

Ashkin-Teller criticality and weak first-order behavior of the phase transition to a fourfold degenerate state in two-dimensional frustrated Ising antiferromagnets

NASA Astrophysics Data System (ADS)

Liu, R. M.; Zhuo, W. Z.; Chen, J.; Qin, M. H.; Zeng, M.; Lu, X. B.; Gao, X. S.; Liu, J.-M.

2017-07-01

We study the thermal phase transition of the fourfold degenerate phases (the plaquette and single-stripe states) in the two-dimensional frustrated Ising model on the Shastry-Sutherland lattice using Monte Carlo simulations. The critical Ashkin-Teller-like behavior is identified both in the plaquette phase region and the single-stripe phase region. The four-state Potts critical end points differentiating the continuous transitions from the first-order ones are estimated based on finite-size-scaling analyses. Furthermore, a similar behavior of the transition to the fourfold single-stripe phase is also observed in the anisotropic triangular Ising model. Thus, this work clearly demonstrates that the transitions to the fourfold degenerate states of two-dimensional Ising antiferromagnets exhibit similar transition behavior.

Approximate ground states of the random-field Potts model from graph cuts

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Kumar, Ravinder; Weigel, Martin; Banerjee, Varsha; Janke, Wolfhard; Puri, Sanjay

2018-05-01

While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analog random-field Potts model corresponds to a multiterminal flow problem that is known to be NP-hard. Hence an efficient exact algorithm is very unlikely to exist. As we show here, it is nevertheless possible to use an embedding of binary degrees of freedom into the Potts spins in combination with graph-cut methods to solve the corresponding ground-state problem approximately in polynomial time. We benchmark this heuristic algorithm using a set of quasiexact ground states found for small systems from long parallel tempering runs. For a not-too-large number q of Potts states, the method based on graph cuts finds the same solutions in a fraction of the time. We employ the new technique to analyze the breakup length of the random-field Potts model in two dimensions.

Optimal region of latching activity in an adaptive Potts model for networks of neurons

NASA Astrophysics Data System (ADS)

Abdollah-nia, Mohammad-Farshad; Saeedghalati, Mohammadkarim; Abbassian, Abdolhossein

2012-02-01

In statistical mechanics, the Potts model is a model for interacting spins with more than two discrete states. Neural networks which exhibit features of learning and associative memory can also be modeled by a system of Potts spins. A spontaneous behavior of hopping from one discrete attractor state to another (referred to as latching) has been proposed to be associated with higher cognitive functions. Here we propose a model in which both the stochastic dynamics of Potts models and an adaptive potential function are present. A latching dynamics is observed in a limited region of the noise(temperature)-adaptation parameter space. We hence suggest noise as a fundamental factor in such alternations alongside adaptation. From a dynamical systems point of view, the noise-adaptation alternations may be the underlying mechanism for multi-stability in attractor-based models. An optimality criterion for realistic models is finally inferred.

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

DOE PAGES

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 increasingmore » 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.« less

Reducing a cortical network to a Potts model yields storage capacity estimates

NASA Astrophysics Data System (ADS)

Naim, Michelangelo; Boboeva, Vezha; Kang, Chol Jun; Treves, Alessandro

2018-04-01

An autoassociative network of Potts units, coupled via tensor connections, has been proposed and analysed as an effective model of an extensive cortical network with distinct short- and long-range synaptic connections, but it has not been clarified in what sense it can be regarded as an effective model. We draw here the correspondence between the two, which indicates the need to introduce a local feedback term in the reduced model, i.e. in the Potts network. An effective model allows the study of phase transitions. As an example, we study the storage capacity of the Potts network with this additional term, the local feedback w, which contributes to drive the activity of the network towards one of the stored patterns. The storage capacity calculation, performed using replica tools, is limited to fully connected networks, for which a Hamiltonian can be defined. To extend the results to the case of intermediate partial connectivity, we also derive the self-consistent signal-to-noise analysis for the Potts network; and finally we discuss the implications for semantic memory in humans.

A curious relationship between Potts glass models

NASA Astrophysics Data System (ADS)

Yamaguchi, Chiaki

2015-08-01

A Potts glass model proposed by Nishimori and Stephen [H. Nishimori, M.J. Stephen, Phys. Rev. B 27, 5644 (1983)] is analyzed by means of the replica mean field theory. This model is a discrete model, has a gauge symmetry, and is called the Potts gauge glass model. By comparing the present results with the results of the conventional Potts glass model, we find the coincidences and differences between the models. We find a coincidence that the property for the Potts glass phase in this model is coincident with that in the conventional model at the mean field level. We find a difference that, unlike in the case of the conventional p-state Potts glass model, this system for large p does not become ferromagnetic at low temperature under a concentration of ferromagnetic interaction. The present results support the act of numerically investigating the present model for study of the Potts glass phase in finite dimensions.

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Coexistence and Extinction Pattern of Asymmetric Cyclic Game Species in a Square Lattice

NASA Astrophysics Data System (ADS)

Dong, Lin-Rong; Li, Yong-Ming; Yang, Guang-Can

2010-06-01

The co-evolutionary dynamics of a cyclic game system is investigated in a two-dimensional square lattice with the asymmetrical rates for three species. Different with the well-mixed system, coexistence and extinction emerge alternately in the system, where a “zero-one" behavior is robust for a small population size, whereas, the system is predominated by coexistence for a big population one. We study in detail the influence about the fluctuation to the change of the state, and find that the difference between the maximal amplitude about the fluctuation and the average intensity determines which state the system is ultimately. In addition, we introduce Potts energy to explain the reason of the “zero-one" behavior. It is shown that the average Potts energy per site is the distance to the “zero-one" behavior in the model.

Radiative corrections to the quark masses in the ferromagnetic Ising and Potts field theories

NASA Astrophysics Data System (ADS)

Rutkevich, Sergei B.

2017-10-01

We consider the Ising Field Theory (IFT), and the 3-state Potts Field Theory (PFT), which describe the scaling limits of the two-dimensional lattice q-state Potts model with q = 2, and q = 3, respectively. At zero magnetic field h = 0, both field theories are integrable away from the critical point, have q degenerate vacua in the ferromagnetic phase, and q (q - 1) particles of the same mass - the kinks interpolating between two different vacua. Application of a weak magnetic field induces confinement of kinks into bound states - the "mesons" (for q = 2 , 3) consisting predominantly of two kinks, and "baryons" (for q = 3), which are essentially the three-kink excitations. The kinks in the confinement regime are also called "the quarks". We review and refine the Form Factor Perturbation Theory (FFPT), adapting it to the analysis of the confinement problem in the limit of small h, and apply it to calculate the corrections to the kink (quark) masses induced by the multi-kink fluctuations caused by the weak magnetic field. It is shown that the subleading third-order ∼h3 correction to the kink mass vanishes in the IFT. The leading second order ∼h2 correction to the kink mass in the 3-state PFT is estimated by truncation the infinite form factor expansion at the first term representing contribution of the two-kink fluctuations into the kink self-energy.

Potts-model critical manifolds revisited

DOE PAGES

Scullard, Christian R.; Jacobsen, Jesper Lykke

2016-02-11

We compute the critical polynomials for the q-state Potts model on all Archimedean lattices, using a parallel implementation of the algorithm of Ref. [1] 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 findmore » 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-Kadano phase for the lattices studied.« less

Coherent Anomaly Method Calculation on the Cluster Variation Method. II.

NASA Astrophysics Data System (ADS)

Wada, Koh; Watanabe, Naotosi; Uchida, Tetsuya

The critical exponents of the bond percolation model are calculated in the D(= 2,3,…)-dimensional simple cubic lattice on the basis of Suzuki's coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s-state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s→1 limit of the s-state Potts model.

From Principal Component to Direct Coupling Analysis of Coevolution in Proteins: Low-Eigenvalue Modes are Needed for Structure Prediction

PubMed Central

Cocco, Simona; Monasson, Remi; Weigt, Martin

2013-01-01

Various approaches have explored the covariation of residues in multiple-sequence alignments of homologous proteins to extract functional and structural information. Among those are principal component analysis (PCA), which identifies the most correlated groups of residues, and direct coupling analysis (DCA), a global inference method based on the maximum entropy principle, which aims at predicting residue-residue contacts. In this paper, inspired by the statistical physics of disordered systems, we introduce the Hopfield-Potts model to naturally interpolate between these two approaches. The Hopfield-Potts model allows us to identify relevant ‘patterns’ of residues from the knowledge of the eigenmodes and eigenvalues of the residue-residue correlation matrix. We show how the computation of such statistical patterns makes it possible to accurately predict residue-residue contacts with a much smaller number of parameters than DCA. This dimensional reduction allows us to avoid overfitting and to extract contact information from multiple-sequence alignments of reduced size. In addition, we show that low-eigenvalue correlation modes, discarded by PCA, are important to recover structural information: the corresponding patterns are highly localized, that is, they are concentrated in few sites, which we find to be in close contact in the three-dimensional protein fold. PMID:23990764

Coherent Anomaly Method Calculation on the Cluster Variation Method. II. Critical Exponents of Bond Percolation Model

NASA Astrophysics Data System (ADS)

Wada, Koh; Watanabe, Naotosi; Uchida, Tetsuya

1991-10-01

The critical exponents of the bond percolation model are calculated in the D(=2, 3, \\cdots)-dimensional simple cubic lattice on the basis of Suzuki’s coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s-state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s→1 limit of the s-state Potts model.

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

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 .

Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model

NASA Astrophysics Data System (ADS)

Pan, Xue; Zhang, Yanhua; Chen, Lizhu; Xu, Mingmei; Wu, Yuanfang

2018-01-01

We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class. Supported by Fund Project of National Natural Science Foundation of China (11647093, 11405088, 11521064), Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University (2016RC004) and the Major State Basic Research Development Program of China (2014CB845402)

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.

Multipoint Green's functions in 1 + 1 dimensional integrable quantum field theories

DOE PAGES

Babujian, H. M.; Karowski, M.; Tsvelik, A. M.

2017-02-14

We calculate the multipoint Green functions in 1+1 dimensional integrable quantum field theories. We use the crossing formula for general models and calculate the 3 and 4 point functions taking in to account only the lower nontrivial intermediate states contributions. Then we apply the general results to the examples of the scaling Z 2 Ising model, sinh-Gordon model and Z 3 scaling Potts model. We demonstrate this calculations explicitly. The results can be applied to physical phenomena as for example to the Raman scattering.

Bubbly vertex dynamics: A dynamical and geometrical model for epithelial tissues with curved cell shapes

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.

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

PubMed

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

2015-10-01

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

Ground-state entropy of the potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice

PubMed

Chang; Shrock

2000-10-01

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and W(q), the exponent of the ground-state entropy, for the q-state Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on square lattice strips, of width L(y)=3 and L(y)=4 vertices and arbitrarily great length Lx vertices, with both free and periodic boundary conditions. The resultant values of W for a range of physical q values are compared with each other and with the values for the full two-dimensional lattice. These results give insight into the effect of such nonnearest-neighbor couplings on the ground-state entropy. We show that the q=2 (Ising) and q=4 Potts antiferromagnets have zero-temperature critical points on the Lx-->infinity limits of the strips that we study. With the generalization of q from Z+ to C, we determine the analytic structure of W(q) in the q plane for the various cases.

Bayesian Image Segmentations by Potts Prior and Loopy Belief Propagation

NASA Astrophysics Data System (ADS)

Tanaka, Kazuyuki; Kataoka, Shun; Yasuda, Muneki; Waizumi, Yuji; Hsu, Chiou-Ting

2014-12-01

This paper presents a Bayesian image segmentation model based on Potts prior and loopy belief propagation. The proposed Bayesian model involves several terms, including the pairwise interactions of Potts models, and the average vectors and covariant matrices of Gauss distributions in color image modeling. These terms are often referred to as hyperparameters in statistical machine learning theory. In order to determine these hyperparameters, we propose a new scheme for hyperparameter estimation based on conditional maximization of entropy in the Potts prior. The algorithm is given based on loopy belief propagation. In addition, we compare our conditional maximum entropy framework with the conventional maximum likelihood framework, and also clarify how the first order phase transitions in loopy belief propagations for Potts models influence our hyperparameter estimation procedures.

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.

CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm: 2D and 3D Ising, Potts, and XY models

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.A. Hawick, A. Leist, and D. P. Playne, Parallel Computing 36 (2010) 655-678 [2] O. Kalentev, A. Rai, S. Kemnitzb, and R. Schneider, J. Parallel Distrib. Comput. 71 (2011) 615-620

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.

Inverse finite-size scaling for high-dimensional significance analysis

NASA Astrophysics Data System (ADS)

Xu, Yingying; Puranen, Santeri; Corander, Jukka; Kabashima, Yoshiyuki

2018-06-01

We propose an efficient procedure for significance determination in high-dimensional dependence learning based on surrogate data testing, termed inverse finite-size scaling (IFSS). The IFSS method is based on our discovery of a universal scaling property of random matrices which enables inference about signal behavior from much smaller scale surrogate data than the dimensionality of the original data. As a motivating example, we demonstrate the procedure for ultra-high-dimensional Potts models with order of 1010 parameters. IFSS reduces the computational effort of the data-testing procedure by several orders of magnitude, making it very efficient for practical purposes. This approach thus holds considerable potential for generalization to other types of complex models.

Boundary-field-driven control of discontinuous phase transitions on hyperbolic lattices

NASA Astrophysics Data System (ADS)

Lee, Yoju; Verstraete, Frank; Gendiar, Andrej

2016-08-01

The multistate Potts models on two-dimensional hyperbolic lattices are studied with respect to various boundary effects. The free energy is numerically calculated using the corner transfer matrix renormalization group method. We analyze phase transitions of the Potts models in the thermodynamic limit with respect to contracted boundary layers. A false phase transition is present even if a couple of the boundary layers are contracted. Its significance weakens, as the number of the contracted boundary layers increases, until the correct phase transition (deep inside the bulk) prevails over the false one. For this purpose, we derive a thermodynamic quantity, the so-called bulk excess free energy, which depends on the contracted boundary layers and memorizes additional boundary effects. In particular, the magnetic field is imposed on the outermost boundary layer. While the boundary magnetic field does not affect the second-order phase transition in the bulk if suppressing all the boundary effects on the hyperbolic lattices, the first-order (discontinuous) phase transition is significantly sensitive to the boundary magnetic field. Contrary to the phase transition on the Euclidean lattices, the discontinuous phase transition on the hyperbolic lattices can be continuously controlled (within a certain temperature coexistence region) by varying the boundary magnetic field.

Critical excitation spectrum of a quantum chain with a local three-spin coupling.

PubMed

McCabe, John F; Wydro, Tomasz

2011-09-01

Using the phenomenological renormalization group (PRG), we evaluate the low-energy excitation spectrum along the critical line of a quantum spin chain having a local interaction between three Ising spins and longitudinal and transverse magnetic fields, i.e., a Turban model. The low-energy excitation spectrum found with the PRG agrees with the spectrum predicted for the (D(4),A(4)) conformal minimal model under a nontrivial correspondence between translations at the critical line and discrete lattice translations. Under this correspondence, the measurements confirm a prediction that the critical line of this quantum spin chain and the critical point of the two-dimensional three-state Potts model are in the same universality class.

Multiscale multifractal DCCA and complexity behaviors of return intervals for Potts price model

NASA Astrophysics Data System (ADS)

Wang, Jie; Wang, Jun; Stanley, H. Eugene

2018-02-01

To investigate the characteristics of extreme events in financial markets and the corresponding return intervals among these events, we use a Potts dynamic system to construct a random financial time series model of the attitudes of market traders. We use multiscale multifractal detrended cross-correlation analysis (MM-DCCA) and Lempel-Ziv complexity (LZC) perform numerical research of the return intervals for two significant China's stock market indices and for the proposed model. The new MM-DCCA method is based on the Hurst surface and provides more interpretable cross-correlations of the dynamic mechanism between different return interval series. We scale the LZC method with different exponents to illustrate the complexity of return intervals in different scales. Empirical studies indicate that the proposed return intervals from the Potts system and the real stock market indices hold similar statistical properties.

A Q-Ising model application for linear-time image segmentation

NASA Astrophysics Data System (ADS)

Bentrem, Frank W.

2010-10-01

A computational method is presented which efficiently segments digital grayscale images by directly applying the Q-state Ising (or Potts) model. Since the Potts model was first proposed in 1952, physicists have studied lattice models to gain deep insights into magnetism and other disordered systems. For some time, researchers have realized that digital images may be modeled in much the same way as these physical systems ( i.e., as a square lattice of numerical values). A major drawback in using Potts model methods for image segmentation is that, with conventional methods, it processes in exponential time. Advances have been made via certain approximations to reduce the segmentation process to power-law time. However, in many applications (such as for sonar imagery), real-time processing requires much greater efficiency. This article contains a description of an energy minimization technique that applies four Potts (Q-Ising) models directly to the image and processes in linear time. The result is analogous to partitioning the system into regions of four classes of magnetism. This direct Potts segmentation technique is demonstrated on photographic, medical, and acoustic images.

Potts-model formulation of the random resistor network

NASA Astrophysics Data System (ADS)

Harris, A. B.; Lubensky, T. C.

1987-05-01

The randomly diluted resistor network is formulated in terms of an n-replicated s-state Potts model with a spin-spin coupling constant J in the limit when first n, then s, and finally 1/J go to zero. This limit is discussed and to leading order in 1/J the generalized susceptibility is shown to reproduce the results of the accompanying paper where the resistor network is treated using the xy model. This Potts Hamiltonian is converted into a field theory by the usual Hubbard-Stratonovich transformation and thereby a renormalization-group treatment is developed to obtain the corrections to the critical exponents to first order in ɛ=6-d, where d is the spatial dimensionality. The recursion relations are shown to be the same as for the xy model. Their detailed analysis (given in the accompanying paper) gives the resistance crossover exponent as φ1=1+ɛ/42, and determines the critical exponent, t for the conductivity of the randomly diluted resistor network at concentrations, p, just above the percolation threshold: t=(d-2)ν+φ1, where ν is the critical exponent for the correlation length at the percolation threshold. These results correct previously accepted results giving φ=1 to all orders in ɛ. The new result for φ1 removes the paradox associated with the numerical result that t>1 for d=2, and also shows that the Alexander-Orbach conjecture, while numerically quite accurate, is not exact, since it disagrees with the ɛ expansion.

On the nature of a supposed water model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heckmann, Lotta, E-mail: lotta@fkp.tu-darmstadt.de; 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-densitymore » 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.« less

Random-fractal Ansatz for the configurations of two-dimensional critical systems

NASA Astrophysics Data System (ADS)

Lee, Ching Hua; Ozaki, Dai; Matsueda, Hiroaki

2016-12-01

Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an Ansatz ensemble of random fractal images. By virtue of the central limit theorem, our Ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter Σ in the random fractal Ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.

Potts Model in One-Dimension on Directed Small-World Networks

NASA Astrophysics Data System (ADS)

Aquino, Édio O.; Lima, F. W. S.; Araújo, Ascânio D.; Costa Filho, Raimundo N.

2018-06-01

The critical properties of the Potts model with q=3 and 8 states in one-dimension on directed small-world networks are investigated. This disordered system is simulated by updating it with the Monte Carlo heat bath algorithm. The Potts model on these directed small-world networks presents in fact a second-order phase transition with a new set of critical exponents for q=3 considering a rewiring probability p=0.1. For q=8 the system exhibits only a first-order phase transition independent of p.

Conformal Field Theories in the Epsilon and 1/N Expansions

NASA Astrophysics Data System (ADS)

Fei, Lin

In this thesis, we study various conformal field theories in two different approximation schemes - the epsilon-expansion in dimensional continuation, and the large N expansion. We first propose a cubic theory in d = 6 - epsilon as the UV completion of the quartic scalar O(N) theory in d > 4. We study this theory to three-loop order and show that various operator dimensions are consistent with large-N results. This theory possesses an IR stable fixed point at real couplings for N > 1038, suggesting the existence of a perturbatively unitary interacting O(N) symmetric CFT in d = 5. Extending this model to Sp(N) symmetric theories, we find an interacting non-unitary CFT in d = 5. For the special case of Sp(2), the IR fixed point possesses an enhanced symmetry given by the supergroup OSp(1|2). We also observe that various operator dimensions of the Sp(2) theory match those from the 0-state Potts model. We provide a graph theoretic proof showing that the zero, two, and three-point functions in the Sp(2) model and the 0-state Potts model indeed match to all orders in perturbation theory, strongly suggesting their equivalence. We then study two fermionic theories in d = 2 + epsilon - the Gross-Neveu model and the Nambu-Jona-Lasinio model, together with their UV completions in d = 4 - epsilon given by the Gross-Neveu-Yukawa and the Nambu-Jona-Lasinio-Yukawa theories. We compute their sphere free energy and certain operator dimensions, passing all checks against large- N results. We use two sided Pade approximations with our epsilon-expansion results to obtain estimates of various quantities in the physical dimension d = 3. Finally, we provide evidence that the N=1 Gross-Neveu-Yukawa model which contains a 2-component Majorana fermion, and the N= 2 Nambu-Jona-Lasinion-Yukawa model which contains a 2-component Dirac fermion, both have emergent supersymmetry.

Phase diagram of the triangular-lattice Potts antiferromagnet

DOE PAGES

Jacobsen, Jesper Lykke; Salas, Jesus; Scullard, Christian R.

2017-07-28

Here, we study the phase diagram of the triangular-lattice Q-state Potts model in the realmore » $(Q, v)$ -plane, where $$v={\\rm e}^J-1$$ is the temperature variable. Our first goal is to provide an obviously missing feature of this diagram: the position of the antiferromagnetic critical curve. This curve turns out to possess a bifurcation point with two branches emerging from it, entailing important consequences for the global phase diagram. We have obtained accurate numerical estimates for the position of this curve by combining the transfer-matrix approach for strip graphs with toroidal boundary conditions and the recent method of critical polynomials. The second goal of this work is to study the corresponding $$A_{p-1}$$ RSOS model on the torus, for integer $$p=4, 5, \\ldots, 8$$ . We clarify its relation to the corresponding Potts model, in particular concerning the role of boundary conditions. For certain values of p, we identify several new critical points and regimes for the RSOS model and we initiate the study of the flows between the corresponding field theories.« less

Exploring first-order phase transitions with population annealing

NASA Astrophysics Data System (ADS)

Barash, Lev Yu.; Weigel, Martin; Shchur, Lev N.; Janke, Wolfhard

2017-03-01

Population annealing is a hybrid of sequential and Markov chain Monte Carlo methods geared towards the efficient parallel simulation of systems with complex free-energy landscapes. Systems with first-order phase transitions are among the problems in computational physics that are difficult to tackle with standard methods such as local-update simulations in the canonical ensemble, for example with the Metropolis algorithm. It is hence interesting to see whether such transitions can be more easily studied using population annealing. We report here our preliminary observations from population annealing runs for the two-dimensional Potts model with q > 4, where it undergoes a first-order transition.

Benchmarking Inverse Statistical Approaches for Protein Structure and Design with Exactly Solvable Models.

PubMed

Jacquin, Hugo; Gilson, Amy; Shakhnovich, Eugene; Cocco, Simona; Monasson, Rémi

2016-05-01

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.

Potts and percolation models on bowtie lattices

NASA Astrophysics Data System (ADS)

Ding, Chengxiang; Wang, Yancheng; Li, Yang

2012-08-01

We give the exact critical frontier of the Potts model on bowtie lattices. For the case of q=1, the critical frontier yields the thresholds of bond percolation on these lattices, which are exactly consistent with the results given by Ziff [J. Phys. A0305-447010.1088/0305-4470/39/49/003 39, 15083 (2006)]. For the q=2 Potts model on a bowtie A lattice, the critical point is in agreement with that of the Ising model on this lattice, which has been exactly solved. Furthermore, we do extensive Monte Carlo simulations of the Potts model on a bowtie A lattice with noninteger q. Our numerical results, which are accurate up to seven significant digits, are consistent with the theoretical predictions. We also simulate the site percolation on a bowtie A lattice, and the threshold is sc=0.5479148(7). In the simulations of bond percolation and site percolation, we find that the shape-dependent properties of the percolation model on a bowtie A lattice are somewhat different from those of an isotropic lattice, which may be caused by the anisotropy of the lattice.

Applications of conformal field theory to problems in 2D percolation

NASA Astrophysics Data System (ADS)

Simmons, Jacob Joseph Harris

This thesis explores critical two-dimensional percolation in bounded regions in the continuum limit. The main method which we employ is conformal field theory (CFT). Our specific results follow from the null-vector structure of the c = 0 CFT that applies to critical two-dimensional percolation. We also make use of the duality symmetry obeyed at the percolation point, and the fact that percolation may be understood as the q-state Potts model in the limit q → 1. Our first results describe the correlations between points in the bulk and boundary intervals or points, i.e. the probability that the various points or intervals are in the same percolation cluster. These quantities correspond to order-parameter profiles under the given conditions, or cluster connection probabilities. We consider two specific cases: an anchoring interval, and two anchoring points. We derive results for these and related geometries using the CFT null-vectors for the corresponding boundary condition changing (bcc) operators. In addition, we exhibit several exact relationships between these probabilities. These relations between the various bulk-boundary connection probabilities involve parameters of the CFT called operator product expansion (OPE) coefficients. We then compute several of these OPE coefficients, including those arising in our new probability relations. Beginning with the familiar CFT operator φ1,2, which corresponds to a free-fixed spin boundary change in the q-state Potts model, we then develop physical interpretations of the bcc operators. We argue that, when properly normalized, higher-order bcc operators correspond to successive fusions of multiple φ1,2, operators. Finally, by identifying the derivative of φ1,2 with the operator φ1,4, we derive several new quantities called first crossing densities. These new results are then combined and integrated to obtain the three previously known crossing quantities in a rectangle: the probability of a horizontal crossing cluster, the probability of a cluster crossing both horizontally and vertically, and the expected number of horizontal crossing clusters. These three results were known to be solutions to a certain fifth-order differential equation, but until now no physically meaningful explanation had appeared. This differential equation arises naturally in our derivation.

Late onset Pott's paraplegia in patients with upper thoracic sharp kyphosis.

PubMed

Zhang, Zhengfeng

2012-02-01

The purpose of this study was to determine the clinical results of patients with late onset upper thoracic sharp Pott's kyphosis and to predict the prognosis for Pott's paraplegics. The study included five patients who developed late onset upper thoracic (T1-T4) sharp Pott's kyphosis/kyphoscoliosis within a period from 19 to 37 years after the active disease was healed. The kyphosis angle of the patients ranged from 95° to 105°. Among them, three patients suffered onset of paraplegia ranging from 26 to 31 years after spinal tuberculosis was healed. The duration of neurological deterioration before surgery ranged from four to five years. All patients underwent decompressive surgery with an attempt to correct the curve. Neurological status was evaluated using the ASIA impairment classification and the motor score. Postoperatively, kyphosis correction ranged from 20° to 30° for five patients. No neurological deficit occurred in two patients with normal neurological status. Two ASIA D paraplegics remained unchanged after surgery and no further improvement was found at one year follow-up. One ASIA C paralysis deteriorated neurologically to ASIA B after surgery and persisted to a deterioration of neurological status at one year follow-up. Upper thoracic sharp Pott's kyphosis and neurological deficits occur progressively. The neurological recovery or improvement of Pott's paraplegics with upper thoracic severe sharp kyphosis results in poor prognosis after decompressive surgery.

Coupled Finite Element ? Potts Model Simulations of Grain Growth in Copper Interconnects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Radhakrishnan, Balasubramaniam; Gorti, Sarma B

The paper addresses grain growth in copper interconnects in the presence of thermal expansion mismatch stresses. The evolution of grain structure and texture in copper in the simultaneous presence of two driving forces, curvature and elastic stored energy difference, is modeled by using a hybrid Potts model simulation approach. The elastic stored energy is calculated by using the commercial finite element code ABAQUS, where the effect of elastic anisotropy on the thermal mismatch stress and strain distribution within a polycrystalline grain structure is modeled through a user material (UMAT) interface. Parametric studies on the effect of trench width and themore » height of the overburden were carried out. The results show that the grain structure and texture evolution are significantly altered by the presence of elastic strain energy.« less

Excited state TBA and renormalized TCSA in the scaling Potts model

NASA Astrophysics Data System (ADS)

Lencsés, M.; Takács, G.

2014-09-01

We consider the field theory describing the scaling limit of the Potts quantum spin chain using a combination of two approaches. The first is the renormalized truncated conformal space approach (TCSA), while the second one is a new thermodynamic Bethe Ansatz (TBA) system for the excited state spectrum in finite volume. For the TCSA we investigate and clarify several aspects of the renormalization procedure and counter term construction. The TBA system is first verified by comparing its ultraviolet limit to conformal field theory and the infrared limit to exact S matrix predictions. We then show that the TBA and the renormalized TCSA match each other to a very high precision for a large range of the volume parameter, providing both a further verification of the TBA system and a demonstration of the efficiency of the TCSA renormalization procedure. We also discuss the lessons learned from our results concerning recent developments regarding the low-energy scattering of quasi-particles in the quantum Potts spin chain.

Monte Carlo Study of the Fish-like Patterns of Anthracenes on Cu(111)

NASA Astrophysics Data System (ADS)

Kim, Kwangmoo; Einstein, T. L.; Sun, Dezheng; Kim, Dae-Ho; Bartels, Ludwig

2011-03-01

Using Monte Carlo calculations of the two-dimensional triangular lattice with a 2-component 3-state Potts model, we demonstrate a mechanism for the spontaneous formation of fish-like patterns of anthracene (AC) molecules on Cu(111) by sputtering and annealing, then cooling to ~ 80 K. The two components are an AC on a hollow site and another on a bridge site of Cu(111). The liquid crystal model with two separate parts, positional and orientational, only explains a part of the fish-like pattern, not the whole regular pattern. Our model fixes the positional order of AC's into the triangular lattice and the orientational order into three angles as observed in the experiments. The variation of the coverages of AC's is reflected in the change of the ratio of two components in our model. We also try to understand the compression of AC's with the introduction of Gaussian dispersion of AC's about their triangular lattice sites. Supported primarily by NSF Grants CHE 07-50334 with a secondary support from NSF-MRSEC at the University of Maryland, DMR05-20471. Work at UCR supported primarily by NSF CHE 07-49949.

Periodic p-adic Gibbs Measures of q-State Potts Model on Cayley Trees I: The Chaos Implies the Vastness of the Set of p-Adic Gibbs Measures

NASA Astrophysics Data System (ADS)

Ahmad, Mohd Ali Khameini; Liao, Lingmin; Saburov, Mansoor

2018-06-01

We study the set of p-adic Gibbs measures of the q-state Potts model on the Cayley tree of order three. We prove the vastness of the set of the periodic p-adic Gibbs measures for such model by showing the chaotic behavior of the corresponding Potts-Bethe mapping over Q_p for the prime numbers p≡1 (mod 3). In fact, for 0< |θ -1|_p< |q|_p^2 < 1 where θ =\\exp _p(J) and J is a coupling constant, there exists a subsystem that is isometrically conjugate to the full shift on three symbols. Meanwhile, for 0< |q|_p^2 ≤ |θ -1|_p< |q|_p < 1, there exists a subsystem that is isometrically conjugate to a subshift of finite type on r symbols where r ≥ 4. However, these subshifts on r symbols are all topologically conjugate to the full shift on three symbols. The p-adic Gibbs measures of the same model for the prime numbers p=2,3 and the corresponding Potts-Bethe mapping are also discussed. On the other hand, for 0< |θ -1|_p< |q|_p < 1, we remark that the Potts-Bethe mapping is not chaotic when p=3 and p≡ 2 (mod 3) and we could not conclude the vastness of the set of the periodic p-adic Gibbs measures. In a forthcoming paper with the same title, we will treat the case 0< |q|_p ≤ |θ -1|_p < 1 for all prime numbers p.

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).

Lung Cancer Pathological Image Analysis Using a Hidden Potts Model

PubMed Central

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

2017-01-01

Nowadays, many biological data are acquired via images. In this article, we study the pathological images scanned from 205 patients with lung cancer with the goal to find out the relationship between the survival time and the spatial distribution of different types of cells, including lymphocyte, stroma, and tumor cells. Toward this goal, we model the spatial distribution of different types of cells using a modified Potts model for which the parameters represent interactions between different types of cells and estimate the parameters of the Potts model using the double Metropolis-Hastings algorithm. The double Metropolis-Hastings algorithm allows us to simulate samples approximately from a distribution with an intractable normalizing constant. Our numerical results indicate that the spatial interaction between the lymphocyte and tumor cells is significantly associated with the patient’s survival time, and it can be used together with the cell count information to predict the survival of the patients. PMID:28615918

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

NASA Astrophysics Data System (ADS)

Branco, Nilton; Girardi, Daniel

2012-02-01

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

Energy and enthalpy distribution functions for a few physical systems.

PubMed

Wu, K L; Wei, J H; Lai, S K; Okabe, Y

2007-08-02

The present work is devoted to extracting the energy or enthalpy distribution function of a physical system from the moments of the distribution using the maximum entropy method. This distribution theory has the salient traits that it utilizes only the experimental thermodynamic data. The calculated distribution functions provide invaluable insight into the state or phase behavior of the physical systems under study. As concrete evidence, we demonstrate the elegance of the distribution theory by studying first a test case of a two-dimensional six-state Potts model for which simulation results are available for comparison, then the biphasic behavior of the binary alloy Na-K whose excess heat capacity, experimentally observed to fall in a narrow temperature range, has yet to be clarified theoretically, and finally, the thermally induced state behavior of a collection of 16 proteins.

Metastability and nucleation in the 2D-Potts ferromagnet

NASA Astrophysics Data System (ADS)

de Berganza, Miguel Ibáñez

2009-01-01

The nature of the temperature-driven transition of the 2D q>4-Potts model, and the associated metastability, are studied. The problem was firstly investigated by Binder [1,2] in 1981, who discussed the existence of metastable states in a temperature interval below the critical point, which is first-order for q>4. Starting from the droplet expansion theory for the 2D Potts condensation point (Meunier & Morel, 2000 [3]), we compare the metastability derived from the theory with the dynamic metastability found with a local updating rule dynamics. The results are interpreted in terms of the microscopic mechanisms of nucleation, and compared to those described by Classical Nucleation Theory for the Ising model in an external field, which result to be different in several aspects.

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

NASA Astrophysics Data System (ADS)

Xu, Kaixuan; Wang, Jun

2017-02-01

In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model.

Critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field.

PubMed

Dias, D A; Xavier, J C; Plascak, J A

2017-01-01

The phase diagram and the critical behavior of the spin-1 and the spin-3/2 two-dimensional Baxter-Wu model in a crystal field are studied by conventional finite-size scaling and conformal invariance theory. The phase diagram of this model, for the spin-1 case, is qualitatively the same as those of the diluted 4-states Potts model and the spin-1 Blume-Capel model. However, for the present case, instead of a tricritical point one has a pentacritical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. On the other hand, for the spin-3/2 case, the phase diagram is much richer and can present, besides a pentacritical point, an additional multicritical end point. Our results also support that the universality class of the critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field is the same as the pure Baxter-Wu model, even at the multicritical points.

[Pott's Disease in Upper Thoracic Vertebrae in a Two-Year-Old Boy: Case Report].

PubMed

Cortez-Bazán, Nathaly; Delgado, Jennifer R; Galdos, Omar; Huicho, Luis

2018-01-01

Pott's disease is a health problem in developing countries and its diagnosis in children is a challenge. Here we present the case of a two-year-old boy with Pott's disease involving T1 to T3 thoracic vertebrae. The clinical presentation was characterized by difficulty walking, fever, cough, and dyspnea. At physical examination, kyphosis and bony prominence were observed in the cervicodorsal area. A positive tuberculin test was obtained, and Mycobacterium tuberculosis was isolated via culture of the gastric aspiration sample. The spine MRI showed a chronic abscess, destruction of two vertebrae, and bone marrow compression. The patient experienced some improvement with anti-TB therapy. Here, we emphasize the importance of giving consideration to the clinical suspicion for the early detection of this condition, as well as a quick TB-treatment start so as to avoid the disability and mortality associated to this disease.

Critical exponents of the 3D antiferromagnetic three-state Potts model using the coherent-anomaly method

NASA Astrophysics Data System (ADS)

Kolesik, Miroslav; Suzuki, Masuo

1995-02-01

The antiferromagnetic three-state Potts model on the simple-cubic lattice is studied using the coherent-anomaly method (CAM). The CAM analysis provides the estimates for the critical exponents which indicate the XY universality class, namely α = -0.011, β = 0.351, γ = 1.309 and δ = 4.73. This observation corroborates the results of the recent Monte Carlo simulations, and disagrees with the proposal of a new universality class.

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 experiments on range expansions of inoculations of Escherichia coli and Saccharomyces cerevisiae.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jacobsen, Jesper Lykke; Salas, Jesus; Scullard, Christian R.

Here, we study the phase diagram of the triangular-lattice Q-state Potts model in the realmore » $(Q, v)$ -plane, where $$v={\\rm e}^J-1$$ is the temperature variable. Our first goal is to provide an obviously missing feature of this diagram: the position of the antiferromagnetic critical curve. This curve turns out to possess a bifurcation point with two branches emerging from it, entailing important consequences for the global phase diagram. We have obtained accurate numerical estimates for the position of this curve by combining the transfer-matrix approach for strip graphs with toroidal boundary conditions and the recent method of critical polynomials. The second goal of this work is to study the corresponding $$A_{p-1}$$ RSOS model on the torus, for integer $$p=4, 5, \\ldots, 8$$ . We clarify its relation to the corresponding Potts model, in particular concerning the role of boundary conditions. For certain values of p, we identify several new critical points and regimes for the RSOS model and we initiate the study of the flows between the corresponding field theories.« less

Statistical mechanics of two-dimensional shuffled foams: Geometry-topology correlation in small or large disorder limits

NASA Astrophysics Data System (ADS)

Durand, Marc; Kraynik, Andrew M.; van Swol, Frank; Käfer, Jos; Quilliet, Catherine; Cox, Simon; Ataei Talebi, Shirin; Graner, François

2014-06-01

Bubble monolayers are model systems for experiments and simulations of two-dimensional packing problems of deformable objects. We explore the relation between the distributions of the number of bubble sides (topology) and the bubble areas (geometry) in the low liquid fraction limit. We use a statistical model [M. Durand, Europhys. Lett. 90, 60002 (2010), 10.1209/0295-5075/90/60002] which takes into account Plateau laws. We predict the correlation between geometrical disorder (bubble size dispersity) and topological disorder (width of bubble side number distribution) over an extended range of bubble size dispersities. Extensive data sets arising from shuffled foam experiments, surface evolver simulations, and cellular Potts model simulations all collapse surprisingly well and coincide with the model predictions, even at extremely high size dispersity. At moderate size dispersity, we recover our earlier approximate predictions [M. Durand, J. Kafer, C. Quilliet, S. Cox, S. A. Talebi, and F. Graner, Phys. Rev. Lett. 107, 168304 (2011), 10.1103/PhysRevLett.107.168304]. At extremely low dispersity, when approaching the perfectly regular honeycomb pattern, we study how both geometrical and topological disorders vanish. We identify a crystallization mechanism and explore it quantitatively in the case of bidisperse foams. Due to the deformability of the bubbles, foams can crystallize over a larger range of size dispersities than hard disks. The model predicts that the crystallization transition occurs when the ratio of largest to smallest bubble radii is 1.4.

Antiferromagnetic Potts Model on the Erdős-Rényi Random Graph

NASA Astrophysics Data System (ADS)

Contucci, Pierluigi; Dommers, Sander; Giardinà, Cristian; Starr, Shannon

2013-10-01

We study the antiferromagnetic Potts model on the Poissonian Erdős-Rényi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis we prove the existence of a phase transition at a positive critical temperature. Upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution (recovered in the framework of Derrida-Ruelle probability cascades) and from an entropy positivity argument.

Multiscale dynamics of biological cells with chemotactic interactions: From a discrete stochastic model to a continuous description

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.

A Literature Review of Empowerment With a Suggested Empowerment Model for the BDF

DTIC Science & Technology

2003-12-01

rights movement, feminism , and others. Potterfield (1999) indicates that through personal conversation with management and employee empowerment...corporate culture and the style of management. Potts and Sykes (1993, p.63) state: In the traditional corporate culture, policy manuals often...Connecticut, 1999. 19. Potts, T. and Sykes , A., Executive Talent, 1st ed., Irwin, Illinois, 1993. 20. Quinn, R.E. and Spreitzer, G.M., “The Road

Statistical mechanics of human resource allocation

NASA Astrophysics Data System (ADS)

Inoue, Jun-Ichi; Chen, He

2014-03-01

We provide a mathematical platform to investigate the network topology of agents, say, university graduates who are looking for their positions in labor markets. The basic model is described by the so-called Potts spin glass which is well-known in the research field of statistical physics. In the model, each Potts spin (a tiny magnet in atomic scale length) represents the action of each student, and it takes a discrete variable corresponding to the company he/she applies for. We construct the energy to include three distinct effects on the students' behavior, namely, collective effect, market history and international ranking of companies. In this model system, the correlations (the adjacent matrix) between students are taken into account through the pairwise spin-spin interactions. We carry out computer simulations to examine the efficiency of the model. We also show that some chiral representation of the Potts spin enables us to obtain some analytical insights into our labor markets. This work was financially supported by Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science No. 25330278.

A hybrid parallel framework for the cellular Potts model simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 approachmore » 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}).« less

Solution of the sign problem in the Potts model at fixed fermion number

NASA Astrophysics Data System (ADS)

Alexandru, Andrei; Bergner, Georg; Schaich, David; Wenger, Urs

2018-06-01

We consider the heavy-dense limit of QCD at finite fermion density in the canonical formulation and approximate it by a three-state Potts model. In the strong-coupling limit, the model is free of the sign problem. Away from the strong coupling, the sign problem is solved by employing a cluster algorithm which allows to average each cluster over the Z (3 ) sectors. Improved estimators for physical quantities can be constructed by taking into account the triality of the clusters, that is, their transformation properties with respect to Z (3 ) transformations.

Anomalous metastability in a temperature-driven transition

NASA Astrophysics Data System (ADS)

Ibáñez Berganza, M.; Coletti, P.; Petri, A.

2014-06-01

The Langer theory of metastability provides a description of the lifetime and properties of the metastable phase of the Ising model field-driven transition, describing the magnetic-field-driven transition in ferromagnets and the chemical-potential-driven transition of fluids. An immediate further step is to apply it to the study of a transition driven by the temperature, as the one exhibited by the two-dimensional Potts model. For this model, a study based on the analytical continuation of the free energy (Meunier J. L. and Morel A., Eur. Phys. J. B, 13 (2000) 341) predicts the anomalous vanishing of the metastable temperature range in the large-system-size limit, an issue that has been controversial since the eighties. By a GPU algorithm we compare the Monte Carlo dynamics with the theory. For temperatures close to the transition we obtain agreement and characterize the dependence on the system size, which is essentially different with respect to the Ising case. For smaller temperatures, we observe the onset of stationary states with non-Boltzmann statistics, not predicted by the theory.

3D microstructural evolution of primary recrystallization and grain growth in cold rolled single-phase aluminum alloys

NASA Astrophysics Data System (ADS)

Adam, Khaled; Zöllner, Dana; Field, David P.

2018-04-01

Modeling the microstructural evolution during recrystallization is a powerful tool for the profound understanding of alloy behavior and for use in optimizing engineering properties through annealing. In particular, the mechanical properties of metallic alloys are highly dependent upon evolved microstructure and texture from the softening process. In the present work, a Monte Carlo (MC) Potts model was used to model the primary recrystallization and grain growth in cold rolled single-phase Al alloy. The microstructural representation of two kinds of dislocation densities, statistically stored dislocations and geometrically necessary dislocations were quantified based on the ViscoPlastic Fast Fourier transform method. This representation was then introduced into the MC Potts model to identify the favorable sites for nucleation where orientation gradients and entanglements of dislocations are high. Additionally, in situ observations of non-isothermal microstructure evolution for single-phase aluminum alloy 1100 were made to validate the simulation. The influence of the texture inhomogeneity is analyzed from a theoretical point of view using an orientation distribution function for deformed and evolved texture.

Statistics and dynamics of attractor networks with inter-correlated patterns

NASA Astrophysics Data System (ADS)

Kropff, E.

2007-02-01

In an embodied feature representation view, the semantic memory represents concepts in the brain by the associated activation of the features that describe it, each one of them processed in a differentiated region of the cortex. This system has been modeled with a Potts attractor network. Several studies of feature representation show that the correlation between patterns plays a crucial role in semantic memory. The present work focuses on two aspects of the effect of correlations in attractor networks. In first place, it assesses how a Potts network can store a set of patterns with non-trivial correlations between them. This is done through a simple and biologically plausible modification to the classical learning rule. In second place, it studies the complexity of latching transitions between attractor states, and how this complexity can be controlled.

Magnetic quasi-long-range ordering in nematic systems due to competition between higher-order couplings

NASA Astrophysics Data System (ADS)

Žukovič, Milan; Kalagov, Georgii

2018-05-01

Critical properties of the two-dimensional X Y model involving solely nematic-like terms of the second and third orders are investigated by spin-wave analysis and Monte Carlo simulation. It is found that, even though neither of the nematic-like terms alone can induce magnetic ordering, their coexistence and competition leads to an extended phase of the magnetic quasi-long-range-order phase, wedged between the two nematic-like phases induced by the respective couplings. Thus, except for the multicritical point, at which all the phases meet, for any finite value of the coupling parameters ratio there are two phase transition: one from the paramagnetic phase to one of the two nematic-like phases followed by another one at lower temperatures to the magnetic phase. The finite-size scaling analysis indicates that the phase transitions between the magnetic and nematic-like phases belong to the Ising and three-state Potts universality classes. Inside the competition-induced algebraic magnetic phase, the spin-pair correlation function is found to decay even much more slowly than in the standard X Y model with purely magnetic interactions. Such a magnetic phase is characterized by an extremely low vortex-antivortex pair density attaining a minimum close to the point at which the two couplings are of about equal strength.

Process-Structure Linkages Using a Data Science Approach: Application to Simulated Additive Manufacturing Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Popova, Evdokia; Rodgers, Theron M.; Gong, Xinyi

A novel data science workflow is developed and demonstrated to extract process-structure linkages (i.e., reduced-order model) for microstructure evolution problems when the final microstructure depends on (simulation or experimental) processing parameters. Our workflow consists of four main steps: data pre-processing, microstructure quantification, dimensionality reduction, and extraction/validation of process-structure linkages. These methods that can be employed within each step vary based on the type and amount of available data. In this paper, this data-driven workflow is applied to a set of synthetic additive manufacturing microstructures obtained using the Potts-kinetic Monte Carlo (kMC) approach. Additive manufacturing techniques inherently produce complex microstructures thatmore » can vary significantly with processing conditions. Using the developed workflow, a low-dimensional data-driven model was established to correlate process parameters with the predicted final microstructure. In addition, the modular workflows developed and presented in this work facilitate easy dissemination and curation by the broader community.« less

Process-Structure Linkages Using a Data Science Approach: Application to Simulated Additive Manufacturing Data

DOE PAGES

Popova, Evdokia; Rodgers, Theron M.; Gong, Xinyi; ...

2017-03-13

A novel data science workflow is developed and demonstrated to extract process-structure linkages (i.e., reduced-order model) for microstructure evolution problems when the final microstructure depends on (simulation or experimental) processing parameters. Our workflow consists of four main steps: data pre-processing, microstructure quantification, dimensionality reduction, and extraction/validation of process-structure linkages. These methods that can be employed within each step vary based on the type and amount of available data. In this paper, this data-driven workflow is applied to a set of synthetic additive manufacturing microstructures obtained using the Potts-kinetic Monte Carlo (kMC) approach. Additive manufacturing techniques inherently produce complex microstructures thatmore » can vary significantly with processing conditions. Using the developed workflow, a low-dimensional data-driven model was established to correlate process parameters with the predicted final microstructure. In addition, the modular workflows developed and presented in this work facilitate easy dissemination and curation by the broader community.« less

Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the potts model.

PubMed

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.

Four competing interactions for models with an uncountable set of spin values on a Cayley tree

NASA Astrophysics Data System (ADS)

Rozikov, U. A.; Haydarov, F. H.

2017-06-01

We consider models with four competing interactions ( external field, nearest neighbor, second neighbor, and three neighbors) and an uncountable set [0, 1] of spin values on the Cayley tree of order two. We reduce the problem of describing the splitting Gibbs measures of the model to the problem of analyzing solutions of a nonlinear integral equation and study some particular cases for Ising and Potts models. We also show that periodic Gibbs measures for the given models either are translation invariant or have the period two. We present examples where periodic Gibbs measures with the period two are not unique.

Reminiscences regarding Professor R.N. Christiansen

NASA Astrophysics Data System (ADS)

Swarup, Govind

2008-11-01

In this short paper I describe my initiation into the field of radio astronomy fifty years ago, under the guidance of Professor W.N. ('Chris') Christiansen, soon after I joined the C.S.I.R.O.'s Division of Radiophysics (RP) in Sydney, Australia, in 1953 under a 2-year Colombo Plan Fellowship. During the early 1950s Christiansen had developed a remarkable 21 cm interferometric grating array of 32 east-west aligned parabolic dishes and another array of 16 dishes in a north-south direction at Potts Hill. Christiansen and Warburton used these two arrays to scan the Sun strip-wise yielding radio brightness distribution at various position angles. During a three month period I assisted them in making a 2-dimensional map of the Sun by a complex Fourier transform process. In the second year of my Fellowship, Parthasarathy and I converted the 32-antenna east-west grating array to study solar radio emission at 60cm. During this work, I noticed that the procedure adopted by Christiansen for phase adjustment of the grating array was time consuming. Based on this experience, I later developed an innovative technique at Stanford in 1959 for phase adjustment of long transmission lines and paths in space. In a bid to improve on the method used by Christiansen to make a 2-dimensional map of the Sun from strip scans, I suggested to R.N. Bracewell in 1962 a revolutionary method for direct 2-dimensional imaging without Fourier transforms. Bracewell and Riddle developed the method for making a 2-dimensional map of the Moon using strip scans obtained with the 32 element interferometer at Stanford. The method has since revolutionized medical tomography. I describe these developments here to highlight my initial work with Christiansen and to show how new ideas often are developed by necessity and have their origin in prior experience! The 32 Potts Hill solar grating array dishes were eventually donated by the C.S.I.R.0. to India and were set up by me at Kalyan near Mumbai, forming the core of the first radio astronomy group in India. This group went on to construct two of the world's largest radio telescopes, the Ooty Radio Telescope and the Giant Metrewave Radio Telescope. Chris Christiansen was not only my guru but also a mentor and a friend for more than fifty years. I fondly remember his very warm personality.

Harvey Cushing, the spine surgeon: the surgical treatment of Pott disease.

