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...... 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...
Representation of the contextual statistical model by hyperbolic amplitudes
International Nuclear Information System (INIS)
Khrennikov, Andrei
2005-01-01
We continue the development of a so-called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric cos-interference, there exist contexts producing the hyperbolic cos-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators. This paper can be considered as the first step towards hyperbolic quantum probability. We also discuss possibilities of experimental verification of hyperbolic quantum mechanics: in physics of elementary particles, string theory as well as in experiments with nonphysical systems, e.g., in psychology, cognitive sciences, and economy
Considerations on the hyperbolic complex Klein-Gordon equation
International Nuclear Information System (INIS)
Ulrych, S.
2010-01-01
This article summarizes and consolidates investigations on hyperbolic complex numbers with respect to the Klein-Gordon equation for fermions and bosons. The hyperbolic complex numbers are applied in the sense that complex extensions of groups and algebras are performed not with the complex unit, but with the product of complex and hyperbolic unit. The modified complexification is the key ingredient for the theory. The Klein-Gordon equation is represented in this framework in the form of the first invariant of the Poincare group, the mass operator, in order to emphasize its geometric origin. The possibility of new interactions arising from hyperbolic complex gauge transformations is discussed.
Holographic complexity of cold hyperbolic black holes
International Nuclear Information System (INIS)
Barbón, José L.F.; Martín-García, Javier
2015-01-01
AdS black holes with hyperbolic horizons provide strong-coupling descriptions of thermal CFT states on hyperboloids. The low-temperature limit of these systems is peculiar. In this note we show that, in addition to a large ground state degeneracy, these states also have an anomalously large holographic complexity, scaling logarithmically with the temperature. We speculate on whether this fact generalizes to other systems whose extreme infrared regime is formally controlled by Conformal Quantum Mechanics, such as various instances of near-extremal charged black holes.
The Kerr geometry, complex world lines and hyperbolic strings
International Nuclear Information System (INIS)
Burinskii, A.Ya.
1994-01-01
In the Lind-Newman representation the Kerr geometry is created by a source moving along an analytical complex world line. An equivalence of the complex world line and complex (hyperbolic) string is considered. Therefore the hyperbolic string may play the role of the complex source of the Kerr geometry. The Kerr solution with the complex string source acquires Regge behavior of the angular momentum. (orig.)
Hyperbolic mapping of complex networks based on community information
Wang, Zuxi; Li, Qingguang; Jin, Fengdong; Xiong, Wei; Wu, Yao
2016-08-01
To improve the hyperbolic mapping methods both in terms of accuracy and running time, a novel mapping method called Community and Hyperbolic Mapping (CHM) is proposed based on community information in this paper. Firstly, an index called Community Intimacy (CI) is presented to measure the adjacency relationship between the communities, based on which a community ordering algorithm is introduced. According to the proposed Community-Sector hypothesis, which supposes that most nodes of one community gather in a same sector in hyperbolic space, CHM maps the ordered communities into hyperbolic space, and then the angular coordinates of nodes are randomly initialized within the sector that they belong to. Therefore, all the network nodes are so far mapped to hyperbolic space, and then the initialized angular coordinates can be optimized by employing the information of all nodes, which can greatly improve the algorithm precision. By applying the proposed dual-layer angle sampling method in the optimization procedure, CHM reduces the time complexity to O(n2) . The experiments show that our algorithm outperforms the state-of-the-art methods.
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...
Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models
Giona, M.; Brasiello, A.; Crescitelli, S.
2015-11-01
One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.
A strictly hyperbolic equilibrium phase transition model
International Nuclear Information System (INIS)
Allaire, G; Faccanoni, G; Kokh, S.
2007-01-01
This Note is concerned with the strict hyperbolicity of the compressible Euler equations equipped with an equation of state that describes the thermodynamical equilibrium between the liquid phase and the vapor phase of a fluid. The proof is valid for a very wide class of fluids. The argument only relies on smoothness assumptions and on the classical thermodynamical stability assumptions, that requires a definite negative Hessian matrix for each phase entropy as a function of the specific volume and internal energy. (authors)
Hyperbolic and semi-parametric models in finance
Bingham, N. H.; Kiesel, Rüdiger
2001-02-01
The benchmark Black-Scholes-Merton model of mathematical finance is parametric, based on the normal/Gaussian distribution. Its principal parametric competitor, the hyperbolic model of Barndorff-Nielsen, Eberlein and others, is briefly discussed. Our main theme is the use of semi-parametric models, incorporating the mean vector and covariance matrix as in the Markowitz approach, plus a non-parametric part, a scalar function incorporating features such as tail-decay. Implementation is also briefly discussed.
Generalized heat-transport equations: parabolic and hyperbolic models
Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio
2018-03-01
We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.
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...
Nonlinear sigma models with compact hyperbolic target spaces
International Nuclear Information System (INIS)
Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; Stoica, Bogdan; Stokes, James
2016-01-01
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems, Sov. Phys. JETP 34 (1972) 610. J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [http://inspirehep.net/search?p=find+J+%22J.Phys.,C6,1181%22]. . Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
Nonlinear sigma models with compact hyperbolic target spaces
Energy Technology Data Exchange (ETDEWEB)
Gubser, Steven [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States); Saleem, Zain H. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); National Center for Physics, Quaid-e-Azam University Campus,Islamabad 4400 (Pakistan); Schoenholz, Samuel S. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Stokes, James [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States)
2016-06-23
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems, Sov. Phys. JETP 34 (1972) 610. J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [http://inspirehep.net/search?p=find+J+%22J.Phys.,C6,1181%22]. . Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
Inozemtsev's hyperbolic spin model and its related spin chain
International Nuclear Information System (INIS)
Barba, J.C.; Finkel, F.; Gonzalez-Lopez, A.; Rodriguez, M.A.
2010-01-01
In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane-Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm-Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane-Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos.
A parabolic-hyperbolic system modelling a moving cell
Directory of Open Access Journals (Sweden)
Fabiana Cardetti
2009-08-01
Full Text Available In this article, we study the existence and uniqueness of local solutions for a moving boundary problem governed by a coupled parabolic-hyperbolic system. The results can be applied to cell movement, extending a result obtained by Choi, Groulx, and Lui in 2005.
Modified hyperbolic sine model for titanium dioxide-based memristive thin films
Abu Bakar, Raudah; Syahirah Kamarozaman, Nur; Fazlida Hanim Abdullah, Wan; Herman, Sukreen Hana
2018-03-01
Since the emergence of memristor as the newest fundamental circuit elements, studies on memristor modeling have been evolved. To date, the developed models were based on the linear model, linear ionic drift model using different window functions, tunnelling barrier model and hyperbolic-sine function based model. Although using hyperbolic-sine function model could predict the memristor electrical properties, the model was not well fitted to the experimental data. In order to improve the performance of the hyperbolic-sine function model, the state variable equation was modified. On the one hand, the addition of window function cannot provide an improved fitting. By multiplying the Yakopcic’s state variable model to Chang’s model on the other hand resulted in the closer agreement with the TiO2 thin film experimental data. The percentage error was approximately 2.15%.
Policy Effects in Hyperbolic vs. Exponential Models of Consumption and Retirement.
Gustman, Alan L; Steinmeier, Thomas L
2012-06-01
This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest.Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used.
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.
Chaotic Dynamics in Smart Grid and Suppression Scheme via Generalized Fuzzy Hyperbolic Model
Sun, Q.; Wang, Y.; Yang, J.; Qiu, Y.; Zhang, H.
2014-01-01
This paper presents a method to control chaotic behavior of a typical Smart Grid based on generalized fuzzy hyperbolic model (GFHM). As more and more distributed generations (DG) are incorporated into the Smart Grid, the chaotic behavior occurs increasingly. To verify the behavior, a dynamic model
Geometry of hyperbolic monopoles
International Nuclear Information System (INIS)
Nash, C.
1986-01-01
The hyperbolic monopoles of Atiyah [M. F. Atiyah, Commun. Math. Phys. 93, 471 (1984); ''Magnetic monopoles in hyperbolic space,'' in Proceedings of the International Colloquium on Vector Bundles (Tata Institute, Bombay, 1984)] and Chakrabarti [A. Chakrabarti, J. Math. Phys. 27, 340 (1986)] are introduced and their geometric properties and relations to instantons and ordinary monopoles clarified. A key tool is the use of the ball model of hyperbolic space to construct and examine solutions
Dynamic hyperbolic geometry: building intuition and understanding mediated by a Euclidean model
Moreno-Armella, Luis; Brady, Corey; Elizondo-Ramirez, Rubén
2018-05-01
This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become thinkable the mathematical community needed to accumulate over twenty centuries of reflection and effort: a precious instance of distributed intelligence at the cultural level. In geometry education after this crisis, relations between intuitions and geometrical reasoning must be established philosophically, rather than taken for granted. One approach seeks intuitive supports only for Euclidean explorations, viewing non-Euclidean inquiry as fundamentally non-intuitive in nature. We argue for moving beyond such an impoverished approach, using dynamic geometry environments to develop new intuitions even in the extremely challenging setting of hyperbolic geometry. Our efforts reverse the typical direction, using formal structures as a source for a new family of intuitions that emerge from exploring a digital model of hyperbolic geometry. This digital model is elaborated within a Euclidean dynamic geometry environment, enabling a conceptual dance that re-configures Euclidean knowledge as a support for building intuitions in hyperbolic space-intuitions based not directly on physical experience but on analogies extending Euclidean concepts.
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.
Blasjo, Viktor|info:eu-repo/dai/nl/338038108
2013-01-01
We discuss how a creature accustomed to Euclidean space would fare in a world of hyperbolic or spherical geometry, and conversely. Various optical illusions and counterintuitive experiences arise, which can be explicated mathematically using plane models of these geometries.
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 ...
Shock and rarefaction waves in a hyperbolic model of incompressible materials
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Tommaso Ruggeri
2013-01-01
Full Text Available The aim of the present paper is to investigate shock and rarefaction waves in a hyperbolic model of incompressible materials. To this aim, we use the so-called extended quasi-thermal-incompressible (EQTI model, recently proposed by Gouin & Ruggeri (H. Gouin, T. Ruggeri, Internat. J. Non-Linear Mech. 47 688–693 (2012. In particular, we use as constitutive equation a variant of the well-known Bousinnesq approximation in which the specific volume depends not only on the temperature but also on the pressure. The limit case of ideal incompressibility, namely when the thermal expansion coefficient and the compressibility factor vanish, is also considered.
