The probability of connectivity in a hyperbolic model of complex networks
Bode, Michel; Fountoulakis, Nikolaos; Müller, Tobias
2016-01-01
We consider a model for complex networks that was introduced by Krioukov et al. (Phys Rev E 82 (2010) 036106). In this model, N points are chosen randomly inside a disk on the hyperbolic plane according to a distorted version of the uniform distribution and any two of them are joined by an edge if
Hyperbolic isometries of systolic complexes
DEFF Research Database (Denmark)
Prytula, Tomasz Pawel
The main topics of this thesis are the geometric features of systolic complexesarising from the actions of hyperbolic isometries. The thesis consists ofan introduction followed by two articles.Given a hyperbolic isometry h of a systolic complex X, our central theme isto study the minimal displace......The main topics of this thesis are the geometric features of systolic complexesarising from the actions of hyperbolic isometries. The thesis consists ofan introduction followed by two articles.Given a hyperbolic isometry h of a systolic complex X, our central theme isto study the minimal...... displacement set of h and its relation to the actions of h onX and on the systolic boundary ∂X. We describe the coarse-geometric structureof the minimal displacement set and establish some of its properties that can beseen as a form of quasi-convexity. We apply our results to the study of geometricand...... algebraic-topological features of systolic groups. In addition, we provide newexamples of systolic groups.In the first article we show that the minimal displacement set of a hyperbolicisometry of a systolic complex is quasi-isometric to the product of a tree andthe real line. We use this theorem...
Hyperbolic Metamaterials with Complex Geometry
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei
2016-01-01
We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...
KAWA lecture notes on complex hyperbolic geometry
Rousseau, Erwan
2016-01-01
These lecture notes are based on a mini-course given at the fifth KAWA Winter School on March 24-29, 2014 at CIRM, Marseille. They provide an introduction to hyperbolicity of complex algebraic varieties namely the geometry of entire curves, and a description of some recent developments.
Kummer, E. E.; Siegel, Edward Carl-Ludwig
2011-03-01
Clock-model Archimedes [http://linkage.rockeller.edu/ wli/moved.8.04/ 1fnoise/ index. ru.html] HYPERBOLICITY inevitability throughout physics/pure-maths: Newton-law F=ma, Heisenberg and classical uncertainty-principle=Parseval/Plancherel-theorems causes FUZZYICS definition: (so miscalled) "complexity" = UTTER-SIMPLICITY!!! Watkins[www.secamlocal.ex.ac.uk/people/staff/mrwatkin/]-Hubbard[World According to Wavelets (96)-p.14!]-Franklin[1795]-Fourier[1795;1822]-Brillouin[1922] dual/inverse-space(k,w) analysis key to Fourier-unification in Archimedes hyperbolicity inevitability progress up Siegel cognition hierarchy-of-thinking (HoT): data-info.-know.-understand.-meaning-...-unity-simplicity = FUZZYICS!!! Frohlich-Mossbauer-Goldanskii-del Guidice [Nucl.Phys.B:251,375(85);275,185 (86)]-Young [arXiv-0705.4678y2, (5/31/07] theory of health/life=aqueous-electret/ ferroelectric protoplasm BEC = Archimedes-Siegel [Schrodinger Cent.Symp.(87); Symp.Fractals, MRS Fall Mtg.(89)-5-pprs] 1/w-"noise" Zipf-law power-spectrum hyperbolicity INEVITABILITY= Chi; Dirac delta-function limit w=0 concentration= BEC = Chi-Quong.
The 'golden' hyperbolic models of Universe
Energy Technology Data Exchange (ETDEWEB)
Stakhov, Alexey [International Club of the Golden Section, 6 McCreary Trail, Bolton, Ont., L7E 2C8 (Canada)]. E-mail: goldenmuseum@rogers.com; Rozin, Boris [International Club of the Golden Section, 6 McCreary Trail, Bolton, Ont., L7E 2C8 (Canada)]. E-mail: rozinb@yahoo.com
2007-10-15
This article presents a review of new mathematical models of the hyperbolic space. These models are based on the golden section. In this article, the authors discuss the hyperbolic Fibonacci and Lucas functions and the surface of the golden shofar, which are the most important of these models. The authors also introduce, within this article, the golden hyperbolic approach for modeling the universe.
Higgs Bundles and Representations of Complex Hyperbolic Lattices
Maubon, Julien
2015-01-01
International audience; This paper is an introduction to the Higgs bundle theory of Hitchin and Simpson and a survey of its applications to the study of representations of complex hyperbolic lattices into Lie groups of Hermitian type. Some material concerning representations of surface groups will be covered but we shall be mainly interested in higher dimensional lattices, in particular in the proof of the rigidity of maximal representations of such lattices. (Concerning the rigidity of maxim...
Machine learning meets complex networks via coalescent embedding in the hyperbolic space.
Muscoloni, Alessandro; Thomas, Josephine Maria; Ciucci, Sara; Bianconi, Ginestra; Cannistraci, Carlo Vittorio
2017-11-20
Physicists recently observed that realistic complex networks emerge as discrete samples from a continuous hyperbolic geometry enclosed in a circle: the radius represents the node centrality and the angular displacement between two nodes resembles their topological proximity. The hyperbolic circle aims to become a universal space of representation and analysis of many real networks. Yet, inferring the angular coordinates to map a real network back to its latent geometry remains a challenging inverse problem. Here, we show that intelligent machines for unsupervised recognition and visualization of similarities in big data can also infer the network angular coordinates of the hyperbolic model according to a geometrical organization that we term "angular coalescence." Based on this phenomenon, we propose a class of algorithms that offers fast and accurate "coalescent embedding" in the hyperbolic circle even for large networks. This computational solution to an inverse problem in physics of complex systems favors the application of network latent geometry techniques in disciplines dealing with big network data analysis including biology, medicine, and social science.
Hyperbolic Plykin attractor can exist in neuron models
DEFF Research Database (Denmark)
Belykh, V.; Belykh, I.; Mosekilde, Erik
2005-01-01
Strange hyperbolic attractors are hard to find in real physical systems. This paper provides the first example of a realistic system, a canonical three-dimensional (3D) model of bursting neurons, that is likely to have a strange hyperbolic attractor. Using a geometrical approach to the study...... of the neuron model, we derive a flow-defined Poincare map giving ail accurate account of the system's dynamics. In a parameter region where the neuron system undergoes bifurcations causing transitions between tonic spiking and bursting, this two-dimensional map becomes a map of a disk with several periodic...... holes. A particular case is the map of a disk with three holes, matching the Plykin example of a planar hyperbolic attractor. The corresponding attractor of the 3D neuron model appears to be hyperbolic (this property is not verified in the present paper) and arises as a result of a two-loop (secondary...
A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model
Energy Technology Data Exchange (ETDEWEB)
Samet Y. Kadioglu; Robert Nourgaliev; Nam Dinh
2011-10-01
We introduce a novel approach for the hyperbolization of the well-known two-phase six equation flow model. The six-equation model has been frequently used in many two-phase flow applications such as bubbly fluid flows in nuclear reactors. One major drawback of this model is that it can be arbitrarily non-hyperbolic resulting in difficulties such as numerical instability issues. Non-hyperbolic behavior can be associated with complex eigenvalues that correspond to characteristic matrix of the system. Complex eigenvalues are often due to certain flow parameter choices such as the definition of inter-facial pressure terms. In our method, we prevent the characteristic matrix receiving complex eigenvalues by fine tuning the inter-facial pressure terms with an iterative procedure. In this way, the characteristic matrix possesses all real eigenvalues meaning that the characteristic wave speeds are all real therefore the overall two-phase flowmodel becomes hyperbolic. The main advantage of this is that one can apply less diffusive highly accurate high resolution numerical schemes that often rely on explicit calculations of real eigenvalues. We note that existing non-hyperbolic models are discretized mainly based on low order highly dissipative numerical techniques in order to avoid stability issues.
Active shielding model for hyperbolic equations
Ryaben'kii, Victor S.; Utyuzhnikov, Sergei V.
2006-12-01
The problem of active shielding (AS) in application to hyperbolic equations is analysed. According to the problem, two domains effecting each other via distributed source terms are considered. It is required to implement additional sources nearby the common boundary of the domains in order to "isolate" one domain from the action of the other domain. It is important to note that the total field of the original sources is only known. In the paper, the theory of difference potentials is applied to the system of hyperbolic equations for the first time. It allows one to obtain a one-layer AS not requiring any additional computations. Local one-layer and two-layer AS sources are obtained for an arbitrary hyperbolic system. The solution does not require either the knowledge of the Green's function or the specific characteristics of the sources and medium. The optimal one-layer AS solution is derived in the case of free space. In particular, the results are applicable to the system of acoustics equations. The questions related to a practical realization including the mutual situation of the primary and secondary sources, as well as the measurement point, are discussed. The active noise shielding can be realized via a one-layer source term requiring the measurements only at one layer nearby the domain shielded.
Tamma, Kumar K.; D'Costa, Joseph F.
1991-01-01
This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.
Hyperbolic Hopfield neural networks.
Kobayashi, M
2013-02-01
In recent years, several neural networks using Clifford algebra have been studied. Clifford algebra is also called geometric algebra. Complex-valued Hopfield neural networks (CHNNs) are the most popular neural networks using Clifford algebra. The aim of this brief is to construct hyperbolic HNNs (HHNNs) as an analog of CHNNs. Hyperbolic algebra is a Clifford algebra based on Lorentzian geometry. In this brief, a hyperbolic neuron is defined in a manner analogous to a phasor neuron, which is a typical complex-valued neuron model. HHNNs share common concepts with CHNNs, such as the angle and energy. However, HHNNs and CHNNs are different in several aspects. The states of hyperbolic neurons do not form a circle, and, therefore, the start and end states are not identical. In the quantized version, unlike complex-valued neurons, hyperbolic neurons have an infinite number of states.
Kinks and branes in models with hyperbolic interactions
Bazeia, D.; Lima, Elisama E. M.; Losano, L.
2017-09-01
In this work, we investigate several models described by a single real scalar field with nonpolynomial interactions, constructed to support topological solutions. We do this using the deformation procedure to introduce a function which allows to construct two distinct families of hyperbolic potentials, controlled by three distinct parameters, in the standard formalism. In this way, the procedure allows us to get analytical solutions, and then investigate the energy density, linear stability and zero mode. We move on and introduce a nonstandard formalism to obtain compact solutions, analytically. We also investigate these hyperbolic models in the braneworld context, considering both the standard and nonstandard possibilities. The results show how to construct distinct braneworld models which are implemented via the first-order formalism and are stable against fluctuation of the metric tensor.
Modeling and analysis of linear hyperbolic systems of balance laws
Bartecki, Krzysztof
2016-01-01
This monograph focuses on the mathematical modeling of distributed parameter systems in which mass/energy transport or wave propagation phenomena occur and which are described by partial differential equations of hyperbolic type. The case of linear (or linearized) 2 x 2 hyperbolic systems of balance laws is considered, i.e., systems described by two coupled linear partial differential equations with two variables representing physical quantities, depending on both time and one-dimensional spatial variable. Based on practical examples of a double-pipe heat exchanger and a transportation pipeline, two typical configurations of boundary input signals are analyzed: collocated, wherein both signals affect the system at the same spatial point, and anti-collocated, in which the input signals are applied to the two different end points of the system. The results of this book emerge from the practical experience of the author gained during his studies conducted in the experimental installation of a heat exchange cente...
The quasi-one-dimensional hyperbolic model of hydraulic fracturing
Directory of Open Access Journals (Sweden)
Aidar M. Il'yasov
2016-12-01
Full Text Available The paper describes a quasi-one-dimensional hyperbolic model of hydraulic fracture growth assuming for the hydraulic fracturing that stress intensity is much higher than fracture resistance. The mode under analysis, which accounts for convective and unsteady terms in the fluid flow equation, is a generalization of the Perkins–Kern–Nordgren local model. It has been proved that the obtained system of differential equations is a quasi-linear strictly hyperbolic system, for which the characteristics were found as well as their correlations. For the case of the Coriolis correction neglect, the Riemann invariants were found. Neglecting the injected fluid leak-off and viscosity, the Riemann waves, similar to simple plane waves in gas dynamics, were defined and their properties were studied. The evolutionism of fracture boundaries was investigated. The initial boundary value problem was set for fracture growth. It has been shown that the neglect of dissipative terms in the presented model allows constructing a simple wave theory analogous to the theory of one-dimensional gas dynamics for isentropic plane waves.
Takemura, Kazuhisa; Murakami, Hajime
2016-01-01
A probability weighting function (w(p)) is considered to be a nonlinear function of probability (p) in behavioral decision theory. This study proposes a psychophysical model of probability weighting functions derived from a hyperbolic time discounting model and a geometric distribution. The aim of the study is to show probability weighting functions from the point of view of waiting time for a decision maker. Since the expected value of a geometrically distributed random variable X is 1/p, we formulized the probability weighting function of the expected value model for hyperbolic time discounting as w(p) = (1 - k log p)(-1). Moreover, the probability weighting function is derived from Loewenstein and Prelec's (1992) generalized hyperbolic time discounting model. The latter model is proved to be equivalent to the hyperbolic-logarithmic weighting function considered by Prelec (1998) and Luce (2001). In this study, we derive a model from the generalized hyperbolic time discounting model assuming Fechner's (1860) psychophysical law of time and a geometric distribution of trials. In addition, we develop median models of hyperbolic time discounting and generalized hyperbolic time discounting. To illustrate the fitness of each model, a psychological experiment was conducted to assess the probability weighting and value functions at the level of the individual participant. The participants were 50 university students. The results of individual analysis indicated that the expected value model of generalized hyperbolic discounting fitted better than previous probability weighting decision-making models. The theoretical implications of this finding are discussed.
A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns
Directory of Open Access Journals (Sweden)
Virginie Konlack Socgnia
2014-01-01
Full Text Available We discuss the calibration of the univariate and multivariate generalized hyperbolic distributions, as well as their hyperbolic, variance gamma, normal inverse Gaussian, and skew Student’s t-distribution subclasses for the daily log-returns of seven of the most liquid mining stocks listed on the Johannesburg Stocks Exchange. To estimate the model parameters from historic distributions, we use an expectation maximization based algorithm for the univariate case and a multicycle expectation conditional maximization estimation algorithm for the multivariate case. We assess the goodness of fit statistics using the log-likelihood, the Akaike information criterion, and the Kolmogorov-Smirnov distance. Finally, we inspect the temporal stability of parameters and note implications as criteria for distinguishing between models. To better understand the dependence structure of the stocks, we fit the MGHD and subclasses to both the stock returns and the two leading principal components derived from the price data. While the MGHD could fit both data subsets, we observed that the multivariate normality of the stock return residuals, computed by removing shared components, suggests that the departure from normality can be explained by the structure in the common factors.
Complex hyperbolic-function method and its applications to nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Bai Chenglin [School of Physics Science and Information Engineering, Liaocheng University, Shandong 252059 (China); Zhao Hong [School of Physics Science and Information Engineering, Liaocheng University, Shandong 252059 (China)]. E-mail: lcced_bcl@hotmail.com
2006-06-19
Based on computerized symbolic computation, a complex hyperbolic-function method is proposed for the general nonlinear equations of mathematical physics in a unified way. In this method, we assume that exact solutions for a given general nonlinear equations be the superposition of different powers of the sech-function, tanh-function and/or their combinations. After finishing some direct calculations, we can finally obtain the exact solutions expressed by the complex hyperbolic function. The characteristic feature of this method is that we can derive exact solutions to the general nonlinear equations directly without transformation. Some illustrative equations, such as the (1+1)-dimensional coupled Schrodinger-KdV equation (2+1)-dimensional Davey-Stewartson equation and Hirota-Maccari equation, are investigated by this means and new exact solutions are found.
Complex hyperbolic-function method and its applications to nonlinear equations
Bai, Cheng-Lin; Zhao, Hong
2006-06-01
Based on computerized symbolic computation, a complex hyperbolic-function method is proposed for the general nonlinear equations of mathematical physics in a unified way. In this method, we assume that exact solutions for a given general nonlinear equations be the superposition of different powers of the sech-function, tanh-function and/or their combinations. After finishing some direct calculations, we can finally obtain the exact solutions expressed by the complex hyperbolic function. The characteristic feature of this method is that we can derive exact solutions to the general nonlinear equations directly without transformation. Some illustrative equations, such as the (1+1)-dimensional coupled Schrödinger KdV equation, (2+1)-dimensional Davey Stewartson equation and Hirota Maccari equation, are investigated by this means and new exact solutions are found.
Owhadi, Houman; Zhang, Lei
2017-10-01
Implicit schemes are popular methods for the integration of time dependent PDEs such as hyperbolic and parabolic PDEs. However the necessity to solve corresponding linear systems at each time step constitutes a complexity bottleneck in their application to PDEs with rough coefficients. We present a generalization of gamblets introduced in [62] enabling the resolution of these implicit systems in near-linear complexity and provide rigorous a-priori error bounds on the resulting numerical approximations of hyperbolic and parabolic PDEs. These generalized gamblets induce a multiresolution decomposition of the solution space that is adapted to both the underlying (hyperbolic and parabolic) PDE (and the system of ODEs resulting from space discretization) and to the time-steps of the numerical scheme.
A combined Preisach–Hyperbolic Tangent model for magnetic hysteresis of Terfenol-D
Energy Technology Data Exchange (ETDEWEB)
Talebian, Soheil [Department of Mechanical Engineering, Tarbiat Modares University, Tehran (Iran, Islamic Republic of); Hojjat, Yousef, E-mail: yhojjat@modares.ac.ir [Department of Mechanical Engineering, Tarbiat Modares University, Tehran (Iran, Islamic Republic of); Ghodsi, Mojtaba [Department of Mechanical and Industrial Engineering, Sultan Qaboos University, Muscat (Oman); Karafi, Mohammad Reza [Department of Mechanical Engineering, Tarbiat Modares University, Tehran (Iran, Islamic Republic of); Mirzamohammadi, Shahed [Department of Mechanical Engineering, Shahid Rajaee University, Tehran (Iran, Islamic Republic of)
2015-12-15
This study presents a new model using the combination of Preisach and Hyperbolic Tangent models, to predict the magnetic hysteresis of Terfenol-D at different frequencies. Initially, a proper experimental setup was fabricated and used to obtain different magnetic hysteresis curves of Terfenol-D; such as major, minor and reversal loops. Then, it was shown that the Hyperbolic Tangent model is precisely capable of modeling the magnetic hysteresis of the Terfenol-D for both rate-independent and rate-dependent cases. Empirical equations were proposed with respect to magnetic field frequency which can calculate the non-dimensional coefficients needed by the model. These empirical equations were validated at new frequencies of 100 Hz and 300 Hz. Finally, the new model was developed through the combination of Preisach and Hyperbolic Tangent models. In the combined model, analytical relations of the Hyperbolic Tangent model for the first order reversal loops determined the weighting function of the Preisach model. This model reduces the required experiments and errors due to numerical differentiations generally needed for characterization of the Preisach function. In addition, it can predict the rate-dependent hysteresis as well as rate-independent hysteresis. - Highlights: • Different hysteresis curves of Terfenol-D are experimentally obtained at 0–200 Hz. • A new model is presented using combination of Preisach and Hyperbolic Tangent models. • The model predicts both rate-independent and rate-dependent hystereses of Terfenol-D. • The analytical model reduces the numerical errors and number of required experiments.
Hyperbolic Gradient Operator and Hyperbolic Back-Propagation Learning Algorithms.
Nitta, Tohru; Kuroe, Yasuaki
2017-03-23
In this paper, we first extend the Wirtinger derivative which is defined for complex functions to hyperbolic functions, and derive the hyperbolic gradient operator yielding the steepest descent direction by using it. Next, we derive the hyperbolic backpropagation learning algorithms for some multilayered hyperbolic neural networks (NNs) using the hyperbolic gradient operator. It is shown that the use of the Wirtinger derivative reduces the effort necessary for the derivation of the learning algorithms by half, simplifies the representation of the learning algorithms, and makes their computer programs easier to code. In addition, we discuss the differences between the derived Hyperbolic-BP rules and the complex-valued backpropagation learning rule (Complex-BP). Finally, we make some experiments with the derived learning algorithms. As a result, we find that the convergence rates of the Hyperbolic-BP learning algorithms are high even if the fully activation functions are used, and discover that the Hyperbolic-BP learning algorithm for the hyperbolic NN with the split-type hyperbolic activation function has an ability to learn hyperbolic rotation as its inherent property.
Poyato, David; Soler, Juan
2016-01-01
This paper deals with the derivation and analysis of a compressible Euler-type equation with singular commutator, which is derived from a hyperbolic limit of the kinetic description to the Cucker-Smale model of interacting individuals
Rivera, Maria J; López Molina, Juan A; Trujillo, Macarena; Romero-Garcia, Vicente; Berjano, Enrique J
2010-01-01
In this paper we outline our main findings about the differences between the use of the Bioheat Equation and the Hyperbolic Bioheat Equation in theoretical models for Radiofrequency (RF) ablation. At the moment, we have been working on the analytical approach to solve both equations, but more recently, we have considered numerical models based on the Finite Element Method (FEM). As a first step to use FEM, we conducted a comparative study between the temperature profiles obtained from the analytical solutions and those obtained from FEM. Regarding the differences between both methods, we obtain agreement in less than 5% of relative differences. Then FEM is a good alternative to model heating of biological tissues using BE and HBE in, for example, more complex and realistic geometries.
De La Rosa Gomez, Alejandro; MacKay, Niall; Regelskis, Vidas
2017-04-01
We present a general method of folding an integrable spin chain, defined on a line, to obtain an integrable open spin chain, defined on a half-line. We illustrate our method through two fundamental models with sl2 Lie algebra symmetry: the Heisenberg XXX and the Inozemtsev hyperbolic spin chains. We obtain new long-range boundary Hamiltonians and demonstrate that they exhibit Yangian symmetries, thus ensuring integrability of the models we obtain. The method presented provides a ;bottom-up; approach for constructing integrable boundaries and can be applied to any spin chain model.
Inflation with hyperbolic potential in the braneworld model
Indian Academy of Sciences (India)
In this paper we study inflationary dynamics with a scalar field in an inverse coshyperbolic potential in the braneworld model. We note that a sufficient inflation may be obtained with the potential considering slow-roll approximation in the high energy limit. We determine the minimum values of the initial inflaton field required ...
Inflation with hyperbolic potential in the braneworld model
Indian Academy of Sciences (India)
Abstract. In this paper we study inflationary dynamics with a scalar field in an inverse coshyperbolic potential in the braneworld model. We note that a sufficient inflation may be obtained with the potential considering slow-roll approximation in the high energy limit. We determine the minimum values of the initial inflaton field ...
Evolution of the structure factor in a hyperbolic model of spinodal decomposition
Lecoq, N.; Zapolsky, H.; Galenko, P.
2009-10-01
We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. The memory effects are seen to affect the dynamics of phase transition at short times. The process of fast spinodal decomposition associated with a conserved order parameter - concentration is studied numerically. Details of a semi-implicit numerical scheme used to simulate the kinetics of spinodal decomposition and evolution of the structure factor are discussed. Analysis of the modeled structure factor predicted by a hyperbolic model of spinodal decomposition is presented in comparison with the parabolic model of Cahn and Hilliard. It is shown that during initial periods of decomposition the structure factor exhibits wave behavior. Analytical treatments explain such behavior by existence of damped oscillations in structure factor at earliest stages of phase separation and at large values of the wave-number. These oscillations disappear gradually in time and the hyperbolic evolution approaches the pure dissipative parabolic evolution of spinodal decomposition.
Yudin, M. S.
2017-11-01
In this paper the effects of an inversion layer in a stratified atmosphere on the surface wind speed and pressure are investigated with models based on the compressible Navier-Stokes equations in two dimensions. Artificial compressibility is introduced into the models in order to make the governing equations hyperbolic. For comparison with available simulation data, the physical processes under study are assumed to be adiabatic. Plain orography is considered in surface pressure simulations with a finite-difference version of the model, while surface wind speed effects are estimated in artificial cold front propagation over a hill with a finite-element version of the model. The front surface is described in both models by an equation for advection of a scalar substance, which is solved with a third-order semi-Lagrangian procedure. The results of simulations show various meteorological effects in agreement with observations and in accordance with a theory proposed by Charba [3].
Focal surfaces of hyperbolic cylinders
Georgiev, Georgi Hristov; Pavlov, Milen Dimov
2017-12-01
Cylindrical surfaces have many applications in geometric modeling, architecture and other branches of engineering. In this paper, we describe two cylindrical surfaces associated to a given hyperbolic cylinder. The first one is a focal surface which is determined by reciprocal principle curvature of the hyperbolic cylinder. The second one is a generalized focal surface obtained by reciprocal mean curvature of the same hyperbolic cylinder. In particular, we show that each of these surfaces admits three different parametric representations. As consequence, it is proved that the focal and generalized focal surfaces of the hyperbolic cylinder are rational surfaces. An illustrative example is included.
Hyperbolicity in median graphs
Indian Academy of Sciences (India)
If is hyperbolic, we denote by () the sharp hyperbolicity constant of , i.e., ( X ) = inf { ≥ 0 : X is − hyperbolic } . In this paper we study the hyperbolicity of median graphs and we also obtain some results about general hyperbolic graphs. In particular, we prove that a median graph is hyperbolic if and only if its ...
Jardón Kojakhmetov, H.; Scherpen, Jacquelien M.A.
In this letter we investigate a class of slow-fast systems for which the classical model order reduction technique based on singular perturbations does not apply due to the lack of a Normally Hyperbolic critical manifold. We show, however, that there exists a class of slow-fast systems that after a
Effect of Compressibility on Hyperbolicity and Choke Flow Criterion of the Two-phase Two-fluid Model
Energy Technology Data Exchange (ETDEWEB)
Suneet Singh; Vincent A. Mousseau
2008-09-01
The standard two-phase two-fluid model lacks hyperbolicity which results in oscillations in the numerical solutions. For the incompressible two-phase flows an exact correction term can be derived which when added to the momentum equations makes the model hyperbolic. No such straightforward approach exists for the similar compressible flows. In the current work, the effect of the compressibility on the characteristic equation is analyzed. It is shown that the hyperbolicity of the system depends only on the slip velocity and not on the phasic velocities, independently. Moreover, a slip Mach number is defined and a non-dimensional characteristic equation is derived. It is shown that for the small values of slip Mach number the effect of the compressibility on the hyperbolicity can be ignored. To verify the above analysis, the characteristic equation for the two-phase compressible flows is numerically solved and results compared with the values obtained with the analytical solution for incompressible flows. Numerical solution of the two-phase two-fluid model for the benchmark problem is used to further verify the abovementioned analysis. Furthermore, the eigenvalues of the characteristic equation are obtained as a power series expansion about the point where the slip Mach number is zero. These eigenvalues are used to develop a choking criterion for the compressible two-phase flows.
A Hyperbolic Ontology Visualization Tool for Model Application Programming Interface Documentation
Hyman, Cody
2011-01-01
Spacecraft modeling, a critically important portion in validating planned spacecraft activities, is currently carried out using a time consuming method of mission to mission model implementations and integration. A current project in early development, Integrated Spacecraft Analysis (ISCA), aims to remedy this hindrance by providing reusable architectures and reducing time spent integrating models with planning and sequencing tools. The principle objective of this internship was to develop a user interface for an experimental ontology-based structure visualization of navigation and attitude control system modeling software. To satisfy this, a number of tree and graph visualization tools were researched and a Java based hyperbolic graph viewer was selected for experimental adaptation. Early results show promise in the ability to organize and display large amounts of spacecraft model documentation efficiently and effectively through a web browser. This viewer serves as a conceptual implementation for future development but trials with both ISCA developers and end users should be performed to truly evaluate the effectiveness of continued development of such visualizations.
Contracting isometries of CAT(0) cube complexes and acylindrical hyperbolicity of diagram groups
Genevois, Anthony
2016-01-01
The main technical result of this paper is to characterize the contracting isometries of a CAT(0) cube complex without any assumption on its local finiteness. Afterwards, we introduce the combinatorial boundary of a CAT(0) cube complex, and we show that contracting isometries are strongly related to isolated points at infinity, when the complex is locally finite. This boundary turns out to appear naturally in the context of Guba and Sapir's diagram groups, and we apply our main criterion to d...
Sources of hyperbolic geometry
Stillwell, John
1996-01-01
This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...
A H-Infinity Control for Path Tracking with Fuzzy Hyperbolic Tangent Model
Directory of Open Access Journals (Sweden)
Guangsi Shi
2016-01-01
Full Text Available To achieve the goal of driver-less underground mining truck, a fuzzy hyperbolic tangent model is established for path tracking on an underground articulated mining truck. Firstly, the sample data of parameters are collected by the driver controlling articulated vehicle at a speed of 3 m/s, including both the lateral position deviation and the variation of heading angle deviation. Then, according to the improved adaptive BP neural network model and deriving formula of mediation rate of error estimator by the method of Cauchy robust, the weights are identified. Finally, H-infinity control controller is designed to control steering angle. The results of hardware-in-the-loop simulation show that lateral position deviation, heading angle deviation, and steering angle of the vehicle can be controlled, respectively, at 0.024 m, 0.08 rad, and 0.21 rad. All the deviations are asymptotically stable, and error control is in less than 2%. The method is demonstrated to be effective and reliable in path tracking for the underground vehicles.
Hyperbolicity of projective hypersurfaces
Diverio, Simone
2016-01-01
This book presents recent advances on Kobayashi hyperbolicity in complex geometry, especially in connection with projective hypersurfaces. This is a very active field, not least because of the fascinating relations with complex algebraic and arithmetic geometry. Foundational works of Serge Lang and Paul A. Vojta, among others, resulted in precise conjectures regarding the interplay of these research fields (e.g. existence of Zariski dense entire curves should correspond to the (potential) density of rational points). Perhaps one of the conjectures which generated most activity in Kobayashi hyperbolicity theory is the one formed by Kobayashi himself in 1970 which predicts that a very general projective hypersurface of degree large enough does not contain any (non-constant) entire curves. Since the seminal work of Green and Griffiths in 1979, later refined by J.-P. Demailly, J. Noguchi, Y.-T. Siu and others, it became clear that a possible general strategy to attack this problem was to look at particular algebr...
On oscillatory convection with the Cattaneo–Christov hyperbolic heat-flow model
Bissell, J. J.
2015-01-01
Adoption of the hyperbolic Cattaneo–Christov heat-flow model in place of the more usual parabolic Fourier law is shown to raise the possibility of oscillatory convection in the classic Bénard problem of a Boussinesq fluid heated from below. By comparing the critical Rayleigh numbers for stationary and oscillatory convection, Rc and RS respectively, oscillatory convection is found to represent the preferred form of instability whenever the Cattaneo number C exceeds a threshold value CT≥8/27π2≈0.03. In the case of free boundaries, analytical approaches permit direct treatment of the role played by the Prandtl number P1, which—in contrast to the classical stationary scenario—can impact on oscillatory modes significantly owing to the non-zero frequency of convection. Numerical investigation indicates that the behaviour found analytically for free boundaries applies in a qualitatively similar fashion for fixed boundaries, while the threshold Cattaneo number CT is computed as a function of P1∈[10−2,10+2] for both boundary regimes. PMID:25792960
Proof of Concept: Model Based Bionic Muscle with Hyperbolic Force-Velocity Relation
Directory of Open Access Journals (Sweden)
D. F. B. Haeufle
2012-01-01
Full Text Available Recently, the hyperbolic Hill-type force-velocity relation was derived from basic physical components. It was shown that a contractile element CE consisting of a mechanical energy source (active element AE, a parallel damper element (PDE, and a serial element (SE exhibits operating points with hyperbolic force-velocity dependency. In this paper, a technical proof of this concept was presented. AE and PDE were implemented as electric motors, SE as a mechanical spring. The force-velocity relation of this artificial CE was determined in quick release experiments. The CE exhibited hyperbolic force-velocity dependency. This proof of concept can be seen as a well-founded starting point for the development of Hill-type artificial muscles.
Effects of nanoparticles on the peristaltic motion of tangent hyperbolic fluid model in an annulus
Directory of Open Access Journals (Sweden)
S. Nadeem
2015-12-01
Full Text Available In the present article, effects of nanoparticles on the peristaltic flow of tangent hyperbolic fluid in an annulus are described. The two-dimensional equations of tangent hyperbolic fluid are solved by using the assumptions of low Reynolds number and long wavelength. Analytical solution is obtained with the help of homotopy perturbation and Adomian decomposition method for velocity, temperature and nanoparticles concentration. Solutions are discussed through graphs. Solutions for pressure rise, temperature, nanoparticles concentration, pressure gradient and streamlines are plotted for various emerging parameters. It is found that the temperature profile increases with increase in Brownian motion and thermophoresis parameter. It is also found that the size of the trapped bolus in triangular wave is smaller as compared to other waves. Further, the comparison of both analytical solutions is presented.
Borsche, Raul; Kall, Jochen
2016-12-01
In this paper we construct high order finite volume schemes on networks of hyperbolic conservation laws with coupling conditions involving ODEs. We consider two generalized Riemann solvers at the junction, one of Toro-Castro type and a solver of Harten, Enquist, Osher, Chakravarthy type. The ODE is treated with a Taylor method or an explicit Runge-Kutta scheme, respectively. Both resulting high order methods conserve quantities exactly if the conservation is part of the coupling conditions. Furthermore we present a technique to incorporate lumped parameter models, which arise from simplifying parts of a network. The high order convergence and the robust capturing of shocks are investigated numerically in several test cases.
Hyperbolic groupoids and duality
Nekrashevych, Volodymyr
2015-01-01
The author introduces a notion of hyperbolic groupoids, generalizing the notion of a Gromov hyperbolic group. Examples of hyperbolic groupoids include actions of Gromov hyperbolic groups on their boundaries, pseudogroups generated by expanding self-coverings, natural pseudogroups acting on leaves of stable (or unstable) foliation of an Anosov diffeomorphism, etc. The author describes a duality theory for hyperbolic groupoids. He shows that for every hyperbolic groupoid \\mathfrak{G} there is a naturally defined dual groupoid \\mathfrak{G}^\\top acting on the Gromov boundary of a Cayley graph of \\
Rañada, Manuel F.
2014-04-01
The higher order superintegrability of the Tremblay-Turbiner-Winternitz system (related to the harmonic oscillator) is studied on the two-dimensional spherical and hyperbolic spaces, S_\\kappa ^2 (κ > 0) and H_{\\kappa }^2 (κ Tremblay-Turbiner-Winternitz system on S_\\kappa ^2 (κ > 0) and H_{\\kappa }^2 (κ < 0), and to the explicit expression of the constants of motion.
Udwadia, F. E.; Garba, J. A.
1983-01-01
This paper deals with the identification of spatially varying parameters in systems of finite spatial extent which can be described by second order hyperbolic differential equations. Two questions have been addressed. The first deals with 'partial identification' and inquires into the possibility of retrieving all the eigenvalues of the system from response data obtained at one location x-asterisk epsilon (0, 1). The second deals with the identification of the distributed coefficients rho(x), a(x) and b(x). Sufficient conditions for unique identification of all the eigenvalues of the system are obtained, and conditions under which the coefficients can be uniquely identified using suitable response data obtained at one point in the spatial domain are determined. Application of the results and their usefulness is demonstrated in the identification of the properties of tall building structural systems subjected to dynamic load environments.
DEFF Research Database (Denmark)
Risager, Morten S.; Södergren, Carl Anders
2017-01-01
It is well known that the angles in a lattice acting on hyperbolic n -space become equidistributed. In this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. Using this formula we determine, among other things, the asymptotic behavior of the den...
Hyperbolicity in median graphs
Indian Academy of Sciences (India)
(Math. Sci.) Vol. 123, No. 4, November 2013, pp. 455–467. c Indian Academy of Sciences. Hyperbolicity in median graphs. JOSÉ M SIGARRETA. Facultad de Matemáticas ... median graphs and we also obtain some results about general hyperbolic graphs. ... Note that to exclude multiple edges and loops is not an important.
Nonlinear hyperbolic waves in multidimensions
Prasad, Phoolan
2001-01-01
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...
Hyperbolic partial differential equations
Witten, Matthew
1986-01-01
Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M
Directory of Open Access Journals (Sweden)
Kevin John Flynn
2016-09-01
Full Text Available Rectangular hyperbolic type 2 (RHt2; Michaelis-Menten or Monod -like functions are commonly used to describe predation kinetics in plankton models, either alone or together with a prey selectivity algorithm deploying the same half-saturation constant for all prey types referenced to external prey biomass abundance. We present an analysis that indicates that such descriptions are liable to give outputs that are not plausible according to encounter theory. This is especially so for multi-prey type applications or where changes are made to the maximum feeding rate during a simulation. The RHt2 approach also gives no or limited potential for descriptions of events such as true de-selection of prey, effects of turbulence on encounters, or changes in grazer motility with satiation. We present an alternative, which carries minimal parameterisation effort and computational cost, linking allometric algorithms relating prey abundance and encounter rates to a prey-selection function controlled by satiation. The resultant Satiation-Controlled-Encounter-Based (SCEB function provides a flexible construct describing numeric predator-prey interactions with biomass-feedback control of grazing. The SCEB function includes an attack component similar to that in the Holling disk equation but SCEB differs in having only a single (satiation-based handling constant and an explicit maximum grazing rate. We argue that there is no justification for continuing to deploy RHt2 functions to describe plankton predator-prey interactions.
Covariant Hyperbolization of Force-free Electrodynamics
Carrasco, Federico
2016-01-01
Force-Free Flectrodynamics (FFE) is a non-linear system of equations modeling the evolution of the electromagnetic field, in the presence of a magnetically dominated relativistic plasma. This configuration arises on several astrophysical scenarios, which represent exciting laboratories to understand physics in extreme regimes. We show that this system, when restricted to the correct constraint submanifold, is symmetric hyperbolic. In numerical applications is not feasible to keep the system in that submanifold, and so, it is necessary to analyze its structure first in the tangent space of that submanifold and then in a whole neighborhood of it. As already shown by Pfeiffer, a direct (or naive) formulation of this system (in the whole tangent space) results in a weakly hyperbolic system of evolution equations for which well-possednes for the initial value formulation does not follows. Using the generalized symmetric hyperbolic formalism due to Geroch, we introduce here a covariant hyperbolization for the FFE s...
Hyperbolic metamaterial lens with hydrodynamic nonlocal response
DEFF Research Database (Denmark)
Yan, Wei; Mortensen, N. Asger; Wubs, Martijn
2013-01-01
We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves of the f......We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves...... in the local-response approximation and in the hydrodynamic Drude model can differ considerably. In particular, the optimal frequency for imaging in the nonlocal theory is blueshifted with respect to that in the local theory. Thus, to detect whether nonlocal response is at work in a hyperbolic metamaterial, we...... propose to measure the near-field distribution of a hyperbolic metamaterial lens....
Design of Hyperbolic Billiards
Wojtkowski, Maciej P.
2007-07-01
We formulate a general framework for the construction of hyperbolic billiards. Spherical symmetry is exploited for a simple treatment of billiards with spherical caps and soft billiards in higher dimensions. Other examples include the Papenbrock stadium.
Hyperbolic geometry for colour metrics.
Farup, Ivar
2014-05-19
It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., constant negative curvature) for the chromatic plane can significantly improve the performance of Euclidean colour metrics to the point where they are statistically significantly better than state-of-the-art non-Euclidean metrics on standard data sets. The resulting hyperbolic geometry nicely models both qualitatively and quantitatively the hue super-importance phenomenon observed in colour order systems.
Can rodents conceive hyperbolic spaces?
Urdapilleta, Eugenio; Troiani, Francesca; Stella, Federico; Treves, Alessandro
2015-06-06
The grid cells discovered in the rodent medial entorhinal cortex have been proposed to provide a metric for Euclidean space, possibly even hardwired in the embryo. Yet, one class of models describing the formation of grid unit selectivity is entirely based on developmental self-organization, and as such it predicts that the metric it expresses should reflect the environment to which the animal has adapted. We show that, according to self-organizing models, if raised in a non-Euclidean hyperbolic cage rats should be able to form hyperbolic grids. For a given range of grid spacing relative to the radius of negative curvature of the hyperbolic surface, such grids are predicted to appear as multi-peaked firing maps, in which each peak has seven neighbours instead of the Euclidean six, a prediction that can be tested in experiments. We thus demonstrate that a useful universal neuronal metric, in the sense of a multi-scale ruler and compass that remain unaltered when changing environments, can be extended to other than the standard Euclidean plane. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
A hierarchy of simple hyperbolic two-fluid models for bubbly flows
Drui, Florence; Kokh, Samuel; Massot, Marc
2016-01-01
With the objective of modeling both separate and disperse two-phase flows, we use in this paper a methodology for deriving two-fluid models that do not assume any flow topology. This methodology is based on a variational principle and on entropy dissipation requirement. Some of the models that are such derived and studied are already known in the contexts of the description of separate-or disperse-phase flows. However, we here propose an arrangement of these models into a hierarchy based on their links through relaxation parameters. Moreover, the models are shown to be compatible with the description of a monodisperse bubbly flow and, within this frame, the relaxation parameters can be identified. This identification is finally verified and discussed through comparisons with experimental measures of sound dispersion and with dispersion relations of a reference model for bubbly media.
a New Prony-Based Circular-Hyperbolic Decomposition
FAHEY, S. O'F.; SULEIMAN, B. M.; NAYFEH, A. H.; HAJJ, M. R.
2001-04-01
We introduce a new closed-form decomposition technique for estimating the model parameters of an evenly sampled signal known to be composed of circular and hyperbolic sine and cosine functions in the presence of Gaussian white noise. The techniqe is closely related to Prony's method and hereditary algorithms that fit complex exponential functions to evenly sampled data. The circular and hyperbolic sine and cosine functions are obtained by adding constraints that limit the form of the characteristic polynomial coefficients. It avoids the leakage effects associated with the discrete fourier transform (DFT) for circular sine and cosine functions. When the signal contains frequency components that are not rational multiples of each other, the proposed decomposition yields amplitude and phase parameters that are more accurate than those obtained with the DFT in moderate levels of noise. First, we review Prony's method and one hereditary algorithm (the complex exponential algorithm). Then, we detail three implementation procedures of the new technique. The first is a two-stage least-squares approach. The second utilises a novel concept of noise reduction which is attributed to Pisarenko. The last provides additional means of noise reduction through a covariance formulation that avoids zero-lag terms. Experimental and numerical examples of the application of the circular-hyperbolic decomposition (CHD) are given.
Bifurcation of Hyperbolic Planforms
Chossat, Pascal; Faye, Grégory; Faugeras, Olivier
2011-02-01
Motivated by a model for the perception of textures by the visual cortex in primates, we analyze the bifurcation of periodic patterns for nonlinear equations describing the state of a system defined on the space of structure tensors, when these equations are further invariant with respect to the isometries of this space. We show that the problem reduces to a bifurcation problem in the hyperbolic plane {D} (Poincaré disc). We make use of the concept of a periodic lattice in {D} to further reduce the problem to one on a compact Riemann surface {D}/\\varGamma, where Γ is a cocompact, torsion-free Fuchsian group. The knowledge of the symmetry group of this surface allows us to use the machinery of equivariant bifurcation theory. Solutions which generically bifurcate are called "H-planforms", by analogy with the "planforms" introduced for pattern formation in Euclidean space. This concept is applied to the case of an octagonal periodic pattern, where we are able to classify all possible H-planforms satisfying the hypotheses of the Equivariant Branching Lemma. These patterns are, however, not straightforward to compute, even numerically, and in the last section we describe a method for computation illustrated with a selection of images of octagonal H-planforms.
The Contributions of Neuroticism and Childhood Maltreatment to Hyperbolic Temperament
Hopwood, Christopher J.; Zanarini, Mary C.
2011-01-01
Zanarini and colleagues have proposed that hyperbolic temperament, involving a preponderance of negative emotions and cognitions combined with a need for those dysphoric inner states to be validated and understood, underlies borderline symptomatology. This study examined neuroticism and childhood maltreatment as predictors of hyperbolic features measured 10 years later in a clinical sample. Neuroticism and childhood maltreatment were significant and independent predictors of prospective hyperbolic temperament. These findings expand upon the hyperbolic temperament model of borderline phenomenology by depicting its developmental antecedents. PMID:23013348
Thermal hyperbolic metamaterials.
Guo, Yu; Jacob, Zubin
2013-06-17
We explore the near-field radiative thermal energy transfer properties of hyperbolic metamaterials. The presence of unique electromagnetic states in a broad bandwidth leads to super-planckian thermal energy transfer between metamaterials separated by a nano-gap. We consider practical phonon-polaritonic metamaterials for thermal engineering in the mid-infrared range and show that the effect exists in spite of the losses, absorption and finite unit cell size. For thermophotovoltaic energy conversion applications requiring energy transfer in the near-infrared range we introduce high temperature hyperbolic metamaterials based on plasmonic materials with a high melting point. Our work paves the way for practical high temperature radiative thermal energy transfer applications of hyperbolic metamaterials.
Symmetry analysis for hyperbolic equilibria using a TB/dengue fever model
Massoukou, R. Y. M.'Pika; Govinder, K. S.
2016-08-01
We investigate the interplay between Lie symmetry analysis and dynamical systems analysis. As an example, we take a toy model describing the spread of TB and dengue fever. We first undertake a comprehensive dynamical systems analysis including a discussion about local stability. For those regions in which such analyzes cannot be translated to global behavior, we undertake a Lie symmetry analysis. It is shown that the Lie analysis can be useful in providing information for systems where the (local) dynamical systems analysis breaks down.
Free-energy analysis of spin models on hyperbolic lattice geometries.
Serina, Marcel; Genzor, Jozef; Lee, Yoju; Gendiar, Andrej
2016-04-01
We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy normalized per lattice site of various multistate spin models in the thermal equilibrium on distinct non-Euclidean surface lattices of the infinite sizes. Whereas the free energy is calculated numerically by means of the corner transfer matrix renormalization group algorithm, the radius of curvature has an analytic expression. Two tasks are considered in this work. First, we search for such a lattice geometry, which minimizes the free energy per site. We conjecture that the only Euclidean flat geometry results in the minimal free energy per site regardless of the spin model. Second, the relations among the free energy, the radius of curvature, and the phase transition temperatures are analyzed. We found out that both the free energy and the phase transition temperature inherit the structure of the lattice geometry and asymptotically approach the profile of the Gaussian radius of curvature. This achievement opens new perspectives in the AdS-CFT correspondence theories.
Hyperbolic partial differential equations
Lax, Peter D
2006-01-01
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of soluti
Directory of Open Access Journals (Sweden)
Oleg Svatos
2013-01-01
Full Text Available In this paper we analyze complexity of time limits we can find especially in regulated processes of public administration. First we review the most popular process modeling languages. There is defined an example scenario based on the current Czech legislature which is then captured in discussed process modeling languages. Analysis shows that the contemporary process modeling languages support capturing of the time limit only partially. This causes troubles to analysts and unnecessary complexity of the models. Upon unsatisfying results of the contemporary process modeling languages we analyze the complexity of the time limits in greater detail and outline lifecycles of a time limit using the multiple dynamic generalizations pattern. As an alternative to the popular process modeling languages there is presented PSD process modeling language, which supports the defined lifecycles of a time limit natively and therefore allows keeping the models simple and easy to understand.