PubMed

Bydon, Ali; Dasenbrock, Hormuzdiyar H; Pendleton, Courtney; McGirt, Matthew J; Gokaslan, Ziya L; Quinones-Hinojosa, Alfredo

2011-08-01

Review of historical archival records. Describe Harvey Cushing's patients with spinal pathology. Harvey Cushing was a pioneer of modern surgery but his work on spine remains largely unknown. Review of the Chesney Medical Archives of the Johns Hopkins Hospital from 1896 to 1912. This is the first time that Cushing's spinal cases while he was at the Johns Hopkins Hospital, including those with Pott disease, have been described.Cushing treated three young men with psoas abscesses secondary to Pott disease during his residency: he drained the abscesses, debrided any accompanying necrotic vertebral bodies, irrigated the cavity with salt, and left the incision open to close by secondary intention. Although Cushing used Koch's "tuberculin therapy" (of intravenous administration of isolated tubercular bacilli) in one patient, he did not do so in the other two, likely because of the poor response of this first patient. Later in his tenure, Cushing performed a laminectomy on a patient with kyphosis and paraplegia secondary to Pott disease. These cases provide a view of Cushing early in his career, pointing to the extraordinary degree of independence that he had during his residency under William Steward Halsted; these cases may have been important in the surgical upbringing both of Cushing and his coresident, William Stevenson Baer, who became the first professor of Orthopedics at Johns Hopkins Hospital. At the turn of the last century, Pott disease was primarily treated by immobilization with bed rest, braces, and plaster-of-paris jackets; some surgeons also employed gradual correction of the deformity by hyperextension. Patients who failed a trial of conservative therapy (of months to years) were treated with a laminectomy. However, the limitations of these strategies led to the development of techniques that form the basis of contemporary spine surgery-instrumentation and fusion.

An efficient Cellular Potts Model algorithm that forbids cell fragmentation

NASA Astrophysics Data System (ADS)

Durand, Marc; Guesnet, Etienne

2016-11-01

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

Together They Stand: Interpreting Not-At-Issue Content.

PubMed

Frazier, Lyn; Dillon, Brian; Clifton, Charles

2018-06-01

Potts unified the account of appositives, parentheticals, expressives, and honorifics as 'Not- At-Issue' (NAI) content, treating them as a natural class semantically in behaving like root (unembedded) structures, typically expressing speaker commitments, and being interpreted independently of At-Issue content. We propose that NAI content expresses a complete speech act distinct from the speech act of the containing utterance. The speech act hypothesis leads us to expect the semantic properties Potts established. We present experimental confirmation of two intuitive observations made by Potts: first that speech act adverbs should be acceptable as NAI content, supporting the speech act hypothesis; and second, that when two speech acts are expressed as successive sentences, the comprehender assumes they are related by some discourse coherence relation, whereas an NAI speech act need not bear a restrictive discourse coherence relation to its containing utterance, though overall sentences containing relevant content are rated more acceptable than those that do not. The speech act hypothesis accounts for these effects, and further accounts for why judgments of syntactic complexity or evaluations of whether or not a statement is true interact with the at-issue status of the material being judged or evaluated.

Three-state Potts model on non-local directed small-world lattices

NASA Astrophysics Data System (ADS)

Ferraz, Carlos Handrey Araujo; Lima, José Luiz Sousa

2017-10-01

In this paper, we study the non-local directed Small-World (NLDSW) disorder effects in the three-state Potts model as a form to capture the essential features shared by real complex systems where non-locality effects play a important role in the behavior of these systems. Using Monte Carlo techniques and finite-size scaling analysis, we estimate the infinite lattice critical temperatures and the leading critical exponents in this model. In particular, we investigate the first- to second-order phase transition crossover when NLDSW links are inserted. A cluster-flip algorithm was used to reduce the critical slowing down effect in our simulations. We find that for a NLDSW disorder densities p

An unusual cause of headache: Pott's puffy tumour.

PubMed

McDermott, Cian; O'Sullivan, Ronan; McMahon, Geraldine

2007-06-01

Osteomyelitis of the frontal bone (eponymously known as Pott's puffy tumour) is an extremely rare and potentially life-threatening complication of frontal sinusitis. The entity was first described by Sir Percival Pott, an 18th century neurosurgeon. It is today considered a historical vignette with the introduction of modern antimicrobial agents. Early diagnosis and immediate active treatment are necessary to prevent severe neurologic sequelae. We report on a case of Pott's puffy tumour in a previously healthy young man with a progressively worsening headache and swelling of the frontal bone. Computed tomography and magnetic resonance imaging revealed features characteristic of this condition. Following emergency sinus trephination and 6 weeks of parenteral and enteral antibiotic therapy, the patient achieved a complete recovery.

Spin systems and Political Districting Problem

NASA Astrophysics Data System (ADS)

Chou, Chung-I.; Li, Sai-Ping

2007-03-01

The aim of the Political Districting Problem is to partition a territory into electoral districts subject to some constraints such as contiguity, population equality, etc. In this paper, we apply statistical physics methods to Political Districting Problem. We will show how to transform the political problem to a spin system, and how to write down a q-state Potts model-like energy function in which the political constraints can be written as interactions between sites or external fields acting on the system. Districting into q voter districts is equivalent to finding the ground state of this q-state Potts model. Searching for the ground state becomes an optimization problem, where optimization algorithms such as the simulated annealing method and Genetic Algorithm can be employed here.

Insights in connecting phenotypes in bacteria to coevolutionary information

NASA Astrophysics Data System (ADS)

Cheng, Ryan; Morcos, Faruck; Hayes, Ryan; Helm, Rodney; Levine, Herbert; Onuchic, Jose

It has long been known that protein sequences are far from random. These sequences have been evolutionarily selected to maintain their ability to fold into stable, three-dimensional folded structures as well as their ability to form macromolecular assemblies, perform catalytic functions, etc. For these reasons, there exist quantifiable mutational patterns in the collection of sequence data for a protein family arising from the need to maintain favorable residue-residue interactions to facilitate folding as well as cellular function. Here, we focus on studying the correlated mutational patterns that give rise to interaction specificity in bacterial two-component signaling (TCS) systems. TCS proteins have evolved to be able to preferentially bind and transfer a phosphate group to their signaling partner while avoiding phosphotransfer with non-partners. We infer a Potts model Hamiltonian governing the correlated mutational patterns that are observed in the sequence data of TCS partners and apply this model to recently published in vivo mutational data. Our findings further support the notion that statistical models built from sequence data can be used to predict bacterial phenotypes as well as engineer interaction specificity between non-partner TCS proteins. This research has been supported by the NSF INSPIRE Award (MCB-1241332) and by the CTBP sponsored by the NSF (Grant PHY- 1427654).

Hybrid Defect Phase Transition: Renormalization Group and Monte Carlo Analysis

NASA Astrophysics Data System (ADS)

Kaufman, Miron; Diep, H. T.

2010-03-01

For the q-state Potts model with 2 < q <= 4 on the square lattice with a defect line, the order parameter on the defect line jumps discontinuously from zero to a nonzero value while the defect energy varies continuously with the temperature at the critical temperature. Monte-Carlo simulations (H. T. Diep, M. Kaufman, Phys Rev E 2009) of the q-state Potts model on a square lattice with a line of defects verify the renormalization group prediction (M. Kaufman, R. B. Griffiths, Phys Rev B 1982) on the occurrence of the hybrid transition on the defect line. This is interesting since for those q values the bulk transition is continuous. This hybrid (continuous - discontinuous) defect transition is induced by the infinite range correlations at the bulk critical point.

Structure of interfaces at phase coexistence. Theory and numerics

NASA Astrophysics Data System (ADS)

Delfino, Gesualdo; Selke, Walter; Squarcini, Alessio

2018-05-01

We compare results of the exact field theory of phase separation in two dimensions with Monte Carlo simulations for the q-state Potts model with boundary conditions producing an interfacial region separating two pure phases. We confirm in particular the theoretical predictions that below critical temperature the surplus of non-boundary colors appears in drops along a single interface, while for q  >  4 at critical temperature there is formation of two interfaces enclosing a macroscopic disordered layer. These qualitatively different structures of the interfacial region can be discriminated through a measurement at a single point for different system sizes.

Deep neural networks for direct, featureless learning through observation: The case of two-dimensional spin models

NASA Astrophysics Data System (ADS)

Mills, Kyle; Tamblyn, Isaac

2018-03-01

We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4 ×4 Ising model. Using its success at this task, we motivate the study of the larger 8 ×8 Ising model, showing that the deep neural network can learn the nearest-neighbor Ising Hamiltonian after only seeing a vanishingly small fraction of configuration space. Additionally, we show that the neural network has learned both the energy and magnetization operators with sufficient accuracy to replicate the low-temperature Ising phase transition. We then demonstrate the ability of the neural network to learn other spin models, teaching the convolutional deep neural network to accurately predict the long-range interaction of a screened Coulomb Hamiltonian, a sinusoidally attenuated screened Coulomb Hamiltonian, and a modified Potts model Hamiltonian. In the case of the long-range interaction, we demonstrate the ability of the neural network to recover the phase transition with equivalent accuracy to the numerically exact method. Furthermore, in the case of the long-range interaction, the benefits of the neural network become apparent; it is able to make predictions with a high degree of accuracy, and do so 1600 times faster than a CUDA-optimized exact calculation. Additionally, we demonstrate how the neural network succeeds at these tasks by looking at the weights learned in a simplified demonstration.

Ferromagnetic Potts models with multisite interaction

NASA Astrophysics Data System (ADS)

Schreiber, Nir; Cohen, Reuven; Haber, Simi

2018-03-01

We study the q -state Potts model with four-site interaction on a square lattice. Based on the asymptotic behavior of lattice animals, it is argued that when q ≤4 the system exhibits a second-order phase transition and when q >4 the transition is first order. The q =4 model is borderline. We find 1 /lnq to be an upper bound on Tc, the exact critical temperature. Using a low-temperature expansion, we show that 1 /(θ lnq ) , where θ >1 is a q -dependent geometrical term, is an improved upper bound on Tc. In fact, our findings support Tc=1 /(θ lnq ) . This expression is used to estimate the finite correlation length in first-order transition systems. These results can be extended to other lattices. Our theoretical predictions are confirmed numerically by an extensive study of the four-site interaction model using the Wang-Landau entropic sampling method for q =3 ,4 ,5 . In particular, the q =4 model shows an ambiguous finite-size pseudocritical behavior.

Fermionic Field Theory for Trees and Forests

NASA Astrophysics Data System (ADS)

Caracciolo, Sergio; Jacobsen, Jesper Lykke; Saleur, Hubert; Sokal, Alan D.; Sportiello, Andrea

2004-08-01

We prove a generalization of Kirchhoff’s matrix-tree theorem in which a large class of combinatorial objects are represented by non-Gaussian Grassmann integrals. As a special case, we show that unrooted spanning forests, which arise as a q→0 limit of the Potts model, can be represented by a Grassmann theory involving a Gaussian term and a particular bilocal four-fermion term. We show that this latter model can be mapped, to all orders in perturbation theory, onto the N-vector model at N=-1 or, equivalently, onto the σ model taking values in the unit supersphere in R1|2. It follows that, in two dimensions, this fermionic model is perturbatively asymptotically free.

Randomized Controlled Study on Safety and Feasibility of Transfusion Trigger Score of Emergency Operations.

PubMed

Liu, De-Xing; Liu, Jin; Zhang, Fan; Zhang, Qiu-Ying; Xie, Mian; Zhu, Zhao-Qiong

2015-07-05

Due to the floating of the guideline, there is no evidence-based evaluation index on when to start the blood transfusion for patients with hemoglobin (Hb) level between 7 and 10 g/dl. As a result, the trigger point of blood transfusion may be different in the emergency use of the existing transfusion guidelines. The present study was designed to evaluate whether the scheme can be safely and effectively used for emergency patients, so as to be supported by multicenter and large sample data in the future. From June 2013 to June 2014, patients were randomly divided into the experimental group (Peri-operative Transfusion Trigger Score of Emergency [POTTS-E] group) and the control group (control group). The between-group differences in the patients' demography and baseline information, mortality and blood transfusion-related complications, heart rate, resting arterial pressure, body temperature, and Hb values were compared. The consistency of red blood cell (RBC) transfusion standards of the two groups of patients with the current blood transfusion guideline, namely the compliance of the guidelines, utilization rate, and per-capita consumption of autologous RBC were analyzed. During the study period, a total of 72 patients were recorded, and 65 of them met the inclusion criteria, which included 33 males and 32 females with a mean age of (34.8 ± 14.6) years. 50 underwent abdomen surgery, 4 underwent chest surgery, 11 underwent arms and legs surgery. There was no statistical difference between the two groups for demography and baseline information. There was also no statistical differences between the two groups in anesthesia time, intraoperative rehydration, staying time in postanesthetic care unit, emergency hospitalization, postoperative 72 h Acute Physiologic Assessment and Chronic Health Evaluation II scores, blood transfusion-related complications and mortality. Only the POTTS-E group on the 1 st postoperative day Hb was lower than group control, P < 0.05. POTTS-E group was totally (100%) conformed to the requirements of the transfusion guideline to RBC infusion, which was higher than that of the control group (81.25%), P < 0.01.There were no statistical differences in utilization rates of autologous blood of the two groups; the utilization rates of allogeneic RBC, total allogeneic RBC and total RBC were 48.48%, 51.5%, and 75.7% in POTTS-E group, which were lower than those of the control group (84.3%, 84.3%, and 96.8%) P < 0.05 or P < 0.01. Per capita consumption of intraoperative allogeneic RBC, total allogeneic RBC and total RBC were 0 (0, 3.0), 2.0 (0, 4.0), and 3.1 (0.81, 6.0) in POTTS-E groups were all lower than those of control group (4.0 [2.0, 4.0], 4.0 [2.0, 6.0] and 5.8 [2.7, 8.2]), P < 0.05 or P < 0.001. Peri-operative Transfusion Trigger Score-E evaluation scheme is used to guide the application of RBC. There are no differences in the recent prognosis of patients with the traditional transfusion guidelines. This scheme is safe; Compared with doctor experience-based subjective assessment, the scoring scheme was closer to patient physiological needs for transfusion and more reasonable; Utilization rate and the per capita consumption of RBC are obviously declined, which has clinical significance and is feasible. Based on the abovementioned three points, POTTS-E scores scheme is safe, reasonable, and practicable and has the value for carrying out multicenter and large sample clinical researches.

Grain Boundary Conformed Volumetric Mesh Generation from a Three-Dimensional Voxellated Polycrystalline Microstructure

NASA Astrophysics Data System (ADS)

Lee, Myeong-Jin; Jeon, Young-Ju; Son, Ga-Eun; Sung, Sihwa; Kim, Ju-Young; Han, Heung Nam; Cho, Soo Gyeong; Jung, Sang-Hyun; Lee, Sukbin

2018-07-01

We present a new comprehensive scheme for generating grain boundary conformed, volumetric mesh elements from a three-dimensional voxellated polycrystalline microstructure. From the voxellated image of a polycrystalline microstructure obtained from the Monte Carlo Potts model in the context of isotropic normal grain growth simulation, its grain boundary network is approximated as a curvature-maintained conformal triangular surface mesh using a set of in-house codes. In order to improve the surface mesh quality and to adjust mesh resolution, various re-meshing techniques in a commercial software are applied to the approximated grain boundary mesh. It is found that the aspect ratio, the minimum angle and the Jacobian value of the re-meshed surface triangular mesh are successfully improved. Using such an enhanced surface mesh, conformal volumetric tetrahedral elements of the polycrystalline microstructure are created using a commercial software, again. The resultant mesh seamlessly retains the short- and long-range curvature of grain boundaries and junctions as well as the realistic morphology of the grains inside the polycrystal. It is noted that the proposed scheme is the first to successfully generate three-dimensional mesh elements for polycrystals with high enough quality to be used for the microstructure-based finite element analysis, while the realistic characteristics of grain boundaries and grains are maintained from the corresponding voxellated microstructure image.

Grain Boundary Conformed Volumetric Mesh Generation from a Three-Dimensional Voxellated Polycrystalline Microstructure

NASA Astrophysics Data System (ADS)

Lee, Myeong-Jin; Jeon, Young-Ju; Son, Ga-Eun; Sung, Sihwa; Kim, Ju-Young; Han, Heung Nam; Cho, Soo Gyeong; Jung, Sang-Hyun; Lee, Sukbin

2018-03-01

We present a new comprehensive scheme for generating grain boundary conformed, volumetric mesh elements from a three-dimensional voxellated polycrystalline microstructure. From the voxellated image of a polycrystalline microstructure obtained from the Monte Carlo Potts model in the context of isotropic normal grain growth simulation, its grain boundary network is approximated as a curvature-maintained conformal triangular surface mesh using a set of in-house codes. In order to improve the surface mesh quality and to adjust mesh resolution, various re-meshing techniques in a commercial software are applied to the approximated grain boundary mesh. It is found that the aspect ratio, the minimum angle and the Jacobian value of the re-meshed surface triangular mesh are successfully improved. Using such an enhanced surface mesh, conformal volumetric tetrahedral elements of the polycrystalline microstructure are created using a commercial software, again. The resultant mesh seamlessly retains the short- and long-range curvature of grain boundaries and junctions as well as the realistic morphology of the grains inside the polycrystal. It is noted that the proposed scheme is the first to successfully generate three-dimensional mesh elements for polycrystals with high enough quality to be used for the microstructure-based finite element analysis, while the realistic characteristics of grain boundaries and grains are maintained from the corresponding voxellated microstructure image.

Reconstruction of a Real World Social Network using the Potts Model and Loopy Belief Propagation.

PubMed

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.

Reconstruction of a Real World Social Network using the Potts Model and Loopy Belief Propagation

PubMed Central

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

Fast Segmentation From Blurred Data in 3D Fluorescence Microscopy.

PubMed

Storath, Martin; Rickert, Dennis; Unser, Michael; Weinmann, Andreas

2017-10-01

We develop a fast algorithm for segmenting 3D images from linear measurements based on the Potts model (or piecewise constant Mumford-Shah model). To that end, we first derive suitable space discretizations of the 3D Potts model, which are capable of dealing with 3D images defined on non-cubic grids. Our discretization allows us to utilize a specific splitting approach, which results in decoupled subproblems of moderate size. The crucial point in the 3D setup is that the number of independent subproblems is so large that we can reasonably exploit the parallel processing capabilities of the graphics processing units (GPUs). Our GPU implementation is up to 18 times faster than the sequential CPU version. This allows to process even large volumes in acceptable runtimes. As a further contribution, we extend the algorithm in order to deal with non-negativity constraints. We demonstrate the efficiency of our method for combined image deconvolution and segmentation on simulated data and on real 3D wide field fluorescence microscopy data.

ARC-2006-ACD06-0050-055

NASA Image and Video Library

2006-03-14

Space Shuttle 3% scale model to analyze removal of PAL ramp and other effects in the 11 ft. w.t. from left to right Rabi Meha, Ames AO, Grey Potts, Boeing, Bill Van Zuylen, Ames AO, Chris Radbourne and Rob Kornienko

Density of states, Potts zeros, and Fisher zeros of the Q

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Seung-Yeon; Creswick, Richard J.

2001-06-01

The Q-state Potts model can be extended to noninteger and even complex Q by expressing the partition function in the Fortuin-Kasteleyn (F-K) representation. In the F-K representation the partition function Z(Q,a) is a polynomial in Q and v=a{minus}1 (a=e{sup {beta}J}) and the coefficients of this polynomial, {Phi}(b,c), are the number of graphs on the lattice consisting of b bonds and c connected clusters. We introduce the random-cluster transfer matrix to compute {Phi}(b,c) exactly on finite square lattices with several types of boundary conditions. Given the F-K representation of the partition function we begin by studying the critical Potts model Z{submore » CP}=Z(Q,a{sub c}(Q)), where a{sub c}(Q)=1+{radical}Q. We find a set of zeros in the complex w={radical}Q plane that map to (or close to) the Beraha numbers for real positive Q. We also identify {tilde Q}{sub c}(L), the value of Q for a lattice of width L above which the locus of zeros in the complex p=v/{radical}Q plane lies on the unit circle. By finite-size scaling we find that 1/{tilde Q}{sub c}(L){r_arrow}0 as L{r_arrow}{infinity}. We then study zeros of the antiferromagnetic (AF) Potts model in the complex Q plane and determine Q{sub c}(a), the largest value of Q for a fixed value of a below which there is AF order. We find excellent agreement with Baxter{close_quote}s conjecture Q{sub c}{sup AF}(a)=(1{minus}a)(a+3). We also investigate the locus of zeros of the ferromagnetic Potts model in the complex Q plane and confirm that Q{sub c}{sup FM}(a)=(a{minus}1){sup 2}. We show that the edge singularity in the complex Q plane approaches Q{sub c} as Q{sub c}(L){similar_to}Q{sub c}+AL{sup {minus}y{sub q}}, and determine the scaling exponent y{sub q} for several values of Q. Finally, by finite-size scaling of the Fisher zeros near the antiferromagnetic critical point we determine the thermal exponent y{sub t} as a function of Q in the range 2{le}Q{le}3. Using data for lattices of size 3{le}L{le}8 we find that y{sub t} is a smooth function of Q and is well fitted by y{sub t}=(1+Au+Bu{sup 2})/(C+Du) where u={minus}(2/{pi})cos{sup {minus}1}({radical}Q/2). For Q=3 we find y{sub t}{approx_equal}0.6; however if we include lattices up to L=12 we find y{sub t}{approx_equal}0.50(8) in rough agreement with a recent result of Ferreira and Sokal [J. Stat. Phys. >96, 461 (1999)].« less

76 FR 75942 - Qualification of Drivers; Exemption Applications; Vision

Federal Register 2010, 2011, 2012, 2013, 2014

2011-12-05

... renewable two-year period. They are: Anthony Brandano (MA) William R. Braun (NM) Stanley E. Elliott (UT.... Mallory (OK) Eldon Miles (IN) Norman V. Myers (WA) Jack E. Potts, Jr. (PA) Neal A. Richard (LA) John E...

78 FR 67452 - Qualification of Drivers; Exemption Applications; Vision

Federal Register 2010, 2011, 2012, 2013, 2014

2013-11-12

... exemption for a renewable two-year period. They are: Anthony Brandano (MA) Stanley E. Elliott (UT) Elmer E...) Raymond P. Madron (MD) Ronald S. Mallory (OK) Eldon Miles (IN) Norman V. Myers (WA) Jack E. Potts, Jr. (PA...

Measurement-noise maximum as a signature of a phase transition.

PubMed

Chen, Zhi; Yu, Clare C

2007-02-02

We propose that a maximum in measurement noise can be used as a signature of a phase transition. As an example, we study the energy and magnetization noise spectra associated with first- and second-order phase transitions by using Monte Carlo simulations of the Ising model and 5-state Potts model in two dimensions. For a finite size system, the total noise power and the low frequency white noise S(f0 and the total noise power vanishes. f(-1)(knee) is approximately the equilibration time.

Collective firm bankruptcies and phase transition in rating dynamics

NASA Astrophysics Data System (ADS)

Sieczka, P.; Hołyst, J. A.

2009-10-01

We present a simple model of firm rating evolution. We consider two sources of defaults: individual dynamics of economic development and Potts-like interactions between firms. We show that such a defined model leads to phase transition, which results in collective defaults. The existence of the collective phase depends on the mean interaction strength. For small interaction strength parameters, there are many independent bankruptcies of individual companies. For large parameters, there are giant collective defaults of firm clusters. In the case when the individual firm dynamics favors dumping of rating changes, there is an optimal strength of the firm's interactions from the systemic risk point of view. in here

Effect of Inherited Genetic Information on Stochastic Predator-Prey Model

NASA Astrophysics Data System (ADS)

Duda, Artur; Dyś, Paweł; Nowicka, Alekandra; Dudek, Mirosław R.

We discuss the Lotka-Volterra dynamics of two populations, preys and predators, in the case when the predators posses a genetic information. The genetic information is inherited according to the rules of the Penna model of genetic evolution. Each individual of the predator population is uniquely determined by sex, genotype and phenotype. In our case, the genes are represented by 8-bit integers and the phenotypes are defined with the help of the 8-state Potts model Hamiltonian. We showed that during time evolution, the population of the predators can experience a series of dynamical phase transitions which are connected with the different types of the dominant phenotypes present in the population.

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

Fa Yueh (Fred) Wu was born on 5 January 1932 in Nanking (now known as Nanjing), China, the capital of the Nationalist government. Wu began kindergarten in 1937 in a comfortable setting, as his father held a relatively high government position. But the Sino-Japanese war broke out in July 1937, and Nanking fell to Japanese hands in November. Fleeing the Japanese, his parents brought Wu to their hometown in Hunan, and then to the war capital Chungking (now Chongqing) in 1938, where they lived for eight years until the end of the war. Around that time the Japanese began bombing Chungking, and Wu's childhood memories were dominated by air raids, bombings and burning not dissimilar to those experienced by Londoners during the war. At times the air raids lasted for days disrupting everyday lives in Chungking, including Wu's schooling. One day during a fierce bombing raid, a bomb fell in their garden reducing a pavilion and the surrounding pond to a huge crater; another bomb fell just a few metres from the tunnel where his family took shelter, almost sealing the only entrance. The family moved the very next day to the countryside. As a result of the war, Wu attended seven schools before finishing his primary education. Fortunately, by the time he entered junior high school in 1943, the Japanese forces were on the wane and Wu entered the elite middle school, Nankai. His early academic performance in Nankai seemed to him mediocre, but he nevertheless impressed his geometry teacher by showing bursts of talent. With hindsight, this early interest in geometry may have led to his later insights in graphical analyses of statistical systems. The family returned to Nanking in 1946 after the Victory over Japan Day. By this time his father had become elected to the Legislative Yuan, the equivalent of the US Senate. Wu entered high school in Nanking in 1946. Since he came from an elite school in Chungking, he excelled in most of his classes, especially mathematics. Notwithstanding his academic success, Wu probably spent more time playing Chinese chess, a board game similar to international chess. He ranked high in a city-wide tournament and often played blind-folded games. He also spent time playing bridge, a game he learned in Nankai and kept up throughout his years in the US. He also loved puzzles and riddles. But the good days did not last long, as the civil war drew closer to Nanking with the Communists winning. The family fled Nanking once again, following a zigzag path and traveling by boat, train, car and then by boat again, eventually reaching Taiwan in June 1949. By this time, the Nationalists had lost most of China, and there was no hope of returning to the mainland. Wu entered the Naval College of Technology to study electrical engineering, giving up an opportunity to study mathematics in the National Taiwan University, although his real interest was in mathematics. In 1954, Wu graduated from the Naval College with a BS degree and the commission of Ensign. Recognizing his outstanding academic record in the College, the Chinese Navy sent him to the US in 1955 to study radar and sonar and to receive training as an instructor. He stayed at the Naval School of Electronics in San Francisco and at the Instructor's School in San Diego. Wu felt that he benefited from the instructor's training much more than from the electronics school, as the training helped him to develop teaching and presentation skills that served him well throughout his career. The Navy assigned him to teach electronics in the Naval Academy when he returned to Taiwan in 1956. Wu was interested in attending a graduate school. The only institution that offered a graduate degree in Taiwan at the time was Taiwan's newly re-established Tsing Hua University. In its hurried retreat to Taiwan, the Nationalist government left the original Tsing Hua University, one of China's best-known institutions of higher learning with a history dating back to the 19th century, behind in Beijing. In 1956, after gaining footing in Taiwan, the Nationalist government revived Tsing Hua, and began offering a two-year Master's degree in nuclear science. Wu decided to apply for admission but faced considerable obstacles since he was in the Navy. After one year's effort, mostly on his father's part, Wu finally entered Tsing Hua in 1957. He completed the two-year program with an experimental thesis in 1959. By this time, the US was pushing for a scientific renaissance after the launch of the Soviet satellite Sputnik. Wu received offers of teaching assistantships from several physics departments in the US, and chose to continue his graduate education at Washington University in St. Louis in 1959. At Washington University he studied many-body theory under the late Eugene Feenberg and produced several influential papers [1, 2] on ground state properties of liquid helium-3 and liquid helium-4. In 1963, he published a paper on formulating cluster expansions in an N-body problem [3], extending the Mayer expansion to systems with indexed many-body interactions, which appeared to have escaped the attention of the community of statistical physics that it deserved. The expansion made extensive use of graphical terms, demonstrating his prowess in graphical analysis at an early stage of his career. Wu's interest in many-body theory continued over the years, with subsequent works on the electron gas, adsorbed systems, and the long-perplexing problem of density correlations in Fermi and Bose systems. After obtaining his PhD from Washington University in 1963, Wu went on to teach at Virginia Polytechnic Institute (VPI) as an assistant professor. In February 1967, Wu met Elliott Lieb who was visiting VPI to give a talk on the Bethe ansatz evaluation of the entropy of two-dimensional ice, a 6-vertex model. Wu soon realized the underlying graphical aspects of two-dimensional vertex models and solved the thermodynamics of a related 5-vertex model using the Pfaffian approach. The result was 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 lattice [8], a model which proved to be useful in his later research. In 1973, Wu returned to Tsing Hua as a visiting professor and worked with colleague K Y Lin. They published two important papers introducing staggered vertex models for the first time [10, 11]. In other important work they clarified the nature of the phase diagram of the Ashkin-Teller model, and found it to have two phase transitions [9]. In the 1970s Wu traveled to Taiwan, Australia, Europe and to China when it re-opened. He met H N V Temperley in Aberdeen, Scotland in 1976, and collaborated with H J Brascamp and H Kunz in Lausanne to establish a number of rigorous results on vertex models, including a proof of the equivalence of boundary conditions for the 6-vertex model [13, 14]. From 1979 to 1980, Wu resided in the Netherlands and Germany, where he was the guest of Piet Kasteleyn at Leiden, Hans van Leeuwen at Delft and Kurt Binder in Juelich. It was in Juelich that Wu completed the 1982 review paper on the Potts model [37], a paper that has been cited 70 or more times every year since its publication. Another important work in that period is a 1976 graphical analysis of the Potts model on the triangular lattice in collaboration with Baxter and Kelland [15]. This paper provided an elegant and conceptually easy description of the duality relation of the model, complementary to the algebraic analysis of Temperley and Lieb [16]. Four years later, Wu and Lin further refined the graphical aspects to reduce the model to a 5-vertex model, under which the duality relation appears as a simple spatial symmetry [18]. The Wu-Lin formulation of the Potts model is used by Jacobsen and Sculland in an analysis of the kagome-lattice Potts model in their first paper in this issue [39]. In other pioneering work in 1976, Wu and Y K Wang introduced a spin model with chiral interactions and its duality relation in Fourier space [19]. Prior to that time, studies of spin models had invariably been confined to models with symmetric interactions. In 1977 Wu published an influential paper on spanning trees [20]. In it, he derived the spanning tree constants of the regular two-dimensional lattices. Since then, he has been the co-author of several papers extending this work to a variety of other two-dimensional Archimedean lattices [21-23]. In this issue Guttmann1 and Rogers solve the three-dimensional version of this problem, which has resisted attack for more than 30 years [40]. The connection between spanning trees and dimers was previously highlighted by Neville Temperley in 1974 [17]. The ideas from number theory needed to obtain the spanning tree constant of three-dimensional lattices, notably logarithmic Mahler measures, are further discussed in the article by Glasser2 in this issue [41]. Wu has had a long and productive collaboration with Maillard, particularly on aspects of the Ising model. Maillard also wrote the definitive description of Wu's many scientific contributions at the time of Wu's 70th birthday [24]. The paper was later included among the biographies of great names such as Newton and Feynman in the History of Physics: Individual Biographies section in the MIT Net Advance of Physics website [59]. Further developments in the Ising model are highlighted in the article by Boukraa, Hassani and Maillard3 in this issue [42]. Maillard's article also appears as the introduction to a wonderful collection of Wu's works that appeared in 2009 [25], entitled Exactly Solved Models: A Journey in Statistical Mechanics. The relation between bond percolation and the random-cluster formulation of the Potts model was pioneered by Kasteleyn and Fortuin in 1969 [26]. Later, in a 1977 paper, Wu showed how to rederive this relation in a different setting and used it to obtain various quantities of interest in the bond percolation problem, including critical exponents, from the exact solution of the Potts model [27]. A few months later, in collaboration with Kunz, he showed that site percolation can also be related to the Potts model [28]. Problems in bond percolation are treated in this issue by several works. The paper by Hu, Blöte4 and Deng5 investigates how the imposition of a 'canonical' constraint, that there be an equal number of open and closed edges, affects the universal properties [43]. The paper by Ziff6, Scullard, Wierman and Sedlock exactly solves inhomogeneous percolation on lattices of the bow-tie and checkerboard types [44]. In a 1979 paper on Potts model critical points, Wu proposed a conjecture, now known as the homogeneity hypothesis, on the location of the critical point of the kagome lattice [29]. Since then, numerous studies have been carried out to test the validity of that conjecture [12]. However, many of these tests proved to be inconclusive since they produced results extremely close to the conjectured value. The puzzle is finally solved by Jacobsen and Scullard in their two papers in this issue [39, 45]. Using a graphical analysis based on the Wu-Lin 5-vertex formulation, they recover the Wu conjecture of the kagome-lattice critical point as the first-order approximation in a well-defined graphical analysis. This establishes once and for all the approximate nature of the Wu conjecture. These investigations, and the exact solutions found by Wu, raised the question as to the conditions under which a lattice model is exactly solvable. Quite recently, such questions have been addressed through the technique of discrete holomorphicity (DH). This direction is represented in this issue by the contributions of Alam and Batchelor7, where the connection between DH and Yang-Baxter integrability is investigated [46]. DH is also a key ingredient in recent rigorous proofs that certain lattice models converge, in the continuum limit, to conformally invariant probabilistic processes known as Schramm-Loewner evolution (SLE). The theme of SLE appears within this issue in the article by Alberts, Kozdron and Lawler [47]. Finally, DH observables are used in this issue by Duminil-Copin to prove the divergence of the correlation length for the Potts model (in its formulation in terms of Fortuin-Kasteleyn clusters) when 1 <= q <= 4 [48]. Establishing the phase diagrams of lattice models is a recurrent theme in Wu's works. In an interesting but little-known work from 2000 with Guo and Blöte [30], he has shown that, contrary to common belief, the O(n) model on the honeycomb lattice has a second-order phase transition for n > 2. The question of phase diagrams for O(n)-type models is taken up in this issue by Blöte, Wang and Guo8 [49]. In 1983-84, Wu joined the National Science Foundation as the Director of the Condensed Matter Theory Program for 18 months. His duty was managing funding to individual researchers in condensed matter theory in the US. The 18-month tour in Washington offered Wu a bird's-eye view of condensed matter physics research in US universities, an understanding that proved useful to his later researches. Throughout his career, Wu has insisted on the general applicability of graphical analysis to a variety of lattices. This aspect was highlighted in his 1988 paper on the Potts model and graph theory [31], in which he derived a number of equivalences with (di)chromatic and flow polynomials on arbitrary planar graphs, both for the partition function and correlation functions. An earlier result in the same vein is the equivalence of the Potts model on a planar graph with a loop model on the corresponding medial graph, found in 1976 in collaboration with Baxter and Kelland [15]. Building on these results, and on recent progress in the combinatorial approach to planar maps, Borot, Bouttier and Guitter systematically investigate properties of percolation and Potts models on random planar maps in their contribution to this issue [50]. Wu has published extensively on dimer enumerations. His work includes exact enumerations on non-orientable surfaces and surfaces with a single boundary defect. In this issue, Lu and Zhang consider dimer enumerations on the Klein bottle, which is an example of a non-orientable surface [51]. Another contribution is the paper by Ciucu and Fischer, considering dimer coverings of a domain with a defect (hole) in the interior [52]. Wu has also worked extensively in knot theory. He has constructed new knot invariants based on statistical mechanical models [61, 62], and published a well-received review of knot invariants for physicists [32], which elucidates the connection of knot invariants with statistical mechanics. In 2004, Wu presented a new formulation of resistance networks [33], which permits the derivation of the exact expression of the resistance between two arbitrary nodes in any network. He later extended the formulation to impedance networks [34], a work which has since attracted interest in applications in petroleum research. These works can perhaps be seen as a distant echo of Wu's Navy training in electronics, more than 50 years earlier. In recent years Wu has developed this topic in joint work with Essam9, who together with Brak has related work on lattice paths in this issue [53]. A cognate paper by Arrowsmith, Bhatti and Essam also appears [54]. Wu has made other contributions to asymptotic analysis, for example in relation to dimers in his recent papers, where he also uses results from conformal invariance [60]. This thread is taken up by the article of Izmailian10 in this issue [55]. In 1997, Wu reported, in a short paper, a new formulation of duality relations of Potts correlation functions for n spins residing on the boundary of a lattice [35]. He gave the examples of n = 2 and 3, and remarked that the formulation can be extended to higher values of n 'in a straightforward fashion'. But the extension is by no means straightforward11 and its solution was eventually found by Wu and his student H Y Huang [36]. They found that the correlation functions are not all independent when n = 4 and higher. They also deduced the connecting relations expressing crossing correlations in terms of non-crossing correlations, thus resolving the discrepancy. Nowadays the interest in integrable systems largely transcends the realm of equilibrium statistical physics. Important and fundamental applications have appeared in out-of-equilibrium physics, in combinatorics, and in the study of certain dualities between string theories and gauge theories known under the common epithet of AdS/CFT duality. This last trend is represented in this issue by the contribution of Kostov [56]. Other interests of Wu in both quantum and classical systems are reflected in the article by Barry12, Muttalib and Tanaka [57], and in the paper by Bauer, Bernard and Benoist on iterated stochastic measurements [58]. This latter paper appears very timely, since it is inspired by the experiments carried out in the group of Serge Haroche who earned the 2012 Nobel Prize in Physics. Wu met his wife Ching Tse (Jane) in Taipei. They married in 1963 in St. Louis, Missouri. They have three daughters; Yvonne, a Professor of Child Neurology at the University of California San Francisco, Yolanda, a women's rights lawyer and a teacher of Suzuki violin, and Yelena, a postdoc in Child Clinical Psychology at Cincinnati Children's Hospital. Fred and Jane have five grandchildren. Wu left four siblings behind when he left China in 1949, and reunited with them after a 30-year separation for the first time in 1979. Two sisters and one brother are now deceased, and his younger brother, who also has three daughters, lives a comfortable life in retirement in Kunming, China. It has been a pleasure to assemble this collection of papers on the occasion of Fred's 80th birthday, and we wish to thank him for providing much of the biographical information on which this introduction is based. We are also grateful to all the contributors for providing such a diverse and decidedly very modern panorama of the topic of lattice models and integrability, and for meeting the strict deadlines necessary to ensure the completion of this issue before the year 2012 draws to an end. Fred Wu continues to be a highly productive, imaginative scientist, and we look forward to a continuing body of excellent work. Meanwhile, we wish him many more years of a happy and healthy life. 1Wu met Tony Guttmann at the University of Newcastle, Australia, back in 1973 when Guttmann invited him to visit. Over the years their paths have crossed countless times at conferences and workshops, and during Wu's visits to Australia and Guttmann's to America; their families became close friends in the process, with Wu's wife Jane assisting Guttmann's wife Susette in her professional duties when they both visited Taiwan. 2Wu met Larry Glasser in 1968 at MIT and also visited him later at Clarkson. They collaborated in 2003 on a paper later published in the Ramanujan Journal in 2005, in which they evaluated an integral for the entropy of spanning trees on the triangular lattice. 3Wu and Jean-Marie Maillard enjoyed joint research grants, organised between the NSF and the CNRS. They also got together frequently in Taiwan and at conferences including one in Paris on the Yang-Baxter equation in 1992. They have many joint papers, including one of Wu's favorites, a 1992 J. Phys. A: Math. Gen. paper on thermal transmissivity. In that paper they put the loosely defined term transmissivity onto a rigorous footing. 4Henk Blöte and Wu first met in 1973 in Delft. Since then they have visited each other frequently, as Blöte made regular visits to the University of Rhode Island (near Boston) and Beijing Normal University, intersecting those of Wu. They first collaborated in a 1989 paper in which they obtained a closed-form expression for the critical curve of the honeycomb antiferromagnetic Ising model and checked the formula against finite-size analysis. This combination of checking an a priori derivation against high-precision numerical analysis set the tone of Wu's later collaborations with Blöte and his students. 5Youjin Deng obtained his PhD in 2004 under the direction of Blöte at Delft. Wu served on Deng's Dissertation Committee and participated in his graduation ceremony. 6Through Wu's recent works on the Potts model he got to know Bob Ziff well. They exchanged preprints and e-mails, and often had lengthy discussions on minute points, including the use and origin of the term 'hemp-leaf lattice'. 7Wu and Murray Batchelor met at the Australia National University in 1990 and again in 1995, and their paths have crossed at many conferences and workshops. 8Wenan Guo likewise obtained his PhD under the supervision of Blöte in Delft. Wu and Guo know each other well from Wu's visits to the Beijing Normal University where he is an honorary professor. He has collaborated with Guo, on the subject of finite-size analysis using the transfer matrix approach, in several of his recent papers. 9Wu first met John Essam at King's College, London in 1978. Followoing Wu's 2006 closed-form expression of the corner-to-corner resistance of an M × N resistor network in the form of a double summation, they combined forces in 2008 at a workshop in Cambridge, and derived the asymptotic expansion of that expression. 10Nickolay Izmailian holds positions in Armenia and Taiwan. Wu and Izmailian collaborated in a paper in 2000 on the exact solution of a 6-vertex model with bond defects. Most recently they collaborated on the exact enumeration of dimers on a cylinder with a single boundary defect. 11Wu's acquaintance with Jesper Jacobsen goes back to this period, when the latter pointed out this fact in a comment to Wu's first paper on this subject. They have since crossed paths on various occasions, most recently at a 2008 workshop at the Isaac Newton Institute in Cambridge. 12Jerry Barry is another long-term collaborator of Wu's. They have met at numerous conferences and workshops. In one meeting in 1989, Barry called Wu's attention to a three-dimensional spin model on the pyrochlore lattice that appeared to be soluble. They soon solved the Ising model on that lattice. In 1997 they collaborated on a paper obtaining the phase diagram of a ternary polymer model.

Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations.

PubMed

Lv, Jian-Ping; Deng, Youjin; Jacobsen, Jesper Lykke; Salas, Jesús; Sokal, Alan D

2018-04-01

We provide a criterion based on graph duality to predict whether the three-state Potts antiferromagnet on a plane quadrangulation has a zero- or finite-temperature critical point, and its universality class. The former case occurs for quadrangulations of self-dual type, and the zero-temperature critical point has central charge c=1. The latter case occurs for quadrangulations of non-self-dual type, and the critical point belongs to the universality class of the three-state Potts ferromagnet. We have tested this criterion against high-precision computations on four lattices of each type, with very good agreement. We have also found that the Wang-Swendsen-Kotecký algorithm has no critical slowing-down in the former case, and critical slowing-down in the latter.

Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations

NASA Astrophysics Data System (ADS)

Lv, Jian-Ping; Deng, Youjin; Jacobsen, Jesper Lykke; Salas, Jesús; Sokal, Alan D.

2018-04-01

We provide a criterion based on graph duality to predict whether the three-state Potts antiferromagnet on a plane quadrangulation has a zero- or finite-temperature critical point, and its universality class. The former case occurs for quadrangulations of self-dual type, and the zero-temperature critical point has central charge c =1 . The latter case occurs for quadrangulations of non-self-dual type, and the critical point belongs to the universality class of the three-state Potts ferromagnet. We have tested this criterion against high-precision computations on four lattices of each type, with very good agreement. We have also found that the Wang-Swendsen-Kotecký algorithm has no critical slowing-down in the former case, and critical slowing-down in the latter.

Multilevel discretized random field models with 'spin' correlations for the simulation of environmental spatial data

NASA Astrophysics Data System (ADS)

Žukovič, Milan; Hristopulos, Dionissios T.

2009-02-01

A current problem of practical significance is how to analyze large, spatially distributed, environmental data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show by means of numerical simulations that the spatial correlations between variables can be captured by interactions between 'spins'. The spins represent multilevel discretizations of environmental variables with respect to a number of pre-defined thresholds. The spatial dependence between the 'spins' is imposed by means of short-range interactions. We present two approaches, inspired by the Ising and Potts models, that generate conditional simulations of spatially distributed variables from samples with missing data. Currently, the sampling and simulation points are assumed to be at the nodes of a regular grid. The conditional simulations of the 'spin system' are forced to respect locally the sample values and the system statistics globally. The second constraint is enforced by minimizing a cost function representing the deviation between normalized correlation energies of the simulated and the sample distributions. In the approach based on the Nc-state Potts model, each point is assigned to one of Nc classes. The interactions involve all the points simultaneously. In the Ising model approach, a sequential simulation scheme is used: the discretization at each simulation level is binomial (i.e., ± 1). Information propagates from lower to higher levels as the simulation proceeds. We compare the two approaches in terms of their ability to reproduce the target statistics (e.g., the histogram and the variogram of the sample distribution), to predict data at unsampled locations, as well as in terms of their computational complexity. The comparison is based on a non-Gaussian data set (derived from a digital elevation model of the Walker Lake area, Nevada, USA). We discuss the impact of relevant simulation parameters, such as the domain size, the number of discretization levels, and the initial conditions.

FAST TRACK COMMUNICATION: Exact and simple results for the XYZ and strongly interacting fermion chains

NASA Astrophysics Data System (ADS)

Fendley, Paul; Hagendorf, Christian

2010-10-01

We conjecture exact and simple formulas for some physical quantities in two quantum chains. A classic result of this type is Onsager, Kaufman and Yang's formula for the spontaneous magnetization in the Ising model, subsequently generalized to the chiral Potts models. We conjecture that analogous results occur in the XYZ chain when the couplings obey JxJy + JyJz + JxJz = 0, and in a related fermion chain with strong interactions and supersymmetry. We find exact formulas for the magnetization and gap in the former, and the staggered density in the latter, by exploiting the fact that certain quantities are independent of finite-size effects.

Harvey Cushing, the Spine Surgeon

PubMed Central

Bydon, Ali; Dasenbrock, Hormuzdiyar H.; Pendleton, Courtney; McGirt, Matthew J.; Gokaslan, Ziya L.; Quinones-Hinojosa, Alfredo

2015-01-01

Study Design Review of historical archival records. Objective Describe Harvey Cushing's patients with spinal pathology. Summary of Background Data Harvey Cushing was a pioneer of modern surgery but his work on spine remains largely unknown. Methods Review of the Chesney Medical Archives of the Johns Hopkins Hospital from 1896 to 1912. Results This is the first time that Cushing's spinal cases while he was at the Johns Hopkins Hospital, including those with Pott disease, have been described. Cushing treated three young men with psoas abscesses secondary to Pott disease during his residency: he drained the abscesses, debrided any accompanying necrotic vertebral bodies, irrigated the cavity with salt, and left the incision open to close by secondary intention. Although Cushing used Koch's “tuberculin therapy” (of intravenous administration of isolated tubercular bacilli) in one patient, he did not do so in the other two, likely because of the poor response of this first patient. Later in his tenure, Cushing performed a laminectomy on a patient with kyphosis and paraplegia secondary to Pott disease. Conclusion These cases provide a view of Cushing early in his career, pointing to the extraordinary degree of independence that he had during his residency under William Steward Halsted; these cases may have been important in the surgical upbringing both of Cushing and his coresident, William Stevenson Baer, who became the first professor of Orthopedics at Johns Hopkins Hospital. At the turn of the last century, Pott disease was primarily treated by immobilization with bed rest, braces, and plaster-of-paris jackets; some surgeons also employed gradual correction of the deformity by hyperextension. Patients who failed a trial of conservative therapy (of months to years) were treated with a laminectomy. However, the limitations of these strategies led to the development of techniques that form the basis of contemporary spine surgery—instrumentation and fusion. PMID:21224751

Computed Tomography-Guided Biopsy for Potts Disease: An Institutional Experience from an Endemic Developing Country

PubMed Central

Waqas, Muhammad; Qadeer, Mohsin; Faiz, Faizuddin; Alvi, Mohammad Ali

2015-01-01

Study Design A retrospective chart review. Purpose In endemic resource poor countries like Pakistan, most patients are diagnosed and treated for Potts disease on clinical and radiological grounds without a routine biopsy. The purpose of this study was to evaluate the use and effect of computed tomography (CT)-guided biopsy in the management of Potts disease since the technique is becoming increasingly available. Overview of Literature CT-guided biopsy of spinal lesions is routinely performed. Literature on the utility of the technique in endemic resource poor countries is little. Methods This study was conducted at the Neurosurgery section of Aga Khan University Hospital Karachi. All the patients with suspected Potts disease who underwent CT-guided biopsy during the 7 year period from 2007 to 2013 were included in this study. Details of the procedure, histopathology and microbiology were recorded. Results One hundred and seventy-eight patients were treated for suspected Potts disease during the study period. CT-guided biopsies of the spinal lesions were performed in 91 patients (51.12%). Of the 91 procedures, 22 (24.2%) were inconclusive because of inadequate sample (10), normal tissue (6) or reactive tissue (6). Sixty-nine biopsies were positive (75.8%). Granulomatous inflammation was seen in 58 patients (84.05%), positive acid-fast bacillus (AFB) smear in 4 (5.7%) and positive AFB culture in 12 patients (17.3%). All 91 cases in which CT-guided biopsy was performed responded positively to antituberculosis therapy (ATT). Conclusions 75.8% of the specimens yielded positive diagnoses. Granulomatous inflammation on histopathology was the commonest diagnostic feature. In this series, the rates of positive AFB smear and culture were low compared to previous literature. PMID:26097654

Multi-Scale Modeling in Morphogenesis: A Critical Analysis of the Cellular Potts Model

PubMed Central

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

Yang-Lee zeros, Julia sets, and their singularity spectra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, B.; Lin, B.

1989-05-01

We have studied the global scaling properties of the Julia sets of the Yang-Lee zeros of the s-state Potts model on the diamond hierarchical lattice. The singularity spectrum f(..cap alpha..) and the generalized dimension D/sub q/ are calculated for different s values. General observations are made on their variations.

FAST TRACK COMMUNICATION: Ground-state fidelity and entanglement entropy for the quantum three-state Potts model in one spatial dimension

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.

[Pott's puffy tumor: a rare complication of frontal sinusitis].

PubMed

Aínsa Laguna, D; Pons Morales, S; Muñoz Tormo-Figueres, A; Vega Senra, M I; Otero Reigada, M C

2014-05-01

Pott's puffy tumor is a rare complication of frontal sinusitis characterized by swelling and edema in the brow due to a subperiosteal abscess associated with frontal osteomyelitis. Added complications are cellulitis by extension to the orbit and intracranial infection by posterior extension, with high risk of meningitis, intracranial abscess, and venous sinus thrombosis. Early diagnosis and aggressive medical or surgical treatment are essential for optimal recovery of affected patients. In the antibiotic age it is extremely rare, with very few cases described in the recent literature. A case is presented of a Pott inflammatory tumor in a 7 year-old boy, as a complication of acute pansinusitis who presented with front preseptal swelling and intracranial involvement with thrombosis of ophthalmic and superior orbital veins and frontal epidural abscess extending to the subarachnoid space. Copyright © 2013 Asociación Española de Pediatría. Published by Elsevier Espana. All rights reserved.

Une localisation exceptionnelle de la tuberculose vertébrale Mal de Pott sous-occipital

PubMed Central

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

Iterative Potts and Blake–Zisserman minimization for the recovery of functions with discontinuities from indirect measurements

PubMed Central

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. PMID:27547074

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.

Direct handling of sharp interfacial energy for microstructural evolution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernández–Rivera, Efraín; Tikare, Veena; Noirot, Laurence

In this study, we introduce a simplification to the previously demonstrated hybrid Potts–phase field (hPPF), which relates interfacial energies to microstructural sharp interfaces. The model defines interfacial energy by a Potts-like discrete interface approach of counting unlike neighbors, which we use to compute local curvature. The model is compared to the hPPF by studying interfacial characteristics and grain growth behavior. The models give virtually identical results, while the new model allows the simulator more direct control of interfacial energy.