Hyperbolicity of the Nonlinear Models of Maxwell's Equations
Serre, Denis
. We consider the class of nonlinear models of electromagnetism that has been described by Coleman & Dill [7]. A model is completely determined by its energy density W(B,D). Viewing the electromagnetic field (B,D) as a 3×2 matrix, we show that polyconvexity of W implies the local well-posedness of the Cauchy problem within smooth functions of class Hs with s>1+d/2. The method follows that designed by Dafermos in his book [9] in the context of nonlinear elasticity. We use the fact that B×D is a (vectorial, non-convex) entropy, and we enlarge the system from 6 to 9 equations. The resulting system admits an entropy (actually the energy) that is convex. Since the energy conservation law does not derive from the system of conservation laws itself (Faraday's and Ampère's laws), but also needs the compatibility relations divB=divD=0 (the latter may be relaxed in order to take into account electric charges), the energy density is not an entropy in the classical sense. Thus the system cannot be symmetrized, strictly speaking. However, we show that the structure is close enough to symmetrizability, so that the standard estimates still hold true.
Iversen, Birger
1992-01-01
Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics
A Synthesizable VHDL Model of the Exact Solution for Three-dimensional Hyperbolic Positioning System
Directory of Open Access Journals (Sweden)
Ralph Bucher
2002-01-01
Full Text Available This paper presents a synthesizable VHDL model of a three-dimensional hyperbolic positioning system algorithm. The algorithm obtains an exact solution for the three-dimensional location of a mobile given the locations of four fixed stations (like a global positioning system [GPS] satellite or a base station in a cell and the signal time of arrival (TOA from the mobile to each station. The detailed derivation of the steps required in the algorithm is presented. A VHDL model of the algorithm was implemented and simulated using the IEEE numeric_std package. Signals were described by a 32-bit vector. Simulation results predict location of the mobile is off by 1 m for best case and off by 36 m for worst case. A C + + program using real numbers was used as a benchmark for the accuracy and precision of the VHDL model. The model can be easily synthesized for low power hardware implementation.
International Nuclear Information System (INIS)
Popov, A.D.
1991-01-01
We introduce hyperbolic strings as closed bosonic strings with the target space R d-1,1 xT q+1,1 which has an additional time-like dimension in the internal space. The Fock spaces of the q-parametric family of standard bosonic, fermionic and heterotic strings with the target spaces of dimension n≤d+q are shown to be embedded into the Fock space of hyperbolic strings. The condition of the absence of anomaly fixes d and q for all three types of strings written in a bosonized form. (orig.)
Chaotic Dynamics in Smart Grid and Suppression Scheme via Generalized Fuzzy Hyperbolic Model
Directory of Open Access Journals (Sweden)
Qiuye Sun
2014-01-01
Full Text Available This paper presents a method to control chaotic behavior of a typical Smart Grid based on generalized fuzzy hyperbolic model (GFHM. As more and more distributed generations (DG are incorporated into the Smart Grid, the chaotic behavior occurs increasingly. To verify the behavior, a dynamic model which describes a power system with DG is presented firstly. Then, the simulation result shows that the power system can lead to chaos under certain initial conditions. Based on the universal approximation of GFHM, we confirm that the chaotic behavior could be suppressed by a new controller, which is designed by means of solving a linear matrix inequality (LMI. This approach could make a good application to suppress the chaos in Smart Grid. Finally, a numerical example is given to demonstrate the effectiveness of the proposed chaotic suppression strategy.
Entropic Constitutive Relation and Modeling for Fourier and Hyperbolic Heat Conductions
Directory of Open Access Journals (Sweden)
Shu-Nan Li
2017-12-01
Full Text Available Most existing phenomenological heat conduction models are expressed by temperature and heat flux distributions, whose definitions might be debatable in heat conductions with strong non-equilibrium. The constitutive relations of Fourier and hyperbolic heat conductions are here rewritten by the entropy and entropy flux distributions in the frameworks of classical irreversible thermodynamics (CIT and extended irreversible thermodynamics (EIT. The entropic constitutive relations are then generalized by Boltzmann–Gibbs–Shannon (BGS statistical mechanics, which can avoid the debatable definitions of thermodynamic quantities relying on local equilibrium. It shows a possibility of modeling heat conduction through entropic constitutive relations. The applicability of the generalizations by BGS statistical mechanics is also discussed based on the relaxation time approximation, and it is found that the generalizations require a sufficiently small entropy production rate.
International Nuclear Information System (INIS)
Pusztai, B.G.
2011-01-01
In a symplectic reduction framework we construct action-angle systems of canonical coordinates for both the hyperbolic Sutherland and the rational Ruijsenaars-Schneider-van Diejen integrable models associated with the C n root system. The presented dual reduction picture permits us to establish the action-angle duality between these many-particle systems.
Advanced Semi-Implicit Method (ASIM) for hyperbolic two-fluid model
International Nuclear Information System (INIS)
Lee, Sung Jae; Chung, Moon Sun
2003-01-01
Introducing the interfacial pressure jump terms based on the surface tension into the momentum equations of two-phase two-fluid model, the system of governing equations is turned mathematically into the hyperbolic system. The eigenvalues of the equation system become always real representing the void wave and the pressure wave propagation speeds as shown in the previous manuscript. To solve the interfacial pressure jump terms with void fraction gradients implicitly, the conventional semi-implicit method should be modified as an intermediate iteration method for void fraction at fractional time step. This Advanced Semi-Implicit Method (ASIM) then becomes stable without conventional additive terms. As a consequence, including the interfacial pressure jump terms with the advanced semi-implicit method, the numerical solutions of typical two-phase problems can be more stable and sound than those calculated exclusively by using any other terms like virtual mass, or artificial viscosity
International Nuclear Information System (INIS)
Boutin, B.
2009-11-01
This thesis concerns the mathematical and numerical study of nonlinear hyperbolic partial differential equations. A first part deals with an emergent problematic: the coupling of hyperbolic equations. The pursued applications are linked with the mathematical coupling of computing platforms, dedicated to an adaptative simulation of multi-scale phenomena. We propose and analyze a new coupling formalism based on extended PDE systems avoiding the geometric treatment of the interfaces. In addition, it allows to formulate the problem in a multidimensional setting, with possible covering of the coupled models. This formalism allows in particular to equip the coupling procedure with viscous regularization mechanisms, useful in the selection of natural discontinuous solutions. We analyze existence and uniqueness in the framework of a parabolic regularization a la Dafermos. Existence of a solution holds true under very general conditions but failure of uniqueness may naturally arise as soon as resonance occurs at the interfaces. Next, we highlight that our extended PDE framework gives rise to another regularization strategy based on thick interfaces. In this setting, we prove existence and uniqueness of the solutions of the Cauchy problem for initial data in L ∞ . The main tool consists in the derivation of a flexible and robust finite volume method for general triangulation which is analyzed in the setting of entropy measure-valued solutions by DiPerna. The second part is devoted to the definition of a finite volume scheme for the computing of nonclassical solutions of a scalar conservation law based on a kinetic relation. This scheme offers the feature to be stricto sensu conservative, in opposition to a Glimm approach that is only statistically conservative. The validity of our approach is illustrated through numerical examples. (author)
International Nuclear Information System (INIS)
Cohl, H S; Kalnins, E G
2012-01-01
Due to the isotropy of d-dimensional hyperbolic space, there exists a spherically symmetric fundamental solution for its corresponding Laplace–Beltrami operator. The R-radius hyperboloid model of hyperbolic geometry with R > 0 represents a Riemannian manifold with negative-constant sectional curvature. We obtain a spherically symmetric fundamental solution of Laplace’s equation on this manifold in terms of its geodesic radius. We give several matching expressions for this fundamental solution including a definite integral over reciprocal powers of the hyperbolic sine, finite summation expressions over hyperbolic functions, Gauss hypergeometric functions and in terms of the associated Legendre function of the second kind with order and degree given by d/2 − 1 with real argument greater than unity. We also demonstrate uniqueness for a fundamental solution of Laplace’s equation on this manifold in terms of a vanishing decay at infinity. In rotationally invariant coordinate systems, we compute the azimuthal Fourier coefficients for a fundamental solution of Laplace’s equation on the R-radius hyperboloid. For d ⩾ 2, we compute the Gegenbauer polynomial expansion in geodesic polar coordinates for a fundamental solution of Laplace’s equation on this negative-constant curvature Riemannian manifold. In three dimensions, an addition theorem for the azimuthal Fourier coefficients of a fundamental solution for Laplace’s equation is obtained through comparison with its corresponding Gegenbauer expansion. (paper)
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.
Decay Rates of Interactive Hyperbolic-Parabolic PDE Models with Thermal Effects on the Interface
International Nuclear Information System (INIS)
Lasiecka, I.; Lebiedzik, C.
2000-01-01
We consider coupled PDE systems comprising of a hyperbolic and a parabolic-like equation with an interface on a portion of the boundary. These models are motivated by structural acoustic problems. A specific prototype consists of a wave equation defined on a three-dimensional bounded domain Ω coupled with a thermoelastic plate equation defined on Γ 0 -a flat surface of the boundary Ω. Thus, the coupling between the wave and the plate takes place on the interface Γ 0 . The main issue studied here is that of uniform stability of the overall interactive model. Since the original (uncontrolled) model is only strongly stable, but not uniformly stable, the question becomes: what is the 'minimal amount' of dissipation necessary to obtain uniform decay rates for the energy of the overall system? Our main result states that boundary nonlinear dissipation placed only on a suitable portion of the part of the boundary which is complementary to Γ 0 , suffices for the stabilization of the entire structure. This result is new with respect to the literature on several accounts: (i) thermoelasticity is accounted for in the plate model; (ii) the plate model does not account for any type of mechanical damping, including the structural damping most often considered in the literature; (iii) there is no mechanical damping placed on the interface Γ 0 ; (iv) the boundary damping is nonlinear without a prescribed growth rate at the origin; (v) the undamped portions of the boundary partial Ω are subject to Neumann (rather than Dirichlet) boundary conditions, which is a recognized difficulty in the context of stabilization of wave equations, due to the fact that the strong Lopatinski condition does not hold. The main mathematical challenge is to show how the thermal energy is propagated onto the hyperbolic component of the structure. This is achieved by using a recently developed sharp theory of boundary traces corresponding to wave and plate equations, along with the analytic
International Nuclear Information System (INIS)
Pusztai, B.G.
2012-01-01
In this paper, we construct canonical action-angle variables for both the hyperbolic BC n Sutherland and the rational BC n Ruijsenaars-Schneider-van Diejen models with three independent coupling constants. As a byproduct of our symplectic reduction approach, we establish the action-angle duality between these many-particle systems. The presented dual reduction picture builds upon the construction of a Lax matrix for the BC n -type rational Ruijsenaars-Schneider-van Diejen model.