Energy Technology Data Exchange (ETDEWEB)
Brown, T.W.
2010-11-15
The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super- Yang-Mills. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich- Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces. (orig.)
Adsorption-desorption reactions are important processes that affect the transport of contaminants in the environment. Surface complexation models are chemical models that can account for the effects of variable chemical conditions, such as pH, on adsorption reactions. These models define specific ...
p-Capacity and p-Hyperbolicity of Submanifolds
DEFF Research Database (Denmark)
Holopainen, Ilkka; Markvorsen, Steen; Palmer, Vicente
2009-01-01
We use explicit solutions to a drifted Laplace equation in warped product model spaces as comparison constructions to show p-hyperbolicity of a large class of submanifolds for p >= 2. The condition for p-hyperbolicity is expressed in terms of upper support functions for the radial sectional curva...
Gualdesi, Lavinio
2017-04-01
Mooring lines in the Ocean might be seen as a pretty simple seamanlike activity. Connecting valuable scientific instrumentation to it transforms this simple activity into a sophisticated engineering support which needs to be accurately designed, developed, deployed, monitored and hopefully recovered with its precious load of scientific data. This work is an historical travel along the efforts carried out by scientists all over the world to successfully predict mooring line behaviour through both mathematical simulation and experimental verifications. It is at first glance unexpected how many factors one must observe to get closer and closer to a real ocean situation. Most models have dual applications for mooring lines and towed bodies lines equations. Numerous references are provided starting from the oldest one due to Isaac Newton. In his "Philosophiae Naturalis Principia Matematica" (1687) the English scientist, while discussing about the law of motion for bodies in resistant medium, is envisaging a hyperbolic fitting to the phenomenon including asymptotic behaviour in non-resistant media. A non-exhaustive set of mathematical simulations of the mooring lines trajectory prediction is listed hereunder to document how the subject has been under scientific focus over almost a century. Pode (1951) Prior personal computers diffusion a tabular form of calculus of cable geometry was used by generations of engineers keeping in mind the following limitations and approximations: tangential drag coefficients were assumed to be negligible. A steady current flow was assumed as in the towed configuration. Cchabra (1982) Finite Element Method that assumes an arbitrary deflection angle for the top first section and calculates equilibrium equations down to the sea floor iterating up to a compliant solution. Gualdesi (1987) ANAMOOR. A Fortran Program based on iterative methods above including experimental data from intensive mooring campaign. Database of experimental drag
Energy Technology Data Exchange (ETDEWEB)
Vay, J.-L.; Geddes, C. G. R.; Cormier-Michel, E.; Grote, D. P.
2010-09-21
Laser driven plasma accelerators promise much shorter particle accelerators but their development requires detailed simulations that challenge or exceed current capabilities. We report the first direct simulations of stages up to 1 TeV from simulations using a Lorentz boosted calculation frame resulting in a million times speedup, thanks to a frame boost as high as gamma = 1300. Effects of the hyperbolic rotation in Minkowski space resulting from the frame boost on the laser propagation in the plasma is shown to be key in the mitigation of a numerical instability that was limiting previous attempts.
Debating complexity in modeling
Hunt, Randall J.; Zheng, Chunmiao
1999-01-01
Complexity in modeling would seem to be an issue of universal importance throughout the geosciences, perhaps throughout all science, if the debate last year among groundwater modelers is any indication. During the discussion the following questions and observations made up the heart of the debate.
Leão, William L.; Chen, Ming-Hui
2017-01-01
A stochastic volatility-in-mean model with correlated errors using the generalized hyperbolic skew Student-t (GHST) distribution provides a robust alternative to the parameter estimation for daily stock returns in the absence of normality. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for parameter estimation. The deviance information, the Bayesian predictive information and the log-predictive score criterion are used to assess the fit of the proposed model. The proposed method is applied to an analysis of the daily stock return data from the Standard & Poor’s 500 index (S&P 500). The empirical results reveal that the stochastic volatility-in-mean model with correlated errors and GH-ST distribution leads to a significant improvement in the goodness-of-fit for the S&P 500 index returns dataset over the usual normal model. PMID:29333210
Leão, William L; Abanto-Valle, Carlos A; Chen, Ming-Hui
2017-01-01
A stochastic volatility-in-mean model with correlated errors using the generalized hyperbolic skew Student-t (GHST) distribution provides a robust alternative to the parameter estimation for daily stock returns in the absence of normality. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for parameter estimation. The deviance information, the Bayesian predictive information and the log-predictive score criterion are used to assess the fit of the proposed model. The proposed method is applied to an analysis of the daily stock return data from the Standard & Poor's 500 index (S&P 500). The empirical results reveal that the stochastic volatility-in-mean model with correlated errors and GH-ST distribution leads to a significant improvement in the goodness-of-fit for the S&P 500 index returns dataset over the usual normal model.
Boccara, Nino
2010-01-01
Modeling Complex Systems, 2nd Edition, explores the process of modeling complex systems, providing examples from such diverse fields as ecology, epidemiology, sociology, seismology, and economics. It illustrates how models of complex systems are built and provides indispensable mathematical tools for studying their dynamics. This vital introductory text is useful for advanced undergraduate students in various scientific disciplines, and serves as an important reference book for graduate students and young researchers. This enhanced second edition includes: . -recent research results and bibliographic references -extra footnotes which provide biographical information on cited scientists who have made significant contributions to the field -new and improved worked-out examples to aid a student’s comprehension of the content -exercises to challenge the reader and complement the material Nino Boccara is also the author of Essentials of Mathematica: With Applications to Mathematics and Physics (Springer, 2007).
Simulation in Complex Modelling
DEFF Research Database (Denmark)
Nicholas, Paul; Ramsgaard Thomsen, Mette; Tamke, Martin
2017-01-01
This paper will discuss the role of simulation in extended architectural design modelling. As a framing paper, the aim is to present and discuss the role of integrated design simulation and feedback between design and simulation in a series of projects under the Complex Modelling framework. Complex...... performance, engage with high degrees of interdependency and allow the emergence of design agency and feedback between the multiple scales of architectural construction. This paper presents examples for integrated design simulation from a series of projects including Lace Wall, A Bridge Too Far and Inflated...... Restraint developed for the research exhibition Complex Modelling, Meldahls Smedie Gallery, Copenhagen in 2016. Where the direct project aims and outcomes have been reported elsewhere, the aim for this paper is to discuss overarching strategies for working with design integrated simulation....
Pilyugin, Sergei Yu
2017-01-01
Focusing on the theory of shadowing of approximate trajectories (pseudotrajectories) of dynamical systems, this book surveys recent progress in establishing relations between shadowing and such basic notions from the classical theory of structural stability as hyperbolicity and transversality. Special attention is given to the study of "quantitative" shadowing properties, such as Lipschitz shadowing (it is shown that this property is equivalent to structural stability both for diffeomorphisms and smooth flows), and to the passage to robust shadowing (which is also equivalent to structural stability in the case of diffeomorphisms, while the situation becomes more complicated in the case of flows). Relations between the shadowing property of diffeomorphisms on their chain transitive sets and the hyperbolicity of such sets are also described. The book will allow young researchers in the field of dynamical systems to gain a better understanding of new ideas in the global qualitative theory. It will also be of int...
Brun, Ch.; Chollet, J. P.
2009-04-01
The behaviour of the Atmospheric Boundary layer (ABL) along alpine valleys is strongly dependent on the day-night thermodynamic cycle and might impact meteorology and air pollution prediction. At night, the ABL is stably stratified and the radiative cooling of the surface yields the development of a katabatic flow (Doran and Horst 1983, Monti et al. 2002). This flow consists of a downslope wall-jet which has the structure of both wall turbulence in the inner-layer zone and shear layer turbulence in the outer-layer zone and enhances a relative mixing eventhough stable stratification is considered (Baines 2005). A full 3D description of such flow by mean of Large Eddy Simulation of turbulence (LES) has not yet been achieved, except recently on relatively simple slopes (Skyllingstad 2003, Smith and Skyllingstad 2005) or including geostrophic wind forcing (Cuxart et al. 2006, Cuxart and Jimenez 2006). This is the purpose of the present study to accurately describe the ABL on a hyperbolic tangent slope with stable stratification. The numerical code used, Meso-NH, has been developed in CNRM/Meteo-France and Laboratoire d'Aérologie Toulouse, and consists of an anelastic non-hydrostatic model solving the pseudo-incompressible Navier-Stokes equations with a Boussinesq approximation. About 5 million grid points are necessary to afford a relatively precise description of the flow in the vicinity of the surface, with a special refinement in the vertical direction to capture the wall-jet developing along the slope. The setting of initial and boundary conditions is crucial for the simulation of stable ABL. Initial conditions consist of air at rest following a stable temperature profile with a constant Brunt-Väisälä frequency N=0.013. At the surface two sets of boundary conditions have been considered, first a rough surface condition, second an ideal case with slip conditions. A constant surface cooling q_w=-30 W/m2 is applied on the stably stratified fluid initially at rest
Thermal Hyperbolic Metamaterials
Guo, Yu; Jacob, Zubin
2013-01-01
We explore the near-field radiative thermal energy transfer properties of hyperbolic metamaterials. The presence of unique electromagnetic states in a broad bandwidth leads to super-planckian thermal energy transfer between metamaterials separated by a nano-gap. We consider practical phonon-polaritonic metamaterials for thermal engineering in the mid-infrared range and show that the effect exists in spite of the losses, absorption and finite unit cell size. For thermophotovoltaic energy conve...
Modeling complexes of modeled proteins.
Anishchenko, Ivan; Kundrotas, Petras J; Vakser, Ilya A
2017-03-01
Structural characterization of proteins is essential for understanding life processes at the molecular level. However, only a fraction of known proteins have experimentally determined structures. This fraction is even smaller for protein-protein complexes. Thus, structural modeling of protein-protein interactions (docking) primarily has to rely on modeled structures of the individual proteins, which typically are less accurate than the experimentally determined ones. Such "double" modeling is the Grand Challenge of structural reconstruction of the interactome. Yet it remains so far largely untested in a systematic way. We present a comprehensive validation of template-based and free docking on a set of 165 complexes, where each protein model has six levels of structural accuracy, from 1 to 6 Å C α RMSD. Many template-based docking predictions fall into acceptable quality category, according to the CAPRI criteria, even for highly inaccurate proteins (5-6 Å RMSD), although the number of such models (and, consequently, the docking success rate) drops significantly for models with RMSD > 4 Å. The results show that the existing docking methodologies can be successfully applied to protein models with a broad range of structural accuracy, and the template-based docking is much less sensitive to inaccuracies of protein models than the free docking. Proteins 2017; 85:470-478. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Applications of Hyperbolic Metamaterial Substrates
Directory of Open Access Journals (Sweden)
Yu Guo
2012-01-01
Full Text Available We review the properties of hyperbolic metamaterials and show that they are promising candidates as substrates for nanoimaging, nanosensing, fluorescence engineering, and controlling thermal emission. Hyperbolic metamaterials can support unique bulk modes, tunable surface plasmon polaritons, and surface hyperbolic states (Dyakonov plasmons that can be used for a variety of applications. We compare the effective medium predictions with practical realizations of hyperbolic metamaterials to show their potential for radiative decay engineering, bioimaging, subsurface sensing, metaplasmonics, and super-Planckian thermal emission.
Network Mapping by Replaying Hyperbolic Growth
Papadopoulos, Fragkiskos; Psomas, Constantinos; Krioukov, Dmitri
2012-01-01
Recent years have shown a promising progress in understanding geometric underpinnings behind the structure, function, and dynamics of many complex networks in nature and society. However these promises cannot be readily fulfilled and lead to important practical applications, without a simple, reliable, and fast network mapping method to infer the latent geometric coordinates of nodes in a real network. Here we present HyperMap, a simple method to map a given real network to its hyperbolic spa...
Properties of hyperbolic Pascal triangles
Belbachir, Hacene; Németh, László; Szalay, László
2017-08-01
Here we summarize some results on a recently introduced new generalization of Pascal's triangle called hyperbolic Pascal triangles. The name comes from the mathematical background, which goes back to regular mosaics on the hyperbolic plane. A few open questions will also be posed.
Predictive Surface Complexation Modeling
Energy Technology Data Exchange (ETDEWEB)
Sverjensky, Dimitri A. [Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Earth and Planetary Sciences
2016-11-29
Surface complexation plays an important role in the equilibria and kinetics of processes controlling the compositions of soilwaters and groundwaters, the fate of contaminants in groundwaters, and the subsurface storage of CO_{2} and nuclear waste. Over the last several decades, many dozens of individual experimental studies have addressed aspects of surface complexation that have contributed to an increased understanding of its role in natural systems. However, there has been no previous attempt to develop a model of surface complexation that can be used to link all the experimental studies in order to place them on a predictive basis. Overall, my research has successfully integrated the results of the work of many experimentalists published over several decades. For the first time in studies of the geochemistry of the mineral-water interface, a practical predictive capability for modeling has become available. The predictive correlations developed in my research now enable extrapolations of experimental studies to provide estimates of surface chemistry for systems not yet studied experimentally and for natural and anthropogenically perturbed systems.
Polystochastic Models for Complexity
Iordache, Octavian
2010-01-01
This book is devoted to complexity understanding and management, considered as the main source of efficiency and prosperity for the next decades. Divided into six chapters, the book begins with a presentation of basic concepts as complexity, emergence and closure. The second chapter looks to methods and introduces polystochastic models, the wave equation, possibilities and entropy. The third chapter focusing on physical and chemical systems analyzes flow-sheet synthesis, cyclic operations of separation, drug delivery systems and entropy production. Biomimetic systems represent the main objective of the fourth chapter. Case studies refer to bio-inspired calculation methods, to the role of artificial genetic codes, neural networks and neural codes for evolutionary calculus and for evolvable circuits as biomimetic devices. The fifth chapter, taking its inspiration from systems sciences and cognitive sciences looks to engineering design, case base reasoning methods, failure analysis, and multi-agent manufacturing...
Witten, Matthew
1983-01-01
Hyperbolic Partial Differential Equations, Volume 1: Population, Reactors, Tides and Waves: Theory and Applications covers three general areas of hyperbolic partial differential equation applications. These areas include problems related to the McKendrick/Von Foerster population equations, other hyperbolic form equations, and the numerical solution.This text is composed of 15 chapters and begins with surveys of age specific population interactions, populations models of diffusion, nonlinear age dependent population growth with harvesting, local and global stability for the nonlinear renewal eq
Advanced fabrication of hyperbolic metamaterials
DEFF Research Database (Denmark)
Shkondin, Evgeniy; Sukham, Johneph; Panah, Mohammad Esmail Aryaee
2017-01-01
Hyperbolic metamaterials can provide unprecedented properties in accommodation of high-k (high wave vector) waves and enhancement of the optical density of states. To reach such performance the metamaterials have to be fabricated with as small imperfections as possible. Here we report on our...... advances in two approaches in fabrication of optical metamaterials. We deposit ultrathin ultrasmooth gold layers with the assistance of organic material (APTMS) adhesion layer. The technology supports the stacking of such layers in a multiperiod construction with alumina spacers between gold films, which...... is expected to exhibit hyperbolic properties in the visible range. As the second approach we apply the atomic layer deposition technique to arrange vertical alignment of layers or pillars of heavily doped ZnO or TiN, which enables us to produce hyperbolic metamaterials for the near- and mid-infrared ranges....
The spectrum of hyperbolic surfaces
Bergeron, Nicolas
2016-01-01
This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithmetic hyperbolic surfaces”, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss. The fruit of several graduate level courses at Orsay...
Complex systems models: engineering simulations
Polack, Fiona A. C.; Hoverd, Tim; Sampson, Adam T.; Stepney, Susan; Timmis, Jon,
2008-01-01
As part of research towards the CoSMoS unified infrastructure for modelling and simulating complex systems, we review uses of definitional and descriptive models in natural science and computing, and existing integrated platforms. From these, we identify requirements for engineering models of complex systems, and consider how some of the requirements could be met, using state-of-the-art model management and a mobile, process-oriented computing paradigm.
Quasi-Hyperbolicity and Delay Semigroups
Directory of Open Access Journals (Sweden)
Shard Rastogi
2016-01-01
Full Text Available We study quasi-hyperbolicity of the delay semigroup associated with the equation u′(t=Bu(t+Φut, where ut is the history function and (B,D(B is the generator of a quasi-hyperbolic semigroup. We give conditions under which the associated solution semigroup of this equation generates a quasi-hyperbolic semigroup.
Height in splittings of hyperbolic groups
Indian Academy of Sciences (India)
Suppose is a hyperbolic subgroup of a hyperbolic group . Assume there exists > 0 such that the intersection of essentially distinct conjugates of is always finite. Further assume splits over with hyperbolic vertex and edge groups and the two inclusions of are quasi-isometric embeddings. Then is ...
z -classes of isometries of the hyperbolic space
Gongopadhyay, Krishnendu; Kulkarni, Ravi S.
Let G be a group. Two elements x, y are said to be z -equivalent if their centralizers are conjugate in G . The class equation of G is the partition of G into conjugacy classes. Further decomposition of conjugacy classes into z -classes provides important information about the internal structure of the group; cf. J. Ramanujan Math. Soc. 22 (2007), 35-56, for the elaboration of this theme. Let I(H^n) denote the group of isometries of the hyperbolic n -space, and let I_o(H^n) be the identity component of I(H^n) . We show that the number of z -classes in I(H^n) is finite. We actually compute their number; cf. theorem 1.3. We interpret the finiteness of z -classes as accounting for the finiteness of ``dynamical types'' in I(H^n) . Along the way we also parametrize conjugacy classes. We mainly use the linear model of the hyperbolic space for this purpose. This description of parametrizing conjugacy classes appears to be new; cf. Academic Press, New York, 1974, 49-87 and Conformal geometry (Bonn, 1985/1986), 41-64, Aspects Math., E12, Vieweg, Braunschweig, 1988, for previous attempts. Ahlfors (Differential Geometry and Complex Analysis (Springer, 1985), 65-73) suggested the use of Clifford algebras to deal with higher dimensional hyperbolic geometry; cf. Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 15-27, Quasiconformal Mappings and Analysis (Springer, 1998), 109-139, Complex Variables Theory Appl. 15 (1990), 125-133, and Adv. Math. 101 (1993), 87-113. These works may be compared to the approach suggested in this paper. In dimensions 2 and 3 , by remarkable Lie-theoretic isomorphisms, I_o(H2) and I_o(H3) can be lifted to GL_o(2, R) , and GL(2, C) respectively. For orientation-reversing isometries there are some modifications of these liftings. Using these liftings, in the appendix A, we have introduced a single numerical invariant c(A) , to classify the elements of I(H2) and I(H3) , and explained the classical terminology. Using the ``Iwasawa decomposition'' of I
Linearization of hyperbolic resonant germs
Bonckaert, P; Naudot, [No Value; Yang, JH
In this paper we develop an explicit normal form conjugacy procedure, called an 'LMT normal form', to study linearization of a smooth vector field in the neighbourhood of a hyperbolic equilibrium point with resonant eigenvalues. We give an asymptotic expression for such a linearization in terms of
Development of hyperbolic solution method for two fluids equation system
Energy Technology Data Exchange (ETDEWEB)
Lee, Sung Jae; Chang, Won Pyo
1997-07-01
Using the concept of surface tension thickness, the mathematical ill-posedness of the two fluids equation system can now be removed by splitting the pressure discontinuity of the two fluids interface. The bulk modulus L1 and L2 derived from the concept of surface tension thickness makes two fluids equation system hyperbolic type. The hyperbolic equation system has five complete sets of eigenvectors, each of which having real eigenvalues. Three sets of them represents the propagation speeds of the physical properties for individual flow regimes such as the dispersed, the slug, and the separated flows. The propagation characteristics of these eigenvalues have good agreements with both the experimental data and other theoretical results in two-phase mixture. The feature of the hyperbolic model allows to apply advanced numerical upwind technique such as Flux vector splitting (FVS) method. The numerical test show that the characteristics of equation system clearly classify all flow regimes. (author). 25 refs., 3 tabs., 20 figs.
Hyperbolic Triangle Centers The Special Relativistic Approach
Ungar, A.A
2010-01-01
After A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein’s special theory of relativity, the purpose of his new book is to introduce hyperbolic barycentric coordinates, another important concept to embed Euclidean geometry into hyperbolic geometry. It will be demonstrated that, in full analogy to classical mechanics where barycentric coordinates are related to the Newtonian mass, barycentric coordinates are related to the Einsteinian relativistic mass in hyperbolic geometry. Contrary to general belief, Einstein’s relativistic mass hence meshes up extraordinarily well with Minkowski’s four-vector formalism of special relativity. In Euclidean geometry, barycentric coordinates can be used to determine various triangle centers. While there are many known Euclidean triangle centers, only few hyperbolic triangle centers are known, and none of the known hyperbolic triangle centers has been determined analytic...
Gromov hyperbolicity in Cartesian product graphs
Indian Academy of Sciences (India)
manifolds and the hyperbolicity of a simple graph; hence, it is useful to know hyperbolicity criteria for graphs. In our study on hyperbolic graphs we use the notations of [10]. We now give the basic facts about Gromov's spaces. If γ is a continuous curve in a metric space (X, d), we say that γ is a geodesic if it is an isometry, i.e. ...
Hyperbolic contraction measuring systems for extensional flow
Nyström, M.; Tamaddon Jahromi, H. R.; Stading, M.; Webster, M. F.
2017-08-01
In this paper an experimental method for extensional measurements on medium viscosity fluids in contraction flow is evaluated through numerical simulations and experimental measurements. This measuring technique measures the pressure drop over a hyperbolic contraction, caused by fluid extension and fluid shear, where the extensional component is assumed to dominate. The present evaluative work advances our previous studies on this experimental method by introducing several contraction ratios and addressing different constitutive models of varying shear and extensional response. The constitutive models included are those of the constant viscosity Oldroyd-B and FENE-CR models, and the shear-thinning LPTT model. Examining the results, the impact of shear and first normal stress difference on the measured pressure drop are studied through numerical pressure drop predictions. In addition, stream function patterns are investigated to detect vortex development and influence of contraction ratio. The numerical predictions are further related to experimental measurements for the flow through a 15:1 contraction ratio with three different test fluids. The measured pressure drops are observed to exhibit the same trends as predicted in the numerical simulations, offering close correlation and tight predictive windows for experimental data capture. This result has demonstrated that the hyperbolic contraction flow is well able to detect such elastic fluid properties and that this is matched by numerical predictions in evaluation of their flow response. The hyperbolical contraction flow technique is commended for its distinct benefits: it is straightforward and simple to perform, the Hencky strain can be set by changing contraction ratio, non-homogeneous fluids can be tested, and one can directly determine the degree of elastic fluid behaviour. Based on matching of viscometric extensional viscosity response for FENE-CR and LPTT models, a decline is predicted in pressure drop for
Computational models of complex systems
Dabbaghian, Vahid
2014-01-01
Computational and mathematical models provide us with the opportunities to investigate the complexities of real world problems. They allow us to apply our best analytical methods to define problems in a clearly mathematical manner and exhaustively test our solutions before committing expensive resources. This is made possible by assuming parameter(s) in a bounded environment, allowing for controllable experimentation, not always possible in live scenarios. For example, simulation of computational models allows the testing of theories in a manner that is both fundamentally deductive and experimental in nature. The main ingredients for such research ideas come from multiple disciplines and the importance of interdisciplinary research is well recognized by the scientific community. This book provides a window to the novel endeavours of the research communities to present their works by highlighting the value of computational modelling as a research tool when investigating complex systems. We hope that the reader...
Complex Networks in Psychological Models
Wedemann, R. S.; Carvalho, L. S. A. V. D.; Donangelo, R.
We develop schematic, self-organizing, neural-network models to describe mechanisms associated with mental processes, by a neurocomputational substrate. These models are examples of real world complex networks with interesting general topological structures. Considering dopaminergic signal-to-noise neuronal modulation in the central nervous system, we propose neural network models to explain development of cortical map structure and dynamics of memory access, and unify different mental processes into a single neurocomputational substrate. Based on our neural network models, neurotic behavior may be understood as an associative memory process in the brain, and the linguistic, symbolic associative process involved in psychoanalytic working-through can be mapped onto a corresponding process of reconfiguration of the neural network. The models are illustrated through computer simulations, where we varied dopaminergic modulation and observed the self-organizing emergent patterns at the resulting semantic map, interpreting them as different manifestations of mental functioning, from psychotic through to normal and neurotic behavior, and creativity.
Building systems from simple hyperbolic ones
Zwart, Heiko J.; Le Gorrec, Y.; Maschke, B.
In this article we introduce a technique that derives from the existence and uniqueness of solutions to a simple hyperbolic partial differential equation (p.d.e.) the existence and uniqueness of solutions to hyperbolic and parabolic p.d.e.’s. Among others, we show that starting with an impedance
Plasmonic waveguides cladded by hyperbolic metamaterials
DEFF Research Database (Denmark)
Ishii, Satoshi; Shalaginov, Mikhail Y.; Babicheva, Viktoriia E.
2014-01-01
Strongly anisotropic media with hyperbolic dispersion can be used for claddings of plasmonic waveguides (PWs). In order to analyze the fundamental properties of such waveguides, we analytically study 1D waveguides arranged from a hyperbolic metamaterial (HMM) in a HMM-Insulator-HMM (HIH) structure...
IMPLEMENTATIONS AND PRACTICAL APPLICATIONS OF HYPERBOLIC METAMATERIALS
Directory of Open Access Journals (Sweden)
A. V. Shchelokova
2014-03-01
Full Text Available The paper presents a review on hyperbolic metamaterials which are normally described by the permittivity and permeability tensors with the components of the opposite sign. Therefore, the hyperbolic metamaterials have the hyperbolic isofrequency surfaces in the wave vector space. It leads to a number of unusual properties, such as the negative refraction, the diverging density of photonic states, ultra-high rate of spontaneous emission and increasing of subwavelength fields. The presence of the unique properties mentioned above makes the concept of hyperbolic metamaterials promising for research in modern science and explains the attempts of research groups around the world to realize structures with hyperbolic isofrequency curve suitable for applications in different frequency ranges. Hyperbolic metamaterials realized as layered metal-dielectric structures, arrays of nanowires, graphene layers, as well as artificial transmission lines are considered in the paper. Possible practical applications of hyperbolic metamaterials are described including hyperlens able to increase the nanoscale objects; wire mediums applied for spectroscopy to improve the resolution and increasing the distance to the object being scanned. Hyperbolic metamaterials are noted to be extremely promising for applications in nanophotonics, including single-photon generation, sensing and photovoltaics.
Complex fluids modeling and algorithms
Saramito, Pierre
2016-01-01
This book presents a comprehensive overview of the modeling of complex fluids, including many common substances, such as toothpaste, hair gel, mayonnaise, liquid foam, cement and blood, which cannot be described by Navier-Stokes equations. It also offers an up-to-date mathematical and numerical analysis of the corresponding equations, as well as several practical numerical algorithms and software solutions for the approximation of the solutions. It discusses industrial (molten plastics, forming process), geophysical (mud flows, volcanic lava, glaciers and snow avalanches), and biological (blood flows, tissues) modeling applications. This book is a valuable resource for undergraduate students and researchers in applied mathematics, mechanical engineering and physics.
Prediction models in complex terrain
DEFF Research Database (Denmark)
Marti, I.; Nielsen, Torben Skov; Madsen, Henrik
2001-01-01
The objective of the work is to investigatethe performance of HIRLAM in complex terrain when used as input to energy production forecasting models, and to develop a statistical model to adapt HIRLAM prediction to the wind farm. The features of the terrain, specially the topography, influence...... are calculated using on-line measurements of power production as well as HIRLAM predictions as input thus taking advantage of the auto-correlation, which is present in the power production for shorter pediction horizons. Statistical models are used to discribe the relationship between observed energy production...... the performance of HIRLAM in particular with respect to wind predictions. To estimate the performance of the model two spatial resolutions (0,5 Deg. and 0.2 Deg.) and different sets of HIRLAM variables were used to predict wind speed and energy production. The predictions of energy production for the wind farms...
Hyperbolic Chaos A Physicist’s View
Kuznetsov, Sergey P
2012-01-01
"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.
The art and science of hyperbolic tessellations.
Van Dusen, B; Taylor, R P
2013-04-01
The visual impact of hyperbolic tessellations has captured artists' imaginations ever since M.C. Escher generated his Circle Limit series in the 1950s. The scaling properties generated by hyperbolic geometry are different to the fractal scaling properties found in nature's scenery. Consequently, prevalent interpretations of Escher's art emphasize the lack of connection with nature's patterns. However, a recent collaboration between the two authors proposed that Escher's motivation for using hyperbolic geometry was as a method to deliberately distort nature's rules. Inspired by this hypothesis, this year's cover artist, Ben Van Dusen, embeds natural fractals such as trees, clouds and lightning into a hyperbolic scaling grid. The resulting interplay of visual structure at multiple size scales suggests that hybridizations of fractal and hyperbolic geometries provide a rich compositional tool for artists.
Variable Lebesgue spaces and hyperbolic systems
2014-01-01
This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some mor...
Hyperbolic accelerating beams and their relation with Hermite-Gaussian beams.
Huang, Chaohong; Li, Hanqing; Wu, Jianfeng; Yan, Yupeng
2018-02-01
We derive the initial distributions of phase and complex amplitude of accelerating beams with arbitrary predesigned hyperbolic trajectories using the caustic-design method and explore the relation between these beams and Hermite-Gaussian beams. The results show the hyperbolic accelerating beams are a larger class of beams than Hermite-Gaussian beams. When the bending parameter is an integer, the hyperbolic accelerating beams have a similar initial complex amplitude distribution and almost the same propagating characteristics as Hermite-Gaussian beams. Through the analysis of the ray-based method, we also derive an approximate expression for the initial complex amplitude of Hermite-Gaussian beams after introducing an amplitude distribution function. Although the proposed approximate expressions of complex amplitude are more complex than the usually used Hermite-Gaussian function, they explicitly indicate the information on local amplitude, wave vector, and internal ray structure (including caustics) of these beams and thus provide us clearer geometrical insights into these beams.
On the Way to Appropriate Model Complexity
Höge, M.
2016-12-01
When statistical models are used to represent natural phenomena they are often too simple or too complex - this is known. But what exactly is model complexity? Among many other definitions, the complexity of a model can be conceptualized as a measure of statistical dependence between observations and parameters (Van der Linde, 2014). However, several issues remain when working with model complexity: A unique definition for model complexity is missing. Assuming a definition is accepted, how can model complexity be quantified? How can we use a quantified complexity to the better of modeling? Generally defined, "complexity is a measure of the information needed to specify the relationships between the elements of organized systems" (Bawden & Robinson, 2015). The complexity of a system changes as the knowledge about the system changes. For models this means that complexity is not a static concept: With more data or higher spatio-temporal resolution of parameters, the complexity of a model changes. There are essentially three categories into which all commonly used complexity measures can be classified: (1) An explicit representation of model complexity as "Degrees of freedom" of a model, e.g. effective number of parameters. (2) Model complexity as code length, a.k.a. "Kolmogorov complexity": The longer the shortest model code, the higher its complexity (e.g. in bits). (3) Complexity defined via information entropy of parametric or predictive uncertainty. Preliminary results show that Bayes theorem allows for incorporating all parts of the non-static concept of model complexity like data quality and quantity or parametric uncertainty. Therefore, we test how different approaches for measuring model complexity perform in comparison to a fully Bayesian model selection procedure. Ultimately, we want to find a measure that helps to assess the most appropriate model.
Chen, G.; Zheng, Q.; Coleman, M.; Weerakoon, S.
1983-01-01
This paper briefly reviews convergent finite difference schemes for hyperbolic initial boundary value problems and their applications to boundary control systems of hyperbolic type which arise in the modelling of vibrations. These difference schemes are combined with the primal and the dual approaches to compute the optimal control in the unconstrained case, as well as the case when the control is subject to inequality constraints. Some of the preliminary numerical results are also presented.
Molecular modeling of polynucleotide complexes.
Meneksedag-Erol, Deniz; Tang, Tian; Uludağ, Hasan
2014-08-01
Delivery of polynucleotides into patient cells is a promising strategy for treatment of genetic disorders. Gene therapy aims to either synthesize desired proteins (DNA delivery) or suppress expression of endogenous genes (siRNA delivery). Carriers constitute an important part of gene therapeutics due to limitations arising from the pharmacokinetics of polynucleotides. Non-viral carriers such as polymers and lipids protect polynucleotides from intra and extracellular threats and facilitate formation of cell-permeable nanoparticles through shielding and/or bridging multiple polynucleotide molecules. Formation of nanoparticulate systems with optimal features, their cellular uptake and intracellular trafficking are crucial steps for an effective gene therapy. Despite the great amount of experimental work pursued, critical features of the nanoparticles as well as their processing mechanisms are still under debate due to the lack of instrumentation at atomic resolution. Molecular modeling based computational approaches can shed light onto the atomic level details of gene delivery systems, thus provide valuable input that cannot be readily obtained with experimental techniques. Here, we review the molecular modeling research pursued on critical gene therapy steps, highlight the knowledge gaps in the field and providing future perspectives. Existing modeling studies revealed several important aspects of gene delivery, such as nanoparticle formation dynamics with various carriers, effect of carrier properties on complexation, carrier conformations in endosomal stages, and release of polynucleotides from carriers. Rate-limiting steps related to cellular events (i.e. internalization, endosomal escape, and nuclear uptake) are now beginning to be addressed by computational approaches. Limitations arising from current computational power and accuracy of modeling have been hindering the development of more realistic models. With the help of rapidly-growing computational power
Clawpack: Building an open source ecosystem for solving hyperbolic PDEs
Iverson, Richard M.; Mandli, K.T.; Ahmadia, Aron J.; Berger, M.J.; Calhoun, Donna; George, David L.; Hadjimichael, Y.; Ketcheson, David I.; Lemoine, Grady L.; LeVeque, Randall J.
2016-01-01
Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a description of our current development model. Clawpack: building an open source ecosystem for solving hyperbolic PDEs.
Thermodynamic modeling of complex systems
DEFF Research Database (Denmark)
Liang, Xiaodong
been developed, which has avoided the numerical pitfalls of having more than three volume roots in the real application range. It has been shown that it is possible to directly use the original PC-SAFT parameters with the new universal constants for the systems considered in this thesis. Finally...... after an oil spill. Engineering thermodynamics could be applied in the state-of-the-art sonar products through advanced artificial technology, if the speed of sound, solubility and density of oil-seawater systems could be satisfactorily modelled. The addition of methanol or glycols into unprocessed well...... streams during subsea pipelines is necessary to inhibit gas hydrate formation, and the offshore reservoirs often mean complicated temperature and pressure conditions. Accurate description of the phase behavior and thermalphysical properties of complex systems containing petroleum fluids and polar...
Interpolated pressure laws in two-fluid simulations and hyperbolicity
Helluy, Philippe; Jung, Jonathan
2014-01-01
We consider a two-fluid compressible flow. Each fluid obeys a stiffened gas pressure law. The continuous model is well defined without considering mixture regions. However, for numerical applications it is often necessary to consider artificial mixtures, because the two-fluid interface is diffused by the numerical scheme. We show that classic pressure law interpolations lead to a non-convex hyperbolicity domain and failure of well-known numerical schemes. We propose a physically relevant pres...
Boundary behaviour of automorphisms of a hyperbolic space
Zorich, V. A.
2017-08-01
An automorphism of a Euclidean ball extends to a homeomorphic mapping of the closed ball even when the quasiconformality coefficient of the mapping increases unboundedly but in a controlled way upon approaching the boundary of the ball. By means of Poincaré's conformally Euclidean model of the Lobachevsky space, this yields a condition under which an automorphism of a hyperbolic space still extends to the ideal boundary (the absolute) of the space when translated into geometric language. Bibliography: 28 titles.
Some problems on nonlinear hyperbolic equations and applications
Peng, YueJun
2010-01-01
This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.
Linear response function for coupled hyperbolic attractors
Jiang, M
2004-01-01
We prove that when we take the thermodynamic limit in the context of coupled hyperbolic attractors, Ruelle's derivative formula of the SRB measure with respect to the underlying dynamical system remains true if one of the terms is interpreted appropriately.
Invariant manifolds near hyperbolic fixed points
Homburg, A.J.
2006-01-01
Abstract: In these notes, we discuss obstructions to the existence of local invariant manifolds of some smoothness class, near hyperbolic fixed points of diffeomorphisms. We present an elementary construction for continuously differentiable invariant manifolds that are not necessarily normally
Rothe's method to semilinear hyperbolic integrodifferential equations
Directory of Open Access Journals (Sweden)
D. Bahaguna
1990-01-01
Full Text Available In this paper we consider an application of Rothe's method to abstract semi-linear hyperbolic integrodifferential equations in Hilbert spaces. With the aid of Rothe's method we establish the existence of a unique strong solution.
DEFF Research Database (Denmark)
Isaeva, Olga B.; Kuznetsov, Sergey P.; Mosekilde, Erik
2011-01-01
model corresponds to the situation of equality of natural frequencies of the partial oscillators, and another to a nonresonant ratio of the oscillation frequencies relating to each of the two pairs. Dynamics of all models are illustrated with diagrams indicating the transformation of the angular......The paper proposes an approach to constructing feasible examples of dynamical systems with hyperbolic chaotic attractors based on the successive transfer of excitation between two pairs of self-oscillators that are alternately active. An angular variable that measures the relations of the current...... amplitudes for the two oscillators of each pair undergoes a transformation in accordance with the expanding circle map during each cycle of the process. We start with equations describing the dynamics in terms of complex or real amplitudes and then examine two models based on van der Pol oscillators. One...
Hyperbolic differential operators and related problems
Ancona, Vincenzo
2003-01-01
Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the top
Hyperbolic metamaterials: Novel physics and applications
Smolyaninov, Igor I.; Smolyaninova, Vera N.
2017-10-01
Hyperbolic metamaterials were originally introduced to overcome the diffraction limit of optical imaging. Soon thereafter it was realized that hyperbolic metamaterials demonstrate a number of novel phenomena resulting from the broadband singular behavior of their density of photonic states. These novel phenomena and applications include super resolution imaging, new stealth technologies, enhanced quantum-electrodynamic effects, thermal hyperconductivity, superconductivity, and interesting gravitation theory analogues. Here we briefly review typical material systems, which exhibit hyperbolic behavior and outline important novel applications of hyperbolic metamaterials. In particular, we will describe recent imaging experiments with plasmonic metamaterials and novel VCSEL geometries, in which the Bragg mirrors may be engineered in such a way that they exhibit hyperbolic metamaterial properties in the long wavelength infrared range, so that they may be used to efficiently remove excess heat from the laser cavity. We will also discuss potential applications of three-dimensional self-assembled photonic hypercrystals, which are based on cobalt ferrofluids in external magnetic field. This system bypasses 3D nanofabrication issues, which typically limit metamaterial applications. Photonic hypercrystals combine the most interesting features of hyperbolic metamaterials and photonic crystals.
Stability and boundary stabilization of 1-D hyperbolic systems
Bastin, Georges
2016-01-01
This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary...
Hyperbolic Conservation Laws and Related Analysis with Applications
Holden, Helge; Karlsen, Kenneth
2014-01-01
This book presents thirteen papers, representing the most significant advances and current trends in nonlinear hyperbolic conservation laws and related analysis with applications. Topics covered include a survey on multidimensional systems of conservation laws as well as novel results on liquid crystals, conservation laws with discontinuous flux functions, and applications to sedimentation. Also included are articles on recent advances in the Euler equations and the Navier-Stokes-Fourier-Poisson system, in addition to new results on collective phenomena described by the Cucker-Smale model. The Workshop on Hyperbolic Conservation Laws and Related Analysis with Applications at the International Centre for Mathematical Sciences (Edinburgh, UK) held in Edinburgh, September 2011, produced this fine collection of original research and survey articles. Many leading mathematicians attended the event and submitted their contributions for this volume. It is addressed to researchers and graduate students inter...
Teacher Modeling Using Complex Informational Texts
Fisher, Douglas; Frey, Nancy
2015-01-01
Modeling in complex texts requires that teachers analyze the text for factors of qualitative complexity and then design lessons that introduce students to that complexity. In addition, teachers can model the disciplinary nature of content area texts as well as word solving and comprehension strategies. Included is a planning guide for think aloud.
Invisible Hyperbolic Metamaterial Nanotube at Visible Frequency
Kim, Kyoung-Ho; No, You-Shin; Chang, Sehwan; Choi, Jae-Hyuck; Park, Hong-Gyu
2015-01-01
Subwavelength-scale metal and dielectric nanostructures have served as important building blocks for electromagnetic metamaterials, providing unprecedented opportunities for manipulating the optical response of the matter. Recently, hyperbolic metamaterials have been drawing particular interest because of their unusual optical properties and functionalities, such as negative refraction and hyperlensing of light. Here, as a promising application of a hyperbolic metamaterial at visible frequency, we propose an invisible nanotube that consists of metal and dielectric alternating thin layers. The theoretical study of the light scattering of the layered nanotube reveals that almost-zero scattering can be achieved at a specific wavelength when the transverse-electric- or transverse-magnetic-polarized light is incident to the nanotube. In addition, the layered nanotube can be described as a radial-anisotropic hyperbolic metamaterial nanotube. The low scattering occurs when the effective permittivity of the hyperbolic nanotube in the angular direction is near zero, and thus the invisibility of the layered nanotube can be efficiently obtained by analyzing the equivalent hyperbolic nanotube. Our new method to design and tune an invisible nanostructure represents a significant step toward the practical implementation of unique nanophotonic devices such as invisible photodetectors and low-scattering near-field optical microscopes. PMID:26522815
Cubulated groups: thickness, relative hyperbolicity, and simplicial boundaries
Behrstock, Jason; Hagen, Mark F.
2012-01-01
Let G be a group acting geometrically on a CAT(0) cube complex X. We prove first that G is hyperbolic relative to the collection P of subgroups if and only if the simplicial boundary of X is the disjoint union of a nonempty discrete set, together with a pairwise-disjoint collection of subcomplexes corresponding, in the appropriate sense, to elements of P. As a special case of this result is a new proof, in the cubical case, of a Theorem of Hruska--Kleiner regarding Tits boundaries of relative...
Outer compositions of hyperbolic/loxodromic linear fractional transfomations
Directory of Open Access Journals (Sweden)
John Gill
1992-01-01
Full Text Available It is shown, using classical means, that the outer composition of hyperbolic or loxodromic linear fractional transformations {fn}, where fn→f, converges to α, the attracting fixed point of f, for all complex numbers z, with one possible exception, z0. I.e.,Fn(z:=fn∘fn−1∘…∘f1(z→αWhen z0 exists, Fn(z0→β, the repelling fixed point of f. Applications include the analytic theory of reverse continued fractions.
Hyperbolic conservation laws in continuum physics
Dafermos, Constantine M
2016-01-01
This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conser...
Notes on relatively hyperbolic groups and relatively quasiconvex subgroups
Matsuda, Yoshifumi; Oguni, Shin-ichi; Yamagata, Saeko
2013-01-01
We define relatively quasiconvex subgroups of relatively hyperbolic groups in the sense of Osin and show that such subgroups have expected properties. Also we state several definitions equivalent to the definition of relatively hyperbolic groups in the sense of Osin.
Near-field heat transfer between multilayer hyperbolic metamaterials
Energy Technology Data Exchange (ETDEWEB)
Biehs, Svend-Age [Oldenburg Univ. (Germany). Inst. fuer Physik; Ben-Abdallah, Philippe [Univ. Paris-Sud 11, Palaiseau (France). Lab. Charles Fabry; Univ. Sherbrooke, PQ (Canada). Dept. of Mechanical Engineering
2017-05-01
We review the near-field radiative heat flux between hyperbolic materials focusing on multilayer hyperbolic meta-materials. We discuss the formation of the hyperbolic bands, the impact of ordering of the multilayer slabs, as well as the impact of the first single layer on the heat transfer. Furthermore, we compare the contribution of surface modes to that of hyperbolic modes. Finally, we also compare the exact results with predictions from effective medium theory.
Cuspidal discrete series for projective hyperbolic spaces
DEFF Research Database (Denmark)
Andersen, Nils Byrial; Flensted-Jensen, Mogens
2013-01-01
Abstract. We have in [1] proposed a definition of cusp forms on semisimple symmetric spaces G/H, involving the notion of a Radon transform and a related Abel transform. For the real non-Riemannian hyperbolic spaces, we showed that there exists an infinite number of cuspidal discrete series......, and at most finitely many non-cuspidal discrete series, including in particular the spherical discrete series. For the projective spaces, the spherical discrete series are the only non-cuspidal discrete series. Below, we extend these results to the other hyperbolic spaces, and we also study the question...
Advanced Research Workshop on Nonlinear Hyperbolic Problems
Serre, Denis; Raviart, Pierre-Arnaud
1987-01-01
The field of nonlinear hyperbolic problems has been expanding very fast over the past few years, and has applications - actual and potential - in aerodynamics, multifluid flows, combustion, detonics amongst other. The difficulties that arise in application are of theoretical as well as numerical nature. In fact, the papers in this volume of proceedings deal to a greater extent with theoretical problems emerging in the resolution of nonlinear hyperbolic systems than with numerical methods. The volume provides an excellent up-to-date review of the current research trends in this area.
Clawpack: building an open source ecosystem for solving hyperbolic PDEs
Directory of Open Access Journals (Sweden)
Kyle T. Mandli
2016-08-01
Full Text Available Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a description of our current development model.
Clawpack: building an open source ecosystem for solving hyperbolic PDEs
Mandli, Kyle T.
2016-08-08
Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a description of our current development model.
Steger, Joseph L.
1989-01-01
Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, an extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.
Magnetism in one-dimensional metamaterials: Double hyperbolic media and magnetic surface states
Papadakis, Georgia T; Davoyan, Artur; Yeh, Pochi; Atwater, Harry A
2016-01-01
Metamaterials with magnetic properties have been widely investigated with rather complex two- and three-dimensional resonant structures. Here we propose conceptually and demonstrate experimentally a mechanism for broadband optical magnetism in simpler one-dimensional systems. We experimentally demonstrate that alternating high-index dielectric/metal multilayer hyperbolic metamaterials can exhibit a strong magnetic response including variously {\\mu}>1 to {\\mu}<0. By engineering the electric permittivity as well, we reveal an epsilon and mu near zero regime. We show that modifications of internal metamaterial structure can lead to either type I or type II magnetic hyperbolic dispersion, thereby generalizing the notion of a hyperbolic metamaterial to encompass both TE and TM polarizations in simple multilayer geometries. Finally, we show that a negative magnetic response can give rise to TE interface-bound states, analogous to their TM counterparts, surface plasmon polaritons.
Modelling the structure of complex networks
DEFF Research Database (Denmark)
Herlau, Tue
networks has been independently studied as mathematical objects in their own right. As such, there has been both an increased demand for statistical methods for complex networks as well as a quickly growing mathematical literature on the subject. In this dissertation we explore aspects of modelling complex......A complex network is a systems in which a discrete set of units interact in a quantifiable manner. Representing systems as complex networks have become increasingly popular in a variety of scientific fields including biology, social sciences and economics. Parallel to this development complex....... The next chapters will treat some of the various symmetries, representer theorems and probabilistic structures often deployed in the modelling complex networks, the construction of sampling methods and various network models. The introductory chapters will serve to provide context for the included written...