Direct handling of sharp interfacial energy for microstructural evolution

DOE PAGES

Hernández–Rivera, Efraín; Tikare, Veena; Noirot, Laurence; ...

2014-08-24

In this study, we introduce a simplification to the previously demonstrated hybrid Potts–phase field (hPPF), which relates interfacial energies to microstructural sharp interfaces. The model defines interfacial energy by a Potts-like discrete interface approach of counting unlike neighbors, which we use to compute local curvature. The model is compared to the hPPF by studying interfacial characteristics and grain growth behavior. The models give virtually identical results, while the new model allows the simulator more direct control of interfacial energy.

Surface tension and modeling of cellular intercalation during zebrafish gastrulation.

PubMed

Calmelet, Colette; Sepich, Diane

2010-04-01

In this paper we discuss a model of zebrafish embryo notochord development based on the effect of surface tension of cells at the boundaries. We study the process of interaction of mesodermal cells at the boundaries due to adhesion and cortical tension, resulting in cellular intercalation. From in vivo experiments, we obtain cell outlines of time-lapse images of cell movements during zebrafish embryo development. Using Cellular Potts Model, we calculate the total surface energy of the system of cells at different time intervals at cell contacts. We analyze the variations of total energy depending on nature of cell contacts. We demonstrate that our model can be viable by calculating the total surface energy value for experimentally observed configurations of cells and showing that in our model these configurations correspond to a decrease in total energy values in both two and three dimensions.

Holographic entanglement entropy in Suzuki-Trotter decomposition of spin systems.

PubMed

Matsueda, Hiroaki

2012-03-01

In quantum spin chains at criticality, two types of scaling for the entanglement entropy exist: one comes from conformal field theory (CFT), and the other is for entanglement support of matrix product state (MPS) approximation. On the other hand, the quantum spin-chain models can be mapped onto two-dimensional (2D) classical ones by the Suzuki-Trotter decomposition. Motivated by the scaling and the mapping, we introduce information entropy for 2D classical spin configurations as well as a spectrum, and examine their basic properties in the Ising and the three-state Potts models on the square lattice. They are defined by the singular values of the reduced density matrix for a Monte Carlo snapshot. We find scaling relations of the entropy compatible with the CFT and the MPS results. Thus, we propose that the entropy is a kind of "holographic" entanglement entropy. At T(c), the spin configuration is fractal, and various sizes of ordered clusters coexist. Then, the singular values automatically decompose the original snapshot into a set of images with different length scales, respectively. This is the origin of the scaling. In contrast to the MPS scaling, long-range spin correlation can be described by only few singular values. Furthermore, the spectrum, which is a set of logarithms of the singular values, also seems to be a holographic entanglement spectrum. We find multiple gaps in the spectrum, and in contrast to the topological phases, the low-lying levels below the gap represent spontaneous symmetry breaking. These contrasts are strong evidence of the dual nature of the holography. Based on these observations, we discuss the amount of information contained in one snapshot.

Monte Carlo renormalization-group study of the Baxter-Wu model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Novotny, M.A.; Landau, D.P.; Swendsen, R.H.

1982-07-01

The effectiveness of a Monte Carlo renormalization-group method is studied by applying it to the Baxter-Wu model (Ising spins on a triangular lattice with three-spin interactions). The calculations yield three relevent eigenvalues in good agreement with exact or conjectured results. We demonstrate that the method is capable of distinguishing between models expected to be in the same universality class, when one of them (four-state Potts) exhibits logarithmic corrections to the usual power-law singularities and the other (Baxter-Wu) does not.

Towards the Truly Predictive 3D Modeling of Recrystallization and Grain Growth in Advanced Technical Alloys

DTIC Science & Technology

2010-06-11

MODELING WITH IMPLEMENTED GBI AND MD DATA (STEADY STATE GB MIGRATION) PAGE 48 5. FORMATION AND ANALYSIS OF GB PROPERTIES DATABASE PAGE 53 5.1...Relative GB energy for specified GBM averaged on possible GBIs PAGE 53 5.2. Database validation on available experimental data PAGE 56 5.3. Comparison...PAGE 70 Fig. 6.11. MC Potts Rex. and GG software: (a) modeling volume analysis; (b) searching for GB energy value within included database . PAGE

Coordination and Collective Decision Making

DTIC Science & Technology

2015-08-21

Fisheries , (06 2014): 1. doi: 10.1111/faf.12084 L. Giuggioli, J. R. Potts, D. I. Rubenstein, S. A. Levin. Stigmergy, collective actions, and animal ...terrestrial and marine food webs, as well as enabling interspecies interactions such as reproduction. Eulerian models describe aggregations of animals in...achieved in decision-making. Animal groups frequently display highly coordinated movements, and provide an excellent vehicle by which to understand

The construction of general basis functions in reweighting ensemble dynamics simulations: Reproduce equilibrium distribution in complex systems from multiple short simulation trajectories

NASA Astrophysics Data System (ADS)

Zhang, Chuan-Biao; Ming, Li; Xin, Zhou

2015-12-01

Ensemble simulations, which use multiple short independent trajectories from dispersive initial conformations, rather than a single long trajectory as used in traditional simulations, are expected to sample complex systems such as biomolecules much more efficiently. The re-weighted ensemble dynamics (RED) is designed to combine these short trajectories to reconstruct the global equilibrium distribution. In the RED, a number of conformational functions, named as basis functions, are applied to relate these trajectories to each other, then a detailed-balance-based linear equation is built, whose solution provides the weights of these trajectories in equilibrium distribution. Thus, the sufficient and efficient selection of basis functions is critical to the practical application of RED. Here, we review and present a few possible ways to generally construct basis functions for applying the RED in complex molecular systems. Especially, for systems with less priori knowledge, we could generally use the root mean squared deviation (RMSD) among conformations to split the whole conformational space into a set of cells, then use the RMSD-based-cell functions as basis functions. We demonstrate the application of the RED in typical systems, including a two-dimensional toy model, the lattice Potts model, and a short peptide system. The results indicate that the RED with the constructions of basis functions not only more efficiently sample the complex systems, but also provide a general way to understand the metastable structure of conformational space. Project supported by the National Natural Science Foundation of China (Grant No. 11175250).

Pott disease in the thoracolumbar spine with marked kyphosis and progressive paraplegia necessitating posterior vertebral column resection and anterior reconstruction with a cage.

PubMed

Pappou, Ioannis P; Papadopoulos, Elias C; Swanson, Andrew N; Mermer, Matthew J; Fantini, Gary A; Urban, Michael K; Russell, Linda; Cammisa, Frank P; Girardi, Federico P

2006-02-15

Case report. To report on a patient with Pott disease, progressive neurologic deficit, and severe kyphotic deformity, who had medical treatment fail and required posterior/anterior decompression with instrumented fusion. Treatment options will be discussed. Tuberculous spondylitis is an increasingly common disease worldwide, with an estimated prevalence of 800,000 cases. Surgical treatment consisting of extensive posterior decompression/instrumented fusion and 3-level posterior vertebral column resection, followed by anterior debridement/fusion with cage reconstruction. Neurologic improvement at 6-month follow-up (Frankel B to Frankel D), with evidence of radiographic fusion. A 70-year-old patient with progressive Pott paraplegia and severe kyphotic deformity, for whom medical treatment failed is presented. A posterior vertebral column resection, multiple level posterior decompression, and instrumented fusion, followed by an anterior interbody fusion with cage was used to decompress the spinal cord, restore sagittal alignment, and debride the infection. At 6-month follow-up, the patient obtained excellent pain relief, correction of deformity, elimination of the tuberculous foci, and significant recovery of neurologic function.

Tuberculous spondylitis diagnosed through Xpert MTB/RIF assay in urine: a case report.

PubMed

Sikalengo, George; Ramirez, Adria; Faini, Diana; Mwamelo, Kim; Battegay, Manuel; Jugheli, Levan; Hatz, Christoph; Reither, Klaus; Letang, Emilio

2016-09-26

Extrapulmonary tuberculosis (EPTB) is associated with high rates of morbidity and mortality. Diagnosis of EPTB is challenging in resource-limited settings due to difficulties in obtaining samples, as well as the paucibacillarity of the specimens. Skeletal tuberculosis accounts for 10-35 % of EPTB cases, with vertebral osteomyelitis (Pott's disease) representing 50 % of the cases. We present two cases of suspected Pott's disease, diagnosed through GeneXpert MTB/RIF assay in urine at a rural Tanzanian hospital. Case I A 49-year old male, HIV-1 positive, on co-formulated tenofovir disoproxil fumarate/lamivudine/efavirenz since 2009 and CD4 counts of 205 cells/μL (13 %). He presented with lower back pain and progressive lower limb weakness for two weeks prior to admission. The physical examination revealed bilateral flaccid paraplegia with reduced reflexes, but otherwise unremarkable findings. A lateral lumbar X-ray showed noticeable reduction of intervertebral space between L4 and L5, and a small calcification in the anterior longitudinal ligament between L4 and L5, being compatible with focal spondylosis deformans but inconclusive with regard to tuberculous spondylitis. An abdominal ultrasound showed normal kidneys, bladder and prostate gland. The urinalysis and complete blood counts (CBC) were normal. M. Tuberculosis was detected through GeneXpert MTB/RIF in centrifuged urine, with no resistance to rifampicin. Case II A 76-year old female, HIV-1 negative, presented with lower back pain and progressive weakness and numbness of the lower limbs for two months prior to admission. The physical examination revealed paraplegia, but otherwise unremarkable findings. The lumbosacral X-ray findings were compatible with spondylosis deformans of the lumbar spine and possible tuberculous spondylitis in L3-L4. The abdominal and renal ultrasound showed normal kidneys and bladder. The urinalysis and CBC were normal. M. Tuberculosis was detected through GeneXpert MTB/RIF in centrifuged urine, with no resistance to rifampicin. We report two cases of suspected tuberculous spondylitis diagnosed through Xpert MTB/RIF in urine samples from a rural Tanzanian hospital. Urine testing using Xpert MTB/RIF reflects disseminated disease and renal involvement, and may offer a feasible additional diagnostic approach for Pott's disease in rural Africa.

La structure de Jordan des matrices de transfert des modeles de boucles et la relation avec les hamiltoniens XXZ

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 couple sectors d and d' when specific constraints on λ, d, d' and N are satisfied. For the model of critical dense polymers (β = 0) on the strip, the eigenvalues of ρ(DN(λ, u)) were known, but their degeneracies only conjectured. By constructing an isomorphism between the link modules on the strip and a subspace of spin modules of the XXZ model at q = i, we prove this conjecture. We also show that the restriction of the Hamiltonian to any sector d is diagonalizable, and that the XX Hamiltonian has rank 2 Jordan cells when N is even. Finally, we study the Jordan structure of the transfer matrix T N(λ, ν) for periodic boundary conditions. When λ = πa/b and a, b ∈ Z× , the matrix TN(λ, ν) has Jordan blocks between sectors, but also within sectors. The approach using FN admits a generalization to the present case and allows us to probe the Jordan cells that tie different sectors. The rank of these cells exceeds 2 in some cases and can grow indefinitely with N. For the Jordan blocks within a sector, we show that the link modules on the cylinder and the XXZ spin modules are isomorphic except for specific curves in the (q, ν) plane. By using the behavior of the transformation ĩd N in a neighborhood of the critical values (qc, ν c), we explicitly build Jordan partners of rank 2 and discuss the existence of Jordan cells with higher rank. Keywords : phase transitions, Ising model, Potts model, Fortuin-Kasteleyn model, transfer matrix method, XXZ Hamiltonian, logarithmic conformal field theory, Jordan structure.

Symmetry breaking and the geometry of reduced density matrices

NASA Astrophysics Data System (ADS)

Zauner, V.; Draxler, D.; Vanderstraeten, L.; Haegeman, J.; Verstraete, F.

2016-11-01

The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. We demonstrate that the existence of symmetry breaking is a consequence of the geometric structure of the convex set of reduced density matrices of all possible many body wavefunctions. The surfaces of these convex bodies exhibit non-analyticities, which signal the emergence of symmetry breaking and of an associated order parameter and also show different characteristics for different types of phase transitions. We illustrate this with three paradigmatic examples of many body systems exhibiting symmetry breaking: the quantum Ising model, the classical q-state Potts model in two-dimensions at finite temperature and the ideal Bose gas in three-dimensions at finite temperature. This state based viewpoint on phase transitions provides a unique novel tool for studying exotic many body phenomena in quantum and classical systems.

Percolation on bipartite scale-free networks

NASA Astrophysics Data System (ADS)

Hooyberghs, H.; Van Schaeybroeck, B.; Indekeu, J. O.

2010-08-01

Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of unlike type. Such bipartite graphs appear in many social networks, for instance in affiliation networks and in sexual-contact networks in which both types of nodes show the scale-free characteristic for the degree distribution. During the depreciation process, an edge between nodes with degrees k and q is retained with a probability proportional to (, where α is positive so that links between hubs are more prone to failure. The removal process is studied analytically by introducing a generating functions theory. We deduce exact self-consistent equations describing the system at a macroscopic level and discuss the percolation transition. Critical exponents are obtained by exploiting the Fortuin-Kasteleyn construction which provides a link between our model and a limit of the Potts model.

Entanglement entropy of the Q≥4 quantum Potts chain.

PubMed

Lajkó, Péter; Iglói, Ferenc

2017-01-01

The entanglement entropy S is an indicator of quantum correlations in the ground state of a many-body quantum system. At a second-order quantum phase-transition point in one dimension S generally has a logarithmic singularity. Here we consider quantum spin chains with a first-order quantum phase transition, the prototype being the Q-state quantum Potts chain for Q>4 and calculate S across the transition point. According to numerical, density matrix renormalization group results at the first-order quantum phase transition point S shows a jump, which is expected to vanish for Q→4^{+}. This jump is calculated in leading order as ΔS=lnQ[1-4/Q-2/(QlnQ)+O(1/Q^{2})].

Star-triangle and star-star relations in statistical mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baxter, R.J.

1997-01-20

The homogeneous three-layer Zamolodchikov model is equivalent to a four-state model on the checkerboard lattice which closely resembles the four-state critical Potts model, but with some of its Boltzmann weights negated. Here the author shows that it satisfies a star-to-reverse-star (or simply star-star) relation, even though they know of no star-triangle relation for this model. For any nearest-neighbor checkerboard model, they show that this star-star relation is sufficient to ensure that the decimated model (where half the spins have been summed over) satisfies a twisted Yang-Baxter relation. This ensures that the transfer matrices of the original model commute in pairs,more » which is an adequate condition for solvability.« less

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of the s=3/2 Ising model from renormalization-group theory.

PubMed

Yunus, Çağın; Renklioğlu, 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.

A study on the effects of temperature and substrate structure on the templated two-phase film growth via a hybrid model

NASA Astrophysics Data System (ADS)

Lu, Xiao; Li, Jia; Zhu, Jian-Gang; Laughlin, David E.; Zhu, Jingxi

2018-06-01

Templated growth of two-phase thin films can achieve desirably ordered microstructures. In such cases, the microstructure of the growing films follows the topography of the template. By combining the Potts model Monte Carlo simulation and the "level set" method, an attempt was previously made to understand the physical mechanism behind the templated growth process. In the current work, this model is further used to study the effect of two parameters within the templated growth scenario, namely, the temperature and the geometric features of the template. The microstructure of the thin film grown with different lattice temperatures and domes is analyzed. It is found that within a moderate temperature range, the effect of geometric features took control of the ordering of the microstructure by its influence on the surface energy gradient. Interestingly, within this temperature range, as the temperature is increased, an ordered microstructure forms on a template without the optimal geometric features, which seems to be a result of competition between the kinetics and the thermodynamics during deposition. However, when the temperature was either above or below this temperature range, the template provided no guide to the whole deposition so that no ordered microstructure formed.

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.

A gradient system solution to Potts mean field equations and its electronic implementation.

PubMed

Urahama, K; Ueno, S

1993-03-01

A gradient system solution method is presented for solving Potts mean field equations for combinatorial optimization problems subject to winner-take-all constraints. In the proposed solution method the optimum solution is searched by using gradient descent differential equations whose trajectory is confined within the feasible solution space of optimization problems. This gradient system is proven theoretically to always produce a legal local optimum solution of combinatorial optimization problems. An elementary analog electronic circuit implementing the presented method is designed on the basis of current-mode subthreshold MOS technologies. The core constituent of the circuit is the winner-take-all circuit developed by Lazzaro et al. Correct functioning of the presented circuit is exemplified with simulations of the circuits implementing the scheme for solving the shortest path problems.

Racekiela andina sp. nov. (Spongillida: Spongillidae): first report of a freshwater sponge from the Venezuelan Andes.

PubMed

Hernández, Victor M Q; Barreat, José G N

2017-10-31

The genus Racekiela Bass & Volkmer-Ribeiro, 1998 comprises six species of freshwater sponges distributed along the Palaearctic, Nearctic and Neotropical regions (Van Soest et al. 2017). They are characterized by an isodictyal skeleton solely of acanthoxeas, sparse spongin fibers, and tri-layered gemmules with radially embedded gemmoscleres of two types, short birotules and long pseudobirotules (Manconi & Pronzato 2002; Volkmer-Ribeiro & Machado 2007). Four species occur in the Northern Hemisphere: R. biceps (Lindenschmidt, 1950) from Michigan (Lindenschmidt 1950), R. pictouensis (Potts, 1885) from eastern Canada to New York (Penney & Racek 1968), R. ryderii (Potts, 1882) which ranges from eastern North America to the British Isles, Faroes and Norway (Manconi & Pronzato 2002), and the recently described R. montemflumina Carballo, Cruz-Barraza, Yáñez & Gómez, 2017 from Northwestern Mexico (Carballo et al. 2017). It is worthy to note that R. pictouensis is considered to be an ecomorph of R. ryderii by several authors (Porrier 1977; Ricciardi & Reiswig 1993). The other two species, R. cavernicola (Volkmer-Ribeiro, Bichuette & Machado, 2010) and R. sheilae (Volkmer-Ribeiro, De Rosa-Barbosa & Tavares, 1988), are both known only from Brazil (Volkmer-Ribeiro & Machado 2007; Volkmer-Ribeiro et al. 2010). Here we describe a new member of the genus, found in lakes of high-mountain ecosystems, or páramos, in the Cordillera de Mérida. This constitutes the first record of specimens belonging to Racekiela for the Andes and Venezuela.

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.

Predictions of a Large Magnetocaloric Effect in Co- and Cr-Substituted Heusler Alloys Using First-Principles and Monte Carlo Approaches

NASA Astrophysics Data System (ADS)

Sokolovskiy, Vladimir V.; Buchelnikov, Vasiliy D.; Zagrebin, Mikhail A.; Grünebohm, Anna; Entel, Peter

The effect of Co- and Cr-doping on magnetic and magnetocaloric poperties of Ni-Mn-(In, Ga, Sn, and Al) Heusler alloys has been theoretically studied by combining first principles with Monte Carlo approaches. The magnetic and magnetocaloric properties are obtained as a function of temperature and magnetic field using a mixed type of Potts and Blume-Emery-Griffiths model where the model parameters are obtained from ab initio calculations. The Monte Carlo calculations allowed to make predictions of a giant inverse magnetocaloric effect in partially new hypothetical magnetic Heusler alloys across the martensitic transformation.

A Bayesian Interpretation of First-Order Phase Transitions

NASA Astrophysics Data System (ADS)

Davis, Sergio; Peralta, Joaquín; Navarrete, Yasmín; González, Diego; Gutiérrez, Gonzalo

2016-03-01

In this work we review the formalism used in describing the thermodynamics of first-order phase transitions from the point of view of maximum entropy inference. We present the concepts of transition temperature, latent heat and entropy difference between phases as emergent from the more fundamental concept of internal energy, after a statistical inference analysis. We explicitly demonstrate this point of view by making inferences on a simple game, resulting in the same formalism as in thermodynamical phase transitions. We show that analogous quantities will inevitably arise in any problem of inferring the result of a yes/no question, given two different states of knowledge and information in the form of expectation values. This exposition may help to clarify the role of these thermodynamical quantities in the context of different first-order phase transitions such as the case of magnetic Hamiltonians (e.g. the Potts model).

Index of Ship Structure Committee Publications.

DTIC Science & Technology

1977-12-01

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Transcatheter Potts shunt creation in patients with severe pulmonary arterial hypertension: initial clinical experience.

PubMed

Esch, Jesse J; Shah, Pinak B; Cockrill, Barbara A; Farber, Harrison W; Landzberg, Michael J; Mehra, Mandeep R; Mullen, Mary P; Opotowsky, Alexander R; Waxman, Aaron B; Lock, James E; Marshall, Audrey C

2013-04-01

Patients with severe pulmonary arterial hypertension (PAH) face significant morbidity and death as a consequence of progressive right heart failure. Surgical shunt placement between the left PA and descending aorta (Potts shunt) appears promising for PAH palliation in children; however, surgical mortality is likely to be unacceptably high in adults with PAH. We describe a technique for transcatheter Potts shunt (TPS) creation by fluoroscopically guided retrograde needle perforation of the descending aorta at the site of apposition to the left PA to create a tract for deployment of a covered stent between these vessels. This covered stent-anchored by the vessel walls and surrounding tissue-serves as the shunt. TPS creation was considered in 7 patients and performed in 4. The procedure was technically successful in 3 patients; 1 patient died during the procedure as a result of uncontrolled hemothorax. One acute survivor, critically ill at the time of TPS creation, later died of comorbidities. The 2 mid-term survivors (follow-up of 10 and 4 months) are well at home, with symptomatic improvement and no late complications. The 3 candidate patients in whom the procedure was not performed died within 1 month of consideration, underscoring the tenuous nature of this population. TPS creation is feasible and may offer symptomatic relief to select patients with refractory PAH. Further study of this innovative approach is warranted. Copyright © 2013 International Society for Heart and Lung Transplantation. Published by Elsevier Inc. All rights reserved.

High dimensional land cover inference using remotely sensed modis data

NASA Astrophysics Data System (ADS)

Glanz, Hunter S.

Image segmentation persists as a major statistical problem, with the volume and complexity of data expanding alongside new technologies. Land cover classification, one of the most studied problems in Remote Sensing, provides an important example of image segmentation whose needs transcend the choice of a particular classification method. That is, the challenges associated with land cover classification pervade the analysis process from data pre-processing to estimation of a final land cover map. Many of the same challenges also plague the task of land cover change detection. Multispectral, multitemporal data with inherent spatial relationships have hardly received adequate treatment due to the large size of the data and the presence of missing values. In this work we propose a novel, concerted application of methods which provide a unified way to estimate model parameters, impute missing data, reduce dimensionality, classify land cover, and detect land cover changes. This comprehensive analysis adopts a Bayesian approach which incorporates prior knowledge to improve the interpretability, efficiency, and versatility of land cover classification and change detection. We explore a parsimonious, parametric model that allows for a natural application of principal components analysis to isolate important spectral characteristics while preserving temporal information. Moreover, it allows us to impute missing data and estimate parameters via expectation-maximization (EM). A significant byproduct of our framework includes a suite of training data assessment tools. To classify land cover, we employ a spanning tree approximation to a lattice Potts prior to incorporate spatial relationships in a judicious way and more efficiently access the posterior distribution of pixel labels. We then achieve exact inference of the labels via the centroid estimator. To detect land cover changes, we develop a new EM algorithm based on the same parametric model. We perform simulation studies to validate our models and methods, and conduct an extensive continental scale case study using MODIS data. The results show that we successfully classify land cover and recover the spatial patterns present in large scale data. Application of our change point method to an area in the Amazon successfully identifies the progression of deforestation through portions of the region.

INFFTM: Fast evaluation of 3d Fourier series in MATLAB with an application to quantum vortex reconnections

NASA Astrophysics Data System (ADS)

Caliari, Marco; Zuccher, Simone

2017-04-01

Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of arbitrary points are quite rare, especially in MATLAB language. Here we employ the Nonequispaced Fast Fourier Transform (NFFT, by J. Keiner, S. Kunis, and D. Potts), a C library designed for this purpose, and provide a Matlab® and GNU Octave interface that makes NFFT easily available to the Numerical Analysis community. We test the effectiveness of our package in the framework of quantum vortex reconnections, where pseudospectral Fourier methods are commonly used and local high resolution is required in the post-processing stage. We show that the efficient evaluation of a truncated Fourier series at arbitrary points provides excellent results at a computational cost much smaller than carrying out a numerical simulation of the problem on a sufficiently fine regular grid that can reproduce comparable details of the reconnecting vortices.

Spatio-temporal morphology changes in and quenching effects on the 2D spreading dynamics of cell colonies in both plain and methylcellulose-containing culture media.

PubMed

Muzzio, N E; Pasquale, M A; Huergo, M A C; Bolzán, A E; González, P H; Arvia, A J

2016-06-01

To deal with complex systems, microscopic and global approaches become of particular interest. Our previous results from the dynamics of large cell colonies indicated that their 2D front roughness dynamics is compatible with the standard Kardar-Parisi-Zhang (KPZ) or the quenched KPZ equations either in plain or methylcellulose (MC)-containing gel culture media, respectively. In both cases, the influence of a non-uniform distribution of the colony constituents was significant. These results encouraged us to investigate the overall dynamics of those systems considering the morphology and size, the duplication rate, and the motility of single cells. For this purpose, colonies with different cell populations (N) exhibiting quasi-circular and quasi-linear growth fronts in plain and MC-containing culture media are investigated. For small N, the average radial front velocity and its change with time depend on MC concentration. MC in the medium interferes with cell mitosis, contributes to the local enlargement of cells, and increases the distribution of spatio-temporal cell density heterogeneities. Colony spreading in MC-containing media proceeds under two main quenching effects, I and II; the former mainly depending on the culture medium composition and structure and the latter caused by the distribution of enlarged local cell domains. For large N, colony spreading occurs at constant velocity. The characteristics of cell motility, assessed by measuring their trajectories and the corresponding velocity field, reflect the effect of enlarged, slow-moving cells and the structure of the medium. Local average cell size distribution and individual cell motility data from plain and MC-containing media are qualitatively consistent with the predictions of both the extended cellular Potts models and the observed transition of the front roughness dynamics from a standard KPZ to a quenched KPZ. In this case, quenching effects I and II cooperate and give rise to the quenched-KPZ equation. Seemingly, these results show a possible way of linking the cellular Potts models and the 2D colony front roughness dynamics.

Monte Carlo modeling of recrystallization processes in α-uranium

DOE PAGES

Steiner, M. A.; McCabe, R. J.; Garlea, E.; ...

2017-08-01

In this study, starting with electron backscattered diffraction (EBSD) data obtained from a warm clock-rolled α-uranium deformation microstructure, a Potts Monte Carlo model was used to simulate static site-saturated recrystallization while testing a number of different conditions for the assignment of recrystallized nuclei within the microstructure. The simulations support observations that recrystallized nuclei within α-uranium form preferentially on non-twin high-angle grain boundary sites at 450 °C, and demonstrate that the most likely nucleation sites on these boundaries can be identified by the surrounding degree of Kernel Average Misorientation (KAM), which may be considered as a proxy for the local geometricallymore » necessary dislocation (GND) density.« less

Exploring load, velocity, and surface disorder dependence of friction with one-dimensional and two-dimensional models.

PubMed

Dagdeviren, Omur E

2018-08-03

The effect of surface disorder, load, and velocity on friction between a single asperity contact and a model surface is explored with one-dimensional and two-dimensional Prandtl-Tomlinson (PT) models. We show that there are fundamental physical differences between the predictions of one-dimensional and two-dimensional models. The one-dimensional model estimates a monotonic increase in friction and energy dissipation with load, velocity, and surface disorder. However, a two-dimensional PT model, which is expected to approximate a tip-sample system more realistically, reveals a non-monotonic trend, i.e. friction is inert to surface disorder and roughness in wearless friction regime. The two-dimensional model discloses that the surface disorder starts to dominate the friction and energy dissipation when the tip and the sample interact predominantly deep into the repulsive regime. Our numerical calculations address that tracking the minimum energy path and the slip-stick motion are two competing effects that determine the load, velocity, and surface disorder dependence of friction. In the two-dimensional model, the single asperity can follow the minimum energy path in wearless regime; however, with increasing load and sliding velocity, the slip-stick movement dominates the dynamic motion and results in an increase in friction by impeding tracing the minimum energy path. Contrary to the two-dimensional model, when the one-dimensional PT model is employed, the single asperity cannot escape to the minimum energy minimum due to constraint motion and reveals only a trivial dependence of friction on load, velocity, and surface disorder. Our computational analyses clarify the physical differences between the predictions of the one-dimensional and two-dimensional models and open new avenues for disordered surfaces for low energy dissipation applications in wearless friction regime.

Correlation of diffusion tensor imaging parameters with neural status in Pott's spine.

PubMed

Jain, Nikhil; Saini, Namita Singh; Kumar, Sudhir; Rajagopalan, Mukunth; Chakraborti, Kanti Lal; Jain, Anil Kumar

2016-04-29

Diffusion tensor imaging (DTI) has been used in cervical trauma and spondylotic myelopathy, and it has been found to correlate with neural deficit and prognosticate neural recovery. Such a correlation has not been studied in Pott's spine with paraplegia. Hence, this prospective study has been used to find correlation of DTI parameters with neural deficit in these patients. Thirty-four patients of spinal TB were enrolled and DTI was performed before the start of treatment and after six months. Fractional anisotropy (FA), Mean diffusivity (MD), and Tractography were studied. Neurological deficit was graded by the Jain and Sinha scoring. Changes in FA and MD at and below the site of lesion (SOL) were compared to above the SOL (control) using the unpaired t-test. Pre-treatment and post-treatment values were also compared using the paired t-test. Correlation of DTI parameters with neurological score was done by Pearson's correlation. Subjective assessment of Tractography images was done. Mean average FA was not significantly decreased at the SOL in patients with paraplegia as compared to control. After six months of treatment, a significant decrease (p = 0.02) in mean average FA at the SOL compared to pre-treatment was seen. Moderate positive correlation (r = 0.49) between mean average FA and neural score after six months of treatment was found. Tractography images were not consistent with severity of paraplegia. Unlike spondylotic myelopathy and trauma, epidural collection and its organized inflammatory tissue in Pott's spine precludes accurate assessment of diffusion characteristics of the compressed cord.

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.

Ramp and periodic dynamics across non-Ising critical points

NASA Astrophysics Data System (ADS)

Ghosh, Roopayan; Sen, Arnab; Sengupta, K.

2018-01-01

We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a Z3 or Z4 symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform state to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation, for finite-size boson chains with L ≤24 using exact diagonalization (ED), of the excitation density D , the wave function overlap F , and the excess energy Q at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which D and Q show Kibble-Zurek scaling. We find, based on numerical analysis with L ≤24 , that such scaling is consistent with that expected from critical exponents of the q -state Potts universality class with q =3 ,4 . For the periodic protocol, we show that the model displays near-perfect dynamical freezing at specific frequencies; at these frequencies D ,Q →0 and |F |→1 . We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.

Method for protein structure alignment

DOEpatents

Blankenbecler, Richard; Ohlsson, Mattias; Peterson, Carsten; Ringner, Markus

2005-02-22

This invention provides a method for protein structure alignment. More particularly, the present invention provides a method for identification, classification and prediction of protein structures. The present invention involves two key ingredients. First, an energy or cost function formulation of the problem simultaneously in terms of binary (Potts) assignment variables and real-valued atomic coordinates. Second, a minimization of the energy or cost function by an iterative method, where in each iteration (1) a mean field method is employed for the assignment variables and (2) exact rotation and/or translation of atomic coordinates is performed, weighted with the corresponding assignment variables.

Road networks as collections of minimum cost paths

NASA Astrophysics Data System (ADS)

Wegner, Jan Dirk; Montoya-Zegarra, Javier Alexander; Schindler, Konrad

2015-10-01

We present a probabilistic representation of network structures in images. Our target application is the extraction of urban roads from aerial images. Roads appear as thin, elongated, partially curved structures forming a loopy graph, and this complex layout requires a prior that goes beyond standard smoothness and co-occurrence assumptions. In the proposed model the network is represented as a union of 1D paths connecting distant (super-)pixels. A large set of putative candidate paths is constructed in such a way that they include the true network as much as possible, by searching for minimum cost paths in the foreground (road) likelihood. Selecting the optimal subset of candidate paths is posed as MAP inference in a higher-order conditional random field. Each path forms a higher-order clique with a type of clique potential, which attracts the member nodes of cliques with high cumulative road evidence to the foreground label. That formulation induces a robust PN -Potts model, for which a global MAP solution can be found efficiently with graph cuts. Experiments with two road data sets show that the proposed model significantly improves per-pixel accuracies as well as the overall topological network quality with respect to several baselines.

Dynamics of Cell Ensembles on Adhesive Micropatterns: Bridging the Gap between Single Cell Spreading and Collective Cell Migration

PubMed Central

Albert, Philipp J.; Schwarz, Ulrich S.

2016-01-01

The collective dynamics of multicellular systems arise from the interplay of a few fundamental elements: growth, division and apoptosis of single cells; their mechanical and adhesive interactions with neighboring cells and the extracellular matrix; and the tendency of polarized cells to move. Micropatterned substrates are increasingly used to dissect the relative roles of these fundamental processes and to control the resulting dynamics. Here we show that a unifying computational framework based on the cellular Potts model can describe the experimentally observed cell dynamics over all relevant length scales. For single cells, the model correctly predicts the statistical distribution of the orientation of the cell division axis as well as the final organisation of the two daughters on a large range of micropatterns, including those situations in which a stable configuration is not achieved and rotation ensues. Large ensembles migrating in heterogeneous environments form non-adhesive regions of inward-curved arcs like in epithelial bridge formation. Collective migration leads to swirl formation with variations in cell area as observed experimentally. In each case, we also use our model to predict cell dynamics on patterns that have not been studied before. PMID:27054883

Inference of epistatic effects in a key mitochondrial protein

NASA Astrophysics Data System (ADS)

Nelson, Erik D.; Grishin, Nick V.

2018-06-01

We use Potts model inference to predict pair epistatic effects in a key mitochondrial protein—cytochrome c oxidase subunit 2—for ray-finned fishes. We examine the effect of phylogenetic correlations on our predictions using a simple exact fitness model, and we find that, although epistatic effects are underpredicted, they maintain a roughly linear relationship to their true (model) values. After accounting for this correction, epistatic effects in the protein are still relatively weak, leading to fitness valleys of depth 2 N s ≃-5 in compensatory double mutants. Interestingly, positive epistasis is more pronounced than negative epistasis, and the strongest positive effects capture nearly all sites subject to positive selection in fishes, similar to virus proteins evolving under selection pressure in the context of drug therapy.

Comparison of two-dimensional and quasi-one-dimensional scramjet models by the example of VAG experiment

NASA Astrophysics Data System (ADS)

Seleznev, R. K.

2017-02-01

In the paper two-dimensional and quasi-one dimensional models for scramjet combustion chamber are described. Comparison of the results of calculations for the two-dimensional and quasi-one dimensional code by the example of VAG experiment are presented.

Network of likes and dislikes: Conflict and membership

NASA Astrophysics Data System (ADS)

Park, Hye Jin; Yi, Su Do; Kim, Dae Joong; Kim, Beom Jun

2016-11-01

We all have friends and foes. In the study of complex networks, such a pairwise interaction is described by a directed link since the relation is not necessarily symmetric. We study a real network constructed from a survey in which each individual chooses five members (s)he wants to work with, and other five (s)he does not like to work together. Although everyone's outdegrees for such like and dislike links are fixed to five, respectively, it is found that indegree sequence for each type of links exhibits very different behaviors. We also pursue to answer the question of proper divisions of the organization based on the concept of happiness defined for each directed relation. For example, two individuals connected by like (dislike) links in both directions are happy if they belong to the same (different) group(s). We then adopt the framework of the q-state Potts model with long-ranged ferromagnetic and antiferromagnetic interactions and discuss the group structure in the organization that minimizes a suitably defined unhappiness.

System for generating two-dimensional masks from a three-dimensional model using topological analysis

DOEpatents

Schiek, Richard [Albuquerque, NM

2006-06-20

A method of generating two-dimensional masks from a three-dimensional model comprises providing a three-dimensional model representing a micro-electro-mechanical structure for manufacture and a description of process mask requirements, reducing the three-dimensional model to a topological description of unique cross sections, and selecting candidate masks from the unique cross sections and the cross section topology. The method further can comprise reconciling the candidate masks based on the process mask requirements description to produce two-dimensional process masks.

Baroreflex regulation of blood pressure during dynamic exercise

NASA Technical Reports Server (NTRS)

Raven, P. B.; Potts, J. T.; Shi, X.; Blomqvist, C. G. (Principal Investigator)

1997-01-01

From the work of Potts et al. Papelier et al. and Shi et al. it is readily apparent that the arterial (aortic and carotid) baroreflexes are reset to function at the prevailing ABP of exercise. The blood pressure of exercise is the result of the hemodynamic (cardiac output and TPR) responses, which appear to be regulated by two redundant neural control systems, "Central Command" and the "exercise pressor reflex". Central Command is a feed-forward neural control system that operates in parallel with the neural regulation of the locomotor system and appears to establish the hemodynamic response to exercise. Within the central nervous system it appears that the HLR may be the operational site for Central Command. Specific neural sites within the HLR have been demonstrated in animals to be active during exercise. With the advent of positron emission tomography (PET) and single-photon emission computed tomography (SPECT), the anatomical areas of the human brain related to Central Command are being mapped. It also appears that the Nucleus Tractus Solitarius and the ventrolateral medulla may serve as an integrating site as they receive neural information from the working muscles via the group III/IV muscle afferents as well as from higher brain centers. This anatomical site within the CNS is now the focus of many investigations in which arterial baroreflex function, Central Command and the "exercise pressor reflex" appear to demonstrate inhibitory or facilitatory interaction. The concept of whether Central Command is the prime mover in the resetting of the arterial baroreceptors to function at the exercising ABP or whether the resetting is an integration of the "exercise pressor reflex" information with that of Central Command is now under intense investigation. However, it would be justified to conclude, from the data of Bevegard and Shepherd, Dicarlo and Bishop, Potts et al., and Papelier et al. that the act of exercise results in the resetting of the arterial baroreflex. In addition, if, as we have proposed, the cardiopulmonary baroreceptors primarily monitors and reflexly regulates cardiac filling volume, it would seem from the data of Mack et al. and Potts et al. that the cardiopulmonary baroreceptor is also reset at the beginning of exercise. Therefore, investigations of the neural mechanisms of regulation involving Central Command and cardiopulmonary afferents, similar to those being undertaken for the arterial baroreflex, need to be established.

Boundary States and Broken Bulk Symmetries in WAr Minimal Models

NASA Astrophysics Data System (ADS)

Caldeira, Alexandre F.; Wheater, J. F.

We review the free-field formalism for boundary states. The multi-component free-field formalism is then used to study the boundary states of (p',p) rational conformal field theories having a W symmetry of the type Ar. We show how the classification of primary fields for these models is obtained by demanding modular covariance of cylinder amplitudes and that the resulting modular S matrix satisfies all the necessary conditions. Basis states satisfying the boundary conditions are found in the form of coherent states and as expected we find that W violating states can be found for all these models. We construct consistent physical boundary states for all the rank 2 (p + 1,p) models (of which the already known case of the 3-state Potts model is the simplest example) and find that the W violating sector possesses a direct analogue of the Verlinde formula.

Proceedings of the Joint Magnetism and Magnetic Materials-Intermag Conference (6th) Held in Albuquerque, New Mexico on 20-23 June 1994. Journal of Applied Physics. Volume 76. Number 10. Part 2

DTIC Science & Technology

1994-06-23

were studied as-cast and for pertItgoal FsI cNhi,, measured in the prsenlt work and calcult•ted for the after annealing for four days at 1000 ’C and...H. Eschrig MGP Research Group "Electron Systems," Technical University Dresden, D-01062 Dresden, Germany Magnetic and specific-heat studies of U2T2X...University, Kazan 420 008, Russia The phase transition in the continual random n-component Potts model is studied by the renormalization group method. It is

A cellular Potts model for the MMP-dependent and -independent cancer cell migration in matrix microtracks of different dimensions

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.

Aspergillus vertebral osteomyelitis in immunocompetent patients.

PubMed

Sethi, Somika; Siraj, Fouzia; Kalra, Kl; Chopra, P

2012-03-01

Fungal infections are one of the important cause of morbidity and mortality in immunocompromised patients. Aspergillus vertebral osteomyelitis is extremely rare. We report two cases of aspergillus vertebral osteomyelitis in immunocompetent men in the absence of an underlying disorder. The clinical and radiological findings were suggestive of Pott's spine. The absolute CD4, CD8 counts and their ratio were normal. The HIV status was negative in both patients. Both patients underwent surgical decompression. The histopathology of tissue obtained were suggestive of aspergillus osteomyelitis. One patient had antifungal treatment for 3 months and was doing well at 1 year followup, whereas other patient did not turnup after 2 months.

Aspergillus vertebral osteomyelitis in immunocompetent patients

PubMed Central

Sethi, Somika; Siraj, Fouzia; Kalra, KL; Chopra, P

2012-01-01

Fungal infections are one of the important cause of morbidity and mortality in immunocompromised patients. Aspergillus vertebral osteomyelitis is extremely rare. We report two cases of aspergillus vertebral osteomyelitis in immunocompetent men in the absence of an underlying disorder. The clinical and radiological findings were suggestive of Pott's spine. The absolute CD4, CD8 counts and their ratio were normal. The HIV status was negative in both patients. Both patients underwent surgical decompression. The histopathology of tissue obtained were suggestive of aspergillus osteomyelitis. One patient had antifungal treatment for 3 months and was doing well at 1 year followup, whereas other patient did not turnup after 2 months. PMID:22448068

Two-dimensional Mathematical Model of Oil-bearing Materials in Extrusion-type Transportation over Rectangular Screw Core

NASA Astrophysics Data System (ADS)

Gukasyan, A. V.; Koshevoy, E. P.; Kosachev, V. S.

2018-05-01

A comparative analysis of alternative models for plastic flow in extrusive transportation of oil-bearing materials was conducted; the research was directed at determining the function describing the screw core throughput capacity of the press (extruder). Transition from a one-dimensional model to a two-dimensional model significantly improves the mathematical model and allows using two-dimensional rheological models determining the throughput of the screw core.

The storage capacity of Potts models for semantic memory retrieval

NASA Astrophysics Data System (ADS)

Kropff, Emilio; Treves, Alessandro

2005-08-01

We introduce and analyse a minimal network model of semantic memory in the human brain. The model is a global associative memory structured as a collection of N local modules, each coding a feature, which can take S possible values, with a global sparseness a (the average fraction of features describing a concept). We show that, under optimal conditions, the number cM of modules connected on average to a module can range widely between very sparse connectivity (high dilution, c_{M}/N\\to 0 ) and full connectivity (c_{M}\\to N ), maintaining a global network storage capacity (the maximum number pc of stored and retrievable concepts) that scales like pc~cMS2/a, with logarithmic corrections consistent with the constraint that each synapse may store up to a fraction of a bit.

Stability-to-instability transition in the structure of large-scale networks

NASA Astrophysics Data System (ADS)

Hu, Dandan; Ronhovde, Peter; Nussinov, Zohar

2012-12-01

We examine phase transitions between the “easy,” “hard,” and “unsolvable” phases when attempting to identify structure in large complex networks (“community detection”) in the presence of disorder induced by network “noise” (spurious links that obscure structure), heat bath temperature T, and system size N. The partition of a graph into q optimally disjoint subgraphs or “communities” inherently requires Potts-type variables. In earlier work [Philos. Mag.1478-643510.1080/14786435.2011.616547 92, 406 (2012)], when examining power law and other networks (and general associated Potts models), we illustrated that transitions in the computational complexity of the community detection problem typically correspond to spin-glass-type transitions (and transitions to chaotic dynamics in mechanical analogs) at both high and low temperatures and/or noise. The computationally “hard” phase exhibits spin-glass type behavior including memory effects. The region over which the hard phase extends in the noise and temperature phase diagram decreases as N increases while holding the average number of nodes per community fixed. This suggests that in the thermodynamic limit a direct sharp transition may occur between the easy and unsolvable phases. When present, transitions at low temperature or low noise correspond to entropy driven (or “order by disorder”) annealing effects, wherein stability may initially increase as temperature or noise is increased before becoming unsolvable at sufficiently high temperature or noise. Additional transitions between contending viable solutions (such as those at different natural scales) are also possible. Identifying community structure via a dynamical approach where “chaotic-type” transitions were found earlier. The correspondence between the spin-glass-type complexity transitions and transitions into chaos in dynamical analogs might extend to other hard computational problems. In this work, we examine large networks (with a power law distribution in cluster size) that have a large number of communities (q≫1). We infer that large systems at a constant ratio of q to the number of nodes N asymptotically tend towards insolvability in the limit of large N for any positive T. The asymptotic behavior of temperatures below which structure identification might be possible, T×=O[1/lnq], decreases slowly, so for practical system sizes, there remains an accessible, and generally easy, global solvable phase at low temperature. We further employ multivariate Tutte polynomials to show that increasing q emulates increasing T for a general Potts model, leading to a similar stability region at low T. Given the relation between Tutte and Jones polynomials, our results further suggest a link between the above complexity transitions and transitions associated with random knots.

A two-dimensional kinematic dynamo model of the ionospheric magnetic field at Venus

NASA Technical Reports Server (NTRS)

Cravens, T. E.; Wu, D.; Shinagawa, H.

1990-01-01

The results of a high-resolution, two-dimensional, time dependent, kinematic dynamo model of the ionospheric magnetic field of Venus are presented. Various one-dimensional models are considered and the two-dimensional model is then detailed. In this model, the two-dimensional magnetic induction equation, the magnetic diffusion-convection equation, is numerically solved using specified plasma velocities. Origins of the vertical velocity profile and of the horizontal velocities are discussed. It is argued that the basic features of the vertical magnetic field profile remain unaltered by horizontal flow effects and also that horizontal plasma flow can strongly affect the magnetic field for altitudes above 300 km.

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 scenario it was in the range p ∈ [ 8 , 10 ] . Because of the parallel capabilities of the algorithm, a large-scale execution of the parallel family trees strategy in a supercomputer could contribute to the study of wider strip lattices.

Tomato yield responses to soil-incorporated dried distillers grains

USDA-ARS?s Scientific Manuscript database

Dried distiller's grains (DDGs) are a coproduct of dry-grind corn ethanol production, most of which are used for animal feed, and are sold for under $150/metric ton. Developing higher-value uses for DDGs can increase the profitability of corn-based ethanol. Although DDGs applied directly to a pott...

Efficiency losses in the pollination services market: A data envelopment analysis

USDA-ARS?s Scientific Manuscript database

Honeybees, mainly known for producing honey, also provide critical ecosystems services (Goulson, 2003; Potts et al., 2010). Their pollination is vital to the production of numerous cash crops that the U.S.’s agricultural sector depends on, particularly almonds (Aizen and Harder 2009, Bond et al. 201...

[Ancient disease, but not a thing of the past: Pott's paraplegia in an HIV-positive health-care worker].

PubMed

Jurado, Leonardo F

2017-04-01

Centro de Investigación UNINAVARRA-CINA, Fundación Universitaria Navarra, Neiva, ColombiaGrupo de Investigación MICOBAC-UN, Departamento de Microbiología, Facultad de Medicina, Universidad Nacional de Colombia, Bogotá, D.C., Colombia.

Continuum modeling of three-dimensional truss-like space structures

NASA Technical Reports Server (NTRS)

Nayfeh, A. H.; Hefzy, M. S.

1978-01-01

A mathematical and computational analysis capability has been developed for calculating the effective mechanical properties of three-dimensional periodic truss-like structures. Two models are studied in detail. The first, called the octetruss model, is a three-dimensional extension of a two-dimensional model, and the second is a cubic model. Symmetry considerations are employed as a first step to show that the specific octetruss model has four independent constants and that the cubic model has two. The actual values of these constants are determined by averaging the contributions of each rod element to the overall structure stiffness. The individual rod member contribution to the overall stiffness is obtained by a three-dimensional coordinate transformation. The analysis shows that the effective three-dimensional elastic properties of both models are relatively close to each other.

Current status of one- and two-dimensional numerical models: Successes and limitations

NASA Technical Reports Server (NTRS)

Schwartz, R. J.; Gray, J. L.; Lundstrom, M. S.

1985-01-01

The capabilities of one and two-dimensional numerical solar cell modeling programs (SCAP1D and SCAP2D) are described. The occasions when a two-dimensional model is required are discussed. The application of the models to design, analysis, and prediction are presented along with a discussion of problem areas for solar cell modeling.

Charting the Replica Symmetric Phase

NASA Astrophysics Data System (ADS)

Coja-Oghlan, Amin; Efthymiou, Charilaos; Jaafari, Nor; Kang, Mihyun; Kapetanopoulos, Tobias

2018-02-01

Diluted mean-field models are spin systems whose geometry of interactions is induced by a sparse random graph or hypergraph. Such models play an eminent role in the statistical mechanics of disordered systems as well as in combinatorics and computer science. In a path-breaking paper based on the non-rigorous `cavity method', physicists predicted not only the existence of a replica symmetry breaking phase transition in such models but also sketched a detailed picture of the evolution of the Gibbs measure within the replica symmetric phase and its impact on important problems in combinatorics, computer science and physics (Krzakala et al. in Proc Natl Acad Sci 104:10318-10323, 2007). In this paper we rigorise this picture completely for a broad class of models, encompassing the Potts antiferromagnet on the random graph, the k-XORSAT model and the diluted k-spin model for even k. We also prove a conjecture about the detection problem in the stochastic block model that has received considerable attention (Decelle et al. in Phys Rev E 84:066106, 2011).

Modeling Three-Dimensional Flow in Confined Aquifers by Superposition of Both Two- and Three-Dimensional Analytic Functions

NASA Astrophysics Data System (ADS)

Haitjema, Henk M.

1985-10-01

A technique is presented to incorporate three-dimensional flow in a Dupuit-Forchheimer model. The method is based on superposition of approximate analytic solutions to both two- and three-dimensional flow features in a confined aquifer of infinite extent. Three-dimensional solutions are used in the domain of interest, while farfield conditions are represented by two-dimensional solutions. Approximate three- dimensional solutions have been derived for a partially penetrating well and a shallow creek. Each of these solutions satisfies the condition that no flow occurs across the confining layers of the aquifer. Because of this condition, the flow at some distance of a three-dimensional feature becomes nearly horizontal. Consequently, remotely from a three-dimensional feature, its three-dimensional solution is replaced by a corresponding two-dimensional one. The latter solution is trivial as compared to its three-dimensional counterpart, and its use greatly enhances the computational efficiency of the model. As an example, the flow is modeled between a partially penetrating well and a shallow creek that occur in a regional aquifer system.

Concentration data and dimensionality in groundwater models: evaluation using inverse modelling

USGS Publications Warehouse

Barlebo, H.C.; Hill, M.C.; Rosbjerg, D.; Jensen, K.H.