Energy Technology Data Exchange (ETDEWEB)
Tarantili, P.A.; Koullas, D.P.; Christakopoulos, P.; Kekos, D.; Koukios, E.G.; Macris, B.J. [National Technical Univ. of Athens (Greece). Dept. of Chemical Engineering
1996-10-01
The effect of cross-synergism in enzymatic hydrolysis of ball-milled Avicell, alkali-treated straw cellulose (ATSC), cotton and filter paper was investigated using mixtures of Fusarium oxysporum and Neurospora crassa enzymes. The experimental data were fitted according to an empirical hyperbolic model which utilized two parameters, the maximum conversion ({chi}{sub max}) and the enzymatic hydrolysis time corresponding to 50% of {chi}{sub max} (t{sub 1/2}). The model can predict conversion of polysaccharides as a function of hydrolysis time. Both model parameters were found to be strongly dependent on the crystallinity index as well as on the degree of delignification of the substrate. Up to 60% cellulose hydrolysis can be achieved when the crystallinity index of Avicell is reduced from 94.8% to 63.3%. The percentage increase of {chi}{sub max} due to delignification was higher than the corresponding increase of t{sub 1/2}. The extent of cross-synergism depends strongly on crystallinity index and degree of delignification. This type of synergism has been found to be significant in the case of substrates which are resistant to hydrolysis, such as Avicell (with high crystallinity index) or cotton. Cross-synergism phenomena caused by enzymatic mixtures can double cellulose hydrolysis yield with delignified straw as compared to the hydrolysis yields achieved by single-microorganism cellulases. (author)
International Nuclear Information System (INIS)
Akram, Safia; Nadeem, S.
2014-01-01
In the current study, sway of nanofluid on peristaltic transport of a hyperbolic tangent fluid model in the incidence of tending magnetic field has been argued. The governing equations of a nanofluid are first modeled and then simplified under lubrication approach. The coupled nonlinear equations of temperature and nano particle volume fraction are solved analytically using a homotopy perturbation technique. The analytical solution of the stream function and pressure gradient are carried out using perturbation technique. The graphical results of the problem under discussion are also being brought under consideration to see the behavior of various physical parameters. - Highlights: • The main motivation of this work is that we want to see the behavior of nanofluids in peristaltic flows. • In literature few articles are available on this, but no article is available in asymmetric channel on the new fluid model hyperbolic tangent fluid. • So we want to fill the gap in literature studying this
Energy Technology Data Exchange (ETDEWEB)
Akram, Safia, E-mail: safia_akram@yahoo.com [Department of Basic Sciences, MCS, National University of Sciences and Technology, Rawalpindi 46000 (Pakistan); Nadeem, S. [Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000 (Pakistan)
2014-05-01
In the current study, sway of nanofluid on peristaltic transport of a hyperbolic tangent fluid model in the incidence of tending magnetic field has been argued. The governing equations of a nanofluid are first modeled and then simplified under lubrication approach. The coupled nonlinear equations of temperature and nano particle volume fraction are solved analytically using a homotopy perturbation technique. The analytical solution of the stream function and pressure gradient are carried out using perturbation technique. The graphical results of the problem under discussion are also being brought under consideration to see the behavior of various physical parameters. - Highlights: • The main motivation of this work is that we want to see the behavior of nanofluids in peristaltic flows. • In literature few articles are available on this, but no article is available in asymmetric channel on the new fluid model hyperbolic tangent fluid. • So we want to fill the gap in literature studying this.
Hyperbolicity in median graphs
Indian Academy of Sciences (India)
mic problems in hyperbolic spaces and hyperbolic graphs have been .... that in general the main obstacle is that we do not know the location of ...... [25] Jonckheere E and Lohsoonthorn P, A hyperbolic geometry approach to multipath routing,.
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...
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...
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.
Energy Technology Data Exchange (ETDEWEB)
Smolyaninov, Igor I., E-mail: smoly@umd.edu
2014-11-15
Modern advances in transformation optics and electromagnetic metamaterials made possible experimental demonstrations of highly unusual curvilinear “optical spaces”, such as various geometries necessary for electromagnetic cloaking. Recently we demonstrated that mapping light intensity in a hyperbolic metamaterial may also model the flow of time in an effective (2+1) dimensional Minkowski spacetime. Curving such an effective spacetime creates experimental model of a toy “big bang”. Here we demonstrate that at low light levels this model may be used to emulate a fully covariant version of quantum mechanics in a (2+1) dimensional Minkowski spacetime. When quantum mechanical description is applied near the toy “big bang”, the Everett's “universal wave function” formalism arises naturally, in which the wave function of the model “universe” appears to be a quantum superposition of mutually orthogonal “parallel universe” states.
Hyperbolic manifolds as vacuum solutions in Kaluza-Klein theories
International Nuclear Information System (INIS)
Aref'eva, I.Ya.; Volovich, I.V.
1985-08-01
The relevance of compact hyperbolic manifolds in the context of Kaluza-Klein theories is discussed. Examples of spontaneous compactification on hyperbolic manifolds including d dimensional (d>=8) Einstein-Yang-Mills gravity and 11-dimensional supergravity are considered. Some mathematical facts about hyperbolic manifolds essential for the physical content of the theory are briefly summarized. Non-linear σ-models based on hyperbolic manifolds are discussed. (author)
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
Energy Technology Data Exchange (ETDEWEB)
Pusztai, B.G., E-mail: gpusztai@math.u-szeged.hu
2013-09-11
In this paper, we investigate the scattering properties of the hyperbolic BC{sub n} Sutherland and the rational BC{sub n} Ruijsenaars–Schneider–van Diejen many-particle systems with three independent coupling constants. Utilizing the recently established action-angle duality between these classical integrable models, we construct their wave and scattering maps. In particular, we prove that for both particle systems the scattering map has a factorized form.
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.
Conformal hyperbolicity of Lorentzian warped products
International Nuclear Information System (INIS)
Markowitz, M.J.
1982-01-01
A space-time M is said to be conformally hyperbolic if the intrinsic conformal Lorentz pseudodistance dsub(M) is a true distance. In this paper criteria are derived which insure the conformal hyperbolicity of certain space-times which are generalizations of the Robertson-Walker spaces. Then dsub(M) is determined explicitly for Einstein-de Sitter space, and important cosmological model. (author)
Conformal hyperbolicity of Lorentzian warped products
Energy Technology Data Exchange (ETDEWEB)
Markowitz, M.J. (Chicago Univ., IL (USA). Dept. of Mathematics)
1982-12-01
A space-time M is said to be conformally hyperbolic if the intrinsic conformal Lorentz pseudodistance dsub(M) is a true distance. In this paper criteria are derived which insure the conformal hyperbolicity of certain space-times which are generalizations of the Robertson-Walker spaces. Then dsub(M) is determined explicitly for Einstein-de Sitter space, and important cosmological model.
Piecewise linear regression splines with hyperbolic covariates
International Nuclear Information System (INIS)
Cologne, John B.; Sposto, Richard
1992-09-01
Consider the problem of fitting a curve to data that exhibit a multiphase linear response with smooth transitions between phases. We propose substituting hyperbolas as covariates in piecewise linear regression splines to obtain curves that are smoothly joined. The method provides an intuitive and easy way to extend the two-phase linear hyperbolic response model of Griffiths and Miller and Watts and Bacon to accommodate more than two linear segments. The resulting regression spline with hyperbolic covariates may be fit by nonlinear regression methods to estimate the degree of curvature between adjoining linear segments. The added complexity of fitting nonlinear, as opposed to linear, regression models is not great. The extra effort is particularly worthwhile when investigators are unwilling to assume that the slope of the response changes abruptly at the join points. We can also estimate the join points (the values of the abscissas where the linear segments would intersect if extrapolated) if their number and approximate locations may be presumed known. An example using data on changing age at menarche in a cohort of Japanese women illustrates the use of the method for exploratory data analysis. (author)
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......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 density function in both the small and large variable limits. This extends earlier results by Boca, Pasol, Popa and Zaharescu and Kelmer and Kontorovich in dimension 2 to general dimension n . Our proofs use the decay of matrix coefficients together with a number of careful estimates, and lead...
Admissibility and hyperbolicity
Barreira, Luís; Valls, Claudia
2018-01-01
This book gives a comprehensive overview of the relationship between admissibility and hyperbolicity. Essential theories and selected developments are discussed with highlights to applications. The dedicated readership includes researchers and graduate students specializing in differential equations and dynamical systems (with emphasis on hyperbolicity) who wish to have a broad view of the topic and working knowledge of its techniques. The book may also be used as a basis for appropriate graduate courses on hyperbolicity; the pointers and references given to further research will be particularly useful. The material is divided into three parts: the core of the theory, recent developments, and applications. The first part pragmatically covers the relation between admissibility and hyperbolicity, starting with the simpler case of exponential contractions. It also considers exponential dichotomies, both for discrete and continuous time, and establishes corresponding results building on the arguments for exponent...
Vortices on hyperbolic surfaces
International Nuclear Information System (INIS)
Manton, Nicholas S; Rink, Norman A
2010-01-01
It is shown that Abelian Higgs vortices on a hyperbolic surface M can be constructed geometrically from holomorphic maps f: M → N, where N is also a hyperbolic surface. The fields depend on f and on the metrics of M and N. The vortex centres are the ramification points, where the derivative of f vanishes. The magnitude of the Higgs field measures the extent to which f is locally an isometry. Witten's construction of vortices on the hyperbolic plane is rederived, and new examples of vortices on compact surfaces and on hyperbolic surfaces of revolution are obtained. The interpretation of these solutions as SO(3)-invariant, self-dual SU(2) Yang-Mills fields on R 4 is also given.
Uniqueness conditions in a hyperbolic model for oil recovery by steamdrive
J. Bruining; C.J. van Duijn (Hans)
1998-01-01
textabstractIn this paper we study a one-dimensional model for oil recovery by steamdrive. This model consists of two parts: a (global) interface model and a (local) steam condensation/capillary diffusion model. In the interface model a steam condensation front (SCF) is present as an internal
Curvature and temperature of complex networks.
Krioukov, Dmitri; Papadopoulos, Fragkiskos; Vahdat, Amin; Boguñá, Marián
2009-09-01
We show that heterogeneous degree distributions in observed scale-free topologies of complex networks can emerge as a consequence of the exponential expansion of hidden hyperbolic space. Fermi-Dirac statistics provides a physical interpretation of hyperbolic distances as energies of links. The hidden space curvature affects the heterogeneity of the degree distribution, while clustering is a function of temperature. We embed the internet into the hyperbolic plane and find a remarkable congruency between the embedding and our hyperbolic model. Besides proving our model realistic, this embedding may be used for routing with only local information, which holds significant promise for improving the performance of internet routing.
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 Rendezvous at Mars: Risk Assessments and Mitigation Strategies
Jedrey, Ricky; Landau, Damon; Whitley, Ryan
2015-01-01
Given the current interest in the use of flyby trajectories for human Mars exploration, a key requirement is the capability to execute hyperbolic rendezvous. Hyperbolic rendezvous is used to transport crew from a Mars centered orbit, to a transiting Earth bound habitat that does a flyby. Representative cases are taken from future potential missions of this type, and a thorough sensitivity analysis of the hyperbolic rendezvous phase is performed. This includes early engine cutoff, missed burn times, and burn misalignment. A finite burn engine model is applied that assumes the hyperbolic rendezvous phase is done with at least two burns.
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.
International Nuclear Information System (INIS)
Brown, T.W.
2010-11-01
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.)