Molecular simulation and modeling of complex I.
Hummer, Gerhard; Wikström, Mårten
2016-07-01
Molecular modeling and molecular dynamics simulations play an important role in the functional characterization of complex I. With its large size and complicated function, linking quinone reduction to proton pumping across a membrane, complex I poses unique modeling challenges. Nonetheless, simulations have already helped in the identification of possible proton transfer pathways. Simulations have also shed light on the coupling between electron and proton transfer, thus pointing the way in the search for the mechanistic principles underlying the proton pump. In addition to reviewing what has already been achieved in complex I modeling, we aim here to identify pressing issues and to provide guidance for future research to harness the power of modeling in the functional characterization of complex I. This article is part of a Special Issue entitled Respiratory complex I, edited by Volker Zickermann and Ulrich Brandt. Copyright © 2016 Elsevier B.V. All rights reserved.
Domain decomposition methods for hyperbolic problems
Indian Academy of Sciences (India)
problems using domain decomposition but this technique faces difficulties if the system becomes characteristic at the inter-element boundaries. By making the inter-element boundaries move faster than the fastest wave speed associated with the hyperbolic system we are able to overcome this problem. Keywords. Domain ...
Domain decomposition methods for hyperbolic problems
Indian Academy of Sciences (India)
In this paper a method is developed for solving hyperbolic initial boundary value problems in one space dimension using domain decomposition, which can be extended to problems in several space dimensions. We minimize a functional which is the sum of squares of the 2 norms of the residuals and a term which is the ...
The homogeneous geometries of real hyperbolic space
DEFF Research Database (Denmark)
Castrillón López, Marco; Gadea, Pedro Martínez; Swann, Andrew Francis
We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanhecke, of the corresponding homogeneous tensors. We use ...
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
Abstract. In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable dis- crete metric space. Moreover, we use the techniques of Ozawa's to prove that a fine hyperbolic graph has the metric invariant translation approximation property.
Gromov hyperbolicity in lexicographic product graphs
Indian Academy of Sciences (India)
41
mathematics and computer science. Some large graphs are composed from some existing smaller ones by using several products of graphs, and many ... spread of viruses through on the internet (see [30, 31]). Furthermore, hyperbolic spaces are useful in secure transmission of information on the network (see [29, 30, 31, ...
From Anosov dynamics to hyperbolic attractors
Indian Academy of Sciences (India)
For conservative systems, hyperbolic chaos is represented by Anosov dynamics, when a .... site faces of the cubic cell may be thought as identified, and in this sense we deal with a compact ..... The scale along the vertical axis is indicated at the top in the right part of the figure. Here k is the steepness factor of frequency ...
Fibonacci words, hyperbolic tilings and grossone
Margenstern, Maurice
2015-04-01
In this paper, we study the contribution of the theory of grossone to the study of infinite Fibonacci words, combining this tool with the help of a particular tiling of the hyperbolic plane: the tiling { 7, 3 } , called the heptagrid. With the help of the numeral system based on grossone, we obtain a richer family of infinite Fibonacci words compared with the traditional approach.
On the hyperbolicity condition in linear elasticity
Directory of Open Access Journals (Sweden)
Remigio Russo
1991-05-01
Full Text Available This talk, which is mainly expository and based on [2-5], discusses the hyperbolicity conditions in linear elastodynamics. Particular emphasis is devoted to the key role it plays in the uniqueness questions associated with the mixed boundary-initial value problem in unbounded domains.
Asymptotic dimension of relatively hyperbolic groups
Osin, D. V.
2004-01-01
Suppose that a finitely generated group $G$ is hyperbolic relative to a collection of subgroups $\\{H_1, ..., H_m\\} $. We prove that if each of the subgroups $H_1, ..., H_m$ has finite asymptotic dimension, then asymptotic dimension of $G$ is also finite.
Algorithms for computing normally hyperbolic invariant manifolds
Broer, H.W.; Osinga, H.M.; Vegter, G.
An effcient algorithm is developed for the numerical computation of normally hyperbolic invariant manifolds, based on the graph transform and Newton's method. It fits in the perturbation theory of discrete dynamical systems and therefore allows application to the setting of continuation. A
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use the techniques of Ozawa's to prove that a fine hyperbolic graph has the metric invariant translation approximation property.
Hyperbolic spaces are of strictly negative type
DEFF Research Database (Denmark)
Hjorth, Poul G.; Kokkendorff, Simon L.; Markvorsen, Steen
2002-01-01
We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative...
Height in splittings of hyperbolic groups
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
We define the height of a finite subgroup to be 0. The following question of Swarup [9] formulates the problem we would like to address in this paper: Question. Suppose H is a finitely presented subgroup of a hyperbolic group G. If H has finite height, is H quasiconvex in G? A special case to be considered is when G splits ...
Mathematical Properties on the Hyperbolicity of Interval Graphs
Directory of Open Access Journals (Sweden)
Juan C. Hernández-Gómez
2017-11-01
Full Text Available Gromov hyperbolicity is an interesting geometric property, and so it is natural to study it in the context of geometric graphs. In particular, we are interested in interval and indifference graphs, which are important classes of intersection and Euclidean graphs, respectively. Interval graphs (with a very weak hypothesis and indifference graphs are hyperbolic. In this paper, we give a sharp bound for their hyperbolicity constants. The main result in this paper is the study of the hyperbolicity constant of every interval graph with edges of length 1. Moreover, we obtain sharp estimates for the hyperbolicity constant of the complement of any interval graph with edges of length 1.
Models of complex attitude systems
DEFF Research Database (Denmark)
Sørensen, Bjarne Taulo
production systems was modelled. The analysis was based on data from a cross-cultural survey involving 1931 participants from Belgium, Denmark, Germany and Poland. The survey questionnaire contained measures of personal value orientations and attitudes towards environment and nature, industrial food...
The hyperbolic step potential: Anti-bound states, SUSY partners and Wigner time delays
Energy Technology Data Exchange (ETDEWEB)
Gadella, M. [Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, E-47011 Valladolid (Spain); Kuru, Ş. [Department of Physics, Faculty of Science, Ankara University, 06100 Ankara (Turkey); Negro, J., E-mail: jnegro@fta.uva.es [Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, E-47011 Valladolid (Spain)
2017-04-15
We study the scattering produced by a one dimensional hyperbolic step potential, which is exactly solvable and shows an unusual interest because of its asymmetric character. The analytic continuation of the scattering matrix in the momentum representation has a branch cut and an infinite number of simple poles on the negative imaginary axis which are related with the so called anti-bound states. This model does not show resonances. Using the wave functions of the anti-bound states, we obtain supersymmetric (SUSY) partners which are the series of Rosen–Morse II potentials. We have computed the Wigner reflection and transmission time delays for the hyperbolic step and such SUSY partners. Our results show that the more bound states a partner Hamiltonian has the smaller is the time delay. We also have evaluated time delays for the hyperbolic step potential in the classical case and have obtained striking similitudes with the quantum case. - Highlights: • The scattering matrix of hyperbolic step potential is studied. • The scattering matrix has a branch cut and an infinite number of poles. • The poles are associated to anti-bound states. • Susy partners using antibound states are computed. • Wigner time delays for the hyperbolic step and partner potentials are compared.
Theory of hyperbolic stratified nanostructures for surface-enhanced Raman scattering
Wong, Herman M. K.; Dezfouli, Mohsen Kamandar; Axelrod, Simon; Hughes, Stephen; Helmy, Amr S.
2017-11-01
We theoretically investigate the enhancement of surface enhanced Raman spectroscopy (SERS) using hyperbolic stratified nanostructures and compare to metal nanoresonators. The photon Green function of each nanostructure within its environment is first obtained from a semianalytical modal theory, which is used in a quantum optics formalism of the molecule-nanostructure interaction to model the SERS spectrum. An intuitive methodology is presented for calculating the single-molecule enhancement factor (SMEF), which is also able to predict known experimental SERS enhancement factors of a gold nanodimer. We elucidate the important figures-of-merit of the enhancement and explore these for different designs. We find that the use of hyperbolic stratified materials can enhance the photonic local density of states (LDOS) by close to two times in comparison to pure metal nanostructures, when both designed to work at the same operating wavelengths. However, the increased LDOS is accompanied by higher electric field concentration within the lossy hyperbolic material, which leads to increased quenching that serves to reduce the overall detected SERS enhancement in the far field. For nanoresonators with resonant localized surface plasmon wavelengths in the near-infrared, the SMEF for the hyperbolic stratified nanostructure is approximately one order of magnitude lower than the pure metal counterpart. Conversely, we show that by detecting the Raman signal using a near-field probe, hyperbolic materials can provide an improvement in SERS enhancement compared to using pure metal nanostructures when the probe is sufficiently close (<50 nm ) to the Raman active molecule at the plasmonic hotspot.
Epitaxial thin films for hyperbolic metamaterials
Fullager, D.; Alisafaee, H.; Tsu, R.; Fiddy, M. A.
2014-02-01
Recent progress in the area of hyperbolic metamaterials (HMMs) has sparked interest in transparent conducting oxides (TCOs) that behave as plasmonic media in the near-IR and at optical frequencies for imaging and sensing applications. It has been shown that by depositing alternating layers of negative-epsilon/positive-epsilon materials, a medium can be created with unusual index values such as near zero. HMMs support high-k waves corresponding to a diverging photonic density of states (PDOS), the quantity determining phenomena such as spontaneous and thermal emission. Also, modeling such structures allows evanescent fields containing sub-wavelength information to be coupled to propagating radiation. We investigate the optical, electronic, and physical properties of radio frequency plasma-assisted molecular beam epitaxial (RF-MBE) growth of alternating layers of ZnO and TCO of uniform thickness for HMM applications. Preliminary work creating HMMs with ZnO and Al-doped ZnO (AZO) has shown a negative real part of the permittivity at near-IR whose modulus is proportional to the number density of Al dopant. However, increasing the Al content of the AZO increases the transmission losses to unacceptable levels for device applications at industry standard wavelengths. A TCO with conductivity and physical structure superior to that of AZO is gallium-doped ZnO (GZO). Uniformly grown GZO has been demonstrated to possess improved crystal quality over AZO due to the higher diffusivity of Al in the ZnO. AZO and GZO HMM structures grown by RF-MBE are characterized by scanning electron microscopy (SEM), atomic force microscopy (AFM), X-ray diffraction (XRD), Hall effect, four-point probing, deeplevel transient spectroscopy (DLTS), ellipsometry, visible and ultraviolet spectroscopy (UV-VIS) and in-situ reflection high energy electron diffraction (RHEED).
Hyperbolicity of second order in space systems of evolution equations
Energy Technology Data Exchange (ETDEWEB)
Gundlach, Carsten [School of Mathematics, University of Southampton, Southampton SO17 1BJ (United Kingdom); Martin-GarcIa, Jose M [Instituto de Estructura de la Materia, Centro de Fisica Miguel A Catalan, CSIC, Serrano 123, 28006 Madrid (Spain)
2006-08-21
A possible definition of strong/symmetric hyperbolicity for a second-order system of evolution equations is that it admits a reduction to first order which is strongly/symmetric hyperbolic. We investigate the general system that admits a reduction to first order and give necessary and sufficient criteria for strong/symmetric hyperbolicity of the reduction in terms of the principal part of the original second-order system. An alternative definition of strong hyperbolicity is based on the existence of a complete set of characteristic variables, and an alternative definition of symmetric hyperbolicity is based on the existence of a conserved (up to lower-order terms) energy. Both these definitions are made without any explicit reduction. Finally, strong hyperbolicity can be defined through a pseudo-differential reduction to first order. We prove that both definitions of symmetric hyperbolicity are equivalent and that all three definitions of strong hyperbolicity are equivalent (in three space dimensions). We show how to impose maximally dissipative boundary conditions on any symmetric hyperbolic second-order system. We prove that if the second-order system is strongly hyperbolic, any closed constraint evolution system associated with it is also strongly hyperbolic, and that the characteristic variables of the constraint system are derivatives of a subset of the characteristic variables of the main system, with the same speeds.
Mixture model analysis of complex samples
Wedel, M; ter Hofstede, F; Steenkamp, JBEM
1998-01-01
We investigate the effects of a complex sampling design on the estimation of mixture models. An approximate or pseudo likelihood approach is proposed to obtain consistent estimates of class-specific parameters when the sample arises from such a complex design. The effects of ignoring the sample
Computational Modeling of Complex Protein Activity Networks
Schivo, Stefano; Leijten, Jeroen; Karperien, Marcel; Post, Janine N.; Prignet, Claude
2017-01-01
Because of the numerous entities interacting, the complexity of the networks that regulate cell fate makes it impossible to analyze and understand them using the human brain alone. Computational modeling is a powerful method to unravel complex systems. We recently described the development of a
Modeling Musical Complexity: Commentary on Eerola (2016
Directory of Open Access Journals (Sweden)
Joshua Albrecht
2016-07-01
Full Text Available In his paper, "Expectancy violation and information-theoretic models of melodic complexity," Eerola compares a number of models that correlate musical features of monophonic melodies with participant ratings of perceived melodic complexity. He finds that fairly strong results can be achieved using several different approaches to modeling perceived melodic complexity. The data used in this study are gathered from several previously published studies that use widely different types of melodies, including isochronous folk melodies, isochronous 12-tone rows, and rhythmically complex African folk melodies. This commentary first briefly reviews the article's method and main findings, then suggests a rethinking of the theoretical framework of the study. Finally, some of the methodological issues of the study are discussed.
Complex system modelling for veterinary epidemiology.
Lanzas, Cristina; Chen, Shi
2015-02-01
The use of mathematical models has a long tradition in infectious disease epidemiology. The nonlinear dynamics and complexity of pathogen transmission pose challenges in understanding its key determinants, in identifying critical points, and designing effective mitigation strategies. Mathematical modelling provides tools to explicitly represent the variability, interconnectedness, and complexity of systems, and has contributed to numerous insights and theoretical advances in disease transmission, as well as to changes in public policy, health practice, and management. In recent years, our modelling toolbox has considerably expanded due to the advancements in computing power and the need to model novel data generated by technologies such as proximity loggers and global positioning systems. In this review, we discuss the principles, advantages, and challenges associated with the most recent modelling approaches used in systems science, the interdisciplinary study of complex systems, including agent-based, network and compartmental modelling. Agent-based modelling is a powerful simulation technique that considers the individual behaviours of system components by defining a set of rules that govern how individuals ("agents") within given populations interact with one another and the environment. Agent-based models have become a recent popular choice in epidemiology to model hierarchical systems and address complex spatio-temporal dynamics because of their ability to integrate multiple scales and datasets. Copyright © 2014 Elsevier B.V. All rights reserved.
Outada, Nisrine
2016-09-01
I have read with great interest the paper [5] where the authors present an overview and critical analysis of the literature on the modeling of the crowd dynamics with special attention to evacuation dynamics. The approach developed is based on suitable development of methods of the kinetic theory. Interactions, which lead to the decision choice, are modeled by theoretical tools of stochastic evolutionary game theory [11,12]. However, the paper [5] provides not only a survey focused on topics of great interest for our society, but also it looks ahead to a variety of interesting and challenging mathematical problems. Specifically, I am interested in the derivation of macroscopic (hydrodynamic) models from the underlying description given from the kinetic theory approach, more specifically by the kinetic theory for active particles [8]. A general reference on crowd modeling is the recently published book [10].
Modeling complex work systems - method meets reality
van der Veer, Gerrit C.; Hoeve, Machteld; Lenting, Bert
1996-01-01
Modeling an existing task situation is often a first phase in the (re)design of information systems. For complex systems design, this model should consider both the people and the organization involved, the work, and situational aspects. Groupware Task Analysis (GTA) as part of a method for the
Gromov hyperbolicity in Cartesian product graphs
Indian Academy of Sciences (India)
If is a geodesic metric space and x 1 , x 2 , x 3 ∈ X , a geodesic triangle T = { x 1 , x 2 , x 3 } is the union of the three geodesics [ x 1 x 2 ] , [ x 2 x 3 ] and [ x 3 x 1 ] in . The space is -hyperbolic (in the Gromov sense) if any side of is contained in a -neighborhood of the union of the two other sides, for every geodesic ...
Interpolation lattices for hyperbolic cross trigonometric polynomials
National Research Council Canada - National Science Library
Kämmerer, Lutz; Kunis, Stefan; Potts, Daniel
2012-01-01
... hardly deteriorates for functions in an appropriate scale of spaces of dominating mixed smoothness; see e.g. [23,26,19,18,22,2,20,24] . The FFT has been adapted to this thin discretisation as the hyperbolic cross fast Fourier transform (HCFFT), which uses C d N log d N floating point operations, in [1,9] . The HCFFT has been used in pseudo-spect...
Studies in the Hyperbolic Circle Problem
DEFF Research Database (Denmark)
Cherubini, Giacomo
In this thesis we study the remainder term e(s) in the hyperbolic lattice point counting problem. Our main approach to this problem is that of the spectral theory of automorphic forms. We show that the function e(s) exhibits properties similar to those of almost periodic functions, and we study d...... distribution for certain integral versions of it. Finally we describe what results can be obtained by application of fractional calculus, especially fractional integration to small order, to the problem....
Updating the debate on model complexity
Simmons, Craig T.; Hunt, Randall J.
2012-01-01
As scientists who are trying to understand a complex natural world that cannot be fully characterized in the field, how can we best inform the society in which we live? This founding context was addressed in a special session, “Complexity in Modeling: How Much is Too Much?” convened at the 2011 Geological Society of America Annual Meeting. The session had a variety of thought-provoking presentations—ranging from philosophy to cost-benefit analyses—and provided some areas of broad agreement that were not evident in discussions of the topic in 1998 (Hunt and Zheng, 1999). The session began with a short introduction during which model complexity was framed borrowing from an economic concept, the Law of Diminishing Returns, and an example of enjoyment derived by eating ice cream. Initially, there is increasing satisfaction gained from eating more ice cream, to a point where the gain in satisfaction starts to decrease, ending at a point when the eater sees no value in eating more ice cream. A traditional view of model complexity is similar—understanding gained from modeling can actually decrease if models become unnecessarily complex. However, oversimplified models—those that omit important aspects of the problem needed to make a good prediction—can also limit and confound our understanding. Thus, the goal of all modeling is to find the “sweet spot” of model sophistication—regardless of whether complexity was added sequentially to an overly simple model or collapsed from an initial highly parameterized framework that uses mathematics and statistics to attain an optimum (e.g., Hunt et al., 2007). Thus, holistic parsimony is attained, incorporating “as simple as possible,” as well as the equally important corollary “but no simpler.”
Discontinuous Galerkin Method for Hyperbolic Conservation Laws
Mousikou, Ioanna
2016-11-11
Hyperbolic conservation laws form a special class of partial differential equations. They describe phenomena that involve conserved quantities and their solutions show discontinuities which reflect the formation of shock waves. We consider one-dimensional systems of hyperbolic conservation laws and produce approximations using finite difference, finite volume and finite element methods. Due to stability issues of classical finite element methods for hyperbolic conservation laws, we study the discontinuous Galerkin method, which was recently introduced. The method involves completely discontinuous basis functions across each element and it can be considered as a combination of finite volume and finite element methods. We illustrate the implementation of discontinuous Galerkin method using Legendre polynomials, in case of scalar equations and in case of quasi-linear systems, and we review important theoretical results about stability and convergence of the method. The applications of finite volume and discontinuous Galerkin methods to linear and non-linear scalar equations, as well as to the system of elastodynamics, are exhibited.
Multifaceted Modelling of Complex Business Enterprises.
Chakraborty, Subrata; Mengersen, Kerrie; Fidge, Colin; Ma, Lin; Lassen, David
2015-01-01
We formalise and present a new generic multifaceted complex system approach for modelling complex business enterprises. Our method has a strong focus on integrating the various data types available in an enterprise which represent the diverse perspectives of various stakeholders. We explain the challenges faced and define a novel approach to converting diverse data types into usable Bayesian probability forms. The data types that can be integrated include historic data, survey data, and management planning data, expert knowledge and incomplete data. The structural complexities of the complex system modelling process, based on various decision contexts, are also explained along with a solution. This new application of complex system models as a management tool for decision making is demonstrated using a railway transport case study. The case study demonstrates how the new approach can be utilised to develop a customised decision support model for a specific enterprise. Various decision scenarios are also provided to illustrate the versatility of the decision model at different phases of enterprise operations such as planning and control.
Multifaceted Modelling of Complex Business Enterprises.
Directory of Open Access Journals (Sweden)
Subrata Chakraborty
Full Text Available We formalise and present a new generic multifaceted complex system approach for modelling complex business enterprises. Our method has a strong focus on integrating the various data types available in an enterprise which represent the diverse perspectives of various stakeholders. We explain the challenges faced and define a novel approach to converting diverse data types into usable Bayesian probability forms. The data types that can be integrated include historic data, survey data, and management planning data, expert knowledge and incomplete data. The structural complexities of the complex system modelling process, based on various decision contexts, are also explained along with a solution. This new application of complex system models as a management tool for decision making is demonstrated using a railway transport case study. The case study demonstrates how the new approach can be utilised to develop a customised decision support model for a specific enterprise. Various decision scenarios are also provided to illustrate the versatility of the decision model at different phases of enterprise operations such as planning and control.
Complexity, Modeling, and Natural Resource Management
Directory of Open Access Journals (Sweden)
Paul Cilliers
2013-09-01
Full Text Available This paper contends that natural resource management (NRM issues are, by their very nature, complex and that both scientists and managers in this broad field will benefit from a theoretical understanding of complex systems. It starts off by presenting the core features of a view of complexity that not only deals with the limits to our understanding, but also points toward a responsible and motivating position. Everything we do involves explicit or implicit modeling, and as we can never have comprehensive access to any complex system, we need to be aware both of what we leave out as we model and of the implications of the choice of our modeling framework. One vantage point is never sufficient, as complexity necessarily implies that multiple (independent conceptualizations are needed to engage the system adequately. We use two South African cases as examples of complex systems - restricting the case narratives mainly to the biophysical domain associated with NRM issues - that make the point that even the behavior of the biophysical subsystems themselves are already complex. From the insights into complex systems discussed in the first part of the paper and the lessons emerging from the way these cases have been dealt with in reality, we extract five interrelated generic principles for practicing science and management in complex NRM environments. These principles are then further elucidated using four further South African case studies - organized as two contrasting pairs - and now focusing on the more difficult organizational and social side, comparing the human organizational endeavors in managing such systems.
Optical Broadband High Pass Transmission Property of Thin Film Hyperbolic Metamaterial
Tang, Y.; Man, X.; Adam, A.J.L.; Urbach, H.P.
2015-01-01
Here we report the modeling, fabrication and measurement of a type II Hyperbolic Metamaterial (HMM) consisting of 10 pairs Ag/Al2O3 subwavelength layers to demonstrate the high pass filter property of type II HMM. The HMM is deposited on the hypotenuse side of a TiO2 prism and covered with a
Algorithm and program for equidistant hyperbolic R-M-summation of seismic fluctuations
Energy Technology Data Exchange (ETDEWEB)
Inagamov, R.Sh.; Shadybekov, B.U.
1981-01-01
A description is made of an algorithm and program for transforming seismic recordings by summing fluctuations using hyperbolic lines with uniformly controllable change in the location of the summation lines and its curvature, as well as a brief clarification of the control test task in which processing of a multiple-channel model seismogram is presented.
Positive temporal dependence of the biological clock implies hyperbolic discounting
Directory of Open Access Journals (Sweden)
Debajyoti eRay
2011-01-01
Full Text Available Temporal preferences of animals and humans often exhibit inconsistencies, whereby an earlier, smaller reward may be preferred when it occurs immediately but not when it is delayed. Such choices reflect hyperbolic discounting of future rewards, rather than the exponential discounting required for temporal consistency. Simultaneously, however, evidence has emerged that suggests that animals and humans have an internal representation of time that often differs from the calendar time used in detection of temporal inconsistencies. Here, we prove that temporal inconsistencies emerge if fixed durations in calendar time are experienced as positively related (positive quadrant dependent. Hence, what are time-consistent choices within the time framework of the decision maker appear as time-inconsistent to an outsider who analyzes choices in calendar time. As the biological clock becomes more variable, the fit of the hyperbolic discounting model improves. A recent alternative explanation for temporal choice inconsistencies builds on persistent under-estimation of the length of distant time intervals. By increasing the expected speed of our stochastic biological clock for time farther into the future, we can emulate this explanation. Ours is therefore an encompassing theoretical framework that predicts context-dependent degrees of intertemporal choice inconsistencies, to the extent that context can generate changes in autocorrelation, variability, and expected speed of the biological clock. Our finding should lead to novel experiments that will clarify the role of time perception in impulsivity, with critical implications for, among others, our understanding of aging, drug abuse and pathological gambling.
Fatigue modeling of materials with complex microstructures
DEFF Research Database (Denmark)
Qing, Hai; Mishnaevsky, Leon
2011-01-01
with the phenomenological model of fatigue damage growth. As a result, the fatigue lifetime of materials with complex structures can be determined as a function of the parameters of their structures. As an example, the fatigue lifetimes of wood modeled as a cellular material with multilayered, fiber reinforced walls were...... determined for different parameters of wood microstructures. In so doing, 3D hierarchical finite element models of softwood, and a computational technique, including the repeating restart and model change procedures, have been employed to model the fatigue response of latewood....
Estimates of the Hyperbolic Radius Gradient and Schwarz–Pick Inequalities for the Eccentric Annulus
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D.Kh. Giniyatova
2016-06-01
Full Text Available Let Ω and Π be hyperbolic domains in the complex plane C. By A(Ω, Π we shall designate the class of functions f which are holomorphic or meromorphic in Ω and such that f(Ω ϲ Π. Estimates of the higher derivatives |f(n(z| of the analytic functions from the class A(Ω, Π with the punishing factor Cn(Ω, Π is one of the main problems of geometric theory of functions. These estimates are commonly referred to as Schwarz–Pick inequalities. Many results concerning this problem have been obtained for simply connected domains. Therefore, the research interest in such problems for finitely connected domains is natural. As known, the constant C2(Ω, Π for any pairs of hyperbolic domains depends only on the hyperbolic radius gradient of the corresponding domains. The main result of this paper is estimates of the hyperbolic radius gradient and the punishing factor in the Schwarz–Pick inequality for the eccentric annulus. We also consider the extreme case – the randomly punctured circle.
Nonreciprocity and one-way topological transitions in hyperbolic metamaterials
Leviyev, A.; Stein, B.; Christofi, A.; Galfsky, T.; Krishnamoorthy, H.; Kuskovsky, I. L.; Menon, V.; Khanikaev, A. B.
2017-07-01
Control of the electromagnetic waves in nano-scale structured materials is crucial to the development of next generation photonic circuits and devices. In this context, hyperbolic metamaterials, where elliptical isofrequency surfaces are morphed into surfaces with exotic hyperbolic topologies when the structure parameters are tuned, have shown unprecedented control over light propagation and interaction. Here we show that such topological transitions can be even more unusual when the hyperbolic metamaterial is endowed with nonreciprocity. Judicious design of metamaterials with reduced spatial symmetries, together with the breaking of time-reversal symmetry through magnetization, is shown to result in nonreciprocal dispersion and one-way topological phase transitions in hyperbolic metamaterials.
Hyperbolic functions with configuration theorems and equivalent and equidecomposable figures
Shervatov, V G; Skornyakov, L A; Boltyanskii, V G
2007-01-01
This single-volume compilation of three books centers on Hyperbolic Functions, an introduction to the relationship between the hyperbolic sine, cosine, and tangent, and the geometric properties of the hyperbola. The development of the hyperbolic functions, in addition to those of the trigonometric (circular) functions, appears in parallel columns for comparison. A concluding chapter introduces natural logarithms and presents analytic expressions for the hyperbolic functions.The second book, Configuration Theorems, requires only the most elementary background in plane and solid geometry. It dis
DEFF Research Database (Denmark)
Ishii, Satoshi; Babicheva, Viktoriia E.; Shalaginov, Mikhail Y.
2016-01-01
Hyperbolic metamaterials possess unique optical properties owing to their hyperbolic dispersion. As hyperbolic metamaterials can be constructed just from periodic multilayers of metals and dielectrics, they have attracted considerable attention in the nanophotonics community. Here, we review some...
Complex Systems and Self-organization Modelling
Bertelle, Cyrille; Kadri-Dahmani, Hakima
2009-01-01
The concern of this book is the use of emergent computing and self-organization modelling within various applications of complex systems. The authors focus their attention both on the innovative concepts and implementations in order to model self-organizations, but also on the relevant applicative domains in which they can be used efficiently. This book is the outcome of a workshop meeting within ESM 2006 (Eurosis), held in Toulouse, France in October 2006.
A cognitive model for software architecture complexity
Bouwers, E.; Lilienthal, C.; Visser, J.; Van Deursen, A.
2010-01-01
Evaluating the complexity of the architecture of a softwaresystem is a difficult task. Many aspects have to be considered to come to a balanced assessment. Several architecture evaluation methods have been proposed, but very few define a quality model to be used during the evaluation process. In
Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption.
Othman, Mohamed A K; Guclu, Caner; Capolino, Filippo
2013-03-25
We investigate a novel implementation of hyperbolic metamaterial (HM) at far-infrared frequencies composed of stacked graphene sheets separated by thin dielectric layers. Using the surface conductivity model of graphene, we derive the homogenization formula for the multilayer structure by treating graphene sheets as lumped layers with complex admittances. Homogenization results and limits are investigated by comparison with a transfer matrix formulation for the HM constituent layers. We show that infrared iso-frequency wavevector dispersion characteristics of the proposed HM can be tuned by varying the chemical potential of the graphene sheets via electrostatic biasing. Accordingly, reflection and transmission properties for a film made of graphene-dielectric multilayer are tunable at terahertz frequencies, and we investigate the limits in using the homogenized model compared to the more accurate transfer matrix model. We also propose to use graphene-based HM as a super absorber for near-fields generated at its surface. The power emitted by a dipole near the surface of a graphene-based HM is increased dramatically (up to 5 × 10(2) at 2 THz), furthermore we show that most of the scattered power is directed into the HM. The validity and limits of the homogenized HM model are assessed also for near-fields and show that in certain conditions it overestimates the dipole radiated power into the HM.
Complex agent networks: An emerging approach for modeling complex systems
Mei, S.; Zarrabi, N.; Lees, M.; Sloot, P.M.A.
2015-01-01
Complexity and complex systems are all around us: from molecular and cellular systems in biology up to economics and human societies. There is an urgent need for methods that can capture the multi-scale spatio-temporal characteristics of complex systems. Recent emphasis has centered on two methods
Modeling Electromagnetic Scattering From Complex Inhomogeneous Objects
Deshpande, Manohar; Reddy, C. J.
2011-01-01
This software innovation is designed to develop a mathematical formulation to estimate the electromagnetic scattering characteristics of complex, inhomogeneous objects using the finite-element-method (FEM) and method-of-moments (MoM) concepts, as well as to develop a FORTRAN code called FEMOM3DS (Finite Element Method and Method of Moments for 3-Dimensional Scattering), which will implement the steps that are described in the mathematical formulation. Very complex objects can be easily modeled, and the operator of the code is not required to know the details of electromagnetic theory to study electromagnetic scattering.
Special inhomogeneous electromagnetic waves in hyperbolic metamaterials
Kurilkina, S. N.; Petrov, N. S.; Zimin, A. B.; Belyi, V. N.
2017-12-01
Herein, it is shown that under conditions of total internal reflection of plane homogeneous electromagnetic waves at the interface of a hyperbolic metamaterial (HMM) and an ordinary isotropic medium, special inhomogeneous electromagnetic waves are excited in certain circumstances near the surface of the metamaterial and their amplitude changes with distance according to the non-exponential law. The existence conditions for such waves are established for the case when the optical axis is located within the interface plane and forms an angle with the plane of incidence. The energy flux and density of energy of special inhomogeneous waves in a HMM are determined.
Geometry in the large and hyperbolic chaos
Energy Technology Data Exchange (ETDEWEB)
Hasslacher, B.; Mainieri, R.
1998-11-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The authors calculated observables in strongly chaotic systems. This is difficult to do because of a lack of a workable orbit classification for such systems. This is due to global geometrical information from the original dynamical system being entangled in an unknown way throughout the orbit sequence. They used geometrical methods from modern mathematics and recent connections between global geometry and modern quantum field theory to study the natural geometrical objects belonging to hard chaos-hyperbolic manifolds.
On the non-hyperbolicity of a class of exponential polynomials
Directory of Open Access Journals (Sweden)
Gaspar Mora
2017-10-01
Full Text Available In this paper we have constructed a class of non-hyperbolic exponential polynomials that contains all the partial sums of the Riemann zeta function. An exponential polynomial been also defined to illustrate the complexity of the structure of the set defined by the closure of the real projections of its zeros. The sensitivity of this set, when the vector of delays is perturbed, has been analysed. These results have immediate implications in the theory of the neutral differential equations.
DEFF Research Database (Denmark)
Zhukovsky, Sergei; Lavrinenko, Andrei
2012-01-01
We propose proof-of-concept designs of Bragg reflectors and Fabry-Pe´rot resonators for large wave vector waves (Bloch bulk plasmon polaritons) in multilayer metal-dielectric hyperbolic metamaterials. The designs are based on hybrid multilayers having both subwavelength and wavelength......-scale structuring. This multiscale approach is shown to be a promising platform for using bulk plasmonic waves in complex multilayer metamaterials as a new kind of information carriers....
Linking hyperbolic and parabolic p.d.e.’s.
Zwart, Heiko J.; Le Gorrec, Yann; Maschke, B.M.
2011-01-01
In this article we show that from the existence and uniqueness of solutions to a hyperbolic partial differential equation (p.d.e.) existence and uniqueness of parabolic and other hyperbolic p.d.e.’s can be derived. Among others, we show that starting with the (undamped) wave equation we obtain
Computing the Gromov hyperbolicity constant of a discrete metric space
Ismail, Anas
2012-07-01
Although it was invented by Mikhail Gromov, in 1987, to describe some family of groups[1], the notion of Gromov hyperbolicity has many applications and interpretations in different fields. It has applications in Biology, Networking, Graph Theory, and many other areas of research. The Gromov hyperbolicity constant of several families of graphs and geometric spaces has been determined. However, so far, the only known algorithm for calculating the Gromov hyperbolicity constant δ of a discrete metric space is the brute force algorithm with running time O (n4) using the four-point condition. In this thesis, we first introduce an approximation algorithm which calculates a O (log n)-approximation of the hyperbolicity constant δ, based on a layering approach, in time O(n2), where n is the number of points in the metric space. We also calculate the fixed base point hyperbolicity constant δr for a fixed point r using a (max, min)−matrix multiplication algorithm by Duan in time O(n2.688)[2]. We use this result to present a 2-approximation algorithm for calculating the hyper-bolicity constant in time O(n2.688). We also provide an exact algorithm to compute the hyperbolicity constant δ in time O(n3.688) for a discrete metric space. We then present some partial results we obtained for designing some approximation algorithms to compute the hyperbolicity constant δ.
BDI-modelling of complex intracellular dynamics.
Jonker, C M; Snoep, J L; Treur, J; Westerhoff, H V; Wijngaards, W C A
2008-03-07
A BDI-based continuous-time modelling approach for intracellular dynamics is presented. It is shown how temporalized BDI-models make it possible to model intracellular biochemical processes as decision processes. By abstracting from some of the details of the biochemical pathways, the model achieves understanding in nearly intuitive terms, without losing veracity: classical intentional state properties such as beliefs, desires and intentions are founded in reality through precise biochemical relations. In an extensive example, the complex regulation of Escherichia coli vis-à-vis lactose, glucose and oxygen is simulated as a discrete-state, continuous-time temporal decision manager. Thus a bridge is introduced between two different scientific areas: the area of BDI-modelling and the area of intracellular dynamics.
Intrinsic Uncertainties in Modeling Complex Systems.
Energy Technology Data Exchange (ETDEWEB)
Cooper, Curtis S; Bramson, Aaron L.; Ames, Arlo L.
2014-09-01
Models are built to understand and predict the behaviors of both natural and artificial systems. Because it is always necessary to abstract away aspects of any non-trivial system being modeled, we know models can potentially leave out important, even critical elements. This reality of the modeling enterprise forces us to consider the prospective impacts of those effects completely left out of a model - either intentionally or unconsidered. Insensitivity to new structure is an indication of diminishing returns. In this work, we represent a hypothetical unknown effect on a validated model as a finite perturba- tion whose amplitude is constrained within a control region. We find robustly that without further constraints, no meaningful bounds can be placed on the amplitude of a perturbation outside of the control region. Thus, forecasting into unsampled regions is a very risky proposition. We also present inherent difficulties with proper time discretization of models and representing in- herently discrete quantities. We point out potentially worrisome uncertainties, arising from math- ematical formulation alone, which modelers can inadvertently introduce into models of complex systems. Acknowledgements This work has been funded under early-career LDRD project #170979, entitled "Quantify- ing Confidence in Complex Systems Models Having Structural Uncertainties", which ran from 04/2013 to 09/2014. We wish to express our gratitude to the many researchers at Sandia who con- tributed ideas to this work, as well as feedback on the manuscript. In particular, we would like to mention George Barr, Alexander Outkin, Walt Beyeler, Eric Vugrin, and Laura Swiler for provid- ing invaluable advice and guidance through the course of the project. We would also like to thank Steven Kleban, Amanda Gonzales, Trevor Manzanares, and Sarah Burwell for their assistance in managing project tasks and resources.
A Practical Philosophy of Complex Climate Modelling
Schmidt, Gavin A.; Sherwood, Steven
2014-01-01
We give an overview of the practice of developing and using complex climate models, as seen from experiences in a major climate modelling center and through participation in the Coupled Model Intercomparison Project (CMIP).We discuss the construction and calibration of models; their evaluation, especially through use of out-of-sample tests; and their exploitation in multi-model ensembles to identify biases and make predictions. We stress that adequacy or utility of climate models is best assessed via their skill against more naive predictions. The framework we use for making inferences about reality using simulations is naturally Bayesian (in an informal sense), and has many points of contact with more familiar examples of scientific epistemology. While the use of complex simulations in science is a development that changes much in how science is done in practice, we argue that the concepts being applied fit very much into traditional practices of the scientific method, albeit those more often associated with laboratory work.
Modeling auditory evoked potentials to complex stimuli
DEFF Research Database (Denmark)
Rønne, Filip Munch
cochlear compression would be of great benefit, as a more precise diagnose of the deficits underlying a potential hearing impairment in both infants and adults could be obtained. It was demonstrated in this thesis, via experimental recordings and supported by model simulations, that the growth of the ASSR....... Sensorineural hearing impairments is commonly associated with a loss of outer hair-cell functionality, and a measurable consequence is the decreased amount of cochlear compression at frequencies corresponding to the damaged locations in the cochlea. In clinical diagnostics, a fast and objective measure of local...... clinically and in research towards using realistic and complex stimuli, such as speech, to electrophysiologically assess the human hearing. However, to interpret the AEP generation to complex sounds, the potential patterns in response to simple stimuli needs to be understood. Therefore, the model was used...
Layered van der Waals crystals with hyperbolic light dispersion
DEFF Research Database (Denmark)
Gjerding, Morten Niklas; Petersen, R.; Pedersen, T.G.
2017-01-01
Compared to artificially structured hyperbolic metamaterials, whose performance is limited by the finite size of the metallic components, the sparse number of naturally hyperbolic materials recently discovered are promising candidates for the next generation of hyperbolic materials. Using first......-infrared to the ultraviolet. Combined with the emerging field of van der Waals heterostructuring, we demonstrate how the hyperbolic properties can be further controlled by stacking different two-dimensional crystals opening new perspectives for atomic-scale design of photonic metamaterials. As an application, we identify...... candidates for Purcell factor control of emission from diamond nitrogen-vacancy centers.Natural hyperbolic materials retain the peculiar optical properties of traditional metamaterials whilst not requiring artificial structuring. Here, the authors perform a theoretical screening of a large class of natural...
FRAM Modelling Complex Socio-technical Systems
Hollnagel, Erik
2012-01-01
There has not yet been a comprehensive method that goes behind 'human error' and beyond the failure concept, and various complicated accidents have accentuated the need for it. The Functional Resonance Analysis Method (FRAM) fulfils that need. This book presents a detailed and tested method that can be used to model how complex and dynamic socio-technical systems work, and understand both why things sometimes go wrong but also why they normally succeed.
Front tracking for hyperbolic conservation laws
Holden, Helge
2015-01-01
This is the second edition of a well-received book providing the fundamentals of the theory hyperbolic conservation laws. Several chapters have been rewritten, new material has been added, in particular, a chapter on space dependent flux functions, and the detailed solution of the Riemann problem for the Euler equations. Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. From the reviews of the first edition: "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet "I have read the book with great pleasure, and I can recommend it to experts ...
The embedding flows of C hyperbolic diffeomorphisms
Zhang, Xiang
2011-03-01
In [Weigu Li, J. Llibre, Xiang Zhang, Extension of Floquet's theory to nonlinear periodic differential systems and embedding diffeomorphisms in differential flows, Amer. J. Math. 124 (2002) 107-127] we proved that for a germ of C hyperbolic diffeomorphisms F(x)=Ax+f(x) in (R,0), if A has a real logarithm with its eigenvalues weakly nonresonant, then F(x) can be embedded in a C autonomous differential system. Its proof was very complicated, which involved the existence of embedding periodic vector field of F(x) and the extension of the Floquet's theory to nonlinear C periodic differential systems. In this paper we shall provide a simple and direct proof to this last result. Next we shall show that the weakly nonresonant condition in the last result on the real logarithm of A is necessary for some C diffeomorphisms F(x)=Ax+f(x) to have C embedding flows. Finally we shall prove that a germ of C hyperbolic diffeomorphisms F(x)=Ax+f(x) with f(x)=O(|) in (R,0) has a C embedding flow if and only if either A has no negative eigenvalues or A has two equal negative eigenvalues and it can be diagonalizable.
Steger, Joseph L.
1989-01-01
Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.
Complex networks under dynamic repair model
Chaoqi, Fu; Ying, Wang; Kun, Zhao; Yangjun, Gao
2018-01-01
Invulnerability is not the only factor of importance when considering complex networks' security. It is also critical to have an effective and reasonable repair strategy. Existing research on network repair is confined to the static model. The dynamic model makes better use of the redundant capacity of repaired nodes and repairs the damaged network more efficiently than the static model; however, the dynamic repair model is complex and polytropic. In this paper, we construct a dynamic repair model and systematically describe the energy-transfer relationships between nodes in the repair process of the failure network. Nodes are divided into three types, corresponding to three structures. We find that the strong coupling structure is responsible for secondary failure of the repaired nodes and propose an algorithm that can select the most suitable targets (nodes or links) to repair the failure network with minimal cost. Two types of repair strategies are identified, with different effects under the two energy-transfer rules. The research results enable a more flexible approach to network repair.
Complex Constructivism: A Theoretical Model of Complexity and Cognition
Doolittle, Peter E.
2014-01-01
Education has long been driven by its metaphors for teaching and learning. These metaphors have influenced both educational research and educational practice. Complexity and constructivism are two theories that provide functional and robust metaphors. Complexity provides a metaphor for the structure of myriad phenomena, while constructivism…
Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial.
Dai, S; Ma, Q; Liu, M K; Andersen, T; Fei, Z; Goldflam, M D; Wagner, M; Watanabe, K; Taniguchi, T; Thiemens, M; Keilmann, F; Janssen, G C A M; Zhu, S-E; Jarillo-Herrero, P; Fogler, M M; Basov, D N
2015-08-01
Hexagonal boron nitride (h-BN) is a natural hyperbolic material, in which the dielectric constants are the same in the basal plane (ε(t) ≡ ε(x) = ε(y)) but have opposite signs (ε(t)ε(z) graphene on h-BN. Tunability originates from the hybridization of surface plasmon polaritons in graphene with hyperbolic phonon polaritons in h-BN, so that the eigenmodes of the graphene/h-BN heterostructure are hyperbolic plasmon-phonon polaritons. The hyperbolic plasmon-phonon polaritons in graphene/h-BN suffer little from ohmic losses, making their propagation length 1.5-2.0 times greater than that of hyperbolic phonon polaritons in h-BN. The hyperbolic plasmon-phonon polaritons possess the combined virtues of surface plasmon polaritons in graphene and hyperbolic phonon polaritons in h-BN. Therefore, graphene/h-BN can be classified as an electromagnetic metamaterial as the resulting properties of these devices are not present in its constituent elements alone.
Modelling complex networks by random hierarchical graphs
Directory of Open Access Journals (Sweden)
M.Wróbel
2008-06-01
Full Text Available Numerous complex networks contain special patterns, called network motifs. These are specific subgraphs, which occur oftener than in randomized networks of Erdős-Rényi type. We choose one of them, the triangle, and build a family of random hierarchical graphs, being Sierpiński gasket-based graphs with random "decorations". We calculate the important characteristics of these graphs - average degree, average shortest path length, small-world graph family characteristics. They depend on probability of decorations. We analyze the Ising model on our graphs and describe its critical properties using a renormalization-group technique.
Chaos from simple models to complex systems
Cencini, Massimo; Vulpiani, Angelo
2010-01-01
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theor
Tangent hyperbolic circular frequency diverse array radars
Directory of Open Access Journals (Sweden)
Sarah Saeed
2016-03-01
Full Text Available Frequency diverse array (FDA with uniform frequency offset (UFO has been in spot light of research for past few years. Not much attention has been devoted to non-UFOs in FDA. This study investigates tangent hyperbolic (TH function for frequency offset selection scheme in circular FDAs (CFDAs. Investigation reveals a three-dimensional single-maximum beampattern, which promises to enhance system detection capability and signal-to-interference plus noise ratio. Furthermore, by utilising the versatility of TH function, a highly configurable type array system is achieved, where beampatterns of three different configurations of FDA can be generated, just by adjusting a single function parameter. This study further examines the utility of the proposed TH-CFDA in some practical radar scenarios.
Self-Induced Torque in Hyperbolic Metamaterials
Ginzburg, Pavel; Krasavin, Alexey V.; Poddubny, Alexander N.; Belov, Pavel A.; Kivshar, Yuri S.; Zayats, Anatoly V.
2013-07-01
Optical forces constitute a fundamental phenomenon important in various fields of science, from astronomy to biology. Generally, intense external radiation sources are required to achieve measurable effects suitable for applications. Here we demonstrate that quantum emitters placed in a homogeneous anisotropic medium induce self-torques, aligning themselves in the well-defined direction determined by an anisotropy, in order to maximize their radiation efficiency. We develop a universal quantum-mechanical theory of self-induced torques acting on an emitter placed in a material environment. The theoretical framework is based on the radiation reaction approach utilizing the rigorous Langevin local quantization of electromagnetic excitations. We show more than 2 orders of magnitude enhancement of the self-torque by an anisotropic metamaterial with hyperbolic dispersion, having negative ratio of permittivity tensor components, in comparison with conventional anisotropic crystals with the highest naturally available anisotropy.