1998-01-01

A three-dimensional inverse groundwater flow and transport model that fits hydraulic-head and concentration data simultaneously using nonlinear regression is presented and applied to a layered sand and silt groundwater system beneath the Grindsted Landfill in Denmark. The aquifer is composed of rather homogeneous hydrogeologic layers. Two issues common to groundwater flow and transport modelling are investigated: 1) The accuracy of simulated concentrations in the case of calibration with head data alone; and 2) The advantages and disadvantages of using a two-dimensional cross-sectional model instead of a three-dimensional model to simulate contaminant transport when the source is at the land surface. Results show that using only hydraulic heads in the nonlinear regression produces a simulated plume that is profoundly different from what is obtained in a calibration using both hydraulic-head and concentration data. The present study provides a well-documented example of the differences that can occur. Representing the system as a two-dimensional cross-section obviously omits some of the system dynamics. It was, however, possible to obtain a simulated plume cross-section that matched the actual plume cross-section well. The two-dimensional model execution times were about a seventh of those for the three-dimensional model, but some difficulties were encountered in representing the spatially variable source concentrations and less precise simulated concentrations were calculated by the two-dimensional model compared to the three-dimensional model. Summed up, the present study indicates that three dimensional modelling using both hydraulic heads and concentrations in the calibration should be preferred in the considered type of transport studies.

Dimensional reduction for a SIR type model

NASA Astrophysics Data System (ADS)

Cahyono, Edi; Soeharyadi, Yudi; Mukhsar

2018-03-01

Epidemic phenomena are often modeled in the form of dynamical systems. Such model has also been used to model spread of rumor, spread of extreme ideology, and dissemination of knowledge. Among the simplest is SIR (susceptible, infected and recovered) model, a model that consists of three compartments, and hence three variables. The variables are functions of time which represent the number of subpopulations, namely suspect, infected and recovery. The sum of the three is assumed to be constant. Hence, the model is actually two dimensional which sits in three-dimensional ambient space. This paper deals with the reduction of a SIR type model into two variables in two-dimensional ambient space to understand the geometry and dynamics better. The dynamics is studied, and the phase portrait is presented. The two dimensional model preserves the equilibrium and the stability. The model has been applied for knowledge dissemination, which has been the interest of knowledge management.

Using Fitness Landscapes for Rational Hepatitis C Immunogen Design

NASA Astrophysics Data System (ADS)

Hart, Gregory; Ferguson, Andrew

2015-03-01

Hepatitis C virus afflicts 170 million people worldwide, 2-3% of the global population. Prophylactic vaccination offers the most realistic and cost effective hope of controlling this epidemic, particularly in the developing world where expensive drug therapies are unavailable. Despite 20 years of research, the high mutability of the virus, and lack of knowledge of what constitutes effective immune responses, have impeded development of an effective vaccine. Coupling data mining of sequence databases with the Potts model, we have developed a computational approach to systematically identify viral vulnerabilities and perform rational design of vaccine immunogens. We applied our approach to the nonstructural proteins NS3, NSA, NSA, and NSB which are crucial for viral replication.The predictions of our model are in good accord with experimental measurements and clinical observations, and we have used our model to design immunogen candidates to elicit T-cell responses against vulnerable regions of theseviral proteins.

On the Role of Entropy in the Protein Folding Process

NASA Astrophysics Data System (ADS)

Hoppe, Travis

2011-12-01

A protein's ultimate function and activity is determined by the unique three-dimensional structure taken by the folding process. Protein malfunction due to misfolding is the culprit of many clinical disorders, such as abnormal protein aggregations. This leads to neurodegenerative disorders like Huntington's and Alzheimer's disease. We focus on a subset of the folding problem, exploring the role and effects of entropy on the process of protein folding. Four major concepts and models are developed and each pertains to a specific aspect of the folding process: entropic forces, conformational states under crowding, aggregation, and macrostate kinetics from microstate trajectories. The exclusive focus on entropy is well-suited for crowding studies, as many interactions are nonspecific. We show how a stabilizing entropic force can arise purely from the motion of crowders in solution. In addition we are able to make a a quantitative prediction of the crowding effect with an implicit crowding approximation using an aspherical scaled-particle theory. In order to investigate the effects of aggregation, we derive a new operator expansion method to solve the Ising/Potts model with external fields over an arbitrary graph. Here the external fields are representative of the entropic forces. We show that this method reduces the problem of calculating the partition function to the solution of recursion relations. Many of the methods employed are coarse-grained approximations. As such, it is useful to have a viable method for extracting macrostate information from time series data. We develop a method to cluster the microstates into physically meaningful macrostates by grouping similar relaxation times from a transition matrix. Overall, the studied topics allow us to understand deeper the complicated process involving proteins.

Two-dimensional plasmons in the random impedance network model of disordered thin film nanocomposites

NASA Astrophysics Data System (ADS)

Olekhno, N. A.; Beltukov, Y. M.

2018-05-01

Random impedance networks are widely used as a model to describe plasmon resonances in disordered metal-dielectric nanocomposites. Two-dimensional networks are applied when considering thin films despite the fact that such networks correspond to the two-dimensional electrodynamics [Clerc et al., J. Phys. A 29, 4781 (1996), 10.1088/0305-4470/29/16/006]. In the present work, we propose a model of two-dimensional systems with the three-dimensional Coulomb interaction and show that this model is equivalent to the planar network with long-range capacitive links between distant sites. In the case of a metallic film, we obtain the well-known dispersion of two-dimensional plasmons ω ∝√{k } . We study the evolution of resonances with a decrease in the metal filling factor within the framework of the proposed model. In the subcritical region with the metal filling p lower than the percolation threshold pc, we observe a gap with Lifshitz tails in the spectral density of states (DOS). In the supercritical region p >pc , the DOS demonstrates a crossover between plane-wave two-dimensional plasmons and resonances of finite clusters.

VALIDITY OF A TWO-DIMENSIONAL MODEL FOR VARIABLE-DENSITY HYDRODYNAMIC CIRCULATION

EPA Science Inventory

A three-dimensional model of temperatures and currents has been formulated to assist in the analysis and interpretation of the dynamics of stratified lakes. In this model, nonlinear eddy coefficients for viscosity and conductivities are included. A two-dimensional model (one vert...

Firm efficiency and returns-to-scale in the honey bee pollination services industry

USDA-ARS?s Scientific Manuscript database

Honeybees are well-known for producing honey, but they also provide critical ecosystem services through pollination (Goulson, 2003; Potts et al., 2010; Ványi et al., 2012). This pollination service is vital to the production of many cash crops, on which the U.S. agricultural sector depends (Aizen an...

"A matter of physical health and strength”: disciplining the female body and reproducing the Czech national community in the mid-nineteenth century.

PubMed

Frančíková, Dáša

2011-01-01

An 1850 article “Uzavírání sňatku” (“Marriage”) by Czech physician Jan Špott outlined the requirements for those who considered themselves part of the Czech national community. Špott stressed that those concerned with the future national existence had to educate themselves and each other to create healthy offspring. I examine Špott’s article with regard to contemporary ideas about fitness, the role of women, the need to discipline the female body, as well as the importance of education in reproducing the community. This article’s analysis - set in the broader context of the history of women, medicine, and nationalisms - shows that nation-oriented education could be perceived as a way to ensure the nation’s future existence while simultaneously emphasizing the responsibility of individuals, and particularly women, for the reproduction of the community. Špott’s propositions are significant to other nineteenth-century national movements and to postnational contexts where national fitness is a concern.

Laser range profile of cones

NASA Astrophysics Data System (ADS)

Zhou, Wenzhen; Gong, Yanjun; Wang, Mingjun; Gong, Lei

2016-10-01

technology. Laser one-dimensional range profile can reflect the characteristics of the target shape and surface material. These techniques were motivated by applications of laser radar to target discrimination in ballistic missile defense. The radar equation of pulse laser about cone is given in this paper. This paper demonstrates the analytical model of laser one-dimensional range profile of cone based on the radar equation of the pulse laser. Simulations results of laser one-dimensional range profiles of some cones are given. Laser one-dimensional range profiles of cone, whose surface material with diffuse lambertian reflectance, is given in this paper. Laser one-dimensional range profiles of cone, whose surface mater with diffuse materials whose retroreflectance can be modeled closely with an exponential term that decays with increasing incidence angles, is given in this paper. Laser one-dimensional range profiles of different pulse width of cone is given in this paper. The influences of surface material, pulse width, attitude on the one-dimensional range are analyzed. The laser two-dimensional range profile is two-dimensional scattering imaging of pulse laser of target. The two-dimensional range profile of roughness target can provide range resolved information. An analytical model of two-dimensional laser range profile of cone is proposed. The simulations of two-dimensional laser range profiles of some cones are given. Laser two-dimensional range profiles of cone, whose surface mater with diffuse lambertian reflectance, is given in this paper. Laser two-dimensional range profiles of cone, whose surface mater with diffuse materials whose retroreflectance can be modeled closely with an exponential term that decays with increasing incidence angles, is given in this paper. The influence of pulse width, surface material on laser two-dimensional range profile is analyzed. Laser one-dimensional range profile and laser two-dimensional range profile are called as laser range profile (LRP).

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.

Spectral properties near the Mott transition in the two-dimensional t-J model with next-nearest-neighbor hopping

NASA Astrophysics Data System (ADS)

Kohno, Masanori

2018-05-01

The single-particle spectral properties of the two-dimensional t-J model with next-nearest-neighbor hopping are investigated near the Mott transition by using cluster perturbation theory. The spectral features are interpreted by considering the effects of the next-nearest-neighbor hopping on the shift of the spectral-weight distribution of the two-dimensional t-J model. Various anomalous features observed in hole-doped and electron-doped high-temperature cuprate superconductors are collectively explained in the two-dimensional t-J model with next-nearest-neighbor hopping near the Mott transition.

Ab initio quantum mechanical calculation of the reaction probability for the Cl-+PH2Cl→ClPH2+Cl- reaction

NASA Astrophysics Data System (ADS)

Farahani, Pooria; Lundberg, Marcus; Karlsson, Hans O.

2013-11-01

The SN2 substitution reactions at phosphorus play a key role in organic and biological processes. Quantum molecular dynamics simulations have been performed to study the prototype reaction Cl-+PH2Cl→ClPH2+Cl-, using one and two-dimensional models. A potential energy surface, showing an energy well for a transition complex, was generated using ab initio electronic structure calculations. The one-dimensional model is essentially reflection free, whereas the more realistic two-dimensional model displays involved resonance structures in the reaction probability. The reaction rate is almost two orders of magnitude smaller for the two-dimensional compared to the one-dimensional model. Energetic errors in the potential energy surface is estimated to affect the rate by only a factor of two. This shows that for these types of reactions it is more important to increase the dimensionality of the modeling than to increase the accuracy of the electronic structure calculation.

Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. Highway 13 Bridge over the Tar River at Greenville, North Carolina, Using One- and Two-Dimensional Steady-State Hydraulic Models

USGS Publications Warehouse

Wagner, Chad R.

2007-01-01

The use of one-dimensional hydraulic models currently is the standard method for estimating velocity fields through a bridge opening for scour computations and habitat assessment. Flood-flow contraction through bridge openings, however, is hydrodynamically two dimensional and often three dimensional. Although there is awareness of the utility of two-dimensional models to predict the complex hydraulic conditions at bridge structures, little guidance is available to indicate whether a one- or two-dimensional model will accurately estimate the hydraulic conditions at a bridge site. The U.S. Geological Survey, in cooperation with the North Carolina Department of Transportation, initiated a study in 2004 to compare one- and two-dimensional model results with field measurements at complex riverine and tidal bridges in North Carolina to evaluate the ability of each model to represent field conditions. The field data consisted of discharge and depth-averaged velocity profiles measured with an acoustic Doppler current profiler and surveyed water-surface profiles for two high-flow conditions. For the initial study site (U.S. Highway 13 over the Tar River at Greenville, North Carolina), the water-surface elevations and velocity distributions simulated by the one- and two-dimensional models showed appreciable disparity in the highly sinuous reach upstream from the U.S. Highway 13 bridge. Based on the available data from U.S. Geological Survey streamgaging stations and acoustic Doppler current profiler velocity data, the two-dimensional model more accurately simulated the water-surface elevations and the velocity distributions in the study reach, and contracted-flow magnitudes and direction through the bridge opening. To further compare the results of the one- and two-dimensional models, estimated hydraulic parameters (flow depths, velocities, attack angles, blocked flow width) for measured high-flow conditions were used to predict scour depths at the U.S. Highway 13 bridge by using established methods. Comparisons of pier-scour estimates from both models indicated that the scour estimates from the two-dimensional model were as much as twice the depth of the estimates from the one-dimensional model. These results can be attributed to higher approach velocities and the appreciable flow angles at the piers simulated by the two-dimensional model and verified in the field. Computed flood-frequency estimates of the 10-, 50-, 100-, and 500-year return-period floods on the Tar River at Greenville were also simulated with both the one- and two-dimensional models. The simulated water-surface profiles and velocity fields of the various return-period floods were used to compare the modeling approaches and provide information on what return-period discharges would result in road over-topping and(or) pressure flow. This information is essential in the design of new and replacement structures. The ability to accurately simulate water-surface elevations and velocity magnitudes and distributions at bridge crossings is essential in assuring that bridge plans balance public safety with the most cost-effective design. By compiling pertinent bridge-site characteristics and relating them to the results of several model-comparison studies, the framework for developing guidelines for selecting the most appropriate model for a given bridge site can be accomplished.

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

Comparisons between thermodynamic and one-dimensional combustion models of spark-ignition engines

NASA Technical Reports Server (NTRS)

Ramos, J. I.

1986-01-01

Results from a one-dimensional combustion model employing a constant eddy diffusivity and a one-step chemical reaction are compared with those of one-zone and two-zone thermodynamic models to study the flame propagation in a spark-ignition engine. One-dimensional model predictions are found to be very sensitive to the eddy diffusivity and reaction rate data. The average mixing temperature found using the one-zone thermodynamic model is higher than those of the two-zone and one-dimensional models during the compression stroke, and that of the one-dimensional model is higher than those predicted by both thermodynamic models during the expansion stroke. The one-dimensional model is shown to predict an accelerating flame even when the front approaches the cold cylinder wall.

Business Schools' Programs Turn Felons into Entrepreneurs

ERIC Educational Resources Information Center

Mangan, Katherine

2013-01-01

Mike Potts was halfway through a five-year prison sentence outside Houston when he heard about a program that would help him start a business when even buddies with clean records were struggling to find work. The Prison Entrepreneurship Program, run by a nonprofit group of the same name, works with Baylor University's Hankamer School of Business…

44. July 1974. BLACKSMITH SHOP, VIEW LOOKING EAST THROUGH THE ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

44. July 1974. BLACKSMITH SHOP, VIEW LOOKING EAST THROUGH THE DOOR TO THE WOOD SHOP; ON THE LEFT IS THE D. H. POTTS TIRE SHRINKER; TO THE RIGHT OF THE DOOR IS THE BELT CHASE FROM THE BASEMENT LINESHAFT. - Gruber Wagon Works, Pennsylvania Route 183 & State Hill Road at Red Bridge Park, Bernville, Berks County, PA

Autophagy: Suicide Prevention Hotline for the Gut Epithelium.

PubMed

Grizotte-Lake, Mayara; Vaishnava, Shipra

2018-02-14

Autophagy is genetically associated with inflammatory bowel disease (IBD); however, its role remains unclear in disease pathogenesis. Three recent studies reveal a novel cytoprotective role of autophagy during viral, bacterial, and protozoan-triggered IBD (Burger et al., 2018; Matsuzawa-Ishimoto et al., 2017; Pott et al., 2018). Copyright © 2018 Elsevier Inc. All rights reserved.

Modeling Semantic Emotion Space Using a 3D Hypercube-Projection: An Innovative Analytical Approach for the Psychology of Emotions

PubMed Central

Trnka, Radek; Lačev, Alek; Balcar, Karel; Kuška, Martin; Tavel, Peter

2016-01-01

The widely accepted two-dimensional circumplex model of emotions posits that most instances of human emotional experience can be understood within the two general dimensions of valence and activation. Currently, this model is facing some criticism, because complex emotions in particular are hard to define within only these two general dimensions. The present theory-driven study introduces an innovative analytical approach working in a way other than the conventional, two-dimensional paradigm. The main goal was to map and project semantic emotion space in terms of mutual positions of various emotion prototypical categories. Participants (N = 187; 54.5% females) judged 16 discrete emotions in terms of valence, intensity, controllability and utility. The results revealed that these four dimensional input measures were uncorrelated. This implies that valence, intensity, controllability and utility represented clearly different qualities of discrete emotions in the judgments of the participants. Based on this data, we constructed a 3D hypercube-projection and compared it with various two-dimensional projections. This contrasting enabled us to detect several sources of bias when working with the traditional, two-dimensional analytical approach. Contrasting two-dimensional and three-dimensional projections revealed that the 2D models provided biased insights about how emotions are conceptually related to one another along multiple dimensions. The results of the present study point out the reductionist nature of the two-dimensional paradigm in the psychological theory of emotions and challenge the widely accepted circumplex model. PMID:27148130

Modeling and complexity of stochastic interacting Lévy type financial price dynamics

NASA Astrophysics Data System (ADS)

Wang, Yiduan; Zheng, Shenzhou; Zhang, Wei; Wang, Jun; Wang, Guochao

2018-06-01

In attempt to reproduce and investigate nonlinear dynamics of security markets, a novel nonlinear random interacting price dynamics, which is considered as a Lévy type process, is developed and investigated by the combination of lattice oriented percolation and Potts dynamics, which concerns with the instinctive random fluctuation and the fluctuation caused by the spread of the investors' trading attitudes, respectively. To better understand the fluctuation complexity properties of the proposed model, the complexity analyses of random logarithmic price return and corresponding volatility series are preformed, including power-law distribution, Lempel-Ziv complexity and fractional sample entropy. In order to verify the rationality of the proposed model, the corresponding studies of actual security market datasets are also implemented for comparison. The empirical results reveal that this financial price model can reproduce some important complexity features of actual security markets to some extent. The complexity of returns decreases with the increase of parameters γ1 and β respectively, furthermore, the volatility series exhibit lower complexity than the return series

A note on two-dimensional asymptotic magnetotail equilibria

NASA Technical Reports Server (NTRS)

Voigt, Gerd-Hannes; Moore, Brian D.

1994-01-01

In order to understand, on the fluid level, the structure, the time evolution, and the stability of current sheets, such as the magnetotail plasma sheet in Earth's magnetosphere, one has to consider magnetic field configurations that are in magnetohydrodynamic (MHD) force equilibrium. Any reasonable MHD current sheet model has to be two-dimensional, at least in an asymptotic sense (B(sub z)/B (sub x)) = epsilon much less than 1. The necessary two-dimensionality is described by a rather arbitrary function f(x). We utilize the free function f(x) to construct two-dimensional magnetotail equilibria are 'equivalent' to current sheets in empirical three-dimensional models. We obtain a class of asymptotic magnetotail equilibria ordered with respect to the magnetic disturbance index Kp. For low Kp values the two-dimensional MHD equilibria reflect some of the realistic, observation-based, aspects of three-dimensional models. For high Kp values the three-dimensional models do not fit the asymptotic MHD equlibria, which is indicative of their inconsistency with the assumed pressure function. This, in turn, implies that high magnetic activity levels of the real magnetosphere might be ruled by thermodynamic conditions different from local thermodynamic equilibrium.

Validation and application of a two-dimensional model to simulate soil salt transport under mulched drip irrigation

NASA Astrophysics Data System (ADS)

Jiao, Huiqing; Zhao, Chengyi; Sheng, Yu; Chen, Yan; Shi, Jianchu; Li, Baoguo

2017-04-01

Water shortage and soil salinization increasingly become the main constraints for sustainable development of agriculture in Southern Xinjiang, China. Mulched drip irrigation, as a high-efficient water-saving irrigation method, has been widely applied in Southern Xinjiang for cotton production. In order to analyze the reasonability of describing the three-dimensional soil water and salt transport processes under mulched drip irrigation with a relatively simple two-dimensional model, a field experiment was conducted from 2007 to 2015 at Aksu of Southern Xinjiang, and soil water and salt transport processes were simulated through the three-dimensional and two-dimensional models based on COMSOL. Obvious differences were found between three-dimensional and two-dimensional simulations for soil water flow within the early 12 h of irrigation event and for soil salt transport in the area within 15 cm away from drip tubes during the whole irrigation event. The soil water and salt contents simulated by the two-dimensional model, however, agreed well with the mean values between two adjacent emitters simulated by the three-dimensional model, and also coincided with the measurements as corresponding RMSE less than 0.037 cm3 cm-3 and 1.80 g kg-1, indicating that the two-dimensional model was reliable for field irrigation management. Subsequently, the two-dimensional model was applied to simulate the dynamics of soil salinity for five numerical situations and for a widely adopted irrigation pattern in Southern Xinjiang (about 350 mm through mulched drip irrigation during growing season of cotton and total 400 mm through flooding irrigations before sowing and after harvesting). The simulation results indicated that the contribution of transpiration to salt accumulation in root layer was about 75% under mulched drip irrigation. Moreover, flooding irrigations before sowing and after harvesting were of great importance for salt leaching of arable layer, especially in bare strip where drip irrigation water hardly reached, and thus providing suitable root zone environment for cotton. Nevertheless, flooding irrigation should be further optimized to enhance water use efficiency.

Cancer detection based on Raman spectra super-paramagnetic clustering

NASA Astrophysics Data System (ADS)

González-Solís, José Luis; Guizar-Ruiz, Juan Ignacio; Martínez-Espinosa, Juan Carlos; Martínez-Zerega, Brenda Esmeralda; Juárez-López, Héctor Alfonso; Vargas-Rodríguez, Héctor; Gallegos-Infante, Luis Armando; González-Silva, Ricardo Armando; Espinoza-Padilla, Pedro Basilio; Palomares-Anda, Pascual

2016-08-01

The clustering of Raman spectra of serum sample is analyzed using the super-paramagnetic clustering technique based in the Potts spin model. We investigated the clustering of biochemical networks by using Raman data that define edge lengths in the network, and where the interactions are functions of the Raman spectra's individual band intensities. For this study, we used two groups of 58 and 102 control Raman spectra and the intensities of 160, 150 and 42 Raman spectra of serum samples from breast and cervical cancer and leukemia patients, respectively. The spectra were collected from patients from different hospitals from Mexico. By using super-paramagnetic clustering technique, we identified the most natural and compact clusters allowing us to discriminate the control and cancer patients. A special interest was the leukemia case where its nearly hierarchical observed structure allowed the identification of the patients's leukemia type. The goal of this study is to apply a model of statistical physics, as the super-paramagnetic, to find these natural clusters that allow us to design a cancer detection method. To the best of our knowledge, this is the first report of preliminary results evaluating the usefulness of super-paramagnetic clustering in the discipline of spectroscopy where it is used for classification of spectra.

Two-dimensional signal processing with application to image restoration

NASA Technical Reports Server (NTRS)

Assefi, T.

1974-01-01

A recursive technique for modeling and estimating a two-dimensional signal contaminated by noise is presented. A two-dimensional signal is assumed to be an undistorted picture, where the noise introduces the distortion. Both the signal and the noise are assumed to be wide-sense stationary processes with known statistics. Thus, to estimate the two-dimensional signal is to enhance the picture. The picture representing the two-dimensional signal is converted to one dimension by scanning the image horizontally one line at a time. The scanner output becomes a nonstationary random process due to the periodic nature of the scanner operation. Procedures to obtain a dynamical model corresponding to the autocorrelation function of the scanner output are derived. Utilizing the model, a discrete Kalman estimator is designed to enhance the image.

[Rapid prototyping: a very promising method].

PubMed

Haverman, T M; Karagozoglu, K H; Prins, H-J; Schulten, E A J M; Forouzanfar, T

2013-03-01

Rapid prototyping is a method which makes it possible to produce a three-dimensional model based on two-dimensional imaging. Various rapid prototyping methods are available for modelling, such as stereolithography, selective laser sintering, direct laser metal sintering, two-photon polymerization, laminated object manufacturing, three-dimensional printing, three-dimensional plotting, polyjet inkjet technology,fused deposition modelling, vacuum casting and milling. The various methods currently being used in the biomedical sector differ in production, materials and properties of the three-dimensional model which is produced. Rapid prototyping is mainly usedforpreoperative planning, simulation, education, and research into and development of bioengineering possibilities.

Role of the plurality rule in multiple choices

NASA Astrophysics Data System (ADS)

Calvão, A. M.; Ramos, M.; Anteneodo, C.

2016-02-01

People are often challenged to select one among several alternatives. This situation is present not only in decisions about complex issues, e.g. political or academic choices, but also about trivial ones, such as in daily purchases at a supermarket. We tackle this scenario by means of the tools of statistical mechanics. Following this approach, we introduce and analyse a model of opinion dynamics, using a Potts-like state variable to represent the multiple choices, including the ‘undecided state’, which represents the individuals who do not make a choice. We investigate the dynamics over Erdös-Rényi and Barabási-Albert networks, two paradigmatic classes with the small-world property, and we show the impact of the type of network on the opinion dynamics. Depending on the number of available options q and on the degree distribution of the network of contacts, different final steady states are accessible: from a wide distribution of choices to a state where a given option largely dominates. The abrupt transition between them is consistent with the sudden viral dominance of a given option over many similar ones. Moreover, the probability distributions produced by the model are validated by real data. Finally, we show that the model also contemplates the real situation of overchoice, where a large number of similar alternatives makes the choice process harder and indecision prevail.

Two-dimensional lattice Boltzmann model for magnetohydrodynamics.

PubMed

Schaffenberger, Werner; Hanslmeier, Arnold

2002-10-01

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

Role of natural and cultural features in residents' perceptions of rural character

Treesearch

Dori Pynnonen; Dennis Propst; Christine Vogt; Maureen McDonough

2006-01-01

Rural landscapes are rapidly changing as more families migrate in from cities and suburbs, yet there have been few systematic attempts to have residents describe exactly what rural character means to them. As part of a USDA Forest Service research program examining landscape change (Potts et al. 2004), this study focused on the landscape and residents of six...

Particle orbits in two-dimensional equilibrium models for the magnetotail

NASA Technical Reports Server (NTRS)

Karimabadi, H.; Pritchett, P. L.; Coroniti, F. V.

1990-01-01

Assuming that there exist an equilibrium state for the magnetotail, particle orbits are investigated in two-dimensional kinetic equilibrium models for the magnetotail. Particle orbits in the equilibrium field are compared with those calculated earlier with one-dimensional models, where the main component of the magnetic field (Bx) was approximated as either a hyperbolic tangent or a linear function of z with the normal field (Bz) assumed to be a constant. It was found that the particle orbits calculated with the two types of models are significantly different, mainly due to the neglect of the variation of Bx with x in the one-dimensional fields.

Influence of Dzyaloshinskii-Moriya interaction and ballistic spin transport in the two and three-dimensional Heisenberg model

NASA Astrophysics Data System (ADS)

Lima, L. S.

2018-06-01

We study the effect of Dzyaloshisnkii-Moriya interaction on spin transport in the two and three-dimensional Heisenberg antiferromagnetic models in the square lattice and cubic lattice respectively. For the three-dimensional model, we obtain a large peak for the spin conductivity and therefore a finite AC conductivity. For the two-dimensional model, we have gotten the AC spin conductivity tending to the infinity at ω → 0 limit and a suave decreasing in the spin conductivity with increase of ω. We obtain a small influence of the Dzyaloshinskii-Moriya interaction on the spin conductivity in all cases analyzed.

Strongly magnetized classical plasma models

NASA Technical Reports Server (NTRS)

Montgomery, D. C.

1972-01-01

The class of plasma processes for which the so-called Vlasov approximation is inadequate is investigated. Results from the equilibrium statistical mechanics of two-dimensional plasmas are derived. These results are independent of the presence of an external dc magnetic field. The nonequilibrium statistical mechanics of the electrostatic guiding-center plasma, a two-dimensional plasma model, is discussed. This model is then generalized to three dimensions. The guiding-center model is relaxed to include finite Larmor radius effects for a two-dimensional plasma.

Two-Dimensional Versus Three-Dimensional Conceptualization in Astronomy Education

NASA Astrophysics Data System (ADS)

Reynolds, Michael David

Numerous science conceptual issues are naturally three-dimensional. Classroom presentations are often two -dimensional or at best multidimensional. Several astronomy topics are of this nature, e. g. mechanics of the phases of the moon. Textbooks present this three-dimensional topic in two-dimensions; such is often the case in the classroom. This study was conducted to examine conceptions exhibited by pairs of like-sex 11th grade standard physics students as they modeled the lunar phases. Student pairs, 13 male and 13 female, were randomly selected and assigned. Pairing comes closer to classroom emulation, minimizes needs for direct probes, and pair discussion is more likely to display variety and depth. Four hypotheses were addressed: (1) Participants who model three-dimensionally will more likely achieve a higher explanation score. (2) Students who experienced more earth or physical science exposure will more likely model three-dimensionally. (3) Pairs that exhibit a strong science or mathematics preference will more likely model three-dimensionally. (4) Males will model in three dimensions more than females. Students provided background information, including science course exposure and subject preference. Each pair laid out a 16-card set representing two complete lunar phase changes. The pair was asked to explain why the phases occur. Materials were provided for use, including disks, spheres, paper and pen, and flashlight. Activities were videotaped for later evaluation. Statistics of choice was a correlation determination between course preference and model type and ANOVA for the other hypotheses. It was determined that pairs who modeled three -dimensionally achieved a higher score on their phases mechanics explanation at p <.05 level. Pairs with earth science or physical science exposure, those who prefer science or mathematics, and male participants were not more likely to model three-dimensionally. Possible reasons for lack of significance was small sample size and in the case of course preferences, small differences in course preference means. Based on this study, instructors should be aware of dimensionality and student misconceptions. Whenever possible, three-dimensional concepts should be modeled as such. Authors and publishers should consider modeling suggestions and three-dimensional ancillaries.

Hybrid-dimensional modelling of two-phase flow through fractured porous media with enhanced matrix fracture transmission conditions

NASA Astrophysics Data System (ADS)

Brenner, Konstantin; Hennicker, Julian; Masson, Roland; Samier, Pierre

2018-03-01

In this work, we extend, to two-phase flow, the single-phase Darcy flow model proposed in [26], [12] in which the (d - 1)-dimensional flow in the fractures is coupled with the d-dimensional flow in the matrix. Three types of so called hybrid-dimensional two-phase Darcy flow models are proposed. They all account for fractures acting either as drains or as barriers, since they allow pressure jumps at the matrix-fracture interfaces. The models also permit to treat gravity dominated flow as well as discontinuous capillary pressure at the material interfaces. The three models differ by their transmission conditions at matrix fracture interfaces: while the first model accounts for the nonlinear two-phase Darcy flux conservations, the second and third ones are based on the linear single phase Darcy flux conservations combined with different approximations of the mobilities. We adapt the Vertex Approximate Gradient (VAG) scheme to this problem, in order to account for anisotropy and heterogeneity aspects as well as for applicability on general meshes. Several test cases are presented to compare our hybrid-dimensional models to the generic equi-dimensional model, in which fractures have the same dimension as the matrix, leading to deep insight about the quality of the proposed reduced models.

Mixing Regimes in a Spatially Confined, Two-Dimensional, Supersonic Shear Layer

DTIC Science & Technology

1992-07-31

MODEL ................................... 3 THE MODEL PROBLEMS .............................................. 6 THE ONE-DIMENSIONAL PROBLEM...the effects of the numerical diffusion on the spectrum. Guirguis et al.ś and Farouk et al."’ have studied spatially evolving mixing layers for equal...approximations. Physical and Numerical Model General Formulation We solve the time-dependent, two-dimensional, compressible, Navier-Stokes equations for a

Are Young Children's Drawings Canonically Biased?

ERIC Educational Resources Information Center

Picard, Delphine; Durand, Karine

2005-01-01

In a between-subjects design, 4-to 6-year-olds were asked to draw from three-dimensional (3D) models, two-and-a-half-dimensional (212D) models with or without depth cues, or two-dimensional (2D) models of a familiar object (a saucepan) in noncanonical orientations (handle at the back or at the front). Results showed that canonical errors were…

Modeling the Controlled Recrystallization of Particle-Containing Aluminum Alloys

NASA Astrophysics Data System (ADS)

Adam, Khaled; Root, Jameson M.; Long, Zhengdong; Field, David P.

2017-01-01

The recrystallized fraction for AA7050 during the solution heat treatment is highly dependent upon the history of deformation during thermomechanical processing. In this work, a state variable model was developed to predict the recrystallization volume fraction as a function of processing parameters. Particle stimulated nucleation (PSN) was observed as a dominant mechanism of recrystallization in AA7050. The mesoscale Monte Carlo Potts model was used to simulate the evolved microstructure during static recrystallization with the given recrystallization fraction determined already by the state variable model for AA7050 alloy. The spatial inhomogeneity of nucleation is obtained from the measurement of the actual second-phase particle distribution in the matrix identified using backscattered electron (BSE) imaging. The state variable model showed good fit with the experimental results, and the simulated microstructures were quantitatively comparable to the experimental results for the PSN recrystallized microstructure of 7050 aluminum alloy. It was also found that the volume fraction of recrystallization did not proceed as dictated by the Avrami equation in this alloy because of the presence of the growth inhibitors.

A Monte Carlo model for 3D grain evolution during welding

NASA Astrophysics Data System (ADS)

Rodgers, Theron M.; Mitchell, John A.; Tikare, Veena

2017-09-01

Welding is one of the most wide-spread processes used in metal joining. However, there are currently no open-source software implementations for the simulation of microstructural evolution during a weld pass. Here we describe a Potts Monte Carlo based model implemented in the SPPARKS kinetic Monte Carlo computational framework. The model simulates melting, solidification and solid-state microstructural evolution of material in the fusion and heat-affected zones of a weld. The model does not simulate thermal behavior, but rather utilizes user input parameters to specify weld pool and heat-affect zone properties. Weld pool shapes are specified by Bézier curves, which allow for the specification of a wide range of pool shapes. Pool shapes can range from narrow and deep to wide and shallow representing different fluid flow conditions within the pool. Surrounding temperature gradients are calculated with the aide of a closest point projection algorithm. The model also allows simulation of pulsed power welding through time-dependent variation of the weld pool size. Example simulation results and comparisons with laboratory weld observations demonstrate microstructural variation with weld speed, pool shape, and pulsed-power.

Critical exponents for diluted resistor networks

NASA Astrophysics Data System (ADS)

Stenull, O.; Janssen, H. K.; Oerding, K.

1999-05-01

An approach by Stephen [Phys. Rev. B 17, 4444 (1978)] is used to investigate the critical properties of randomly diluted resistor networks near the percolation threshold by means of renormalized field theory. We reformulate an existing field theory by Harris and Lubensky [Phys. Rev. B 35, 6964 (1987)]. By a decomposition of the principal Feynman diagrams, we obtain diagrams which again can be interpreted as resistor networks. This interpretation provides for an alternative way of evaluating the Feynman diagrams for random resistor networks. We calculate the resistance crossover exponent φ up to second order in ɛ=6-d, where d is the spatial dimension. Our result φ=1+ɛ/42+4ɛ2/3087 verifies a previous calculation by Lubensky and Wang, which itself was based on the Potts-model formulation of the random resistor network.

Discussion Summary & Recommendations: Private Sector Members of Roundtable on Higher Education. Meeting at Kathryn, North Dakota, April 5, 2006

ERIC Educational Resources Information Center

North Dakota University System, 2006

2006-01-01

A majority of the private sector members on the Roundtable on Higher Education (See Attachment-A) gathered at the Corporate Adventures training center in Kathryn, North Dakota, on April 5, 2006. Also attending were Senator Ray Holmberg, Chair of the Roundtable on Higher Education and Eddie Dunn on behalf of Dr. Robert Potts, Chancellor of the…

Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices.

PubMed

Español, Malena I; Golovaty, Dmitry; Wilber, J Patrick

2018-01-01

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

Spectral analysis of a two-species competition model: Determining the effects of extreme conditions on the color of noise generated from simulated time series

NASA Astrophysics Data System (ADS)

Golinski, M. R.

2006-07-01

Ecologists have observed that environmental noise affects population variance in the logistic equation for one-species growth. Interactions between deterministic and stochastic dynamics in a one-dimensional system result in increased variance in species population density over time. Since natural populations do not live in isolation, the present paper simulates a discrete-time two-species competition model with environmental noise to determine the type of colored population noise generated by extreme conditions in the long-term population dynamics of competing populations. Discrete Fourier analysis is applied to the simulation results and the calculated Hurst exponent ( H) is used to determine how the color of population noise for the two species corresponds to extreme conditions in population dynamics. To interpret the biological meaning of the color of noise generated by the two-species model, the paper determines the color of noise generated by three reference models: (1) A two-dimensional discrete-time white noise model (0⩽ H<1/2); (2) A two-dimensional fractional Brownian motion model (H=1/2); and (3) A two-dimensional discrete-time model with noise for unbounded growth of two uncoupled species (1/2< H⩽1).

Dynamic colloidal assembly pathways via low dimensional models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Yuguang; Bevan, Michael A., E-mail: mabevan@jhu.edu; Thyagarajan, Raghuram

2016-05-28

Here we construct a low-dimensional Smoluchowski model for electric field mediated colloidal crystallization using Brownian dynamic simulations, which were previously matched to experiments. Diffusion mapping is used to infer dimensionality and confirm the use of two order parameters, one for degree of condensation and one for global crystallinity. Free energy and diffusivity landscapes are obtained as the coefficients of a low-dimensional Smoluchowski equation to capture the thermodynamics and kinetics of microstructure evolution. The resulting low-dimensional model quantitatively captures the dynamics of different assembly pathways between fluid, polycrystal, and single crystals states, in agreement with the full N-dimensional data as characterizedmore » by first passage time distributions. Numerical solution of the low-dimensional Smoluchowski equation reveals statistical properties of the dynamic evolution of states vs. applied field amplitude and system size. The low-dimensional Smoluchowski equation and associated landscapes calculated here can serve as models for predictive control of electric field mediated assembly of colloidal ensembles into two-dimensional crystalline objects.« less

Evaluation of a two-dimensional numerical model for air quality simulation in a street canyon

NASA Astrophysics Data System (ADS)

Okamoto, Shin `Ichi; Lin, Fu Chi; Yamada, Hiroaki; Shiozawa, Kiyoshige

For many urban areas, the most severe air pollution caused by automobile emissions appears along a road surrounded by tall buildings: the so=called street canyon. A practical two-dimensional numerical model has been developed to be applied to this kind of road structure. This model contains two submodels: a wind-field model and a diffusion model based on a Monte Carlo particle scheme. In order to evaluate the predictive performance of this model, an air quality simulation was carried out at three trunk roads in the Tokyo metropolitan area: Nishi-Shimbashi, Aoyama and Kanda-Nishikicho (using SF 6 as a tracer and NO x measurement). Since this model has two-dimensional properties and cannot be used for the parallel wind condition, the perpendicular wind condition was selected for the simulation. The correlation coefficients for the SF 6 and NO x data in Aoyama were 0.67 and 0.62, respectively. When predictive performance of this model is compared with other models, this model is comparable to the SRI model, and superior to the APPS three-dimensional numerical model.

Ferroelasticity in palmierite-type(1  -  x)Pb3(PO4)2 - xPb3(AsO4)2

NASA Astrophysics Data System (ADS)

Bismayer, Ulli; Mihailova, Boriana; Angel, Ross

2017-06-01

Lead phosphate-arsenate Pb3(P1-x As x O4)2 undergoes an improper ferroelastic phase transition from a rhombohedral paraphase R\\bar{3}m to a monoclinic ferrophase C2/c leading to distinct twin boundary patterns. On cooling compounds with x larger than 0.8 undergo further transitions to monoclinic low-temperature phases, whereas the composition with x  =  0.8 shows order-parameter coupling phenomena. The transformation R\\bar{3}m -C2/c was described on the basis of a three-state Potts model and the existence of precursors of monoclinic clusters in the rhombohedral paraphase. The system is one of the best studied improper ferroelastics. Due to its two-mode phonon behaviour the solid solution exhibits multistep temperature- as well as pressure-driven structural transformations with different length and time scales. Relevant investigations and findings of this palmierite-type material have been made by Prof E K H Salje. Some of the most prominent results from x-ray diffraction, optical microscopy and Raman scattering are reviewed, and the potential implications for domain-wall structures and engineering are discussed.

One-dimensional GIS-based model compared with a two-dimensional model in urban floods simulation.

PubMed

Lhomme, J; Bouvier, C; Mignot, E; Paquier, A

2006-01-01

A GIS-based one-dimensional flood simulation model is presented and applied to the centre of the city of Nîmes (Gard, France), for mapping flow depths or velocities in the streets network. The geometry of the one-dimensional elements is derived from the Digital Elevation Model (DEM). The flow is routed from one element to the next using the kinematic wave approximation. At the crossroads, the flows in the downstream branches are computed using a conceptual scheme. This scheme was previously designed to fit Y-shaped pipes junctions, and has been modified here to fit X-shaped crossroads. The results were compared with the results of a two-dimensional hydrodynamic model based on the full shallow water equations. The comparison shows that good agreements can be found in the steepest streets of the study zone, but differences may be important in the other streets. Some reasons that can explain the differences between the two models are given and some research possibilities are proposed.

(2 + 1)-dimensional interacting model of two massless spin-2 fields as a bi-gravity model

NASA Astrophysics Data System (ADS)

Hoseinzadeh, S.; Rezaei-Aghdam, A.

2018-06-01

We propose a new group-theoretical (Chern-Simons) formulation for the bi-metric theory of gravity in (2 + 1)-dimensional spacetime which describe two interacting massless spin-2 fields. Our model has been formulated in terms of two dreibeins rather than two metrics. We obtain our Chern-Simons gravity model by gauging mixed AdS-AdS Lie algebra and show that it has a two dimensional conformal field theory (CFT) at the boundary of the anti de Sitter (AdS) solution. We show that the central charge of the dual CFT is proportional to the mass of the AdS solution. We also study cosmological implications of our massless bi-gravity model.

Hypersonic Combustor Model Inlet CFD Simulations and Experimental Comparisons

NASA Technical Reports Server (NTRS)

Venkatapathy, E.; TokarcikPolsky, S.; Deiwert, G. S.; Edwards, Thomas A. (Technical Monitor)

1995-01-01

Numerous two-and three-dimensional computational simulations were performed for the inlet associated with the combustor model for the hypersonic propulsion experiment in the NASA Ames 16-Inch Shock Tunnel. The inlet was designed to produce a combustor-inlet flow that is nearly two-dimensional and of sufficient mass flow rate for large scale combustor testing. The three-dimensional simulations demonstrated that the inlet design met all the design objectives and that the inlet produced a very nearly two-dimensional combustor inflow profile. Numerous two-dimensional simulations were performed with various levels of approximations such as in the choice of chemical and physical models, as well as numerical approximations. Parametric studies were conducted to better understand and to characterize the inlet flow. Results from the two-and three-dimensional simulations were used to predict the mass flux entering the combustor and a mass flux correlation as a function of facility stagnation pressure was developed. Surface heat flux and pressure measurements were compared with the computed results and good agreement was found. The computational simulations helped determine the inlet low characteristics in the high enthalpy environment, the important parameters that affect the combustor-inlet flow, and the sensitivity of the inlet flow to various modeling assumptions.

Simulation of the June 11, 2010, flood along the Little Missouri River near Langley, Arkansas, using a hydrologic model coupled to a hydraulic model

USGS Publications Warehouse

Westerman, Drew A.; Clark, Brian R.

2013-01-01

The results from the precipitation-runoff hydrologic model, the one-dimensional unsteady-state hydraulic model, and a separate two-dimensional model developed as part of a coincident study, each complement the other in terms of streamflow timing, water-surface elevations, and velocities propagated by the June 11, 2010, flood event. The simulated grids for water depth and stream velocity from each model were directly compared by subtracting the one-dimensional hydraulic model grid from the two-dimensional model grid. The absolute mean difference for the simulated water depth was 0.9 foot. Additionally, the absolute mean difference for the simulated stream velocity was 1.9 feet per second.

Vulnerability of Population and Transportation Infrastructure at the East Bank of Delaware Bay Due to Coastal Flooding in Sea-Level Rise Conditions

DTIC Science & Technology

2013-04-30

resulting impact on residents and transportation infrastructure. The three-dimensional coastal ocean model FVCOM coupled with a two-dimensional...shallow water model is used to simulate hydrodynamic flooding from coastal ocean water with fine-resolution meshes, and a topography-based hydrologic... ocean model FVCOM coupled with a two-dimensional shallow water model is used to simulate hydrodynamic flooding from coastal ocean water with fine

FireStem2D — A two-dimensional heat transfer model for simulating tree stem injury in fires

Treesearch

Efthalia K. Chatziefstratiou; Gil Bohrer; Anthony S. Bova; Ravishankar Subramanian; Renato P.M. Frasson; Amy Scherzer; Bret W. Butler; Matthew B. Dickinson

2013-01-01

FireStem2D, a software tool for predicting tree stem heating and injury in forest fires, is a physically-based, two-dimensional model of stem thermodynamics that results from heating at the bark surface. It builds on an earlier one-dimensional model (FireStem) and provides improved capabilities for predicting fire-induced mortality and injury before a fire occurs by...

Topology of large-scale structure. IV - Topology in two dimensions

NASA Technical Reports Server (NTRS)

Melott, Adrian L.; Cohen, Alexander P.; Hamilton, Andrew J. S.; Gott, J. Richard, III; Weinberg, David H.

1989-01-01

In a recent series of papers, an algorithm was developed for quantitatively measuring the topology of the large-scale structure of the universe and this algorithm was applied to numerical models and to three-dimensional observational data sets. In this paper, it is shown that topological information can be derived from a two-dimensional cross section of a density field, and analytic expressions are given for a Gaussian random field. The application of a two-dimensional numerical algorithm for measuring topology to cross sections of three-dimensional models is demonstrated.

Model of a Negatively Curved Two-Dimensional Space.

ERIC Educational Resources Information Center

Eckroth, Charles A.

1995-01-01

Describes the construction of models of two-dimensional surfaces with negative curvature that are used to illustrate differences in the triangle sum rule for the various Big Bang Theories of the universe. (JRH)

Teaching Science: Eclipse Seasons.

ERIC Educational Resources Information Center

Leyden, Michael B.

1995-01-01

Demonstrates the need for a three-dimensional model as an aid for teaching students why eclipses do not occur every two weeks, as falsely indicated by two-dimensional models such as books, chalkboards, and computer screens. Describes procedure to construct the model. Indicates question related to seasons likely to arise from such a model and…

On the role of radiation and dimensionality in predicting flow opposed flame spread over thin fuels

NASA Astrophysics Data System (ADS)

Kumar, Chenthil; Kumar, Amit

2012-06-01

In this work a flame-spread model is formulated in three dimensions to simulate opposed flow flame spread over thin solid fuels. The flame-spread model is coupled to a three-dimensional gas radiation model. The experiments [1] on downward spread and zero gravity quiescent spread over finite width thin fuel are simulated by flame-spread models in both two and three dimensions to assess the role of radiation and effect of dimensionality on the prediction of the flame-spread phenomena. It is observed that while radiation plays only a minor role in normal gravity downward spread, in zero gravity quiescent spread surface radiation loss holds the key to correct prediction of low oxygen flame spread rate and quenching limit. The present three-dimensional simulations show that even in zero gravity gas radiation affects flame spread rate only moderately (as much as 20% at 100% oxygen) as the heat feedback effect exceeds the radiation loss effect only moderately. However, the two-dimensional model with the gas radiation model badly over-predicts the zero gravity flame spread rate due to under estimation of gas radiation loss to the ambient surrounding. The two-dimensional model was also found to be inadequate for predicting the zero gravity flame attributes, like the flame length and the flame width, correctly. The need for a three-dimensional model was found to be indispensable for consistently describing the zero gravity flame-spread experiments [1] (including flame spread rate and flame size) especially at high oxygen levels (>30%). On the other hand it was observed that for the normal gravity downward flame spread for oxygen levels up to 60%, the two-dimensional model was sufficient to predict flame spread rate and flame size reasonably well. Gas radiation is seen to increase the three-dimensional effect especially at elevated oxygen levels (>30% for zero gravity and >60% for normal gravity flames).

Two dimensional analytical model for a reconfigurable field effect transistor

NASA Astrophysics Data System (ADS)

Ranjith, R.; Jayachandran, Remya; Suja, K. J.; Komaragiri, Rama S.

2018-02-01

This paper presents two-dimensional potential and current models for a reconfigurable field effect transistor (RFET). Two potential models which describe subthreshold and above-threshold channel potentials are developed by solving two-dimensional (2D) Poisson's equation. In the first potential model, 2D Poisson's equation is solved by considering constant/zero charge density in the channel region of the device to get the subthreshold potential characteristics. In the second model, accumulation charge density is considered to get above-threshold potential characteristics of the device. The proposed models are applicable for the device having lightly doped or intrinsic channel. While obtaining the mathematical model, whole body area is divided into two regions: gated region and un-gated region. The analytical models are compared with technology computer-aided design (TCAD) simulation results and are in complete agreement for different lengths of the gated regions as well as at various supply voltage levels.

Review of literature on the finite-element solution of the equations of two-dimensional surface-water flow in the horizontal plane

USGS Publications Warehouse

Lee, Jonathan K.; Froehlich, David C.

1987-01-01

Published literature on the application of the finite-element method to solving the equations of two-dimensional surface-water flow in the horizontal plane is reviewed in this report. The finite-element method is ideally suited to modeling two-dimensional flow over complex topography with spatially variable resistance. A two-dimensional finite-element surface-water flow model with depth and vertically averaged velocity components as dependent variables allows the user great flexibility in defining geometric features such as the boundaries of a water body, channels, islands, dikes, and embankments. The following topics are reviewed in this report: alternative formulations of the equations of two-dimensional surface-water flow in the horizontal plane; basic concepts of the finite-element method; discretization of the flow domain and representation of the dependent flow variables; treatment of boundary conditions; discretization of the time domain; methods for modeling bottom, surface, and lateral stresses; approaches to solving systems of nonlinear equations; techniques for solving systems of linear equations; finite-element alternatives to Galerkin's method of weighted residuals; techniques of model validation; and preparation of model input data. References are listed in the final chapter.

Thermoelastic damping in thin microrings with two-dimensional heat conduction

NASA Astrophysics Data System (ADS)

Fang, Yuming; Li, Pu

2015-05-01

Accurate determination of thermoelastic damping (TED) is very challenging in the design of micro-resonators. Microrings are widely used in many micro-resonators. In the past, to model the TED effect on the microrings, some analytical models have been developed. However, in the previous works, the heat conduction within the microring is modeled by using the one-dimensional approach. The governing equation for heat conduction is solved only for the one-dimensional heat conduction along the radial thickness of the microring. This paper presents a simple analytical model for TED in microrings. The two-dimensional heat conduction over the thermoelastic temperature gradients along the radial thickness and the circumferential direction are considered in the present model. A two-dimensional heat conduction equation is developed. The solution of the equation is represented by the product of an assumed sine series along the radial thickness and an assumed trigonometric series along the circumferential direction. The analytical results obtained by the present 2-D model show a good agreement with the numerical (FEM) results. The limitations of the previous 1-D model are assessed.

USING TWO-DIMENSIONAL HYDRODYNAMIC MODELS AT SCALES OF ECOLOGICAL IMPORTANCE. (R825760)

EPA Science Inventory

Modeling of flow features that are important in assessing stream habitat conditions has been a long-standing interest of stream biologists. Recently, they have begun examining the usefulness of two-dimensional (2-D) hydrodynamic models in attaining this objective. Current modelin...