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.)
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
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...
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....
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).
Hyperbolic metamaterial lens with hydrodynamic nonlocal response.
Yan, Wei; Mortensen, N Asger; Wubs, Martijn
2013-06-17
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 free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion curves numerically. As an application, we find that the focusing characteristics of a HMM lens 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.
Solving hyperbolic heat conduction using electrical simulation
International Nuclear Information System (INIS)
Gheitaghy, A. M.; Talaee, M. R.
2013-01-01
In the present study, the electrical network simulation method is proposed to solve the hyperbolic and parabolic heat conduction problem considering Cattaneo-Vernoute (C.V) constitutive relation. Using this new proposed numerical model and the electrical circuit simulation program HSPICE, transient temperature and heat flux profiles at slab can be obtained easily and quickly. To verify the proposed method, the obtained numerical results for cases of one dimensional two-layer slab under periodic boundary temperature with perfect and imperfect thermal contact are compared with the published results. Comparisons show the proposed technique might be considered as a useful tool in the analysis of parabolic and hyperbolic thermal problems.
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...
International Nuclear Information System (INIS)
Schreckenberg, M
2004-01-01
This book by Nino Boccara presents a compilation of model systems commonly termed as 'complex'. It starts with a definition of the systems under consideration and how to build up a model to describe the complex dynamics. The subsequent chapters are devoted to various categories of mean-field type models (differential and recurrence equations, chaos) and of agent-based models (cellular automata, networks and power-law distributions). Each chapter is supplemented by a number of exercises and their solutions. The table of contents looks a little arbitrary but the author took the most prominent model systems investigated over the years (and up until now there has been no unified theory covering the various aspects of complex dynamics). The model systems are explained by looking at a number of applications in various fields. The book is written as a textbook for interested students as well as serving as a comprehensive reference for experts. It is an ideal source for topics to be presented in a lecture on dynamics of complex systems. This is the first book on this 'wide' topic and I have long awaited such a book (in fact I planned to write it myself but this is much better than I could ever have written it!). Only section 6 on cellular automata is a little too limited to the author's point of view and one would have expected more about the famous Domany-Kinzel model (and more accurate citation!). In my opinion this is one of the best textbooks published during the last decade and even experts can learn a lot from it. Hopefully there will be an actualization after, say, five years since this field is growing so quickly. The price is too high for students but this, unfortunately, is the normal case today. Nevertheless I think it will be a great success! (book review)
Hyperbolic prisms and foams in Hele-Shaw cells
Energy Technology Data Exchange (ETDEWEB)
Tufaile, A., E-mail: tufaile@usp.br [Soft Matter Laboratory, Escola de Artes, Ciencias e Humanidades, Universidade de Sao Paulo, 03828-000, Sao Paulo (Brazil); Tufaile, A.P.B. [Soft Matter Laboratory, Escola de Artes, Ciencias e Humanidades, Universidade de Sao Paulo, 03828-000, Sao Paulo (Brazil)
2011-10-03
The propagation of light in foams creates patterns which are generated due to the reflection and refraction of light. One of these patterns is observed by the formation of multiple mirror images inside liquid bridges in a layer of bubbles in a Hele-Shaw cell. We are presenting the existence of these patterns in foams and their relation with hyperbolic geometry and Sierpinski gaskets using the Poincare disk model. The images obtained from the experiment in foams are compared to the case of hyperbolic optical elements. -- Highlights: → The chaotic scattering of light in foams generating deltoid patterns is based on hyperbolic geometry. → The deltoid patterns are obtained through the Plateau borders in a Hele-Shaw cell. → The Plateau borders act like hyperbolic prism. → Some effects of the refraction and reflection of the light rays were studied using a hyperbolic prism.
International Nuclear Information System (INIS)
Clason, B.; Duquesne, S.; Liess, M.; Schulz, R.; Zauke, G.-P.
2003-01-01
Bioaccumulation of Cd, Pb, Cu and Zn in the Antarctic gammaridean amphipod Paramoera walkeri (Stebbing, 1906) was investigated at Casey station (Australian Antarctic Territory). The main goals were to provide information on accumulation strategies of the organisms tested and to verify toxicokinetic models as a predictive tool. The organisms accumulated metals upon exposure and it was possible to estimate significant model parameters of two-compartment and hyperbolic models. These models were successfully verified in a second toxicokinetic study. However, the application of hyperbolic models appears to be more promising as a predictive tool for metals in amphipods compared to compartment models, which have failed to adequately predict metal accumulation in experiments with increasing external exposures in previous studies. The following kinetic bioconcentration factors (BCFs) for the theoretical equilibrium were determined: 150-630 (Cd), 1600-7000 (Pb), 1700-3800 (Cu) and 670-2400 (Zn). We find decreasing BCFs with increasing external metal dosing but similar results for treatments with and without natural UV radiation and for the combined effect of different exposure regimes (single versus multiple metal exposure) and/or the amphipod collective involved (Beall versus Denison Island). A tentative estimation showed the following sequence of sensitivity of P. walkeri to an increase of soluble metal exposure: 0.2-3.0 μg Cd l -1 , 0.12-0.25 μg Pb l -1 , 0.9-3.0 μg Cu l -1 and 9-26 μg Zn l -1 . Thus, the amphipod investigated proved to be more sensitive as biomonitor compared to gammarids from German coastal waters (with the exception of Cd) and to copepods from the Weddell Sea inferred from literature data
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.
International Nuclear Information System (INIS)
Vay, J.-L.; Geddes, C. G. R.; Cormier-Michel, E.; Grote, D. P.
2011-01-01
The effects of hyperbolic rotation in Minkowski space resulting from the use of Lorentz boosted frames of calculation on laser propagation in plasmas are analyzed. Selection of a boost frame at the laser group velocity is shown to alter the laser spectrum, allowing the use of higher boost velocities. The technique is applied to simulations of laser driven plasma wakefield accelerators, which promise much smaller machines and whose development requires detailed simulations that challenge or exceed current capabilities. Speedups approaching the theoretical optima are demonstrated, producing the first direct simulations of stages up to 1 TeV. This is made possible by a million times speedup thanks to a frame boost with a relativistic factor γ b as high as 1300, taking advantage of the rotation to mitigate an instability that limited previous work.
From Anosov dynamics to hyperbolic attractors
Indian Academy of Sciences (India)
the dynamics on the attractive sets of the self-oscillatory systems and for the original Anosov geodesic flow. The hyperbolic nature ... Hyperbolic theory is a branch of the theory of dynami- ..... Figure 5. Verification of the hyperbolicity criterion for.
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...
Casimir effect in hyperbolic polygons
International Nuclear Information System (INIS)
Ahmedov, H
2007-01-01
Using the point splitting regularization method and the trace formula for the spectra of quantum-mechanical systems in hyperbolic polygons which are the fundamental domains of discrete isometry groups acting in the two-dimensional hyperboloid we calculate the Casimir energy for massless scalar fields in hyperbolic polygons. The dependence of the vacuum energy on the number of vertices is established
Hyperbolic-symmetry vector fields.
Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2015-12-14
We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.
Random walks on the braid group B3 and magnetic translations in hyperbolic geometry
International Nuclear Information System (INIS)
Voituriez, Raphaeel
2002-01-01
We study random walks on the three-strand braid group B 3 , and in particular compute the drift, or average topological complexity of a random braid, as well as the probability of trivial entanglement. These results involve the study of magnetic random walks on hyperbolic graphs (hyperbolic Harper-Hofstadter problem), what enables to build a faithful representation of B 3 as generalized magnetic translation operators for the problem of a quantum particle on the hyperbolic plane
Markov, A V; Korotaev, A V
2008-01-01
models, the hyperbolic pattern of the world population growth arises from a non-linear second-order positive feedback between the demographic growth and technological development (more people - more potential inventors - faster technological growth - the carrying capacity of the Earth grows faster - faster population growth - more people - more potential inventors, and so on). Based on the analogy with macrosociological models and diverse paleontological data, we suggest that the hyperbolic character of biodiversity growth can be similarly accounted for by a non-linear second-order positive feedback between the diversity growth and community structure complexity. The feedback can work via two parallel mechanisms: 1) decreasing extinction rate (more taxa- higher alpha diversity, or mean number of taxa in a community - communities become more complex and stable - extinction rate decreases - more taxa, and so on) and 2) increasing origination rate (new taxa facilitate niche construction; newly formed niches can be occupied by the next "generation" of taxa). The latter possibility makes the mechanisms underlying the hyperbolic growth of biodiversity and human population even more similar, because the total ecospace of the biota is analogous to the "carrying capacity of the Earth" in demography. As far as new species can increase ecospace and facilitate opportunities for additional species entering the community, they are analogous to the "inventors" of the demographic models whose inventions increase the carrying capacity of the Earth. The hyperbolic growth of the Phanerozoic biodiverstiy suggests that "cooperative" interactions between taxa can play an important role in evolution, along with generally accepted competitive interactions. Due to this "cooperation", the evolution of biodiversity acquires some features of a self-accelerating process. Macroevolutionary "cooperation" reveals itself in: 1) increasing stability of communities that arises from alpha diversity growth
Cohen, Timothy; Giudice, Gian F.; Mccullough, Matthew
2018-05-15
We introduce the Hyperbolic Higgs, a novel solution to the little hierarchy problem that features Standard Model neutral scalar top partners. At one-loop order, the protection from ultraviolet sensitivity is due to an accidental non-compact symmetry of the Higgs potential that emerges in the infrared. Once the general features of the effective description are detailed, a completion that relies on a five dimensional supersymmetric framework is provided. Novel phenomenology is compared and contrasted with the Twin Higgs scenario.
Critical opalescence in hyperbolic metamaterials
International Nuclear Information System (INIS)
Smolyaninov, Igor I
2011-01-01
Hyperbolic metamaterials in which the dielectric component exhibits critical opalescence have been considered. It appears that fluctuations of the effective refractive index in these materials are strongly enhanced and so 'virtual electromagnetic black holes' may appear as a result of these fluctuations. Therefore, the behaviour of 'optical space' inside hyperbolic metamaterials looks somewhat similar to the behaviour of real physical space-time on the Planck scale
Critical opalescence in hyperbolic metamaterials
Smolyaninov, Igor I.
2011-12-01
Hyperbolic metamaterials in which the dielectric component exhibits critical opalescence have been considered. It appears that fluctuations of the effective refractive index in these materials are strongly enhanced and so 'virtual electromagnetic black holes' may appear as a result of these fluctuations. Therefore, the behaviour of 'optical space' inside hyperbolic metamaterials looks somewhat similar to the behaviour of real physical space-time on the Planck scale.