Simulation of a Hyperbolic Field Energy Analyzer
Gonzalez-Lizardo, Angel
2016-01-01
Energy analyzers are important plasma diagnostic tools with applications in a broad range of disciplines including molecular spectroscopy, electron microscopy, basic plasma physics, plasma etching, plasma processing, and ion sputtering technology. The Hyperbolic Field Energy Analyzer (HFEA) is a novel device able to determine ion and electron energy spectra and temperatures. The HFEA is well suited for ion temperature and density diagnostics at those situations where ions are scarce. A simulation of the capacities of the HFEA to discriminate particles of a particular energy level, as well as to determine temperature and density is performed in this work. The electric field due the combination of the conical elements, collimator lens, and Faraday cup applied voltage was computed in a well suited three-dimensional grid. The field is later used to compute the trajectory of a set of particles with a predetermined energy distribution. The results include the observation of the particle trajectories inside the sens...
Wind modelling over complex terrain using CFD
Avila, Matias; Owen, Herbert; Folch, Arnau; Prieto, Luis; Cosculluela, Luis
2015-04-01
The present work deals with the numerical CFD modelling of onshore wind farms in the context of High Performance Computing (HPC). The CFD model involves the numerical solution of the Reynolds-Averaged Navier-Stokes (RANS) equations together with a κ-É turbulence model and the energy equation, specially designed for Atmospheric Boundary Layer (ABL) flows. The aim is to predict the wind velocity distribution over complex terrain, using a model that includes meteorological data assimilation, thermal coupling, forested canopy and Coriolis effects. The modelling strategy involves automatic mesh generation, terrain data assimilation and generation of boundary conditions for the inflow wind flow distribution up to the geostrophic height. The CFD model has been implemented in Alya, a HPC multi physics parallel solver able to run with thousands of processors with an optimal scalability, developed in Barcelona Supercomputing Center. The implemented thermal stability and canopy physical model was developed by Sogachev in 2012. The k-É equations are of non-linear convection diffusion reaction type. The implemented numerical scheme consists on a stabilized finite element formulation based on the variational multiscale method, that is known to be stable for this kind of turbulence equations. We present a numerical formulation that stresses on the robustness of the solution method, tackling common problems that produce instability. The iterative strategy and linearization scheme is discussed. It intends to avoid the possibility of having negative values of diffusion during the iterative process, which may lead to divergence of the scheme. These problems are addressed by acting on the coefficients of the reaction and diffusion terms and on the turbulent variables themselves. The k-É equations are highly nonlinear. Complex terrain induces transient flow instabilities that may preclude the convergence of computer flow simulations based on steady state formulation of the
Precalibrating an intermediate complexity climate model
Energy Technology Data Exchange (ETDEWEB)
Edwards, Neil R. [The Open University, Earth and Environmental Sciences, Milton Keynes (United Kingdom); Cameron, David [Centre for Ecology and Hydrology, Edinburgh (United Kingdom); Rougier, Jonathan [University of Bristol, Department of Mathematics, Bristol (United Kingdom)
2011-10-15
Credible climate predictions require a rational quantification of uncertainty, but full Bayesian calibration requires detailed estimates of prior probability distributions and covariances, which are difficult to obtain in practice. We describe a simplified procedure, termed precalibration, which provides an approximate quantification of uncertainty in climate prediction, and requires only that uncontroversially implausible values of certain inputs and outputs are identified. The method is applied to intermediate-complexity model simulations of the Atlantic meridional overturning circulation (AMOC) and confirms the existence of a cliff-edge catastrophe in freshwater-forcing input space. When uncertainty in 14 further parameters is taken into account, an implausible, AMOC-off, region remains as a robust feature of the model dynamics, but its location is found to depend strongly on values of the other parameters. (orig.)
Extension of association models to complex chemicals
DEFF Research Database (Denmark)
Avlund, Ane Søgaard
Summary of “Extension of association models to complex chemicals”. Ph.D. thesis by Ane Søgaard Avlund The subject of this thesis is application of SAFT type equations of state (EoS). Accurate and predictive thermodynamic models are important in many industries including the petroleum industry....... The SAFT EoS was developed 20 years ago, and a large number of papers on the subject has been published since, but many issues still remain unsolved. These issues are both theoretical and practical. The SAFT theory does not account for intramolecular association, it can only treat flexible chains, and does...... functional groups. It is also tested whether increasing the number of sites for DEA (diethanolamine) improves the results. It can be shown from experimental data that intramolecular association is dominating compared to intermolecular association in certain systems, and that the intramolecular association...
Complex polarity reversals in a geodynamo model
Olson, Peter L.; Glatzmaier, Gary A.; Coe, Robert S.
2011-04-01
Complex polarity reversals in numerical dynamos driven by thermo-chemical convection are analyzed in terms of magnetic field intensity variations, transitional field structure, and other observable characteristics. Our most Earth-like dynamos are characterized by long stable polarity chrons with dipole-dominant magnetic fields punctuated by occasional polarity reversals, and are found within a transition region of parameter space between non-reversing strongly dipolar dynamos and chaotic multi-polar-type dynamos. Dynamos in the transition region have elevated dipole terms, reduced quadrupole terms, magnetic energy that decreases slowly with spherical harmonic degree, and broadband dipole frequency spectra. Their axial dipole intensity histograms are trimodal, with large modes representing the stable polarity states and an intermediate mode representing the transitional multi-polar state. The dipole family intensity exceeds the quadrupole family intensity on the core-mantle boundary during stable polarity times, but during transitions the two families are similar. A complex dynamo model reversal is compared with paleomagnetic reconstructions around the Matuyama-Brunhes polarity transition. Both start with a gradual decrease of the dipole intensity, followed by a precursor reversal and transient polarity recovery, then a rapid dipole collapse and a final reversal that initiates with reverse flux generation in one hemisphere. Virtual geomagnetic poles (VGPs) from sites near the reverse flux trace complex paths and cross the equator several thousand years before the simpler VGP paths from more distant sites, and magnetic intensity variations during the dynamo model reversal correlate with intensity variations inferred for the Matuyama-Brunhes transition.
Inexpensive Complex Hand Model Twenty Years Later.
Frenger, Paul
2015-01-01
Twenty years ago the author unveiled his inexpensive complex hand model, which reproduced every motion of the human hand. A control system programmed in the Forth language operated its actuators and sensors. Follow-on papers for this popular project were next presented in Texas, Canada and Germany. From this hand grew the authors meter-tall robot (nicknamed ANNIE: Android With Neural Networks, Intellect and Emotions). It received machine vision, facial expressiveness, speech synthesis and speech recognition; a simian version also received a dexterous ape foot. New artificial intelligence features included op-amp neurons for OCR and simulated emotions, hormone emulation, endocannabinoid receptors, fear-trust-love mechanisms, a Grandmother Cell recognizer and artificial consciousness. Simulated illnesses included narcotic addiction, autism, PTSD, fibromyalgia and Alzheimers disease. The author gave 13 robotics-AI presentations at NASA in Houston since 2006. A meter-tall simian robot was proposed with gripping hand-feet for use with space vehicles and to explore distant planets and moons. Also proposed were: intelligent motorized exoskeletons for astronaut force multiplication; a cognitive prosthesis to detect and alleviate decreased crew mental performance; and a gynoid robot medic to tend astronauts in deep space missions. What began as a complex hand model evolved into an innovative robot-AI within two decades.
Solhjoo, Soheil
A new model has been developed to estimate the flow stress under hot deformation conditions up to the peak of the stress-strain curves. This model is derived from the general form of hyperbolic function by introducing an additional parameter to bring the results to a more acceptable level.
The hidden hyperbolic geometry of international trade: World Trade Atlas 1870–2013
García-Pérez, Guillermo; Boguñá, Marián; Allard, Antoine; Serrano, M. Ángeles
2016-01-01
Here, we present the World Trade Atlas 1870–2013, a collection of annual world trade maps in which distance combines economic size and the different dimensions that affect international trade beyond mere geography. Trade distances, based on a gravity model predicting the existence of significant trade channels, are such that the closer countries are in trade space, the greater their chance of becoming connected. The atlas provides us with information regarding the long-term evolution of the international trade system and demonstrates that, in terms of trade, the world is not flat but hyperbolic, as a reflection of its complex architecture. The departure from flatness has been increasing since World War I, meaning that differences in trade distances are growing and trade networks are becoming more hierarchical. Smaller-scale economies are moving away from other countries except for the largest economies; meanwhile those large economies are increasing their chances of becoming connected worldwide. At the same time, Preferential Trade Agreements do not fit in perfectly with natural communities within the trade space and have not necessarily reduced internal trade barriers. We discuss an interpretation in terms of globalization, hierarchization, and localization; three simultaneous forces that shape the international trade system. PMID:27633649
Delineating parameter unidentifiabilities in complex models
Raman, Dhruva V.; Anderson, James; Papachristodoulou, Antonis
2017-03-01
Scientists use mathematical modeling as a tool for understanding and predicting the properties of complex physical systems. In highly parametrized models there often exist relationships between parameters over which model predictions are identical, or nearly identical. These are known as structural or practical unidentifiabilities, respectively. They are hard to diagnose and make reliable parameter estimation from data impossible. They furthermore imply the existence of an underlying model simplification. We describe a scalable method for detecting unidentifiabilities, as well as the functional relations defining them, for generic models. This allows for model simplification, and appreciation of which parameters (or functions thereof) cannot be estimated from data. Our algorithm can identify features such as redundant mechanisms and fast time-scale subsystems, as well as the regimes in parameter space over which such approximations are valid. We base our algorithm on a quantification of regional parametric sensitivity that we call `multiscale sloppiness'. Traditionally, the link between parametric sensitivity and the conditioning of the parameter estimation problem is made locally, through the Fisher information matrix. This is valid in the regime of infinitesimal measurement uncertainty. We demonstrate the duality between multiscale sloppiness and the geometry of confidence regions surrounding parameter estimates made where measurement uncertainty is non-negligible. Further theoretical relationships are provided linking multiscale sloppiness to the likelihood-ratio test. From this, we show that a local sensitivity analysis (as typically done) is insufficient for determining the reliability of parameter estimation, even with simple (non)linear systems. Our algorithm can provide a tractable alternative. We finally apply our methods to a large-scale, benchmark systems biology model of necrosis factor (NF)-κ B , uncovering unidentifiabilities.
Oniga, E.; Chirilă, C.; Stătescu, F.
2017-02-01
Nowadays, Unmanned Aerial Systems (UASs) are a wide used technique for acquisition in order to create buildings 3D models, providing the acquisition of a high number of images at very high resolution or video sequences, in a very short time. Since low-cost UASs are preferred, the accuracy of a building 3D model created using this platforms must be evaluated. To achieve results, the dean's office building from the Faculty of "Hydrotechnical Engineering, Geodesy and Environmental Engineering" of Iasi, Romania, has been chosen, which is a complex shape building with the roof formed of two hyperbolic paraboloids. Seven points were placed on the ground around the building, three of them being used as GCPs, while the remaining four as Check points (CPs) for accuracy assessment. Additionally, the coordinates of 10 natural CPs representing the building characteristic points were measured with a Leica TCR 405 total station. The building 3D model was created as a point cloud which was automatically generated based on digital images acquired with the low-cost UASs, using the image matching algorithm and different software like 3DF Zephyr, Visual SfM, PhotoModeler Scanner and Drone2Map for ArcGIS. Except for the PhotoModeler Scanner software, the interior and exterior orientation parameters were determined simultaneously by solving a self-calibrating bundle adjustment. Based on the UAS point clouds, automatically generated by using the above mentioned software and GNSS data respectively, the parameters of the east side hyperbolic paraboloid were calculated using the least squares method and a statistical blunder detection. Then, in order to assess the accuracy of the building 3D model, several comparisons were made for the facades and the roof with reference data, considered with minimum errors: TLS mesh for the facades and GNSS mesh for the roof. Finally, the front facade of the building was created in 3D based on its characteristic points using the PhotoModeler Scanner
Using Perspective to Model Complex Processes
Energy Technology Data Exchange (ETDEWEB)
Kelsey, R.L.; Bisset, K.R.
1999-04-04
The notion of perspective, when supported in an object-based knowledge representation, can facilitate better abstractions of reality for modeling and simulation. The object modeling of complex physical and chemical processes is made more difficult in part due to the poor abstractions of state and phase changes available in these models. The notion of perspective can be used to create different views to represent the different states of matter in a process. These techniques can lead to a more understandable model. Additionally, the ability to record the progress of a process from start to finish is problematic. It is desirable to have a historic record of the entire process, not just the end result of the process. A historic record should facilitate backtracking and re-start of a process at different points in time. The same representation structures and techniques can be used to create a sequence of process markers to represent a historic record. By using perspective, the sequence of markers can have multiple and varying views tailored for a particular user's context of interest.
Vincent, Peter
1986-10-01
Particle-size data have been obtained from sieved samples of sand from beach and coastal dune environments at Ainsdale, northwest England. The four parameters of the hyperbolic distribution were calculated for each sample. These, together with additional derived parameters, were the basis of a binomial logit regression model which sought to distinguish the two sand environments. Seventy-five percent of the samples were correctly assigned by logistic equation containing a single independent variable, π, which is a measure of the skewness of the hyperbolic distribution.
Simultaneous exact controllability for Maxwell equations and for a second-order hyperbolic system
Directory of Open Access Journals (Sweden)
Boris V. Kapitonov
2010-02-01
Full Text Available We present a result on "simultaneous" exact controllability for two models that describe two hyperbolic dynamics. One is the system of Maxwell equations and the other a vector-wave equation with a pressure term. We obtain the main result using modified multipliers in order to generate a necessary observability estimate which allow us to use the Hilbert Uniqueness Method (HUM introduced by Lions.
Differentiable dynamical systems an introduction to structural stability and hyperbolicity
Wen, Lan
2016-01-01
This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the \\Omega-stability theorem of Smale. While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study. Selected solutions are available electronically for instructors only. Please send email to textbooks@ams.org for more informatio...
Existence for a class of discrete hyperbolic problems
Directory of Open Access Journals (Sweden)
Luca Rodica
2006-01-01
Full Text Available We investigate the existence and uniqueness of solutions to a class of discrete hyperbolic systems with some nonlinear extreme conditions and initial data, in a real Hilbert space.
Hyperbolic metamaterials: new physics behind a classical problem.
Drachev, Vladimir P; Podolskiy, Viktor A; Kildishev, Alexander V
2013-06-17
Hyperbolic materials enable numerous surprising applications that include far-field subwavelength imaging, nanolithography, and emission engineering. The wavevector of a plane wave in these media follows the surface of a hyperboloid in contrast to an ellipsoid for conventional anisotropic dielectric. The consequences of hyperbolic dispersion were first studied in the 50's pertaining to the problems of electromagnetic wave propagation in the Earth's ionosphere and in the stratified artificial materials of transmission lines. Recent years have brought explosive growth in optics and photonics of hyperbolic media based on metamaterials across the optical spectrum. Here we summarize earlier theories in the Clemmow's prescription for transformation of the electromagnetic field in hyperbolic media and provide a review of recent developments in this active research area.
Hyperbolicity measures democracy in real-world networks
Borassi, Michele; Chessa, Alessandro; Caldarelli, Guido
2015-09-01
In this work, we analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. We provide two improvements in our understanding of this quantity: first of all, in our interpretation, a hyperbolic network is "aristocratic", since few elements "connect" the system, while a non-hyperbolic network has a more "democratic" structure with a larger number of crucial elements. The second contribution is the introduction of the average hyperbolicity of the neighbors of a given node. Through this definition, we outline an "influence area" for the vertices in the graph. We show that in real networks the influence area of the highest degree vertex is small in what we define "local" networks (i.e., social or peer-to-peer networks), and large in "global" networks (i.e., power grid, metabolic networks, or autonomous system networks).
Long-range propagation of plasmon and phonon polaritons in hyperbolic-metamaterial waveguides
Babicheva, Viktoriia E.
2017-12-01
We study photonic multilayer waveguides that include layers of materials and metamaterials with a hyperbolic dispersion (HMM). We consider the long-range propagation of plasmon and phonon polaritons at the dielectric–HMM interface in different waveguide geometries (single boundary or different layers of symmetric cladding). In contrast to the traditional analysis of geometrical parameters, we make an emphasis on the optical properties of constituent materials: solving dispersion equations, we analyze how dielectric and HMM permittivities affect propagation length and mode size of waveguide eigenmodes. We derive figures of merit that should be used for each waveguide in a broad range of permittivity values as well as compare them with plasmonic waveguides. We show that the conventional plasmonic quality factor, which is the ratio of real to imaginary parts of permittivity, is not applicable to the case of waveguides with complex structure. Both telecommunication wavelengths and mid-infrared spectral ranges are of interest considering recent advances in van der Waals materials, such as hexagonal boron nitride. We evaluate the performance of the waveguides with hexagonal boron nitride in the range where it possesses hyperbolic dispersion (wavelength 6.3–7.3 μm), and we show that these waveguides with natural hyperbolic properties have higher propagation lengths than metal-based HMM waveguides.
Kew, Lee Ming; Ali, Norhashidah Hj. Mohd
2015-08-01
In this paper, new group iterative numerical schemes based on the centred and rotated (skewed) seven-point finite difference discretisations are proposed for the solution of a three dimensional second order hyperbolic telegraph equation, subject to specific initial and Dirichlet boundary conditions. Both schemes are shown to be of second order accuracies and unconditionally stable. The scheme derived from the rotated grid stencil results in a reduced linear system with lower computational complexity compared to the scheme derived from the centred approximation formula. A comparative study with other common point iterative methods based on the seven-point centred difference approximation together with their computational complexity analyses is also presented.
Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators
Directory of Open Access Journals (Sweden)
Yang-Yang Chen
2016-01-01
Full Text Available The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure. The homoclinic solution of the self-excited Helmholtz-Duffing oscillator can also be obtained by an extended hyperbolic perturbation method. The application of the present homoclinic solutions to the chaos prediction of the nonautonomous Helmholtz-Duffing oscillator is performed. Effectiveness and advantage of the present solutions are shown by comparisons.
Novel manufacturing technology of hyperbolic plates for shipbuilding
Zhang, Xu; Zhang, Jia-Tai; Liu, Gang; Yuan, S. J.; Wang, Z. R.
2002-06-01
On the basis of the principle of dieless hydrobulging technology, a novel hydrobulging technology for manufacturing hyperbolic plates is proposed. First, a toroidal pipe elbow or a partial toroidal pipe elbow is formed, then the single hydrobulged structure can be cut up into some desired plates. It is proved by experiments and finite element simulation that manufacturing technology of hyperbolic plates adopting integrated hydrobulging forming technology is feasible.
Clinical Complexity in Medicine: A Measurement Model of Task and Patient Complexity.
Islam, R; Weir, C; Del Fiol, G
2016-01-01
Complexity in medicine needs to be reduced to simple components in a way that is comprehensible to researchers and clinicians. Few studies in the current literature propose a measurement model that addresses both task and patient complexity in medicine. The objective of this paper is to develop an integrated approach to understand and measure clinical complexity by incorporating both task and patient complexity components focusing on the infectious disease domain. The measurement model was adapted and modified for the healthcare domain. Three clinical infectious disease teams were observed, audio-recorded and transcribed. Each team included an infectious diseases expert, one infectious diseases fellow, one physician assistant and one pharmacy resident fellow. The transcripts were parsed and the authors independently coded complexity attributes. This baseline measurement model of clinical complexity was modified in an initial set of coding processes and further validated in a consensus-based iterative process that included several meetings and email discussions by three clinical experts from diverse backgrounds from the Department of Biomedical Informatics at the University of Utah. Inter-rater reliability was calculated using Cohen's kappa. The proposed clinical complexity model consists of two separate components. The first is a clinical task complexity model with 13 clinical complexity-contributing factors and 7 dimensions. The second is the patient complexity model with 11 complexity-contributing factors and 5 dimensions. The measurement model for complexity encompassing both task and patient complexity will be a valuable resource for future researchers and industry to measure and understand complexity in healthcare.
Hyperbole, abstract motion and spatial knowledge: sequential versus simultaneous scanning.
Catricalà, Maria; Guidi, Annarita
2012-08-01
Hyperbole is an interesting trope in the perspective of Space Grammar, since it is related to the displacing of a limit (Lausberg in Elemente der literarischen Rhetorik. M.H. Verlag, Munchen 1967; see the Ancient Greek meaning 'to throw over' > 'exaggerate'). Hyperbole semantic mechanisms are related to virtual scanning (Holmqvist and Płuciennik in Imagery in language. Peter Lang, Frankfurt am Main, pp 777-785, 2004). Basic concepts of SIZE and QUANTITY, related image-schemas (IS) and conceptual metaphors (UP IS MORE; IMPORTANT IS BIG: Lakoff 1987, Johnson 1987) are implied in hyperbole processing. The virtual scanning is the simulation of a perceptual domain (here, the vertically oriented space). The virtual limit is defined by expected values on the relevant scale. Since hyperbole is a form of intensification, its linguistic interest lies in cases involving the extremes of a scale, for which a limit can be determined (Schemann 1994). In this experimental study, we analyze the concept of 'limit' in terms of 'abstract motion' and 'oriented space' domains (Langacker 1990) with respect to hyperboles expressed by Italian Verbs of movement. The IS considered are PATH and SOURCE-PATH-GOAL. The latter corresponds to a virtual scale whose limit is arrived at, or overcome, in hyperboles.
Existence and asymptotic behavior of solutions for Henon equations in hyperbolic spaces
Directory of Open Access Journals (Sweden)
Haiyang He
2013-09-01
Full Text Available In this article, we consider the existence and asymptotic behavior of solutions for the Henon equation $$\\displaylines{ -\\Delta_{\\mathbb{B}^N}u=(d(x^{\\alpha}|u|^{p-2}u, \\quad x\\in \\Omega\\cr u=0 \\quad x\\in \\partial \\Omega, }$$ where $\\Delta_{\\mathbb{B}^N}$ denotes the Laplace Beltrami operator on the disc model of the Hyperbolic space $\\mathbb{B}^N$, $d(x=d_{\\mathbb{B}^N}(0,x$, $\\Omega \\subset \\mathbb{B}^N$ is geodesic ball with radius $1$, $\\alpha>0, N\\geq 3$. We study the existence of hyperbolic symmetric solutions when $2
Directory of Open Access Journals (Sweden)
Farahani Hamed Shirinabadi
2017-03-01
Full Text Available The adaptive boundary stabilization is investigated for a class of systems described by second-order hyperbolic PDEs with unknown coefficient. The proposed control scheme only utilizes measurement on top boundary and assume anti-damping dynamics on the opposite boundary which is the main feature of our work. To cope with the lack of full state measurements, we introduce Riemann variables which allow us reformulate the second-order in time hyperbolic PDE as a system with linear input-delay dynamics. Then, the infinite-dimensional time-delay tools are employed to design the controller. Simulation results which applied on mathematical model of drilling system are given to demonstrate the effectiveness of the proposed control approach.
Broadband enhancement of local density of states using silicon-compatible hyperbolic metamaterials
Energy Technology Data Exchange (ETDEWEB)
Wang, Yu; Inampudi, Sandeep; Capretti, Antonio [Department of Electrical and Computer Engineering and Photonics Center, Boston University, 8 Saint Mary' s Street Boston, Massachusetts 02215 (United States); Sugimoto, Hiroshi [Department of Electrical and Computer Engineering and Photonics Center, Boston University, 8 Saint Mary' s Street Boston, Massachusetts 02215 (United States); Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University, Rokkodai, Nada, Kobe 657-8501 (Japan); Fujii, Minoru [Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University, Rokkodai, Nada, Kobe 657-8501 (Japan); Dal Negro, Luca, E-mail: dalnegro@bu.edu [Department of Electrical and Computer Engineering and Photonics Center, Boston University, 8 Saint Mary' s Street Boston, Massachusetts 02215 (United States); Division of Materials Science and Engineering, Boston University, 15 Saint Mary' s Street, Brookline, Massachusetts 02446 (United States)
2015-06-15
Light emitting silicon quantum dots by colloidal synthesis were uniformly spin-coated into a 20 nm-thick film and deposited atop a hyperbolic metamaterial of alternating TiN and SiO{sub 2} sub-wavelength layers. Using steady-state and time-resolved photoluminescence spectroscopy as a function of the emission wavelength in partnership with rigorous electromagnetic modeling of dipolar emission, we demonstrate enhanced Local Density of States and coupling to high-k modes in a broad spectral range. These findings provide an alternative approach for the engineering of novel Si-compatible broadband sources that leverage the control of radiative transitions in hyperbolic metamaterials and the flexibility of the widespread Si platform.
Analytical models for complex swirling flows
Borissov, A.; Hussain, V.
1996-11-01
We develops a new class of analytical solutions of the Navier-Stokes equations for swirling flows, and suggests ways to predict and control such flows occurring in various technological applications. We view momentum accumulation on the axis as a key feature of swirling flows and consider vortex-sink flows on curved axisymmetric surfaces with an axial flow. We show that these solutions model swirling flows in a cylindrical can, whirlpools, tornadoes, and cosmic swirling jets. The singularity of these solutions on the flow axis is removed by matching them with near-axis Schlichting and Long's swirling jets. The matched solutions model flows with very complex patterns, consisting of up to seven separation regions with recirculatory 'bubbles' and vortex rings. We apply the matched solutions for computing flows in the Ranque-Hilsch tube, in the meniscus of electrosprays, in vortex breakdown, and in an industrial vortex burner. The simple analytical solutions allow a clear understanding of how different control parameters affect the flow and guide selection of optimal parameter values for desired flow features. These solutions permit extension to other problems (such as heat transfer and chemical reaction) and have the potential of being significantly useful for further detailed investigation by direct or large-eddy numerical simulations as well as laboratory experimentation.
Discrete Element Modeling of Complex Granular Flows
Movshovitz, N.; Asphaug, E. I.
2010-12-01
Granular materials occur almost everywhere in nature, and are actively studied in many fields of research, from food industry to planetary science. One approach to the study of granular media, the continuum approach, attempts to find a constitutive law that determines the material's flow, or strain, under applied stress. The main difficulty with this approach is that granular systems exhibit different behavior under different conditions, behaving at times as an elastic solid (e.g. pile of sand), at times as a viscous fluid (e.g. when poured), or even as a gas (e.g. when shaken). Even if all these physics are accounted for, numerical implementation is made difficult by the wide and often discontinuous ranges in continuum density and sound speed. A different approach is Discrete Element Modeling (DEM). Here the goal is to directly model every grain in the system as a rigid body subject to various body and surface forces. The advantage of this method is that it treats all of the above regimes in the same way, and can easily deal with a system moving back and forth between regimes. But as a granular system typically contains a multitude of individual grains, the direct integration of the system can be very computationally expensive. For this reason most DEM codes are limited to spherical grains of uniform size. However, spherical grains often cannot replicate the behavior of real world granular systems. A simple pile of spherical grains, for example, relies on static friction alone to keep its shape, while in reality a pile of irregular grains can maintain a much steeper angle by interlocking force chains. In the present study we employ a commercial DEM, nVidia's PhysX Engine, originally designed for the game and animation industry, to simulate complex granular flows with irregular, non-spherical grains. This engine runs as a multi threaded process and can be GPU accelerated. We demonstrate the code's ability to physically model granular materials in the three regimes
Boundary-field-driven control of discontinuous phase transitions on hyperbolic lattices.
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.
Xu, Wenjun; Tang, Chen; Zhang, Junjiang; Su, Yonggang; Su, Ray Kai Leung
2015-05-20
Oriented partial differential equation (OPDE)-based filtering methods have been demonstrated to be a powerful tool for denoising while preserving all fringes. In this paper we propose new OPDE-filtering models, named parabolic-hyperbolic oriented partial differential equations (PH-OPDEs), based on variational methods. We test the proposed PH-OPDEs on two computer-simulated and two experimentally obtained ESPI fringe patterns with poor quality, and compare our models with related OPDE models. The experimental results have demonstrated that the new models have significantly better performance in numerical stability and computational efficiency as compared with the previous OPDE models.
Hyperbolic Harmonic Mapping for Surface Registration.
Shi, Rui; Zeng, Wei; Su, Zhengyu; Jiang, Jian; Damasio, Hanna; Lu, Zhonglin; Wang, Yalin; Yau, Shing-Tung; Gu, Xianfeng
2017-05-01
Automatic computation of surface correspondence via harmonic map is an active research field in computer vision, computer graphics and computational geometry. It may help document and understand physical and biological phenomena and also has broad applications in biometrics, medical imaging and motion capture industries. Although numerous studies have been devoted to harmonic map research, limited progress has been made to compute a diffeomorphic harmonic map on general topology surfaces with landmark constraints. This work conquers this problem by changing the Riemannian metric on the target surface to a hyperbolic metric so that the harmonic mapping is guaranteed to be a diffeomorphism under landmark constraints. The computational algorithms are based on Ricci flow and nonlinear heat diffusion methods. The approach is general and robust. We employ our algorithm to study the constrained surface registration problem which applies to both computer vision and medical imaging applications. Experimental results demonstrate that, by changing the Riemannian metric, the registrations are always diffeomorphic and achieve relatively high performance when evaluated with some popular surface registration evaluation standards.
Front tracking for hyperbolic conservation laws
Holden, Helge
2002-01-01
Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet "I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one-semester graduate course." S. Noelle, Book review, German Math. Soc. "Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm.
Hyperbolic theory of relativistic conformal dissipative fluids
Lehner, Luis; Reula, Oscar A.; Rubio, Marcelo E.
2018-01-01
We develop a complete description of the class of conformal relativistic dissipative fluids of divergence form, following the formalism described in [R. Geroch and L. Lindblom, Phys. Rev. D 41, 1855 (1990), 10.1103/PhysRevD.41.1855, S. Pennisi, Some considerations on a non linear approach to extended thermodynamics and in Proceedings of Symposium of Kinetic Theory and Extended Thermodynamics, Bologna, 1987.]. This type of theory is fully described in terms of evolution variables whose dynamics are governed by total divergence-type conservation laws. Specifically, we give a characterization of the whole family of conformal fluids in terms of a single master scalar function defined up to second-order corrections in dissipative effects, which we explicitly find in general form. This allows us to identify the equilibrium states of the theory and derive constitutive relations and a Fourier-like law for the corresponding first-order theory heat flux. Finally, we show that among this class of theories—and near equilibrium configurations—there exist symmetric hyperbolic ones, implying that for them one can define well-posed initial value problems.
Statistical Solutions of Hyperbolic Conservation Laws: Foundations
Fjordholm, U. S.; Lanthaler, S.; Mishra, S.
2017-11-01
We seek to define statistical solutions of hyperbolic systems of conservation laws as time-parametrized probability measures on p-integrable functions. To do so, we prove the equivalence between probability measures on L p spaces and infinite families of correlation measures. Each member of this family, termed a correlation marginal, is a Young measure on a finite-dimensional tensor product domain and provides information about multi-point correlations of the underlying integrable functions. We also prove that any probability measure on a L p space is uniquely determined by certain moments (correlation functions) of the equivalent correlation measure. We utilize this equivalence to define statistical solutions of multi-dimensional conservation laws in terms of an infinite set of equations, each evolving a moment of the correlation marginal. These evolution equations can be interpreted as augmenting entropy measure-valued solutions, with additional information about the evolution of all possible multi-point correlation functions. Our concept of statistical solutions can accommodate uncertain initial data as well as possibly non-atomic solutions, even for atomic initial data. For multi-dimensional scalar conservation laws we impose additional entropy conditions and prove that the resulting entropy statistical solutions exist, are unique and are stable with respect to the 1-Wasserstein metric on probability measures on L 1.
Kelly, Priscilla; Martin, Andrew C.; Kuznetsova, Lyuba
2016-09-01
A special class of nano-layered hyperbolic metamaterials (HMMs) has received special attention recently due to their unique optical property, namely that the dispersion of the dielectric constant for HMMs exhibits a topological transition in the iso-frequency surface from an ellipsoid to a hyperboloid. Using aluminum in metal-dielectric nano-layered structures offers several advantages over currently used noble metals. The plasma frequency of the aluminum is higher than that of gold or silver. As a result, aluminum exhibits metallic characteristics over a broader spectral range than gold and silver. In addition, SiO2 is used as the dielectric for this hyperbolic metamaterial because it could be easily integrated into current CMOS technology and has near-zero losses in the UV region. In this investigation, we use generalized spectroscopic ellipsometry to study the distribution of Al within nano-layered samples fabricated using the RF sputtering technique under varying fabrication parameters with a goal of achieving hyperbolic dispersion. In our work, we developed an approach to analyzing generalized spectroscopic ellipsometry data for anisotropic Al/SiO2 structures with strong absorption, which uses the 4x4 transfer matrix approach, also known as the Berreman-formalism. This developed approach allows obtaining permittivity in all three dimensions and importing theoretical permittivity models which are tailored to the Al/SiO2 material's optical and electrical properties. In this work, we investigate the methods of reducing Al oxidation during fabrication by means of varying the fabrication temperatures and pressure by fitting data from RC2 Ellipsometer (A.C. Woollam Co.), which has dual rotating compensators. Applications for this Al/SiO2 hyperbolic metamaterial will also be discussed.
Complex networks repair strategies: Dynamic models
Fu, Chaoqi; Wang, Ying; Gao, Yangjun; Wang, Xiaoyang
2017-09-01
Network repair strategies are tactical methods that restore the efficiency of damaged networks; however, unreasonable repair strategies not only waste resources, they are also ineffective for network recovery. Most extant research on network repair focuses on static networks, but results and findings on static networks cannot be applied to evolutionary dynamic networks because, in dynamic models, complex network repair has completely different characteristics. For instance, repaired nodes face more severe challenges, and require strategic repair methods in order to have a significant effect. In this study, we propose the Shell Repair Strategy (SRS) to minimize the risk of secondary node failures due to the cascading effect. Our proposed method includes the identification of a set of vital nodes that have a significant impact on network repair and defense. Our identification of these vital nodes reduces the number of switching nodes that face the risk of secondary failures during the dynamic repair process. This is positively correlated with the size of the average degree 〈 k 〉 and enhances network invulnerability.
Influence of boundary conditions on the solution of a hyperbolic thermoelasticity problem
Vitokhin, Evgeniy Yu.; Babenkov, Mikhail B.
2017-03-01
We consider a series of problems with a short laser impact on a thin metal layer accounting various boundary conditions of the first and second kind. The behavior of the material is modeled by the hyperbolic thermoelasticity of Lord-Shulman type. We obtain analytical solutions of the problems in the semi-coupled formulation and numerical solutions in the coupled formulation. Numerical solutions are compared with the analytical ones. The analytical solutions of the semi-coupled problems and numerical solutions of the coupled problems show qualitative match. The solutions of hyperbolic thermoelasticity problems are compared with those obtained in the frame of the classical thermoelasticity. It was determined that the most prominent difference between the classical and hyperbolic solutions arises in the problem with fixed boundaries and constant temperature on them. The smallest differences were observed in the problem with unconstrained, thermally insulated edges. It was shown that a cooling zone is observed if the boundary conditions of the first kind are given for the temperature. Analytical expressions for the velocities of the quasiacoustic and quasithermal fronts as well as the critical value for the attenuation coefficient of the excitation impulse are verified numerically.
A new empirical complex electrical resistivity model
Kavian, M.; Slob, E.C.; Mulder, W.A.
2012-01-01
Macroscopic measurements of electrical resistivity require frequency-dependent effective models that honor the microscopic effects observable in macroscopic measurements. Effective models based on microscopic physics exist alongside with empirical models. We adopted an empirical model approach to
Super-Coulombic atom-atom interactions in hyperbolic media
Cortes, Cristian L.; Jacob, Zubin
2017-01-01
Dipole-dipole interactions, which govern phenomena such as cooperative Lamb shifts, superradiant decay rates, Van der Waals forces and resonance energy transfer rates, are conventionally limited to the Coulombic near-field. Here we reveal a class of real-photon and virtual-photon long-range quantum electrodynamic interactions that have a singularity in media with hyperbolic dispersion. The singularity in the dipole-dipole coupling, referred to as a super-Coulombic interaction, is a result of an effective interaction distance that goes to zero in the ideal limit irrespective of the physical distance. We investigate the entire landscape of atom-atom interactions in hyperbolic media confirming the giant long-range enhancement. We also propose multiple experimental platforms to verify our predicted effect with phonon-polaritonic hexagonal boron nitride, plasmonic super-lattices and hyperbolic meta-surfaces as well. Our work paves the way for the control of cold atoms above hyperbolic meta-surfaces and the study of many-body physics with hyperbolic media.
Computing the Gromov hyperbolicity of a discrete metric space
Fournier, Hervé
2015-02-12
We give exact and approximation algorithms for computing the Gromov hyperbolicity of an n-point discrete metric space. We observe that computing the Gromov hyperbolicity from a fixed base-point reduces to a (max,min) matrix product. Hence, using the (max,min) matrix product algorithm by Duan and Pettie, the fixed base-point hyperbolicity can be determined in O(n2.69) time. It follows that the Gromov hyperbolicity can be computed in O(n3.69) time, and a 2-approximation can be found in O(n2.69) time. We also give a (2log2n)-approximation algorithm that runs in O(n2) time, based on a tree-metric embedding by Gromov. We also show that hyperbolicity at a fixed base-point cannot be computed in O(n2.05) time, unless there exists a faster algorithm for (max,min) matrix multiplication than currently known.
Hyperbolicity Measures "Democracy" in Real-World Networks
Borassi, Michele; Caldarelli, Guido
2015-01-01
We analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. In our interpretation, a network with small hyperbolicity is "aristocratic", because it contains a small set of vertices involved in many shortest paths, so that few elements "connect" the systems, while a network with large hyperbolicity has a more "democratic" structure with a larger number of crucial elements. We prove mathematically the soundness of this interpretation, and we derive its consequences by analyzing a large dataset of real-world networks. We confirm and improve previous results on hyperbolicity, and we analyze them in the light of our interpretation. Moreover, we study (for the first time in our knowledge) the hyperbolicity of the neighborhood of a given vertex. This allows to define an "influence area" for the vertices in the graph. We show that the influence area of the highest degree vertex is small in what we define "local" networks, like most social or peer-to-peer ne...
Drikakis, D.
2002-07-01
The paper describes the use of numerical methods for hyperbolic conservation laws as an embedded turbulence modelling approach. Different Godunov-type schemes are utilized in computations of Burgers' turbulence and a two-dimensional mixing layer. The schemes include a total variation diminishing, characteristic-based scheme which is developed in this paper using the flux limiter approach. The embedded turbulence modelling property of the above methods is demonstrated through coarsely resolved large eddy simulations with and without subgrid scale models. Copyright
Complex Modeling - SAHG | LSDB Archive [Life Science Database Archive metadata
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Full Text Available lex Modeling Data detail Data name Complex Modeling DOI 10.18908/lsdba.nbdc01193-00.... About This Database Database Description Download License Update History of This Database Site Policy | Contact Us Complex Modeling - SAHG | LSDB Archive ... ...switchLanguage; BLAST Search Image Search Home About Archive Update History Data List Contact us SAHG Comp
Mixed Effects Models for Complex Data
Wu, Lang
2009-01-01
Presenting effective approaches to address missing data, measurement errors, censoring, and outliers in longitudinal data, this book covers linear, nonlinear, generalized linear, nonparametric, and semiparametric mixed effects models. It links each mixed effects model with the corresponding class of regression model for cross-sectional data and discusses computational strategies for likelihood estimations of mixed effects models. The author briefly describes generalized estimating equations methods and Bayesian mixed effects models and explains how to implement standard models using R and S-Pl
Bulk plasmon-polaritons in hyperbolic nanorod metamaterial waveguides
Vasilantonakis, Nikolaos; Nasir, Mazhar E; Dickson, Wayne; Wurtz, Gregory A; Zayats, Anatoly V
2015-01-01
Hyperbolic metamaterials comprised of an array of plasmonic nanorods provide a unique platform for designing optical sensors and integrating nonlinear and active nanophotonic functionalities. In this work, the waveguiding properties and mode structure of planar anisotropic metamaterial waveguides are characterized experimentally and theoretically. While ordinary modes are the typical guided modes of the highly anisotropic waveguides, extraordinary modes, below the effective plasma frequency, exist in a hyperbolic metamaterial slab in the form of bulk plasmon-polaritons, in analogy to planar-cavity exciton-polaritons in semiconductors. They may have very low or negative group velocity with high effective refractive indices (up to 10) and have an unusual cut-off from the high-frequency side, providing deep-subwavelength (λ0/6–λ0/8 waveguide thickness) single-mode guiding. These properties, dictated by the hyperbolic anisotropy of the metamaterial, may be tuned by altering the geometrical parameters of the nanorod composite. PMID:26693254
Dynamics beyond uniform hyperbolicity a global geometric and probabilistic perspective
Bonatti, Christian; Viana, Marcelo
2005-01-01
The notion of uniform hyperbolicity, introduced by Steve Smale in the early sixties, unified important developments and led to a remarkably successful theory for a large class of systems: uniformly hyperbolic systems often exhibit complicated evolution which, nevertheless, is now rather well understood, both geometrically and statistically.Another revolution has been taking place in the last couple of decades, as one tries to build a global theory for "most" dynamical systems, recovering as much as possible of the conclusions of the uniformly hyperbolic case, in great generality. This book aims to put such recent developments in a unified perspective, and to point out open problems and likely directions for further progress. It is aimed at researchers, both young and senior, willing to get a quick, yet broad, view of this part of dynamics. Main ideas, methods, and results are discussed, at variable degrees of depth, with references to the original works for details and complementary information.
Hyperbolicity, sinks and measure in one dimensional dynamics
Mañé, Ricardo
1985-12-01
Let f be a C 2 map of the circle or the interval and let Σ( f) denote the complement of the basins of attraction of the attracting periodic orbits. We prove that Σ( f) is a hyperbolic expanding set if (and obviously only if) every periodic point is hyperbolic and Σ( f) doesn't contain the critical point. This is the real one dimensional version of Fatou's hyperbolicity criteria for holomorphic endomorphisms of the Riemann sphere. We also explore other applications of the techniques used for the result above, proving, for instance, that for every C 2 immersion f of the circle (i.e. a map of the circle onto itself without critical points), either its Julia set has measure zero or it is the whole circle and then f is ergodic, i.e. positively invariant Borel sets have zero or full measure.
BDI-modelling of complex intracellular dynamics.
Jonker, C.M.; Snoep, J.L.; Treur, J.; Westerhoff, H.V.; Wijngaards, W.C.A.
2008-01-01
A BDI-based continuous-time modelling approach for intracellular dynamics is presented. It is shown how temporalised BDI-models make it possible to model intracellular biochemical processes as decision processes. By abstracting from some of the details of the biochemical pathways, the model achieves
Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
Directory of Open Access Journals (Sweden)
Golovaty Yuriy
2017-04-01
Full Text Available We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.
Field-effect induced tunability in planar hyperbolic metamaterials
Papadakis, Georgia T
2015-01-01
We demonstrate that use of the field effect to tune the effective optical parameters of a layered hyperbolic metamaterial leads to topological transitions in its dispersion characteristics in the optical regime. Field effect gating electrically modulates the permittivity in transparent conductive oxides via changes in the carrier density. These permittivity changes lead to active extreme modulation of ~200% of the effective electromagnetic parameters along with active control of the anisotropic dispersion surface of hyperbolic metamaterials and enable the opening and closing of photonic band gaps.
Field-effect induced tunability in hyperbolic metamaterials
Papadakis, Georgia T.; Atwater, Harry A.
2015-11-01
We demonstrate that use of the field effect enables tuning of the effective optical parameters of a layered hyperbolic metamaterial at optical frequencies. Field-effect gating electrically modulates the permittivity in transparent conductive oxides via changes in the carrier density. These permittivity changes lead to active modulation of the effective electromagnetic parameters along with active control of the anisotropic dispersion surface of hyperbolic metamaterials and enable the opening and closing of photonic band gaps. Tunability of the effective electric permittivity and magnetic permeability also leads to topological transitions in the optical dispersion characteristics.
Modelling and estimation of dynamic instability in complex economic systems
Wang, J.
2015-01-01
This thesis sheds some lights on the on-going discussions on modelling the economy as a complex evolving system. It introduces a complex systems approach and attempts to unfold the underlying mechanisms of dynamic instability in complex economic system. Moreover, it contributes to the ongoing
Effects of nonlocal response on the density of states of hyperbolic metamaterials
DEFF Research Database (Denmark)
Yan, Wei; Wubs, Martijn; Mortensen, N. Asger
2012-01-01
of the nonlocal response of the electron gas in the metal on the hyperbolic metamaterials. By using mean field theory, we derive the effective material parameters of the hyperbolic metamaterials. The original unbounded hyperbolic dispersion is found to be cut off at the wavevector inverse to the Fermi velocity...
Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy; Zanotti, Olindo
2017-11-01
In this paper, we propose a new unified first order hyperbolic model of Newtonian continuum mechanics coupled with electro-dynamics. The model is able to describe the behavior of moving elasto-plastic dielectric solids as well as viscous and inviscid fluids in the presence of electro-magnetic fields. It is actually a very peculiar feature of the proposed PDE system that viscous fluids are treated just as a special case of elasto-plastic solids. This is achieved by introducing a strain relaxation mechanism in the evolution equations of the distortion matrix A, which in the case of purely elastic solids maps the current configuration to the reference configuration. The model also contains a hyperbolic formulation of heat conduction as well as a dissipative source term in the evolution equations for the electric field given by Ohm's law. Via formal asymptotic analysis we show that in the stiff limit, the governing first order hyperbolic PDE system with relaxation source terms tends asymptotically to the well-known viscous and resistive magnetohydrodynamics (MHD) equations. Furthermore, a rigorous derivation of the model from variational principles is presented, together with the transformation of the Euler-Lagrange differential equations associated with the underlying variational problem from Lagrangian coordinates to Eulerian coordinates in a fixed laboratory frame. The present paper hence extends the unified first order hyperbolic model of Newtonian continuum mechanics recently proposed in [110,42] to the more general case where the continuum is coupled with electro-magnetic fields. The governing PDE system is symmetric hyperbolic and satisfies the first and second principle of thermodynamics, hence it belongs to the so-called class of symmetric hyperbolic thermodynamically compatible systems (SHTC), which have been studied for the first time by Godunov in 1961 [61] and later in a series of papers by Godunov and Romenski [67,69,119]. An important feature of the
The utility of Earth system Models of Intermediate Complexity
Weber, S.L.
2010-01-01
Intermediate-complexity models are models which describe the dynamics of the atmosphere and/or ocean in less detail than conventional General Circulation Models (GCMs). At the same time, they go beyond the approach taken by atmospheric Energy Balance Models (EBMs) or ocean box models by
Advances in dynamic network modeling in complex transportation systems
Ukkusuri, Satish V
2013-01-01
This book focuses on the latest in dynamic network modeling, including route guidance and traffic control in transportation systems and other complex infrastructure networks. Covers dynamic traffic assignment, flow modeling, mobile sensor deployment and more.
Are complex DCE-MRI models supported by clinical data?