Statistical Physics on the Eve of the 21st Century: in Honour of J B McGuire on the Occasion of His 65th Birthday

NASA Astrophysics Data System (ADS)

Batchelor, Murray T.; Wille, Luc T.

The Table of Contents for the book is as follows: * Preface * Modelling the Immune System - An Example of the Simulation of Complex Biological Systems * Brief Overview of Quantum Computation * Quantal Information in Statistical Physics * Modeling Economic Randomness: Statistical Mechanics of Market Phenomena * Essentially Singular Solutions of Feigenbaum- Type Functional Equations * Spatiotemporal Chaotic Dynamics in Coupled Map Lattices * Approach to Equilibrium of Chaotic Systems * From Level to Level in Brain and Behavior * Linear and Entropic Transformations of the Hydrophobic Free Energy Sequence Help Characterize a Novel Brain Polyprotein: CART's Protein * Dynamical Systems Response to Pulsed High-Frequency Fields * Bose-Einstein Condensates in the Light of Nonlinear Physics * Markov Superposition Expansion for the Entropy and Correlation Functions in Two and Three Dimensions * Calculation of Wave Center Deflection and Multifractal Analysis of Directed Waves Through the Study of su(1,1)Ferromagnets * Spectral Properties and Phases in Hierarchical Master Equations * Universality of the Distribution Functions of Random Matrix Theory * The Universal Chiral Partition Function for Exclusion Statistics * Continuous Space-Time Symmetries in a Lattice Field Theory * Quelques Cas Limites du Problème à N Corps Unidimensionnel * Integrable Models of Correlated Electrons * On the Riemann Surface of the Three-State Chiral Potts Model * Two Exactly Soluble Lattice Models in Three Dimensions * Competition of Ferromagnetic and Antiferromagnetic Order in the Spin-l/2 XXZ Chain at Finite Temperature * Extended Vertex Operator Algebras and Monomial Bases * Parity and Charge Conjugation Symmetries and S Matrix of the XXZ Chain * An Exactly Solvable Constrained XXZ Chain * Integrable Mixed Vertex Models Ftom the Braid-Monoid Algebra * From Yang-Baxter Equations to Dynamical Zeta Functions for Birational Tlansformations * Hexagonal Lattice Directed Site Animals * Direction in the Star-Triangle Relations * A Self-Avoiding Walk Through Exactly Solved Lattice Models in Statistical Mechanics

A recipe for constructing frustration-free Hamiltonians with gauge and matter fields in one and two dimensions

NASA Astrophysics Data System (ADS)

Bernabé Ferreira, Miguel Jorge; Ibieta Jimenez, Juan Pablo; Padmanabhan, Pramod; Teôtonio Sobrinho, Paulo

2015-12-01

State sum constructions, such as Kuperberg’s algorithm, give partition functions of physical systems, like lattice gauge theories, in various dimensions by associating local tensors or weights with different parts of a closed triangulated manifold. Here we extend this construction by including matter fields to build partition functions in both two and three space-time dimensions. The matter fields introduce new weights to the vertices and they correspond to Potts spin configurations described by an {A}-module with an inner product. Performing this construction on a triangulated manifold with a boundary we obtain transfer matrices which are decomposed into a product of local operators acting on vertices, links and plaquettes. The vertex and plaquette operators are similar to the ones appearing in the quantum double models (QDMs) of Kitaev. The link operator couples the gauge and the matter fields, and it reduces to the usual interaction terms in known models such as {{{Z}}}2 gauge theory with matter fields. The transfer matrices lead to Hamiltonians that are frustration-free and are exactly solvable. According to the choice of the initial input, that of the gauge group and a matter module, we obtain interesting models which have a new kind of ground state degeneracy that depends on the number of equivalence classes in the matter module under gauge action. Some of the models have confined flux excitations in the bulk which become deconfined at the surface. These edge modes are protected by an energy gap provided by the link operator. These properties also appear in ‘confined Walker-Wang’ models which are 3D models having interesting surface states. Apart from the gauge excitations there are also excitations in the matter sector which are immobile and can be thought of as defects like in the Ising model. We only consider bosonic matter fields in this paper.

Coupled boundary and finite element analysis of vibration from railway tunnels—a comparison of two- and three-dimensional models

NASA Astrophysics Data System (ADS)

Andersen, L.; Jones, C. J. C.

2006-06-01

The analysis of vibration from railway tunnels is of growing interest as new and higher-speed railways are built under the ground to address the transport problems of growing modern urban areas. Such analysis can be carried out using numerical methods but models and therefore computing times can be large. There is a need to be able to apply very fast calculations that can be used in tunnel design and studies of environmental impacts. Taking advantage of the fact that tunnels often have a two-dimensional geometry in the sense that the cross section is constant along the tunnel axis, it is useful to evaluate the potential uses of two-dimensional models before committing to much more costly three-dimensional approaches. The vibration forces in the track due to the passage of a train are by nature three-dimensional and a complete analysis undoubtedly requires a model of three-dimensional wave propagation. The aim of this paper is to investigate the quality of the information that can be gained from a two-dimensional model of a railway tunnel. The vibration transmission from the tunnel floor to the ground surface is analysed for the frequency range relevant to the perception of whole body vibration (about 4-80 Hz). A coupled finite element and boundary element scheme is applied in both two and three dimensions. Two tunnel designs are considered: a cut-and-cover tunnel for a double track and a single-track tunnel dug with the New Austrian tunnelling method (NATM).

Cold spray nozzle mach number limitation

NASA Astrophysics Data System (ADS)

Jodoin, B.

2002-12-01

The classic one-dimensional isentropic flow approach is used along with a two-dimensional axisymmetric numerical model to show that the exit Mach number of a cold spray nozzle should be limited due to two factors. To show this, the two-dimensional model is validated with experimental data. Although both models show that the stagnation temperature is an important limiting factor, the one-dimensional approach fails to show how important the shock-particle interactions are at limiting the nozzle Mach number. It is concluded that for an air nozzle spraying solid powder particles, the nozzle Mach number should be set between 1.5 and 3 to limit the negative effects of the high stagnation temperature and of the shock-particle interactions.

Development of a two-dimensional zonally averaged statistical-dynamical model. III - The parameterization of the eddy fluxes of heat and moisture

NASA Technical Reports Server (NTRS)

Stone, Peter H.; Yao, Mao-Sung

1990-01-01

A number of perpetual January simulations are carried out with a two-dimensional zonally averaged model employing various parameterizations of the eddy fluxes of heat (potential temperature) and moisture. The parameterizations are evaluated by comparing these results with the eddy fluxes calculated in a parallel simulation using a three-dimensional general circulation model with zonally symmetric forcing. The three-dimensional model's performance in turn is evaluated by comparing its results using realistic (nonsymmetric) boundary conditions with observations. Branscome's parameterization of the meridional eddy flux of heat and Leovy's parameterization of the meridional eddy flux of moisture simulate the seasonal and latitudinal variations of these fluxes reasonably well, while somewhat underestimating their magnitudes. New parameterizations of the vertical eddy fluxes are developed that take into account the enhancement of the eddy mixing slope in a growing baroclinic wave due to condensation, and also the effect of eddy fluctuations in relative humidity. The new parameterizations, when tested in the two-dimensional model, simulate the seasonal, latitudinal, and vertical variations of the vertical eddy fluxes quite well, when compared with the three-dimensional model, and only underestimate the magnitude of the fluxes by 10 to 20 percent.

Comparison of 2D Finite Element Modeling Assumptions with Results From 3D Analysis for Composite Skin-Stiffener Debonding

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Paris, Isbelle L.; OBrien, T. Kevin; Minguet, Pierre J.

2004-01-01

The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane-strain elements as well as three different generalized plane strain type approaches were performed. The computed skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with delamination length. For more accurate predictions, however, a three-dimensional analysis is required.

Influence of 2D Finite Element Modeling Assumptions on Debonding Prediction for Composite Skin-stiffener Specimens Subjected to Tension and Bending

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Minguet, Pierre J.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane strain elements as well as three different generalized plane strain type approaches were performed. The computed deflections, skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with lamination length. For more accurate predictions, however, a three-dimensional analysis is required.

Nonlocal continuous models for forced vibration analysis of two- and three-dimensional ensembles of single-walled carbon nanotubes

NASA Astrophysics Data System (ADS)

Kiani, Keivan

2014-06-01

Novel nonlocal discrete and continuous models are proposed for dynamic analysis of two- and three-dimensional ensembles of single-walled carbon nanotubes (SWCNTs). The generated extra van der Waals forces between adjacent SWCNTs due to their lateral motions are evaluated via Lennard-Jones potential function. Using a nonlocal Rayleigh beam model, the discrete and continuous models are developed for both two- and three-dimensional ensembles of SWCNTs acted upon by transverse dynamic loads. The capabilities of the proposed continuous models in capturing the vibration behavior of SWCNTs ensembles are then examined through various numerical simulations. A reasonably good agreement between the results of the continuous models and those of the discrete ones is also reported. The effects of the applied load frequency, intertube spaces, and small-scale parameter on the transverse dynamic responses of both two- and three-dimensional ensembles of SWCNTs are explained. The proposed continuous models would be very useful for dynamic analyses of large populated ensembles of SWCNTs whose discrete models suffer from both computational efforts and labor costs.

Three-Dimensional Printing of a Scalable Molecular Model and Orbital Kit for Organic Chemistry Teaching and Learning

ERIC Educational Resources Information Center

Penny, Matthew R.; Cao, Zi Jing; Patel, Bhaven; dos Santos, Bruno Sil; Asquith, Christopher R. M.; Szulc, Blanka R.; Rao, Zenobia X.; Muwaffak, Zaid; Malkinson, John P.; Hilton, Stephen T.

2017-01-01

Three-dimensional (3D) chemical models are a well-established learning tool used to enhance the understanding of chemical structures by converting two-dimensional paper or screen outputs into realistic three-dimensional objects. While commercial atom model kits are readily available, there is a surprising lack of large molecular and orbital models…

The Particle inside a Ring: A Two-Dimensional Quantum Problem Visualized by Scanning Tunneling Microscopy

ERIC Educational Resources Information Center

Ellison, Mark D.

2008-01-01

The one-dimensional particle-in-a-box model used to introduce quantum mechanics to students suffers from a tenuous connection to a real physical system. This article presents a two-dimensional model, the particle confined within a ring, that directly corresponds to observations of surface electrons in a metal trapped inside a circular barrier.…

A study of frontal dynamics with application to the Australian summertime 'cool change'

NASA Technical Reports Server (NTRS)

Reeder, Michael J.; Smith, Roger K.

1987-01-01

The dynamics of frontal evolution is examined in terms of the Australian summertime cool change using a two-dimensional numerical model. The model is synthesized from observational data on surface cold fronts obtained during the Australian Cold Fronts Research Program, and the model develops a quasi-steady surface cold front during the 24 hours of integration. The characteristics of this model are compared with those of a kinematic model; it is observed that the features of the two models correspond. The two-dimensional and kinematic models are also compared with a 24-hour prediction of the cold front of February 1983 using the three-dimensional nested-grid model of the Australian Numerical Meteorology Research Center, developed by Gauntlett et al. (1984). Good correlation between these models is detected.

The role of gap edge instabilities in setting the depth of planet gaps in protoplanetary discs

NASA Astrophysics Data System (ADS)

Hallam, P. D.; Paardekooper, S.-J.

2017-08-01

It is known that an embedded massive planet will open a gap in a protoplanetary disc via angular momentum exchange with the disc material. The resulting surface density profile of the disc is investigated for one-dimensional and two-dimensional disc models and, in agreement with previous work, it is found that one-dimensional gaps are significantly deeper than their two-dimensional counterparts for the same initial conditions. We find, by applying one-dimensional torque density distributions to two-dimensional discs containing no planet, that the excitement of the Rossby wave instability and the formation of Rossby vortices play a critical role in setting the equilibrium depth of the gap. Being a two-dimensional instability, this is absent from one-dimensional simulations and does not limit the equilibrium gap depth there. We find similar gap depths between two-dimensional gaps formed by torque density distributions, in which the Rossby wave instability is present, and two-dimensional planet gaps, in which no Rossby wave instability is present. This can be understood if the planet gap is maintained at marginal stability, even when there is no obvious Rossby wave instability present. Further investigation shows the final equilibrium gap depth is very sensitive to the form of the applied torque density distribution, and using improved one-dimensional approximations from three-dimensional simulations can go even further towards reducing the discrepancy between one- and two-dimensional models, especially for lower mass planets. This behaviour is found to be consistent across discs with varying parameters.

A Comparison of Simplified Two-dimensional Flow Models Exemplified by Water Flow in a Cavern

NASA Astrophysics Data System (ADS)

Prybytak, Dzmitry; Zima, Piotr

2017-12-01

The paper shows the results of a comparison of simplified models describing a two-dimensional water flow in the example of a water flow through a straight channel sector with a cavern. The following models were tested: the two-dimensional potential flow model, the Stokes model and the Navier-Stokes model. In order to solve the first two, the boundary element method was employed, whereas to solve the Navier-Stokes equations, the open-source code library OpenFOAM was applied. The results of numerical solutions were compared with the results of measurements carried out on a test stand in a hydraulic laboratory. The measurements were taken with an ADV probe (Acoustic Doppler Velocimeter). Finally, differences between the results obtained from the mathematical models and the results of laboratory measurements were analysed.

One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers Equation with Movement Direction as a Variable

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu; Ishibashi, Kazuya

2018-06-01

We study self-propelled particles by direct numerical simulation of the nonlinear Kramers equation for self-propelled particles. In our previous paper, we studied self-propelled particles with velocity variables in one dimension. In this paper, we consider another model in which each particle exhibits directional motion. The movement direction is expressed with a variable ϕ. We show that one-dimensional solitary wave states appear in direct numerical simulations of the nonlinear Kramers equation in one- and two-dimensional systems, which is a generalization of our previous result. Furthermore, we find two-dimensionally localized states in the case that each self-propelled particle exhibits rotational motion. The center of mass of the two-dimensionally localized state exhibits circular motion, which implies collective rotating motion. Finally, we consider a simple one-dimensional model equation to qualitatively understand the formation of the solitary wave state.

Analytical solutions of the two-dimensional Dirac equation for a topological channel intersection

NASA Astrophysics Data System (ADS)

Anglin, J. R.; Schulz, A.

2017-01-01

Numerical simulations in a tight-binding model have shown that an intersection of topologically protected one-dimensional chiral channels can function as a beam splitter for noninteracting fermions on a two-dimensional lattice [Qiao, Jung, and MacDonald, Nano Lett. 11, 3453 (2011), 10.1021/nl201941f; Qiao et al., Phys. Rev. Lett. 112, 206601 (2014), 10.1103/PhysRevLett.112.206601]. Here we confirm this result analytically in the corresponding continuum k .p model, by solving the associated two-dimensional Dirac equation, in the presence of a "checkerboard" potential that provides a right-angled intersection between two zero-line modes. The method by which we obtain our analytical solutions is systematic and potentially generalizable to similar problems involving intersections of one-dimensional systems.

The Reconstruction of Three-Dimensional Morphological and Electrical Paraneters from Two-Dimensional Sections of Neurones

NASA Astrophysics Data System (ADS)

Brawn, A. D.; Wheal, H. V.

1986-07-01

A system is described which can be used to create a three-dimensional model of a neurone from the central nervous system. This model can then be used to obtain quantitative data on the physical and electrical pro, perties of the neurone. Living neurones are either raised in culture, or taken from in vitro preparations of brain tissue and optically sectioned. These two-dimensional sections are digitised, and input to a 68008-based microcomputer. The system reconstructs the three-dimensional structure of the neurone, both geanetrically and electrically. The user can a) View the structure fran any point at any angle b) "Move through" the structure along any given vector c) Nave through" the structure following a neurone process d) Fire the neurone at any point, and "watch" the action potentials propagate e) Vary the parameters of the electrical model of a process element. The system is targeted to a research programme on epilepsy, which makes frequent use of both geometric and electrical neurone modelling. Current techniques which may involve crude histology and two-dimensional drawings have considerable short camings.

Role of a computer-generated three-dimensional laryngeal model in anatomy teaching for advanced learners.

PubMed

Tan, S; Hu, A; Wilson, T; Ladak, H; Haase, P; Fung, K

2012-04-01

(1) To investigate the efficacy of a computer-generated three-dimensional laryngeal model for laryngeal anatomy teaching; (2) to explore the relationship between students' spatial ability and acquisition of anatomical knowledge; and (3) to assess participants' opinion of the computerised model. Forty junior doctors were randomised to undertake laryngeal anatomy study supplemented by either a three-dimensional computer model or two-dimensional images. Outcome measurements comprised a laryngeal anatomy test, the modified Vandenberg and Kuse mental rotation test, and an opinion survey. Mean scores ± standard deviations for the anatomy test were 15.7 ± 2.0 for the 'three dimensions' group and 15.5 ± 2.3 for the 'standard' group (p = 0.7222). Pearson's correlation between the rotation test scores and the scores for the spatial ability questions in the anatomy test was 0.4791 (p = 0.086, n = 29). Opinion survey answers revealed significant differences in respondents' perceptions of the clarity and 'user friendliness' of, and their preferences for, the three-dimensional model as regards anatomical study. The three-dimensional computer model was equivalent to standard two-dimensional images, for the purpose of laryngeal anatomy teaching. There was no association between students' spatial ability and functional anatomy learning. However, students preferred to use the three-dimensional model.

Duct flow nonuniformities: Effect of struts in SSME HGM II(+)

NASA Technical Reports Server (NTRS)

Burke, Roger

1988-01-01

A numerical study, using the INS3D flow solver, of laminar and turbulent flow around a two dimensional strut, and three dimensional flow around a strut in an annulus is presented. A multi-block procedure was used to calculate two dimensional laminar flow around two struts in parallel, with each strut represented by one computational block. Single block calculations were performed for turbulent flow around a two dimensional strut, using a Baldwin-Lomax turbulence model to parameterize the turbulent shear stresses. A modified Baldwin-Lomax model was applied to the case of a three dimensional strut in an annulus. The results displayed the essential features of wing-body flows, including the presence of a horseshoe vortex system at the junction of the strut and the lower annulus surface. A similar system was observed at the upper annulus surface. The test geometries discussed were useful in developing the capability to perform multiblock calculations, and to simulate turbulent flow around obstructions located between curved walls. Both of these skills will be necessary to model the three dimensional flow in the strut assembly of the SSME. Work is now in progress on performing a three dimensional two block turbulent calculation of the flow in the turnaround duct (TAD) and strut/fuel bowl juncture region.

Chimera patterns in two-dimensional networks of coupled neurons.

PubMed

Schmidt, Alexander; Kasimatis, Theodoros; Hizanidis, Johanne; Provata, Astero; Hövel, Philipp

2017-03-01

We discuss synchronization patterns in networks of FitzHugh-Nagumo and leaky integrate-and-fire oscillators coupled in a two-dimensional toroidal geometry. A common feature between the two models is the presence of fast and slow dynamics, a typical characteristic of neurons. Earlier studies have demonstrated that both models when coupled nonlocally in one-dimensional ring networks produce chimera states for a large range of parameter values. In this study, we give evidence of a plethora of two-dimensional chimera patterns of various shapes, including spots, rings, stripes, and grids, observed in both models, as well as additional patterns found mainly in the FitzHugh-Nagumo system. Both systems exhibit multistability: For the same parameter values, different initial conditions give rise to different dynamical states. Transitions occur between various patterns when the parameters (coupling range, coupling strength, refractory period, and coupling phase) are varied. Many patterns observed in the two models follow similar rules. For example, the diameter of the rings grows linearly with the coupling radius.

Chimera patterns in two-dimensional networks of coupled neurons

NASA Astrophysics Data System (ADS)

Schmidt, Alexander; Kasimatis, Theodoros; Hizanidis, Johanne; Provata, Astero; Hövel, Philipp

2017-03-01

We discuss synchronization patterns in networks of FitzHugh-Nagumo and leaky integrate-and-fire oscillators coupled in a two-dimensional toroidal geometry. A common feature between the two models is the presence of fast and slow dynamics, a typical characteristic of neurons. Earlier studies have demonstrated that both models when coupled nonlocally in one-dimensional ring networks produce chimera states for a large range of parameter values. In this study, we give evidence of a plethora of two-dimensional chimera patterns of various shapes, including spots, rings, stripes, and grids, observed in both models, as well as additional patterns found mainly in the FitzHugh-Nagumo system. Both systems exhibit multistability: For the same parameter values, different initial conditions give rise to different dynamical states. Transitions occur between various patterns when the parameters (coupling range, coupling strength, refractory period, and coupling phase) are varied. Many patterns observed in the two models follow similar rules. For example, the diameter of the rings grows linearly with the coupling radius.

CFD modeling of two-stage ignition in a rapid compression machine: Assessment of zero-dimensional approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mittal, Gaurav; Raju, Mandhapati P.; Sung, Chih-Jen

2010-07-15

In modeling rapid compression machine (RCM) experiments, zero-dimensional approach is commonly used along with an associated heat loss model. The adequacy of such approach has not been validated for hydrocarbon fuels. The existence of multi-dimensional effects inside an RCM due to the boundary layer, roll-up vortex, non-uniform heat release, and piston crevice could result in deviation from the zero-dimensional assumption, particularly for hydrocarbons exhibiting two-stage ignition and strong thermokinetic interactions. The objective of this investigation is to assess the adequacy of zero-dimensional approach in modeling RCM experiments under conditions of two-stage ignition and negative temperature coefficient (NTC) response. Computational fluidmore » dynamics simulations are conducted for n-heptane ignition in an RCM and the validity of zero-dimensional approach is assessed through comparisons over the entire NTC region. Results show that the zero-dimensional model based on the approach of 'adiabatic volume expansion' performs very well in adequately predicting the first-stage ignition delays, although quantitative discrepancy for the prediction of the total ignition delays and pressure rise in the first-stage ignition is noted even when the roll-up vortex is suppressed and a well-defined homogeneous core is retained within an RCM. Furthermore, the discrepancy is pressure dependent and decreases as compressed pressure is increased. Also, as ignition response becomes single-stage at higher compressed temperatures, discrepancy from the zero-dimensional simulations reduces. Despite of some quantitative discrepancy, the zero-dimensional modeling approach is deemed satisfactory from the viewpoint of the ignition delay simulation. (author)« less

Prediction of La0.6Sr0.4Co0.2Fe0.8O3 cathode microstructures during sintering: Kinetic Monte Carlo (KMC) simulations calibrated by artificial neural networks

NASA Astrophysics Data System (ADS)

Yan, Zilin; Kim, Yongtae; Hara, Shotaro; Shikazono, Naoki

2017-04-01

The Potts Kinetic Monte Carlo (KMC) model, proven to be a robust tool to study all stages of sintering process, is an ideal tool to analyze the microstructure evolution of electrodes in solid oxide fuel cells (SOFCs). Due to the nature of this model, the input parameters of KMC simulations such as simulation temperatures and attempt frequencies are difficult to identify. We propose a rigorous and efficient approach to facilitate the input parameter calibration process using artificial neural networks (ANNs). The trained ANN reduces drastically the number of trial-and-error of KMC simulations. The KMC simulation using the calibrated input parameters predicts the microstructures of a La0.6Sr0.4Co0.2Fe0.8O3 cathode material during sintering, showing both qualitative and quantitative congruence with real 3D microstructures obtained by focused ion beam scanning electron microscopy (FIB-SEM) reconstruction.

Wilson loops in supersymmetric gauge theories

NASA Astrophysics Data System (ADS)

Pestun, Vasily

This thesis is devoted to several exact computations in four-dimensional supersymmetric gauge field theories. In the first part of the thesis we prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N = 4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N = 2 and the N* = 2 supersymmetric Yang-Mills theory on a four-sphere. Circular supersymmetric Wilson loops in four-dimensional N = 2 superconformal gauge theory are treated similarly. In the second part we consider supersymmetric Wilson loops of arbitrary shape restricted to a two-dimensional sphere in the four-dimensional N = 4 supersymmetric Yang-Mills theory. We show that expectation value for these Wilson loops can be exactly computed using a two-dimensional theory closely related to the topological two-dimensional Higgs-Yang-Mills theory, or two-dimensional Yang-Mills theory for the complexified gauge group.

Multichoice minority game.

PubMed

Ein-Dor, L; Metzler, R; Kanter, I; Kinzel, W

2001-06-01

The generalization of the problem of adaptive competition, known as the minority game, to the case of K possible choices for each player, is addressed, and applied to a system of interacting perceptrons with input and output units of a type of K-state Potts spins. An optimal solution of this minority game, as well as the dynamic evolution of the adaptive strategies of the players, are solved analytically for a general K and compared with numerical simulations.

The design and development of a two-dimensional adaptive truss structure

NASA Technical Reports Server (NTRS)

Kuwao, Fumihiro; Motohashi, Shoichi; Yoshihara, Makoto; Takahara, Kenichi; Natori, Michihiro

1987-01-01

The functional model of a two dimensional adaptive truss structure which can purposefully change its geometrical configuration is introduced. The details of design and fabrication such as kinematic analysis, dynamic characteristics analysis and some test results are presented for the demonstration of this two dimensional truss concept.

Mixing of gaseous reactants in chemical generation of atomic iodine for COIL: two-dimensional study

NASA Astrophysics Data System (ADS)

Jirasek, Vit; Spalek, Otomar; Kodymova, Jarmila; Censky, Miroslav

2003-11-01

Two-dimensional CFD model was applied for the study of mixing and reaction between gaseous chlorine dioxide and nitrogen monoxide diluted with nitrogen during atomic iodine generation. The influence of molecular diffusion on the production of atomic chlorine as a precursor of atomic iodine was predominantly studied. The results were compared with one-dimensional modeling of the system.

A system for extracting 3-dimensional measurements from a stereo pair of TV cameras

NASA Technical Reports Server (NTRS)

Yakimovsky, Y.; Cunningham, R.

1976-01-01

Obtaining accurate three-dimensional (3-D) measurement from a stereo pair of TV cameras is a task requiring camera modeling, calibration, and the matching of the two images of a real 3-D point on the two TV pictures. A system which models and calibrates the cameras and pairs the two images of a real-world point in the two pictures, either manually or automatically, was implemented. This system is operating and provides three-dimensional measurements resolution of + or - mm at distances of about 2 m.

Coupled chaotic fluctuations in a model of international trade and innovation: Some preliminary results

NASA Astrophysics Data System (ADS)

Sushko, Iryna; Gardini, Laura; Matsuyama, Kiminori

2018-05-01

We consider a two-dimensional continuous noninvertible piecewise smooth map, which characterizes the dynamics of innovation activities in the two-country model of trade and product innovation proposed in [7]. This two-dimensional map can be viewed as a coupling of two one-dimensional skew tent maps, each of which characterizes the innovation dynamics in each country in the absence of trade, and the coupling parameter depends inversely on the trade cost between the two countries. Hence, this model offers a laboratory for studying how a decline in the trade cost, or globalization, might synchronize endogenous fluctuations of innovation activities in the two countries. In this paper, we focus on the bifurcation scenarios, how the phase portrait of the two-dimensional map changes with a gradual decline of the trade cost, leading to border collision, merging, expansion and final bifurcations of the coexisting chaotic attractors. An example of peculiar border collision bifurcation leading to an increase of dimension of the chaotic attractor is also presented.

Further two-dimensional code development for Stirling space engine components

NASA Technical Reports Server (NTRS)

Ibrahim, Mounir; Tew, Roy C.; Dudenhoefer, James E.

1990-01-01

The development of multidimensional models of Stirling engine components is described. Two-dimensional parallel plate models of an engine regenerator and a cooler were used to study heat transfer under conditions of laminar, incompressible oscillating flow. Substantial differences in the nature of the temperature variations in time over the cycle were observed for the cooler as contrasted with the regenerator. When the two-dimensional cooler model was used to calculate a heat transfer coefficient, it yields a very different result from that calculated using steady-flow correlations. Simulation results for the regenerator and the cooler are presented.

A multi scale multi-dimensional thermo electrochemical modelling of high capacity lithium-ion cells

NASA Astrophysics Data System (ADS)

Tourani, Abbas; White, Peter; Ivey, Paul

2014-06-01

Lithium iron phosphate (LFP) and lithium manganese oxide (LMO) are competitive and complementary to each other as cathode materials for lithium-ion batteries, especially for use in electric vehicles. A multi scale multi-dimensional physic-based model is proposed in this paper to study the thermal behaviour of the two lithium-ion chemistries. The model consists of two sub models, a one dimensional (1D) electrochemical sub model and a two dimensional (2D) thermo-electric sub model, which are coupled and solved concurrently. The 1D model predicts the heat generation rate (Qh) and voltage (V) of the battery cell through different load cycles. The 2D model of the battery cell accounts for temperature distribution and current distribution across the surface of the battery cell. The two cells are examined experimentally through 90 h load cycles including high/low charge/discharge rates. The experimental results are compared with the model results and they are in good agreement. The presented results in this paper verify the cells temperature behaviour at different operating conditions which will lead to the design of a cost effective thermal management system for the battery pack.

Particle-tracking analysis of contributing areas of public-supply wells in simple and complex flow systems, Cape Cod, Massachusetts

USGS Publications Warehouse

Barlow, Paul M.

1997-01-01

Steady-state, two- and three-dimensional, ground-water-flow models coupled with particle tracking were evaluated to determine their effectiveness in delineating contributing areas of wells pumping from stratified-drift aquifers of Cape Cod, Massachusetts. Several contributing areas delineated by use of the three-dimensional models do not conform to simple ellipsoidal shapes that are typically delineated by use of two-dimensional analytical and numerical modeling techniques and included discontinuous areas of the water table.

Modeling Primary Breakup: A Three-Dimensional Eulerian Level Set/Vortex Sheet Method for Two-Phase Interface Dynamics

NASA Technical Reports Server (NTRS)

Herrmann, M.

2003-01-01

This paper is divided into four parts. First, the level set/vortex sheet method for three-dimensional two-phase interface dynamics is presented. Second, the LSS model for the primary breakup of turbulent liquid jets and sheets is outlined and all terms requiring subgrid modeling are identified. Then, preliminary three-dimensional results of the level set/vortex sheet method are presented and discussed. Finally, conclusions are drawn and an outlook to future work is given.

Multiexponential models of (1+1)-dimensional dilaton gravity and Toda-Liouville integrable models

NASA Astrophysics Data System (ADS)

de Alfaro, V.; Filippov, A. T.

2010-01-01

We study general properties of a class of two-dimensional dilaton gravity (DG) theories with potentials containing several exponential terms. We isolate and thoroughly study a subclass of such theories in which the equations of motion reduce to Toda and Liouville equations. We show that the equation parameters must satisfy a certain constraint, which we find and solve for the most general multiexponential model. It follows from the constraint that integrable Toda equations in DG theories generally cannot appear without accompanying Liouville equations. The most difficult problem in the two-dimensional Toda-Liouville (TL) DG is to solve the energy and momentum constraints. We discuss this problem using the simplest examples and identify the main obstacles to solving it analytically. We then consider a subclass of integrable two-dimensional theories where scalar matter fields satisfy the Toda equations and the two-dimensional metric is trivial. We consider the simplest case in some detail. In this example, we show how to obtain the general solution. We also show how to simply derive wavelike solutions of general TL systems. In the DG theory, these solutions describe nonlinear waves coupled to gravity and also static states and cosmologies. For static states and cosmologies, we propose and study a more general one-dimensional TL model typically emerging in one-dimensional reductions of higher-dimensional gravity and supergravity theories. We especially attend to making the analytic structure of the solutions of the Toda equations as simple and transparent as possible.

Spin-Imbalanced Quasi-Two-Dimensional Fermi Gases

NASA Astrophysics Data System (ADS)

Ong, W.; Cheng, Chingyun; Arakelyan, I.; Thomas, J. E.

2015-03-01

We measure the density profiles for a Fermi gas of Li 6 containing N1 spin-up atoms and N2 spin-down atoms, confined in a quasi-two-dimensional geometry. The spatial profiles are measured as a function of spin imbalance N2/N1 and interaction strength, which is controlled by means of a collisional (Feshbach) resonance. The measured cloud radii and central densities are in disagreement with mean-field Bardeen-Cooper-Schrieffer theory for a true two-dimensional system. We find that the data for normal-fluid mixtures are reasonably well fit by a simple two-dimensional polaron model of the free energy. Not predicted by the model is a phase transition to a spin-balanced central core, which is observed above a critical value of N2/N1. Our observations provide important benchmarks for predictions of the phase structure of quasi-two-dimensional Fermi gases.

On some structure-turbulence interaction problems

NASA Technical Reports Server (NTRS)

Maekawa, S.; Lin, Y. K.

1976-01-01

The interactions between a turbulent flow structure; responding to its excitation were studied. The turbulence was typical of those associated with a boundary layer, having a cross-spectral density indicative of convection and statistical decay. A number of structural models were considered. Among the one-dimensional models were an unsupported infinite beam and a periodically supported infinite beam. The fuselage construction of an aircraft was then considered. For the two-dimensional case a simple membrane was used to illustrate the type of formulation applicable to most two-dimensional structures. Both the one-dimensional and two-dimensional structures studied were backed by a cavity filled with an initially quiescent fluid to simulate the acoustic environment when the structure forms one side of a cabin of a sea vessel or aircraft.

Vfold: a web server for RNA structure and folding thermodynamics prediction.

PubMed

Xu, Xiaojun; Zhao, Peinan; Chen, Shi-Jie

2014-01-01

The ever increasing discovery of non-coding RNAs leads to unprecedented demand for the accurate modeling of RNA folding, including the predictions of two-dimensional (base pair) and three-dimensional all-atom structures and folding stabilities. Accurate modeling of RNA structure and stability has far-reaching impact on our understanding of RNA functions in human health and our ability to design RNA-based therapeutic strategies. The Vfold server offers a web interface to predict (a) RNA two-dimensional structure from the nucleotide sequence, (b) three-dimensional structure from the two-dimensional structure and the sequence, and (c) folding thermodynamics (heat capacity melting curve) from the sequence. To predict the two-dimensional structure (base pairs), the server generates an ensemble of structures, including loop structures with the different intra-loop mismatches, and evaluates the free energies using the experimental parameters for the base stacks and the loop entropy parameters given by a coarse-grained RNA folding model (the Vfold model) for the loops. To predict the three-dimensional structure, the server assembles the motif scaffolds using structure templates extracted from the known PDB structures and refines the structure using all-atom energy minimization. The Vfold-based web server provides a user friendly tool for the prediction of RNA structure and stability. The web server and the source codes are freely accessible for public use at "http://rna.physics.missouri.edu".

Stereoscopic Projection in Organic Chemistry: Bridging the Gap between Two and Three Dimensions.

ERIC Educational Resources Information Center

Rozzelle, Arlene A.; Rosenfeld, Stuart M.

1985-01-01

Shows how to make stereo slides of three-dimensional molecular models. The slides have been used to teach chirality, conformational isomerism, how models and two-dimensional representations embody selected aspects of structure, and fundamentals of using the specific model set required in a particular organic chemistry course. (JN)

Shortest-path constraints for 3D multiobject semiautomatic segmentation via clustering and Graph Cut.

PubMed

Kéchichian, Razmig; Valette, Sébastien; Desvignes, Michel; Prost, Rémy

2013-11-01

We derive shortest-path constraints from graph models of structure adjacency relations and introduce them in a joint centroidal Voronoi image clustering and Graph Cut multiobject semiautomatic segmentation framework. The vicinity prior model thus defined is a piecewise-constant model incurring multiple levels of penalization capturing the spatial configuration of structures in multiobject segmentation. Qualitative and quantitative analyses and comparison with a Potts prior-based approach and our previous contribution on synthetic, simulated, and real medical images show that the vicinity prior allows for the correct segmentation of distinct structures having identical intensity profiles and improves the precision of segmentation boundary placement while being fairly robust to clustering resolution. The clustering approach we take to simplify images prior to segmentation strikes a good balance between boundary adaptivity and cluster compactness criteria furthermore allowing to control the trade-off. Compared with a direct application of segmentation on voxels, the clustering step improves the overall runtime and memory footprint of the segmentation process up to an order of magnitude without compromising the quality of the result.

Analysis of Particle-Stimulated Nucleation (PSN)-Dominated Recrystallization for Hot-Rolled 7050 Aluminum Alloy

NASA Astrophysics Data System (ADS)

Adam, Khaled F.; Long, Zhengdong; Field, David P.

2017-04-01

In 7xxx series aluminum alloys, the constituent large and small second-phase particles present during deformation process. The fraction and spatial distribution of these second-phase particles significantly influence the recrystallized structure, kinetics, and texture in the subsequent treatment. In the present work, the Monte Carlo Potts model was used to model particle-stimulated nucleation (PSN)-dominated recrystallization and grain growth in high-strength aluminum alloy 7050. The driving force for recrystallization is deformation-induced stored energy, which is also strongly affected by the coarse particle distribution. The actual microstructure and particle distribution of hot-rolled plate were used as an initial point for modeling of recrystallization during the subsequent solution heat treatment. Measurements from bright-field TEM images were performed to enhance qualitative interpretations of the developed microstructure. The influence of texture inhomogeneity has been demonstrated from a theoretical point of view using pole figures. Additionally, in situ annealing measurements in SEM were performed to track the orientational and microstructural changes and to provide experimental support for the recrystallization mechanism of PSN in AA7050.

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).

A Monte Carlo model for 3D grain evolution during welding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rodgers, Theron M.; Mitchell, John A.; Tikare, Veena

Welding is one of the most wide-spread processes used in metal joining. However, there are currently no open-source software implementations for the simulation of microstructural evolution during a weld pass. Here we describe a Potts Monte Carlo based model implemented in the SPPARKS kinetic Monte Carlo computational framework. The model simulates melting, solidification and solid-state microstructural evolution of material in the fusion and heat-affected zones of a weld. The model does not simulate thermal behavior, but rather utilizes user input parameters to specify weld pool and heat-affect zone properties. Weld pool shapes are specified by Bezier curves, which allow formore » the specification of a wide range of pool shapes. Pool shapes can range from narrow and deep to wide and shallow representing different fluid flow conditions within the pool. Surrounding temperature gradients are calculated with the aide of a closest point projection algorithm. Furthermore, the model also allows simulation of pulsed power welding through time-dependent variation of the weld pool size. Example simulation results and comparisons with laboratory weld observations demonstrate microstructural variation with weld speed, pool shape, and pulsed-power.« less

A Monte Carlo model for 3D grain evolution during welding

DOE PAGES

Rodgers, Theron M.; Mitchell, John A.; Tikare, Veena

2017-08-04

Welding is one of the most wide-spread processes used in metal joining. However, there are currently no open-source software implementations for the simulation of microstructural evolution during a weld pass. Here we describe a Potts Monte Carlo based model implemented in the SPPARKS kinetic Monte Carlo computational framework. The model simulates melting, solidification and solid-state microstructural evolution of material in the fusion and heat-affected zones of a weld. The model does not simulate thermal behavior, but rather utilizes user input parameters to specify weld pool and heat-affect zone properties. Weld pool shapes are specified by Bezier curves, which allow formore » the specification of a wide range of pool shapes. Pool shapes can range from narrow and deep to wide and shallow representing different fluid flow conditions within the pool. Surrounding temperature gradients are calculated with the aide of a closest point projection algorithm. Furthermore, the model also allows simulation of pulsed power welding through time-dependent variation of the weld pool size. Example simulation results and comparisons with laboratory weld observations demonstrate microstructural variation with weld speed, pool shape, and pulsed-power.« less

Two-dimensional analytic weighting functions for limb scattering

NASA Astrophysics Data System (ADS)

Zawada, D. J.; Bourassa, A. E.; Degenstein, D. A.

2017-10-01

Through the inversion of limb scatter measurements it is possible to obtain vertical profiles of trace species in the atmosphere. Many of these inversion methods require what is often referred to as weighting functions, or derivatives of the radiance with respect to concentrations of trace species in the atmosphere. Several radiative transfer models have implemented analytic methods to calculate weighting functions, alleviating the computational burden of traditional numerical perturbation methods. Here we describe the implementation of analytic two-dimensional weighting functions, where derivatives are calculated relative to atmospheric constituents in a two-dimensional grid of altitude and angle along the line of sight direction, in the SASKTRAN-HR radiative transfer model. Two-dimensional weighting functions are required for two-dimensional inversions of limb scatter measurements. Examples are presented where the analytic two-dimensional weighting functions are calculated with an underlying one-dimensional atmosphere. It is shown that the analytic weighting functions are more accurate than ones calculated with a single scatter approximation, and are orders of magnitude faster than a typical perturbation method. Evidence is presented that weighting functions for stratospheric aerosols calculated under a single scatter approximation may not be suitable for use in retrieval algorithms under solar backscatter conditions.

Two-dimensional ground-water flow model of the Cretaceous aquifer system of Lee County and vicinity, Mississippi

USGS Publications Warehouse

Kernodle, John Michael

1981-01-01

A two-dimensional ground-water flow model of the Eutaw-McShan and Gordo aquifers in the area of Lee County, Miss., was successfully calibrated and verified using data from six long-term observation wells and two intensive studies of areal water levels. The water levels computed by the model were found to be most sensitive to changes in simulated aquifer hydraulic conductivity and to changes in head in the overlying Coffee Sand aquifer. The two-dimensional model performed reasonably well in simulating the aquifer system except possibly in southern Lee County and southward where a clay bed at the top of the Gordo Formation partially isolated the Gordo from the overlying Eutaw-McShan aquifer. The verified model was used to determine theoretical aquifer response to increased ground-water withdrawal to the year 2000. Two estimated rates of increase and five possible well field locations were examined. (USGS)

Effect of the fiber-matrix interphase on the transverse tensile strength of the unidirectional composite material

NASA Technical Reports Server (NTRS)

Tsai, H. C.; Arocho, A. M.

1992-01-01

A simple one-dimensional fiber-matrix interphase model has been developed and analytical results obtained correlated well with available experimental data. It was found that by including the interphase between the fiber and matrix in the model, much better local stress results were obtained than with the model without the interphase. A more sophisticated two-dimensional micromechanical model, which included the interphase properties was also developed. Both one-dimensional and two-dimensional models were used to study the effect of the interphase properties on the local stresses at the fiber, interphase and matrix. From this study, it was found that interphase modulus and thickness have significant influence on the transverse tensile strength and mode of failure in fiber reinforced composites.

Entropic manifestations of topological order in three dimensions

NASA Astrophysics Data System (ADS)

Bullivant, Alex; Pachos, Jiannis K.

2016-03-01

We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological properties is richer than the two-dimensional case. In addition to the reduction of the entropy caused by a nonzero vacuum expectation value of contractible loop operators, a topological invariant emerges that increases the entropy if the model consists of nontrivially braiding anyons. As a result the three-dimensional topological entanglement entropy provides only partial information about the two entropic topological invariants.

Integrating Intracellular Dynamics Using CompuCell3D and Bionetsolver: Applications to Multiscale Modelling of Cancer Cell Growth and Invasion

PubMed Central

Andasari, Vivi; Roper, Ryan T.; Swat, Maciej H.; Chaplain, Mark A. J.

2012-01-01

In this paper we present a multiscale, individual-based simulation environment that integrates CompuCell3D for lattice-based modelling on the cellular level and Bionetsolver for intracellular modelling. CompuCell3D or CC3D provides an implementation of the lattice-based Cellular Potts Model or CPM (also known as the Glazier-Graner-Hogeweg or GGH model) and a Monte Carlo method based on the metropolis algorithm for system evolution. The integration of CC3D for cellular systems with Bionetsolver for subcellular systems enables us to develop a multiscale mathematical model and to study the evolution of cell behaviour due to the dynamics inside of the cells, capturing aspects of cell behaviour and interaction that is not possible using continuum approaches. We then apply this multiscale modelling technique to a model of cancer growth and invasion, based on a previously published model of Ramis-Conde et al. (2008) where individual cell behaviour is driven by a molecular network describing the dynamics of E-cadherin and -catenin. In this model, which we refer to as the centre-based model, an alternative individual-based modelling technique was used, namely, a lattice-free approach. In many respects, the GGH or CPM methodology and the approach of the centre-based model have the same overall goal, that is to mimic behaviours and interactions of biological cells. Although the mathematical foundations and computational implementations of the two approaches are very different, the results of the presented simulations are compatible with each other, suggesting that by using individual-based approaches we can formulate a natural way of describing complex multi-cell, multiscale models. The ability to easily reproduce results of one modelling approach using an alternative approach is also essential from a model cross-validation standpoint and also helps to identify any modelling artefacts specific to a given computational approach. PMID:22461894

Supersymmetric gauged matrix models from dimensional reduction on a sphere

NASA Astrophysics Data System (ADS)

Closset, Cyril; Ghim, Dongwook; Seong, Rak-Kyeong

2018-05-01

It was recently proposed that N = 1 supersymmetric gauged matrix models have a duality of order four — that is, a quadrality — reminiscent of infrared dualities of SQCD theories in higher dimensions. In this note, we show that the zero-dimensional quadrality proposal can be inferred from the two-dimensional Gadde-Gukov-Putrov triality. We consider two-dimensional N = (0, 2) SQCD compactified on a sphere with the half-topological twist. For a convenient choice of R-charge, the zero-mode sector on the sphere gives rise to a simple N = 1 gauged matrix model. Triality on the sphere then implies a triality relation for the supersymmetric matrix model, which can be completed to the full quadrality.

Exact results for quench dynamics and defect production in a two-dimensional model.

PubMed

Sengupta, K; Sen, Diptiman; Mondal, Shreyoshi

2008-02-22

We show that for a d-dimensional model in which a quench with a rate tau(-1) takes the system across a (d-m)-dimensional critical surface, the defect density scales as n approximately 1/tau(mnu/(znu+1)), where nu and z are the correlation length and dynamical critical exponents characterizing the critical surface. We explicitly demonstrate that the Kitaev model provides an example of such a scaling with d = 2 and m = nu = z = 1. We also provide the first example of an exact calculation of some multispin correlation functions for a two-dimensional model that can be used to determine the correlation between the defects. We suggest possible experiments to test our theory.

Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

DOE PAGES

Pouranvari, Mohammad; Zhang, Yuhui; Yang, Kun

2015-01-01

We calculate numerically the entanglement entropy of free fermion ground states in one-, two-, and three-dimensional Anderson models and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.

Beta functions in Chirally deformed supersymmetric sigma models in two dimensions

NASA Astrophysics Data System (ADS)

Vainshtein, Arkady

2016-10-01

We study two-dimensional sigma models where the chiral deformation diminished the original 𝒩 = (2, 2) supersymmetry to the chiral one, 𝒩 = (0, 2). Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional 𝒩 = 1 theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the β functions in terms of the anomalous dimensions analogous to the NSVZ β function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.

Beta Functions in Chirally Deformed Supersymmetric Sigma Models in Two Dimensions

NASA Astrophysics Data System (ADS)

Vainshtein, Arkady

We study two-dimensional sigma models where the chiral deformation diminished the original 𝒩 =(2, 2) supersymmetry to the chiral one, 𝒩 =(0, 2). Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional 𝒩 = 1 theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the β functions in terms of the anomalous dimensions analogous to the NSVZ β function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.

Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pouranvari, Mohammad; Zhang, Yuhui; Yang, Kun

We calculate numerically the entanglement entropy of free fermion ground states in one-, two-, and three-dimensional Anderson models and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.

The Ames two-dimensional stratosphere-mesospheric model. [chemistry and transport of SST pollution

NASA Technical Reports Server (NTRS)

Whitten, R. C.; Borucki, W. J.; Watson, V. R.; Capone, L. A.; Maples, A. L.; Riegel, C. A.

1974-01-01

A two-dimensional model of the stratosphere and mesosphere has recently been developed at Ames Research Center. The model contains chemistry based on 18 species that are solved for at each step and a seasonally-varying transport model based on both winds and eddy transport. The model is described and a preliminary assessment of the impact of supersonic aircraft flights on the ozone layer is given.

A new definition for an old entity: improved definition of mitral valve prolapse using three-dimensional echocardiography and color-coded parametric models.

PubMed

Addetia, Karima; Mor-Avi, Victor; Weinert, Lynn; Salgo, Ivan S; Lang, Roberto M

2014-01-01

Differentiating between mitral valve (MV) prolapse (MVP) and MV billowing (MVB) on two-dimensional echocardiography is challenging. The aim of this study was to test the hypothesis that color-coded models of maximal leaflet displacement from the annular plane into the atrium derived from three-dimensional transesophageal echocardiography would allow discrimination between these lesions. Three-dimensional transesophageal echocardiographic imaging of the MV was performed in 50 patients with (n = 38) and without (n = 12) degenerative MV disease. Definitive diagnosis of MVP versus MVB was made using inspection of dynamic three-dimensional renderings and multiple two-dimensional cut planes extracted from three-dimensional data sets. This was used as a reference standard to test an alternative approach, wherein the color-coded parametric models were inspected for integrity of the coaptation line and location of the maximally displaced portion of the leaflet. Diagnostic interpretations of these models by two independent readers were compared with the reference standard. In all cases of MVP, the color-coded models depicted loss of integrity of the coaptation line and maximal leaflet displacement extending to the coaptation line. MVB was depicted by preserved leaflet apposition with maximal displacement away from the coaptation line. Interpretation of the 50 color-coded models by novice readers took 5 to 10 min and resulted in good agreement with the reference technique (κ = 0.81 and κ = 0.73 for the two readers). Three-dimensional color-coded models provide a static display of MV leaflet displacement, allowing differentiation between MVP and MVB, without the need to inspect multiple planes and while taking into account the saddle shape of the mitral annulus. Copyright © 2014 American Society of Echocardiography. Published by Mosby, Inc. All rights reserved.

The Effect of Common Therapeutic Drugs on Vision

DTIC Science & Technology

1975-05-01

and has been aug- 1964; Potts, 196ut Carr et al, 1968; gested for the treatment of infectious Leopold, 1968). mononucleosis (Cawley and Myers, 1962). It...studies are complicated ble changes in the eyes of guinea pigs, not only by variations in dosage, slight effects in rabbits and monkeys, ch.l’nic or...serious ocular complications : blurring of vi- 1. Aralen was developed as a ma- sion, difficulty in accommodation, larial suppressive and is still

Pott's disease in Moroccan children: clinical features and investigation of the interleukin-12/interferon-γ pathway.

PubMed

El Azbaoui, S; Alaoui Mrani, N; Sabri, A; Jouhadi, Z; Ailal, F; Bousfiha, A A; Najib, J; El Hafidi, N; Deswarte, C; Schurr, E; Bustamante, J; Boisson-Dupuis, S; Casanova, J-L; Abel, L; El Baghdadi, J

2015-12-01

Tuberculosis spondylodiscitis (TS), or Pott's disease, an extra-pulmonary form of tuberculosis (TB), is rare and difficult to diagnose in children. Some cases of severe TB in children were recently explained by inborn errors of immunity affecting the interleukin-12/interferon-gamma (IL-12/IFN-γ) axis. To analyse clinical data on Moroccan children with TS, and to perform immunological and genetic explorations of the IL-12/IFN-γ axis. We studied nine children with TS diagnosed between 2012 and 2014. We investigated the IL-12/IFN-γ circuit by both whole-blood assays and sequencing of the coding regions of 14 core genes of this pathway. A diagnosis of TS was based on a combination of clinical, biological, histological and radiological data. QuantiFERON(®)-TB Gold In-Tube results were positive in 75% of patients. Whole-blood assays showed normal IL-12 and IFN-γ production in all but one patient, who displayed impaired decreased response to IL-12. No candidate disease-causing mutations were detected in the exonic regions of the 14 genes. TS diagnosis in children remains challenging, and is based largely on imaging. Further investigations of TS in children are required to determine the role of genetic defects in pathways that may or may not be related to the IL-12/IFN-γ axis.