Path integration on hyperbolic spaces
Energy Technology Data Exchange (ETDEWEB)
Grosche, C [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
1991-11-01
Quantum mechanics on the hyperbolic spaces of rank one is discussed by path integration technique. Hyperbolic spaces are multi-dimensional generalisation of the hyperbolic plane, i.e. the Poincare upper half-plane endowed with a hyperbolic geometry. We evalute the path integral on S{sub 1} {approx equal} SO (n,1)/SO(n) and S{sub 2} {approx equal} SU(n,1)/S(U(1) x U(n)) in a particular coordinate system, yielding explicitly the wave-functions and the energy spectrum. Futhermore we can exploit a general property of all these spaces, namely that they can be parametrized by a pseudopolar coordinate system. This allows a separation in path integration over spheres and an additional path integration over the remaining hyperbolic coordinate, yielding effectively a path integral for a modified Poeschl-Teller potential. Only continuous spectra can exist in all the cases. For all the hyperbolic spaces of rank one we find a general formula for the largest lower bound (zero-point energy) of the spectrum which is given by E{sub O} = h{sup 2} /8m(m{sub {alpha}} +2m{sub 2} {alpha}){sup 2} (m {alpha} and m{sub 2}{alpha} denote the dimension of the root subspace corresponding to the roots {alpha} and 2{alpha}, respectively). I also discuss the case, where a constant magnetic field on H{sup n} is incorporated. (orig.).
Path integration on hyperbolic spaces
International Nuclear Information System (INIS)
Grosche, C.
1991-11-01
Quantum mechanics on the hyperbolic spaces of rank one is discussed by path integration technique. Hyperbolic spaces are multi-dimensional generalisation of the hyperbolic plane, i.e. the Poincare upper half-plane endowed with a hyperbolic geometry. We evalute the path integral on S 1 ≅ SO (n,1)/SO(n) and S 2 ≅ SU(n,1)/S[U(1) x U(n)] in a particular coordinate system, yielding explicitly the wave-functions and the energy spectrum. Futhermore we can exploit a general property of all these spaces, namely that they can be parametrized by a pseudopolar coordinate system. This allows a separation in path integration over spheres and an additional path integration over the remaining hyperbolic coordinate, yielding effectively a path integral for a modified Poeschl-Teller potential. Only continuous spectra can exist in all the cases. For all the hyperbolic spaces of rank one we find a general formula for the largest lower bound (zero-point energy) of the spectrum which is given by E O = h 2 /8m(m α +2m 2 α) 2 (m α and m 2 α denote the dimension of the root subspace corresponding to the roots α and 2α, respectively). I also discuss the case, where a constant magnetic field on H n is incorporated. (orig.)
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 free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion curves numerically. As an application, we find that the focusing characteristics of a HMM lens...... 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...
Diffusive instabilities in hyperbolic reaction-diffusion equations
Zemskov, Evgeny P.; Horsthemke, Werner
2016-03-01
We investigate two-variable reaction-diffusion systems of the hyperbolic type. A linear stability analysis is performed, and the conditions for diffusion-driven instabilities are derived. Two basic types of eigenvalues, real and complex, are described. Dispersion curves for both types of eigenvalues are plotted and their behavior is analyzed. The real case is related to the Turing instability, and the complex one corresponds to the wave instability. We emphasize the interesting feature that the wave instability in the hyperbolic equations occurs in two-variable systems, whereas in the parabolic case one needs three reaction-diffusion equations.
Hyperbolicity and constrained evolution in linearized gravity
International Nuclear Information System (INIS)
Matzner, Richard A.
2005-01-01
Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint equations remain solved under the action of the evolution, and one approach is to simply monitor them (unconstrained evolution). Since computational solution of differential equations introduces almost inevitable errors, it is clearly 'more correct' to introduce a scheme which actively maintains the constraints by solution (constrained evolution). This has shown promise in computational settings, but the analysis of the resulting mixed elliptic hyperbolic method has not been completely carried out. We present such an analysis for one method of constrained evolution, applied to a simple vacuum system, linearized gravitational waves. We begin with a study of the hyperbolicity of the unconstrained Einstein equations. (Because the study of hyperbolicity deals only with the highest derivative order in the equations, linearization loses no essential details.) We then give explicit analytical construction of the effect of initial data setting and constrained evolution for linearized gravitational waves. While this is clearly a toy model with regard to constrained evolution, certain interesting features are found which have relevance to the full nonlinear Einstein equations
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
A discussion of hyperbolicity in CATHENA 4. Virtual mass and phase-to-interface pressure differences
International Nuclear Information System (INIS)
Aydemir, Nusret U.
2012-01-01
It is well known that the one-dimensional equations of motion for two-phase flow are non-hyperbolic. Non-hyperbolicity can lead to numerical instabilities, destroying the solution. However, researchers in the last few decades were able to show that inclusion of virtual mass and/or phase-to-interface pressure differences in the momentum equations successfully render the equations of motion hyperbolic. In the present paper, the effect of including virtual mass and phase-to-interface pressure terms in the momentum equations on the hyperbolicity of the two-phase model in the CATHENA 4 code is discussed. The study is motivated by the fact that the inclusion of either model has been shown in the open literature to lead to a hyperbolic system separately. However, no known study exists that examine hyperbolicity in the presence of both these terms in the momentum equations. In this work, both terms are considered in the model equations simultaneously and their implications on the hyperbolicity of the two-phase model are discussed. Specifically, it is shown that in the case of mixed flow, there is a distinct region of non-hyperbolicity that developers need to be aware of when their equations include both the virtual mass and the phase-to-interface terms. Selecting the coefficients of phase-to-interface pressure difference terms properly ensures that the equations are hyperbolic for a wide range of conditions. (orig.)
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...
Reversed phase propagation for hyperbolic surface waves
DEFF Research Database (Denmark)
Repän, Taavi; Novitsky, Andrey; Willatzen, Morten
2018-01-01
Magnetic properties can be used to control phase propagation in hyperbolic metamaterials. However, in the visible spectrum magnetic properties are difficult to obtain. We discuss hyperbolic surface waves allowing for a similar control over phase, achieved without magnetic properties....
Universal asymptotics in hyperbolicity breakdown
International Nuclear Information System (INIS)
Bjerklöv, Kristian; Saprykina, Maria
2008-01-01
We study a scenario for the disappearance of hyperbolicity of invariant tori in a class of quasi-periodic systems. In this scenario, the system loses hyperbolicity because two invariant directions come close to each other, losing their regularity. In a recent paper, based on numerical results, Haro and de la Llave (2006 Chaos 16 013120) discovered a quantitative universality in this scenario, namely, that the minimal angle between the two invariant directions has a power law dependence on the parameters and the exponents of the power law are universal. We present an analytic proof of this result
Appropriate complexity landscape modeling
Larsen, Laurel G.; Eppinga, Maarten B.; Passalacqua, Paola; Getz, Wayne M.; Rose, Kenneth A.; Liang, Man
Advances in computing technology, new and ongoing restoration initiatives, concerns about climate change's effects, and the increasing interdisciplinarity of research have encouraged the development of landscape-scale mechanistic models of coupled ecological-geophysical systems. However,
Exact Solutions for Einstein's Hyperbolic Geometric Flow
International Nuclear Information System (INIS)
He Chunlei
2008-01-01
In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow
Right-angled polyhedra and hyperbolic 3-manifolds
Vesnin, A. Yu.
2017-04-01
Hyperbolic 3-manifolds whose fundamental groups are subgroups of finite index in right-angled Coxeter groups are under consideration. The construction of such manifolds is associated with regular colourings of the faces of polyhedra and, in particular, with 4-colourings. The following questions are discussed: the structure of the set of right-angled polytopes in Lobachevskii space; examples of orientable and non-orientable manifolds, including the classical Löbell manifold constructed in 1931; connections between the Hamiltonian property of a polyhedron and the existence of hyperelliptic involutions of manifolds; the volumes and complexity of manifolds; isometry between hyperbolic manifolds constructed from 4-colourings. Bibliography: 89 titles.
Origin of hyperbolicity in brain-to-brain coordination networks
Tadić, Bosiljka; Andjelković, Miroslav; Šuvakov, Milovan
2018-02-01
Hyperbolicity or negative curvature of complex networks is the intrinsic geometric proximity of nodes in the graph metric space, which implies an improved network function. Here, we investigate hidden combinatorial geometries in brain-to-brain coordination networks arising through social communications. The networks originate from correlations among EEG signals previously recorded during spoken communications comprising of 14 individuals with 24 speaker-listener pairs. We find that the corresponding networks are delta-hyperbolic with delta_max=1 and the graph diameter D=3 in each brain. While the emergent hyperbolicity in the two-brain networks satisfies delta_max/D/2 neuronal correlation patterns ranging from weak coordination to super-brain structure. These topology features are in qualitative agreement with the listener’s self-reported ratings of own experience and quality of the speaker, suggesting that studies of the cross-brain connector networks can reveal new insight into the neural mechanisms underlying human social behavior.
Cognitive Procedures and Hyperbolic Discounting
Nir, A.
2004-01-01
"Hyperbolic discount functions are characterized by a relatively high discount rate over short horizons and a relatively low discount rate over long horizons" (Laibson 1997).We suggest two cognitive procedures where individuals perceive future utility as decreasing at a decreasing rate as a function
Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics
Energy Technology Data Exchange (ETDEWEB)
Kuznetsov, Sergei P [Saratov Branch, Kotel' nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov (Russian Federation)
2011-02-28
Research is reviewed on the identification and construction of physical systems with chaotic dynamics due to uniformly hyperbolic attractors (such as the Plykin attraction or the Smale-Williams solenoid). Basic concepts of the mathematics involved and approaches proposed in the literature for constructing systems with hyperbolic attractors are discussed. Topics covered include periodic pulse-driven models; dynamics models consisting of periodically repeated stages, each described by its own differential equations; the construction of systems of alternately excited coupled oscillators; the use of parametrically excited oscillations; and the introduction of delayed feedback. Some maps, differential equations, and simple mechanical and electronic systems exhibiting chaotic dynamics due to the presence of uniformly hyperbolic attractors are presented as examples. (reviews of topical problems)
Outcrossings of safe regions by generalized hyperbolic processes
DEFF Research Database (Denmark)
Klüppelberg, Claudia; Rasmussen, Morten Grud
2013-01-01
We present a simple Gaussian mixture model in space and time with generalized hyperbolic marginals. Starting with Rice’s celebrated formula for level upcrossings and outcrossings of safe regions we investigate the consequences of the mean-variance mixture model on such quantities. We obtain...
Epidemic modeling in complex realities.
Colizza, Vittoria; Barthélemy, Marc; Barrat, Alain; Vespignani, Alessandro
2007-04-01
In our global world, the increasing complexity of social relations and transport infrastructures are key factors in the spread of epidemics. In recent years, the increasing availability of computer power has enabled both to obtain reliable data allowing one to quantify the complexity of the networks on which epidemics may propagate and to envision computational tools able to tackle the analysis of such propagation phenomena. These advances have put in evidence the limits of homogeneous assumptions and simple spatial diffusion approaches, and stimulated the inclusion of complex features and heterogeneities relevant in the description of epidemic diffusion. In this paper, we review recent progresses that integrate complex systems and networks analysis with epidemic modelling and focus on the impact of the various complex features of real systems on the dynamics of epidemic spreading.