DEFF Research Database (Denmark)
Duan, Chong; Kallehauge, Jesper F; Bretthorst, G Larry
2016-01-01
PURPOSE: To ascertain whether complex dynamic contrast enhanced (DCE) MRI tracer kinetic models are supported by data acquired in the clinic and to determine the consequences of limited contrast-to-noise. METHODS: Generically representative in silico and clinical (cervical cancer) DCE-MRI data were...... to both model selection and parameter estimation. Indeed, as contrast-to-noise decreased, complex DCE models became less probable and simpler models more probable. The less complex TM and CTUM were the optimal models for the DCE-MRI data acquired in the clinic. [In cervical tumors, Ktrans, Fp, and PS...... increased after radiotherapy (P = 0.004, 0.002, and 0.014, respectively)]. CONCLUSION: Caution is advised when considering application of complex DCE-MRI kinetic models to data acquired in the clinic. It follows that data-driven model selection is an important prerequisite to DCE-MRI analysis. Model...
The Cognitive Complexity in Modelling the Group Decision Process
Directory of Open Access Journals (Sweden)
Barna Iantovics
2010-06-01
Full Text Available The paper investigates for some basic contextual factors (such
us the problem complexity, the users' creativity and the problem space complexity the cognitive complexity associated with modelling the group decision processes (GDP in e-meetings. The analysis is done by conducting a socio-simulation experiment for an envisioned collaborative software tool that acts as a stigmergic environment for modelling the GDP. The simulation results revels some interesting design guidelines for engineering some contextual functionalities that minimize the cognitive complexity associated with modelling the GDP.
Disentangling nestedness from models of ecological complexity.
James, Alex; Pitchford, Jonathan W; Plank, Michael J
2012-07-12
Complex networks of interactions are ubiquitous and are particularly important in ecological communities, in which large numbers of species exhibit negative (for example, competition or predation) and positive (for example, mutualism) interactions with one another. Nestedness in mutualistic ecological networks is the tendency for ecological specialists to interact with a subset of species that also interact with more generalist species. Recent mathematical and computational analysis has suggested that such nestedness increases species richness. By examining previous results and applying computational approaches to 59 empirical data sets representing mutualistic plant–pollinator networks, we show that this statement is incorrect. A simpler metric—the number of mutualistic partners a species has—is a much better predictor of individual species survival and hence, community persistence. Nestedness is, at best, a secondary covariate rather than a causative factor for biodiversity in mutualistic communities. Analysis of complex networks should be accompanied by analysis of simpler, underpinning mechanisms that drive multiple higher-order network properties.
Modeling Electronic Properties of Complex Oxides
Krishnaswamy, Karthik
Complex oxides are a class of materials that have recently emerged as potential candidates for electronic applications owing to their interesting electronic properties. The goal of this dissertation is to develop a fundamental understanding of these electronic properties using a combination of first-principles approaches based on density functional theory (DFT), and Schr odinger-Poisson (SP) simulation (Abstract shortened by ProQuest.
Mixture model analysis of complex samples
Wedel, M.; Hofstede, F. ter; Steenkamp, J.-B.E.M.
1997-01-01
This paper investigates asymmetric effects of monetary policy over the business cycle. A two-state Markov Switching Model is employed to model both recessions and expansions. For the United States and Germany, strong evidence is found that monetary policy is more effective in a recession than during
Uncertainty and Complexity in Mathematical Modeling
Cannon, Susan O.; Sanders, Mark
2017-01-01
Modeling is an effective tool to help students access mathematical concepts. Finding a math teacher who has not drawn a fraction bar or pie chart on the board would be difficult, as would finding students who have not been asked to draw models and represent numbers in different ways. In this article, the authors will discuss: (1) the properties of…
Physical nature of volume plasmon polaritons in hyperbolic metamaterials
DEFF Research Database (Denmark)
Zhukovsky, Sergei; Kidwai, Omar; Sipe, J. E.
2013-01-01
We investigate electromagnetic wave propagation in multilayered metal-dielectric hyperbolic metamaterials (HMMs). We demonstrate that high-k propagating waves in HMMs are volume plasmon polaritons. The volume plasmon polariton band is formed by coupling of short-range surface plasmon polariton...
Poincar\\'{e} Sobolev equations in the Hyperbolic space
Bhakta, Mousomi; Sandeep, K.
2011-01-01
We study the a priori estimates,existence/nonexistence of radial sign changing solution, and the Palais-Smale characterisation of the problem $-\\De_{\\Bn}u - \\la u = |u|^{p-1}u, u\\in H^1(\\Bn)$ in the hyperbolic space $\\Bn$ where $1
Hyperbolic lattice-point counting and modular symbols
DEFF Research Database (Denmark)
N. Petridis, Yiannis; Risager, Morten S.
2009-01-01
For a cocompact group $\\G$ of $\\slr$ we fix a real non-zero harmonic 1-form $\\alpha$. We study the asymptotics of the hyperbolic lattice-counting problem for $\\G$ under restrictions imposed by the modular symbols $\\modsym{\\gamma}{\\a}$. We prove that the normalized values of the modular symbols, w...
Discontinuous Galerkin error estimation for linear symmetrizable hyperbolic systems
Adjerid, Slimane; Weinhart, Thomas
2011-01-01
We present an a posteriori error analysis for the discontinuous Galerkin discretization error of first-order linear symmetrizable hyperbolic systems of partial differential equations with smooth solutions. We perform a local error analysis by writing the local error as a series and showing that its
High-Order CESE Methods for Solving Hyperbolic PDEs (Preprint)
2011-05-03
system of coupled hyperbolic PDE’s with arbitrarily high-order con- vergence . Numerical results show that the extended algorithm can achieve higher...Velocity- Stress Equations for Waves in Solids of Hexagonal Symmetry Solved by the Space-Time CESE Method. ASME Journal of Vibration and Acoustics, 133 (2
Bound states in a hyperbolic asymmetric double-well
Energy Technology Data Exchange (ETDEWEB)
Hartmann, R. R., E-mail: richard.hartmann@dlsu.edu.ph [Physics Department, De La Salle University, 2401 Taft Avenue, Manila (Philippines)
2014-01-15
We report a new class of hyperbolic asymmetric double-well whose bound state wavefunctions can be expressed in terms of confluent Heun functions. An analytic procedure is used to obtain the energy eigenvalues and the criterion for the potential to support bound states is discussed.
Plasmonic Terahertz Amplification in Graphene-Based Asymmetric Hyperbolic Metamaterial
Directory of Open Access Journals (Sweden)
Igor Nefedov
2015-05-01
Full Text Available We propose and theoretically explore terahertz amplification, based on stimulated generation of plasmons in graphene asymmetric hyperbolic metamaterials (AHMM, strongly coupled to terahertz radiation. In contrast to the terahertz amplification in resonant nanocavities, AHMM provides a wide-band THz amplification without any reflection in optically thin graphene multilayers.
Layered van der Waals crystals with hyperbolic light dispersion
DEFF Research Database (Denmark)
Gjerding, Morten Niklas; Petersen, R.; Pedersen, T.G.
2017-01-01
-infrared to the ultraviolet. Combined with the emerging field of van der Waals heterostructuring, we demonstrate how the hyperbolic properties can be further controlled by stacking different two-dimensional crystals opening new perspectives for atomic-scale design of photonic metamaterials. As an application, we identify...
Hyperboles not turning to metaphors : How to explain audience cooperativeness?
van den Hoven, P.J.|info:eu-repo/dai/nl/070378096
2016-01-01
We observe that an audience attempts to interpret the relation between a source domain and a target domain as a hyperbole before interpreting it as a metaphor. It could also first try a metaphorical reading or attempt several possible readings and successively select the relevant outcome. But it
Figurative framing : Shaping public discourse through metaphor, hyperbole and irony
Burgers, C.; Konijn, E.A.; Steen, G.J.
2016-01-01
Framing is an important concept in communication, yet many framing studies set out to develop frames relevant to only one issue. We expand framing theory by introducing figurative framing. We posit that figurative language types like metaphor, hyperbole and irony are important in shaping public
Figurative framing: Shaping public discourse through metaphor, hyperbole and irony
Burgers, C.F.; Konijn, E.A.; Steen, G.J.
2016-01-01
Framing is an important concept in communication, yet many framing studies set out to develop frames relevant to only one issue. We expand framing theory by introducing figurative framing. We posit that figurative language types like metaphor, hyperbole and irony are important in shaping public
Finite-width plasmonic waveguides with hyperbolic multilayer cladding
DEFF Research Database (Denmark)
Babicheva, Viktoriia; Shalaginov, Mikhail Y.; Ishii, Satoshi
2015-01-01
Engineering plasmonic metamaterials with anisotropic optical dispersion enables us to tailor the properties of metamaterial-based waveguides. We investigate plasmonic waveguides with dielectric cores and multilayer metal-dielectric claddings with hyperbolic dispersion. Without using any......, are strongly absorbed. By avoiding the resonant widths in the design of the actual waveguides, the strong absorption can be eliminated. (C) 2015 Optical Society of America...
Hybrid plasmonic/semiconductor nanoparticle monolayer assemblies as hyperbolic metamaterials
DEFF Research Database (Denmark)
Zhukovsky, Sergei; Ozel, Tuncay; Mutlugun, Evren
2014-01-01
We show that hybrid nanostructures made of alternating colloidal semiconductor quantum dot and metal nanoparticle monolayers can function as multilayer hyperbolic meta-materials. By choosing the thickness of the spacer between the quantum dot and nanoparticle layers, one can achieve the indefinite...
ALL OR NOTHING: A SEMANTIC ANALYSIS OF HYPERBOLE
Directory of Open Access Journals (Sweden)
Laura Cano Mora
2009-10-01
Full Text Available This paper focuses on hyperbole, a long neglected form of non-literal language despite its pervasiveness
in everyday speech. It addresses the production process of exaggeration, since a crucial limitation in
figurative language theories is the production and usage of figures of speech, probably due to the intensive
research effort on their comprehension. The aim is to analyse hyperbole from a semantic perspective in order
to devise a semasiological taxonomy which enables us to understand the nature and uses of the trope. In
order to analyse and classify hyperbolic items a corpus of naturally occurring conversations extracted from
the British National Corpus was examined. The results suggest that the evaluative and quantitative dimensions
are key, defining features which often co-occur and should therefore be present in any definition of this
figure of speech. A remarkable preference for negative affect, auxesis and absolute terms when engaging in
hyperbole is also observed.
Spatial mode-selective waveguide with hyperbolic cladding
Tang, Y.; Xi, Z.; Xu, M.; Bäumer, S.M.B.; Adam, A.J.L.; Urbach, H.P.
2016-01-01
Hyperbolic metamaterials (HMMs) are anisotropic materials with a permittivity tensor that has both positive and negative eigenvalues. Here we report that by using a type II HMM as a cladding material, a waveguide that only supports higher-order modes can be achieved, while the lower-order modes
Linking Complexity and Sustainability Theories: Implications for Modeling Sustainability Transitions
Directory of Open Access Journals (Sweden)
Camaren Peter
2014-03-01
Full Text Available In this paper, we deploy a complexity theory as the foundation for integration of different theoretical approaches to sustainability and develop a rationale for a complexity-based framework for modeling transitions to sustainability. We propose a framework based on a comparison of complex systems’ properties that characterize the different theories that deal with transitions to sustainability. We argue that adopting a complexity theory based approach for modeling transitions requires going beyond deterministic frameworks; by adopting a probabilistic, integrative, inclusive and adaptive approach that can support transitions. We also illustrate how this complexity-based modeling framework can be implemented; i.e., how it can be used to select modeling techniques that address particular properties of complex systems that we need to understand in order to model transitions to sustainability. In doing so, we establish a complexity-based approach towards modeling sustainability transitions that caters for the broad range of complex systems’ properties that are required to model transitions to sustainability.
Modeling Power Systems as Complex Adaptive Systems
Energy Technology Data Exchange (ETDEWEB)
Chassin, David P.; Malard, Joel M.; Posse, Christian; Gangopadhyaya, Asim; Lu, Ning; Katipamula, Srinivas; Mallow, J V.
2004-12-30
Physical analogs have shown considerable promise for understanding the behavior of complex adaptive systems, including macroeconomics, biological systems, social networks, and electric power markets. Many of today's most challenging technical and policy questions can be reduced to a distributed economic control problem. Indeed, economically based control of large-scale systems is founded on the conjecture that the price-based regulation (e.g., auctions, markets) results in an optimal allocation of resources and emergent optimal system control. This report explores the state-of-the-art physical analogs for understanding the behavior of some econophysical systems and deriving stable and robust control strategies for using them. We review and discuss applications of some analytic methods based on a thermodynamic metaphor, according to which the interplay between system entropy and conservation laws gives rise to intuitive and governing global properties of complex systems that cannot be otherwise understood. We apply these methods to the question of how power markets can be expected to behave under a variety of conditions.
Mathematical modeling and optimization of complex structures
Repin, Sergey; Tuovinen, Tero
2016-01-01
This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include: * Computer simulation methods in mechanics, physics, and biology; * Variational problems and methods; minimiz...
Cellular Potts modeling of complex multicellular behaviors in tissue morphogenesis
T. Hirashima (Tsuyoshi); E.G. Rens (Lisanne); R.M.H. Merks (Roeland)
2017-01-01
textabstractMathematical modeling is an essential approach for the understanding of complex multicellular behaviors in tissue morphogenesis. Here, we review the cellular Potts model (CPM; also known as the Glazier-Graner-Hogeweg model), an effective computational modeling framework. We discuss its
Smart modeling and simulation for complex systems practice and theory
Ren, Fenghui; Zhang, Minjie; Ito, Takayuki; Tang, Xijin
2015-01-01
This book aims to provide a description of these new Artificial Intelligence technologies and approaches to the modeling and simulation of complex systems, as well as an overview of the latest scientific efforts in this field such as the platforms and/or the software tools for smart modeling and simulating complex systems. These tasks are difficult to accomplish using traditional computational approaches due to the complex relationships of components and distributed features of resources, as well as the dynamic work environments. In order to effectively model the complex systems, intelligent technologies such as multi-agent systems and smart grids are employed to model and simulate the complex systems in the areas of ecosystem, social and economic organization, web-based grid service, transportation systems, power systems and evacuation systems.
A complex autoregressive model and application to monthly temperature forecasts
Directory of Open Access Journals (Sweden)
X. Gu
2005-11-01
Full Text Available A complex autoregressive model was established based on the mathematic derivation of the least squares for the complex number domain which is referred to as the complex least squares. The model is different from the conventional way that the real number and the imaginary number are separately calculated. An application of this new model shows a better forecast than forecasts from other conventional statistical models, in predicting monthly temperature anomalies in July at 160 meteorological stations in mainland China. The conventional statistical models include an autoregressive model, where the real number and the imaginary number are separately disposed, an autoregressive model in the real number domain, and a persistence-forecast model.
Understanding complex urban systems integrating multidisciplinary data in urban models
Gebetsroither-Geringer, Ernst; Atun, Funda; Werner, Liss
2016-01-01
This book is devoted to the modeling and understanding of complex urban systems. This second volume of Understanding Complex Urban Systems focuses on the challenges of the modeling tools, concerning, e.g., the quality and quantity of data and the selection of an appropriate modeling approach. It is meant to support urban decision-makers—including municipal politicians, spatial planners, and citizen groups—in choosing an appropriate modeling approach for their particular modeling requirements. The contributors to this volume are from different disciplines, but all share the same goal: optimizing the representation of complex urban systems. They present and discuss a variety of approaches for dealing with data-availability problems and finding appropriate modeling approaches—and not only in terms of computer modeling. The selection of articles featured in this volume reflect a broad variety of new and established modeling approaches such as: - An argument for using Big Data methods in conjunction with Age...
Modeling Complexity : The Limits to Prediction
Directory of Open Access Journals (Sweden)
Michael Batty
2001-12-01
Full Text Available A working definition of a complex system is of an entity which is coherent in some recognizable way but whose elements, interactions, and dynamics generate structures admitting surprise and novelty which cannot be defined a priori. Complex systems are therefore more than the sum of their parts, and a consequence of this is that any model of their structure is necessarily incomplete and partial. Models represent simplifications of a system in which salient parts and processes are simulated and given this definition, many models will exist of any particular complex system. In this paper, we explore the impact of complexity in validating models of such systems. We begin with definitions of complexity, complex systems, and models thereof. We identify the key issues as being concerned with the characterization of system equilibrium, system environment, and the way systems and their elements extend and scale. As our perspective on these issues changes, then so do our models and this has implications for their testing and validation. We develop these, introducing changes in the meaning of validity posed by the use to which such models are to be put in terms of their users. We draw these ideas together as conclusions about the limits posed to prediction in complex systems. We illustrate our arguments using various examples from the field of urban systems theory and urban science.
Modelling Complex Inlet Geometries in CFD
DEFF Research Database (Denmark)
Skovgaard, M.; Nielsen, Peter V.
field. In order to apply CFD for this purpose it is essential to be able to model the inlet conditions precisely and effectively, in a way which is comprehensible to the manufacturer of inlet devices and in a way which can be coped with by the computer. In this paper a universal method is presented...
The sigma model on complex projective superspaces
Energy Technology Data Exchange (ETDEWEB)
Candu, Constantin; Mitev, Vladimir; Schomerus, Volker [DESY, Hamburg (Germany). Theory Group; Quella, Thomas [Amsterdam Univ. (Netherlands). Inst. for Theoretical Physics; Saleur, Hubert [CEA Saclay, 91 - Gif-sur-Yvette (France). Inst. de Physique Theorique; USC, Los Angeles, CA (United States). Physics Dept.
2009-08-15
The sigma model on projective superspaces CP{sup S-1} {sup vertical} {sup stroke} {sup S} gives rise to a continuous family of interacting 2D conformal field theories which are parametrized by the curvature radius R and the theta angle {theta}. Our main goal is to determine the spectrum of the model, non-perturbatively as a function of both parameters. We succeed to do so for all open boundary conditions preserving the full global symmetry of the model. In string theory parlor, these correspond to volume filling branes that are equipped with a monopole line bundle and connection. The paper consists of two parts. In the first part, we approach the problem within the continuum formulation. Combining combinatorial arguments with perturbative studies and some simple free field calculations, we determine a closed formula for the partition function of the theory. This is then tested numerically in the second part. There we propose a spin chain regularization of the CP{sup S-1} {sup vertical} {sup stroke} {sup S} model with open boundary conditions and use it to determine the spectrum at the conformal fixed point. The numerical results are in remarkable agreement with the continuum analysis. (orig.)
Modeling the assembly order of multimeric heteroprotein complexes.
Directory of Open Access Journals (Sweden)
Lenna X Peterson
2018-01-01
modeling and will be an indispensable approach for studying protein complexes.
Modeling the assembly order of multimeric heteroprotein complexes.
Peterson, Lenna X; Togawa, Yoichiro; Esquivel-Rodriguez, Juan; Terashi, Genki; Christoffer, Charles; Roy, Amitava; Shin, Woong-Hee; Kihara, Daisuke
2018-01-01
Protein-protein interactions are the cornerstone of numerous biological processes. Although an increasing number of protein complex structures have been determined using experimental methods, relatively fewer studies have been performed to determine the assembly order of complexes. In addition to the insights into the molecular mechanisms of biological function provided by the structure of a complex, knowing the assembly order is important for understanding the process of complex formation. Assembly order is also practically useful for constructing subcomplexes as a step toward solving the entire complex experimentally, designing artificial protein complexes, and developing drugs that interrupt a critical step in the complex assembly. There are several experimental methods for determining the assembly order of complexes; however, these techniques are resource-intensive. Here, we present a computational method that predicts the assembly order of protein complexes by building the complex structure. The method, named Path-LzerD, uses a multimeric protein docking algorithm that assembles a protein complex structure from individual subunit structures and predicts assembly order by observing the simulated assembly process of the complex. Benchmarked on a dataset of complexes with experimental evidence of assembly order, Path-LZerD was successful in predicting the assembly pathway for the majority of the cases. Moreover, when compared with a simple approach that infers the assembly path from the buried surface area of subunits in the native complex, Path-LZerD has the strong advantage that it can be used for cases where the complex structure is not known. The path prediction accuracy decreased when starting from unbound monomers, particularly for larger complexes of five or more subunits, for which only a part of the assembly path was correctly identified. As the first method of its kind, Path-LZerD opens a new area of computational protein structure modeling and will be
Parallel hyperbolic PDE simulation on clusters: Cell versus GPU
Rostrup, Scott; De Sterck, Hans
2010-12-01
Increasingly, high-performance computing is looking towards data-parallel computational devices to enhance computational performance. Two technologies that have received significant attention are IBM's Cell Processor and NVIDIA's CUDA programming model for graphics processing unit (GPU) computing. In this paper we investigate the acceleration of parallel hyperbolic partial differential equation simulation on structured grids with explicit time integration on clusters with Cell and GPU backends. The message passing interface (MPI) is used for communication between nodes at the coarsest level of parallelism. Optimizations of the simulation code at the several finer levels of parallelism that the data-parallel devices provide are described in terms of data layout, data flow and data-parallel instructions. Optimized Cell and GPU performance are compared with reference code performance on a single x86 central processing unit (CPU) core in single and double precision. We further compare the CPU, Cell and GPU platforms on a chip-to-chip basis, and compare performance on single cluster nodes with two CPUs, two Cell processors or two GPUs in a shared memory configuration (without MPI). We finally compare performance on clusters with 32 CPUs, 32 Cell processors, and 32 GPUs using MPI. Our GPU cluster results use NVIDIA Tesla GPUs with GT200 architecture, but some preliminary results on recently introduced NVIDIA GPUs with the next-generation Fermi architecture are also included. This paper provides computational scientists and engineers who are considering porting their codes to accelerator environments with insight into how structured grid based explicit algorithms can be optimized for clusters with Cell and GPU accelerators. It also provides insight into the speed-up that may be gained on current and future accelerator architectures for this class of applications. Program summaryProgram title: SWsolver Catalogue identifier: AEGY_v1_0 Program summary URL
Modeling complex systems: From the individual to the collective
Malmgren, R. Dean
Over the past decade, researchers have identified several unifying properties of complex networks across technological, biological, and sociological disciplines. Although it is believed that these ubiquitous structural properties of complex networks may be explained by a unifying model, there is scarcely any evidence for an all-encompassing model which describes the evolution of all complex systems. In this thesis, we take some first steps toward understanding the evolution of complex system by developing models for how individuals behave in response to environmental queues and interactions with other individuals. A distinguishing feature of this research is the systematic use of Monte Carlo hypothesis testing, which enables us to statistically test our models against empirical data and quantify the significance of the agreement. Using this methodology, we develop a model of human communication patterns and identify intruiguing correlations in mentorship networks.
Are complex DCE-MRI models supported by clinical data?
Duan, Chong; Kallehauge, Jesper F; Bretthorst, G Larry; Tanderup, Kari; Ackerman, Joseph J H; Garbow, Joel R
2017-03-01
To ascertain whether complex dynamic contrast enhanced (DCE) MRI tracer kinetic models are supported by data acquired in the clinic and to determine the consequences of limited contrast-to-noise. Generically representative in silico and clinical (cervical cancer) DCE-MRI data were examined. Bayesian model selection evaluated support for four compartmental DCE-MRI models: the Tofts model (TM), Extended Tofts model, Compartmental Tissue Uptake model (CTUM), and Two-Compartment Exchange model. Complex DCE-MRI models were more sensitive to noise than simpler models with respect to both model selection and parameter estimation. Indeed, as contrast-to-noise decreased, complex DCE models became less probable and simpler models more probable. The less complex TM and CTUM were the optimal models for the DCE-MRI data acquired in the clinic. [In cervical tumors, Ktrans, Fp, and PS increased after radiotherapy (P = 0.004, 0.002, and 0.014, respectively)]. Caution is advised when considering application of complex DCE-MRI kinetic models to data acquired in the clinic. It follows that data-driven model selection is an important prerequisite to DCE-MRI analysis. Model selection is particularly important when high-order, multiparametric models are under consideration. (Parameters obtained from kinetic modeling of cervical cancer clinical DCE-MRI data showed significant changes at an early stage of radiotherapy.) Magn Reson Med 77:1329-1339, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
Modelling the luminescence of iridium cyclometalated complexes encapsulated in cucurbituril.
Alrawashdeh, Lubna R; Cronin, Michael P; Day, Anthony I; Wallace, Lynne; Woodward, Clifford E
2018-01-15
Iridium(iii) cyclometalated complexes in aqueous solution often display relatively weak luminescence. It has been shown in previous work that this emission can be significantly enhanced (by up to two orders of magnitude) by encapsulation in cucurbit[10]uril (Q[10]). Luminescence lifetime measurements suggest a dynamic self-quenching mechanism is active, possibly due to displacement of an excited guest complex via collision with an unbound complex. We devise a model for the association of a group of iridium(iii) cyclometalated complexes with Q[10]. The model parameters are then fitted to steady-state emission titration curves. The excellent agreement of experimental data with the model provides valuable mechanistic information relating to the way this class of metal complexes interact and associate with the Q[10] host.
DEFF Research Database (Denmark)
Henningsen, Arne; Fabricius, Ole; Olsen, Jakob Vesterlund
2014-01-01
Based on a theoretical microeconomic model, we econometrically estimate investment utilization, adjustment costs, and technical efficiency in Danish pig farms based on a large unbalanced panel dataset. As our theoretical model indicates that adjustment costs are caused both by increased inputs...... and by reduced outputs, we estimate hyperbolic distance functions that account for reduced technical efficiency both in terms of increased inputs and reduced outputs. We estimate these hyperbolic distance functions as “efficiency effect frontiers” with the Translog functional form and a dynamic specification...... of investment activities by the maximum likelihood method so that we can estimate the adjustment costs that occur in the year of the investment and the three following years. Our results show that investments are associated with significant adjustment costs, especially in the year in which the investment...
Fluid flow modeling in complex areas*, **
Directory of Open Access Journals (Sweden)
Poullet Pascal
2012-04-01
Full Text Available We show first results of 3D simulation of sea currents in a realistic context. We use the full Navier–Stokes equations for incompressible viscous fluid. The problem is solved using a second order incremental projection method associated with the finite volume of the staggered (MAC scheme for the spatial discretization. After validation on classical cases, it is used in a numerical simulation of the Pointe à Pitre harbour area. The use of the fictious domain method permits us to take into account the complexity of bathymetric data and allows us to work with regular meshes and thus preserves the efficiency essential for a 3D code. Dans cette étude, nous présentons les premiers résultats de simulation d’un écoulement d’un fluide incompressible visqueux dans un contexte environnemental réel. L’approche utilisée utilise une méthode de domaines fictifs pour une prise en compte d’un domaine physique tridimensionnel très irrégulier. Le schéma numérique combine un schéma de projection incrémentale et des volumes finis utilisant des volumes de contrôle adaptés à un maillage décalé. Les tests de validation sont menés pour les cas tests de la cavité double entraînée ainsi que l’écoulement dans un canal avec un obstacle placé de manière asymmétrique.
Castro, Manuel J.; Gallardo, José M.; Marquina, Antonio
2017-10-01
We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function, and compare them with Chebyshev-based PVM solvers. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Another important feature of the proposed methods is that they are suitable to be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems for which the Jacobians involve complex expressions, e.g., the relativistic magnetohydrodynamics (RMHD) equations. On the other hand, the proposed Jacobian-free solvers have also been extended to the case of approximate DOT (Dumbser-Osher-Toro) methods, which can be regarded as simple and efficient approximations to the classical Osher-Solomon method, sharing most of it interesting features and being applicable to general hyperbolic systems. To test the properties of our schemes a number of numerical experiments involving the RMHD equations are presented, both in one and two dimensions. The obtained results are in good agreement with those found in the literature and show that our schemes are robust and accurate, running stable under a satisfactory time step restriction. It is worth emphasizing that, although this work focuses on RMHD, the proposed schemes are suitable to be applied to general hyperbolic systems.
Shah, Syed Awais Wahab
2017-11-24
This paper addresses the problem of blind demixing of instantaneous mixtures in a multiple-input multiple-output communication system. The main objective is to present efficient blind source separation (BSS) algorithms dedicated to moderate or high-order QAM constellations. Four new iterative batch BSS algorithms are presented dealing with the multimodulus (MM) and alphabet matched (AM) criteria. For the optimization of these cost functions, iterative methods of Givens and hyperbolic rotations are used. A pre-whitening operation is also utilized to reduce the complexity of design problem. It is noticed that the designed algorithms using Givens rotations gives satisfactory performance only for large number of samples. However, for small number of samples, the algorithms designed by combining both Givens and hyperbolic rotations compensate for the ill-whitening that occurs in this case and thus improves the performance. Two algorithms dealing with the MM criterion are presented for moderate order QAM signals such as 16-QAM. The other two dealing with the AM criterion are presented for high-order QAM signals. These methods are finally compared with the state of art batch BSS algorithms in terms of signal-to-interference and noise ratio, symbol error rate and convergence rate. Simulation results show that the proposed methods outperform the contemporary batch BSS algorithms.
Toward Modeling the Intrinsic Complexity of Test Problems
Shoufan, Abdulhadi
2017-01-01
The concept of intrinsic complexity explains why different problems of the same type, tackled by the same problem solver, can require different times to solve and yield solutions of different quality. This paper proposes a general four-step approach that can be used to establish a model for the intrinsic complexity of a problem class in terms of…
Blueprints for Complex Learning: The 4C/ID-Model.
van Merrienboer, Jeroen J. G.; Clark, Richard E.; de Croock, Marcel B. M.
2002-01-01
Describes the four-component instructional design system (4C/ID-model) developed for the design of training programs for complex skills. Discusses the structure of training blueprints for complex learning and associated instructional methods, focusing on learning tasks, supportive information, just-in-time information, and part-task practice.…
Classrooms as Complex Adaptive Systems: A Relational Model
Burns, Anne; Knox, John S.
2011-01-01
In this article, we describe and model the language classroom as a complex adaptive system (see Logan & Schumann, 2005). We argue that linear, categorical descriptions of classroom processes and interactions do not sufficiently explain the complex nature of classrooms, and cannot account for how classroom change occurs (or does not occur), over…
Modeling Air-Quality in Complex Terrain Using Mesoscale and ...
African Journals Online (AJOL)
Air-quality in a complex terrain (Colorado-River-Valley/Grand-Canyon Area, Southwest U.S.) is modeled using a higher-order closure mesoscale model and a higher-order closure dispersion model. Non-reactive tracers have been released in the Colorado-River valley, during winter and summer 1992, to study the ...
On a pure hyperbolic alternative to the Navier-Stokes equations
Peshkov, Ilya
2014-01-01
We discuss a pure hyperbolic alternative to the Navier-Stokes equations, which are of parabolic type. As a result of the substitution of the concept of the viscosity coefficient by a microphysics-based temporal characteristic, particle settled life (PSL) time, it becomes possible to formulate a model for viscous fluids in a form of first order hyperbolic partial differential equations. Moreover, the concept of PSL time allows the use the same model for flows of viscous fluids (Newtonian or non-Newtonian) as well as irreversible deformation of solids. In the theory presented, a continuum is interpreted as a system of particles, or in the case of fluids, fluid parcels connected by bonds; the internal resistance to flow is interpreted as elastic stretching of the particle bonds; and a flow is a result of bond destructions and rearrangements of particles. Finally, we examine the model for simple shear flows of Newtonian fluids and demonstrate that Newton's viscous law can be obtained in the framework of the devel...
Elmetennani, Shahrazed
2017-04-01
This dissertation addresses the flow control problem in hyperbolic heat transfer mechanisms. It raises in concentrated distributed solar collectors to enhance their production efficiency under the unpredictable variations of the solar energy and the external disturbances. These factors which are either locally measured (the solar irradiance) or inaccessible for measurement (the collectors’ cleanliness) affect the source term of the distributed model and represent a major difficulty for the control design. Moreover, the temperature in the collector can only be measured at the boundaries. In this dissertation, we propose new adaptive control approaches to provide the adequate level of heat while coping with the unpredictable varying disturbances. First, we design model based control strategies for a better efficiency, in terms of accuracy and response time, with a relatively reduced complexity. Second, we enhance the controllers with on-line adaptation laws to continuously update the efficient value of the external conditions. In this study, we approach the control problem using both, the infinite dimensional model (late lumping) and a finite dimensional approximate representation (early lumping). For the early lumping approach, we introduce a new reduced order bilinear approximate model for system analysis and control design. This approximate state representation is then used to derive a nonlinear state feedback resorting to Lyapunov stability theory. To compensate for the external disturbances and the approximation uncertainties, an adaptive controller is developed based on a phenomenological representation of the system dynamics. For the late lumping approach, we propose two PDE based controllers by stabilization of the reference tracking error distributed profile. The control laws are explicitly defined as functions of the available measurement. The first one is obtained using a direct approach for error stabilization while the second one is derived through a
Modelling the self-organization and collapse of complex networks
Indian Academy of Sciences (India)
Modelling the self-organization and collapse of complex networks. Sanjay Jain Department of Physics and Astrophysics, University of Delhi Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore Santa Fe Institute, Santa Fe, New Mexico.
Reduction of the complexity of product modelling by modularisation
DEFF Research Database (Denmark)
Andreasen, Mogens Myrup
1998-01-01
The complexity in handling product aspects in design and production may be reduced by using approaches, which are applied in the field of modular engineering. This unit-oriented "spelling" of products, leading to product models with encapsulation, is introduced.......The complexity in handling product aspects in design and production may be reduced by using approaches, which are applied in the field of modular engineering. This unit-oriented "spelling" of products, leading to product models with encapsulation, is introduced....
Coping with Complexity Model Reduction and Data Analysis
Gorban, Alexander N
2011-01-01
This volume contains the extended version of selected talks given at the international research workshop 'Coping with Complexity: Model Reduction and Data Analysis', Ambleside, UK, August 31 - September 4, 2009. This book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.
Applications of Nonlinear Dynamics Model and Design of Complex Systems
In, Visarath; Palacios, Antonio
2009-01-01
This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.
Size and complexity in model financial systems.
Arinaminpathy, Nimalan; Kapadia, Sujit; May, Robert M
2012-11-06
The global financial crisis has precipitated an increasing appreciation of the need for a systemic perspective toward financial stability. For example: What role do large banks play in systemic risk? How should capital adequacy standards recognize this role? How is stability shaped by concentration and diversification in the financial system? We explore these questions using a deliberately simplified, dynamic model of a banking system that combines three different channels for direct transmission of contagion from one bank to another: liquidity hoarding, asset price contagion, and the propagation of defaults via counterparty credit risk. Importantly, we also introduce a mechanism for capturing how swings in "confidence" in the system may contribute to instability. Our results highlight that the importance of relatively large, well-connected banks in system stability scales more than proportionately with their size: the impact of their collapse arises not only from their connectivity, but also from their effect on confidence in the system. Imposing tougher capital requirements on larger banks than smaller ones can thus enhance the resilience of the system. Moreover, these effects are more pronounced in more concentrated systems, and continue to apply, even when allowing for potential diversification benefits that may be realized by larger banks. We discuss some tentative implications for policy, as well as conceptual analogies in ecosystem stability and in the control of infectious diseases.
Perturbed Strong Stability Preserving Time-Stepping Methods For Hyperbolic PDEs
Hadjimichael, Yiannis
2017-09-30
A plethora of physical phenomena are modelled by hyperbolic partial differential equations, for which the exact solution is usually not known. Numerical methods are employed to approximate the solution to hyperbolic problems; however, in many cases it is difficult to satisfy certain physical properties while maintaining high order of accuracy. In this thesis, we develop high-order time-stepping methods that are capable of maintaining stability constraints of the solution, when coupled with suitable spatial discretizations. Such methods are called strong stability preserving (SSP) time integrators, and we mainly focus on perturbed methods that use both upwind- and downwind-biased spatial discretizations. Firstly, we introduce a new family of third-order implicit Runge–Kuttas methods with arbitrarily large SSP coefficient. We investigate the stability and accuracy of these methods and we show that they perform well on hyperbolic problems with large CFL numbers. Moreover, we extend the analysis of SSP linear multistep methods to semi-discretized problems for which different terms on the right-hand side of the initial value problem satisfy different forward Euler (or circle) conditions. Optimal perturbed and additive monotonicity-preserving linear multistep methods are studied in the context of such problems. Optimal perturbed methods attain augmented monotonicity-preserving step sizes when the different forward Euler conditions are taken into account. On the other hand, we show that optimal SSP additive methods achieve a monotonicity-preserving step-size restriction no better than that of the corresponding non-additive SSP linear multistep methods. Furthermore, we develop the first SSP linear multistep methods of order two and three with variable step size, and study their optimality. We describe an optimal step-size strategy and demonstrate the effectiveness of these methods on various one- and multi-dimensional problems. Finally, we establish necessary conditions
Kumar, Vivek; Raghurama Rao, S. V.
2008-04-01
Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally
Understanding complex urban systems multidisciplinary approaches to modeling
Gurr, Jens; Schmidt, J
2014-01-01
Understanding Complex Urban Systems takes as its point of departure the insight that the challenges of global urbanization and the complexity of urban systems cannot be understood – let alone ‘managed’ – by sectoral and disciplinary approaches alone. But while there has recently been significant progress in broadening and refining the methodologies for the quantitative modeling of complex urban systems, in deepening the theoretical understanding of cities as complex systems, or in illuminating the implications for urban planning, there is still a lack of well-founded conceptual thinking on the methodological foundations and the strategies of modeling urban complexity across the disciplines. Bringing together experts from the fields of urban and spatial planning, ecology, urban geography, real estate analysis, organizational cybernetics, stochastic optimization, and literary studies, as well as specialists in various systems approaches and in transdisciplinary methodologies of urban analysis, the volum...
Bladder Cancer: A Simple Model Becomes Complex
Pierro, Giovanni Battista Di; Gulia, Caterina; Cristini, Cristiano; Fraietta, Giorgio; Marini, Lorenzo; Grande, Pietro; Gentile, Vincenzo; Piergentili, Roberto
2012-01-01
Bladder cancer is one of the most frequent malignancies in developed countries and it is also characterized by a high number of recurrences. Despite this, several authors in the past reported that only two altered molecular pathways may genetically explain all cases of bladder cancer: one involving the FGFR3 gene, and the other involving the TP53 gene. Mutations in any of these two genes are usually predictive of the malignancy final outcome. This cancer may also be further classified as low-grade tumors, which is always papillary and in most cases superficial, and high-grade tumors, not necessarily papillary and often invasive. This simple way of considering this pathology has strongly changed in the last few years, with the development of genome-wide studies on expression profiling and the discovery of small non-coding RNA affecting gene expression. An easy search in the OMIM (On-line Mendelian Inheritance in Man) database using “bladder cancer” as a query reveals that genes in some way connected to this pathology are approximately 150, and some authors report that altered gene expression (up- or down-regulation) in this disease may involve up to 500 coding sequences for low-grade tumors and up to 2300 for high-grade tumors. In many clinical cases, mutations inside the coding sequences of the above mentioned two genes were not found, but their expression changed; this indicates that also epigenetic modifications may play an important role in its development. Indeed, several reports were published about genome-wide methylation in these neoplastic tissues, and an increasing number of small non-coding RNA are either up- or down-regulated in bladder cancer, indicating that impaired gene expression may also pass through these metabolic pathways. Taken together, these data reveal that bladder cancer is far to be considered a simple model of malignancy. In the present review, we summarize recent progress in the genome-wide analysis of bladder cancer, and analyse non
Resolution of a shock in hyperbolic systems modified by weak dispersion
El, G. A.
2005-09-01
We present a way to deal with dispersion-dominated "shock-type" transition in the absence of completely integrable structure for the systems that one may characterize as strictly hyperbolic regularized by a small amount of dispersion. The analysis is performed by assuming that the dispersive shock transition between two different constant states can be modeled by an expansion fan solution of the associated modulation (Whitham) system for the short-wavelength nonlinear oscillations in the transition region (the so-called Gurevich-Pitaevskii problem). We consider both single-wave and bidirectional systems. The main mathematical assumption is that of hyperbolicity of the Whitham system for the solutions of our interest. By using general properties of the Whitham averaging for a certain class of nonlinear dispersive systems and specific features of the Cauchy data prescription on characteristics we derive a set of transition conditions for the dispersive shock, actually bypassing full integration of the modulation equations. Along with the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations as model examples, we consider a nonintegrable system describing fully nonlinear ion-acoustic waves in collisionless plasma. In all cases our transition conditions are in complete agreement with previous analytical and numerical results.
7th International Conference on Hyperbolic Problems Theory, Numerics, Applications
Jeltsch, Rolf
1999-01-01
These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phe...
8th International Conference on Hyperbolic Problems : Theory, Numerics, Applications
Warnecke, Gerald
2001-01-01
The Eighth International Conference on Hyperbolic Problems - Theory, Nu merics, Applications, was held in Magdeburg, Germany, from February 27 to March 3, 2000. It was attended by over 220 participants from many European countries as well as Brazil, Canada, China, Georgia, India, Israel, Japan, Taiwan, und the USA. There were 12 plenary lectures, 22 further invited talks, and around 150 con tributed talks in parallel sessions as well as posters. The speakers in the parallel sessions were invited to provide a poster in order to enhance the dissemination of information. Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. Despite considerable progress, the mathematical theory is still strug gling with fundamental open problems concerning systems of such equations in multiple space dimensions. For various applications the development of accurate and efficient numerical schemes for computat...
Hyperbolic conservation laws and the compensated compactness method
Lu, Yunguang
2002-01-01
The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics. Until now, however, most accounts of this method have been confined to research papers. Offering the first comprehensive treatment, Hyperbolic Conservation Laws and the Compensated Compactness Method gathers together into a single volume the essential ideas and developments.The authors begin with the fundamental theorems, then consider the Cauchy problem of the scalar equation, build a framework for L8 estimates of viscosity solutions, and introduce the Invariant Region Theory. The study then turns to methods for symmetric systems of two equations and two equations with quadratic flux, and the extension of these methods to the Le Roux system. After examining the system of polytropic gas dynamics (g-law), the authors first study two special systems of one-dimensional Euler equations, then consider the general Euler equations for one-dimensional com...
Hyperbolic Metamaterial Nano-Resonators Make Poor Single Photon Sources
Axelrod, Simon; Wong, Herman M K; Helmy, Amr S; Hughes, Stephen
2016-01-01
We study the optical properties of quantum dipole emitters coupled to hyperbolic metamaterial nano-resonators using a semi-analytical quasinormal mode approach. We show that coupling to metamaterial nano-resonators can lead to significant Purcell enhancements that are nearly an order of magnitude larger than those of plasmonic resonators with comparable geometry. However, the associated single photon output $\\beta$-factors are extremely low (around 10%), far smaller than those of comparable sized metallic resonators (70%). Using a quasinormal mode expansion of the photon Green function, we describe how the low $\\beta$-factors are due to increased Ohmic quenching arising from redshifted resonances, larger quality factors and stronger confinement of light within the metal. In contrast to current wisdom, these results suggest that hyperbolic metamaterial nano-structures make poor choices for single photon sources.
Single qubit operations using microwave hyperbolic secant pulses
Ku, H. S.; Long, J. L.; Wu, X.; Bal, M.; Lake, R. E.; Barnes, Edwin; Economou, Sophia E.; Pappas, D. P.
2017-10-01
It has been known since the early days of quantum mechanics that hyperbolic secant pulses possess the unique property that they can perform full-cycle Rabi oscillations on two-level quantum systems independently of the pulse detuning. More recently, it was realized that they induce detuning-controlled phases without changing state populations. Here, we experimentally demonstrate the properties of hyperbolic secant pulses on superconducting transmon qubits and contrast them with the more commonly used Gaussian and square waves. We further show that these properties can be exploited to implement phase gates, nominally without exiting the computational subspace. This enables us to demonstrate a microwave-driven Z rotation with a single control parameter, the detuning.
Tunable VO{sub 2}/Au hyperbolic metamaterial
Energy Technology Data Exchange (ETDEWEB)
Prayakarao, S.; Noginov, M. A., E-mail: mnoginov@nsu.edu [Center for Materials Research, Norfolk State University, Norfolk, Virginia 23504 (United States); Mendoza, B.; Devine, A. [Summer Research Program, Center for Materials Research, Norfolk State University, Norfolk, Virginia 23504 (United States); Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14850 (United States); Kyaw, C. [Summer Research Program, Center for Materials Research, Norfolk State University, Norfolk, Virginia 23504 (United States); Dover, R. B. van [Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14850 (United States); Liberman, V. [MIT LINCOLN Laboratory, 244 Wood Street, Lexington, Massachusetts 02420 (United States)
2016-08-08
Vanadium dioxide (VO{sub 2}) is known to have a semiconductor-to-metal phase transition at ∼68 °C. Therefore, it can be used as a tunable component of an active metamaterial. The lamellar metamaterial studied in this work is composed of subwavelength VO{sub 2} and Au layers and is designed to undergo a temperature controlled transition from the optical hyperbolic phase to the metallic phase. VO{sub 2} films and VO{sub 2}/Au lamellar metamaterial stacks have been fabricated and studied in electrical conductivity and optical (transmission and reflection) experiments. The observed temperature-dependent changes in the reflection and transmission spectra of the metamaterials and VO{sub 2} thin films are in a good qualitative agreement with theoretical predictions. The demonstrated optical hyperbolic-to-metallic phase transition is a unique physical phenomenon with the potential to enable advanced control of light-matter interactions.
Operator-Based Preconditioning of Stiff Hyperbolic Systems
Energy Technology Data Exchange (ETDEWEB)
Reynolds, Daniel R.; Samtaney, Ravi; Woodward, Carol S.
2009-02-09
We introduce an operator-based scheme for preconditioning stiff components encoun- tered in implicit methods for hyperbolic systems of partial differential equations posed on regular grids. The method is based on a directional splitting of the implicit operator, followed by a char- acteristic decomposition of the resulting directional parts. This approach allows for solution to any number of characteristic components, from the entire system to only the fastest, stiffness-inducing waves. We apply the preconditioning method to stiff hyperbolic systems arising in magnetohydro- dynamics and gas dynamics. We then present numerical results showing that this preconditioning scheme works well on problems where the underlying stiffness results from the interaction of fast transient waves with slowly-evolving dynamics, scales well to large problem sizes and numbers of processors, and allows for additional customization based on the specific problems under study.
Visualising very large phylogenetic trees in three dimensional hyperbolic space
Directory of Open Access Journals (Sweden)
Liberles David A
2004-04-01
Full Text Available Abstract Background Common existing phylogenetic tree visualisation tools are not able to display readable trees with more than a few thousand nodes. These existing methodologies are based in two dimensional space. Results We introduce the idea of visualising phylogenetic trees in three dimensional hyperbolic space with the Walrus graph visualisation tool and have developed a conversion tool that enables the conversion of standard phylogenetic tree formats to Walrus' format. With Walrus, it becomes possible to visualise and navigate phylogenetic trees with more than 100,000 nodes. Conclusion Walrus enables desktop visualisation of very large phylogenetic trees in 3 dimensional hyperbolic space. This application is potentially useful for visualisation of the tree of life and for functional genomics derivatives, like The Adaptive Evolution Database (TAED.
Spectral theory of infinite-area hyperbolic surfaces
Borthwick, David
2016-01-01
This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added. Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constan...
On Another Edge of Defocusing: Hyperbolicity of Asymmetric Lemon Billiards
Bunimovich, Leonid; Zhang, Hong-Kun; Zhang, Pengfei
2016-02-01
Defocusing mechanism provides a way to construct chaotic (hyperbolic) billiards with focusing components by separating all regular components of the boundary of a billiard table sufficiently far away from each focusing component. If all focusing components of the boundary of the billiard table are circular arcs, then the above separation requirement reduces to that all circles obtained by completion of focusing components are contained in the billiard table. In the present paper we demonstrate that a class of convex tables— asymmetric lemons, whose boundary consists of two circular arcs, generate hyperbolic billiards. This result is quite surprising because the focusing components of the asymmetric lemon table are extremely close to each other, and because these tables are perturbations of the first convex ergodic billiard constructed more than 40 years ago.