The pivotal role of angiogenesis in a multi-scale modeling of tumor growth exhibiting the avascular and vascular phases.

PubMed

Salavati, Hooman; Soltani, M; Amanpour, Saeid

2018-05-06

The mechanisms involved in tumor growth mainly occur at the microenvironment, where the interactions between the intracellular, intercellular and extracellular scales mediate the dynamics of tumor. In this work, we present a multi-scale model of solid tumor dynamics to simulate the avascular and vascular growth as well as tumor-induced angiogenesis. The extracellular and intercellular scales are modeled using partial differential equations and cellular Potts model, respectively. Also, few biochemical and biophysical rules control the dynamics of intracellular level. On the other hand, the growth of melanoma tumors is modeled in an animal in-vivo study to evaluate the simulation. The simulation shows that the model successfully reproduces a completed image of processes involved in tumor growth such as avascular and vascular growth as well as angiogenesis. The model incorporates the phenotypes of cancerous cells including proliferating, quiescent and necrotic cells, as well as endothelial cells during angiogenesis. The results clearly demonstrate the pivotal effect of angiogenesis on the progression of cancerous cells. Also, the model exhibits important events in tumor-induced angiogenesis like anastomosis. Moreover, the computational trend of tumor growth closely follows the observations in the experimental study. Copyright © 2018 Elsevier Inc. All rights reserved.

Special Holonomy and Two-Dimensional Supersymmetric Sigma-Models

NASA Astrophysics Data System (ADS)

Stojevic, Vid

2006-11-01

Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy are characterized by symmetries related to covariantly constant forms that these manifolds hold, which are generally non-linear and close in a field dependent sense. The thesis explores various aspects of the special holonomy symmetries.

Pressure distribution under flexible polishing tools. II - Cylindrical (conical) optics

NASA Astrophysics Data System (ADS)

Mehta, Pravin K.

1990-10-01

A previously developed eigenvalue model is extended to determine polishing pressure distribution by rectangular tools with unequal stiffness in two directions on cylindrical optics. Tool misfit is divided into two simplified one-dimensional problems and one simplified two-dimensional problem. Tools with nonuniform cross-sections are treated with a new one-dimensional eigenvalue algorithm, permitting evaluation of tool designs where the edge is more flexible than the interior. This maintains edge pressure variations within acceptable parameters. Finite element modeling is employed to resolve upper bounds, which handle pressure changes in the two-dimensional misfit element. Paraboloids and hyperboloids from the NASA AXAF system are treated with the AXAFPOD software for this method, and are verified with NASTRAN finite element analyses. The maximum deviation from the one-dimensional azimuthal pressure variation is predicted to be 10 percent and 20 percent for paraboloids and hyperboloids, respectively.

Lubricant dynamics under sliding condition in disk drives

NASA Astrophysics Data System (ADS)

Wu, Lin

2006-07-01

In this paper, we develop a two-dimensional flow model for the lubricant flow dynamics under a sliding head in disk drives. Our two-dimensional model includes important physics such as viscous force, external air shearing stress, air bearing pressure, centrifugal force, disjoining pressure, and surface tension. Our analysis shows that the lubricant flow dynamics under the sliding condition is a fully two-dimensional phenomenon and the circumferential lubricant flow is strongly coupled to the radial flow. It is necessary to have a two-dimensional flow model that couples the circumferential and radial flows together and includes all important physics to achieve realistic predictions. Our results show that the external air shearing stress has a dominant effect on the lubricant flow dynamics. Both velocity slippage at wall and Poiseuille flow effects have to be considered in the evaluation of the air shearing stress under the head. The nonuniform air bearing pressure has a non-negligible effect on the lubricant film dynamics mostly through the Poiseuille flow effect on the air shearing stress but not from its direct pushing or sucking effect on the lubricant surface. Prediction of the formation of lubricant depletion tracks under a sliding head using the two-dimensional model agrees reasonably well with the existing experimental measurements.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Snider, D.M.; O`Rourke, P.J.; Andrews, M.J.

1997-06-01

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

Coupling Processes Between Atmospheric Chemistry and Climate

NASA Technical Reports Server (NTRS)

Ko, M. K. W.; Weisenstein, Debra; Shia, Run-Li; Sze, N. D.

1997-01-01

This is the first semi-annual report for NAS5-97039 summarizing work performed for January 1997 through June 1997. Work in this project is related to NAS1-20666, also funded by NASA ACMAP. The work funded in this project also benefits from work at AER associated with the AER three-dimensional isentropic transport model funded by NASA AEAP and the AER two-dimensional climate-chemistry model (co-funded by Department of Energy). The overall objective of this project is to improve the understanding of coupling processes between atmospheric chemistry and climate. Model predictions of the future distributions of trace gases in the atmosphere constitute an important component of the input necessary for quantitative assessments of global change. We will concentrate on the changes in ozone and stratospheric sulfate aerosol, with emphasis on how ozone in the lower stratosphere would respond to natural or anthropogenic changes. The key modeling tools for this work are the AER two-dimensional chemistry-transport model, the AER two-dimensional stratospheric sulfate model, and the AER three-wave interactive model with full chemistry.

Computational technique and performance of Transient Inundation Model for Rivers--2 Dimensional (TRIM2RD) : a depth-averaged two-dimensional flow model

USGS Publications Warehouse

Fulford, Janice M.

2003-01-01

A numerical computer model, Transient Inundation Model for Rivers -- 2 Dimensional (TrimR2D), that solves the two-dimensional depth-averaged flow equations is documented and discussed. The model uses a semi-implicit, semi-Lagrangian finite-difference method. It is a variant of the Trim model and has been used successfully in estuarine environments such as San Francisco Bay. The abilities of the model are documented for three scenarios: uniform depth flows, laboratory dam-break flows, and large-scale riverine flows. The model can start computations from a ?dry? bed and converge to accurate solutions. Inflows are expressed as source terms, which limits the use of the model to sufficiently long reaches where the flow reaches equilibrium with the channel. The data sets used by the investigation demonstrate that the model accurately propagates flood waves through long river reaches and simulates dam breaks with abrupt water-surface changes.

Two-dimensional Ising model on random lattices with constant coordination number

NASA Astrophysics Data System (ADS)

Schrauth, Manuel; Richter, Julian A. J.; Portela, Jefferson S. E.

2018-02-01

We study the two-dimensional Ising model on networks with quenched topological (connectivity) disorder. In particular, we construct random lattices of constant coordination number and perform large-scale Monte Carlo simulations in order to obtain critical exponents using finite-size scaling relations. We find disorder-dependent effective critical exponents, similar to diluted models, showing thus no clear universal behavior. Considering the very recent results for the two-dimensional Ising model on proximity graphs and the coordination number correlation analysis suggested by Barghathi and Vojta [Phys. Rev. Lett. 113, 120602 (2014), 10.1103/PhysRevLett.113.120602], our results indicate that the planarity and connectedness of the lattice play an important role on deciding whether the phase transition is stable against quenched topological disorder.

PNS calculations for 3-D hypersonic corner flow with two turbulence models

NASA Technical Reports Server (NTRS)

Smith, Gregory E.; Liou, May-Fun; Benson, Thomas J.

1988-01-01

A three-dimensional parabolized Navier-Stokes code has been used as a testbed to investigate two turbulence models, the McDonald Camarata and Bushnell Beckwith model, in the hypersonic regime. The Bushnell Beckwith form factor correction to the McDonald Camarata mixing length model has been extended to three-dimensional flow by use of an inverse averaging of the resultant length scale contributions from each wall. Two-dimensional calculations are compared with experiment for Mach 18 helium flow over a 4-deg wedge. Corner flow calculations have been performed at Mach 11.8 for a Reynolds number of .67 x 10 to the 6th, based on the duct half-width, and a freestream stagnation temperature of 1750-deg Rankine.

Numerically exploring the 1D-2D dimensional crossover on spin dynamics in the doped Hubbard model

DOE PAGES

Kung, Y. F.; Bazin, C.; Wohlfeld, K.; ...

2017-11-02

Using determinant quantum Monte Carlo (DQMC) simulations, we systematically study the doping dependence of the crossover from one to two dimensions and its impact on the magnetic properties of the Hubbard model. A square lattice of chains is used, in which the dimensionality can be tuned by varying the interchain coupling t ⊥. The dynamical spin structure factor and static quantities, such as the static spin susceptibility and nearest-neighbor spin correlation function, are characterized in the one- and two-dimensional limits as a benchmark. When the dimensionality is tuned between these limits, the magnetic properties, while evolving smoothly from one tomore » two dimensions, drastically change regardless of the doping level. This suggests that the spin excitations in the two-dimensional Hubbard model, even in the heavily doped case, cannot be explained using the spinon picture known from one dimension. In conclusion, the DQMC calculations are complemented by cluster perturbation theory studies to form a more complete picture of how the crossover occurs as a function of doping and how doped holes impact magnetic order.« less

On the modeling of the bottom particles segregation with non-linear diffusion equations: application to the marine sand ripples

NASA Astrophysics Data System (ADS)

Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander

2015-04-01

The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.

TWO-DIMENSIONAL MODELING OF CURRENT CIRCULATION AND CONTAMINANT TRANSPORT IN SURFACE WATERS

EPA Science Inventory

The main objectives of this paper are to briefly describe and evaluate three different applications of two-dimensional, depth-averaged, finite-element models for hydrodynamics (RMA2) and transport (RMA4) ([1] and [2], respectively), which were run using the FastTABS user interfac...

Measurement of air and VOC vapor fluxes during gas-driven soil remediation: bench-scale experiments.

PubMed

Kim, Heonki; Kim, Taeyun; Shin, Seungyeop; Annable, Michael D

2012-09-04

In this laboratory study, an experimental method was developed for the quantitative analyses of gas fluxes in soil during advective air flow. One-dimensional column and two- and three-dimensional flow chamber models were used in this study. For the air flux measurement, n-octane vapor was used as a tracer, and it was introduced in the air flow entering the physical models. The tracer (n-octane) in the gas effluent from the models was captured for a finite period of time using a pack of activated carbon, which then was analyzed for the mass of n-octane. The air flux was calculated based on the mass of n-octane captured by the activated carbon and the inflow concentration. The measured air fluxes are in good agreement with the actual values for one- and two-dimensional model experiments. Using both the two- and three-dimensional models, the distribution of the air flux at the soil surface was measured. The distribution of the air flux was found to be affected by the depth of the saturated zone. The flux and flux distribution of a volatile contaminant (perchloroethene) was also measured by using the two-dimensional model. Quantitative information of both air and contaminant flux may be very beneficial for analyzing the performance of gas-driven subsurface remediation processes including soil vapor extraction and air sparging.

Partial spline models for the inclusion of tropopause and frontal boundary information in otherwise smooth two- and three-dimensional objective analysis

NASA Technical Reports Server (NTRS)

Shiau, Jyh-Jen; Wahba, Grace; Johnson, Donald R.

1986-01-01

A new method, based on partial spline models, is developed for including specified discontinuities in otherwise smooth two- and three-dimensional objective analyses. The method is appropriate for including tropopause height information in two- and three-dimensinal temperature analyses, using the O'Sullivan-Wahba physical variational method for analysis of satellite radiance data, and may in principle be used in a combined variational analysis of observed, forecast, and climate information. A numerical method for its implementation is described and a prototype two-dimensional analysis based on simulated radiosonde and tropopause height data is shown. The method may also be appropriate for other geophysical problems, such as modeling the ocean thermocline, fronts, discontinuities, etc.

Tight-Binding Study of Polarons in Two-Dimensional Systems: Implications for Organic Field-Effect Transistor Materials

NASA Astrophysics Data System (ADS)

Lei, Jie

2011-03-01

In order to understand the electronic and transport properties of organic field-effect transistor (FET) materials, we theoretically studied the polarons in two-dimensional systems using a tight-binding model with the Holstein type and Su--Schrieffer--Heeger type electron--lattice couplings. By numerical calculations, it was found that a carrier accepts four kinds of localization, which are named the point polaron, two-dimensional polaron, one-dimensional polaron, and the extended state. The degree of localization is sensitive to the following parameters in the model: the strength and type of electron--lattice couplings, and the signs and relative magnitudes of transfer integrals. When a parameter set for a single-crystal phase of pentacene is applied within the Holstein model, a considerably delocalized hole polaron is found, consistent with the bandlike transport mechanism.

Variational asymptotic modeling of composite dimensionally reducible structures

NASA Astrophysics Data System (ADS)

Yu, Wenbin

A general framework to construct accurate reduced models for composite dimensionally reducible structures (beams, plates and shells) was formulated based on two theoretical foundations: decomposition of the rotation tensor and the variational asymptotic method. Two engineering software systems, Variational Asymptotic Beam Sectional Analysis (VABS, new version) and Variational Asymptotic Plate and Shell Analysis (VAPAS), were developed. Several restrictions found in previous work on beam modeling were removed in the present effort. A general formulation of Timoshenko-like cross-sectional analysis was developed, through which the shear center coordinates and a consistent Vlasov model can be obtained. Recovery relations are given to recover the asymptotic approximations for the three-dimensional field variables. A new version of VABS has been developed, which is a much improved program in comparison to the old one. Numerous examples are given for validation. A Reissner-like model being as asymptotically correct as possible was obtained for composite plates and shells. After formulating the three-dimensional elasticity problem in intrinsic form, the variational asymptotic method was used to systematically reduce the dimensionality of the problem by taking advantage of the smallness of the thickness. The through-the-thickness analysis is solved by a one-dimensional finite element method to provide the stiffnesses as input for the two-dimensional nonlinear plate or shell analysis as well as recovery relations to approximately express the three-dimensional results. The known fact that there exists more than one theory that is asymptotically correct to a given order is adopted to cast the refined energy into a Reissner-like form. A two-dimensional nonlinear shell theory consistent with the present modeling process was developed. The engineering computer code VAPAS was developed and inserted into DYMORE to provide an efficient and accurate analysis of composite plates and shells. Numerical results are compared with the exact solutions, and the excellent agreement proves that one can use VAPAS to analyze composite plates and shells efficiently and accurately. In conclusion, rigorous modeling approaches were developed for composite beams, plates and shells within a general framework. No such consistent and general treatment is found in the literature. The associated computer programs VABS and VAPAS are envisioned to have many applications in industry.

An intermediate-scale model for thermal hydrology in low-relief permafrost-affected landscapes

DOE PAGES

Jan, Ahmad; Coon, Ethan T.; Painter, Scott L.; ...

2017-07-10

Integrated surface/subsurface models for simulating the thermal hydrology of permafrost-affected regions in a warming climate have recently become available, but computational demands of those new process-rich simu- lation tools have thus far limited their applications to one-dimensional or small two-dimensional simulations. We present a mixed-dimensional model structure for efficiently simulating surface/subsurface thermal hydrology in low-relief permafrost regions at watershed scales. The approach replaces a full three-dimensional system with a two-dimensional overland thermal hydrology system and a family of one-dimensional vertical columns, where each column represents a fully coupled surface/subsurface thermal hydrology system without lateral flow. The system is then operatormore » split, sequentially updating the overland flow system without sources and the one-dimensional columns without lateral flows. We show that the app- roach is highly scalable, supports subcycling of different processes, and compares well with the corresponding fully three-dimensional representation at significantly less computational cost. Those advances enable recently developed representations of freezing soil physics to be coupled with thermal overland flow and surface energy balance at scales of 100s of meters. Furthermore developed and demonstrated for permafrost thermal hydrology, the mixed-dimensional model structure is applicable to integrated surface/subsurface thermal hydrology in general.« less

Model of chiral spin liquids with Abelian and non-Abelian topological phases

NASA Astrophysics Data System (ADS)

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio; Tsvelik, A. M.

2017-12-01

We present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, the Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.

Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face

NASA Astrophysics Data System (ADS)

Di Nucci, Carmine

2018-05-01

This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.

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.

Dynamical systems approach to the study of a sociophysics agent-based model

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 agentmore » 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.« less

Numerical modelling techniques of soft soil improvement via stone columns: A brief review

NASA Astrophysics Data System (ADS)

Zukri, Azhani; Nazir, Ramli

2018-04-01

There are a number of numerical studies on stone column systems in the literature. Most of the studies found were involved with two-dimensional analysis of the stone column behaviour, while only a few studies used three-dimensional analysis. The most popular software utilised in those studies was Plaxis 2D and 3D. Other types of software that used for numerical analysis are DIANA, EXAMINE, ZSoil, ABAQUS, ANSYS, NISA, GEOSTUDIO, CRISP, TOCHNOG, CESAR, GEOFEM (2D & 3D), FLAC, and FLAC 3. This paper will review the methodological approaches to model stone column numerically, both in two-dimensional and three-dimensional analyses. The numerical techniques and suitable constitutive model used in the studies will also be discussed. In addition, the validation methods conducted were to verify the numerical analysis conducted will be presented. This review paper also serves as a guide for junior engineers through the applicable procedures and considerations when constructing and running a two or three-dimensional numerical analysis while also citing numerous relevant references.

Observed light yield of scintillation pixels: Extending the two-ray model

NASA Astrophysics Data System (ADS)

Kantorski, Igor; Jurkowski, Jacek; Drozdowski, Winicjusz

2016-09-01

In this paper we propose an extended, two dimensional model describing the propagation of scintillation photons inside a cuboid crystal until they reach a PMT window. In the simplest approach the model considers two main reasons for light losses: standard absorption obeying the classical Lambert-Beer law and non-ideal reflectivity of the "mummy" covering formed by several layers of Teflon tape wrapping the sample. Results of the model calculations are juxtaposed with experimental data as well as with predictions of an earlier, one dimensional model.

Efficient processing of two-dimensional arrays with C or C++

USGS Publications Warehouse

Donato, David I.

2017-07-20

Because fast and efficient serial processing of raster-graphic images and other two-dimensional arrays is a requirement in land-change modeling and other applications, the effects of 10 factors on the runtimes for processing two-dimensional arrays with C and C++ are evaluated in a comparative factorial study. This study’s factors include the choice among three C or C++ source-code techniques for array processing; the choice of Microsoft Windows 7 or a Linux operating system; the choice of 4-byte or 8-byte array elements and indexes; and the choice of 32-bit or 64-bit memory addressing. This study demonstrates how programmer choices can reduce runtimes by 75 percent or more, even after compiler optimizations. Ten points of practical advice for faster processing of two-dimensional arrays are offered to C and C++ programmers. Further study and the development of a C and C++ software test suite are recommended.Key words: array processing, C, C++, compiler, computational speed, land-change modeling, raster-graphic image, two-dimensional array, software efficiency

Verification and transfer of thermal pollution model. Volume 6: User's manual for 1-dimensional numerical model

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.

1982-01-01

The six-volume report: describes the theory of a three dimensional (3-D) mathematical thermal discharge model and a related one dimensional (1-D) model, includes model verification at two sites, and provides a separate user's manual for each model. The 3-D model has two forms: free surface and rigid lid. The former, verified at Anclote Anchorage (FL), allows a free air/water interface and is suited for significant surface wave heights compared to mean water depth; e.g., estuaries and coastal regions. The latter, verified at Lake Keowee (SC), is suited for small surface wave heights compared to depth (e.g., natural or man-made inland lakes) because surface elevation has been removed as a parameter.

Role of dimensionality in Axelrod's model for the dissemination of culture

NASA Astrophysics Data System (ADS)

Klemm, Konstantin; Eguíluz, Víctor M.; Toral, Raúl; Miguel, Maxi San

2003-09-01

We analyze a model of social interaction in one- and two-dimensional lattices for a moderate number of features. We introduce an order parameter as a function of the overlap between neighboring sites. In a one-dimensional chain, we observe that the dynamics is consistent with a second-order transition, where the order parameter changes continuously and the average domain diverges at the transition point. However, in a two-dimensional lattice the order parameter is discontinuous at the transition point characteristic of a first-order transition between an ordered and a disordered state.

Two-dimensional Anderson-Hubbard model in the DMFT + {Sigma} approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuchinskii, E. Z., E-mail: kuchinsk@iep.uran.ru; Kuleeva, N. A.; Nekrasov, I. A.

The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + {Sigma} approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular 'bare' density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The 'correlated metal,' Mott insulator, and correlated Anderson insulator phases are identified from the evolution ofmore » the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.« less

The construction of a two-dimensional reproducing kernel function and its application in a biomedical model.

PubMed

Guo, Qi; Shen, Shu-Ting

2016-04-29

There are two major classes of cardiac tissue models: the ionic model and the FitzHugh-Nagumo model. During computer simulation, each model entails solving a system of complex ordinary differential equations and a partial differential equation with non-flux boundary conditions. The reproducing kernel method possesses significant applications in solving partial differential equations. The derivative of the reproducing kernel function is a wavelet function, which has local properties and sensitivities to singularity. Therefore, study on the application of reproducing kernel would be advantageous. Applying new mathematical theory to the numerical solution of the ventricular muscle model so as to improve its precision in comparison with other methods at present. A two-dimensional reproducing kernel function inspace is constructed and applied in computing the solution of two-dimensional cardiac tissue model by means of the difference method through time and the reproducing kernel method through space. Compared with other methods, this method holds several advantages such as high accuracy in computing solutions, insensitivity to different time steps and a slow propagation speed of error. It is suitable for disorderly scattered node systems without meshing, and can arbitrarily change the location and density of the solution on different time layers. The reproducing kernel method has higher solution accuracy and stability in the solutions of the two-dimensional cardiac tissue model.

Global isostatic geoid anomalies for plate and boundary layer models of the lithosphere

NASA Technical Reports Server (NTRS)

Hager, B. H.

1981-01-01

Commonly used one dimensional geoid models predict that the isostatic geoid anomaly over old ocean basins for the boundary layer thermal model of the lithosphere is a factor of two greater than that for the plate model. Calculations presented, using the spherical analogues of the plate and boundary layer thermal models, show that for the actual global distribution of plate ages, one dimensional models are not accurate and a spherical, fully three dimensional treatment is necessary. The maximum difference in geoid heights predicted for the two models is only about two meters. The thermal structure of old lithosphere is unlikely to be resolvable using global geoid anomalies. Stripping the effects of plate aging and a hypothetical uniform, 35 km, isostatically-compensated continental crust from the observed geoid emphasizes that the largest-amplitude geoid anomaly is the geoid low of almost 120 m over West Antarctica, a factor of two greater than the low of 60 m over Ceylon.

Power-induced evolution and increased dimensionality of nonlinear modes in reorientational soft matter.

PubMed

Laudyn, Urszula A; Jung, Paweł S; Zegadło, Krzysztof B; Karpierz, Miroslaw A; Assanto, Gaetano

2014-11-15

We demonstrate the evolution of higher order one-dimensional guided modes into two-dimensional solitary waves in a reorientational medium. The observations, carried out at two different wavelengths in chiral nematic liquid crystals, are in good agreement with a simple nonlocal nonlinear model.

Verification and transfer of thermal pollution model. Volume 4: User's manual for three-dimensional rigid-lid model

NASA Technical Reports Server (NTRS)

Lee, S. S.; Nwadike, E. V.; Sinha, S. E.

1982-01-01

The theory of a three dimensional (3-D) mathematical thermal discharge model and a related one dimensional (1-D) model are described. Model verification at two sites, a separate user's manual for each model are included. The 3-D model has two forms: free surface and rigid lid. The former allows a free air/water interface and is suited for significant surface wave heights compared to mean water depth, estuaries and coastal regions. The latter is suited for small surface wave heights compared to depth because surface elevation was removed as a parameter. These models allow computation of time dependent velocity and temperature fields for given initial conditions and time-varying boundary conditions. The free surface model also provides surface height variations with time.

Numerical two-dimensional calculations of the formation of the solar nebula

NASA Technical Reports Server (NTRS)

Bodenheimer, Peter H.

1991-01-01

Numerical two dimensional calculations of the formation of the solar nebula are presented. The following subject areas are covered: (1) observational constraints of the properties of the initial solar nebula; (2) the physical problem; (3) review if two dimensional calculations of the formation phase; (4) recent models with hydrodynamics and radiative transport; and (5) further evolution of the system.

Multi-dimensional rheology-based two-phase model for sediment transport and applications to sheet flow and pipeline scour

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Cheng-Hsien; Department of Water Resources and Environmental Engineering, Tamkang University, New Taipei City 25137, Taiwan; Low, Ying Min, E-mail: ceelowym@nus.edu.sg

2016-05-15

Sediment transport is fundamentally a two-phase phenomenon involving fluid and sediments; however, many existing numerical models are one-phase approaches, which are unable to capture the complex fluid-particle and inter-particle interactions. In the last decade, two-phase models have gained traction; however, there are still many limitations in these models. For example, several existing two-phase models are confined to one-dimensional problems; in addition, the existing two-dimensional models simulate only the region outside the sand bed. This paper develops a new three-dimensional two-phase model for simulating sediment transport in the sheet flow condition, incorporating recently published rheological characteristics of sediments. The enduring-contact, inertial,more » and fluid viscosity effects are considered in determining sediment pressure and stresses, enabling the model to be applicable to a wide range of particle Reynolds number. A k − ε turbulence model is adopted to compute the Reynolds stresses. In addition, a novel numerical scheme is proposed, thus avoiding numerical instability caused by high sediment concentration and allowing the sediment dynamics to be computed both within and outside the sand bed. The present model is applied to two classical problems, namely, sheet flow and scour under a pipeline with favorable results. For sheet flow, the computed velocity is consistent with measured data reported in the literature. For pipeline scour, the computed scour rate beneath the pipeline agrees with previous experimental observations. However, the present model is unable to capture vortex shedding; consequently, the sediment deposition behind the pipeline is overestimated. Sensitivity analyses reveal that model parameters associated with turbulence have strong influence on the computed results.« less

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

USGS Publications Warehouse

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

1997-01-01

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

Gate-controlled-diodes in silicon-on-sapphire: A computer simulation

NASA Technical Reports Server (NTRS)

Gassaway, J. D.

1974-01-01

The computer simulation of the electrical behavior of a Gate-Controlled Diode (GCD) fabricated in Silicon-On-Sapphire (SOS) was described. A procedure for determining lifetime profiles from capacitance and reverse current measurements on the GCD was established. Chapter 1 discusses the SOS structure and points out the need of lifetime profiles to assist in device design for GCD's and bipolar transistors. Chapter 2 presents the one-dimensional analytical formula for electrostatic analysis of the SOS-GCD which are useful for data interpretation and setting boundary conditions on a simplified two-dimensional analysis. Chapter 3 gives the results of a two-dimensional analysis which treats the field as one-dimensional until the silicon film is depleted and the field penetrates the sapphire substrate. Chapter 4 describes a more complete two-dimensional model and gives results of programs implementing the model.

A three-dimensional model to assess the effect of ankle joint axis misalignments in ankle-foot orthoses.

PubMed

Fatone, Stefania; Johnson, William Brett; Tucker, Kerice

2016-04-01

Misalignment of an articulated ankle-foot orthosis joint axis with the anatomic joint axis may lead to discomfort, alterations in gait, and tissue damage. Theoretical, two-dimensional models describe the consequences of misalignments, but cannot capture the three-dimensional behavior of ankle-foot orthosis use. The purpose of this project was to develop a model to describe the effects of ankle-foot orthosis ankle joint misalignment in three dimensions. Computational simulation. Three-dimensional scans of a leg and ankle-foot orthosis were incorporated into a link segment model where the ankle-foot orthosis joint axis could be misaligned with the anatomic ankle joint axis. The leg/ankle-foot orthosis interface was modeled as a network of nodes connected by springs to estimate interface pressure. Motion between the leg and ankle-foot orthosis was calculated as the ankle joint moved through a gait cycle. While the three-dimensional model corroborated predictions of the previously published two-dimensional model that misalignments in the anterior -posterior direction would result in greater relative motion compared to misalignments in the proximal -distal direction, it provided greater insight showing that misalignments have asymmetrical effects. The three-dimensional model has been incorporated into a freely available computer program to assist others in understanding the consequences of joint misalignments. Models and simulations can be used to gain insight into functioning of systems of interest. We have developed a three-dimensional model to assess the effect of ankle joint axis misalignments in ankle-foot orthoses. The model has been incorporated into a freely available computer program to assist understanding of trainees and others interested in orthotics. © The International Society for Prosthetics and Orthotics 2014.

Headache of a diagnosis: frontotemporal pain and inflammation associated with osteolysis.

PubMed

Tacon, Lyndal J; Parkinson, Jonathon F; Hudson, Bernard J; Brewer, Janice M; Little, Nicholas S; Clifton-Bligh, Roderick J

2008-11-17

A 62-year-old woman presented with left frontotemporal pain, scalp tenderness and raised levels of inflammatory markers. Temporal arteritis was considered likely, and symptoms resolved with prednisone therapy. This delayed diagnostic bone biopsy until a soft tissue abscess formed, and Pott's puffy tumour associated with Prevotella osteomyelitis of the frontal bone was diagnosed. This case highlights the value of early histopathological examination, and is a reminder of a condition seen frequently in the pre-antibiotic era.

Verification and transfer of thermal pollution model. Volume 2: User's manual for 3-dimensional free-surface model

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Tuann, S. Y.; Lee, C. R.

1982-01-01

The six-volume report: describes the theory of a three-dimensional (3-D) mathematical thermal discharge model and a related one-dimensional (1-D) model, includes model verification at two sites, and provides a separate user's manual for each model. The 3-D model has two forms: free surface and rigid lid. The former, verified at Anclote Anchorage (FL), allows a free air/water interface and is suited for significant surface wave heights compared to mean water depth; e.g., estuaries and coastal regions. The latter, verified at Lake Keowee (SC), is suited for small surface wave heights compared to depth. These models allow computation of time-dependent velocity and temperature fields for given initial conditions and time-varying boundary conditions.

Three-Dimensional Model of Heat and Mass Transfer in Fractured Rocks to Estimate Environmental Conditions Along Heated Drifts

NASA Astrophysics Data System (ADS)

Fedors, R. W.; Painter, S. L.

2004-12-01

Temperature gradients along the thermally-perturbed drifts of the potential high-level waste repository at Yucca Mountain, Nevada, will drive natural convection and associated heat and mass transfer along drifts. A three-dimensional, dual-permeability, thermohydrological model of heat and mass transfer was used to estimate the magnitude of temperature gradients along a drift. Temperature conditions along heated drifts are needed to support estimates of repository-edge cooling and as input to computational fluid dynamics modeling of in-drift axial convection and the cold-trap process. Assumptions associated with abstracted heat transfer models and two-dimensional thermohydrological models weakly coupled to mountain-scale thermal models can readily be tested using the three-dimensional thermohydrological model. Although computationally expensive, the fully coupled three-dimensional thermohydrological model is able to incorporate lateral heat transfer, including host rock processes of conduction, convection in gas phase, advection in liquid phase, and latent-heat transfer. Results from the three-dimensional thermohydrological model showed that weakly coupling three-dimensional thermal and two-dimensional thermohydrological models lead to underestimates of temperatures and underestimates of temperature gradients over large portions of the drift. The representative host rock thermal conductivity needed for abstracted heat transfer models are overestimated using the weakly coupled models. If axial flow patterns over large portions of drifts are not impeded by the strong cross-sectional flow patterns imparted by the heat rising directly off the waste package, condensation from the cold-trap process will not be limited to the extreme ends of each drift. Based on the three-dimensional thermohydrological model, axial temperature gradients occur sooner over a larger portion of the drift, though high gradients nearest the edge of the potential repository are dampened. This abstract is an independent product of CNWRA and does not necessarily reflect the view or regulatory position of the Nuclear Regulatory Commission.

Wake Management Strategies for Reduction of Turbomachinery Fan Noise

NASA Technical Reports Server (NTRS)

Waitz, Ian A.

1998-01-01

The primary objective of our work was to evaluate and test several wake management schemes for the reduction of turbomachinery fan noise. Throughout the course of this work we relied on several tools. These include 1) Two-dimensional steady boundary-layer and wake analyses using MISES (a thin-shear layer Navier-Stokes code), 2) Two-dimensional unsteady wake-stator interaction simulations using UNSFLO, 3) Three-dimensional, steady Navier-Stokes rotor simulations using NEWT, 4) Internal blade passage design using quasi-one-dimensional passage flow models developed at MIT, 5) Acoustic modeling using LINSUB, 6) Acoustic modeling using VO72, 7) Experiments in a low-speed cascade wind-tunnel, and 8) ADP fan rig tests in the MIT Blowdown Compressor.

Modeling of two-dimensional overland flow in a vegetative filter

Treesearch

Matthew J. Helmers; Dean E. Eisenhauer; Thomas G. Franti; Michael G. Dosskey

2002-01-01

Water transports sediment and other pollutants through vegetative filters. It is often assumed that the overland flow is uniformly distributed across the vegetative filter, but this research indicates otherwise. The objective of this study was to model the two-dimensional overland water flow through a vegetative filter, accounting for variation in microtopography,...

Analysis of spatial thermal field in a magnetic bearing

NASA Astrophysics Data System (ADS)

Wajnert, Dawid; Tomczuk, Bronisław

2018-03-01

This paper presents two mathematical models for temperature field analysis in a new hybrid magnetic bearing. Temperature distributions have been calculated using a three dimensional simulation and a two dimensional one. A physical model for temperature testing in the magnetic bearing has been developed. Some results obtained from computer simulations were compared with measurements.

Model of quantum kinetics of spin-orbit coupled two-dimensional electron gas in the presence of strong electromagnetic field

NASA Astrophysics Data System (ADS)

Turkin, Yaroslav V.; Kuptsov, Pavel V.

2018-04-01

A quantum model of spin dynamics of spin-orbit coupled two-dimensional electron gas in the presence of strong high- frequency electromagnetic field is suggested. Interaction of electrons with optical phonons is taken into account in the second order of perturbation theory.

Two-dimensional finite element heat transfer model of softwood. Part II, Macrostructural effects

Treesearch

Hongmei Gu; John F. Hunt

2006-01-01

A two-dimensional finite element model was used to study the effects of structural features on transient heat transfer in softwood lumber with various orientations. Transient core temperature was modeled for lumber samples “cut” from various locations within a simulated log. The effects of ring orientation, earlywood to latewood (E/L) ratio, and ring density were...

Statistical Signal Models and Algorithms for Image Analysis

DTIC Science & Technology

1984-10-25

In this report, two-dimensional stochastic linear models are used in developing algorithms for image analysis such as classification, segmentation, and object detection in images characterized by textured backgrounds. These models generate two-dimensional random processes as outputs to which statistical inference procedures can naturally be applied. A common thread throughout our algorithms is the interpretation of the inference procedures in terms of linear prediction

Terahertz signal detection in a short gate length field-effect transistor with a two-dimensional electron gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vostokov, N. V., E-mail: vostokov@ipm.sci-nnov.ru; Shashkin, V. I.

2015-11-28

We consider the problem of non-resonant detection of terahertz signals in a short gate length field-effect transistor having a two-dimensional electron channel with zero external bias between the source and the drain. The channel resistance, gate-channel capacitance, and quadratic nonlinearity parameter of the transistor during detection as a function of the gate bias voltage are studied. Characteristics of detection of the transistor connected in an antenna with real impedance are analyzed. The consideration is based on both a simple one-dimensional model of the transistor and allowance for the two-dimensional distribution of the electric field in the transistor structure. The resultsmore » given by the different models are discussed.« less

Techniques for interpretation of geoid anomalies

NASA Technical Reports Server (NTRS)

Chapman, M. E.

1979-01-01

For purposes of geological interpretation, techniques are developed to compute directly the geoid anomaly over models of density within the earth. Ideal bodies such as line segments, vertical sheets, and rectangles are first used to calculate the geoid anomaly. Realistic bodies are modeled with formulas for two-dimensional polygons and three-dimensional polyhedra. By using Fourier transform methods the two-dimensional geoid is seen to be a filtered version of the gravity field, in which the long-wavelength components are magnified and the short-wavelength components diminished.

On the dynamics of the Ising model of cooperative phenomena

PubMed Central

Montroll, Elliott W.

1981-01-01

A two-dimensional (and to some degree three-dimensional) version of Glauber's one-dimensional spin relaxation model is described. The model is constructed to yield the Ising model of cooperative phenomena at equilibrium. A complete hierarchy of differential equations for multispin correlation functions is constructed. Some remarks are made concerning the solution of them for the initial value problem of determining the relaxation of an initial set of spin distributions. PMID:16592955

Thermal modeling of phase change solidification in thermal control devices including natural convection effects

NASA Technical Reports Server (NTRS)

Ukanwa, A. O.; Stermole, F. J.; Golden, J. O.

1972-01-01

Natural convection effects in phase change thermal control devices were studied. A mathematical model was developed to evaluate natural convection effects in a phase change test cell undergoing solidification. Although natural convection effects are minimized in flight spacecraft, all phase change devices are ground tested. The mathematical approach to the problem was to first develop a transient two-dimensional conduction heat transfer model for the solidification of a normal paraffin of finite geometry. Next, a transient two-dimensional model was developed for the solidification of the same paraffin by a combined conduction-natural-convection heat transfer model. Throughout the study, n-hexadecane (n-C16H34) was used as the phase-change material in both the theoretical and the experimental work. The models were based on the transient two-dimensional finite difference solutions of the energy, continuity, and momentum equations.

Studies for the 3-Dimensional Structure, Composition, and Dynamic of Io's Atmosphere

NASA Technical Reports Server (NTRS)

Smyth, William H.

2001-01-01

Research work is discussed for the following: (1) the exploration of new H and Cl chemistry in Io's atmosphere using the already developed two-dimensional multi-species hydrodynamic model of Wong and Smyth; and (2) for the development of a new three-dimensional multi-species hydrodynamic model for Io's atmosphere.

Model Prediction of Self-Rotating Excitons in Two-Dimensional Transition-Metal Dichalcogenides

NASA Astrophysics Data System (ADS)

Trushin, Maxim; Goerbig, Mark Oliver; Belzig, Wolfgang

2018-05-01

Using the quasiclassical concept of Berry curvature we demonstrate that a Dirac exciton—a pair of Dirac quasiparticles bound by Coulomb interactions—inevitably possesses an intrinsic angular momentum making the exciton effectively self-rotating. The model is applied to excitons in two-dimensional transition metal dichalcogenides, in which the charge carriers are known to be described by a Dirac-like Hamiltonian. We show that the topological self-rotation strongly modifies the exciton spectrum and, as a consequence, resolves the puzzle of the overestimated two-dimensional polarizability employed to fit earlier spectroscopic measurements.

A Two-Dimensional Linear Bicharacteristic Scheme for Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.

2002-01-01

The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on one-dimensional electromagnetic wave propagation problems. This memorandum extends the Linear Bicharacteristic Scheme for computational electromagnetics to model lossy dielectric and magnetic materials and perfect electrical conductors in two dimensions. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media and for perfect electrical conductors. Both the Transverse Electric and Transverse Magnetic polarizations are considered. Computational requirements and a Fourier analysis are also discussed. Heterogeneous media are modeled through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for two-dimensional model problems on uniform grids, and the Finite Difference Time Domain (FDTD) algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the two-dimensional explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has less phase velocity error.

Nonclassical models of the theory of plates and shells

NASA Astrophysics Data System (ADS)

Annin, Boris D.; Volchkov, Yuri M.

2017-11-01

Publications dealing with the study of methods of reducing a three-dimensional problem of the elasticity theory to a two-dimensional problem of the theory of plates and shells are reviewed. Two approaches are considered: the use of kinematic and force hypotheses and expansion of solutions of the three-dimensional elasticity theory in terms of the complete system of functions. Papers where a three-dimensional problem is reduced to a two-dimensional problem with the use of several approximations of each of the unknown functions (stresses and displacements) by segments of the Legendre polynomials are also reviewed.

Columnar organization of orientation domains in V1

NASA Astrophysics Data System (ADS)

Liedtke, Joscha; Wolf, Fred

In the primary visual cortex (V1) of primates and carnivores, the functional architecture of basic stimulus selectivities appears similar across cortical layers (Hubel & Wiesel, 1962) justifying the use of two-dimensional cortical models and disregarding organization in the third dimension. Here we show theoretically that already small deviations from an exact columnar organization lead to non-trivial three-dimensional functional structures. We extend two-dimensional random field models (Schnabel et al., 2007) to a three-dimensional cortex by keeping a typical scale in each layer and introducing a correlation length in the third, columnar dimension. We examine in detail the three-dimensional functional architecture for different cortical geometries with different columnar correlation lengths. We find that (i) topological defect lines are generally curved and (ii) for large cortical curvatures closed loops and reconnecting topological defect lines appear. This theory extends the class of random field models by introducing a columnar dimension and provides a systematic statistical assessment of the three-dimensional functional architecture of V1 (see also (Tanaka et al., 2011)).

Extended frequency turbofan model

NASA Technical Reports Server (NTRS)

Mason, J. R.; Park, J. W.; Jaekel, R. F.

1980-01-01

The fan model was developed using two dimensional modeling techniques to add dynamic radial coupling between the core stream and the bypass stream of the fan. When incorporated into a complete TF-30 engine simulation, the fan model greatly improved compression system frequency response to planar inlet pressure disturbances up to 100 Hz. The improved simulation also matched engine stability limits at 15 Hz, whereas the one dimensional fan model required twice the inlet pressure amplitude to stall the simulation. With verification of the two dimensional fan model, this program formulated a high frequency F-100(3) engine simulation using row by row compression system characteristics. In addition to the F-100(3) remote splitter fan, the program modified the model fan characteristics to simulate a proximate splitter version of the F-100(3) engine.

An Assessment of Five Modeling Approaches for Thermo-Mechanical Stress Analysis of Laminated Composite Panels

NASA Technical Reports Server (NTRS)

Noor, A. K.; Malik, M.

2000-01-01

A study is made of the effects of variation in the lamination and geometric parameters, and boundary conditions of multi-layered composite panels on the accuracy of the detailed response characteristics obtained by five different modeling approaches. The modeling approaches considered include four two-dimensional models, each with five parameters to characterize the deformation in the thickness direction, and a predictor-corrector approach with twelve displacement parameters. The two-dimensional models are first-order shear deformation theory, third-order theory; a theory based on trigonometric variation of the transverse shear stresses through the thickness, and a discrete layer theory. The combination of the following four key elements distinguishes the present study from previous studies reported in the literature: (1) the standard of comparison is taken to be the solutions obtained by using three-dimensional continuum models for each of the individual layers; (2) both mechanical and thermal loadings are considered; (3) boundary conditions other than simply supported edges are considered; and (4) quantities compared include detailed through-the-thickness distributions of transverse shear and transverse normal stresses. Based on the numerical studies conducted, the predictor-corrector approach appears to be the most effective technique for obtaining accurate transverse stresses, and for thermal loading, none of the two-dimensional models is adequate for calculating transverse normal stresses, even when used in conjunction with three-dimensional equilibrium equations.

Capacity of Heterogeneous Mobile Wireless Networks with D-Delay Transmission Strategy.

PubMed

Wu, Feng; Zhu, Jiang; Xi, Zhipeng; Gao, Kai

2016-03-25

This paper investigates the capacity problem of heterogeneous wireless networks in mobility scenarios. A heterogeneous network model which consists of n normal nodes and m helping nodes is proposed. Moreover, we propose a D-delay transmission strategy to ensure that every packet can be delivered to its destination nodes with limited delay. Different from most existing network schemes, our network model has a novel two-tier architecture. The existence of helping nodes greatly improves the network capacity. Four types of mobile networks are studied in this paper: i.i.d. fast mobility model and slow mobility model in two-dimensional space, i.i.d. fast mobility model and slow mobility model in three-dimensional space. Using the virtual channel model, we present an intuitive analysis of the capacity of two-dimensional mobile networks and three-dimensional mobile networks, respectively. Given a delay constraint D, we derive the asymptotic expressions for the capacity of the four types of mobile networks. Furthermore, the impact of D and m to the capacity of the whole network is analyzed. Our findings provide great guidance for the future design of the next generation of networks.

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

DOE PAGES

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe; ...

2018-02-26

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one andmore » two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.« less

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one andmore » two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.« less

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

NASA Astrophysics Data System (ADS)

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe; Robinson, Neil J.; Tsvelik, Alexei M.

2018-04-01

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb–Liniger model, 1  +  1D quantum chromodynamics, as well as Landau–Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.

New developments in the theoretical treatment of low dimensional strongly correlated systems.

PubMed

James, Andrew J A; Konik, Robert M; Lecheminant, Philippe; Robinson, Neil; Tsvelik, Alexei M

2017-10-09

We review two important non-perturbative approaches for extracting the physics of low- dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of confor- mal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme- tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro- modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics. © 2017 IOP Publishing Ltd.

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods.

PubMed

James, Andrew J A; Konik, Robert M; Lecheminant, Philippe; Robinson, Neil J; Tsvelik, Alexei M

2018-02-26

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1  +  1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaufman, Allan N.; Tracy, Eugene R.; Brizard, Alain J.

The process of resonant wave conversion (often called linear mode conversion) has traditionally been analyzed with a spatially one-dimensional slab model, for which the rays propagate in a two-dimensional phase space. However, it has recently been shown [E. R. Tracy and A. N. Kaufman, Phys. Rev. Lett. 91, 130402 (2003)] that multidimensional rays have a helical structure for conversion in two or more spatial dimensions (if their dispersion matrix is generic). In that case, a one-dimensional model is inadequate; a correct analysis requires two spatial dimensions and, thus, four-dimensional phase space. A cold-plasma model is introduced in this paper whichmore » exhibits ray helicity in conversion regions where the density and magnetic field gradients are significantly nonparallel. For illustration, such regions are identified in a model of the poloidal plane of a deuterium-tritium tokamak plasma. In each conversion region, characterized by a six-sector topology, rays in the sector for incident and reflected magnetosonic waves exhibit significant helicity. A detailed analytic and numerical study of helical rays in this sector is developed for a 'symmetric-wedge' model.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaufman, Allan N.; Tracy, Eugene R.; Brizard, Alain J.

The process of resonant wave conversion (often called linear mode conversion) has traditionally been analyzed with a spatially one-dimensional slab model, for which the rays propagate in a two-dimensional phase space. However, it has recently been shown [E.R. Tracy and A.N. Kaufman, Phys. Rev. Lett. 91, 130402 (2003)] that multidimensional rays have a helical structure for conversion in two or more spatial dimensions (if their dispersion matrix is generic). In that case, a one-dimensional model is inadequate; a correct analysis requires two spatial dimensions and, thus, four-dimensional phase space. In this paper we show that a cold plasma model willmore » exhibit ray helicity in conversion regions where the density and magnetic field gradients are significantly non-parallel. For illustration, we examine a model of the poloidal plane of a deuterium-tritium tokamak plasma, and identify such a region. In this region, characterized by a six-sector topology, rays in the sector for incident and reflected magnetosonic waves exhibit significant helicity. We introduce a ''symmetric-wedge'' model, to develop a detailed analytic and numerical study of helical rays in this sector.« less

A VLSI implementation for synthetic aperture radar image processing

NASA Technical Reports Server (NTRS)

Premkumar, A.; Purviance, J.

1990-01-01

A simple physical model for the Synthetic Aperture Radar (SAR) is presented. This model explains the one dimensional and two dimensional nature of the received SAR signal in the range and azimuth directions. A time domain correlator, its algorithm, and features are explained. The correlator is ideally suited for VLSI implementation. A real time SAR architecture using these correlators is proposed. In the proposed architecture, the received SAR data is processed using one dimensional correlators for determining the range while two dimensional correlators are used to determine the azimuth of a target. The architecture uses only three different types of custom VLSI chips and a small amount of memory.

Two-dimensional airflow modeling underpredicts the wind velocity over dunes

PubMed Central

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

2015-01-01

We investigate the average turbulent wind field over a barchan dune by means of Computational Fluid Dynamics. We find that the fractional speed-up ratio of the wind velocity over the three-dimensional barchan shape differs from the one obtained from two-dimensional calculations of the airflow over the longitudinal cut along the dune’s symmetry axis — that is, over the equivalent transverse dune of same size. This finding suggests that the modeling of the airflow over the central slice of barchan dunes is insufficient for the purpose of the quantitative description of barchan dune dynamics as three-dimensional flow effects cannot be neglected. PMID:26572966

Three-dimensional modeling of the plasma arc in arc welding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, G.; Tsai, H. L.; Hu, J.

2008-11-15

Most previous three-dimensional modeling on gas tungsten arc welding (GTAW) and gas metal arc welding (GMAW) focuses on the weld pool dynamics and assumes the two-dimensional axisymmetric Gaussian distributions for plasma arc pressure and heat flux. In this article, a three-dimensional plasma arc model is developed, and the distributions of velocity, pressure, temperature, current density, and magnetic field of the plasma arc are calculated by solving the conservation equations of mass, momentum, and energy, as well as part of the Maxwell's equations. This three-dimensional model can be used to study the nonaxisymmetric plasma arc caused by external perturbations such asmore » an external magnetic field. It also provides more accurate boundary conditions when modeling the weld pool dynamics. The present work lays a foundation for true three-dimensional comprehensive modeling of GTAW and GMAW including the plasma arc, weld pool, and/or electrode.« less

A two-dimensional algebraic quantum liquid produced by an atomic simulator of the quantum Lifshitz model

NASA Astrophysics Data System (ADS)

Po, Hoi Chun; Zhou, Qi

2015-08-01

Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems.

Detection of Subtle Context-Dependent Model Inaccuracies in High-Dimensional Robot Domains.

PubMed

Mendoza, Juan Pablo; Simmons, Reid; Veloso, Manuela

2016-12-01

Autonomous robots often rely on models of their sensing and actions for intelligent decision making. However, when operating in unconstrained environments, the complexity of the world makes it infeasible to create models that are accurate in every situation. This article addresses the problem of using potentially large and high-dimensional sets of robot execution data to detect situations in which a robot model is inaccurate-that is, detecting context-dependent model inaccuracies in a high-dimensional context space. To find inaccuracies tractably, the robot conducts an informed search through low-dimensional projections of execution data to find parametric Regions of Inaccurate Modeling (RIMs). Empirical evidence from two robot domains shows that this approach significantly enhances the detection power of existing RIM-detection algorithms in high-dimensional spaces.

Continued development and validation of the AER two-dimensional interactive model

NASA Technical Reports Server (NTRS)

Ko, M. K. W.; Sze, N. D.; Shia, R. L.; Mackay, M.; Weisenstein, D. K.; Zhou, S. T.

1996-01-01

Results from two-dimensional chemistry-transport models have been used to predict the future behavior of ozone in the stratosphere. Since the transport circulation, temperature, and aerosol surface area are fixed in these models, they cannot account for the effects of changes in these quantities, which could be modified because of ozone redistribution and/or other changes in the troposphere associated with climate changes. Interactive two-dimensional models, which calculate the transport circulation and temperature along with concentrations of the chemical species, could provide answers to complement the results from three-dimension model calculations. In this project, we performed the following tasks in pursuit of the respective goals: (1) We continued to refine the 2-D chemistry-transport model; (2) We developed a microphysics model to calculate the aerosol loading and its size distribution; (3) The treatment of physics in the AER 2-D interactive model were refined in the following areas--the heating rate in the troposphere, and wave-forcing from propagation of planetary waves.