Computation of Hyperbolic Structures in Knot Theory
Weeks, Jeffrey R.
2003-01-01
This chapter from the upcoming Handbook of Knot Theory (eds. Menasco and Thistlethwaite) shows how to construct hyperbolic structures on link complements and perform hyperbolic Dehn filling. Along with a new elementary exposition of the standard ideas from Thurston's work, the article includes never-before-published explanations of SnapPea's algorithms for triangulating a link complement efficiently and for converging quickly to the hyperbolic structure while avoiding singularities in the par...
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...
Complexity-aware simple modeling.
Gómez-Schiavon, Mariana; El-Samad, Hana
2018-02-26
Mathematical models continue to be essential for deepening our understanding of biology. On one extreme, simple or small-scale models help delineate general biological principles. However, the parsimony of detail in these models as well as their assumption of modularity and insulation make them inaccurate for describing quantitative features. On the other extreme, large-scale and detailed models can quantitatively recapitulate a phenotype of interest, but have to rely on many unknown parameters, making them often difficult to parse mechanistically and to use for extracting general principles. We discuss some examples of a new approach-complexity-aware simple modeling-that can bridge the gap between the small-scale and large-scale approaches. Copyright © 2018 Elsevier Ltd. All rights reserved.
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.
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...
Analysis of magnetic electron lens with secant hyperbolic field distribution
International Nuclear Information System (INIS)
Pany, S.S.; Ahmed, Z.; Dubey, B.P.
2014-01-01
Electron-optical imaging instruments like Scanning Electron Microscope (SEM) and Transmission Electron Microscope (TEM) use specially designed solenoid electromagnets for focusing of the electron beam. Indicators of imaging performance of these instruments, like spatial resolution, have a strong correlation with the focal characteristics of the magnetic lenses, which in turn have been shown to be sensitive to the details of the spatial distribution of the axial magnetic field. Owing to the complexity of designing practical lenses, empirical mathematical expressions are important to obtain the desired focal properties. Thus the degree of accuracy of such models in representing the actual field distribution determines accuracy of the calculations and ultimately the performance of the lens. Historically, the mathematical models proposed by Glaser [1] and Ramberg [2] have been extensively used. In this paper the authors discuss another model with a secant-hyperbolic type magnetic field distribution function, and present a comparison between models, utilizing results from finite element-based field simulations as the reference for evaluating performance
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.
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...... our analysis to show that the moduli space of homogeneous structures on real hyperbolic space has two connected components....
On a new class of hyperbolic functions
International Nuclear Information System (INIS)
Stakhov, Alexey; Rozin, Boris
2005-01-01
This article presents the results of some new research on a new class of hyperbolic functions that unite the characteristics of the classical hyperbolic functions and the recurring Fibonacci and Lucas series. The hyperbolic Fibonacci and Lucas functions, which are the being extension of Binet's formulas for the Fibonacci and Lucas numbers in continuous domain, transform the Fibonacci numbers theory into 'continuous' theory because every identity for the hyperbolic Fibonacci and Lucas functions has its discrete analogy in the framework of the Fibonacci and Lucas numbers. Taking into consideration a great role played by the hyperbolic functions in geometry and physics, ('Lobatchevski's hyperbolic geometry', 'Four-dimensional Minkowski's world', etc.), it is possible to expect that the new theory of the hyperbolic functions will bring to new results and interpretations on mathematics, biology, physics, and cosmology. In particular, the result is vital for understanding the relation between transfinitness i.e. fractal geometry and the hyperbolic symmetrical character of the disintegration of the neural vacuum, as pointed out by El Naschie [Chaos Solitons and Fractals 17 (2003) 631
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.
Model complexity control for hydrologic prediction
Schoups, G.; Van de Giesen, N.C.; Savenije, H.H.G.
2008-01-01
A common concern in hydrologic modeling is overparameterization of complex models given limited and noisy data. This leads to problems of parameter nonuniqueness and equifinality, which may negatively affect prediction uncertainties. A systematic way of controlling model complexity is therefore
On Hubbard-Stratonovich transformations over hyperbolic domains
International Nuclear Information System (INIS)
Fyodorov, Yan V
2005-01-01
We discuss and prove the validity of the Hubbard-Stratonovich (HS) identities over hyperbolic domains which are used frequently in studies on disordered systems and random matrices. We also introduce a counterpart of the HS identity arising in disordered systems with 'chiral' symmetry. Apart from this we outline a way of deriving the nonlinear σ-model from the gauge-invariant Wegner k-orbital model avoiding the use of the HS transformations
Testable Implications of Quasi-Hyperbolic and Exponential Time Discounting
Echenique, Federico; Imai, Taisuke; Saito, Kota
2014-01-01
We present the first revealed-preference characterizations of the models of exponential time discounting, quasi-hyperbolic time discounting, and other time-separable models of consumers’ intertemporal decisions. The characterizations provide non-parametric revealed-preference tests, which we take to data using the results of a recent experiment conducted by Andreoni and Sprenger (2012). For such data, we find that less than half the subjects are consistent with exponential discounting, and on...
A Gyrovector Space Approach to Hyperbolic Geometry
Ungar, Abraham
2009-01-01
The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. T
Stability problems for linear hyperbolic systems
International Nuclear Information System (INIS)
Eckhoff, K.S.
1975-05-01
The stability properties for the trivial solution of a general linear hyperbolic system of partial differential equations of the first order are studied. It is shown that results may be obtained by studying the stability properties of certain systems of ordinary differential equations which can be constructed from the hyperbolic system (the so-called transport equations). In some cases the associated stability problem for the transport equations can in fact be shown to be equivalent to the stability problem for the hyperbolic system, but in general the transport equations will only give the necessary conditions for stability. (Auth.)
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.
Nonparametric Bayesian Modeling of Complex Networks
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Mørup, Morten
2013-01-01
an infinite mixture model as running example, we go through the steps of deriving the model as an infinite limit of a finite parametric model, inferring the model parameters by Markov chain Monte Carlo, and checking the model?s fit and predictive performance. We explain how advanced nonparametric models......Modeling structure in complex networks using Bayesian nonparametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This article provides a gentle introduction to nonparametric Bayesian modeling of complex networks: Using...
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.
Electromagnetic ``black holes'' in hyperbolic metamaterials
Smolyaninov, Igor
2013-03-01
We demonstrate that spatial variations of the dielectric tensor components in a hyperbolic metamaterial may lead to formation of electromagnetic ``black holes'' inside this metamaterial. Similar to real black holes, horizon area of the electromagnetic ``black holes'' is quantized in units of the effective ``Planck scale'' squared. Potential experimental realizations of such electromagnetic ``black holes'' will be considered. For example, this situation may be realized in a hyperbolic metamaterial in which the dielectric component exhibits critical opalescence.
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...
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
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......-principles calculations, we extend the number of known naturally hyperbolic materials to the broad class of layered transition metal dichalcogenides (TMDs). The diverse electronic properties of the transition metal dichalcogenides result in a large variation of the hyperbolic frequency regimes ranging from the near...... materials with hyperbolic dispersion among the family of layered transition metal dichalcogenides....
Life Insurance and Annuity Demand under Hyperbolic Discounting
Directory of Open Access Journals (Sweden)
Siqi Tang
2018-04-01
Full Text Available In this paper, we analyse and construct a lifetime utility maximisation model with hyperbolic discounting. Within the model, a number of assumptions are made: complete markets, actuarially fair life insurance/annuity is available, and investors have time-dependent preferences. Time dependent preferences are in contrast to the usual case of constant preferences (exponential discounting. We find: (1 investors (realistically demand more life insurance after retirement (in contrast to the standard model, which showed strong demand for life annuities, and annuities are rarely purchased; (2 optimal consumption paths exhibit a humped shape (which is usually only found in incomplete markets under the assumptions of the standard model.
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...
Causality and hyperbolicity of Lovelock theories
International Nuclear Information System (INIS)
Reall, Harvey S; Tanahashi, Norihiro; Way, Benson
2014-01-01
In Lovelock theories, gravity can travel faster or slower than light. The causal structure is determined by the characteristic hypersurfaces. We generalize a recent result of Izumi to prove that any Killing horizon is a characteristic hypersurface for all gravitational degrees of freedom of a Lovelock theory. Hence gravitational signals cannot escape from the region inside such a horizon. We investigate the hyperbolicity of Lovelock theories by determining the characteristic hypersurfaces for various backgrounds. First we consider Ricci flat type N spacetimes. We show that characteristic hypersurfaces are generically all non-null and that Lovelock theories are hyperbolic in any such spacetime. Next we consider static, maximally symmetric black hole solutions of Lovelock theories. Again, characteristic surfaces are generically non-null. For some small black holes, hyperbolicity is violated near the horizon. This implies that the stability of such black holes is not a well-posed problem. (paper)
Computing the Gromov hyperbolicity constant of a discrete metric space
Ismail, Anas
2012-01-01
, 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
Multilayer cladding with hyperbolic dispersion for plasmonic waveguides
DEFF Research Database (Denmark)
Babicheva, Viktoriia; Shalaginov, Mikhail Y.; Ishii, Satoshi
2015-01-01
We study the properties of plasmonic waveguides with a dielectric core and multilayer metal-dielectric claddings that possess hyperbolic dispersion. The waveguides hyperbolic multilayer claddings show better performance in comparison to conventional plasmonic waveguides. © OSA 2015....
Homoclinic Ω-explosion and domains of hyperbolicity
International Nuclear Information System (INIS)
Sten'kin, O V; Shil'nikov, L P
1998-01-01
The existence of domains of hyperbolicity is proved for general one-parameter families of multidimensional systems that undergo a homoclinic Ω-explosion and the structure of the hyperbolic sets is studied for such families
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.
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...
Congruence Approximations for Entrophy Endowed Hyperbolic Systems
Barth, Timothy J.; Saini, Subhash (Technical Monitor)
1998-01-01
Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.
Hyperbolic metamaterials: Nonlocal response regularizes broadband supersingularity
DEFF Research Database (Denmark)
Yan, Wei; Wubs, Martijn; Mortensen, N. Asger
2012-01-01
We study metamaterials known as hyperbolic media that in the usual local-response approximation exhibit hyperbolic dispersion and an associated broadband singularity in the density of states. Instead, from the more microscopic hydrodynamic Drude theory we derive qualitatively different optical...... properties of these metamaterials, due to the free-electron nonlocal optical response of their metal constituents. We demonstrate that nonlocal response gives rise to a large-wavevector cutoff in the dispersion that is inversely proportional to the Fermi velocity of the electron gas, but also for small...
Osteosarcoma models : understanding complex disease
Mohseny, Alexander Behzad
2012-01-01
A mesenchymal stem cell (MSC) based osteosarcoma model was established. The model provided evidence for a MSC origin of osteosarcoma. Normal MSCs transformed spontaneously to osteosarcoma-like cells which was always accompanied by genomic instability and loss of the Cdkn2a locus. Accordingly loss of
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.