Vitokhin, Evgeniy Yu.; Ivanova, Elena A.
2017-11-01
The Maxwell-Cattaneo heat conduction theory, the Lord-Shulman theory of thermoelasticity and a hyperbolic theory of thermoviscoelasticity are studied. The dispersion relations are analyzed in the case when a solution is represented in the form of an exponential function decreasing in time. Simple formulas that quite accurately approximate the dispersion curves are obtained. Based on the results of analysis of the dispersion relations, an experimental method of determination of the heat flux relaxation time is suggested.
Zeroth-order transmission resonance in hyperbolic metamaterials
Huang, Zun; Narimanov, Evgenii E.
2013-01-01
We present a new approach to subwavelength optical confinement, based on hyperbolic media in planar Fabry-Perot geometry. Unlike higher-order resonance modes in indefinite metamaterial cavities, the predicted resonance corresponds to 0th-order mode and can be observed in planar systems. Our approach combines subwavelength light confinement with strong radiative coupling, enabling a practical planar design of nanolasers and subwavelength waveguides. (C) 2013 Optical Society of America
Zeroth-order transmission resonance in hyperbolic metamaterials.
Huang, Zun; Narimanov, Evgenii E
2013-06-17
We present a new approach to subwavelength optical confinement, based on hyperbolic media in planar Fabry-Perot geometry. Unlike higher-order resonance modes in indefinite metamaterial cavities, the predicted resonance corresponds to 0th-order mode and can be observed in planar systems. Our approach combines subwavelength light confinement with strong radiative coupling, enabling a practical planar design of nanolasers and subwavelength waveguides.
Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series
Zhang, Zhihua
2014-01-01
Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842
Inextendibilty of the Maximal Global Hyperbolic Development in Electrogowdy spacetimes
Directory of Open Access Journals (Sweden)
Nungesser Ernesto
2013-09-01
Full Text Available The problem of determinism in General Relativity appears even if one assumes that the spacetime is globally hyperbolic, i.e. that it contains a hypersurface that is intersected by any causal curve exactly once. The strong cosmic censorship hypothesis is essentially the hypothesis that General Relativity is a predictable theory and thus a crucial issue in Classical General Relativity. We sketch here the proof for the case of Electrogowdy spacetimes.
Relatively hyperbolic extensions of groups and Cannon–Thurston ...
Indian Academy of Sciences (India)
In [6], the existence of a Cannon–Thurston map for the embedding i: K → G was proved, where K and G are respectively the Cayley graphs of K and G. In this paper, we will generalize these results to the case where the kernel is strongly hyperbolic relative to a cusp subgroup. One of our main theorems states: Theorem 2.10 ...
Non-Euclidean Fourier inversion on super-hyperbolic space
Alldridge, Alexander; Palzer, Wolfgang
2016-01-01
For the super-hyperbolic space in any dimension, we introduce the non-Euclidean Helgason--Fourier transform. We prove an inversion formula exhibiting residue contributions at the poles of the Harish-Chandra c-function, signalling discrete parts in the spectrum. The proof is based on a detailed study of the spherical superfunctions, using recursion relations and localization techniques to normalize them precisely, careful estimates of their derivatives, and a rigorous analysis of the boundary ...
Mathematical Properties of the Hyperbolicity of Circulant Networks
Directory of Open Access Journals (Sweden)
Juan C. Hernández
2015-01-01
Full Text Available If X is a geodesic metric space and x1,x2,x3∈X, a geodesic triangle T={x1,x2,x3} is the union of the three geodesics [x1x2], [x2x3], and [x3x1] in X. The space X is δ-hyperbolic (in the Gromov sense if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. The study of the hyperbolicity constant in networks is usually a very difficult task; therefore, it is interesting to find bounds for particular classes of graphs. A network is circulant if it has a cyclic group of automorphisms that includes an automorphism taking any vertex to any other vertex. In this paper we obtain several sharp inequalities for the hyperbolicity constant of circulant networks; in some cases we characterize the graphs for which the equality is attained.
Optic axis-driven new horizons for hyperbolic metamaterials
Directory of Open Access Journals (Sweden)
Boardman Allan D.
2015-01-01
Full Text Available The broad assertion here is that the current hyperbolic metamaterial world is only partially served by investigations that incorporate only some limited version of anisotropy. Even modest deviations of the optic axis from the main propagation axis lead to new phase shifts, which not only compete with those created by absorption but end up dominating them. Some progress has been attempted in the literature by introducing the terms “asymmetric hyperbolic media”, but it appears that this kind of asymmetry only involves an optic axis at an angle to the interface of a uniaxial crystal. From a device point of view, many new prospects should appear and the outcomes of the investigations presented here yield a new general theory. It is emphasised that the orientation of the optic axis is a significant determinant in the resulting optical properties. Whereas for conventional anisotropic waveguides homogeneous propagating waves occur over a limited range of angular dispositions of the optic axis it is shown that for a hyperbolic guide a critical angular setting exists, above which the guided waves are always homogeneous. This has significant implications for metawaveguide designs. The resulting structures are more tolerant to optic axis misalignment.
The Complexity of Model Checking Higher-Order Fixpoint Logic
DEFF Research Database (Denmark)
Axelsson, Roland; Lange, Martin; Somla, Rafal
2007-01-01
provides complexity results for its model checking problem. In particular we consider its fragments HFLk,m which are formed using types of bounded order k and arity m only. We establish k-ExpTime-completeness for model checking each HFLk,m fragment. For the upper bound we reduce the problem to the problem...
Stochastic simulation of HIV population dynamics through complex network modelling
Sloot, P. M. A.; Ivanov, S. V.; Boukhanovsky, A. V.; van de Vijver, D. A. M. C.; Boucher, C. A. B.
We propose a new way to model HIV infection spreading through the use of dynamic complex networks. The heterogeneous population of HIV exposure groups is described through a unique network degree probability distribution. The time evolution of the network nodes is modelled by a Markov process and
Stochastic simulation of HIV population dynamics through complex network modelling
Sloot, P.M.A.; Ivanov, S.V.; Boukhanovsky, A.V.; van de Vijver, D.A.M.C.; Boucher, C.A.B.
2008-01-01
We propose a new way to model HIV infection spreading through the use of dynamic complex networks. The heterogeneous population of HIV exposure groups is described through a unique network degree probability distribution. The time evolution of the network nodes is modelled by a Markov process and
The effects of model and data complexity on predictions from species distributions models
DEFF Research Database (Denmark)
García-Callejas, David; Bastos, Miguel
2016-01-01
. In contrast, geometrical characteristics of the data were related to model performance in several ways: complex datasets were consistently more difficult to model, and the complexity of the data was affected by the choice of predictors and the type of data analyzed. Given our definition of complexity, our...
Complexation and molecular modeling studies of europium(III)-gallic acid-amino acid complexes.
Taha, Mohamed; Khan, Imran; Coutinho, João A P
2016-04-01
With many metal-based drugs extensively used today in the treatment of cancer, attention has focused on the development of new coordination compounds with antitumor activity with europium(III) complexes recently introduced as novel anticancer drugs. The aim of this work is to design new Eu(III) complexes with gallic acid, an antioxida'nt phenolic compound. Gallic acid was chosen because it shows anticancer activity without harming health cells. As antioxidant, it helps to protect human cells against oxidative damage that implicated in DNA damage, cancer, and accelerated cell aging. In this work, the formation of binary and ternary complexes of Eu(III) with gallic acid, primary ligand, and amino acids alanine, leucine, isoleucine, and tryptophan was studied by glass electrode potentiometry in aqueous solution containing 0.1M NaNO3 at (298.2 ± 0.1) K. Their overall stability constants were evaluated and the concentration distributions of the complex species in solution were calculated. The protonation constants of gallic acid and amino acids were also determined at our experimental conditions and compared with those predicted by using conductor-like screening model for realistic solvation (COSMO-RS) model. The geometries of Eu(III)-gallic acid complexes were characterized by the density functional theory (DFT). The spectroscopic UV-visible and photoluminescence measurements are carried out to confirm the formation of Eu(III)-gallic acid complexes in aqueous solutions. Copyright © 2016 Elsevier Inc. All rights reserved.
Theory, Characterization and Applications of Infrared Hyperbolic Metamaterials
Fullager, Daniel B.
Hyperbolic Metamaterials (HMMs) are engineered structures capable of supporting lightmatter interactions that are not normally observed in naturally occuring material systems. These unusual responses are enabled by an enhancement of the photonic density of states (PDOS) in the material. The PDOS enhancement is a result of deliberately introduced anisotropy via a permittivity sign-change in HMM structures which increases the number and frequency spread of possible wave vectors that propagate in the material. Subwavelength structural features allow effective medium theories to be invoked to construct the k-space isofrequency quadratic curves that, for HMMs, result in the k-space isofrequency contour transitioning from being a bounded surface to an unbounded one. Since the PDOS is the integral of the differential volume between k-space contours, unbounded manifolds lead to the implication of an infinite or otherwise drastically enhanced PDOS. Since stored heat can be thought of as a set of non-radiative electromagnetic modes, in this dissertation we demonstrate that HMMs provide an ideal platform to attempt to modify the thermal/IR emissivity of a material. We also show that HMMs provide a platform for broadband plasmonic sensing. The advent of commercial two photon polymerization tools has enabled the rapid production of nano- and microstructures which can be used as scaffolds for directive infrared scatterers. We describe how such directive components can be used to address thermal management needs in vacuum environments in order to maximize radiative thermal transfer. In this context, the fundamental limitations of enhanced spon- taneous emission due to conjugate impedance matched scatterers are also explored. The HMM/conjugate scatterer system's performance is strongly correlated with the dielectric function of the negative permittivity component of the HMM. In order to fully understand the significance of these engineered materials, we examine in detail the
Bim Automation: Advanced Modeling Generative Process for Complex Structures
Banfi, F.; Fai, S.; Brumana, R.
2017-08-01
The new paradigm of the complexity of modern and historic structures, which are characterised by complex forms, morphological and typological variables, is one of the greatest challenges for building information modelling (BIM). Generation of complex parametric models needs new scientific knowledge concerning new digital technologies. These elements are helpful to store a vast quantity of information during the life cycle of buildings (LCB). The latest developments of parametric applications do not provide advanced tools, resulting in time-consuming work for the generation of models. This paper presents a method capable of processing and creating complex parametric Building Information Models (BIM) with Non-Uniform to NURBS) with multiple levels of details (Mixed and ReverseLoD) based on accurate 3D photogrammetric and laser scanning surveys. Complex 3D elements are converted into parametric BIM software and finite element applications (BIM to FEA) using specific exchange formats and new modelling tools. The proposed approach has been applied to different case studies: the BIM of modern structure for the courtyard of West Block on Parliament Hill in Ottawa (Ontario) and the BIM of Masegra Castel in Sondrio (Italy), encouraging the dissemination and interaction of scientific results without losing information during the generative process.
Pedigree models for complex human traits involving the mitochrondrial genome
Energy Technology Data Exchange (ETDEWEB)
Schork, N.J.; Guo, S.W. (Univ. of Michigan, Ann Arbor, MI (United States))
1993-12-01
Recent biochemical and molecular-genetic discoveries concerning variations in human mtDNA have suggested a role for mtDNA mutations in a number of human traits and disorders. Although the importance of these discoveries cannot be emphasized enough, the complex natures of mitochondrial biogenesis, mutant mtDNA phenotype expression, and the maternal inheritance pattern exhibited by mtDNA transmission make it difficult to develop models that can be used routinely in pedigree analyses to quantify and test hypotheses about the role of mtDNA in the expression of a trait. In the present paper, the authors describe complexities inherent in mitochondrial biogenesis and genetic transmission and show how these complexities can be incorporated into appropriate mathematical models. The authors offer a variety of likelihood-based models which account for the complexities discussed. The derivation of the models is meant to stimulate the construction of statistical tests for putative mtDNA contribution to a trait. Results of simulation studies which make use of the proposed models are described. The results of the simulation studies suggest that, although pedigree models of mtDNA effects can be reliable, success in mapping chromosomal determinants of a trait does not preclude the possibility that mtDNA determinants exist for the trait as well. Shortcomings inherent in the proposed models are described in an effort to expose areas in need of additional research. 58 refs., 5 figs., 2 tabs.
Systems Engineering Metrics: Organizational Complexity and Product Quality Modeling
Mog, Robert A.
1997-01-01
Innovative organizational complexity and product quality models applicable to performance metrics for NASA-MSFC's Systems Analysis and Integration Laboratory (SAIL) missions and objectives are presented. An intensive research effort focuses on the synergistic combination of stochastic process modeling, nodal and spatial decomposition techniques, organizational and computational complexity, systems science and metrics, chaos, and proprietary statistical tools for accelerated risk assessment. This is followed by the development of a preliminary model, which is uniquely applicable and robust for quantitative purposes. Exercise of the preliminary model using a generic system hierarchy and the AXAF-I architectural hierarchy is provided. The Kendall test for positive dependence provides an initial verification and validation of the model. Finally, the research and development of the innovation is revisited, prior to peer review. This research and development effort results in near-term, measurable SAIL organizational and product quality methodologies, enhanced organizational risk assessment and evolutionary modeling results, and 91 improved statistical quantification of SAIL productivity interests.
Minimal model for complex dynamics in cellular processes
Suguna, C.; Chowdhury, Kanchan K.; Sinha, Somdatta
1999-11-01
Cellular functions are controlled and coordinated by the complex circuitry of biochemical pathways regulated by genetic and metabolic feedback processes. This paper aims to show, with the help of a minimal model of a regulated biochemical pathway, that the common nonlinearities and control structures present in biomolecular interactions are capable of eliciting a variety of functional dynamics, such as homeostasis, periodic, complex, and chaotic oscillations, including transients, that are observed in various cellular processes.
Calcium-Amidoborane-Ammine Complexes : Thermal Decomposition of Model Systems
Harder, Sjoerd; Spielmann, Jan; Tobey, Briac
Hydrocarbon-soluble model systems for the calcium-amidoborane-ammine complex Ca(NH2BH3)2.(NH3)2 were prepared and structurally characterized. The following complexes were obtained by the reaction of RNH2BH3 (R=H, Me, iPr, DIPP; DIPP=2,6-diisopropylphenyl) with Ca(DIPP-nacnac)(NH2).(NH3)2
Uncertainty analysis of complex hydro-biogeochemical models
Houska, Tobias
2017-01-01
This thesis is about complex hydro-biogeochemical models and their practical applications. Several modelling practices and their associated uncertainty are investigated in this joined project of the working groups of Prof. Dr. Lutz Breuer, Justus Liebig University Giessen, and Prof. Dr. Klaus Butterbach-Bahl at Karlsruhe Institute of Technology. The aim of the project is to develop strategies for reducing the climate footprint of agricultural production and to quantify uncertainties of model-...
Modeling and Correspondence of Topologically Complex 3D Shapes
Alhashim, Ibraheem
2015-01-01
3D shape creation and modeling remains a challenging task especially for novice users. Many methods in the field of computer graphics have been proposed to automate the often repetitive and precise operations needed during the modeling of detailed shapes. This report surveys different approaches of shape modeling and correspondence especially for shapes exhibiting topological complexity. We focus on methods designed to help generate or process shapes with large number of interconnected compon...
Complex groundwater flow systems as traveling agent models
López-Corona, Oliver; Escolero, Oscar; González, Tomás; Morales-Casique, Eric
2014-01-01
Analyzing field data from pumping tests, we show that as with many other natural phenomena, groundwater flow exhibits a complex dynamics described by 1/f power spectrum. This result is theoretically studied within an agent perspective. Using a traveling agent model, we prove that this statistical behavior emerges when the medium is complex. Some heuristic reasoning is provided to justify both spatial and dynamic complexity, as the result of the superposition of an infinite number of stochastic processes. Even more, we show that this implies that non-Kolmogorovian probability is needed for its study, and provide a set of new partial differential equations for groundwater flow.
Stability of Rotor Systems: A Complex Modelling Approach
DEFF Research Database (Denmark)
Kliem, Wolfhard; Pommer, Christian; Stoustrup, Jakob
1996-01-01
with the results of the classical approach using Rayleighquotients. Several rotor systems are tested: a simple Laval rotor, a Laval rotor with additional elasticity and damping in thr bearings, and a number of rotor systems with complex symmetric 4x4 randomly generated matrices.......A large class of rotor systems can be modelled by a complex matrix differential equation of secondorder. The angular velocity of the rotor plays the role of a parameter. We apply the Lyapunov matrix equation in a complex setting and prove two new stability results which are compared...
A Complex Systems Model Approach to Quantified Mineral Resource Appraisal
Gettings, M.E.; Bultman, M.W.; Fisher, F.S.
2004-01-01
For federal and state land management agencies, mineral resource appraisal has evolved from value-based to outcome-based procedures wherein the consequences of resource development are compared with those of other management options. Complex systems modeling is proposed as a general framework in which to build models that can evaluate outcomes. Three frequently used methods of mineral resource appraisal (subjective probabilistic estimates, weights of evidence modeling, and fuzzy logic modeling) are discussed to obtain insight into methods of incorporating complexity into mineral resource appraisal models. Fuzzy logic and weights of evidence are most easily utilized in complex systems models. A fundamental product of new appraisals is the production of reusable, accessible databases and methodologies so that appraisals can easily be repeated with new or refined data. The data are representations of complex systems and must be so regarded if all of their information content is to be utilized. The proposed generalized model framework is applicable to mineral assessment and other geoscience problems. We begin with a (fuzzy) cognitive map using (+1,0,-1) values for the links and evaluate the map for various scenarios to obtain a ranking of the importance of various links. Fieldwork and modeling studies identify important links and help identify unanticipated links. Next, the links are given membership functions in accordance with the data. Finally, processes are associated with the links; ideally, the controlling physical and chemical events and equations are found for each link. After calibration and testing, this complex systems model is used for predictions under various scenarios.
Hill, Renee J.; Chopra, Pradeep; Richardi, Toni
2012-01-01
Abstract Explaining the etiology of Complex Regional Pain Syndrome (CRPS) from the psychogenic model is exceedingly unsophisticated, because neurocognitive deficits, neuroanatomical abnormalities, and distortions in cognitive mapping are features of CRPS pathology. More importantly, many people who have developed CRPS have no history of mental illness. The psychogenic model offers comfort to physicians and mental health practitioners (MHPs) who have difficulty understanding pain maintained by...
Christoforou, Cleopatra
2017-12-10
We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity is useful to provide measure valued weak versus strong uniqueness theorems for the hyperbolic problem. Also, it yields a convergence result in the zero-viscosity limit to smooth solutions in an Lp framework. The relative entropy identity is also developed for the system of gas dynamics for viscous and heat conducting gases, and for the system of thermoviscoelasticity with viscosity and heat-conduction. Existing differences between the example and the general hyperbolic theory are underlined.
Energy Technology Data Exchange (ETDEWEB)
Goldsby, Michael E.; Mayo, Jackson R.; Bhattacharyya, Arnab (Massachusetts Institute of Technology, Cambridge, MA); Armstrong, Robert C.; Vanderveen, Keith
2008-09-01
The goal of this research was to examine foundational methods, both computational and theoretical, that can improve the veracity of entity-based complex system models and increase confidence in their predictions for emergent behavior. The strategy was to seek insight and guidance from simplified yet realistic models, such as cellular automata and Boolean networks, whose properties can be generalized to production entity-based simulations. We have explored the usefulness of renormalization-group methods for finding reduced models of such idealized complex systems. We have prototyped representative models that are both tractable and relevant to Sandia mission applications, and quantified the effect of computational renormalization on the predictive accuracy of these models, finding good predictivity from renormalized versions of cellular automata and Boolean networks. Furthermore, we have theoretically analyzed the robustness properties of certain Boolean networks, relevant for characterizing organic behavior, and obtained precise mathematical constraints on systems that are robust to failures. In combination, our results provide important guidance for more rigorous construction of entity-based models, which currently are often devised in an ad-hoc manner. Our results can also help in designing complex systems with the goal of predictable behavior, e.g., for cybersecurity.
Nostradamus 2014 prediction, modeling and analysis of complex systems
Suganthan, Ponnuthurai; Chen, Guanrong; Snasel, Vaclav; Abraham, Ajith; Rössler, Otto
2014-01-01
The prediction of behavior of complex systems, analysis and modeling of its structure is a vitally important problem in engineering, economy and generally in science today. Examples of such systems can be seen in the world around us (including our bodies) and of course in almost every scientific discipline including such “exotic” domains as the earth’s atmosphere, turbulent fluids, economics (exchange rate and stock markets), population growth, physics (control of plasma), information flow in social networks and its dynamics, chemistry and complex networks. To understand such complex dynamics, which often exhibit strange behavior, and to use it in research or industrial applications, it is paramount to create its models. For this purpose there exists a rich spectrum of methods, from classical such as ARMA models or Box Jenkins method to modern ones like evolutionary computation, neural networks, fuzzy logic, geometry, deterministic chaos amongst others. This proceedings book is a collection of accepted ...
Waves in hyperbolic and double negative metamaterials including rogues and solitons
Boardman, A. D.; Alberucci, A.; Assanto, G.; Grimalsky, V. V.; Kibler, B.; McNiff, J.; Nefedov, I. S.; Rapoport, Yu G.; Valagiannopoulos, C. A.
2017-11-01
considered with a model of the response of hyperbolic metamaterials in terms of the homogenisation (‘effective medium’) approach. The model has a macroscopic dielectric tensor encompassing at least one negative eigenvalue. It is shown that light propagating in the presence of hyperbolic dispersion undergoes negative (anomalous) diffraction. The theory is ten broadened out to include the influence of the orientation of the optical axis with respect to the propagation wave vector. Optical rogue waves are discussed in terms of how they are influenced, but not suppressed, by a metamaterial background. It is strongly discussed that metamaterials and optical rogue waves have both been making headlines in recent years and that they are, separately, large areas of research to study. A brief background of the inevitable linkage of them is considered and important new possibilities are discussed. After this background is revealed some new rogue wave configurations combining the two areas are presented alongside a discussion of the way forward for the future.
Modelling nutrient reduction targets - model structure complexity vs. data availability
Capell, Rene; Lausten Hansen, Anne; Donnelly, Chantal; Refsgaard, Jens Christian; Arheimer, Berit
2015-04-01
In most parts of Europe, macronutrient concentrations and loads in surface water are currently affected by human land use and land management choices. Moreover, current macronutrient concentration and load levels often violate European Water Framework Directive (WFD) targets and effective measures to reduce these levels are sought after by water managers. Identifying such effective measures in specific target catchments should consider the four key processes release, transport, retention, and removal, and thus physical catchment characteristics as e.g. soils and geomorphology, but also management data such as crop distribution and fertilizer application regimes. The BONUS funded research project Soils2Sea evaluates new, differentiated regulation strategies to cost-efficiently reduce nutrient loads to the Baltic Sea based on new knowledge of nutrient transport and retention processes between soils and the coast. Within the Soils2Sea framework, we here examine the capability of two integrated hydrological and nutrient transfer models, HYPE and Mike SHE, to model runoff and nitrate flux responses in the 100 km2 Norsminde catchment, Denmark, comparing different model structures and data bases. We focus on comparing modelled nitrate reductions within and below the root zone, and evaluate model performances as function of available model structures (process representation within the model) and available data bases (temporal forcing data and spatial information). This model evaluation is performed to aid in the development of model tools which will be used to estimate the effect of new nutrient reduction measures on the catchment to regional scale, where available data - both climate forcing and land management - typically are increasingly limited with the targeted spatial scale and may act as a bottleneck for process conceptualizations and thus the value of a model as tool to provide decision support for differentiated regulation strategies.
Manifold boundaries give "gray-box" approximations of complex models
Transtrum, Mark K
2016-01-01
We discuss a method of parameter reduction in complex models known as the Manifold Boundary Approximation Method (MBAM). This approach, based on a geometric interpretation of statistics, maps the model reduction problem to a geometric approximation problem. It operates iteratively, removing one parameter at a time, by approximating a high-dimension, but thin manifold by its boundary. Although the method makes no explicit assumption about the functional form of the model, it does require that the model manifold exhibit a hierarchy of boundaries, i.e., faces, edges, corners, hyper-corners, etc. We empirically show that a variety of model classes have this curious feature, making them amenable to MBAM. These model classes include models composed of elementary functions (e.g., rational functions, exponentials, and partition functions), a variety of dynamical system (e.g., chemical and biochemical kinetics, Linear Time Invariant (LTI) systems, and compartment models), network models (e.g., Bayesian networks, Marko...
Complexity and agent-based modelling in urban research
DEFF Research Database (Denmark)
Fertner, Christian
influence on the bigger system. Traditional scientific methods or theories often tried to simplify, not accounting complex relations of actors and decision-making. The introduction of computers in simulation made new approaches in modelling, as for example agent-based modelling (ABM), possible, dealing...... of complexity for a majority of science, there exists a huge number of scientific articles, books, tutorials etc. to these topics which doesn’t make it easy for a novice in the field to find the right literature. The literature used gives an optimistic outlook for the future of this methodology, although ABM...
Brackets, sigma models and integrability of generalized complex structures
Energy Technology Data Exchange (ETDEWEB)
Guttenberg, Sebastian [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France); Institut fuer Theoretische Physik, Technische Universitaet Wien, 1040 Vienna (Austria)
2007-06-15
It is shown how derived brackets naturally arise in sigma-models via Poisson- or antibracket, generalizing a recent observation by Alekseev and Strobl. On the way to a precise formulation of this relation, an explicit coordinate expression for the derived bracket is obtained. The generalized Nijenhuis tensor of generalized complex geometry is shown to coincide up to a de-Rham closed term with the derived bracket of the structure with itself and a new coordinate expression for this tensor is presented. The insight is applied to two known two-dimensional sigma models in a background with generalized complex structure.
Simplicity versus complexity in modelling groundwater recharge in Chalk catchments
Directory of Open Access Journals (Sweden)
R. B. Bradford
2002-01-01
Full Text Available Models of varying complexity are available to provide estimates of recharge in headwater Chalk catchments. Some measure of how estimates vary between different models can help guide the choice of model for a particular application. This paper compares recharge estimates derived from four models employing input data at varying spatial resolutions for a Chalk headwater catchment (River Pang, UK over a four-year period (1992-1995 that includes a range of climatic conditions. One model was validated against river flow data to provide a measure of their relative performance. Each model gave similar total recharge for the crucial winter recharge period when evaporation is low. However, the simple models produced relatively lower estimates of the summer and early autumn recharge due to the way in which processes governing recharge especially evaporation and infiltration are represented. The relative uniformity of land use, soil types and rainfall across headwater, drift-free Chalk catchments suggests that complex, distributed models offer limited benefits for recharge estimates at the catchment scale compared to simple models. Nonetheless, distributed models would be justified for studies where the pattern and amount of recharge need to be known in greater detail and to provide more reliable estimates of recharge during years with low rainfall. Keywords: Chalk, modelling, groundwater recharge
Reduced Complexity Channel Models for IMT-Advanced Evaluation
Directory of Open Access Journals (Sweden)
Yu Zhang
2009-01-01
Full Text Available Accuracy and complexity are two crucial aspects of the applicability of a channel model for wideband multiple input multiple output (MIMO systems. For small number of antenna element pairs, correlation-based models have lower computational complexity while the geometry-based stochastic models (GBSMs can provide more accurate modeling of real radio propagation. This paper investigates several potential simplifications of the GBSM to reduce the complexity with minimal impact on accuracy. In addition, we develop a set of broadband metrics which enable a thorough investigation of the differences between the GBSMs and the simplified models. The impact of various random variables which are employed by the original GBSM on the system level simulation are also studied. Both simulation results and a measurement campaign show that complexity can be reduced significantly with a negligible loss of accuracy in the proposed metrics. As an example, in the presented scenarios, the computational time can be reduced by up to 57% while keeping the relative deviation of 5% outage capacity within 5%.
Travelling Waves in Hyperbolic Chemotaxis Equations
Xue, Chuan
2010-10-16
Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235-248, 1971). The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically. © 2010 Society for Mathematical Biology.
Infinite Multiple Membership Relational Modeling for Complex Networks
DEFF Research Database (Denmark)
Mørup, Morten; Schmidt, Mikkel Nørgaard; Hansen, Lars Kai
Learning latent structure in complex networks has become an important problem fueled by many types of networked data originating from practically all fields of science. In this paper, we propose a new non-parametric Bayesian multiplemembership latent feature model for networks. Contrary to existing...... multiplemembership models that scale quadratically in the number of vertices the proposedmodel scales linearly in the number of links admittingmultiple-membership analysis in large scale networks. We demonstrate a connection between the single membership relational model and multiple membership models and show...
Complexity, accuracy and practical applicability of different biogeochemical model versions
Los, F. J.; Blaas, M.
2010-04-01
The construction of validated biogeochemical model applications as prognostic tools for the marine environment involves a large number of choices particularly with respect to the level of details of the .physical, chemical and biological aspects. Generally speaking, enhanced complexity might enhance veracity, accuracy and credibility. However, very complex models are not necessarily effective or efficient forecast tools. In this paper, models of varying degrees of complexity are evaluated with respect to their forecast skills. In total 11 biogeochemical model variants have been considered based on four different horizontal grids. The applications vary in spatial resolution, in vertical resolution (2DH versus 3D), in nature of transport, in turbidity and in the number of phytoplankton species. Included models range from 15 year old applications with relatively simple physics up to present state of the art 3D models. With all applications the same year, 2003, has been simulated. During the model intercomparison it has been noticed that the 'OSPAR' Goodness of Fit cost function (Villars and de Vries, 1998) leads to insufficient discrimination of different models. This results in models obtaining similar scores although closer inspection of the results reveals large differences. In this paper therefore, we have adopted the target diagram by Jolliff et al. (2008) which provides a concise and more contrasting picture of model skill on the entire model domain and for the entire period of the simulations. Correctness in prediction of the mean and the variability are separated and thus enhance insight in model functioning. Using the target diagrams it is demonstrated that recent models are more consistent and have smaller biases. Graphical inspection of time series confirms this, as the level of variability appears more realistic, also given the multi-annual background statistics of the observations. Nevertheless, whether the improvements are all genuine for the particular
Hyperbolic geometry of Kuramoto oscillator networks
Chen, Bolun; Engelbrecht, Jan R.; Mirollo, Renato
2017-09-01
Kuramoto oscillator networks have the special property that their trajectories are constrained to lie on the (at most) 3D orbits of the Möbius group acting on the state space T N (the N-fold torus). This result has been used to explain the existence of the N-3 constants of motion discovered by Watanabe and Strogatz for Kuramoto oscillator networks. In this work we investigate geometric consequences of this Möbius group action. The dynamics of Kuramoto phase models can be further reduced to 2D reduced group orbits, which have a natural geometry equivalent to the unit disk \
Modeling the propagation of mobile malware on complex networks
Liu, Wanping; Liu, Chao; Yang, Zheng; Liu, Xiaoyang; Zhang, Yihao; Wei, Zuxue
2016-08-01
In this paper, the spreading behavior of malware across mobile devices is addressed. By introducing complex networks to model mobile networks, which follows the power-law degree distribution, a novel epidemic model for mobile malware propagation is proposed. The spreading threshold that guarantees the dynamics of the model is calculated. Theoretically, the asymptotic stability of the malware-free equilibrium is confirmed when the threshold is below the unity, and the global stability is further proved under some sufficient conditions. The influences of different model parameters as well as the network topology on malware propagation are also analyzed. Our theoretical studies and numerical simulations show that networks with higher heterogeneity conduce to the diffusion of malware, and complex networks with lower power-law exponents benefit malware spreading.
Modeling data irregularities and structural complexities in data envelopment analysis
Zhu, Joe
2007-01-01
In a relatively short period of time, Data Envelopment Analysis (DEA) has grown into a powerful quantitative, analytical tool for measuring and evaluating performance. It has been successfully applied to a whole variety of problems in many different contexts worldwide. This book deals with the micro aspects of handling and modeling data issues in modeling DEA problems. DEA's use has grown with its capability of dealing with complex "service industry" and the "public service domain" types of problems that require modeling of both qualitative and quantitative data. This handbook treatment deals with specific data problems including: imprecise or inaccurate data; missing data; qualitative data; outliers; undesirable outputs; quality data; statistical analysis; software and other data aspects of modeling complex DEA problems. In addition, the book will demonstrate how to visualize DEA results when the data is more than 3-dimensional, and how to identify efficiency units quickly and accurately.
Stålne, Kristian; Kjellström, Sofia; Utriainen, Jukka
2016-01-01
An important aspect of higher education is to educate students who can manage complex relationships and solve complex problems. Teachers need to be able to evaluate course content with regard to complexity, as well as evaluate students' ability to assimilate complex content and express it in the form of a learning outcome. One model for evaluating…
ABOUT COMPLEX APPROACH TO MODELLING OF TECHNOLOGICAL MACHINES FUNCTIONING
Directory of Open Access Journals (Sweden)
A. A. Honcharov
2015-01-01
Full Text Available Problems arise in the process of designing, production and investigation of a complicated technological machine. These problems concern not only properties of some types of equipment but they have respect to regularities of control object functioning as a whole. A technological machine is thought of as such technological complex where it is possible to lay emphasis on a control system (or controlling device and a controlled object. The paper analyzes a number of existing approaches to construction of models for controlling devices and their functioning. A complex model for a technological machine operation has been proposed in the paper; in other words it means functioning of a controlling device and a controlled object of the technological machine. In this case models of the controlling device and the controlled object of the technological machine can be represented as aggregate combination (elements of these models. The paper describes a conception on realization of a complex model for a technological machine as a model for interaction of units (elements in the controlling device and the controlled object. When a control activation is given to the controlling device of the technological machine its modelling is executed at an algorithmic or logic level and the obtained output signals are interpreted as events and information about them is transferred to executive mechanisms.The proposed scheme of aggregate integration considers element models as object classes and the integration scheme is presented as a combination of object property values (combination of a great many input and output contacts and combination of object interactions (in the form of an integration operator. Spawn of parent object descendants of the technological machine model and creation of their copies in various project parts is one of the most important means of the distributed technological machine modelling that makes it possible to develop complicated models of
Surface complexation modeling or organic acid sorption to goethite
Energy Technology Data Exchange (ETDEWEB)
Evanko, C.R.; Dzombak, D.A. [Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Civil and Environmental Engineering
1999-06-15
Surface complexation modeling was performed using the Generalized Two-Layer Model for a series of low molecular weight organic acids. Sorption of these organic acids to goethite was investigated in a previous study to assess the influence of particular structural features on sorption. Here, the ability to describe the observed sorption behavior for compounds with similar structural features using surface complexation modeling was investigated. A set of surface reactions and equilibrium constants yielding optimal data fits was obtained for each organic acid over a range of total sorbate concentrations. Surface complexation modeling successfully described sorption of a number of the simple organic acids, but an additional hydrophobic component was needed to describe sorption behavior of some compounds with significant hydrophobic character. These compounds exhibited sorption behavior of some compounds with significant hydrophobic character. These compounds exhibited sorption behavior that was inconsistent with ligand exchange mechanisms since sorption behavior of some compounds with significant hydrophobic character. These compounds exhibited sorption behavior that was inconsistent with ligand exchange mechanisms since sorption did not decrease with increasing total sorbate concentration and/or exceeded surface site saturation. Hydrophobic interactions appeared to be most significant for the compound containing a 5-carbon aliphatic chain. Comparison of optimized equilibrium constants for similar surface species showed that model results were consistent with observed sorption behavior: equilibrium constants were highest for compounds having adjacent carboxylic groups, lower for compounds with adjacent phenolic groups, and lowest for compounds with phenolic groups in the ortho position relative to a carboxylic group. Surface complexation modeling was also performed to fit sorption data for Suwannee River fulvic acid. The data could be described well using reactions and
Otway, Thomas H
2015-01-01
This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvatur...
Interactive Visualizations of Complex Seismic Data and Models
Chai, C.; Ammon, C. J.; Maceira, M.; Herrmann, R. B.
2016-12-01
The volume and complexity of seismic data and models have increased dramatically thanks to dense seismic station deployments and advances in data modeling and processing. Seismic observations such as receiver functions and surface-wave dispersion are multidimensional: latitude, longitude, time, amplitude and latitude, longitude, period, and velocity. Three-dimensional seismic velocity models are characterized with three spatial dimensions and one additional dimension for the speed. In these circumstances, exploring the data and models and assessing the data fits is a challenge. A few professional packages are available to visualize these complex data and models. However, most of these packages rely on expensive commercial software or require a substantial time investment to master, and even when that effort is complete, communicating the results to others remains a problem. A traditional approach during the model interpretation stage is to examine data fits and model features using a large number of static displays. Publications include a few key slices or cross-sections of these high-dimensional data, but this prevents others from directly exploring the model and corresponding data fits. In this presentation, we share interactive visualization examples of complex seismic data and models that are based on open-source tools and are easy to implement. Model and data are linked in an intuitive and informative web-browser based display that can be used to explore the model and the features in the data that influence various aspects of the model. We encode the model and data into HTML files and present high-dimensional information using two approaches. The first uses a Python package to pack both data and interactive plots in a single file. The second approach uses JavaScript, CSS, and HTML to build a dynamic webpage for seismic data visualization. The tools have proven useful and led to deeper insight into 3D seismic models and the data that were used to construct them
PROGRAM COMPLEX FOR MODELING OF THE DETAILS HARDENING PROCESS
Directory of Open Access Journals (Sweden)
S. P. Kundas
2004-01-01
Full Text Available In the article there is presented the program complex ThermoSim, consisting of preprocessor, processor and postprocessor and intended for modeling (analysis of thermalphysic processes and characteristics of details of instrument-making and machine-building, diagnostics and optimization of technological processes of heat treatment and details constructions without using the destructive control methods.
Modelling the transition from simple to complex Ca oscillations in ...
Indian Academy of Sciences (India)
2014-04-29
Apr 29, 2014 ... 2Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand. *Corresponding author (Fax, +91-755-2670562; Email, mannumanhas@gmail.com). A mathematical model is proposed which systematically investigates complex calcium oscillations in pancreatic.
Surface complexation modeling of americium sorption onto volcanic tuff.
Ding, M; Kelkar, S; Meijer, A
2014-10-01
Results of a surface complexation model (SCM) for americium sorption on volcanic rocks (devitrified and zeolitic tuff) are presented. The model was developed using PHREEQC and based on laboratory data for americium sorption on quartz. Available data for sorption of americium on quartz as a function of pH in dilute groundwater can be modeled with two surface reactions involving an americium sulfate and an americium carbonate complex. It was assumed in applying the model to volcanic rocks from Yucca Mountain, that the surface properties of volcanic rocks can be represented by a quartz surface. Using groundwaters compositionally representative of Yucca Mountain, americium sorption distribution coefficient (Kd, L/Kg) values were calculated as function of pH. These Kd values are close to the experimentally determined Kd values for americium sorption on volcanic rocks, decreasing with increasing pH in the pH range from 7 to 9. The surface complexation constants, derived in this study, allow prediction of sorption of americium in a natural complex system, taking into account the inherent uncertainty associated with geochemical conditions that occur along transport pathways. Published by Elsevier Ltd.
Soliton solutions for quintic complex Ginzburg-Landau model
Nawaz, B.; Ali, K.; Rizvi, S. T. R.; Younis, M.
2017-10-01
In this paper, we find the rational function solution, confluent hypergeometric functions solutions and solitary wave solutions for quintic complex Ginzburg-Landau (CGLQ) model by using extended trial equation method. We also find some new solitary wave soliton solutions for CGLQ equation by using modified extended tanh-function method.
Fischer and Schrock Carbene Complexes: A Molecular Modeling Exercise
Montgomery, Craig D.
2015-01-01
An exercise in molecular modeling that demonstrates the distinctive features of Fischer and Schrock carbene complexes is presented. Semi-empirical calculations (PM3) demonstrate the singlet ground electronic state, restricted rotation about the C-Y bond, the positive charge on the carbon atom, and hence, the electrophilic nature of the Fischer…
Complexity effects in choice experiments-based models
Dellaert, B.G.C.; Donkers, B.; van Soest, A.H.O.
2012-01-01
Many firms rely on choice experiment–based models to evaluate future marketing actions under various market conditions. This research investigates choice complexity (i.e., number of alternatives, number of attributes, and utility similarity between the most attractive alternatives) and individual
Model-based safety architecture framework for complex systems
Schuitemaker, K.; Rajabali Nejad, Mohammadreza; Braakhuis, J.G.; Podofilini, Luca; Sudret, Bruno; Stojadinovic, Bozidar; Zio, Enrico; Kröger, Wolfgang
2015-01-01
The shift to transparency and rising need of the general public for safety, together with the increasing complexity and interdisciplinarity of modern safety-critical Systems of Systems (SoS) have resulted in a Model-Based Safety Architecture Framework (MBSAF) for capturing and sharing architectural
Modelling and simulating in-stent restenosis with complex automata
Hoekstra, A.G.; Lawford, P.; Hose, R.
2010-01-01
In-stent restenosis, the maladaptive response of a blood vessel to injury caused by the deployment of a stent, is a multiscale system involving a large number of biological and physical processes. We describe a Complex Automata Model for in-stent restenosis, coupling bulk flow, drug diffusion, and
Performance of Random Effects Model Estimators under Complex Sampling Designs
Jia, Yue; Stokes, Lynne; Harris, Ian; Wang, Yan
2011-01-01
In this article, we consider estimation of parameters of random effects models from samples collected via complex multistage designs. Incorporation of sampling weights is one way to reduce estimation bias due to unequal probabilities of selection. Several weighting methods have been proposed in the literature for estimating the parameters of…
An Associational Model for the Diffusion of Complex Innovations.
Barnett, George A.
A paradigm for the study of the diffusion of complex innovations through a society is presented in this paper; the paradigm is useful for studying sociocultural change as innovations diffuse. The model is designed to account for change within social systems rather than in individuals, although it would also be consistent with information…
Fitting Meta-Analytic Structural Equation Models with Complex Datasets
Wilson, Sandra Jo; Polanin, Joshua R.; Lipsey, Mark W.
2016-01-01
A modification of the first stage of the standard procedure for two-stage meta-analytic structural equation modeling for use with large complex datasets is presented. This modification addresses two common problems that arise in such meta-analyses: (a) primary studies that provide multiple measures of the same construct and (b) the correlation…
Parasitic light scattered by complex optical coatings: modelization and metrology
Zerrad, Myriam; Lequime, Michel; Liukaityte, Simona; Amra, Claude
2017-12-01
Optical components realized for space applications have to be mastered in term of parasitic light. This paper present the last improvements performed at the Institute Fresnel to predict and measure scattering losses of optical components with a special care to complex optical coatings. Agreement between numerical models and metrology is now excellent. Some examples will be presented.
Copper complexes as biomimetic models of catechol oxidase : mechanistic studies
Koval, Iryna A.
2006-01-01
The research described in this thesis deals with the synthesis of copper(II) complexes with phenol-based or macrocyclic ligands, which can be regarded as model compounds of the active site of catechol oxidase, and with the mechanism of the catalytic oxidation of catechol mediated by these compounds.
Boundary conditions for hyperbolic systems of partial differentials equations.
Guaily, Amr G; Epstein, Marcelo
2013-07-01
An easy-to-apply algorithm is proposed to determine the correct set(s) of boundary conditions for hyperbolic systems of partial differential equations. The proposed approach is based on the idea of the incoming/outgoing characteristics and is validated by considering two problems. The first one is the well-known Euler system of equations in gas dynamics and it proved to yield set(s) of boundary conditions consistent with the literature. The second test case corresponds to the system of equations governing the flow of viscoelastic liquids.
Light propagation in a magneto-optical hyperbolic biaxial crystal
Kuznetsov, Evgeniy V.; Merzlikin, Alexander M.
2017-12-01
The light propagation through a magneto-optical hyperbolic biaxial crystal is investigated. Magnetization of the structure results in splitting and reconnection of an isofrequency near the self-intersection point and thus it leads to the disappearance of conical refraction in a crystal. In its turn the isofrequency splitting leads to band gap opening and makes it possible to steer the beam. These effects allow to control the light propagation by means of an external magnetostatic field. The Poynting's vector distribution in the crystal is calculated by means of a Fourier transform in order to demonstrate the aforementioned effects.
Optical absorption of hyperbolic metamaterial with stochastic surfaces
DEFF Research Database (Denmark)
Liu, Jingjing; Naik, Gururaj V.; Ishii, Satoshi
2014-01-01
We investigate the absorption properties of planar hyperbolic metamaterials (HMMs) consisting of metal-dielectric multilayers, which support propagating plane waves with anomalously large wavevectors and high photonic-density-of-states over a broad bandwidth. An interface formed by depositing...... indium-tin-oxide nanoparticles on an HMM surface scatters light into the high-k propagating modes of the metamaterial and reduces reflection. We compare the reflection and absorption from an HMM with the nanoparticle cover layer versus those of a metal film with the same thickness also covered...
Non-Euclidean Fourier Inversion on Super-hyperbolic Space
Alldridge, Alexander; Palzer, Wolfgang
2017-05-01
For the super-hyperbolic space in any dimension, we introduce the non-Euclidean Helgason-Fourier transform. We prove an inversion formula exhibiting residue contributions at the poles of the Harish-Chandra c-function, signalling discrete parts in the spectrum. The proof is based on a detailed study of the spherical superfunctions, using recursion relations and localization techniques to normalize them precisely, careful estimates of their derivatives, and a rigorous analysis of the boundary terms appearing in the polar coordinate expression of the invariant integral.
Tunable bulk polaritons of graphene-based hyperbolic metamaterials.
Zhang, Liwei; Zhang, Zhengren; Kang, Chaoyang; Cheng, Bei; Chen, Liang; Yang, Xuefeng; Wang, Jian; Li, Weibing; Wang, Baoji
2014-06-02
The tunable hyperbolic metamaterial (HMM) based on the graphene-dielectric layered structure at THz frequency is presented, and the surface and bulk polaritons of the graphene-based HMM are theoretically studied. It is found that the dispersions of the polaritons can be tuned by varying the Fermi energy of graphene sheets, the graphene-dielectric layers and the layer number of graphene sheets. In addition, the highly confined bulk polariton mode can be excited and is manifested in an attenuated total reflection configuration as a sharp drop in the reflectance. Such properties can be used in tunable optical reflection modulation with the assistance of bulk polaritons.
Engineered surface Bloch waves in graphene-based hyperbolic metamaterials.
Xiang, Yuanjiang; Guo, Jun; Dai, Xiaoyu; Wen, Shuangchun; Tang, Dingyuan
2014-02-10
A kind of tunable hyperbolic metamaterial (HMM) based on the graphene-dielectric layered structure at near-infrared frequencies is presented, and the engineered surface Bloch waves between graphene-based HMM and isotropic medium are investigated. Our calculations demonstrate that the frequency and frequency range of surface Bloch waves existence can be tuned by varying the Fermi energy of graphene sheets via electrostatic biasing. Moreover, we show that the frequency range of surface Bloch waves existence can be broadened by decreasing the thickness of the dielectric in the graphene-dielectric layered structure or by increasing the layer number of graphene sheets.