Statistical investigation of avalanches of three-dimensional small-world networks and their boundary and bulk cross-sections

NASA Astrophysics Data System (ADS)

Najafi, M. N.; Dashti-Naserabadi, H.

2018-03-01

In many situations we are interested in the propagation of energy in some portions of a three-dimensional system with dilute long-range links. In this paper, a sandpile model is defined on the three-dimensional small-world network with real dissipative boundaries and the energy propagation is studied in three dimensions as well as the two-dimensional cross-sections. Two types of cross-sections are defined in the system, one in the bulk and another in the system boundary. The motivation of this is to make clear how the statistics of the avalanches in the bulk cross-section tend to the statistics of the dissipative avalanches, defined in the boundaries as the concentration of long-range links (α ) increases. This trend is numerically shown to be a power law in a manner described in the paper. Two regimes of α are considered in this work. For sufficiently small α s the dominant behavior of the system is just like that of the regular BTW, whereas for the intermediate values the behavior is nontrivial with some exponents that are reported in the paper. It is shown that the spatial extent up to which the statistics is similar to the regular BTW model scales with α just like the dissipative BTW model with the dissipation factor (mass in the corresponding ghost model) m2˜α for the three-dimensional system as well as its two-dimensional cross-sections.

Particle-tracking analysis of contributing areas of public-supply wells in simple and complex flow systems, Cape Cod, Massachusetts

USGS Publications Warehouse

Barlow, P.M.

1994-01-01

Steady-state, two-and three-dimensional, ground-water flow models coupled with a particle- tracking program were evaluated to determine their effectiveness in delineating contributing areas of existing and hypothetical public-supply wells pumping from two contrasting stratified-drift aquifers of Cape Cod, Mass. Several of the contri- buting areas delineated by use of the three- dimensional models do not conform to simple ellipsoidal shapes that are typically delineated by use of a two-dimensional analytical and numerical modeling techniques, include dis- continuous areas of the water table, and do not surround the wells. Because two-dimensional areal models do not account for vertical flow, they cannot adequately represent many of the hydro- geologic and well-design variables that were shown to complicate the delineation of contributing areas in these flow systems, including the presence of discrete lenses of 1ow hydraulic conductivity, large ratios of horizontal to ver- tical hydraulic conductivity, shallow streams, partially penetrating supply wells, and 1ow pumping rates (less than 0.1 million gallons per day). Nevertheless, contributing areas delineated for two wells in the simpler of the two flow systems--a thin (less than 100 feet), single- layer, uniform aquifer with near-ideal boundary conditions--were not significantly different for the two- or three-dimensional models of the natural system, for a pumping rate of 0.5 million gallons per day. Use of particle tracking helped identify the source of water to simulated wells, which included precipitation recharge, wastewater return flow, and pond water. Pond water and wastewater return flow accounted for as much as 73 and 40 percent, respectively, of the water captured by simulated wells.

Equation of State of the Two-Dimensional Hubbard Model

NASA Astrophysics Data System (ADS)

Cocchi, Eugenio; Miller, Luke A.; Drewes, Jan H.; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael

2016-04-01

The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0 ≲U /t ≲20 and temperatures, down to kBT /t =0.63 (2 ) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.

Integral formulae of the canonical correlation functions for the one dimensional transverse Ising model

NASA Astrophysics Data System (ADS)

Inoue, Makoto

2017-12-01

Some new formulae of the canonical correlation functions for the one dimensional quantum transverse Ising model are found by the ST-transformation method using a Morita's sum rule and its extensions for the two dimensional classical Ising model. As a consequence we obtain a time-independent term of the dynamical correlation functions. Differences of quantum version and classical version of these formulae are also discussed.

Transient Stress Wave Propagation in One-Dimensional Micropolar Bodies

DTIC Science & Technology

2009-02-01

based on Biot’s theory of poro- elasticity. Two compressional waves were then observed in the resulting one-dimensional model of a poroelastic column...Lisina, S., Potapov, A., Nesterenko, V., 2001. A nonlinear granular medium with particle rotation: a one-dimensional model . Acoustical Physics 47 (5...zones in failed ceramics, may be modeled using continuum theories incorporating additional kinematic degrees of freedom beyond the scope of classical

Conformal mapping in optical biosensor applications.

PubMed

Zumbrum, Matthew E; Edwards, David A

2015-09-01

Optical biosensors are devices used to investigate surface-volume reaction kinetics. Current mathematical models for reaction dynamics rely on the assumption of unidirectional flow within these devices. However, new devices, such as the Flexchip, include a geometry that introduces two-dimensional flow, complicating the depletion of the volume reactant. To account for this, a previous mathematical model is extended to include two-dimensional flow, and the Schwarz-Christoffel mapping is used to relate the physical device geometry to that for a device with unidirectional flow. Mappings for several Flexchip dimensions are considered, and the ligand depletion effect is investigated for one of these mappings. Estimated rate constants are produced for simulated data to quantify the inclusion of two-dimensional flow in the mathematical model.

Statistical mechanics of shell models for two-dimensional turbulence

NASA Astrophysics Data System (ADS)

Aurell, E.; Boffetta, G.; Crisanti, A.; Frick, P.; Paladin, G.; Vulpiani, A.

1994-12-01

We study shell models that conserve the analogs of energy and enstrophy and hence are designed to mimic fluid turbulence in two-dimensions (2D). The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous to the approach to two-dimensional ideal hydrodynamics of Onsager [Nuovo Cimento Suppl. 6, 279 (1949)], Hopf [J. Rat. Mech. Anal. 1, 87 (1952)], and Lee [Q. Appl. Math. 10, 69 (1952)]. In the presence of forcing and dissipation we observe a forward flux of enstrophy and a backward flux of energy. These fluxes can be understood as mean diffusive drifts from a source to two sinks in a system which is close to local equilibrium with Lagrange multipliers (``shell temperatures'') changing slowly with scale. This is clear evidence that the simplest shell models are not adequate to reproduce the main features of two-dimensional turbulence. The dimensional predictions on the power spectra from a supposed forward cascade of enstrophy and from one branch of the formal statistical equilibrium coincide in these shell models in contrast to the corresponding predictions for the Navier-Stokes and Euler equations in 2D. This coincidence has previously led to the mistaken conclusion that shell models exhibit a forward cascade of enstrophy. We also study the dynamical properties of the models and the growth of perturbations.

Suitability of a three-dimensional model to measure empathy and its relationship with social and normative adjustment in Spanish adolescents: a cross-sectional study

PubMed Central

Gómez-Ortiz, Olga; Ortega-Ruiz, Rosario; Jolliffe, Darrick; Romera, Eva M.

2017-01-01

Objectives (1) To examine the psychometric properties of the Basic Empathy Scale (BES) with Spanish adolescents, comparing a two and a three-dimensional structure;(2) To analyse the relationship between the three-dimensional empathy and social and normative adjustment in school. Design Transversal and ex post facto retrospective study. Confirmatory factorial analysis, multifactorial invariance analysis and structural equations models were used. Participants 747 students (51.3% girls) from Cordoba, Spain, aged 12–17 years (M=13.8; SD=1.21). Results The original two-dimensional structure was confirmed (cognitive empathy, affective empathy), but a three-dimensional structure showed better psychometric properties, highlighting the good fit found in confirmatory factorial analysis and adequate internal consistent valued, measured with Cronbach’s alpha and McDonald’s omega. Composite reliability and average variance extracted showed better indices for a three-factor model. The research also showed evidence of measurement invariance across gender. All the factors of the final three-dimensional BES model were direct and significantly associated with social and normative adjustment, being most strongly related to cognitive empathy. Conclusions This research supports the advances in neuroscience, developmental psychology and psychopathology through a three-dimensional version of the BES, which represents an improvement in the original two-factorial model. The organisation of empathy in three factors benefits the understanding of social and normative adjustment in adolescents, in which emotional disengagement favours adjusted peer relationships. Psychoeducational interventions aimed at improving the quality of social life in schools should target these components of empathy. PMID:28951400

Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction

NASA Astrophysics Data System (ADS)

Cui, Tiangang; Marzouk, Youssef; Willcox, Karen

2016-06-01

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting-both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a heterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.

New techniques for experimental generation of two-dimensional blade-vortex interaction at low Reynolds numbers

NASA Technical Reports Server (NTRS)

Booth, E., Jr.; Yu, J. C.

1986-01-01

An experimental investigation of two dimensional blade vortex interaction was held at NASA Langley Research Center. The first phase was a flow visualization study to document the approach process of a two dimensional vortex as it encountered a loaded blade model. To accomplish the flow visualization study, a method for generating two dimensional vortex filaments was required. The numerical study used to define a new vortex generation process and the use of this process in the flow visualization study were documented. Additionally, photographic techniques and data analysis methods used in the flow visualization study are examined.

Learning control system design based on 2-D theory - An application to parallel link manipulator

NASA Technical Reports Server (NTRS)

Geng, Z.; Carroll, R. L.; Lee, J. D.; Haynes, L. H.

1990-01-01

An approach to iterative learning control system design based on two-dimensional system theory is presented. A two-dimensional model for the iterative learning control system which reveals the connections between learning control systems and two-dimensional system theory is established. A learning control algorithm is proposed, and the convergence of learning using this algorithm is guaranteed by two-dimensional stability. The learning algorithm is applied successfully to the trajectory tracking control problem for a parallel link robot manipulator. The excellent performance of this learning algorithm is demonstrated by the computer simulation results.

On the Sensitivity of Atmospheric Ensembles to Cloud Microphysics in Long-Term Cloud-Resolving Model Simulations

NASA Technical Reports Server (NTRS)

Zeng, Xiping; Tao, Wei-Kuo; Lang, Stephen; Hou, Arthur Y.; Zhang, Minghua; Simpson, Joanne

2008-01-01

Month-long large-scale forcing data from two field campaigns are used to drive a cloud-resolving model (CRM) and produce ensemble simulations of clouds and precipitation. Observational data are then used to evaluate the model results. To improve the model results, a new parameterization of the Bergeron process is proposed that incorporates the number concentration of ice nuclei (IN). Numerical simulations reveal that atmospheric ensembles are sensitive to IN concentration and ice crystal multiplication. Two- (2D) and three-dimensional (3D) simulations are carried out to address the sensitivity of atmospheric ensembles to model dimensionality. It is found that the ensembles with high IN concentration are more sensitive to dimensionality than those with low IN concentration. Both the analytic solutions of linear dry models and the CRM output show that there are more convective cores with stronger updrafts in 3D simulations than in 2D, which explains the differing sensitivity of the ensembles to dimensionality at different IN concentrations.

Lattice model for self-assembly with application to the formation of cytoskeletal-like structures

NASA Astrophysics Data System (ADS)

Stewman, Shannon F.; Dinner, Aaron R.

2007-07-01

We introduce a stochastic approach for self-assembly in systems far from equilibrium. The building blocks are represented by a lattice of discrete variables (Potts-like spins), and physically meaningful mechanisms are obtained by restricting transitions through spatially local rules based on experimental data. We use the method to study nucleation of filopodia-like bundles in a system consisting of purified actin, fascin, actin-related protein 2/3 , and beads coated with Wiskott-Aldrich syndrome protein. Consistent with previous speculation based on static experimental images, we find that bundles derive from Λ -precursor-like patterns of spins on the lattice. The ratcheting of the actin network relative to the surface that represents beads plays an important role in determining the number and orientation of bundles due to the fact that branching is the primary means for generating barbed ends pointed in directions that allow rapid filament growth. By enabling the de novo formation of coexisting morphologies without the computational cost of explicit representation of proteins, the approach introduced complements earlier models of cytoskeletal behavior in vitro and in vivo.

State-of-charge estimation in lithium-ion batteries: A particle filter approach

NASA Astrophysics Data System (ADS)

Tulsyan, Aditya; Tsai, Yiting; Gopaluni, R. Bhushan; Braatz, Richard D.

2016-11-01

The dynamics of lithium-ion batteries are complex and are often approximated by models consisting of partial differential equations (PDEs) relating the internal ionic concentrations and potentials. The Pseudo two-dimensional model (P2D) is one model that performs sufficiently accurately under various operating conditions and battery chemistries. Despite its widespread use for prediction, this model is too complex for standard estimation and control applications. This article presents an original algorithm for state-of-charge estimation using the P2D model. Partial differential equations are discretized using implicit stable algorithms and reformulated into a nonlinear state-space model. This discrete, high-dimensional model (consisting of tens to hundreds of states) contains implicit, nonlinear algebraic equations. The uncertainty in the model is characterized by additive Gaussian noise. By exploiting the special structure of the pseudo two-dimensional model, a novel particle filter algorithm that sweeps in time and spatial coordinates independently is developed. This algorithm circumvents the degeneracy problems associated with high-dimensional state estimation and avoids the repetitive solution of implicit equations by defining a 'tether' particle. The approach is illustrated through extensive simulations.

Locating the quantum critical point of the Bose-Hubbard model through singularities of simple observables.

PubMed

Łącki, Mateusz; Damski, Bogdan; Zakrzewski, Jakub

2016-12-02

We show that the critical point of the two-dimensional Bose-Hubbard model can be easily found through studies of either on-site atom number fluctuations or the nearest-neighbor two-point correlation function (the expectation value of the tunnelling operator). Our strategy to locate the critical point is based on the observation that the derivatives of these observables with respect to the parameter that drives the superfluid-Mott insulator transition are singular at the critical point in the thermodynamic limit. Performing the quantum Monte Carlo simulations of the two-dimensional Bose-Hubbard model, we show that this technique leads to the accurate determination of the position of its critical point. Our results can be easily extended to the three-dimensional Bose-Hubbard model and different Hubbard-like models. They provide a simple experimentally-relevant way of locating critical points in various cold atomic lattice systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nekrasov, Nikita; ITEP, Moscow; Shatashvili, Samson

Supersymmetric vacua of two dimensional N = 4 gauge theories with matter, softly broken by the twisted masses down to N = 2, are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. Examples include: the Heisenberg SU(2)XXX spin chain which is mapped to the two dimensional U(N) theory with fundamental hypermultiplets, the XXZ spin chain which is mapped to the analogous three dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model which are related to the four dimensional theory compactified on T{sup 2}. A consequence of our correspondence ismore » the isomorphism of the quantum cohomology ring of various quiver varieties, such as cotangent bundles to (partial) flag varieties and the ring of quantum integrals of motion of various spin chains. The correspondence extends to any spin group, representations, boundary conditions, and inhomogeneity, it includes Sinh-Gordon and non-linear Schroedinger models as well as the dynamical spin chains like Hubbard model. Compactifications of four dimensional N = 2 theories on a two-sphere lead to the instanton-corrected Bethe equations.« less

Stress concentration investigations using NASTRAN

NASA Technical Reports Server (NTRS)

Gillcrist, M. C.; Parnell, L. A.

1986-01-01

Parametic investigations are performed using several two dimensional finite element formulations to determine their suitability for use in predicting extremum stresses in marine propellers. Comparisons are made of two NASTRAN elements (CTRIM6 and CTRAIA2) wherein elasticity properties have been modified to yield plane strain results. The accuracy of the elements is investigated by comparing finite element stress predictions with experimentally determined stresses in two classical cases: (1) tension in a flat plate with a circular hole; and (2) a filleted flat bar subjected to in-plane bending. The CTRIA2 element is found to provide good results. The displacement field from a three dimensional finite element model of a representative marine propeller is used as the boundary condition for the two dimensional plane strain investigations of stresses in the propeller blade and fillet. Stress predictions from the three dimensional analysis are compared with those from the two dimensional models. The validity of the plane strain modifications to the NASTRAN element is checked by comparing the modified CTRIA2 element stress predictions with those of the ABAQUS plane strain element, CPE4.

Progress Report on SAM Reduced-Order Model Development for Thermal Stratification and Mixing during Reactor Transients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, R.

This report documents the initial progress on the reduced-order flow model developments in SAM for thermal stratification and mixing modeling. Two different modeling approaches are pursued. The first one is based on one-dimensional fluid equations with additional terms accounting for the thermal mixing from both flow circulations and turbulent mixing. The second approach is based on three-dimensional coarse-grid CFD approach, in which the full three-dimensional fluid conservation equations are modeled with closure models to account for the effects of turbulence.

Model of chiral spin liquids with Abelian and non-Abelian topological phases

DOE PAGES

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio; ...

2017-12-15

In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less

Model of chiral spin liquids with Abelian and non-Abelian topological phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio

In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less

Nucleation barrier reconstruction via the seeding method in a lattice model with competing nucleation pathways.

PubMed

Lifanov, Yuri; Vorselaars, Bart; Quigley, David

2016-12-07

We study a three-species analogue of the Potts lattice gas model of nucleation from solution in a regime where partially disordered solute is a viable thermodynamic phase. Using a multicanonical sampling protocol, we compute phase diagrams for the system, from which we determine a parameter regime where the partially disordered phase is metastable almost everywhere in the temperature-fugacity plane. The resulting model shows non-trivial nucleation and growth behaviour, which we examine via multidimensional free energy calculations. We consider the applicability of the model in capturing the multi-stage nucleation mechanisms of polymorphic biominerals (e.g., CaCO 3 ). We then quantitatively explore the kinetics of nucleation in our model using the increasingly popular "seeding" method. We compare the resulting free energy barrier heights to those obtained via explicit free energy calculations over a wide range of temperatures and fugacities, carefully considering the propagation of statistical error. We find that the ability of the "seeding" method to reproduce accurate free energy barriers is dependent on the degree of supersaturation, and severely limited by the use of a nucleation driving force Δμ computed for bulk phases. We discuss possible reasons for this in terms of underlying kinetic assumptions, and those of classical nucleation theory.

Ranges of applicability for the continuum beam model in the mechanics of carbon nanotubes and nanorods

NASA Technical Reports Server (NTRS)

Harik, V. M.

2001-01-01

Limitations in the validity of the continuum beam model for carbon nanotubes (NTs) and nanorods are examined. Applicability of all assumptions used in the model is restricted by the two criteria for geometric parameters that characterize the structure of NTs. The key non-dimensional parameters that control the NT buckling behavior are derived via dimensional analysis of the nanomechanical problem. A mechanical law of geometric similitude for NT buckling is extended from continuum mechanics for different molecular structures. A model applicability map, where two classes of beam-like NTs are identified, is constructed for distinct ranges of non-dimensional parameters. Expressions for the critical buckling loads and strains are tailored for two classes of NTs and compared with the data provided by the molecular dynamics simulations. copyright 2001 Elsevier Science Ltd. All rights reserved.

Three-Dimensional Computer-Assisted Two-Layer Elastic Models of the Face.

PubMed

Ueda, Koichi; Shigemura, Yuka; Otsuki, Yuki; Fuse, Asuka; Mitsuno, Daisuke

2017-11-01

To make three-dimensional computer-assisted elastic models for the face, we decided on five requirements: (1) an elastic texture like skin and subcutaneous tissue; (2) the ability to take pen marking for incisions; (3) the ability to be cut with a surgical knife; (4) the ability to keep stitches in place for a long time; and (5) a layered structure. After testing many elastic solvents, we have made realistic three-dimensional computer-assisted two-layer elastic models of the face and cleft lip from the computed tomographic and magnetic resonance imaging stereolithographic data. The surface layer is made of polyurethane and the inner layer is silicone. Using this elastic model, we taught residents and young doctors how to make several typical local flaps and to perform cheiloplasty. They could experience realistic simulated surgery and understand three-dimensional movement of the flaps.

A mechanism for hot-spot generation in a reactive two-dimensional sheared viscous layer

NASA Astrophysics Data System (ADS)

Timms, Robert; Purvis, Richard; Curtis, John P.

2018-05-01

A two-dimensional model for the non-uniform melting of a thin sheared viscous layer is developed. An asymptotic solution is presented for both a non-reactive and a reactive material. It is shown that the melt front is linearly stable to small perturbations in the non-reactive case, but becomes linearly unstable upon introduction of an Arrhenius source term to model the chemical reaction. Results demonstrate that non-uniform melting acts as a mechanism to generate hot spots that are found to be sufficient to reduce the time to ignition when compared with the corresponding one-dimensional model of melting.

Chaotic oscillator containing memcapacitor and meminductor and its dimensionality reduction analysis.

PubMed

Yuan, Fang; Wang, Guangyi; Wang, Xiaowei

2017-03-01

In this paper, smooth curve models of meminductor and memcapacitor are designed, which are generalized from a memristor. Based on these models, a new five-dimensional chaotic oscillator that contains a meminductor and memcapacitor is proposed. By dimensionality reducing, this five-dimensional system can be transformed into a three-dimensional system. The main work of this paper is to give the comparisons between the five-dimensional system and its dimensionality reduction model. To investigate dynamics behaviors of the two systems, equilibrium points and stabilities are analyzed. And the bifurcation diagrams and Lyapunov exponent spectrums are used to explore their properties. In addition, digital signal processing technologies are used to realize this chaotic oscillator, and chaotic sequences are generated by the experimental device, which can be used in encryption applications.

SPECIAL ISSUE DEVOTED TO THE 80TH BIRTHDAY OF S.A. AKHMANOV: Excitation of coherent polaritons in a two-dimensional atomic lattice

NASA Astrophysics Data System (ADS)

Barinov, I. O.; Alodzhants, A. P.; Arakelyan, Sergei M.

2009-07-01

We describe a new type of spatially periodic structure (lattice models): a polaritonic crystal formed by a two-dimensional lattice of trapped two-level atoms interacting with the electromagnetic field in a cavity (or in a one-dimensional array of tunnelling-coupled microcavities), which allows polaritons to be fully localised. Using a one-dimensional polaritonic crystal as an example, we analyse conditions for quantum degeneracy of a lower-polariton gas and those for quantum optical information recording and storage.

Sensitivity studies and a simple ozone perturbation experiment with a truncated two-dimensional model of the stratosphere

NASA Technical Reports Server (NTRS)

Stordal, Frode; Garcia, Rolando R.

1987-01-01

The 1-1/2-D model of Holton (1986), which is actually a highly truncated two-dimensional model, describes latitudinal variations of tracer mixing ratios in terms of their projections onto second-order Legendre polynomials. The present study extends the work of Holton by including tracers with photochemical production in the stratosphere (O3 and NOy). It also includes latitudinal variations in the photochemical sources and sinks, improving slightly the calculated global mean profiles for the long-lived tracers studied by Holton and improving substantially the latitudinal behavior of ozone. Sensitivity tests of the dynamical parameters in the model are performed, showing that the response of the model to changes in vertical residual meridional winds and horizontal diffusion coefficients is similar to that of a full two-dimensional model. A simple ozone perturbation experiment shows the model's ability to reproduce large-scale latitudinal variations in total ozone column depletions as well as ozone changes in the chemically controlled upper stratosphere.

Perceptual integration of kinematic components in the recognition of emotional facial expressions.

PubMed

Chiovetto, Enrico; Curio, Cristóbal; Endres, Dominik; Giese, Martin

2018-04-01

According to a long-standing hypothesis in motor control, complex body motion is organized in terms of movement primitives, reducing massively the dimensionality of the underlying control problems. For body movements, this low-dimensional organization has been convincingly demonstrated by the learning of low-dimensional representations from kinematic and EMG data. In contrast, the effective dimensionality of dynamic facial expressions is unknown, and dominant analysis approaches have been based on heuristically defined facial "action units," which reflect contributions of individual face muscles. We determined the effective dimensionality of dynamic facial expressions by learning of a low-dimensional model from 11 facial expressions. We found an amazingly low dimensionality with only two movement primitives being sufficient to simulate these dynamic expressions with high accuracy. This low dimensionality is confirmed statistically, by Bayesian model comparison of models with different numbers of primitives, and by a psychophysical experiment that demonstrates that expressions, simulated with only two primitives, are indistinguishable from natural ones. In addition, we find statistically optimal integration of the emotion information specified by these primitives in visual perception. Taken together, our results indicate that facial expressions might be controlled by a very small number of independent control units, permitting very low-dimensional parametrization of the associated facial expression.

Quantifying two-dimensional nonstationary signal with power-law correlations by detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Fan, Qingju; Wu, Yonghong

2015-08-01

In this paper, we develop a new method for the multifractal characterization of two-dimensional nonstationary signal, which is based on the detrended fluctuation analysis (DFA). By applying to two artificially generated signals of two-component ARFIMA process and binomial multifractal model, we show that the new method can reliably determine the multifractal scaling behavior of two-dimensional signal. We also illustrate the applications of this method in finance and physiology. The analyzing results exhibit that the two-dimensional signals under investigation are power-law correlations, and the electricity market consists of electricity price and trading volume is multifractal, while the two-dimensional EEG signal in sleep recorded for a single patient is weak multifractal. The new method based on the detrended fluctuation analysis may add diagnostic power to existing statistical methods.

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

PubMed

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

2011-01-01

In this paper, we use a quantitative structure-retention relationship (QSRR) method to predict the retention times of polychlorinated biphenyls (PCBs) in comprehensive two-dimensional gas chromatography (GC×GC). We analyse the GC×GC retention data taken from the literature by comparing predictive capability of different regression methods. The various models are generated using 70 out of 209 PCB congeners in the calibration stage, while their predictive performance is evaluated on the remaining 139 compounds. The two-dimensional chromatogram is initially estimated by separately modelling retention times of PCBs in the first and in the second column ((1) t (R) and (2) t (R), respectively). In particular, multilinear regression (MLR) combined with genetic algorithm (GA) variable selection is performed to extract two small subsets of predictors for (1) t (R) and (2) t (R) from a large set of theoretical molecular descriptors provided by the popular software Dragon, which after removal of highly correlated or almost constant variables consists of 237 structure-related quantities. Based on GA-MLR analysis, a four-dimensional and a five-dimensional relationship modelling (1) t (R) and (2) t (R), respectively, are identified. Single-response partial least square (PLS-1) regression is alternatively applied to independently model (1) t (R) and (2) t (R) without the need for preliminary GA variable selection. Further, we explore the possibility of predicting the two-dimensional chromatogram of PCBs in a single calibration procedure by using a two-response PLS (PLS-2) model or a feed-forward artificial neural network (ANN) with two output neurons. In the first case, regression is carried out on the full set of 237 descriptors, while the variables previously selected by GA-MLR are initially considered as ANN inputs and subjected to a sensitivity analysis to remove the redundant ones. Results show PLS-1 regression exhibits a noticeably better descriptive and predictive performance than the other investigated approaches. The observed values of determination coefficients for (1) t (R) and (2) t (R) in calibration (0.9999 and 0.9993, respectively) and prediction (0.9987 and 0.9793, respectively) provided by PLS-1 demonstrate that GC×GC behaviour of PCBs is properly modelled. In particular, the predicted two-dimensional GC×GC chromatogram of 139 PCBs not involved in the calibration stage closely resembles the experimental one. Based on the above lines of evidence, the proposed approach ensures accurate simulation of the whole GC×GC chromatogram of PCBs using experimental determination of only 1/3 retention data of representative congeners.

3D evaluation of the effect of disinfectants on dimensional accuracy and stability of two elastomeric impression materials.

PubMed

Soganci, Gokce; Cinar, Duygu; Caglar, Alper; Yagiz, Ayberk

2018-05-31

The aim of this study was to determine and compare the dimensional changes of polyether and vinyl polyether siloxane impression materials under immersion disinfection with two different disinfectants in three time periods. Impressions were obtained from an edentulous master model. Sodium hypochlorite (5.25%) and glutaraldehyde (2%) were used for disinfection and measurements were done 30 min later after making impression before disinfection, after required disinfection period (10 min), and after 24 h storage at room temperature. Impressions were scanned using 3D scanner with 10 microns accuracy and 3D software was used to evaluate the dimensional changes with superimpositioning. Positive and negative deviations were calculated and compared with master model. There was no significant difference between two elastomeric impression materials (p>0.05). It was concluded that dimensional accuracy and stability of two impression materials were excellent and similar.

Investigation of two-dimensional wedge exhaust nozzles for advanced aircraft

NASA Technical Reports Server (NTRS)

Maiden, D. L.; Petit, J. E.

1975-01-01

Two-dimensional wedge nozzle performance characteristics were investigated in a series of wind-tunnel tests. An isolated single-engine/nozzle model was used to study the effects of internal expansion area ratio, aftbody cowl boattail angle, and wedge length. An integrated twin-engine/nozzle model, tested with and without empenage surfaces, included cruise, acceleration, thrust vectoring and thrust reversing nozzle operating modes. Results indicate that the thrust-minus-aftbody drag performance of the twin two-dimensional nozzle integration is significantly higher, for speeds greater than Mach 0.8, than the performance achieved with twin axisymmetric nozzle installations. Significant jet-induced lift was obtained on an aft-mounted lifting surface using a cambered wedge center body to vector thrust. The thrust reversing capabilities of reverser panels installed on the two-dimensional wedge center body were very effective for static or in-flight operation.

A comparison of analog and digital modeling techniques for simulating three-dimensional ground-water flow on Long Island, New York

USGS Publications Warehouse

Reilly, Thomas E.; Harbaugh, Arlen W.

1980-01-01

A three-dimensional electric-analog model of the Long Island, NY , groundwater system constructed by the U.S. Geological Survey in the early 1970 's was used as the basis for developing a digital, three-dimensional finite-difference model. The digital model was needed to provide faster modifications and more rapid solutions to water-management questions. Results generated by the two models are depicted as potentiometric-surface maps of the upper glacial and Magothy aquifers. Results compare favorably for all parts of Long Island except the northwestern part, where hydrologic discontinuities are most prevalent and which the two models represent somewhat differently. The mathematical and hydrologic principles used in development of ground-water models, and the procedures for calibration and acceptance, are presented in nontechnical terms. (USGS)

A thermal analysis of a spirally wound battery using a simple mathematical model

NASA Technical Reports Server (NTRS)

Evans, T. I.; White, R. E.

1989-01-01

A two-dimensional thermal model for spirally wound batteries has been developed. The governing equation of the model is the energy balance. Convective and insulated boundary conditions are used, and the equations are solved using a finite element code called TOPAZ2D. The finite element mesh is generated using a preprocessor to TOPAZ2D called MAZE. The model is used to estimate temperature profiles within a spirally wound D-size cell. The model is applied to the lithium/thionyl chloride cell because of the thermal management problems that this cell exhibits. Simplified one-dimensional models are presented that can be used to predict best and worst temperature profiles. The two-dimensional model is used to predict the regions of maximum temperature within the spirally wound cell. Normal discharge as well as thermal runaway conditions are investigated.

Spintronics: spin accumulation in mesoscopic systems.

PubMed

Johnson, Mark

2002-04-25

In spintronics, in which use is made of the spin degree of freedom of the electron, issues concerning electrical spin injection and detection of electron spin diffusion are fundamentally important. Jedema et al. describe a magneto-resistance study in which they claim to have observed spin accumulation in a mesoscopic copper wire, but their one-dimensional model ignores two-dimensional spin-diffusion effects, which casts doubt on their analysis. A two-dimensional vector formalism of spin transport is called for to model spin-injection experiments, and the identification of spurious background resistance effects is crucial.

Modeling, Monitoring and Fault Diagnosis of Spacecraft Air Contaminants

NASA Technical Reports Server (NTRS)

Ramirez, W. Fred; Skliar, Mikhail; Narayan, Anand; Morgenthaler, George W.; Smith, Gerald J.

1996-01-01

Progress and results in the development of an integrated air quality modeling, monitoring, fault detection, and isolation system are presented. The focus was on development of distributed models of the air contaminants transport, the study of air quality monitoring techniques based on the model of transport process and on-line contaminant concentration measurements, and sensor placement. Different approaches to the modeling of spacecraft air contamination are discussed, and a three-dimensional distributed parameter air contaminant dispersion model applicable to both laminar and turbulent transport is proposed. A two-dimensional approximation of a full scale transport model is also proposed based on the spatial averaging of the three dimensional model over the least important space coordinate. A computer implementation of the transport model is considered and a detailed development of two- and three-dimensional models illustrated by contaminant transport simulation results is presented. The use of a well established Kalman filtering approach is suggested as a method for generating on-line contaminant concentration estimates based on both real time measurements and the model of contaminant transport process. It is shown that high computational requirements of the traditional Kalman filter can render difficult its real-time implementation for high-dimensional transport model and a novel implicit Kalman filtering algorithm is proposed which is shown to lead to an order of magnitude faster computer implementation in the case of air quality monitoring.

Verification and transfer of thermal pollution model. Volume 3: Verification of 3-dimensional rigid-lid model

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.; Sinha, S. K.

1982-01-01

The six-volume report: describes the theory of a three dimensional (3-D) mathematical thermal discharge model and a related one dimensional (1-D) model, includes model verification at two sites, and provides a separate user's manual for each model. The 3-D model has two forms: free surface and rigid lid. The former, verified at Anclote Anchorage (FL), allows a free air/water interface and is suited for significant surface wave heights compared to mean water depth; e.g., estuaries and coastal regions. The latter, verified at Lake Keowee (SC), is suited for small surface wave heights compared to depth (e.g., natural or man-made inland lakes) because surface elevation has been removed as a parameter. These models allow computation of time-dependent velocity and temperature fields for given initial conditions and time-varying boundary conditions. The free-surface model also provides surface height variations with time.

[Study on the influence of bioclogging on permeability of saturated porous media by experiments and models].

PubMed

Yang, Jing; Ye, Shu-jun; Wu, Ji-chun

2011-05-01

This paper studied on the influence of bioclogging on permeability of saturated porous media. Laboratory hydraulic tests were conducted in a two-dimensional C190 sand-filled cell (55 cm wide x 45 cm high x 1.28 cm thick) to investigate growth of the mixed microorganisms (KB-1) and influence of biofilm on permeability of saturated porous media under condition of rich nutrition. Biomass distributions in the water and on the sand in the cell were measured by protein analysis. The biofilm distribution on the sand was observed by confocal laser scanning microscopy. Permeability was measured by hydraulic tests. The biomass levels measured in water and on the sand increased with time, and were highest at the bottom of the cell. The biofilm on the sand at the bottom of the cell was thicker. The results of the hydraulic tests demonstrated that the permeability due to biofilm growth was estimated to be average 12% of the initial value. To investigate the spatial distribution of permeability in the two dimensional cell, three models (Taylor, Seki, and Clement) were used to calculate permeability of porous media with biofilm growth. The results of Taylor's model showed reduction in permeability of 2-5 orders magnitude. The Clement's model predicted 3%-98% of the initial value. Seki's model could not be applied in this study. Conclusively, biofilm growth could obviously decrease the permeability of two dimensional saturated porous media, however, the reduction was much less than that estimated in one dimensional condition. Additionally, under condition of two dimensional saturated porous media with rich nutrition, Seki's model could not be applied, Taylor's model predicted bigger reductions, and the results of Clement's model were closest to the result of hydraulic test.

Limitations to the use of two-dimensional thermal modeling of a nuclear waste repository

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davis, B.W.

1979-01-04

Thermal modeling of a nuclear waste repository is basic to most waste management predictive models. It is important that the modeling techniques accurately determine the time-dependent temperature distribution of the waste emplacement media. Recent modeling studies show that the time-dependent temperature distribution can be accurately modeled in the far-field using a 2-dimensional (2-D) planar numerical model; however, the near-field cannot be modeled accurately enough by either 2-D axisymmetric or 2-D planar numerical models for repositories in salt. The accuracy limits of 2-D modeling were defined by comparing results from 3-dimensional (3-D) TRUMP modeling with results from both 2-D axisymmetric andmore » 2-D planar. Both TRUMP and ADINAT were employed as modeling tools. Two-dimensional results from the finite element code, ADINAT were compared with 2-D results from the finite difference code, TRUMP; they showed almost perfect correspondence in the far-field. This result adds substantially to confidence in future use of ADINAT and its companion stress code ADINA for thermal stress analysis. ADINAT was found to be somewhat sensitive to time step and mesh aspect ratio. 13 figures, 4 tables.« less

The Airborne Optical Systems Testbed (AOSTB)

DTIC Science & Technology

2017-05-31

appropriate color to each pixel in and displayed in a two -dimensional array. Another method is to render a 3D model from the data and display the model as if...USA Distribution A: Public Release ALBOTA@LL.MIT.EDU ABSTRACT Over the last two decades MIT Lincoln Laboratory (MITLL) has pioneered the development... two -dimensional (2D) grid of detectors. Rather than measuring intensity, as in a conventional camera, these detectors measure the photon time-of

Dynamics of an HIV-1 infection model with cell mediated immunity

NASA Astrophysics Data System (ADS)

Yu, Pei; Huang, Jianing; Jiang, Jiao

2014-10-01

In this paper, we study the dynamics of an improved mathematical model on HIV-1 virus with cell mediated immunity. This new 5-dimensional model is based on the combination of a basic 3-dimensional HIV-1 model and a 4-dimensional immunity response model, which more realistically describes dynamics between the uninfected cells, infected cells, virus, the CTL response cells and CTL effector cells. Our 5-dimensional model may be reduced to the 4-dimensional model by applying a quasi-steady state assumption on the variable of virus. However, it is shown in this paper that virus is necessary to be involved in the modeling, and that a quasi-steady state assumption should be applied carefully, which may miss some important dynamical behavior of the system. Detailed bifurcation analysis is given to show that the system has three equilibrium solutions, namely the infection-free equilibrium, the infectious equilibrium without CTL, and the infectious equilibrium with CTL, and a series of bifurcations including two transcritical bifurcations and one or two possible Hopf bifurcations occur from these three equilibria as the basic reproduction number is varied. The mathematical methods applied in this paper include characteristic equations, Routh-Hurwitz condition, fluctuation lemma, Lyapunov function and computation of normal forms. Numerical simulation is also presented to demonstrate the applicability of the theoretical predictions.

The Two- and Three-Dimensional Models of the HK-WISC: A Confirmatory Factor Analysis.

ERIC Educational Resources Information Center

Chan, David W.; Lin, Wen-Ying

1996-01-01

Confirmatory analyses on the Hong Kong Wechsler Intelligence Scale for Children (HK-WISC) provided support for composite score interpretation based on the two- and three-dimensional models across age levels. Test sample was comprised of 1,100 children, ranging in age from 5 to 15 years at all 11 age levels specified by the HK-WISC. (KW)

Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow

NASA Astrophysics Data System (ADS)

Gonzalez, M.

2018-04-01

The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.

Resonant Zener tunneling in two-dimensional periodic photonic lattices.

PubMed

Desyatnikov, Anton S; Kivshar, Yuri S; Shchesnovich, Valery S; Cavalcanti, Solange B; Hickmann, Jandir M

2007-02-15

We study Zener tunneling in two-dimensional photonic lattices and derive, for the case of hexagonal symmetry, the generalized Landau-Zener-Majorana model describing resonant interaction between high-symmetry points of the photonic spectral bands. We demonstrate that this effect can be employed for the generation of Floquet-Bloch modes and verify the model by direct numerical simulations of the tunneling effect.

A solution for two-dimensional mazes with use of chaotic dynamics in a recurrent neural network model.

PubMed

Suemitsu, Yoshikazu; Nara, Shigetoshi

2004-09-01

Chaotic dynamics introduced into a neural network model is applied to solving two-dimensional mazes, which are ill-posed problems. A moving object moves from the position at t to t + 1 by simply defined motion function calculated from firing patterns of the neural network model at each time step t. We have embedded several prototype attractors that correspond to the simple motion of the object orienting toward several directions in two-dimensional space in our neural network model. Introducing chaotic dynamics into the network gives outputs sampled from intermediate state points between embedded attractors in a state space, and these dynamics enable the object to move in various directions. System parameter switching between a chaotic and an attractor regime in the state space of the neural network enables the object to move to a set target in a two-dimensional maze. Results of computer simulations show that the success rate for this method over 300 trials is higher than that of random walk. To investigate why the proposed method gives better performance, we calculate and discuss statistical data with respect to dynamical structure.

Experimental, Theoretical, and Computational Investigation of Separated Nozzle Flows

NASA Technical Reports Server (NTRS)

Hunter, Craig A.

2004-01-01

A detailed experimental, theoretical, and computational study of separated nozzle flows has been conducted. Experimental testing was performed at the NASA Langley 16-Foot Transonic Tunnel Complex. As part of a comprehensive static performance investigation, force, moment, and pressure measurements were made and schlieren flow visualization was obtained for a sub-scale, non-axisymmetric, two-dimensional, convergent- divergent nozzle. In addition, two-dimensional numerical simulations were run using the computational fluid dynamics code PAB3D with two-equation turbulence closure and algebraic Reynolds stress modeling. For reference, experimental and computational results were compared with theoretical predictions based on one-dimensional gas dynamics and an approximate integral momentum boundary layer method. Experimental results from this study indicate that off-design overexpanded nozzle flow was dominated by shock induced boundary layer separation, which was divided into two distinct flow regimes; three- dimensional separation with partial reattachment, and fully detached two-dimensional separation. The test nozzle was observed to go through a marked transition in passing from one regime to the other. In all cases, separation provided a significant increase in static thrust efficiency compared to the ideal prediction. Results indicate that with controlled separation, the entire overexpanded range of nozzle performance would be within 10% of the peak thrust efficiency. By offering savings in weight and complexity over a conventional mechanical exhaust system, this may allow a fixed geometry nozzle to cover an entire flight envelope. The computational simulation was in excellent agreement with experimental data over most of the test range, and did a good job of modeling internal flow and thrust performance. An exception occurred at low nozzle pressure ratios, where the two-dimensional computational model was inconsistent with the three-dimensional separation observed in the experiment. In general, the computation captured the physics of the shock boundary layer interaction and shock induced boundary layer separation in the nozzle, though there were some differences in shock structure compared to experiment. Though minor, these differences could be important for studies involving flow control or thrust vectoring of separated nozzles. Combined with other observations, this indicates that more detailed, three-dimensional computational modeling needs to be conducted to more realistically simulate shock-separated nozzle flows.

Two-Dimensional Analysis of Conical Pulsed Inductive Plasma Thruster Performance

NASA Technical Reports Server (NTRS)

Hallock, A. K.; Polzin, K. A.; Emsellem, G. D.

2011-01-01

A model of the maximum achievable exhaust velocity of a conical theta pinch pulsed inductive thruster is presented. A semi-empirical formula relating coil inductance to both axial and radial current sheet location is developed and incorporated into a circuit model coupled to a momentum equation to evaluate the effect of coil geometry on the axial directed kinetic energy of the exhaust. Inductance measurements as a function of the axial and radial displacement of simulated current sheets from four coils of different geometries are t to a two-dimensional expression to allow the calculation of the Lorentz force at any relevant averaged current sheet location. This relation for two-dimensional inductance, along with an estimate of the maximum possible change in gas-dynamic pressure as the current sheet accelerates into downstream propellant, enables the expansion of a one-dimensional circuit model to two dimensions. The results of this two-dimensional model indicate that radial current sheet motion acts to rapidly decouple the current sheet from the driving coil, leading to losses in axial kinetic energy 10-50 times larger than estimations of the maximum available energy in the compressed propellant. The decreased available energy in the compressed propellant as compared to that of other inductive plasma propulsion concepts suggests that a recovery in the directed axial kinetic energy of the exhaust is unlikely, and that radial compression of the current sheet leads to a loss in exhaust velocity for the operating conditions considered here.

Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh—Rose neuron model

NASA Astrophysics Data System (ADS)

Jia, Bing

2014-03-01

A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh—Rose (HR) neuron model in many recent studies, which can interpret almost all of the previously simulated bifurcation processes with chaos in neural firing patterns. In the present paper, a comb-shaped chaotic region in a two-dimensional parameter space was reproduced, which presented different processes of period-adding bifurcations with chaos with changing one parameter and fixed the other parameter at different levels. In the biological experiments, different period-adding bifurcation scenarios with chaos by decreasing the extra-cellular calcium concentration were observed from some neural pacemakers at different levels of extra-cellular 4-aminopyridine concentration and from other pacemakers at different levels of extra-cellular caesium concentration. By using the nonlinear time series analysis method, the deterministic dynamics of the experimental chaotic firings were investigated. The period-adding bifurcations with chaos observed in the experiments resembled those simulated in the comb-shaped chaotic region using the HR model. The experimental results show that period-adding bifurcations with chaos are preserved in different two-dimensional parameter spaces, which provides evidence of the existence of the comb-shaped chaotic region and a demonstration of the simulation results in different two-dimensional parameter spaces in the HR neuron model. The results also present relationships between different firing patterns in two-dimensional parameter spaces.

A two-dimensional, time-dependent model of suspended sediment transport and bed reworking for continental shelves

USGS Publications Warehouse

Harris, C.K.; Wiberg, P.L.

2001-01-01

A two-dimensional, time-dependent solution to the transport equation is formulated to account for advection and diffusion of sediment suspended in the bottom boundary layer of continental shelves. This model utilizes a semi-implicit, upwind-differencing scheme to solve the advection-diffusion equation across a two-dimensional transect that is configured so that one dimension is the vertical, and the other is a horizontal dimension usually aligned perpendicular to shelf bathymetry. The model calculates suspended sediment concentration and flux; and requires as input wave properties, current velocities, sediment size distributions, and hydrodynamic sediment properties. From the calculated two-dimensional suspended sediment fluxes, we quantify the redistribution of shelf sediment, bed erosion, and deposition for several sediment sizes during resuspension events. The two-dimensional, time-dependent approach directly accounts for cross-shelf gradients in bed shear stress and sediment properties, as well as transport that occurs before steady-state suspended sediment concentrations have been attained. By including the vertical dimension in the calculations, we avoid depth-averaging suspended sediment concentrations and fluxes, and directly account for differences in transport rates and directions for fine and coarse sediment in the bottom boundary layer. A flux condition is used as the bottom boundary condition for the transport equation in order to capture time-dependence of the suspended sediment field. Model calculations demonstrate the significance of both time-dependent and spatial terms on transport and depositional patterns on continental shelves. ?? 2001 Elsevier Science Ltd. All rights reserved.

Crack Modelling for Radiography

NASA Astrophysics Data System (ADS)

Chady, T.; Napierała, L.

2010-02-01

In this paper, possibility of creation of three-dimensional crack models, both random type and based on real-life radiographic images is discussed. Method for storing cracks in a number of two-dimensional matrices, as well algorithm for their reconstruction into three-dimensional objects is presented. Also the possibility of using iterative algorithm for matching simulated images of cracks to real-life radiographic images is discussed.

Make a Halley's Comet Orbit Model.

ERIC Educational Resources Information Center

Podmore, Francis; Fleet, Richard W.

1985-01-01

Describes a simple three-dimensional model of Halley's Comet orbit (which is much more informative than a two-dimensional drawing) to illustrate spatial relationships and visualize how the comet moves relative to the earth. Instructions for model assembly are given along with a template which can be photocopied and glued to cardboard. (JN)

Three-dimensional numerical modeling of water quality and sediment-associated processes in natural lakes

USDA-ARS?s Scientific Manuscript database

This chapter presents the development and application of a three-dimensional water quality model for predicting the distributions of nutrients, phytoplankton, dissolved oxygen, etc., in natural lakes. In this model, the computational domain was divided into two parts: the water column and the bed se...

A model for near-wall dynamics in turbulent Rayleigh Bénard convection

NASA Astrophysics Data System (ADS)

Theerthan, S. Ananda; Arakeri, Jaywant H.

1998-10-01

Experiments indicate that turbulent free convection over a horizontal surface (e.g. Rayleigh Bénard convection) consists of essentially line plumes near the walls, at least for moderately high Rayleigh numbers. Based on this evidence, we propose here a two-dimensional model for near-wall dynamics in Rayleigh Bénard convection and in general for convection over heated horizontal surfaces. The model proposes a periodic array of steady laminar two-dimensional plumes. A plume is fed on either side by boundary layers on the wall. The results from the model are obtained in two ways. One of the methods uses the similarity solution of Rotem & Classen (1969) for the boundary layer and the similarity solution of Fuji (1963) for the plume. We have derived expressions for mean temperature and temperature and velocity fluctuations near the wall. In the second approach, we compute the two-dimensional flow field in a two-dimensional rectangular open cavity. The number of plumes in the cavity depends on the length of the cavity. The plume spacing is determined from the critical length at which the number of plumes increases by one. The results for average plume spacing and the distribution of r.m.s. temperature and velocity fluctuations are shown to be in acceptable agreement with experimental results.

Verification and transfer of thermal pollution model. Volume 5: Verification of 2-dimensional numerical model

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.

1982-01-01

The six-volume report: describes the theory of a three dimensional (3-D) mathematical thermal discharge model and a related one dimensional (1-D) model, includes model verification at two sites, and provides a separate user's manual for each model. The 3-D model has two forms: free surface and rigid lid. The former, verified at Anclote Anchorate (FL), allows a free air/water interface and is suited for significant surface wave heights compared to mean water depth; e.g., estuaries and coastal regions. The latter, verified at Lake Keowee (SC), is suited for small surface wave heights compared to depth (e.g., natural or man-made inland lakes) because surface elevation has been removed as a parameter. These models allow computation of time dependent velocity and temperature fields for given initial conditions and time-varying boundary conditions.

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

NASA Astrophysics Data System (ADS)

Lima, L. S.

2017-09-01

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

Above and beyond short-term mating, long-term mating is uniquely tied to human personality.

PubMed

Holtzman, Nicholas S; Strube, Michael J

2013-12-16

To what extent are personality traits and sexual strategies linked? The literature does not provide a clear answer, as it is based on the Sociosexuality model, a one-dimensional model that fails to measure long-term mating (LTM). An improved two-dimensional model separately assesses long-term and short-term mating (STM; Jackson and Kirkpatrick, 2007). In this paper, we link this two-dimensional model to an array of personality traits (Big 5, Dark Triad, and Schizoid Personality). We collected data from different sources (targets and peers; Study 1), and from different nations (United States, Study 1; India, Study 2). We demonstrate for the first time that, above and beyond STM, LTM captures variation in personality.

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

The subtle interplay between kinetic energy, interactions and dimensionality challenges our comprehension of strongly-correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions, 0 <= U / t <= 20 , and temperatures, down to kB T / t = 0 . 63(2) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities and double occupancies over the whole doping range, and hence our results constitute benchmarks for state-of-the-art theoretical approaches.

Optimization of the lithium/thionyl chloride battery

NASA Technical Reports Server (NTRS)

White, Ralph E.

1987-01-01

The progress which has been made in modeling the lithium/thionyl chloride cell over the past year and proposed research for the coming year are discussed. A one-dimensional mathematical model for a lithium/thionyl chloride cell has been developed and used to investigate methods of improving cell performance. During the course of the work a problem was detected with the banded solver being used. It was replaced with one more reliable. Future work may take one of two directions. The one-dimensional model could be augmented to include additional features and to investigate in more detail the cell temperature behavior, or a simplified two-dimensional model for the spirally wound design of this battery could be developed to investigate the heat flow within the cell.

Implementation of pattern generation algorithm in forming Gilmore and Gomory model for two dimensional cutting stock problem

NASA Astrophysics Data System (ADS)

Octarina, Sisca; Radiana, Mutia; Bangun, Putra B. J.

2018-01-01

Two dimensional cutting stock problem (CSP) is a problem in determining the cutting pattern from a set of stock with standard length and width to fulfill the demand of items. Cutting patterns were determined in order to minimize the usage of stock. This research implemented pattern generation algorithm to formulate Gilmore and Gomory model of two dimensional CSP. The constraints of Gilmore and Gomory model was performed to assure the strips which cut in the first stage will be used in the second stage. Branch and Cut method was used to obtain the optimal solution. Based on the results, it found many patterns combination, if the optimal cutting patterns which correspond to the first stage were combined with the second stage.