Clawpack: building an open source ecosystem for solving hyperbolic PDEs
Mandli, Kyle T.; Ahmadia, Aron J.; Berger, Marsha; Calhoun, Donna; George, David L.; Hadjimichael, Yiannis; Ketcheson, David I.; Lemoine, Grady I.; 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.
The relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations
International Nuclear Information System (INIS)
Liu Chunping; Liu Xiaoping
2004-01-01
First, we investigate the solitary wave solutions of the Burgers equation and the KdV equation, which are obtained by using the hyperbolic function method. Then we present a theorem which will not only give us a clear relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations, but also provide us an approach to construct new exact solutions in complex scalar field. Finally, we apply the theorem to the KdV-Burgers equation and obtain its new exact solutions
Thermodynamic modeling of complex systems
DEFF Research Database (Denmark)
Liang, Xiaodong
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...... is successfully applied to model the phase behaviour of water, chemical and hydrocarbon (oil) containing systems with newly developed pure component parameters for water and chemicals and characterization procedures for petroleum fluids. The performance of the PCSAFT EOS on liquid-liquid equilibria of water...... with hydrocarbons has been under debate for some vii years. An interactive step-wise procedure is proposed to fit the model parameters for small associating fluids by taking the liquid-liquid equilibrium data into account. It is still far away from a simple task to apply PC-SAFT in routine PVT simulations and phase...
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.
Atomic disintegrations for partially hyperbolic diffeomorphisms
Homburg, Ale Jan
2017-01-01
Shub and Wilkinson and Ruelle and Wilkinson studied a class of volume preserving diffeomorphisms on the three dimensional torus that are stably ergodic. The diffeomorphisms are partially hyperbolic and admit an invariant central foliation of circles. The foliation is not absolutely continuous; in
Analytic vortex solutions on compact hyperbolic surfaces
International Nuclear Information System (INIS)
Maldonado, Rafael; Manton, Nicholas S
2015-01-01
We construct, for the first time, abelian Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given implicitly in terms of Schwarz triangle functions and analytic solutions are available for certain highly symmetric configurations. (paper)
The Hyperbolic Sine Cardinal and the Catenary
Sanchez-Reyes, Javier
2012-01-01
The hyperbolic function sinh(x)/x receives scant attention in the literature. We show that it admits a clear geometric interpretation as the ratio between length and chord of a symmetric catenary segment. The inverse, together with the use of dimensionless parameters, furnishes a compact, explicit construction of a general catenary segment of…
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...
Role models for complex networks
Reichardt, J.; White, D. R.
2007-11-01
We present a framework for automatically decomposing (“block-modeling”) the functional classes of agents within a complex network. These classes are represented by the nodes of an image graph (“block model”) depicting the main patterns of connectivity and thus functional roles in the network. Using a first principles approach, we derive a measure for the fit of a network to any given image graph allowing objective hypothesis testing. From the properties of an optimal fit, we derive how to find the best fitting image graph directly from the network and present a criterion to avoid overfitting. The method can handle both two-mode and one-mode data, directed and undirected as well as weighted networks and allows for different types of links to be dealt with simultaneously. It is non-parametric and computationally efficient. The concepts of structural equivalence and modularity are found as special cases of our approach. We apply our method to the world trade network and analyze the roles individual countries play in the global economy.
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....... 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...
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
Models of complex attitude systems
DEFF Research Database (Denmark)
Sørensen, Bjarne Taulo
search algorithms and structural equation models. The results suggest that evaluative judgments of the importance of production system attributes are generated in a schematic manner, driven by personal value orientations. The effect of personal value orientations was strong and largely unmediated...... that evaluative affect propagates through the system in such a way that the system becomes evaluatively consistent and operates as a schema for the generation of evaluative judgments. In the empirical part of the paper, the causal structure of an attitude system from which people derive their evaluations of pork......Existing research on public attitudes towards agricultural production systems is largely descriptive, abstracting from the processes through which members of the general public generate their evaluations of such systems. The present paper adopts a systems perspective on such evaluations...
Higher order Godunov methods for general systems of hyperbolic conservation laws
International Nuclear Information System (INIS)
Bell, J.B.; Colella, P.; Trangenstein, J.A.
1989-01-01
We describe an extension of higher order Godunov methods to general systems of hyperbolic conservation laws. This extension allow the method to be applied to problems that are not strictly hyperbolic and exhibit local linear degeneracies in the wave fields. The method constructs an approximation of the Riemann problem from local wave information. A generalization of the Engquist--Osher flux for systems is then used to compute a numerical flux based on this approximation. This numerical flux replaces the Godunov numerical flux in the algorithm, thereby eliminating the need for a global Riemann problem solution. The additional modifications to the Godunov methodology that are needed to treat loss of strict hyperbolicity are described in detail. The method is applied to some simple model problems for which the glocal analytic structure is known. The method is also applied to the black-oil model for multiphase flow in petroleum reservoirs. copyright 1989 Academic Press, Inc
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.
Elliptical, parabolic, and hyperbolic exchanges of energy in drag reducing plane Couette flows
Pereira, Anselmo S.; Mompean, Gilmar; Thompson, Roney L.; Soares, Edson J.
2017-11-01
In the present paper, we investigate the polymer-turbulence interaction by discriminating between the mechanical responses of this system to three different subdomains: elliptical, parabolic, and hyperbolic, corresponding to regions where the magnitude of vorticity is greater than, equal to, or less than the magnitude of the rate of strain, respectively, in accordance with the Q-criterion. Recently, it was recognized that hyperbolic structures play a crucial role in the drag reduction phenomenon of viscoelastic turbulent flows, thanks to the observation that hyperbolic structures, as well as vortical ones, are weakened by the action of polymers in turbulent flows in a process that can be referred to as flow parabolization. We employ direct numerical simulations of a viscoelastic finite extensible nonlinear elastic model with the Peterlin approximation to examine the transient evolution and statistically steady regimes of a plane Couette flow that has been perturbed from a laminar flow at an initial time and developed a turbulent regime as a result of this perturbation. We have found that even more activity is located within the confines of the hyperbolic structures than in the elliptical ones, which highlights the importance of considering the role of hyperbolic structures in the drag reduction mechanism.
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.
Canadell, Marta; Haro, Àlex
2017-12-01
We present several algorithms for computing normally hyperbolic invariant tori carrying quasi-periodic motion of a fixed frequency in families of dynamical systems. The algorithms are based on a KAM scheme presented in Canadell and Haro (J Nonlinear Sci, 2016. doi: 10.1007/s00332-017-9389-y), to find the parameterization of the torus with prescribed dynamics by detuning parameters of the model. The algorithms use different hyperbolicity and reducibility properties and, in particular, compute also the invariant bundles and Floquet transformations. We implement these methods in several 2-parameter families of dynamical systems, to compute quasi-periodic arcs, that is, the parameters for which 1D normally hyperbolic invariant tori with a given fixed frequency do exist. The implementation lets us to perform the continuations up to the tip of the quasi-periodic arcs, for which the invariant curves break down. Three different mechanisms of breakdown are analyzed, using several observables, leading to several conjectures.
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
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...
Near-field thermal radiation between hyperbolic metamaterials: Graphite and carbon nanotubes
Energy Technology Data Exchange (ETDEWEB)
Liu, X. L.; Zhang, R. Z.; Zhang, Z. M., E-mail: zhuomin.zhang@me.gatech.edu [G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)
2013-11-18
The near-field radiative heat transfer for two hyperbolic metamaterials, namely, graphite and vertically aligned carbon nanotubes (CNTs), is investigated. Graphite is a naturally existing uniaxial medium, while CNT arrays can be modeled as an effective anisotropic medium. Different hyperbolic modes can be separately supported by these materials in certain infrared regions, resulting in a strong enhancement in near-field heat transfer. It is predicted that the heat flux between two CNT arrays can exceed that between SiC plates at any vacuum gap distance and is about 10 times higher with a 10 nm gap.
Onto the stability analysis of hyperbolic secant-shaped Bose-Einstein condensate
Sabari, S.; Murali, R.
2018-05-01
We analyze the stability of the hyperbolic secant-shaped attractive Bose-Einstein condensate in the absence of external trapping potential. The appropriate theoretical model for the system is described by the nonlinear mean-field Gross-Pitaevskii equation with time varying two-body interaction effects. Using the variational method, the stability of the system is analyzed under the influence of time varying two-body interactions. Further we confirm that the stability of the attractive condensate increases by considering the hyperbolic secant-shape profile instead of Gaussian shape. The analytical results are compared with the numerical simulation by employing the split-step Crank-Nicholson method.
An inspection to the hyperbolic heat conduction problem in processed meat
Directory of Open Access Journals (Sweden)
Liu Kuo-Chi
2017-01-01
Full Text Available This paper analyzes a hyperbolic heat conduction problem in processed meat with the non-homogenous initial temperature. This problem is related to an experimental study for the exploration of thermal wave behavior in biological tissue. Because the fundamental solution of the hyperbolic heat conduction model is difficult to be obtained, a modified numerical scheme is extended to solve the problem. The present results deviate from that in the literature and depict that the reliability of the experimentally measured properties presented in the literature is doubtful.
RG cascades in hyperbolic quiver gauge theories
International Nuclear Information System (INIS)
Ahl Laamara, R.; Ait Ben Haddou, M.; Belhaj, A.; Drissi, L.B.; Saidi, E.H.
2004-01-01
In this paper, we provide a general classification of supersymmatric QFT4s into three basic sets: ordinary, affine and indefinite classes. The last class, which has not been enough explored in literature, is shown to share most of properties of ordinary and affine super-QFT4s. This includes, amongst others, its embedding in type II string on local Calabi-Yau threefolds. We give realizations of these supersymmetric QFT4s as D-brane world volume gauge theories. A special interest is devoted to hyperbolic subset for its peculiar features and for the role it plays in type IIB background with non-zero axion. We also study RG flows and duality cascades in case of hyperbolic quiver theories. Comments regarding the full indefinite sector are made
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.”
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....... The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type....
Uncertainty quantification for hyperbolic and kinetic equations
Pareschi, Lorenzo
2017-01-01
This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.
Hyperbolic metamaterial lens with hydrodynamic nonlocal response
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 free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion cu...
Gromov hyperbolicity in lexicographic product graphs
Indian Academy of Sciences (India)
41
on the group [17]. The concept of hyperbolicity appears also in discrete mathematics, algorithms and networking. For .... graph (of a presentation with solvable word problem) there is an algorithm which allows to decide if it is ...... of Theorem 3.14, i.e., dG1◦{w}(Vp, [π(x)π(z)] ∪ [π(z)π(y)]) = δ(G1) with π the canonical projection.
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.