Directory of Open Access Journals (Sweden)
Henry de-Graft Acquah
2013-01-01
Full Text Available Information Criteria provides an attractive basis for selecting the best model from a set of competing asymmetric price transmission models or theories. However, little is understood about the sensitivity of the model selection methods to model complexity. This study therefore fits competing asymmetric price transmission models that differ in complexity to simulated data and evaluates the ability of the model selection methods to recover the true model. The results of Monte Carlo experimentation suggest that in general BIC, CAIC and DIC were superior to AIC when the true data generating process was the standard error correction model, whereas AIC was more successful when the true model was the complex error correction model. It is also shown that the model selection methods performed better in large samples for a complex asymmetric data generating process than with a standard asymmetric data generating process. Except for complex models, AIC's performance did not make substantial gains in recovery rates as sample size increased. The research findings demonstrate the influence of model complexity in asymmetric price transmission model comparison and selection.
Sulis, William H
2017-10-01
Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.
Modelling of Complex Physical Processes in Electrostatic Precipitators
Energy Technology Data Exchange (ETDEWEB)
Kiss, Istvan; Ivancsy, Tamas; Berta, Istvan [Department of Electric Power Engineering, Egry J. u. 18, Budapest H-llll (Hungary); Suda, Jeno, E-mail: kiss.istvan@vet.bme.hu [Department of Fluid Mechanics, Bertalan Lajos 4-6., Budapest H-llll (Hungary)
2011-06-23
Electrostatic precipitator (ESP) models have improved significantly in the past years. The dramatic development of the capacity of computers made it possible to increase the complexity of ESP models. Recently the different interactions between the gas, the electric field with ion space charge and the charged particles to be precipitated can be described more accurately by the newly developed complex approach. However even some of the newest computer models are limited; they are not able to follow the interactions of the complicated physical phenomena properly. For example pulse energisation of short time impulses cannot be described correctly with models assuming continuous corona current. There is another important problem, namely the examined duration of operation. Some of the models determine the trajectories of dust particles assuming that they are unchanged during the operation of an ESP. The validity of this assumption is very limited in such cases, where the development of certain phenomena is time dependent (e.g. back corona formation). In this paper the authors focus on the 'long term' models, analysing such situations in which it is vital to investigate a longer period of operation of ESP-s. Using the newly developed model the effect of back corona, rapping, etc. can be analysed with higher reliability than it has been performed in previous ESP models.
Modeling Complex Nesting Structures in International Business Research
DEFF Research Database (Denmark)
Nielsen, Bo Bernhard; Nielsen, Sabina
2013-01-01
International business (IB) phenomena often involve complex relationships between factors at different levels. Multinational corporations (MNCs) are influenced both by different country and industry environments which may have independent as well as interactive effects on MNC performance. While...... hierarchical random coefficient models (RCM) are often used for the analysis of multilevel phenomena, IB issues often result in more complex nested structures. This paper illustrates how cross-nested multilevel modeling allowing for predictor variables and cross-level interactions at multiple (crossed) levels...... of analysis may yield novel insights to IB research. The results have implications for IB research in its pursuit of an integrative approach to understanding the multilevel determinants of firm internationalization and performance. The paper further illustrates the importance of adequately modeling crossed...
Reduced Complexity Volterra Models for Nonlinear System Identification
Directory of Open Access Journals (Sweden)
Hacıoğlu Rıfat
2001-01-01
Full Text Available A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter′s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identification is addressed in this paper using a Fixed Pole Expansion Technique (FPET within the Volterra model structure. The FPET approach employs orthonormal basis functions derived from fixed (real or complex pole locations to expand the Volterra kernels and reduce the number of estimated parameters. That the performance of FPET can considerably reduce the number of estimated parameters is demonstrated by a digital satellite channel example in which we use the proposed method to identify the channel dynamics. Furthermore, a gradient-descent procedure that adaptively selects the pole locations in the FPET structure is developed in the paper.
Entropy, complexity, and Markov diagrams for random walk cancer models.
Newton, Paul K; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter
2014-12-19
The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.
Elastic Network Model of a Nuclear Transport Complex
Ryan, Patrick; Liu, Wing K.; Lee, Dockjin; Seo, Sangjae; Kim, Young-Jin; Kim, Moon K.
2010-05-01
The structure of Kap95p was obtained from the Protein Data Bank (www.pdb.org) and analyzed RanGTP plays an important role in both nuclear protein import and export cycles. In the nucleus, RanGTP releases macromolecular cargoes from importins and conversely facilitates cargo binding to exportins. Although the crystal structure of the nuclear import complex formed by importin Kap95p and RanGTP was recently identified, its molecular mechanism still remains unclear. To understand the relationship between structure and function of a nuclear transport complex, a structure-based mechanical model of Kap95p:RanGTP complex is introduced. In this model, a protein structure is simply modeled as an elastic network in which a set of coarse-grained point masses are connected by linear springs representing biochemical interactions at atomic level. Harmonic normal mode analysis (NMA) and anharmonic elastic network interpolation (ENI) are performed to predict the modes of vibrations and a feasible pathway between locked and unlocked conformations of Kap95p, respectively. Simulation results imply that the binding of RanGTP to Kap95p induces the release of the cargo in the nucleus as well as prevents any new cargo from attaching to the Kap95p:RanGTP complex.
Entropy, complexity, and Markov diagrams for random walk cancer models
Newton, Paul K.; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter
2014-12-01
The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.
Hill, Renee J.; Chopra, Pradeep; Richardi, Toni
2012-01-01
Abstract Explaining the etiology of Complex Regional Pain Syndrome (CRPS) from the psychogenic model is exceedingly unsophisticated, because neurocognitive deficits, neuroanatomical abnormalities, and distortions in cognitive mapping are features of CRPS pathology. More importantly, many people who have developed CRPS have no history of mental illness. The psychogenic model offers comfort to physicians and mental health practitioners (MHPs) who have difficulty understanding pain maintained by newly uncovered neuro inflammatory processes. With increased education about CRPS through a biopsychosocial perspective, both physicians and MHPs can better diagnose, treat, and manage CRPS symptomatology. PMID:24223338
Hill, Renee J; Chopra, Pradeep; Richardi, Toni
2012-01-01
Explaining the etiology of Complex Regional Pain Syndrome (CRPS) from the psychogenic model is exceedingly unsophisticated, because neurocognitive deficits, neuroanatomical abnormalities, and distortions in cognitive mapping are features of CRPS pathology. More importantly, many people who have developed CRPS have no history of mental illness. The psychogenic model offers comfort to physicians and mental health practitioners (MHPs) who have difficulty understanding pain maintained by newly uncovered neuro inflammatory processes. With increased education about CRPS through a biopsychosocial perspective, both physicians and MHPs can better diagnose, treat, and manage CRPS symptomatology.
Complex humanitarian emergencies: A review of epidemiological and response models
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Burkle Frederick
2006-01-01
Full Text Available Complex emergencies (CEs have been the most common human-generated disaster of the past two decades. These internal conflicts and associated acts of genocide have been poorly understood and poorly managed. This article provides an epidemiological background and understanding of developing and developed countries, and chronic or smoldering countries′ CEs, and explains in detail the prevailing models of response seen by the international community. Even though CEs are declining in number, they have become more complex and dangerous. The UN Charter reform is expected to address internal conflicts and genocide but may not provide a more effective and efficient means to respond.
The Arabic Hyperbolic Pattern "Fa??al" in Two Recent Translations of the Qur'an
El-Zawawy, Amr M.
2014-01-01
The present study addresses the problem of rendering the ?? ?? 'fa??al' hyperbolic pattern into English in two recent translations of the Qur'an. Due to the variety of Qur'an translations and the large amount of hyperbolic forms of Arabic verbs recorded in the Qur'an, only two translations of the Qur'an are consulted and analyzed: these two…
An effective Arakelov-theoretic version of the hyperbolic isogeny theorem
Javanpeykar, Ariyan
2016-05-01
For an integer $e$ and hyperbolic curve $X$ over $\\overline{\\mathbb Q}$, Mochizuki showed that there are only finitely many isomorphism classes of hyperbolic curves $Y$ of Euler characteristic $e$ with the same universal cover as $X$. We use Arakelov theory to prove an effective version of this finiteness statement.
Multiscale modeling of complex materials phenomenological, theoretical and computational aspects
Trovalusci, Patrizia
2014-01-01
The papers in this volume deal with materials science, theoretical mechanics and experimental and computational techniques at multiple scales, providing a sound base and a framework for many applications which are hitherto treated in a phenomenological sense. The basic principles are formulated of multiscale modeling strategies towards modern complex multiphase materials subjected to various types of mechanical, thermal loadings and environmental effects. The focus is on problems where mechanics is highly coupled with other concurrent physical phenomena. Attention is also focused on the historical origins of multiscale modeling and foundations of continuum mechanics currently adopted to model non-classical continua with substructure, for which internal length scales play a crucial role.
Mental Models and the Control of Actions in Complex Environments
DEFF Research Database (Denmark)
Rasmussen, Jens
1987-01-01
of human activities. The need for analysis of complex work scenarios is discussed, together with the necessity of considering several levels of cognitive control depending upon different kinds of internal representations. The development of mental representations during learning and adaptation......The concept of mental models has become an important ingredient in models of the cognitive control of human behaviour. The paper reviews different approaches to the definition of mental models taken in psychology and cognitive sciences, which typically have been considering selected aspects...
Modelling and simulation of gas explosions in complex geometries
Energy Technology Data Exchange (ETDEWEB)
Saeter, Olav
1998-12-31
This thesis presents a three-dimensional Computational Fluid Dynamics (CFD) code (EXSIM94) for modelling and simulation of gas explosions in complex geometries. It gives the theory and validates the following sub-models : (1) the flow resistance and turbulence generation model for densely packed regions, (2) the flow resistance and turbulence generation model for single objects, and (3) the quasi-laminar combustion model. It is found that a simple model for flow resistance and turbulence generation in densely packed beds is able to reproduce the medium and large scale MERGE explosion experiments of the Commission of European Communities (CEC) within a band of factor 2. The model for a single representation is found to predict explosion pressure in better agreement with the experiments with a modified k-{epsilon} model. This modification also gives a slightly improved grid independence for realistic gas explosion approaches. One laminar model is found unsuitable for gas explosion modelling because of strong grid dependence. Another laminar model is found to be relatively grid independent and to work well in harmony with the turbulent combustion model. The code is validated against 40 realistic gas explosion experiments. It is relatively grid independent in predicting explosion pressure in different offshore geometries. It can predict the influence of ignition point location, vent arrangements, different geometries, scaling effects and gas reactivity. The validation study concludes with statistical and uncertainty analyses of the code performance. 98 refs., 96 figs, 12 tabs.
Building Better Ecological Machines: Complexity Theory and Alternative Economic Models
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Jess Bier
2016-12-01
Full Text Available Computer models of the economy are regularly used to predict economic phenomena and set financial policy. However, the conventional macroeconomic models are currently being reimagined after they failed to foresee the current economic crisis, the outlines of which began to be understood only in 2007-2008. In this article we analyze the most prominent of this reimagining: Agent-Based models (ABMs. ABMs are an influential alternative to standard economic models, and they are one focus of complexity theory, a discipline that is a more open successor to the conventional chaos and fractal modeling of the 1990s. The modelers who create ABMs claim that their models depict markets as ecologies, and that they are more responsive than conventional models that depict markets as machines. We challenge this presentation, arguing instead that recent modeling efforts amount to the creation of models as ecological machines. Our paper aims to contribute to an understanding of the organizing metaphors of macroeconomic models, which we argue is relevant conceptually and politically, e.g., when models are used for regulatory purposes.
Parametric Linear Hybrid Automata for Complex Environmental Systems Modeling
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Samar Hayat Khan Tareen
2015-07-01
Full Text Available Environmental systems, whether they be weather patterns or predator-prey relationships, are dependent on a number of different variables, each directly or indirectly affecting the system at large. Since not all of these factors are known, these systems take on non-linear dynamics, making it difficult to accurately predict meaningful behavioral trends far into the future. However, such dynamics do not warrant complete ignorance of different efforts to understand and model close approximations of these systems. Towards this end, we have applied a logical modeling approach to model and analyze the behavioral trends and systematic trajectories that these systems exhibit without delving into their quantification. This approach, formalized by René Thomas for discrete logical modeling of Biological Regulatory Networks (BRNs and further extended in our previous studies as parametric biological linear hybrid automata (Bio-LHA, has been previously employed for the analyses of different molecular regulatory interactions occurring across various cells and microbial species. As relationships between different interacting components of a system can be simplified as positive or negative influences, we can employ the Bio-LHA framework to represent different components of the environmental system as positive or negative feedbacks. In the present study, we highlight the benefits of hybrid (discrete/continuous modeling which lead to refinements among the fore-casted behaviors in order to find out which ones are actually possible. We have taken two case studies: an interaction of three microbial species in a freshwater pond, and a more complex atmospheric system, to show the applications of the Bio-LHA methodology for the timed hybrid modeling of environmental systems. Results show that the approach using the Bio-LHA is a viable method for behavioral modeling of complex environmental systems by finding timing constraints while keeping the complexity of the model
Bridging Mechanistic and Phenomenological Models of Complex Biological Systems.
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Mark K Transtrum
2016-05-01
Full Text Available The inherent complexity of biological systems gives rise to complicated mechanistic models with a large number of parameters. On the other hand, the collective behavior of these systems can often be characterized by a relatively small number of phenomenological parameters. We use the Manifold Boundary Approximation Method (MBAM as a tool for deriving simple phenomenological models from complicated mechanistic models. The resulting models are not black boxes, but remain expressed in terms of the microscopic parameters. In this way, we explicitly connect the macroscopic and microscopic descriptions, characterize the equivalence class of distinct systems exhibiting the same range of collective behavior, and identify the combinations of components that function as tunable control knobs for the behavior. We demonstrate the procedure for adaptation behavior exhibited by the EGFR pathway. From a 48 parameter mechanistic model, the system can be effectively described by a single adaptation parameter τ characterizing the ratio of time scales for the initial response and recovery time of the system which can in turn be expressed as a combination of microscopic reaction rates, Michaelis-Menten constants, and biochemical concentrations. The situation is not unlike modeling in physics in which microscopically complex processes can often be renormalized into simple phenomenological models with only a few effective parameters. The proposed method additionally provides a mechanistic explanation for non-universal features of the behavior.
Bridging Mechanistic and Phenomenological Models of Complex Biological Systems
Transtrum, Mark K.; Qiu, Peng
2016-01-01
The inherent complexity of biological systems gives rise to complicated mechanistic models with a large number of parameters. On the other hand, the collective behavior of these systems can often be characterized by a relatively small number of phenomenological parameters. We use the Manifold Boundary Approximation Method (MBAM) as a tool for deriving simple phenomenological models from complicated mechanistic models. The resulting models are not black boxes, but remain expressed in terms of the microscopic parameters. In this way, we explicitly connect the macroscopic and microscopic descriptions, characterize the equivalence class of distinct systems exhibiting the same range of collective behavior, and identify the combinations of components that function as tunable control knobs for the behavior. We demonstrate the procedure for adaptation behavior exhibited by the EGFR pathway. From a 48 parameter mechanistic model, the system can be effectively described by a single adaptation parameter τ characterizing the ratio of time scales for the initial response and recovery time of the system which can in turn be expressed as a combination of microscopic reaction rates, Michaelis-Menten constants, and biochemical concentrations. The situation is not unlike modeling in physics in which microscopically complex processes can often be renormalized into simple phenomenological models with only a few effective parameters. The proposed method additionally provides a mechanistic explanation for non-universal features of the behavior. PMID:27187545
Determination of Extensional Rheological Properties by Hyperbolic Contraction Flow
Stading, Mats
2008-07-01
Extensional rheologyy is important for diverse applications such as processing of viscoelastic fluids, mouthfeel of semi-solid foods, cell mitosis and baking, and is also a useful tool for testing the applicability of constitutive equations. Despite the documented influence of extensional rheological properties, it is seldom measured due to experimental difficulties. There are only commercial equipments available for low-viscosity fluids by Capillary Breakup and for polymer melts by Meissner-type winding of ribbons around cylinders. Both methods have limited applicability for medium-viscosity fluids such as foods and other biological systems. Contraction flows are extensively studied and a new test method has been developed based on contraction flow through a hyperbolic nozzle. The method is suitable for medium-viscosity fluids and has been validated by comparison to results from Filament Stretching and Capillary Breakup. The hyperbolic contraction flow method has been used to characterize food and medical systems, distinguish between different products having equal shear behavior, quantify ropy mouth feel and to predict foaming behavior of biopolymers.
Tangent-Impulse Interception for a Hyperbolic Target
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Dongzhe Wang
2014-01-01
Full Text Available The two-body interception problem with an upper-bounded tangent impulse for the interceptor on an elliptic parking orbit to collide with a nonmaneuvering target on a hyperbolic orbit is studied. Firstly, four special initial true anomalies whose velocity vectors are parallel to either of the lines of asymptotes for the target hyperbolic orbit are obtained by using Newton-Raphson method. For different impulse points, the solution-existence ranges of the target true anomaly for any conic transfer are discussed in detail. Then, the time-of-flight equation is solved by the secant method for a single-variable piecewise function about the target true anomaly. Considering the sphere of influence of the Earth and the upper bound on the fuel, all feasible solutions are obtained for different impulse points. Finally, a numerical example is provided to apply the proposed technique for all feasible solutions and the global minimum-time solution with initial coasting time.
Exact boundary controllability of nodal profile for quasilinear hyperbolic systems
Li, Tatsien; Gu, Qilong
2016-01-01
This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyp...
Hyperbolic Covariant Coherent Structures in Two Dimensional Flows
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Giovanni Conti
2017-09-01
Full Text Available A new method to describe hyperbolic patterns in two-dimensional flows is proposed. The method is based on the Covariant Lyapunov Vectors (CLVs, which have the properties of being covariant with the dynamics, and thus, being mapped by the tangent linear operator into another CLVs basis, they are norm independent, invariant under time reversal and cannot be orthonormal. CLVs can thus give more detailed information about the expansion and contraction directions of the flow than the Lyapunov vector bases, which are instead always orthogonal. We suggest a definition of Hyperbolic Covariant Coherent Structures (HCCSs, which can be defined on the scalar field representing the angle between the CLVs. HCCSs can be defined for every time instant and could be useful to understand the long-term behavior of particle tracers. We consider three examples: a simple autonomous Hamiltonian system, as well as the non-autonomous “double gyre” and Bickley jet, to see how well the angle is able to describe particular patterns and barriers. We compare the results from the HCCSs with other coherent patterns defined on finite time by the Finite Time Lyapunov Exponents (FTLEs, to see how the behaviors of these structures change asymptotically.
Near-perfect broadband absorption from hyperbolic metamaterial nanoparticles
Riley, Conor T.; Smalley, Joseph S. T.; Brodie, Jeffrey R. J.; Fainman, Yeshaiahu; Sirbuly, Donald J.; Liu, Zhaowei
2017-02-01
Broadband absorbers are essential components of many light detection, energy harvesting, and camouflage schemes. Current designs are either bulky or use planar films that cause problems in cracking and delamination during flexing or heating. In addition, transferring planar materials to flexible, thin, or low-cost substrates poses a significant challenge. On the other hand, particle-based materials are highly flexible and can be transferred and assembled onto a more desirable substrate but have not shown high performance as an absorber in a standalone system. Here, we introduce a class of particle absorbers called transferable hyperbolic metamaterial particles (THMMP) that display selective, omnidirectional, tunable, broadband absorption when closely packed. This is demonstrated with vertically aligned hyperbolic nanotube (HNT) arrays composed of alternating layers of aluminum-doped zinc oxide and zinc oxide. The broadband absorption measures >87% from 1,200 nm to over 2,200 nm with a maximum absorption of 98.1% at 1,550 nm and remains large for high angles. Furthermore, we show the advantages of particle-based absorbers by transferring the HNTs to a polymer substrate that shows excellent mechanical flexibility and visible transparency while maintaining near-perfect absorption in the telecommunications region. In addition, other material systems and geometries are proposed for a wider range of applications.
Realization of mid-infrared graphene hyperbolic metamaterials
Chang, You-Chia; Liu, Che-Hung; Liu, Chang-Hua; Zhang, Siyuan; Marder, Seth R.; Narimanov, Evgenii E.; Zhong, Zhaohui; Norris, Theodore B.
2016-02-01
While metal is the most common conducting constituent element in the fabrication of metamaterials, graphene provides another useful building block, that is, a truly two-dimensional conducting sheet whose conductivity can be controlled by doping. Here we report the experimental realization of a multilayer structure of alternating graphene and Al2O3 layers, a structure similar to the metal-dielectric multilayers commonly used in creating visible wavelength hyperbolic metamaterials. Chemical vapour deposited graphene rather than exfoliated or epitaxial graphene is used, because layer transfer methods are easily applied in fabrication. We employ a method of doping to increase the layer conductivity, and our analysis shows that the doped chemical vapour deposited graphene has good optical properties in the mid-infrared range. We therefore design the metamaterial for mid-infrared operation; our characterization with an infrared ellipsometer demonstrates that the metamaterial experiences an optical topological transition from elliptic to hyperbolic dispersion at a wavelength of 4.5 μm.
An adaptive complex network model for brain functional networks.
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Ignacio J Gomez Portillo
Full Text Available Brain functional networks are graph representations of activity in the brain, where the vertices represent anatomical regions and the edges their functional connectivity. These networks present a robust small world topological structure, characterized by highly integrated modules connected sparsely by long range links. Recent studies showed that other topological properties such as the degree distribution and the presence (or absence of a hierarchical structure are not robust, and show different intriguing behaviors. In order to understand the basic ingredients necessary for the emergence of these complex network structures we present an adaptive complex network model for human brain functional networks. The microscopic units of the model are dynamical nodes that represent active regions of the brain, whose interaction gives rise to complex network structures. The links between the nodes are chosen following an adaptive algorithm that establishes connections between dynamical elements with similar internal states. We show that the model is able to describe topological characteristics of human brain networks obtained from functional magnetic resonance imaging studies. In particular, when the dynamical rules of the model allow for integrated processing over the entire network scale-free non-hierarchical networks with well defined communities emerge. On the other hand, when the dynamical rules restrict the information to a local neighborhood, communities cluster together into larger ones, giving rise to a hierarchical structure, with a truncated power law degree distribution.
Cosmology in the laboratory: An analogy between hyperbolic metamaterials and the Milne universe
Figueiredo, David; Moraes, Fernando; Fumeron, Sébastien; Berche, Bertrand
2017-11-01
This article shows that the compactified Milne universe geometry, a toy model for the big crunch/big bang transition, can be realized in hyperbolic metamaterials, a new class of nanoengineered systems which have recently found its way as an experimental playground for cosmological ideas. On one side, Klein-Gordon particles, as well as tachyons, are used as probes of the Milne geometry. On the other side, the propagation of light in two versions of a liquid crystal-based metamaterial provides the analogy. It is shown that ray and wave optics in the metamaterial mimic, respectively, the classical trajectories and wave function propagation, of the Milne probes, leading to the exciting perspective of realizing experimental tests of particle tunneling through the cosmic singularity, for instance.
RDTM solution of Caputo time fractional-order hyperbolic telegraph equation
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Vineet K. Srivastava
2013-03-01
Full Text Available In this study, a mathematical model has been developed for the second order hyperbolic one-dimensional time fractional Telegraph equation (TFTE. The fractional derivative has been described in the Caputo sense. The governing equations have been solved by a recent reliable semi-analytic method known as the reduced differential transformation method (RDTM. The method is a powerful mathematical technique for solving wide range of problems. Using RDTM method, it is possible to find exact solution as well as closed approximate solution of any ordinary or partial differential equation. Three numerical examples of TFTE have been provided in order to check the effectiveness, accuracy and convergence of the method. The computed results are also depicted graphically.
Hyperbolic Cosine–Exponentiated Exponential Lifetime Distribution and its Application in Reliability
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Omid Kharazmi
2017-02-01
Full Text Available Recently, Kharazmi and Saadatinik (2016 introduced a new family of lifetime distributions called hyperbolic cosine – F (HCF distribution. In the present paper, it is focused on a special case of HCF family with exponentiated exponential distribution as a baseline distribution (HCEE. Various properties of the proposed distribution including explicit expressions for the moments, quantiles, mode, moment generating function, failure rate function, mean residual lifetime, order statistics and expression of the entropy are derived. Estimating parameters of HCEE distribution are obtained by eight estimation methods: maximum likelihood, Bayesian, maximum product of spacings, parametric bootstrap, non-parametric bootstrap, percentile, least-squares and weighted least-squares. A simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators. Finally, one real data set has been analyzed for illustrative purposes and it is observed that the proposed model ﬁts better than Weibull, gamma and generalized exponential distributions.
Predicting the future completing models of observed complex systems
Abarbanel, Henry
2013-01-01
Predicting the Future: Completing Models of Observed Complex Systems provides a general framework for the discussion of model building and validation across a broad spectrum of disciplines. This is accomplished through the development of an exact path integral for use in transferring information from observations to a model of the observed system. Through many illustrative examples drawn from models in neuroscience, fluid dynamics, geosciences, and nonlinear electrical circuits, the concepts are exemplified in detail. Practical numerical methods for approximate evaluations of the path integral are explored, and their use in designing experiments and determining a model's consistency with observations is investigated. Using highly instructive examples, the problems of data assimilation and the means to treat them are clearly illustrated. This book will be useful for students and practitioners of physics, neuroscience, regulatory networks, meteorology and climate science, network dynamics, fluid dynamics, and o...
The semiotics of control and modeling relations in complex systems.
Joslyn, C
2001-01-01
We provide a conceptual analysis of ideas and principles from the systems theory discourse which underlie Pattee's semantic or semiotic closure, which is itself foundational for a school of theoretical biology derived from systems theory and cybernetics, and is now being related to biological semiotics and explicated in the relational biological school of Rashevsky and Rosen. Atomic control systems and models are described as the canonical forms of semiotic organization, sharing measurement relations, but differing topologically in that control systems are circularly and models linearly related to their environments. Computation in control systems is introduced, motivating hierarchical decomposition, hybrid modeling and control systems, and anticipatory or model-based control. The semiotic relations in complex control systems are described in terms of relational constraints, and rules and laws are distinguished as contingent and necessary functional entailments, respectively. Finally, selection as a meta-level of constraint is introduced as the necessary condition for semantic relations in control systems and models.
Singh, Kirmender; Bhattacharyya, A. B.
2017-03-01
Gummel Symmetry Test (GST) has been a benchmark industry standard for MOSFET models and is considered as one of important tests by the modeling community. BSIM4 MOSFET model fails to pass GST as the drain current equation is not symmetrical because drain and source potentials are not referenced to bulk. BSIM6 MOSFET model overcomes this limitation by taking all terminal biases with reference to bulk and using proper velocity saturation (v -E) model. The drain current equation in BSIM6 is charge based and continuous in all regions of operation. It, however, adopts a complicated method to compute source and drain charges. In this work we propose to use conventional charge based method formulated by Enz for obtaining simpler analytical drain current expression that passes GST. For this purpose we adopt two steps: (i) In the first step we use a modified first-order hyperbolic v -E model with adjustable coefficients which is integrable, simple and accurate, and (ii) In the second we use a multiplying factor in the modified first-order hyperbolic v -E expression to obtain correct monotonic asymptotic behavior around the origin of lateral electric field. This factor is of empirical form, which is a function of drain voltage (vd) and source voltage (vs) . After considering both the above steps we obtain drain current expression whose accuracy is similar to that obtained from second-order hyperbolic v -E model. In modified first-order hyperbolic v -E expression if vd and vs is replaced by smoothing functions for the effective drain voltage (vdeff) and effective source voltage (vseff), it will as well take care of discontinuity between linear to saturation regions of operation. The condition of symmetry is shown to be satisfied by drain current and its higher order derivatives, as both of them are odd functions and their even order derivatives smoothly pass through the origin. In strong inversion region and technology node of 22 nm the GST is shown to pass till sixth
An Adaptive Finite Difference Method for Hyperbolic Systems in OneSpace Dimension
Energy Technology Data Exchange (ETDEWEB)
Bolstad, John H. [Stanford Univ., CA (United States); Univ. of California, Berkeley, CA (United States)
1982-06-01
Many problems of physical interest have solutions which are generally quite smooth in a large portion of the region of interest, but have local phenomena such as shocks, discontinuities or large gradients which require much more accurate approximations or finer grids for reasonable accuracy. Examples are atmospheric fronts, ocean currents, and geological discontinuities. In this thesis we develop and partially analyze an adaptive finite difference mesh refinement algorithm for the initial boundary value problem for hyperbolic systems in one space dimension. The method uses clusters of uniform grids which can ''move'' along with pulses or steep gradients appearing in the calculation, and which are superimposed over a uniform coarse grid. Such refinements are created, destroyed, merged, separated, recursively nested or moved based on estimates of the local truncation error. We use a four-way linked tree and sequentially allocated deques (double-ended queues) to perform these operations efficiently. The local truncation error in the interior of the region is estimated using a three-step Richardson extrapolation procedure, which can also be considered a deferred correction method. At the boundaries we employ differences to estimate the error. Our algorithm was implemented using a portable, extensible Fortran preprocessor, to which we added records and pointers. The method is applied to three model problems: the first order wave equation, the second order wave equation, and the inviscid Burgers equation. For the first two model problems our algorithm is shown to be three to five times more efficient (in computing time) than the use of a uniform coarse mesh, for the same accuracy. Furthermore, to our knowledge, our algorithm is the only one which adaptively treats time-dependent boundary conditions for hyperbolic systems.
A corticothalamic circuit model for sound identification in complex scenes.
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Gonzalo H Otazu
Full Text Available The identification of the sound sources present in the environment is essential for the survival of many animals. However, these sounds are not presented in isolation, as natural scenes consist of a superposition of sounds originating from multiple sources. The identification of a source under these circumstances is a complex computational problem that is readily solved by most animals. We present a model of the thalamocortical circuit that performs level-invariant recognition of auditory objects in complex auditory scenes. The circuit identifies the objects present from a large dictionary of possible elements and operates reliably for real sound signals with multiple concurrently active sources. The key model assumption is that the activities of some cortical neurons encode the difference between the observed signal and an internal estimate. Reanalysis of awake auditory cortex recordings revealed neurons with patterns of activity corresponding to such an error signal.
Fundamentals of complex networks models, structures and dynamics
Chen, Guanrong; Li, Xiang
2014-01-01
Complex networks such as the Internet, WWW, transportationnetworks, power grids, biological neural networks, and scientificcooperation networks of all kinds provide challenges for futuretechnological development. In particular, advanced societies havebecome dependent on large infrastructural networks to an extentbeyond our capability to plan (modeling) and to operate (control).The recent spate of collapses in power grids and ongoing virusattacks on the Internet illustrate the need for knowledge aboutmodeling, analysis of behaviors, optimized planning and performancecontrol in such networks. F
A computational framework for modeling targets as complex adaptive systems
Santos, Eugene; Santos, Eunice E.; Korah, John; Murugappan, Vairavan; Subramanian, Suresh
2017-05-01
Modeling large military targets is a challenge as they can be complex systems encompassing myriad combinations of human, technological, and social elements that interact, leading to complex behaviors. Moreover, such targets have multiple components and structures, extending across multiple spatial and temporal scales, and are in a state of change, either in response to events in the environment or changes within the system. Complex adaptive system (CAS) theory can help in capturing the dynamism, interactions, and more importantly various emergent behaviors, displayed by the targets. However, a key stumbling block is incorporating information from various intelligence, surveillance and reconnaissance (ISR) sources, while dealing with the inherent uncertainty, incompleteness and time criticality of real world information. To overcome these challenges, we present a probabilistic reasoning network based framework called complex adaptive Bayesian Knowledge Base (caBKB). caBKB is a rigorous, overarching and axiomatic framework that models two key processes, namely information aggregation and information composition. While information aggregation deals with the union, merger and concatenation of information and takes into account issues such as source reliability and information inconsistencies, information composition focuses on combining information components where such components may have well defined operations. Since caBKBs can explicitly model the relationships between information pieces at various scales, it provides unique capabilities such as the ability to de-aggregate and de-compose information for detailed analysis. Using a scenario from the Network Centric Operations (NCO) domain, we will describe how our framework can be used for modeling targets with a focus on methodologies for quantifying NCO performance metrics.
CFD Modeling of Local Scour under Complex Free Surface Flow
Bihs, Hans; Ahmad, Nadeem; Kamath, Arun; Arntsen, Øivind A.
2017-04-01
In the present study the open-source three-dimensional numerical model REEF3D is used to calculate the complex free surface flow over a spillway, the corresponding hydraulic jump downstream of the spillway and the resulting local scour. The numerical results are compared with experimental data. The transcritical flow changes from supercritical to subcritical after the hydraulic structure, which results in the hydraulic jump. The flow of the hydraulic jump is characterised by the its violent nature and the large amount of turbulence production. While the downstream area of a spillway is typically protected by a concrete apron, scour can still occur downstream of this protection. REEF3D has advanced interface capturing capabilities, with which it is possible to simulate the complex free surface dynamics. With the level set method free surface is modeled as the zero level set of a scalar signed distance function. The flow velocities are calculated together with the pressure on a staggered grid, ensuring a tight velocity-pressure coupling. Complex geometries are modeled with a ghost cell immersed boundary method. The convective terms of the momentum equations, the level set function and the equations of the k-ω turbulence model are discretized with the fifth-order finite difference WENO scheme. Parallelization of the numerical scheme is achieved by using the domain decomposition framework together with the MPI library. The topography of the sediment bed is implicitly described by a level set function. Based on bedload and suspended load transport formulations, the sediment continuity defect in the bed cells is converted into the rate of change of the vertical bed elevation. This strategy has two major advantages: the topology is a well defined surface when calculating the incipient motion on the sloping bed and the sand avalanche. In addition, the numerically error prone re-meshing can be avoided, because the complex boundary surface is accounted for by the immersed
MULTILEVEL RECURRENT MODEL FOR HIERARCHICAL CONTROL OF COMPLEX REGIONAL SECURITY
Directory of Open Access Journals (Sweden)
Andrey V. Masloboev
2014-11-01
Full Text Available Subject of research. The research goal and scope are development of methods and software for mathematical and computer modeling of the regional security information support systems as multilevel hierarchical systems. Such systems are characterized by loosely formalization, multiple-aspect of descendent system processes and their interconnectivity, high level dynamics and uncertainty. The research methodology is based on functional-target approach and principles of multilevel hierarchical system theory. The work considers analysis and structural-algorithmic synthesis problem-solving of the multilevel computer-aided systems intended for management and decision-making information support in the field of regional security. Main results. A hierarchical control multilevel model of regional socio-economic system complex security has been developed. The model is based on functional-target approach and provides both formal statement and solving, and practical implementation of the automated information system structure and control algorithms synthesis problems of regional security management optimal in terms of specified criteria. An approach for intralevel and interlevel coordination problem-solving in the multilevel hierarchical systems has been proposed on the basis of model application. The coordination is provided at the expense of interconnection requirements satisfaction between the functioning quality indexes (objective functions, which are optimized by the different elements of multilevel systems. That gives the possibility for sufficient coherence reaching of the local decisions, being made on the different control levels, under decentralized decision-making and external environment high dynamics. Recurrent model application provides security control mathematical models formation of regional socioeconomic systems, functioning under uncertainty. Practical relevance. The model implementation makes it possible to automate synthesis realization of
The Complex Action Recognition via the Correlated Topic Model
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Hong-bin Tu
2014-01-01
Full Text Available Human complex action recognition is an important research area of the action recognition. Among various obstacles to human complex action recognition, one of the most challenging is to deal with self-occlusion, where one body part occludes another one. This paper presents a new method of human complex action recognition, which is based on optical flow and correlated topic model (CTM. Firstly, the Markov random field was used to represent the occlusion relationship between human body parts in terms of an occlusion state variable. Secondly, the structure from motion (SFM is used for reconstructing the missing data of point trajectories. Then, we can extract the key frame based on motion feature from optical flow and the ratios of the width and height are extracted by the human silhouette. Finally, we use the topic model of correlated topic model (CTM to classify action. Experiments were performed on the KTH, Weizmann, and UIUC action dataset to test and evaluate the proposed method. The compared experiment results showed that the proposed method was more effective than compared methods.
West Closure Complex Pump Intake Model, New Orleans, Louisiana
2013-02-01
in Q/(d5 g)1/2 of 1.0. S /d = 1.3. No information on velocity uniformity at the pump impeller was available. 7. The Davis Pond pump station in New...ER D C/ CH L TR -1 3 -1 West Closure Complex Pump Intake Model, New Orleans, Louisiana C oa st al a n d H yd ra u lic s La b or at...12 2.1 Design of the pump station model
Extending a configuration model to find communities in complex networks
Jin, Di; He, Dongxiao; Hu, Qinghua; Baquero, Carlos; Yang, Bo
2013-09-01
Discovery of communities in complex networks is a fundamental data analysis task in various domains. Generative models are a promising class of techniques for identifying modular properties from networks, which has been actively discussed recently. However, most of them cannot preserve the degree sequence of networks, which will distort the community detection results. Rather than using a blockmodel as most current works do, here we generalize a configuration model, namely, a null model of modularity, to solve this problem. Towards decomposing and combining sub-graphs according to the soft community memberships, our model incorporates the ability to describe community structures, something the original model does not have. Also, it has the property, as with the original model, that it fixes the expected degree sequence to be the same as that of the observed network. We combine both the community property and degree sequence preserving into a single unified model, which gives better community results compared with other models. Thereafter, we learn the model using a technique of nonnegative matrix factorization and determine the number of communities by applying consensus clustering. We test this approach both on synthetic benchmarks and on real-world networks, and compare it with two similar methods. The experimental results demonstrate the superior performance of our method over competing methods in detecting both disjoint and overlapping communities.
A Simple Generation Technique of Complex Geotechnical Computational Model
Directory of Open Access Journals (Sweden)
Hang Lin
2013-01-01
Full Text Available Given that FLAC3D (a geotechnical calculation software is difficult to use for building large, complex, and three-dimensional mining models, the current study proposes a fast and a convenient modeling technique that combines the unique advantages of FLAC3D in numerical calculation and those of SURPAC (a mine design software in three-dimensional modeling, and the interface program was compiled. First, the relationship between the FLAC3D and the SURPAC unit data was examined, and the transformation technique between the data was given. Then, the interface program that transforms the mine design model to calculate the model was compiled using FORTRAN, and the specific steps of the program implementation were described using a large iron and copper mine modeling example. The results show that the proposed transformation technique and its corresponding interface program transformed the SURPAC model into the FLAC3D model, which expedited FLAC3D modeling, verified the validity and feasibility of the transformation technique, and expanded the application spaces of FLAC3D and SURPAC.
Hydrodynamic and kinetic modelling of complex radio-frequency plasmas
Energy Technology Data Exchange (ETDEWEB)
Goedheer, W J; Venema, J [FOM Institute for Plasma Physics ' Rijnhuizen' , Association EURATOM-FOM, Trilateral Euregio Cluster, PO Box 1207, 3430 BE Nieuwegein (Netherlands); Land, V, E-mail: W.J.Goedheer@rijnhuizen.n [Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, TX 76798 (United States)
2009-10-07
In this paper hydrodynamic and kinetic approaches to model low-pressure capacitively coupled complex radio-frequency discharges are discussed and applied to discharges under micro-gravity. Complex plasmas contain dust grains with a large negative charge and are characterized by a strong coupling between the properties of the plasma and those of the dust grains. After a discussion of the physics and methods involved, examples are presented from modelling of experiments under micro-gravity in the PKE-Nefedov reactor on board the International Space Station. These discharges are simulated with a 2D cylindrically symmetric hydrodynamic model. Kinetic effects are studied with a 1D particle-in-cell plus Monte Carlo model in which capture and scattering by dust grains is included. Since experiments are often performed at low pressures, the electron energy distribution function is no longer determined by the local plasma properties. This has consequences for the charging of the dust. Results of simulations with this model are compared with the hydrodynamic results. In addition, we address the behaviour of the dust charge in decaying plasmas.
A 2-D model for friction of complex anisotropic surfaces
Costagliola, Gianluca; Bosia, Federico; Pugno, Nicola M.
2018-03-01
The friction force observed at macroscale is the result of interactions at various lower length scales that are difficult to model in a combined manner. For this reason, simplified approaches are required, depending on the specific aspect to be investigated. In particular, the dimensionality of the system is often reduced, especially in models designed to provide a qualitative description of frictional properties of elastic materials, e.g. the spring-block model. In this paper, we implement for the first time a two dimensional extension of the spring-block model, applying it to structured surfaces and investigating by means of numerical simulations the frictional behaviour of a surface in the presence of features like cavities, pillars or complex anisotropic structures. We show how friction can be effectively tuned by appropriate design of such surface features.
Directory of Open Access Journals (Sweden)
Jiuqing Cheng
Full Text Available The single parameter hyperbolic model has been frequently used to describe value discounting as a function of time and to differentiate substance abusers and non-clinical participants with the model's parameter k. However, k says little about the mechanisms underlying the observed differences. The present study evaluates several alternative models with the purpose of identifying whether group differences stem from differences in subjective valuation, and/or time perceptions. Using three two-parameter models, plus secondary data analyses of 14 studies with 471 indifference point curves, results demonstrated that adding a valuation, or a time perception function led to better model fits. However, the gain in fit due to the flexibility granted by a second parameter did not always lead to a better understanding of the data patterns and corresponding psychological processes. The k parameter consistently indexed group and context (magnitude differences; it is thus a mixed measure of person and task level effects. This was similar for a parameter meant to index payoff devaluation. A time perception parameter, on the other hand, fluctuated with contexts in a non-predicted fashion and the interpretation of its values was inconsistent with prior findings that supported enlarged perceived delays for substance abusers compared to controls. Overall, the results provide mixed support for hyperbolic models of intertemporal choice in terms of the psychological meaning afforded by their parameters.
Issues of diffuse pollution model complexity arising from performance benchmarking
Directory of Open Access Journals (Sweden)
2007-01-01
Full Text Available Flow and nitrate dynamics were simulated in two catchments, the River Aire in northern England and the River Ythan in north-east Scotland. In the case of the Aire, a diffuse pollution model was coupled with a river quality model (CASCADE-QUESTOR; in the study of the Ythan, an integrated model (SWAT was used. In each study, model performance was evaluated for differing levels of spatial representation in input data sets (rainfall, soils and land use. In respect of nitrate concentrations, the performance of the models was compared with that of a regression model based on proportions of land cover. The overall objective was to assess the merits of spatially distributed input data sets. In both catchments, specific measures of quantitative performance showed that models using the most detailed available input data contributed, at best, only a marginal improvement over simpler implementations. Hence, the level of complexity used in input data sets has to be determined, not only on multiple criteria of quantitative performance but also on qualitative assessments, reflecting the specific context of the model application and the current and likely future needs of end-users.
Semiotic aspects of control and modeling relations in complex systems
Energy Technology Data Exchange (ETDEWEB)
Joslyn, C.
1996-08-01
A conceptual analysis of the semiotic nature of control is provided with the goal of elucidating its nature in complex systems. Control is identified as a canonical form of semiotic relation of a system to its environment. As a form of constraint between a system and its environment, its necessary and sufficient conditions are established, and the stabilities resulting from control are distinguished from other forms of stability. These result from the presence of semantic coding relations, and thus the class of control systems is hypothesized to be equivalent to that of semiotic systems. Control systems are contrasted with models, which, while they have the same measurement functions as control systems, do not necessarily require semantic relations because of the lack of the requirement of an interpreter. A hybrid construction of models in control systems is detailed. Towards the goal of considering the nature of control in complex systems, the possible relations among collections of control systems are considered. Powers arguments on conflict among control systems and the possible nature of control in social systems are reviewed, and reconsidered based on our observations about hierarchical control. Finally, we discuss the necessary semantic functions which must be present in complex systems for control in this sense to be present at all.
Experimental and numerical modeling of wind flow over complex topography
Rasouli, Ashkan
Wind mapping is of utmost importance in various wind engineering, wind environment, and wind energy applications. The available wind atlases usually provide wind data with low resolutions relative to the wind turbine height and size and usually neglect the effect of topographic features with relatively large or sudden changes in elevation. Developing a cost effective methodology to predict the wind patterns and to obtain wind maps over any topographic terrain is absolutely needed for wind turbine/farm siting. As the previous analytic and empirical attempts to resolve the flow over topographic features were limited to basic geometries that hardly exist in nature, applying Particle Image Velocimetry (PIV) measurement techniques in wind tunnel and Computational Fluid Dynamics (CFD) techniques in numerical simulation of the flow over topography seems to be the best alternative solution to the problem. PIV measurements and CFD simulations are carried out on a 1:3000 scale model of complex topographic area. Three distinct topographic features are investigated: a valley, a ridge and a hill. The PIV measurements compare well with hot-wire based mean velocity profiles for the three cases. Moreover, the turbulence intensity profiles match well for flow regions without recirculation. The ridge wake region shows discrepancies between the two techniques which are attributed to the complexity of the flow in this region and limitations of both techniques. A procedure incorporating Geographic Information System (GIS) and surface modeling techniques is introduced to build the CFD model of a complex terrain starting from the existing topography maps with desired resolutions. Moreover, a new approach is made to simulate the terrain roughness up to ultimate roughness heights, by implementing arrays of bell-shaped roughness elements in the CFD model. The velocity profiles and velocity vectors were compared with the PIV measurements and were found to be in good agreement near the ground
Sensitivity Analysis in a Complex Marine Ecological Model
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Marcos D. Mateus
2015-05-01
Full Text Available Sensitivity analysis (SA has long been recognized as part of best practices to assess if any particular model can be suitable to inform decisions, despite its uncertainties. SA is a commonly used approach for identifying important parameters that dominate model behavior. As such, SA address two elementary questions in the modeling exercise, namely, how sensitive is the model to changes in individual parameter values, and which parameters or associated processes have more influence on the results. In this paper we report on a local SA performed on a complex marine biogeochemical model that simulates oxygen, organic matter and nutrient cycles (N, P and Si in the water column, and well as the dynamics of biological groups such as producers, consumers and decomposers. SA was performed using a “one at a time” parameter perturbation method, and a color-code matrix was developed for result visualization. The outcome of this study was the identification of key parameters influencing model performance, a particularly helpful insight for the subsequent calibration exercise. Also, the color-code matrix methodology proved to be effective for a clear identification of the parameters with most impact on selected variables of the model.
Integrated Bayesian network framework for modeling complex ecological issues.