Numerical investigation of fluid mud motion using a three-dimensional hydrodynamic and two-dimensional fluid mud coupling model

NASA Astrophysics Data System (ADS)

Yang, Xiaochen; Zhang, Qinghe; Hao, Linnan

2015-03-01

A water-fluid mud coupling model is developed based on the unstructured grid finite volume coastal ocean model (FVCOM) to investigate the fluid mud motion. The hydrodynamics and sediment transport of the overlying water column are solved using the original three-dimensional ocean model. A horizontal two-dimensional fluid mud model is integrated into the FVCOM model to simulate the underlying fluid mud flow. The fluid mud interacts with the water column through the sediment flux, current, and shear stress. The friction factor between the fluid mud and the bed, which is traditionally determined empirically, is derived with the assumption that the vertical distribution of shear stress below the yield surface of fluid mud is identical to that of uniform laminar flow of Newtonian fluid in the open channel. The model is validated by experimental data and reasonable agreement is found. Compared with numerical cases with fixed friction factors, the results simulated with the derived friction factor exhibit the best agreement with the experiment, which demonstrates the necessity of the derivation of the friction factor.

ASTROP2-LE: A Mistuned Aeroelastic Analysis System Based on a Two Dimensional Linearized Euler Solver

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Srivastava, R.; Mehmed, Oral

2002-01-01

An aeroelastic analysis system for flutter and forced response analysis of turbomachines based on a two-dimensional linearized unsteady Euler solver has been developed. The ASTROP2 code, an aeroelastic stability analysis program for turbomachinery, was used as a basis for this development. The ASTROP2 code uses strip theory to couple a two dimensional aerodynamic model with a three dimensional structural model. The code was modified to include forced response capability. The formulation was also modified to include aeroelastic analysis with mistuning. A linearized unsteady Euler solver, LINFLX2D is added to model the unsteady aerodynamics in ASTROP2. By calculating the unsteady aerodynamic loads using LINFLX2D, it is possible to include the effects of transonic flow on flutter and forced response in the analysis. The stability is inferred from an eigenvalue analysis. The revised code, ASTROP2-LE for ASTROP2 code using Linearized Euler aerodynamics, is validated by comparing the predictions with those obtained using linear unsteady aerodynamic solutions.

Numerical simulations - Some results for the 2- and 3-D Hubbard models and a 2-D electron phonon model

NASA Technical Reports Server (NTRS)

Scalapino, D. J.; Sugar, R. L.; White, S. R.; Bickers, N. E.; Scalettar, R. T.

1989-01-01

Numerical simulations on the half-filled three-dimensional Hubbard model clearly show the onset of Neel order. Simulations of the two-dimensional electron-phonon Holstein model show the competition between the formation of a Peierls-CDW state and a superconducting state. However, the behavior of the partly filled two-dimensional Hubbard model is more difficult to determine. At half-filling, the antiferromagnetic correlations grow as T is reduced. Doping away from half-filling suppresses these correlations, and it is found that there is a weak attractive pairing interaction in the d-wave channel. However, the strength of the pair field susceptibility is weak at the temperatures and lattice sizes that have been simulated, and the nature of the low-temperature state of the nearly half-filled Hubbard model remains open.

Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations

NASA Astrophysics Data System (ADS)

Abdulwahhab, Muhammad Alim

2016-10-01

Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.

Student Learning about Biomolecular Self-Assembly Using Two Different External Representations

ERIC Educational Resources Information Center

Host, Gunnar E.; Larsson, Caroline; Olson, Arthur; Tibell, Lena A. E.

2013-01-01

Self-assembly is the fundamental but counterintuitive principle that explains how ordered biomolecular complexes form spontaneously in the cell. This study investigated the impact of using two external representations of virus self-assembly, an interactive tangible three-dimensional model and a static two-dimensional image, on student learning…

A coupled sharp-interface immersed boundary-finite-element method for flow-structure interaction with application to human phonation.

PubMed

Zheng, X; Xue, Q; Mittal, R; Beilamowicz, S

2010-11-01

A new flow-structure interaction method is presented, which couples a sharp-interface immersed boundary method flow solver with a finite-element method based solid dynamics solver. The coupled method provides robust and high-fidelity solution for complex flow-structure interaction (FSI) problems such as those involving three-dimensional flow and viscoelastic solids. The FSI solver is used to simulate flow-induced vibrations of the vocal folds during phonation. Both two- and three-dimensional models have been examined and qualitative, as well as quantitative comparisons, have been made with established results in order to validate the solver. The solver is used to study the onset of phonation in a two-dimensional laryngeal model and the dynamics of the glottal jet in a three-dimensional model and results from these studies are also presented.

Aeroacoustic theory for noncompact wing-gust interaction

NASA Technical Reports Server (NTRS)

Martinez, R.; Widnall, S. E.

1981-01-01

Three aeroacoustic models for noncompact wing-gust interaction were developed for subsonic flow. The first is that for a two dimensional (infinite span) wing passing through an oblique gust. The unsteady pressure field was obtained by the Wiener-Hopf technique; the airfoil loading and the associated acoustic field were calculated, respectively, by allowing the field point down on the airfoil surface, or by letting it go to infinity. The second model is a simple spanwise superposition of two dimensional solutions to account for three dimensional acoustic effects of wing rotation (for a helicopter blade, or some other rotating planform) and of finiteness of wing span. A three dimensional theory for a single gust was applied to calculate the acoustic signature in closed form due to blade vortex interaction in helicopters. The third model is that of a quarter infinite plate with side edge through a gust at high subsonic speed. An approximate solution for the three dimensional loading and the associated three dimensional acoustic field in closed form was obtained. The results reflected the acoustic effect of satisfying the correct loading condition at the side edge.

Spectroscopic properties of a two-dimensional time-dependent Cepheid model. I. Description and validation of the model

NASA Astrophysics Data System (ADS)

Vasilyev, V.; Ludwig, H.-G.; Freytag, B.; Lemasle, B.; Marconi, M.

2017-10-01

Context. Standard spectroscopic analyses of Cepheid variables are based on hydrostatic one-dimensional model atmospheres, with convection treated using various formulations of mixing-length theory. Aims: This paper aims to carry out an investigation of the validity of the quasi-static approximation in the context of pulsating stars. We check the adequacy of a two-dimensional time-dependent model of a Cepheid-like variable with focus on its spectroscopic properties. Methods: With the radiation-hydrodynamics code CO5BOLD, we construct a two-dimensional time-dependent envelope model of a Cepheid with Teff = 5600 K, log g = 2.0, solar metallicity, and a 2.8-day pulsation period. Subsequently, we perform extensive spectral syntheses of a set of artificial iron lines in local thermodynamic equilibrium. The set of lines allows us to systematically study effects of line strength, ionization stage, and excitation potential. Results: We evaluate the microturbulent velocity, line asymmetry, projection factor, and Doppler shifts. The microturbulent velocity, averaged over all lines, depends on the pulsational phase and varies between 1.5 and 2.7 km s-1. The derived projection factor lies between 1.23 and 1.27, which agrees with observational results. The mean Doppler shift is non-zero and negative, -1 km s-1, after averaging over several full periods and lines. This residual line-of-sight velocity (related to the "K-term") is primarily caused by horizontal inhomogeneities, and consequently we interpret it as the familiar convective blueshift ubiquitously present in non-pulsating late-type stars. Limited statistics prevent firm conclusions on the line asymmetries. Conclusions: Our two-dimensional model provides a reasonably accurate representation of the spectroscopic properties of a short-period Cepheid-like variable star. Some properties are primarily controlled by convective inhomogeneities rather than by the Cepheid-defining pulsations. Extended multi-dimensional modelling offers new insight into the nature of pulsating stars.

Suitability of a three-dimensional model to measure empathy and its relationship with social and normative adjustment in Spanish adolescents: a cross-sectional study.

PubMed

Herrera-López, Mauricio; Gómez-Ortiz, Olga; Ortega-Ruiz, Rosario; Jolliffe, Darrick; Romera, Eva M

2017-09-25

(1) To examine the psychometric properties of the Basic Empathy Scale (BES) with Spanish adolescents, comparing a two and a three-dimensional structure;(2) To analyse the relationship between the three-dimensional empathy and social and normative adjustment in school. Transversal and ex post facto retrospective study. Confirmatory factorial analysis, multifactorial invariance analysis and structural equations models were used. 747 students (51.3% girls) from Cordoba, Spain, aged 12-17 years (M=13.8; SD=1.21). The original two-dimensional structure was confirmed (cognitive empathy, affective empathy), but a three-dimensional structure showed better psychometric properties, highlighting the good fit found in confirmatory factorial analysis and adequate internal consistent valued, measured with Cronbach's alpha and McDonald's omega. Composite reliability and average variance extracted showed better indices for a three-factor model. The research also showed evidence of measurement invariance across gender. All the factors of the final three-dimensional BES model were direct and significantly associated with social and normative adjustment, being most strongly related to cognitive empathy. This research supports the advances in neuroscience, developmental psychology and psychopathology through a three-dimensional version of the BES, which represents an improvement in the original two-factorial model. The organisation of empathy in three factors benefits the understanding of social and normative adjustment in adolescents, in which emotional disengagement favours adjusted peer relationships. Psychoeducational interventions aimed at improving the quality of social life in schools should target these components of empathy. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

COMOC 2: Two-dimensional aerodynamics sequence, computer program user's guide

NASA Technical Reports Server (NTRS)

Manhardt, P. D.; Orzechowski, J. A.; Baker, A. J.

1977-01-01

The COMOC finite element fluid mechanics computer program system is applicable to diverse problem classes. The two dimensional aerodynamics sequence was established for solution of the potential and/or viscous and turbulent flowfields associated with subsonic flight of elementary two dimensional isolated airfoils. The sequence is constituted of three specific flowfield options in COMOC for two dimensional flows. These include the potential flow option, the boundary layer option, and the parabolic Navier-Stokes option. By sequencing through these options, it is possible to computationally construct a weak-interaction model of the aerodynamic flowfield. This report is the user's guide to operation of COMOC for the aerodynamics sequence.

Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential

NASA Astrophysics Data System (ADS)

Hussin, Véronique; Marquette, Ian

2011-03-01

We consider classical and quantum one and two-dimensional systems with ladder operators that satisfy generalized Heisenberg algebras. In the classical case, this construction is related to the existence of closed trajectories. In particular, we apply these results to the infinite well and Morse potentials. We discuss how the degeneracies of the permutation symmetry of quantum two-dimensional systems can be explained using products of ladder operators. These products satisfy interesting commutation relations. The two-dimensional Morse quantum system is also related to a generalized two-dimensional Morse supersymmetric model. Arithmetical or accidental degeneracies of such system are shown to be associated to additional supersymmetry.

EFDC1D - A ONE DIMENSIONAL HYDRODYNAMIC AND SEDIMENT TRANSPORT MODEL FOR RIVER AND STREAM NETWORKS: MODEL THEORY AND USERS GUIDE

EPA Science Inventory

This technical report describes the new one-dimensional (1D) hydrodynamic and sediment transport model EFDC1D. This model that can be applied to stream networks. The model code and two sample data sets are included on the distribution CD. EFDC1D can simulate bi-directional unstea...

Bearing-Load Modeling and Analysis Study for Mechanically Connected Structures

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.

2006-01-01

Bearing-load response for a pin-loaded hole is studied within the context of two-dimensional finite element analyses. Pin-loaded-hole configurations are representative of mechanically connected structures, such as a stiffener fastened to a rib of an isogrid panel, that are idealized as part of a larger structural component. Within this context, the larger structural component may be idealized as a two-dimensional shell finite element model to identify load paths and high stress regions. Finite element modeling and analysis aspects of a pin-loaded hole are considered in the present paper including the use of linear and nonlinear springs to simulate the pin-bearing contact condition. Simulating pin-connected structures within a two-dimensional finite element analysis model using nonlinear spring or gap elements provides an effective way for accurate prediction of the local effective stress state and peak forces.

Experimental study and modeling of atomic-scale friction in zigzag and armchair lattice orientations of MoS2.

PubMed

Li, Meng; Shi, Jialin; Liu, Lianqing; Yu, Peng; Xi, Ning; Wang, Yuechao

2016-01-01

Physical properties of two-dimensional materials, such as graphene, black phosphorus, molybdenum disulfide (MoS 2 ) and tungsten disulfide, exhibit significant dependence on their lattice orientations, especially for zigzag and armchair lattice orientations. Understanding of the atomic probe motion on surfaces with different orientations helps in the study of anisotropic materials. Unfortunately, there is no comprehensive model that can describe the probe motion mechanism. In this paper, we report a tribological study of MoS 2 in zigzag and armchair orientations. We observed a characteristic power spectrum and friction force values. To explain our results, we developed a modified, two-dimensional, stick-slip Tomlinson model that allows simulation of the probe motion on MoS 2 surfaces by combining the motion in the Mo layer and S layer. Our model fits well with the experimental data and provides a theoretical basis for tribological studies of two-dimensional materials.

Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?

NASA Astrophysics Data System (ADS)

Troisi, Antonio

2017-03-01

Determining the cosmological field equations is still very much debated and led to a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein theory like higher-order gravity theories and higher-dimensional ones. Both of these two different approaches allow one to define, at the effective level, Einstein field equations equipped with source-like energy-momentum tensors of geometrical origin. In this paper, the possibility is discussed to develop a five-dimensional fourth-order gravity model whose lower-dimensional reduction could provide an interpretation of cosmological four-dimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-D to 4-D reduction procedure. Five-dimensional f( R) field equations turn out to be equivalent, on the four-dimensional hypersurfaces orthogonal to the extra coordinate, to an Einstein-like cosmological model with three matter-energy tensors related with higher derivative and higher-dimensional counter-terms. By considering the gravity model with f(R)=f_0R^n the possibility is investigated to obtain five-dimensional power law solutions. The effective four-dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher-dimensional solutions.

Comparison between PVI2D and Abreu–Johnson’s Model for Petroleum Vapor Intrusion Assessment

PubMed Central

Yao, Yijun; Wang, Yue; Verginelli, Iason; Suuberg, Eric M.; Ye, Jianfeng

2018-01-01

Recently, we have developed a two-dimensional analytical petroleum vapor intrusion model, PVI2D (petroleum vapor intrusion, two-dimensional), which can help users to easily visualize soil gas concentration profiles and indoor concentrations as a function of site-specific conditions such as source strength and depth, reaction rate constant, soil characteristics, and building features. In this study, we made a full comparison of the results returned by PVI2D and those obtained using Abreu and Johnson’s three-dimensional numerical model (AJM). These comparisons, examined as a function of the source strength, source depth, and reaction rate constant, show that PVI2D can provide similar soil gas concentration profiles and source-to-indoor air attenuation factors (within one order of magnitude difference) as those by the AJM. The differences between the two models can be ascribed to some simplifying assumptions used in PVI2D and to some numerical limitations of the AJM in simulating strictly piecewise aerobic biodegradation and no-flux boundary conditions. Overall, the obtained results show that for cases involving homogenous source and soil, PVI2D can represent a valid alternative to more rigorous three-dimensional numerical models. PMID:29398981

A GENERALIZED TWO-COMPONENT MODEL OF SOLAR WIND TURBULENCE AND AB INITIO DIFFUSION MEAN-FREE PATHS AND DRIFT LENGTHSCALES OF COSMIC RAYS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wiengarten, T.; Fichtner, H.; Kleimann, J.

2016-12-10

We extend a two-component model for the evolution of fluctuations in the solar wind plasma so that it is fully three-dimensional (3D) and also coupled self-consistently to the large-scale magnetohydrodynamic equations describing the background solar wind. The two classes of fluctuations considered are a high-frequency parallel-propagating wave-like piece and a low-frequency quasi-two-dimensional component. For both components, the nonlinear dynamics is dominanted by quasi-perpendicular spectral cascades of energy. Driving of the fluctuations by, for example, velocity shear and pickup ions is included. Numerical solutions to the new model are obtained using the Cronos framework, and validated against previous simpler models. Comparing results frommore » the new model with spacecraft measurements, we find improved agreement relative to earlier models that employ prescribed background solar wind fields. Finally, the new results for the wave-like and quasi-two-dimensional fluctuations are used to calculate ab initio diffusion mean-free paths and drift lengthscales for the transport of cosmic rays in the turbulent solar wind.« less

Two-Dimensional Simulation of Left-Handed Metamaterial Flat Lens Using Remcon XFDTD

NASA Technical Reports Server (NTRS)

Wilson, Jeffrey D.; Reinert, Jason M.

2006-01-01

Remcom's XFDTD software was used to model the properties of a two-dimensional left-handed metamaterial (LHM) flat lens. The focusing capability and attenuation of the material were examined. The results showed strong agreement with experimental results and theoretical predictions of focusing effects and focal length. The inherent attenuation in the model corresponds well with the experimental results and implies that the code does a reasonably accurate job of modeling the actual metamaterial.

A two dimensional finite difference time domain analysis of the quiet zone fields of an anechoic chamber

NASA Technical Reports Server (NTRS)

Ryan, Deirdre A.; Luebbers, Raymond J.; Nguyen, Truong X.; Kunz, Karl S.; Steich, David J.

1992-01-01

Prediction of anechoic chamber performance is a difficult problem. Electromagnetic anechoic chambers exist for a wide range of frequencies but are typically very large when measured in wavelengths. Three dimensional finite difference time domain (FDTD) modeling of anechoic chambers is possible with current computers but at frequencies lower than most chamber design frequencies. However, two dimensional FDTD (2D-FTD) modeling enables much greater detail at higher frequencies and offers significant insight into compact anechoic chamber design and performance. A major subsystem of an anechoic chamber for which computational electromagnetic analyses exist is the reflector. First, an analysis of the quiet zone fields of a low frequency anechoic chamber produced by a uniform source and a reflector in two dimensions using the FDTD method is presented. The 2D-FDTD results are compared with results from a three dimensional corrected physical optics calculation and show good agreement. Next, a directional source is substituted for the uniform radiator. Finally, a two dimensional anechoic chamber geometry, including absorbing materials, is considered, and the 2D-FDTD results for these geometries appear reasonable.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

Phase Equilibria of Stored Chemical Energy Reactants.

DTIC Science & Technology

1984-07-25

aluminate-lithium ferrate system. Detection of a Li1 Al4/7Fe 3/704 compound: C. R. Acad. Sci., Ser. C, V. 273, No. 15, p. 888-90. McNicol, B. D. and Pott...thermodynamic properties of lithium ferrate (LiO.5Fe2 .504) and lithium aluminate (LiO 5Al 2 504) from 5 to 545 K: J. Chem. Thermodyn., V. 7, No. 7, p. 693- 2...1977, Study of low-temperature hydrothermal crystallization in lithium oxide-silicon dioxide-water, potassium oxide-silicon dioxide-water, and

Lateral tunneling through voltage-controlled barriers

NASA Technical Reports Server (NTRS)

Manion, S. J.; Bell, L. D.; Kaiser, W. J.; Maker, P. D.; Muller, R. E.

1991-01-01

The paper reports on a detailed experimental investigation of lateral tunneling between electrodes of a two-dimensional electron gas separated by the voltage-controlled barrier of a nanometer Schottky gate. The experimental data are modeled using the WKB method to calculate the tunneling probability of electrons through a barrier whose shape is determined from a solution of the two-dimensional Poisson equation. This model is in excellent agreement with the experimental data over a two order of magnitude range of current.

Effect of Shear Deformation and Continuity on Delamination Modelling with Plate Elements

NASA Technical Reports Server (NTRS)

Glaessgen, E. H.; Riddell, W. T.; Raju, I. S.

1998-01-01

The effects of several critical assumptions and parameters on the computation of strain energy release rates for delamination and debond configurations modeled with plate elements have been quantified. The method of calculation is based on the virtual crack closure technique (VCCT), and models that model the upper and lower surface of the delamination or debond with two-dimensional (2D) plate elements rather than three-dimensional (3D) solid elements. The major advantages of the plate element modeling technique are a smaller model size and simpler geometric modeling. Specific issues that are discussed include: constraint of translational degrees of freedom, rotational degrees of freedom or both in the neighborhood of the crack tip; element order and assumed shear deformation; and continuity of material properties and section stiffness in the vicinity of the debond front, Where appropriate, the plate element analyses are compared with corresponding two-dimensional plane strain analyses.

Two-dimensional random surface model for asperity-contact in elastohydrodynamic lubrication

NASA Technical Reports Server (NTRS)

Coy, J. J.; Sidik, S. M.

1979-01-01

Relations for the asperity-contact time function during elastohydrodynamic lubrication of a ball bearing are presented. The analysis is based on a two-dimensional random surface model, and actual profile traces of the bearing surfaces are used as statistical sample records. The results of the analysis show that transition from 90 percent contact to 1 percent contact occurs within a dimensionless film thickness range of approximately four to five. This thickness ratio is several times large than reported in the literature where one-dimensional random surface models were used. It is shown that low pass filtering of the statistical records will bring agreement between the present results and those in the literature.

A MacCormack-TVD finite difference method to simulate the mass flow in mountainous terrain with variable computational domain

NASA Astrophysics Data System (ADS)

Ouyang, Chaojun; He, Siming; Xu, Qiang; Luo, Yu; Zhang, Wencheng

2013-03-01

A two-dimensional mountainous mass flow dynamic procedure solver (Massflow-2D) using the MacCormack-TVD finite difference scheme is proposed. The solver is implemented in Matlab on structured meshes with variable computational domain. To verify the model, a variety of numerical test scenarios, namely, the classical one-dimensional and two-dimensional dam break, the landslide in Hong Kong in 1993 and the Nora debris flow in the Italian Alps in 2000, are executed, and the model outputs are compared with published results. It is established that the model predictions agree well with both the analytical solution as well as the field observations.

One-dimensional and two-dimensional hydrodynamic modelling derived flow properties: Impacts on aquatic habitat quality predictions

Treesearch

Rohan Benjankar; Daniele Tonina; James McKean

2014-01-01

Studies of the effects of hydrodynamic model dimensionality on simulated flow properties and derived quantities such as aquatic habitat quality are limited. It is important to close this knowledge gap especially now that entire river networks can be mapped at the microhabitat scale due to the advent of point-cloud techniques. This study compares flow properties, such...

Computer modelling of grain microstructure in three dimensions

NASA Astrophysics Data System (ADS)

Narayan, K. Lakshmi

We present a program that generates the two-dimensional micrographs of a three dimensional grain microstructure. The code utilizes a novel scanning, pixel mapping technique to secure statistical distributions of surface areas, grain sizes, aspect ratios, perimeters, number of nearest neighbors and volumes of the randomly nucleated particles. The program can be used for comparing the existing theories of grain growth, and interpretation of two-dimensional microstructure of three-dimensional samples. Special features have been included to minimize the computation time and resource requirements.

An integrated approach to reservoir modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Donaldson, K.

1993-08-01

The purpose of this research is to evaluate the usefulness of the following procedural and analytical methods in investigating the heterogeneity of the oil reserve for the Mississipian Big Injun Sandstone of the Granny Creek field, Clay and Roane counties, West Virginia: (1) relational database, (2) two-dimensional cross sections, (3) true three-dimensional modeling, (4) geohistory analysis, (5) a rule-based expert system, and (6) geographical information systems. The large data set could not be effectively integrated and interpreted without this approach. A relational database was designed to fully integrate three- and four-dimensional data. The database provides an effective means for maintainingmore » and manipulating the data. A two-dimensional cross section program was designed to correlate stratigraphy, depositional environments, porosity, permeability, and petrographic data. This flexible design allows for additional four-dimensional data. Dynamic Graphics[sup [trademark

Two-Dimensional Computational Model for Wave Rotor Flow Dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.

1996-01-01

A two-dimensional (theta,z) Navier-Stokes solver for multi-port wave rotor flow simulation is described. The finite-volume form of the unsteady thin-layer Navier-Stokes equations are integrated in time on multi-block grids that represent the stationary inlet and outlet ports and the moving rotor passages of the wave rotor. Computed results are compared with three-port wave rotor experimental data. The model is applied to predict the performance of a planned four-port wave rotor experiment. Two-dimensional flow features that reduce machine performance and influence rotor blade and duct wall thermal loads are identified. The performance impact of rounding the inlet port wall, to inhibit separation during passage gradual opening, is assessed.

Two-dimensional electronic spectra of the photosynthetic apparatus of green sulfur bacteria

NASA Astrophysics Data System (ADS)

Kramer, Tobias; Rodriguez, Mirta

2017-03-01

Advances in time resolved spectroscopy have provided new insight into the energy transmission in natural photosynthetic complexes. Novel theoretical tools and models are being developed in order to explain the experimental results. We provide a model calculation for the two-dimensional electronic spectra of Cholorobaculum tepidum which correctly describes the main features and transfer time scales found in recent experiments. From our calculation one can infer the coupling of the antenna chlorosome with the environment and the coupling between the chlorosome and the Fenna-Matthews-Olson complex. We show that environment assisted transport between the subunits is the required mechanism to reproduce the experimental two-dimensional electronic spectra.

A critical assessment of flux and source term closures in shallow water models with porosity for urban flood simulations

NASA Astrophysics Data System (ADS)

Guinot, Vincent

2017-11-01

The validity of flux and source term formulae used in shallow water models with porosity for urban flood simulations is assessed by solving the two-dimensional shallow water equations over computational domains representing periodic building layouts. The models under assessment are the Single Porosity (SP), the Integral Porosity (IP) and the Dual Integral Porosity (DIP) models. 9 different geometries are considered. 18 two-dimensional initial value problems and 6 two-dimensional boundary value problems are defined. This results in a set of 96 fine grid simulations. Analysing the simulation results leads to the following conclusions: (i) the DIP flux and source term models outperform those of the SP and IP models when the Riemann problem is aligned with the main street directions, (ii) all models give erroneous flux closures when is the Riemann problem is not aligned with one of the main street directions or when the main street directions are not orthogonal, (iii) the solution of the Riemann problem is self-similar in space-time when the street directions are orthogonal and the Riemann problem is aligned with one of them, (iv) a momentum balance confirms the existence of the transient momentum dissipation model presented in the DIP model, (v) none of the source term models presented so far in the literature allows all flow configurations to be accounted for(vi) future laboratory experiments aiming at the validation of flux and source term closures should focus on the high-resolution, two-dimensional monitoring of both water depth and flow velocity fields.

Field-scale and wellbore modeling of compaction-induced casing failures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hilbert, L.B. Jr.; Gwinn, R.L.; Moroney, T.A.

1999-06-01

Presented in this paper are the results and verification of field- and wellbore-scale large deformation, elasto-plastic, geomechanical finite element models of reservoir compaction and associated casing damage. The models were developed as part of a multidisciplinary team project to reduce the number of costly well failures in the diatomite reservoir of the South Belridge Field near Bakersfield, California. Reservoir compaction of high porosity diatomite rock induces localized shearing deformations on horizontal weak-rock layers and geologic unconformities. The localized shearing deformations result in casing damage or failure. Two-dimensional, field-scale finite element models were used to develop relationships between field operations, surfacemore » subsidence, and shear-induced casing damage. Pore pressures were computed for eighteen years of simulated production and water injection, using a three-dimensional reservoir simulator. The pore pressures were input to the two-dimensional geomechanical field-scale model. Frictional contact surfaces were used to model localized shear deformations. To capture the complex casing-cement-rock interaction that governs casing damage and failure, three-dimensional models of a wellbore were constructed, including a frictional sliding surface to model localized shear deformation. Calculations were compared to field data for verification of the models.« less

Ordering of rods near planar and curved surfaces

NASA Astrophysics Data System (ADS)

Izzo, Dora; de Oliveira, Mário J.

2018-01-01

We study the orientational profile of a semi-infinite system of cylinders bounded in two different ways: by a flat and by a curved wall. The latter corresponds to the interior of a spherical shell, where the dimensions of the rods are comparable to the radius of curvature of the container: they have to accomodate to fill the available space, leading to a rich orientation profile. In order to study these problems, we make a mapping onto a three-state Potts model on a semi-infinite lattice, which is solved using a mean-field approach; we fix the boundary conditions on the surface and in the bulk. In the case of a curved surface, the increase in the effective volume interactions towards the bulk, due to compression, is obtained by increasing the nearest neighbor interactions. The mean-field equations are iterated numerically and we obtain various interesting results concerning the free energy and the orientation profile. We show that there is always a first order transition and the stability of the coexisting phases is strongly affected by the surface. When the surface is disordered and the bulk ordered, the profile may present a step that depends on the degree of disorder on the surface, on the rate of increase of the particle interactions and on the surface external potential. The existence of this step may be relevant to applications in nanotechnology.

Application of Hyperspectral Techniques to Monitoring and Management of Invasive Plant Species Infestation

DTIC Science & Technology

2008-01-01

the sensor is a data cloud in multi- dimensional space with each band generating an axis of dimension. When the data cloud is viewed in two or three...endmember of interest is not a true endmember in the data space . A ) B) Figure 8: Linear mixture models. A ) two- dimensional ...multi- dimensional space . A classifier is a computer algorithm that takes

Compactification on phase space

NASA Astrophysics Data System (ADS)

Lovelady, Benjamin; Wheeler, James

2016-03-01

A major challenge for string theory is to understand the dimensional reduction required for comparison with the standard model. We propose reducing the dimension of the compactification by interpreting some of the extra dimensions as the energy-momentum portion of a phase-space. Such models naturally arise as generalized quotients of the conformal group called biconformal spaces. By combining the standard Kaluza-Klein approach with such a conformal gauge theory, we may start from the conformal group of an n-dimensional Euclidean space to form a 2n-dimensional quotient manifold with symplectic structure. A pair of involutions leads naturally to two n-dimensional Lorentzian manifolds. For n = 5, this leaves only two extra dimensions, with a countable family of possible compactifications and an SO(5) Yang-Mills field on the fibers. Starting with n=6 leads to 4-dimensional compactification of the phase space. In the latter case, if the two dimensions each from spacetime and momentum space are compactified onto spheres, then there is an SU(2)xSU(2) (left-right symmetric electroweak) field between phase and configuration space and an SO(6) field on the fibers. Such a theory, with minor additional symmetry breaking, could contain all parts of the standard model.

Learning of Cross-Sectional Anatomy Using Clay Models

ERIC Educational Resources Information Center

Oh, Chang-Seok; Kim, Ji-Young; Choe, Yeon Hyeon

2009-01-01

We incorporated clay modeling into gross anatomy and neuro-anatomy courses to help students understand cross-sectional anatomy. By making clay models, cutting them and comparing cut surfaces to CT and MR images, students learned how cross-sectional two-dimensional images were created from three-dimensional structure of human organs. Most students…

A novel analytical model for scattering limited electron transport in nano-dimensional InAlAs/InGaAs heterostructure for cryogenic applications

NASA Astrophysics Data System (ADS)

Sharma, Neetika; Verma, Neha; Jogi, Jyotika

2017-11-01

This paper models the scattering limited electron transport in a nano-dimensional In0.52Al0.48As/In0.53Ga0.47As/InP heterostructure. An analytical model for temperature dependent sheet carrier concentration and carrier mobility in a two dimensional electron gas, confined in a triangular potential well has been developed. The model accounts for all the major scattering process including ionized impurity scattering and lattice scattering. Quantum mechanical variational technique is employed for studying the intrasubband scattering mechanism in the two dimensional electron gas. Results of various scattering limited structural parameters such as energy band-gap and functional parameters such as sheet carrier concentration, scattering rate and mobility are presented. The model corroborates the dominance of ionized impurity scattering mechanism at low temperatures and that of lattice scattering at high temperatures, both in turn limiting the carrier mobility. Net mobility obtained taking various scattering mechanisms into account has been found in agreement with earlier reported results, thus validating the model.

Music Signal Processing Using Vector Product Neural Networks

NASA Astrophysics Data System (ADS)

Fan, Z. C.; Chan, T. S.; Yang, Y. H.; Jang, J. S. R.

2017-05-01

We propose a novel neural network model for music signal processing using vector product neurons and dimensionality transformations. Here, the inputs are first mapped from real values into three-dimensional vectors then fed into a three-dimensional vector product neural network where the inputs, outputs, and weights are all three-dimensional values. Next, the final outputs are mapped back to the reals. Two methods for dimensionality transformation are proposed, one via context windows and the other via spectral coloring. Experimental results on the iKala dataset for blind singing voice separation confirm the efficacy of our model.

Stationary Solutions of A One-dimensional Thermodynamic Radiative Sea Ice Model

NASA Astrophysics Data System (ADS)

Taylor, P. D.; Feltham, D. L.

A one-dimensional thermodynamic model of sea ice is coupled to a two-stream radi- ation model and the stationary (time-independent) solutions analysed. The stationary model represents the state of the sea ice subjected to persistent or slowly varying forc- ing. Two physically realisable stationary solutions (real and positive ice thickness) occur for a large range of positive oceanic heat flux ( 20,Wm-2). The two station- ary solutions are due to the two-stream radiation model, which allows radiation to be reflected at the ice-ocean interface. Thick ice ( 1,m) only absorbs radiation near its surface, whereas thin ice ( 0.1,m) absorbs radiation across its entire depth. The two stationary solutions are caused by these two different radiative regimes. The results of this analysis have relevance to the interpretation and implementation of thermody- namic models of sea ice and the interpretation of thickness data.

Multi-GPU hybrid programming accelerated three-dimensional phase-field model in binary alloy

NASA Astrophysics Data System (ADS)

Zhu, Changsheng; Liu, Jieqiong; Zhu, Mingfang; Feng, Li

2018-03-01

In the process of dendritic growth simulation, the computational efficiency and the problem scales have extremely important influence on simulation efficiency of three-dimensional phase-field model. Thus, seeking for high performance calculation method to improve the computational efficiency and to expand the problem scales has a great significance to the research of microstructure of the material. A high performance calculation method based on MPI+CUDA hybrid programming model is introduced. Multi-GPU is used to implement quantitative numerical simulations of three-dimensional phase-field model in binary alloy under the condition of multi-physical processes coupling. The acceleration effect of different GPU nodes on different calculation scales is explored. On the foundation of multi-GPU calculation model that has been introduced, two optimization schemes, Non-blocking communication optimization and overlap of MPI and GPU computing optimization, are proposed. The results of two optimization schemes and basic multi-GPU model are compared. The calculation results show that the use of multi-GPU calculation model can improve the computational efficiency of three-dimensional phase-field obviously, which is 13 times to single GPU, and the problem scales have been expanded to 8193. The feasibility of two optimization schemes is shown, and the overlap of MPI and GPU computing optimization has better performance, which is 1.7 times to basic multi-GPU model, when 21 GPUs are used.

A new model for two-dimensional numerical simulation of pseudo-2D gas-solids fluidized beds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Tingwen; Zhang, Yongmin

2013-10-11

Pseudo-two dimensional (pseudo-2D) fluidized beds, for which the thickness of the system is much smaller than the other two dimensions, is widely used to perform fundamental studies on bubble behavior, solids mixing, or clustering phenomenon in different gas-solids fluidization systems. The abundant data from such experimental systems are very useful for numerical model development and validation. However, it has been reported that two-dimensional (2D) computational fluid dynamic (CFD) simulations of pseudo-2D gas-solids fluidized beds usually predict poor quantitative agreement with the experimental data, especially for the solids velocity field. In this paper, a new model is proposed to improve themore » 2D numerical simulations of pseudo-2D gas-solids fluidized beds by properly accounting for the frictional effect of the front and back walls. Two previously reported pseudo-2D experimental systems were simulated with this model. Compared to the traditional 2D simulations, significant improvements in the numerical predictions have been observed and the predicted results are in better agreement with the available experimental data.« less

Scalar quantum chromodynamics in two dimensions and parton model. [Scalar quarks, SU(N) groups

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shei, S.S.; Tsao, H.S.

1977-05-01

The SU(N) scalar quantum chromodynamics in two space-time dimensions in the large N limit are studied. This is the model of color gauge fields interacting with scalar quarks. It is found that the consensual properties of the four dimensional QCD, i.e., the infrared slavery, quark confinement, the charmonium picture etc. are all realized. Moreover, the current in this model mimics nicely the behaviors of current in the four dimensional QCD, in contrast to the original model of 't Hooft.

Computer modeling of inversion layer MOS solar cells and arrays

NASA Technical Reports Server (NTRS)

Ho, Fat Duen

1991-01-01

A two dimensional numerical model of the inversion layer metal insulator semiconductor (IL/MIS) solar cell is proposed by using the finite element method. The two-dimensional current flow in the device is taken into account in this model. The electrostatic potential distribution, the electron concentration distribution, and the hole concentration distribution for different terminal voltages are simulated. The results of simple calculation are presented. The existing problems for this model are addressed. Future work is proposed. The MIS structures are studied and some of the results are reported.

A finite area scheme for shallow granular flows on three-dimensional surfaces

NASA Astrophysics Data System (ADS)

Rauter, Matthias

2017-04-01

Shallow granular flow models have become a popular tool for the estimation of natural hazards, such as landslides, debris flows and avalanches. The shallowness of the flow allows to reduce the three-dimensional governing equations to a quasi two-dimensional system. Three-dimensional flow fields are replaced by their depth-integrated two-dimensional counterparts, which yields a robust and fast method [1]. A solution for a simple shallow granular flow model, based on the so-called finite area method [3] is presented. The finite area method is an adaption of the finite volume method [4] to two-dimensional curved surfaces in three-dimensional space. This method handles the three dimensional basal topography in a simple way, making the model suitable for arbitrary (but mildly curved) topography, such as natural terrain. Furthermore, the implementation into the open source software OpenFOAM [4] is shown. OpenFOAM is a popular computational fluid dynamics application, designed so that the top-level code mimics the mathematical governing equations. This makes the code easy to read and extendable to more sophisticated models. Finally, some hints on how to get started with the code and how to extend the basic model will be given. I gratefully acknowledge the financial support by the OEAW project "beyond dense flow avalanches". Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics 199, 177-215. Ferziger, J. & Peric, M. 2002 Computational methods for fluid dynamics, 3rd edn. Springer. Tukovic, Z. & Jasak, H. 2012 A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow. Computers & fluids 55, 70-84. Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in physics 12(6), 620-631.

Modeling and control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.

1988-01-01

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

Strong second harmonic generation in two-dimensional ferroelectric IV-monochalcogenides

NASA Astrophysics Data System (ADS)

Panday, Suman Raj; Fregoso, Benjamin M.

2017-11-01

The two-dimensional ferroelectrics GeS, GeSe, SnS and SnSe are expected to have large spontaneous in-plane electric polarization and enhanced shift-current response. Using density functional methods, we show that these materials also exhibit the largest effective second harmonic generation reported so far. It can reach magnitudes up to 10~nm~V-1 which is about an order of magnitude larger than that of prototypical GaAs. To rationalize this result we model the optical response with a simple one-dimensional two-band model along the spontaneous polarization direction. Within this model the second-harmonic generation tensor is proportional to the shift-current response tensor. The large shift current and second harmonic responses of GeS, GeSe, SnS and SnSe make them promising non-linear materials for optoelectronic applications.

A small-scale turbulence model

NASA Technical Reports Server (NTRS)

Lundgren, T. S.

1992-01-01

A model for the small-scale structure of turbulence is reformulated in such a way that it may be conveniently computed. The model is an ensemble of randomly oriented structured two dimensional vortices stretched by an axially symmetric strain flow. The energy spectrum of the resulting flow may be expressed as a time integral involving only the enstrophy spectrum of the time evolving two-dimensional cross section flow, which may be obtained numerically. Examples are given in which a k(exp -5/3) spectrum is obtained by this method without using large wave number asymptotic analysis. The k(exp -5/3) inertial range spectrum is shown to be related to the existence of a self-similar enstrophy preserving range in the two-dimensional enstrophy spectrum. The results are insensitive to time dependence of the strain-rate, including even intermittent on-or-off strains.

Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

NASA Astrophysics Data System (ADS)

Jost, Jürgen; Keßler, Enno; Tolksdorf, Jürgen; Wu, Ruijun; Zhu, Miaomiao

2018-02-01

We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler-Lagrange equations of the two-dimensional nonlinear sigma model with gravitino is calculated explicitly. The gravitino terms pose additional analytic difficulties to show smoothness of its weak solutions which are overcome using Rivière's regularity theory and Riesz potential theory.

Advantages of multigrid methods for certifying the accuracy of PDE modeling

NASA Technical Reports Server (NTRS)

Forester, C. K.

1981-01-01

Numerical techniques for assessing and certifying the accuracy of the modeling of partial differential equations (PDE) to the user's specifications are analyzed. Examples of the certification process with conventional techniques are summarized for the three dimensional steady state full potential and the two dimensional steady Navier-Stokes equations using fixed grid methods (FG). The advantages of the Full Approximation Storage (FAS) scheme of the multigrid technique of A. Brandt compared with the conventional certification process of modeling PDE are illustrated in one dimension with the transformed potential equation. Inferences are drawn for how MG will improve the certification process of the numerical modeling of two and three dimensional PDE systems. Elements of the error assessment process that are common to FG and MG are analyzed.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schroer, Bert

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

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

NASA Astrophysics Data System (ADS)

Schroer, Bert

2006-02-01

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

Dynamics of a neuron model in different two-dimensional parameter-spaces

NASA Astrophysics Data System (ADS)

Rech, Paulo C.

2011-03-01

We report some two-dimensional parameter-space diagrams numerically obtained for the multi-parameter Hindmarsh-Rose neuron model. Several different parameter planes are considered, and we show that regardless of the combination of parameters, a typical scenario is preserved: for all choice of two parameters, the parameter-space presents a comb-shaped chaotic region immersed in a large periodic region. We also show that exist regions close these chaotic region, separated by the comb teeth, organized themselves in period-adding bifurcation cascades.

Two-dimensional heteroclinic attractor in the generalized Lotka-Volterra system

NASA Astrophysics Data System (ADS)

Afraimovich, Valentin S.; Moses, Gregory; Young, Todd

2016-05-01

We study a simple dynamical model exhibiting sequential dynamics. We show that in this model there exist sets of parameter values for which a cyclic chain of saddle equilibria, O k , k=1,\\ldots,p , have two-dimensional unstable manifolds that contain orbits connecting each O k to the next two equilibrium points O k+1 and O k+2 in the chain ({{O}p+1}={{O}1} ). We show that the union of these equilibria and their unstable manifolds form a two-dimensional surface with a boundary that is homeomorphic to a cylinder if p is even and a Möbius strip if p is odd. If, further, each equilibrium in the chain satisfies a condition called ‘dissipativity’, then this surface is asymptotically stable.

Differences in aquatic habitat quality as an impact of one- and two-dimensional hydrodynamic model simulated flow variables

NASA Astrophysics Data System (ADS)

Benjankar, R. M.; Sohrabi, M.; Tonina, D.; McKean, J. A.

2013-12-01

Aquatic habitat models utilize flow variables which may be predicted with one-dimensional (1D) or two-dimensional (2D) hydrodynamic models to simulate aquatic habitat quality. Studies focusing on the effects of hydrodynamic model dimensionality on predicted aquatic habitat quality are limited. Here we present the analysis of the impact of flow variables predicted with 1D and 2D hydrodynamic models on simulated spatial distribution of habitat quality and Weighted Usable Area (WUA) for fall-spawning Chinook salmon. Our study focuses on three river systems located in central Idaho (USA), which are a straight and pool-riffle reach (South Fork Boise River), small pool-riffle sinuous streams in a large meadow (Bear Valley Creek) and a steep-confined plane-bed stream with occasional deep forced pools (Deadwood River). We consider low and high flows in simple and complex morphologic reaches. Results show that 1D and 2D modeling approaches have effects on both the spatial distribution of the habitat and WUA for both discharge scenarios, but we did not find noticeable differences between complex and simple reaches. In general, the differences in WUA were small, but depended on stream type. Nevertheless, spatially distributed habitat quality difference is considerable in all streams. The steep-confined plane bed stream had larger differences between aquatic habitat quality defined with 1D and 2D flow models compared to results for streams with well defined macro-topographies, such as pool-riffle bed forms. KEY WORDS: one- and two-dimensional hydrodynamic models, habitat modeling, weighted usable area (WUA), hydraulic habitat suitability, high and low discharges, simple and complex reaches

Numerical modeling of surface wave development under the action of wind

NASA Astrophysics Data System (ADS)

Chalikov, Dmitry

2018-06-01

The numerical modeling of two-dimensional surface wave development under the action of wind is performed. The model is based on three-dimensional equations of potential motion with a free surface written in a surface-following nonorthogonal curvilinear coordinate system in which depth is counted from a moving surface. A three-dimensional Poisson equation for the velocity potential is solved iteratively. A Fourier transform method, a second-order accuracy approximation of vertical derivatives on a stretched vertical grid and fourth-order Runge-Kutta time stepping are used. Both the input energy to waves and dissipation of wave energy are calculated on the basis of earlier developed and validated algorithms. A one-processor version of the model for PC allows us to simulate an evolution of the wave field with thousands of degrees of freedom over thousands of wave periods. A long-time evolution of a two-dimensional wave structure is illustrated by the spectra of wave surface and the input and output of energy.

Examination of the Effects of Dimensionality on Cognitive Processing in Science: A Computational Modeling Experiment Comparing Online Laboratory Simulations and Serious Educational Games

NASA Astrophysics Data System (ADS)

Lamb, Richard L.

2016-02-01

Within the last 10 years, new tools for assisting in the teaching and learning of academic skills and content within the context of science have arisen. These new tools include multiple types of computer software and hardware to include (video) games. The purpose of this study was to examine and compare the effect of computer learning games in the form of three-dimensional serious educational games, two-dimensional online laboratories, and traditional lecture-based instruction in the context of student content learning in science. In particular, this study examines the impact of dimensionality, or the ability to move along the X-, Y-, and Z-axis in the games. Study subjects ( N = 551) were randomly selected using a stratified sampling technique. Independent strata subsamples were developed based upon the conditions of serious educational games, online laboratories, and lecture. The study also computationally models a potential mechanism of action and compares two- and three-dimensional learning environments. F test results suggest a significant difference for the main effect of condition across the factor of content gain score with large effect. Overall, comparisons using computational models suggest that three-dimensional serious educational games increase the level of success in learning as measured with content examinations through greater recruitment and attributional retraining of cognitive systems. The study supports assertions in the literature that the use of games in higher dimensions (i.e., three-dimensional versus two-dimensional) helps to increase student understanding of science concepts.

[The reconstruction of two-dimensional distributions of gas concentration in the flat flame based on tunable laser absorption spectroscopy].

PubMed

Jiang, Zhi-Shen; Wang, Fei; Xing, Da-Wei; Xu, Ting; Yan, Jian-Hua; Cen, Ke-Fa

2012-11-01

The experimental method by using the tunable diode laser absorption spectroscopy combined with the model and algo- rithm was studied to reconstruct the two-dimensional distribution of gas concentration The feasibility of the reconstruction program was verified by numerical simulation A diagnostic system consisting of 24 lasers was built for the measurement of H2O in the methane/air premixed flame. The two-dimensional distribution of H2O concentration in the flame was reconstructed, showing that the reconstruction results reflect the real two-dimensional distribution of H2O concentration in the flame. This diagnostic scheme provides a promising solution for combustion control.

Two Dimensional Mechanism for Insect Hovering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jane Wang, Z.

2000-09-04

Resolved computation of two dimensional insect hovering shows for the first time that a two dimensional hovering motion can generate enough lift to support a typical insect weight. The computation reveals a two dimensional mechanism of creating a downward dipole jet of counterrotating vortices, which are formed from leading and trailing edge vortices. The vortex dynamics further elucidates the role of the phase relation between the wing translation and rotation in lift generation and explains why the instantaneous forces can reach a periodic state after only a few strokes. The model predicts the lower limits in Reynolds number and amplitudemore » above which the averaged forces are sufficient. (c) 2000 The American Physical Society.« less

A NetCDF version of the two-dimensional energy balance model based on the full multigrid algorithm

NASA Astrophysics Data System (ADS)

Zhuang, Kelin; North, Gerald R.; Stevens, Mark J.

A NetCDF version of the two-dimensional energy balance model based on the full multigrid method in Fortran is introduced for both pedagogical and research purposes. Based on the land-sea-ice distribution, orbital elements, greenhouse gases concentration, and albedo, the code calculates the global seasonal surface temperature. A step-by-step guide with examples is provided for practice.

Monte Carlo calculation of dynamical properties of the two-dimensional Hubbard model

NASA Technical Reports Server (NTRS)

White, S. R.; Scalapino, D. J.; Sugar, R. L.; Bickers, N. E.

1989-01-01

A new method is introduced for analytically continuing imaginary-time data from quantum Monte Carlo calculations to the real-frequency axis. The method is based on a least-squares-fitting procedure with constraints of positivity and smoothness on the real-frequency quantities. Results are shown for the single-particle spectral-weight function and density of states for the half-filled, two-dimensional Hubbard model.

Critical behavior of two-dimensional vesicles in the deflated regime

NASA Technical Reports Server (NTRS)

Banavar, Jayanth R.; Maritan, Amos; Stella, Attilio

1991-01-01

The critical behavior of two-dimensional vesicles in the deflated regime is studied analytically using a mapping onto a gauge model, scaling arguments, and exact inequalities. In agreement with the results of earlier studies the critical behavior is governed by a branched-polymer fixed point. The shape of the critical line in the gauge model is deduced in the weak and in the infinitely deflated regime.

Linear and non-linear infrared response of one-dimensional vibrational Holstein polarons in the anti-adiabatic limit: Optical and acoustical phonon models

NASA Astrophysics Data System (ADS)

Falvo, Cyril

2018-02-01

The theory of linear and non-linear infrared response of vibrational Holstein polarons in one-dimensional lattices is presented in order to identify the spectral signatures of self-trapping phenomena. Using a canonical transformation, the optical response is computed from the small polaron point of view which is valid in the anti-adiabatic limit. Two types of phonon baths are considered: optical phonons and acoustical phonons, and simple expressions are derived for the infrared response. It is shown that for the case of optical phonons, the linear response can directly probe the polaron density of states. The model is used to interpret the experimental spectrum of crystalline acetanilide in the C=O range. For the case of acoustical phonons, it is shown that two bound states can be observed in the two-dimensional infrared spectrum at low temperature. At high temperature, analysis of the time-dependence of the two-dimensional infrared spectrum indicates that bath mediated correlations slow down spectral diffusion. The model is used to interpret the experimental linear-spectroscopy of model α-helix and β-sheet polypeptides. This work shows that the Davydov Hamiltonian cannot explain the observations in the NH stretching range.

Thermodynamics of a Higher Dimensional Noncommutative Inspired Anti-de Sitter-Einstein-Born-Infeld Black Hole

NASA Astrophysics Data System (ADS)

González, Angélica; Linares, Román; Maceda, Marco; Sánchez-Santos, Oscar

2018-04-01

We analyze noncommutative deformations of a higher dimensional anti-de Sitter-Einstein-Born-Infeld black hole. Two models based on noncommutative inspired distributions of mass and charge are discussed and their thermodynamical properties such as the equation of state are explicitly calculated. In the (3 + 1)-dimensional case the Gibbs energy function of each model is used to discuss the presence of phase transitions.

Bak-Tang-Wiesenfeld model in the upper critical dimension: Induced criticality in lower-dimensional subsystems

NASA Astrophysics Data System (ADS)

Dashti-Naserabadi, H.; Najafi, M. N.

2017-10-01

We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension Du=4 . After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the d -dimensional cross sections and the d -dimensional BTW model for d =2 and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops df, which is found to be 1.50 ±0.02 ≈3/2 =dfGFF .