Johnson, Sandra; Mengersen, Kerrie
2012-07-01
The management of environmental problems is multifaceted, requiring varied and sometimes conflicting objectives and perspectives to be considered. Bayesian network (BN) modeling facilitates the integration of information from diverse sources and is well suited to tackling the management challenges of complex environmental problems. However, combining several perspectives in one model can lead to large, unwieldy BNs that are difficult to maintain and understand. Conversely, an oversimplified model may lead to an unrealistic representation of the environmental problem. Environmental managers require the current research and available knowledge about an environmental problem of interest to be consolidated in a meaningful way, thereby enabling the assessment of potential impacts and different courses of action. Previous investigations of the environmental problem of interest may have already resulted in the construction of several disparate ecological models. On the other hand, the opportunity may exist to initiate this modeling. In the first instance, the challenge is to integrate existing models and to merge the information and perspectives from these models. In the second instance, the challenge is to include different aspects of the environmental problem incorporating both the scientific and management requirements. Although the paths leading to the combined model may differ for these 2 situations, the common objective is to design an integrated model that captures the available information and research, yet is simple to maintain, expand, and refine. BN modeling is typically an iterative process, and we describe a heuristic method, the iterative Bayesian network development cycle (IBNDC), for the development of integrated BN models that are suitable for both situations outlined above. The IBNDC approach facilitates object-oriented BN (OOBN) modeling, arguably viewed as the next logical step in adaptive management modeling, and that embraces iterative development
Stability of rotor systems: A complex modelling approach
DEFF Research Database (Denmark)
Kliem, Wolfhard; Pommer, Christian; Stoustrup, Jakob
1998-01-01
The dynamics of a large class of rotor systems can be modelled by a linearized complex matrix differential equation of second order, Mz + (D + iG)(z) over dot + (K + iN)z = 0, where the system matrices M, D, G, K and N are real symmetric. Moreover M and K are assumed to be positive definite and D......, G and N to be positive semidefinite. The complex setting is equivalent to twice as large a system of second order with real matrices. It is well known that rotor systems can exhibit instability for large angular velocities due to internal damping, unsymmetrical steam flow in turbines, or imperfect...... lubrication in the rotor bearings. Theoretically, all information on the stability of the system can be obtained by applying the Routh-Hurwitz criterion. From a practical point of view, however, it is interesting to find stability criteria which are related in a simple way to the properties of the system...
On the complexity of statistical models admitting correlations
Energy Technology Data Exchange (ETDEWEB)
Cafaro, Carlo; Mancini, Stefano, E-mail: carlo.cafaro@unicam.i, E-mail: stefano.mancini@unicam.i [Dipartimento di Fisica, Universita di Camerino, I-62032 Camerino (Italy)
2010-09-15
We compute the asymptotic temporal behavior of the dynamical complexity associated with the maximum probability trajectories on Gaussian statistical manifolds in the presence of correlations between the variables labeling the macrostates of the system. The algorithmic structure of our asymptotic computations is presented and special focus is devoted to the diagonalization procedure that allows us to simplify the problem in a remarkable way. We observe a power-law decay of the information geometric complexity at a rate determined by the correlation coefficient. We conclude that macro-correlations lead to the emergence of an asymptotic information geometric compression of the statistical macrostates explored on the configuration manifold of the model in its evolution between the initial and final macrostates.
Diffusion in higher dimensional SYK model with complex fermions
Cai, Wenhe; Ge, Xian-Hui; Yang, Guo-Hong
2018-01-01
We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential μ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.
Boundary conformal anomalies on hyperbolic spaces and Euclidean balls
Rodriguez-Gomez, Diego; Russo, Jorge G.
2017-12-01
We compute conformal anomalies for conformal field theories with free conformal scalars and massless spin 1/2 fields in hyperbolic space ℍ d and in the ball B^d , for 2≤d≤7. These spaces are related by a conformal transformation. In even dimensional spaces, the conformal anomalies on ℍ2 n and B^{2n} are shown to be identical. In odd dimensional spaces, the conformal anomaly on B^{2n+1} comes from a boundary contribution, which exactly coincides with that of ℍ2 n + 1 provided one identifies the UV short-distance cutoff on B^{2n+1} with the inverse large distance IR cutoff on ℍ2 n + 1, just as prescribed by the conformal map. As an application, we determine, for the first time, the conformal anomaly coefficients multiplying the Euler characteristic of the boundary for scalars and half-spin fields with various boundary conditions in d = 5 and d = 7.
Fabrication of Hyperbolic Metamaterials using Atomic Layer Deposition
DEFF Research Database (Denmark)
Shkondin, Evgeniy
dielectric coatings has been implemented in optical experiment where the effective medium approximation theory (EMA) was tested. Flat dielectric multilayers with strict thicknesses of either 10 or 20 nm of each individual layer, were deposited on Si substrates and characterized using x-ray photoelectron...... final structures using selective Si etch were addressed. Fabrication of HMMs requires the implementation of plasmonic components, and traditionally noble metals are used for such purposes due to their abundant free electrons in the conduction band. However, their large real and imaginary parts of the permittivity...... the concept of hyperbolic medium is explained. Metamaterial design, implementation as well as possible applications are reviewed. Electrodynamically, HMMs are described by a dielectric permittivity tensor ε with components of opposite signs (e.g. εx = εy 0). HMMs possess unusually high wavevector...
Simple and High-Accurate Schemes for Hyperbolic Conservation Laws
Directory of Open Access Journals (Sweden)
Renzhong Feng
2014-01-01
Full Text Available The paper constructs a class of simple high-accurate schemes (SHA schemes with third order approximation accuracy in both space and time to solve linear hyperbolic equations, using linear data reconstruction and Lax-Wendroff scheme. The schemes can be made even fourth order accurate with special choice of parameter. In order to avoid spurious oscillations in the vicinity of strong gradients, we make the SHA schemes total variation diminishing ones (TVD schemes for short by setting flux limiter in their numerical fluxes and then extend these schemes to solve nonlinear Burgers’ equation and Euler equations. The numerical examples show that these schemes give high order of accuracy and high resolution results. The advantages of these schemes are their simplicity and high order of accuracy.
Carleman estimates and applications to inverse problems for hyperbolic systems
Bellassoued, Mourad
2017-01-01
This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions. The formulation is different from that of Dirichlet-to-Neumann maps and can often prove the global uniqueness and Lipschitz stability even with a single measurement. These types of inverse problems include coefficient inverse problems of determining physical parameters in inhomogeneous media that appear in many applications related to electromagnetism, elasticity, and related phenomena. Although the methodology was created in 1981 by Bukhgeim and Klibanov, its comprehensive development has been accomplished only recently. In spite of the wide applicability of the method, there are few monographs focusing on combined accounts of Carleman estimates and applications to inverse problems. The aim in this book is to fill that gap. The basic tool is Carleman estimates, the theory of wh...
Level crossings and turning points of random hyperbolic polynomials
Directory of Open Access Journals (Sweden)
K. Farahmand
1999-01-01
Full Text Available In this paper, we show that the asymptotic estimate for the expected number of K-level crossings of a random hyperbolic polynomial a1sinhx+a2sinh2x+⋯+ansinhnx, where aj(j=1,2,…,n are independent normally distributed random variables with mean zero and variance one, is (1/πlogn. This result is true for all K independent of x, provided K≡Kn=O(n. It is also shown that the asymptotic estimate of the expected number of turning points for the random polynomial a1coshx+a2cosh2x+⋯+ancoshnx, with aj(j=1,2,…,n as before, is also (1/πlogn.
Computation of Quasiperiodic Normally Hyperbolic Invariant Tori: Rigorous Results
Canadell, Marta; Haro, Àlex
2017-12-01
The development of efficient methods for detecting quasiperiodic oscillations and computing the corresponding invariant tori is a subject of great importance in dynamical systems and their applications in science and engineering. In this paper, we prove the convergence of a new Newton-like method for computing quasiperiodic normally hyperbolic invariant tori carrying quasiperiodic motion in smooth families of real-analytic dynamical systems. The main result is stated as an a posteriori KAM-like theorem that allows controlling the inner dynamics on the torus with appropriate detuning parameters, in order to obtain a prescribed quasiperiodic motion. The Newton-like method leads to several fast and efficient computational algorithms, which are discussed and tested in a companion paper (Canadell and Haro in J Nonlinear Sci, 2017. doi: 10.1007/s00332-017-9388-z), in which new mechanisms of breakdown are presented.
Topological vertex, string amplitudes and spectral functions of hyperbolic geometry
Energy Technology Data Exchange (ETDEWEB)
Guimaraes, M.E.X.; Rosa, T.O. [Universidade Federal Fluminense, Instituto de Fisica, Av. Gal. Milton Tavares de Souza, s/n, CEP 24210-346, Niteroi, RJ (Brazil); Luna, R.M. [Universidade Estadual de Londrina, Departamento de Fisica, Caixa Postal 6001, Londrina, Parana (Brazil)
2014-05-15
We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a new straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to the partition functions of Lagrangian branes, refined vertex and open string partition functions, represented by means of formal power series that encode Lie algebra properties. The common feature in our examples lies in the modular properties of the characters of certain representations of the pertinent affine Lie algebras and in the role of Selberg-type spectral functions of a hyperbolic three-geometry associated with q-series in the computation of the string amplitudes. (orig.)
Optimal boundary control and boundary stabilization of hyperbolic systems
Gugat, Martin
2015-01-01
This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary. The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization. Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples. To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled. Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.
High-Order Wave Propagation Algorithms for Hyperbolic Systems
Ketcheson, David I.
2013-01-22
We present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving Riemann problems and calculating fluctuations (not fluxes). The implementation employs weighted essentially nonoscillatory reconstruction in space and strong stability preserving Runge--Kutta integration in time. The method can be extended to arbitrarily high order of accuracy and allows a well-balanced implementation for capturing solutions of balance laws near steady state. This well-balancing is achieved through the $f$-wave Riemann solver and a novel wave-slope WENO reconstruction procedure. The wide applicability and advantageous properties of the method are demonstrated through numerical examples, including problems in nonconservative form, problems with spatially varying fluxes, and problems involving near-equilibrium solutions of balance laws.
Density Large Deviations for Multidimensional Stochastic Hyperbolic Conservation Laws
Barré, J.; Bernardin, C.; Chetrite, R.
2017-12-01
We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law. When the mobility and diffusivity matrices are proportional, i.e. an Einstein-like relation is satisfied, the problem has been solved in Bellettini and Mariani (Bull Greek Math Soc 57:31-45, 2010). When this proportionality does not hold, we compute explicitly the large deviation function for a step-like density profile, and we show that the associated optimal current has a non trivial structure. We also derive a lower bound for the large deviation function, valid for a more general weak solution, and leave the general large deviation function upper bound as a conjecture.
Roe solver with entropy corrector for uncertain hyperbolic systems
Energy Technology Data Exchange (ETDEWEB)
Tryoen, J.; Ern, A. [Univ Paris Est, CERMICS, Ecole Ponts, F-77455 Marne La Vallee 2 (France); Tryoen, J.; Le Maitre, O. [CNRS, LIMSI, F-91403 Orsay (France); Ndjinga, M. [CEA Saclay, DEN, DM2S, SFME, F-91191 Gif Sur Yvette (France)
2010-07-01
This paper deals with intrusive Galerkin projection methods with a Roe-type solver for treating uncertain hyperbolic systems using a finite volume discretization in physical space and a piecewise continuous representation at the stochastic level. The aim of this paper is to design a cost-effective adaptation of the deterministic Dubois and Mehlman corrector to avoid entropy-violating shocks in the presence of sonic points. The adaptation relies on an estimate of the eigenvalues and eigenvectors of the Galerkin Jacobian matrix of the deterministic system of the stochastic modes of the solution and on a correspondence between these approximate eigenvalues and eigenvectors for the intermediate states considered at the interface. We derive some indicators that can be used to decide where a correction is needed, thereby reducing the computational costs considerably. The effectiveness of the proposed corrector is assessed on the Burgers and Euler equations including sonic points. (authors)
Control of gain/absorption in tunable hyperbolic metamaterials.
Janaszek, Bartosz; Tyszka-Zawadzka, Anna; Szczepański, Paweł
2017-06-12
In this paper, the possibility of shaping the gain/absorption spectrum in tunable hyperbolic metamaterial (THMM) composed of subsequent layers of graphene and active/passive material by external biasing is demonstrated. For the first time it has been shown that resonance transitions between different dispersion regimes, i.e., Type I HMM→elliptic, elliptic→Type II HMM, elliptic→Type I HMM, are accompanied by interesting optical effects, such as anisotropic effective gain/absorption enhancement or electromagnetic transparency, all controllable by external voltage. We believe that this kind of tunable metamaterial could lay the foundation for a new class of active/passive media with controllable gain/absorption or electromagnetic transparency.
Critical coupling with graphene-based hyperbolic metamaterials.
Xiang, Yuanjiang; Dai, Xiaoyu; Guo, Jun; Zhang, Han; Wen, Shuangchun; Tang, Dingyuan
2014-06-27
In order to effectively realize and control the critical coupling, a graphene-based hyperbolic metamaterial has been proposed to replace the absorbing thin film in the critically coupled resonance structure. Our calculations demonstrate that the critical coupling effect (near-perfect light absorption) can be achieved at the near-infrared wavelength by using this layered structure, while the critical coupling frequency can be tuned by varying the Fermi energy level of graphene sheets via electrostatic biasing. Moreover, we show that the critical coupling frequency can be tuned by changing the thickness of the dielectric or layer number of the graphene sheets in the unit cell of the graphene-dielectric HMM. The optimization performance has also been indicated, which may offer an opportunity towards the experimental designs of high efficient graphene based critical coupling devices.
A cartesian grid embedded boundary method for hyperbolic conservation laws
Energy Technology Data Exchange (ETDEWEB)
Colella, Phillip; Graves, Daniel T.; Keen, Benjamin J.; Modiano, David
2004-10-03
We present a second-order Godunov algorithm to solve time-dependent hyperbolic systems of conservation laws on irregular domains. Our approach is based on a formally consistent discretization of the conservation laws on a finite-volume grid obtained from intersecting the domain with a Cartesian grid. We address the small-cell stability problem associated with such methods by hybridizing our conservative discretization with a stable, nonconservative discretization at irregular control volumes, and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation. The resulting method is second-order accurate in L{sup 1} for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.
IDMS: inert dark matter model with a complex singlet
Bonilla, Cesar; Sokolowska, Dorota; Darvishi, Neda; Diaz-Cruz, J. Lorenzo; Krawczyk, Maria
2016-06-01
We study an extension of the inert doublet model (IDM) that includes an extra complex singlet of the scalars fields, which we call the IDMS. In this model there are three Higgs particles, among them a SM-like Higgs particle, and the lightest neutral scalar, from the inert sector, remains a viable dark matter (DM) candidate. We assume a non-zero complex vacuum expectation value for the singlet, so that the visible sector can introduce extra sources of CP violation. We construct the scalar potential of IDMS, assuming an exact Z 2 symmetry, with the new singlet being Z 2-even, as well as a softly broken U(1) symmetry, which allows a reduced number of free parameters in the potential. In this paper we explore the foundations of the model, in particular the masses and interactions of scalar particles for a few benchmark scenarios. Constraints from collider physics, in particular from the Higgs signal observed at the Large Hadron Collider with {M}h≈ 125 {{GeV}}, as well as constraints from the DM experiments, such as relic density measurements and direct detection limits, are included in the analysis. We observe significant differences with respect to the IDM in relic density values from additional annihilation channels, interference and resonance effects due to the extended Higgs sector.
Bloch-Redfield equations for modeling light-harvesting complexes.
Jeske, Jan; Ing, David J; Plenio, Martin B; Huelga, Susana F; Cole, Jared H
2015-02-14
We challenge the misconception that Bloch-Redfield equations are a less powerful tool than phenomenological Lindblad equations for modeling exciton transport in photosynthetic complexes. This view predominantly originates from an indiscriminate use of the secular approximation. We provide a detailed description of how to model both coherent oscillations and several types of noise, giving explicit examples. All issues with non-positivity are overcome by a consistent straightforward physical noise model. Herein also lies the strength of the Bloch-Redfield approach because it facilitates the analysis of noise-effects by linking them back to physical parameters of the noise environment. This includes temporal and spatial correlations and the strength and type of interaction between the noise and the system of interest. Finally, we analyze a prototypical dimer system as well as a 7-site Fenna-Matthews-Olson complex in regards to spatial correlation length of the noise, noise strength, temperature, and their connection to the transfer time and transfer probability.
Multiagent model and mean field theory of complex auction dynamics
Chen, Qinghua; Huang, Zi-Gang; Wang, Yougui; Lai, Ying-Cheng
2015-09-01
Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena.
Modeling the Propagation of Mobile Phone Virus under Complex Network
Yang, Wei; Wei, Xi-liang; Guo, Hao; An, Gang; Guo, Lei
2014-01-01
Mobile phone virus is a rogue program written to propagate from one phone to another, which can take control of a mobile device by exploiting its vulnerabilities. In this paper the propagation model of mobile phone virus is tackled to understand how particular factors can affect its propagation and design effective containment strategies to suppress mobile phone virus. Two different propagation models of mobile phone viruses under the complex network are proposed in this paper. One is intended to describe the propagation of user-tricking virus, and the other is to describe the propagation of the vulnerability-exploiting virus. Based on the traditional epidemic models, the characteristics of mobile phone viruses and the network topology structure are incorporated into our models. A detailed analysis is conducted to analyze the propagation models. Through analysis, the stable infection-free equilibrium point and the stability condition are derived. Finally, considering the network topology, the numerical and simulation experiments are carried out. Results indicate that both models are correct and suitable for describing the spread of two different mobile phone viruses, respectively. PMID:25133209
Modeling the propagation of mobile phone virus under complex network.
Yang, Wei; Wei, Xi-liang; Guo, Hao; An, Gang; Guo, Lei; Yao, Yu
2014-01-01
Mobile phone virus is a rogue program written to propagate from one phone to another, which can take control of a mobile device by exploiting its vulnerabilities. In this paper the propagation model of mobile phone virus is tackled to understand how particular factors can affect its propagation and design effective containment strategies to suppress mobile phone virus. Two different propagation models of mobile phone viruses under the complex network are proposed in this paper. One is intended to describe the propagation of user-tricking virus, and the other is to describe the propagation of the vulnerability-exploiting virus. Based on the traditional epidemic models, the characteristics of mobile phone viruses and the network topology structure are incorporated into our models. A detailed analysis is conducted to analyze the propagation models. Through analysis, the stable infection-free equilibrium point and the stability condition are derived. Finally, considering the network topology, the numerical and simulation experiments are carried out. Results indicate that both models are correct and suitable for describing the spread of two different mobile phone viruses, respectively.
Complex Data Modeling and Computationally Intensive Statistical Methods
Mantovan, Pietro
2010-01-01
The last years have seen the advent and development of many devices able to record and store an always increasing amount of complex and high dimensional data; 3D images generated by medical scanners or satellite remote sensing, DNA microarrays, real time financial data, system control datasets. The analysis of this data poses new challenging problems and requires the development of novel statistical models and computational methods, fueling many fascinating and fast growing research areas of modern statistics. The book offers a wide variety of statistical methods and is addressed to statistici
Complex Dynamics of an Adnascent-Type Game Model
Directory of Open Access Journals (Sweden)
Baogui Xin
2008-01-01
Full Text Available The paper presents a nonlinear discrete game model for two oligopolistic firms whose products are adnascent. (In biology, the term adnascent has only one sense, “growing to or on something else,” e.g., “moss is an adnascent plant.” See Webster's Revised Unabridged Dictionary published in 1913 by C. & G. Merriam Co., edited by Noah Porter. The bifurcation of its Nash equilibrium is analyzed with Schwarzian derivative and normal form theory. Its complex dynamics is demonstrated by means of the largest Lyapunov exponents, fractal dimensions, bifurcation diagrams, and phase portraits. At last, bifurcation and chaos anticontrol of this system are studied.
The modeling of complex continua: Fundamental obstacles and grand challenges
Energy Technology Data Exchange (ETDEWEB)
1993-01-01
The research is divided into: discontinuities and adaptive computation, chaotic flows, dispersion of flow in porous media, and nonlinear waves and nonlinear materials. The research program has emphasized innovative computation and theory. The approach depends on abstracting mathematical concepts and computational methods from individual applications to a wide range of problems involving complex continua. The generic difficulties in the modeling of continua that guide this abstraction are multiple length and time scales, microstructures (bubbles, droplets, vortices, crystal defects), and chaotic or random phenomena described by a statistical formulation.
Framework for Modelling Multiple Input Complex Aggregations for Interactive Installations
DEFF Research Database (Denmark)
Padfield, Nicolas; Andreasen, Troels
2012-01-01
We describe a generalized framework as a method and design tool for creating interactive installations with a demand for exploratory meaning creation, not limited to the design stage, but extending into the stage where the installation meets participants and audience. The proposed solution is based...... on fuzzy logic and provides a method for variably balancing interaction and user input with the intention of the artist or director. An experimental design is presented, demonstrating an intuitive interface for parametric modelling of a complex aggregation function. The aggregation function unifies...
Unified Modeling of Complex Real-Time Control Systems
Hai, He; Yi-Fang, Zhong; Chi-lan, Cai
2005-01-01
Submitted on behalf of EDAA (http://www.edaa.com/); International audience; Complex real-time control system is a software dense and algorithms dense system, which needs modern software engineering techniques to design. UML is an object-oriented industrial standard modeling language, used more and more in real-time domain. This paper first analyses the advantages and problems of using UML for real-time control systems design. Then, it proposes an extension of UML-RT to support time-continuous...
The Eemian climate simulated by two models of different complexities
Nikolova, Irina; Yin, Qiuzhen; Berger, Andre; Singh, Umesh; Karami, Pasha
2013-04-01
The Eemian period, also known as MIS-5, experienced warmer than today climate, reduction in ice sheets and important sea-level rise. These interesting features have made the Eemian appropriate to evaluate climate models when forced with astronomical and greenhouse gas forcings different from today. In this work, we present the simulated Eemian climate by two climate models of different complexities, LOVECLIM (LLN Earth system model of intermediate complexity) and CCSM3 (NCAR atmosphere-ocean general circulation model). Feedbacks from sea ice, vegetation, monsoon and ENSO phenomena are discussed to explain the regional similarities/dissimilarities in both models with respect to the pre-industrial (PI) climate. Significant warming (cooling) over almost all the continents during boreal summer (winter) leads to a largely increased (reduced) seasonal contrast in the northern (southern) hemisphere, mainly due to the much higher (lower) insolation received by the whole Earth in boreal summer (winter). The arctic is warmer than at PI through the whole year, resulting from its much higher summer insolation and its remnant effect in the following fall-winter through the interactions between atmosphere, ocean and sea ice. Regional discrepancies exist in the sea-ice formation zones between the two models. Excessive sea-ice formation in CCSM3 results in intense regional cooling. In both models intensified African monsoon and vegetation feedback are responsible for the cooling during summer in North Africa and on the Arabian Peninsula. Over India precipitation maximum is found further west, while in Africa the precipitation maximum migrates further north. Trees and grassland expand north in Sahel/Sahara, trees being more abundant in the results from LOVECLIM than from CCSM3. A mix of forest and grassland occupies continents and expand deep in the high northern latitudes in line with proxy records. Desert areas reduce significantly in Northern Hemisphere, but increase in North
Socio-Environmental Resilience and Complex Urban Systems Modeling
Deal, Brian; Petri, Aaron; Pan, Haozhi; Goldenberg, Romain; Kalantari, Zahra; Cvetkovic, Vladimir
2017-04-01
The increasing pressure of climate change has inspired two normative agendas; socio-technical transitions and socio-ecological resilience, both sharing a complex-systems epistemology (Gillard et al. 2016). Socio-technical solutions include a continuous, massive data gathering exercise now underway in urban places under the guise of developing a 'smart'(er) city. This has led to the creation of data-rich environments where large data sets have become central to monitoring and forming a response to anomalies. Some have argued that these kinds of data sets can help in planning for resilient cities (Norberg and Cumming 2008; Batty 2013). In this paper, we focus on a more nuanced, ecologically based, socio-environmental perspective of resilience planning that is often given less consideration. Here, we broadly discuss (and model) the tightly linked, mutually influenced, social and biophysical subsystems that are critical for understanding urban resilience. We argue for the need to incorporate these sub system linkages into the resilience planning lexicon through the integration of systems models and planning support systems. We make our case by first providing a context for urban resilience from a socio-ecological and planning perspective. We highlight the data needs for this type of resilient planning and compare it to currently collected data streams in various smart city efforts. This helps to define an approach for operationalizing socio-environmental resilience planning using robust systems models and planning support systems. For this, we draw from our experiences in coupling a spatio-temporal land use model (the Landuse Evolution and impact Assessment Model (LEAM)) with water quality and quantity models in Stockholm Sweden. We describe the coupling of these systems models using a robust Planning Support System (PSS) structural framework. We use the coupled model simulations and PSS to analyze the connection between urban land use transformation (social) and water
Confronting perspectives: Modeling perspectival complexity in language and cognition
Directory of Open Access Journals (Sweden)
Sonja Zeman
2017-02-01
Full Text Available In search of a deeper understanding of perspective-taking, the paper aims at isolating the basic components of complex perspectivization tasks. Based on the assumption that perspective is a relational concept constituted by the dynamic relation between a conceptualizer’s point of view and a conceptualized object and, as such, a concept which is shared by both language and cognition, the paper draws a comparison between the developmental stages of cognitive perspectival capabilities, grammatical perspectivization, and viewpoint comprehension in narrative discourse. This comparison leads to a multi-stage model of degrees of perspectival complexity, whereby the most complex tasks in both language and cognition are characterized by a three-point constellation that integrates contrasting internal vs. external perspectives under a superordinated monitoring viewpoint. As a result, the paper argues that a concept of perspective ‘taking’ is not sufficient to capture the specific aspects of L(anguage-perspectivization, but has to be complemented by a concept of ‘confronting’ perspectives. This article is part of the Special Collection: Perspective Taking
Does model performance improve with complexity? A case study with three hydrological models
Orth, Rene; Staudinger, Maria; Seneviratne, Sonia I.; Seibert, Jan; Zappa, Massimiliano
2015-04-01
In recent decades considerable progress has been made in climate model development. Following the massive increase in computational power, models became more sophisticated. At the same time also simple conceptual models have advanced. In this study we validate and compare three hydrological models of different complexity to investigate whether their performance varies accordingly. For this purpose we use runoff and also soil moisture measurements, which allow a truly independent validation, from several sites across Switzerland. The models are calibrated in similar ways with the same runoff data. Our results show that the more complex models HBV and PREVAH outperform the simple water balance model (SWBM) in case of runoff but not for soil moisture. Furthermore the most sophisticated PREVAH model shows an added value compared to the HBV model only in case of soil moisture. Focusing on extreme events we find generally improved performance of the SWBM during drought conditions and degraded agreement with observations during wet extremes. For the more complex models we find the opposite behavior, probably because they were primarily developed for prediction of runoff extremes. As expected given their complexity, HBV and PREVAH have more problems with over-fitting. All models show a tendency towards better performance in lower altitudes as opposed to (pre-) alpine sites. The results vary considerably across the investigated sites. In contrast, the different metrics we consider to estimate the agreement between models and observations lead to similar conclusions, indicating that the performance of the considered models is similar at different time scales as well as for anomalies and long-term means. We conclude that added complexity does not necessarily lead to improved performance of hydrological models, and that performance can vary greatly depending on the considered hydrological variable (e.g. runoff vs. soil moisture) or hydrological conditions (floods vs. droughts).
Simple models for studying complex spatiotemporal patterns of animal behavior
Tyutyunov, Yuri V.; Titova, Lyudmila I.
2017-06-01
Minimal mathematical models able to explain complex patterns of animal behavior are essential parts of simulation systems describing large-scale spatiotemporal dynamics of trophic communities, particularly those with wide-ranging species, such as occur in pelagic environments. We present results obtained with three different modelling approaches: (i) an individual-based model of animal spatial behavior; (ii) a continuous taxis-diffusion-reaction system of partial-difference equations; (iii) a 'hybrid' approach combining the individual-based algorithm of organism movements with explicit description of decay and diffusion of the movement stimuli. Though the models are based on extremely simple rules, they all allow description of spatial movements of animals in a predator-prey system within a closed habitat, reproducing some typical patterns of the pursuit-evasion behavior observed in natural populations. In all three models, at each spatial position the animal movements are determined by local conditions only, so the pattern of collective behavior emerges due to self-organization. The movement velocities of animals are proportional to the density gradients of specific cues emitted by individuals of the antagonistic species (pheromones, exometabolites or mechanical waves of the media, e.g., sound). These cues play a role of taxis stimuli: prey attract predators, while predators repel prey. Depending on the nature and the properties of the movement stimulus we propose using either a simplified individual-based model, a continuous taxis pursuit-evasion system, or a little more detailed 'hybrid' approach that combines simulation of the individual movements with the continuous model describing diffusion and decay of the stimuli in an explicit way. These can be used to improve movement models for many species, including large marine predators.
Mechanistic modeling confronts the complexity of molecular cell biology.
Phair, Robert D
2014-11-05
Mechanistic modeling has the potential to transform how cell biologists contend with the inescapable complexity of modern biology. I am a physiologist-electrical engineer-systems biologist who has been working at the level of cell biology for the past 24 years. This perspective aims 1) to convey why we build models, 2) to enumerate the major approaches to modeling and their philosophical differences, 3) to address some recurrent concerns raised by experimentalists, and then 4) to imagine a future in which teams of experimentalists and modelers build-and subject to exhaustive experimental tests-models covering the entire spectrum from molecular cell biology to human pathophysiology. There is, in my view, no technical obstacle to this future, but it will require some plasticity in the biological research mind-set. © 2014 Phair. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).
Modeling pedestrian's conformity violation behavior: a complex network based approach.
Zhou, Zhuping; Hu, Qizhou; Wang, Wei
2014-01-01
Pedestrian injuries and fatalities present a problem all over the world. Pedestrian conformity violation behaviors, which lead to many pedestrian crashes, are common phenomena at the signalized intersections in China. The concepts and metrics of complex networks are applied to analyze the structural characteristics and evolution rules of pedestrian network about the conformity violation crossings. First, a network of pedestrians crossing the street is established, and the network's degree distributions are analyzed. Then, by using the basic idea of SI model, a spreading model of pedestrian illegal crossing behavior is proposed. Finally, through simulation analysis, pedestrian's illegal crossing behavior trends are obtained in different network structures and different spreading rates. Some conclusions are drawn: as the waiting time increases, more pedestrians will join in the violation crossing once a pedestrian crosses on red firstly. And pedestrian's conformity violation behavior will increase as the spreading rate increases.
Complex system modelling and control through intelligent soft computations
Azar, Ahmad
2015-01-01
The book offers a snapshot of the theories and applications of soft computing in the area of complex systems modeling and control. It presents the most important findings discussed during the 5th International Conference on Modelling, Identification and Control, held in Cairo, from August 31-September 2, 2013. The book consists of twenty-nine selected contributions, which have been thoroughly reviewed and extended before their inclusion in the volume. The different chapters, written by active researchers in the field, report on both current theories and important applications of soft-computing. Besides providing the readers with soft-computing fundamentals, and soft-computing based inductive methodologies/algorithms, the book also discusses key industrial soft-computing applications, as well as multidisciplinary solutions developed for a variety of purposes, like windup control, waste management, security issues, biomedical applications and many others. It is a perfect reference guide for graduate students, r...
Low-complexity stochastic modeling of spatially evolving flows
Zare, Armin; Ran, Wei; Hack, M. J. Philipp; Jovanovic, Mihailo
2016-11-01
Low-complexity approximations of the Navier-Stokes (NS) equations are commonly used for analysis and control of turbulent flows. In particular, stochastically-forced linearized models have been successfully employed to capture structural and statistical features observed in experiments and direct simulations. In this work, we utilize stochastically-forced linearized NS equations and their parabolized equivalents to study the dynamics of flow fluctuations in transitional and turbulent boundary layers. We exploit the streamwise causality of the parabolized model to efficiently propagate statistics of stochastic disturbances into statistics of velocity fluctuations. Our study provides insight into interactions of slowly-varying base flow with streamwise streaks, oblique modes, and Tollmien-Schlichting waves. It also offers a systematic, computationally efficient framework for quantifying the influence of stochastic excitation sources (e.g., free-stream turbulence and surface roughness) on velocity fluctuations in weakly non-parallel flows.
COMPLEX PROGRAMS FOR MODELING HIGHWAY: WAY AND STREAM
Directory of Open Access Journals (Sweden)
A. V. Skrypnikov
2014-01-01
Full Text Available The complexity of the operation of the road caused by continuously varying from picket to picket road conditions caused by a variety of parameters projected (existing road , the variety of types of cars, their technical and economic parameters , a variety of climatic and weather conditions required to develop a complex simulation programs . This paper describes a set of programs that form the core of the subsystem "driver-vehicle-road environment". Optimization of the design solutions developed modules contribute WAY type and columns, not using indicators averaged transport - road performance, and detailed process model of functioning of the road. WAY module provides continuous sequence modeling perception of road elements mechanical subsystem "road-car " (by continuous formation and solution of the equations of motion and the characteristics of this mode. WAY module (with module PARK brings the technical contradiction between the 20-year term of road design and use of existing practices in their justification of design decisions technical parameters of cars today. The complexity of the operation of the road due to the random nature of traffic demanded inclusion in the computer -aided design of roads STREAM module. STREAM module allows to obtain simulation results of a random process, sufficient to optimize the design decisions in general and in the areas of local variation of the plan, longitudinal section, the way the situation, etc. Varie ty of road conditions possible to classify on the specifics of the formation of the flow regimes. This builds on the results of study of the process of movement of cars in the stream.
Green IT engineering concepts, models, complex systems architectures
Kondratenko, Yuriy; Kacprzyk, Janusz
2017-01-01
This volume provides a comprehensive state of the art overview of a series of advanced trends and concepts that have recently been proposed in the area of green information technologies engineering as well as of design and development methodologies for models and complex systems architectures and their intelligent components. The contributions included in the volume have their roots in the authors’ presentations, and vivid discussions that have followed the presentations, at a series of workshop and seminars held within the international TEMPUS-project GreenCo project in United Kingdom, Italy, Portugal, Sweden and the Ukraine, during 2013-2015 and at the 1st - 5th Workshops on Green and Safe Computing (GreenSCom) held in Russia, Slovakia and the Ukraine. The book presents a systematic exposition of research on principles, models, components and complex systems and a description of industry- and society-oriented aspects of the green IT engineering. A chapter-oriented structure has been adopted for this book ...
Use of hyperbolic partial differential equations to generate body fitted coordinates
Steger, J. L.; Sorenson, R. L.
1980-01-01
The hyperbolic scheme is used to efficiently generate smoothly varying grids with good step size control near the body. Although only two dimensional applications are presented, the basic concepts are shown to extend to three dimensions.
Darboux problem for implicit impulsive partial hyperbolic fractional order differential equations
Directory of Open Access Journals (Sweden)
Said Abbas
2011-11-01
Full Text Available In this article we investigate the existence and uniqueness of solutions for the initial value problems, for a class of hyperbolic impulsive fractional order differential equations by using some fixed point theorems.
SRB measures for a class of partially hyperbolic attractors in Hilbert spaces
Lian, Zeng; Liu, Peidong; Lu, Kening
2016-07-01
In this paper, we study the existence of SRB measures and their properties for infinite dimensional dynamical systems in a Hilbert space. We show several results including (i) if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has at least one SRB measure; (ii) if the attractor is uniformly hyperbolic and the system is topological mixing and the splitting is Hölder continuous, then there exists a unique SRB measure which is mixing; (iii) if the attractor is uniformly hyperbolic and the system is non-wondering and the splitting is Hölder continuous, then there exist at most finitely many SRB measures; (iv) for a given hyperbolic measure, there exist at most countably many ergodic components whose basin contains an observable set.
On vanishing at infinity solutions of higher order linear hyperbolic equations
Directory of Open Access Journals (Sweden)
Stavroulakis IP
2002-01-01
Full Text Available In the half strip the linear hyperbolic equation with coefficients and is considered. Sufficient conditions of existence of solutions to this equation satisfying the conditions are established, where and are the integral parts of and .
A modeling process to understand complex system architectures
Robinson, Santiago Balestrini
2009-12-01
In recent decades, several tools have been developed by the armed forces, and their contractors, to test the capability of a force. These campaign level analysis tools, often times characterized as constructive simulations are generally expensive to create and execute, and at best they are extremely difficult to verify and validate. This central observation, that the analysts are relying more and more on constructive simulations to predict the performance of future networks of systems, leads to the two central objectives of this thesis: (1) to enable the quantitative comparison of architectures in terms of their ability to satisfy a capability without resorting to constructive simulations, and (2) when constructive simulations must be created, to quantitatively determine how to spend the modeling effort amongst the different system classes. The first objective led to Hypothesis A, the first main hypotheses, which states that by studying the relationships between the entities that compose an architecture, one can infer how well it will perform a given capability. The method used to test the hypothesis is based on two assumptions: (1) the capability can be defined as a cycle of functions, and that it (2) must be possible to estimate the probability that a function-based relationship occurs between any two types of entities. If these two requirements are met, then by creating random functional networks, different architectures can be compared in terms of their ability to satisfy a capability. In order to test this hypothesis, a novel process for creating representative functional networks of large-scale system architectures was developed. The process, named the Digraph Modeling for Architectures (DiMA), was tested by comparing its results to those of complex constructive simulations. Results indicate that if the inputs assigned to DiMA are correct (in the tests they were based on time-averaged data obtained from the ABM), DiMA is able to identify which of any two
Coevolving complex networks in the model of social interactions
Raducha, Tomasz; Gubiec, Tomasz
2017-04-01
We analyze Axelrod's model of social interactions on coevolving complex networks. We introduce four extensions with different mechanisms of edge rewiring. The models are intended to catch two kinds of interactions-preferential attachment, which can be observed in scientists or actors collaborations, and local rewiring, which can be observed in friendship formation in everyday relations. Numerical simulations show that proposed dynamics can lead to the power-law distribution of nodes' degree and high value of the clustering coefficient, while still retaining the small-world effect in three models. All models are characterized by two phase transitions of a different nature. In case of local rewiring we obtain order-disorder discontinuous phase transition even in the thermodynamic limit, while in case of long-distance switching discontinuity disappears in the thermodynamic limit, leaving one continuous phase transition. In addition, we discover a new and universal characteristic of the second transition point-an abrupt increase of the clustering coefficient, due to formation of many small complete subgraphs inside the network.
Wind Power Curve Modeling in Simple and Complex Terrain
Energy Technology Data Exchange (ETDEWEB)
Bulaevskaya, V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Wharton, S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Irons, Z. [Enel Green Power North America, Andover, MA (United States); Qualley, G. [Pentalum, Colleyville, TX (United States)
2015-02-09
Our previous work on wind power curve modeling using statistical models focused on a location with a moderately complex terrain in the Altamont Pass region in northern California (CA). The work described here is the follow-up to that work, but at a location with a simple terrain in northern Oklahoma (OK). The goal of the present analysis was to determine the gain in predictive ability afforded by adding information beyond the hub-height wind speed, such as wind speeds at other heights, as well as other atmospheric variables, to the power prediction model at this new location and compare the results to those obtained at the CA site in the previous study. While we reach some of the same conclusions at both sites, many results reported for the CA site do not hold at the OK site. In particular, using the entire vertical profile of wind speeds improves the accuracy of wind power prediction relative to using the hub-height wind speed alone at both sites. However, in contrast to the CA site, the rotor equivalent wind speed (REWS) performs almost as well as the entire profile at the OK site. Another difference is that at the CA site, adding wind veer as a predictor significantly improved the power prediction accuracy. The same was true for that site when air density was added to the model separately instead of using the standard air density adjustment. At the OK site, these additional variables result in no significant benefit for the prediction accuracy.
Spectroscopic studies of molybdenum complexes as models for nitrogenase
Energy Technology Data Exchange (ETDEWEB)
Walker, T.P.
1981-05-01
Because biological nitrogen fixation requires Mo, there is an interest in inorganic Mo complexes which mimic the reactions of nitrogen-fixing enzymes. Two such complexes are the dimer Mo/sub 2/O/sub 4/ (cysteine)/sub 2//sup 2 -/ and trans-Mo(N/sub 2/)/sub 2/(dppe)/sub 2/ (dppe = 1,2-bis(diphenylphosphino)ethane). The H/sup 1/ and C/sup 13/ NMR of solutions of Mo/sub 2/O/sub 4/(cys)/sub 2//sup 2 -/ are described. It is shown that in aqueous solution the cysteine ligands assume at least three distinct configurations. A step-wise dissociation of the cysteine ligand is proposed to explain the data. The Extended X-ray Absorption Fine Structure (EXAFS) of trans-Mo(N/sub 2/)/sub 2/(dppe)/sub 2/ is described and compared to the EXAFS of MoH/sub 4/(dppe)/sub 2/. The spectra are fitted to amplitude and phase parameters developed at Bell Laboratories. On the basis of this analysis, one can determine (1) that the dinitrogen complex contains nitrogen and the hydride complex does not and (2) the correct Mo-N distance. This is significant because the Mo inn both complexes is coordinated by four P atoms which dominate the EXAFS. A similar sort of interference is present in nitrogenase due to S coordination of the Mo in the enzyme. This model experiment indicates that, given adequate signal to noise ratios, the presence or absence of dinitrogen coordination to Mo in the enzyme may be determined by EXAFS using existing data analysis techniques. A new reaction between Mo/sub 2/O/sub 4/(cys)/sub 2//sup 2 -/ and acetylene is described to the extent it is presently understood. A strong EPR signal is observed, suggesting the production of stable Mo(V) monomers. EXAFS studies support this suggestion. The Mo K-edge is described. The edge data suggests Mo(VI) is also produced in the reaction. Ultraviolet spectra suggest that cysteine is released in the course of the reaction.
Sparse Estimation Using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models
DEFF Research Database (Denmark)
Pedersen, Niels Lovmand; Manchón, Carles Navarro; Badiu, Mihai Alin
2015-01-01
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued m...
Numerical test for hyperbolicity in chaotic systems with multiple time delays
Kuptsov, Pavel V.; Kuznetsov, Sergey P.
2018-03-01
We develop an extension of the fast method of angles for hyperbolicity verification in chaotic systems with an arbitrary number of time-delay feedback loops. The adopted method is based on the theory of covariant Lyapunov vectors and provides an efficient algorithm applicable for systems with high-dimensional phase space. Three particular examples of time-delay systems are analyzed and in all cases the expected hyperbolicity is confirmed.
Siegfried, Robert
2014-01-01
Robert Siegfried presents a framework for efficient agent-based modeling and simulation of complex systems. He compares different approaches for describing structure and dynamics of agent-based models in detail. Based on this evaluation the author introduces the "General Reference Model for Agent-based Modeling and Simulation" (GRAMS). Furthermore he presents parallel and distributed simulation approaches for execution of agent-based models -from small scale to very large scale. The author shows how agent-based models may be executed by different simulation engines that utilize underlying hard
Unfolding transitions in myosin give rise to the double-hyperbolic force-velocity relation in muscle
DEFF Research Database (Denmark)
Nielsen, Bjørn Gilbert
2003-01-01
This work presents an extension to a recent model of muscle contraction that was based on entropic elasticity (Nielsen 2002 J. Theor Biol. 219 99-119). By using entropic elasticity as the origin of muscle force, various possibilities emerge that can account for the presence of the double-hyperbol......This work presents an extension to a recent model of muscle contraction that was based on entropic elasticity (Nielsen 2002 J. Theor Biol. 219 99-119). By using entropic elasticity as the origin of muscle force, various possibilities emerge that can account for the presence of the double......-hyperbolic force-velocity relation in muscle that was observed by Edman (1988 J. Physiol. 404 301-21). In the present work, it will be argued that a slight change (elongation) of the contour length of the entropic springs involved in their high-force regions is sufficient to produce such a double...... in the entropic spring array from being mainly composed of non-unfolded myosin springs that have a short (i.e. normal) contour length to consisting of a mixture of myosin springs with short and long (unfolded) contour lengths....
Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy; Zanotti, Olindo
2016-06-01
This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell-Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic-parabolic Navier-Stokes-Fourier theory is established for the first time via a formal asymptotic analysis in the stiff relaxation limit. From a numerical point of view, the governing partial differential equations are very challenging, since they form a large nonlinear hyperbolic PDE system that includes stiff source terms and non-conservative products. We apply the successful family of one-step ADER-WENO finite volume (FV) and ADER discontinuous Galerkin (DG) finite element schemes to the HPR model in the stiff
Guliyev, Ayyub; Nabiyev, Shaig
2017-07-01
This paper presents the results of a statistical analysis of the dynamic parameters of 300 comets that have osculating hyperbolic orbits. It is shown that such comets differ from other comets by their large perihelion distances and by a predominance of retrograde motion. It is shown that the values of i, the inclination of the hyperbolic comets, are in comparative excess over the interval 90-120°. The dominance by q, the perihelion distance, renders it difficult to suggest that the excess hyperbolic velocity of these comets can be the result of physical processes that take place in their nuclei. Aspects of the following working hypothesis, that the hyperbolic excess of parameter e might be formed after comets pass through meteoroid streams, are also studied. To evaluate this hypothesis, the distribution of the orbits of hyperbolic comets relative to the plane of motion of 112 established meteoroid streams are analyzed. The number (N) of orbit nodes for hyperbolic comets with respect to the plane of each stream at various distances is calculated. To determine the degree of redundancy of N, a special computing algorithm was applied that provided the expected value nav as well as the standard deviation σ for the number of cometary nodes at the plane of each stream. A comparative analysis of the N and nav values that take σ into account suggests an excess in 40 stream cases. This implies that the passage of comets through meteoroid streams can lead to an acceleration of the comets' heliocentric velocity.
Madani, Amir; Entezar, Samad Roshan
2017-07-01
The transmission properties of a one-dimensional photonic crystal made of alternate layers of an isotropic ordinary dielectric and a graphene-based hyperbolic metamaterial are studied theoretically using the transfer matrix method. The metamaterial layers show hyperbolic dispersion in certain frequency range and are considered as an anisotropic effective medium in which the optical axis is normal to the graphene layers. It is shown that the structure has some photonic band gaps in both the hyperbolic and elliptical frequency regions of the hyperbolic metamaterial layers, which are tunable by changing the chemical potential of the graphene monolayers. Moreover, the characteristics of the transverse-magnetic (TM)-polarized photonic band gaps remarkably depend on the orientation of the optical axis of the hyperbolic metamaterial layers. It is found that the electric field intensity of the propagating modes from the hyperbolic metamaterial frequency region is concentrated in the high-index isotropic layers and the electric field intensity of the propagating modes from the elliptical frequency region is concentrated in the low-index anisotropic layers.
Low-complexity energy disaggregation using appliance load modelling
Directory of Open Access Journals (Sweden)
Hana Altrabalsi
2016-01-01
Full Text Available Large-scale smart metering deployments and energy saving targets across the world have ignited renewed interest in residential non-intrusive appliance load monitoring (NALM, that is, disaggregating total household’s energy consumption down to individual appliances, using purely analytical tools. Despite increased research efforts, NALM techniques that can disaggregate power loads at low sampling rates are still not accurate and/or practical enough, requiring substantial customer input and long training periods. In this paper, we address these challenges via a practical low-complexity lowrate NALM, by proposing two approaches based on a combination of the following machine learning techniques: k-means clustering and Support Vector Machine, exploiting their strengths and addressing their individual weaknesses. The first proposed supervised approach is a low-complexity method that requires very short training period and is fairly accurate even in the presence of labelling errors. The second approach relies on a database of appliance signatures that we designed using publicly available datasets. The database compactly represents over 200 appliances using statistical modelling of measured active power. Experimental results on three datasets from US, Italy, Austria and UK, demonstrate the reliability and practicality.