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
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. PMID:26247591
Modeling OPC complexity for design for manufacturability
Gupta, Puneet; Kahng, Andrew B.; Muddu, Swamy; Nakagawa, Sam; Park, Chul-Hong
2005-11-01
Increasing design complexity in sub-90nm designs results in increased mask complexity and cost. Resolution enhancement techniques (RET) such as assist feature addition, phase shifting (attenuated PSM) and aggressive optical proximity correction (OPC) help in preserving feature fidelity in silicon but increase mask complexity and cost. Data volume increase with rise in mask complexity is becoming prohibitive for manufacturing. Mask cost is determined by mask write time and mask inspection time, which are directly related to the complexity of features printed on the mask. Aggressive RET increase complexity by adding assist features and by modifying existing features. Passing design intent to OPC has been identified as a solution for reducing mask complexity and cost in several recent works. The goal of design-aware OPC is to relax OPC tolerances of layout features to minimize mask cost, without sacrificing parametric yield. To convey optimal OPC tolerances for manufacturing, design optimization should drive OPC tolerance optimization using models of mask cost for devices and wires. Design optimization should be aware of impact of OPC correction levels on mask cost and performance of the design. This work introduces mask cost characterization (MCC) that quantifies OPC complexity, measured in terms of fracture count of the mask, for different OPC tolerances. MCC with different OPC tolerances is a critical step in linking design and manufacturing. In this paper, we present a MCC methodology that provides models of fracture count of standard cells and wire patterns for use in design optimization. MCC cannot be performed by designers as they do not have access to foundry OPC recipes and RET tools. To build a fracture count model, we perform OPC and fracturing on a limited set of standard cells and wire configurations with all tolerance combinations. Separately, we identify the characteristics of the layout that impact fracture count. Based on the fracture count (FC) data
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.
Discontinuous Galerkin Method for Hyperbolic Conservation Laws
Mousikou, Ioanna
2016-01-01
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.
Sutherland models for complex reflection groups
International Nuclear Information System (INIS)
Crampe, N.; Young, C.A.S.
2008-01-01
There are known to be integrable Sutherland models associated to every real root system, or, which is almost equivalent, to every real reflection group. Real reflection groups are special cases of complex reflection groups. In this paper we associate certain integrable Sutherland models to the classical family of complex reflection groups. Internal degrees of freedom are introduced, defining dynamical spin chains, and the freezing limit taken to obtain static chains of Haldane-Shastry type. By considering the relation of these models to the usual BC N case, we are led to systems with both real and complex reflection groups as symmetries. We demonstrate their integrability by means of new Dunkl operators, associated to wreath products of dihedral groups
Yen, Steven T.; Liu, Shiping; Kolpin, Dana W.
1996-01-01
A nonnormal and heteroscedastic Tobit model is used to determine the primary factors that affect nitrate concentrations in near-surface aquifers, using data from the U.S. Geological Survey collected in 1991. Both normality and homoscedasticity of errors are rejected, justifying the use of a nonnormal and heteroscedastic model. The following factors are found to have significant impacts on nitrate concentrations in groundwater: well screen interval, depth to top of aquifers, percentages of urban residential, forest land, and pasture within 3.2 km, dissolved oxygen concentration level, and presence of a chemical facility and feedlot. The effects of explanatory variables on nitrate concentration are explored further by calculating elasticities. Dissolved oxygen concentration level has more notable effects on nitrate concentrations in groundwater than other variables.
Minimum-complexity helicopter simulation math model
Heffley, Robert K.; Mnich, Marc A.
1988-01-01
An example of a minimal complexity simulation helicopter math model is presented. Motivating factors are the computational delays, cost, and inflexibility of the very sophisticated math models now in common use. A helicopter model form is given which addresses each of these factors and provides better engineering understanding of the specific handling qualities features which are apparent to the simulator pilot. The technical approach begins with specification of features which are to be modeled, followed by a build up of individual vehicle components and definition of equations. Model matching and estimation procedures are given which enable the modeling of specific helicopters from basic data sources such as flight manuals. Checkout procedures are given which provide for total model validation. A number of possible model extensions and refinement are discussed. Math model computer programs are defined and listed.
On hyperbolic-dissipative systems of composite type
Tan, Zhong; Wang, Yanjin
2016-01-01
The Shizuta-Kawashima condition plays the fundamental role in guaranteeing global stability for systems of hyperbolic-parabolic/hyperbolic with relaxation. However, there are many important physical systems not satisfying this coupling condition, which are of composite type with regard to dissipation. The compressible Navier-Stokes equations with zero heat conductivity and Euler equations of adiabatic flow through porous media are two typical examples. In this paper, we construct the global unique solution near constant equilibria to these two systems in three dimensions for the small Hℓ (ℓ > 3) initial data. Our proof is based on a reformation of the systems in terms of the pressure, velocity and entropy, a scaled energy estimates with minimal fractional derivative counts in conjunction with the linear L2-L2 decay estimates to extract a fast enough decay of velocity gradient, which is used to close the energy estimates for the non-dissipative entropy. We also include an application to certain two-phase models.
Estimates of the Hyperbolic Radius Gradient and Schwarz–Pick Inequalities for the Eccentric Annulus
Directory of Open Access Journals (Sweden)
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.
Infinite periodic minimal surfaces and their crystallography in the hyperbolic plane
International Nuclear Information System (INIS)
Sadoc, J.F.; Charvolin, J.
1989-01-01
Infinite periodic minimal surfaces are now being introduced to describe some complex structures with large cells, formed by inorganic and organic materials, which can be considered as crystals of surfaces or films. Among them are the spectacular cubic crystalline structures built by amphiphilic molecules in the presence of water. The crystallographic properties of these surfaces are studied from an intrinsic point of view, using operations of groups of symmetry defined by displacements on their surface. This approach takes advantage of the relation existing between these groups and those characterizing the tilings of the hyperbolic plane. First, the general bases of the particular crystallography of the hyperbolic plane are presented. Then the translation subgroups of the hyperbolic plane are determined in one particular case, that of the tiling involved in the problem of cubic structures of liquid crystals. Finally, it is shown that the infinite periodic minimal surfaces used to describe these structures can be obtained from the hyperbolic plane when some translations are forced to identity. This is indeed formally analogous to the simple process of transformation of a Euclidean plane into a cylinder, when a translation of the plane is forced to identity by rolling the plane onto itself. Thus, this approach transforms the 3D problem of infinite periodic minimal surfaces into a 2D problem and, although the latter is to be treated in a non-Euclidean space, provides a relatively simple formalism for the investigation of infinite periodic surfaces in general and the study of the geometrical transformations relating them. (orig.)
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
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.
Geometric Modelling with a-Complexes
Gerritsen, B.H.M.; Werff, K. van der; Veltkamp, R.C.
2001-01-01
The shape of real objects can be so complicated, that only a sampling data point set can accurately represent them. Analytic descriptions are too complicated or impossible. Natural objects, for example, can be vague and rough with many holes. For this kind of modelling, a-complexes offer advantages
The Kuramoto model in complex networks
Rodrigues, Francisco A.; Peron, Thomas K. DM.; Ji, Peng; Kurths, Jürgen
2016-01-01
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.
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
Comparing flood loss models of different complexity
Schröter, Kai; Kreibich, Heidi; Vogel, Kristin; Riggelsen, Carsten; Scherbaum, Frank; Merz, Bruno
2013-04-01
Any deliberation on flood risk requires the consideration of potential flood losses. In particular, reliable flood loss models are needed to evaluate cost-effectiveness of mitigation measures, to assess vulnerability, for comparative risk analysis and financial appraisal during and after floods. In recent years, considerable improvements have been made both concerning the data basis and the methodological approaches used for the development of flood loss models. Despite of that, flood loss models remain an important source of uncertainty. Likewise the temporal and spatial transferability of flood loss models is still limited. This contribution investigates the predictive capability of different flood loss models in a split sample cross regional validation approach. For this purpose, flood loss models of different complexity, i.e. based on different numbers of explaining variables, are learned from a set of damage records that was obtained from a survey after the Elbe flood in 2002. The validation of model predictions is carried out for different flood events in the Elbe and Danube river basins in 2002, 2005 and 2006 for which damage records are available from surveys after the flood events. The models investigated are a stage-damage model, the rule based model FLEMOps+r as well as novel model approaches which are derived using data mining techniques of regression trees and Bayesian networks. The Bayesian network approach to flood loss modelling provides attractive additional information concerning the probability distribution of both model predictions and explaining variables.
Complex scaling in the cluster model
International Nuclear Information System (INIS)
Kruppa, A.T.; Lovas, R.G.; Gyarmati, B.
1987-01-01
To find the positions and widths of resonances, a complex scaling of the intercluster relative coordinate is introduced into the resonating-group model. In the generator-coordinate technique used to solve the resonating-group equation the complex scaling requires minor changes in the formulae and code. The finding of the resonances does not need any preliminary guess or explicit reference to any asymptotic prescription. The procedure is applied to the resonances in the relative motion of two ground-state α clusters in 8 Be, but is appropriate for any systems consisting of two clusters. (author) 23 refs.; 5 figs
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...
Modeling of anaerobic digestion of complex substrates
International Nuclear Information System (INIS)
Keshtkar, A. R.; Abolhamd, G.; Meyssami, B.; Ghaforian, H.
2003-01-01
A structured mathematical model of anaerobic conversion of complex organic materials in non-ideally cyclic-batch reactors for biogas production has been developed. The model is based on multiple-reaction stoichiometry (enzymatic hydrolysis, acidogenesis, aceto genesis and methano genesis), microbial growth kinetics, conventional material balances in the liquid and gas phases for a cyclic-batch reactor, liquid-gas interactions, liquid-phase equilibrium reactions and a simple mixing model which considers the reactor volume in two separate sections: the flow-through and the retention regions. The dynamic model describes the effects of reactant's distribution resulting from the mixing conditions, time interval of feeding, hydraulic retention time and mixing parameters on the process performance. The model is applied in the simulation of anaerobic digestion of cattle manure under different operating conditions. The model is compared with experimental data and good correlations are obtained
Quasilinear Hyperbolic Systems, Compressible Flows, and Waves
Sharma, Vishnu D
2010-01-01
Filled with practical examples, this book presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications. It emphasizes nonlinear theory and introduces some of the most active research in the field. The author elucidates all necessary mathematical concepts in the first three chapters, including an introduction to general wave propagation problems. He highlights the application of various approaches, such as singular surface theory, asymptotic methods, and self-similarity, to solve practical physical problems from areas, including gasdynamics, radiation g
Design of a hyperbolic microwave metallic lens
International Nuclear Information System (INIS)
Uckan, T.
1979-12-01
Due to problems caused by multiple reflections in the cavity walls of the EBT fusion research device, the use of a horn becomes important for the directivity of waves in the millimetric range. An ordinary dielectric lens cannot be used because of plasma-wall interactions. Microwave metallic lenses, designed to focus the energy into a plane wave, can improve the directivity considerably. By implementing a 70-GHz standard-gain horn with a delay-type hyperbolic lens, which consists of a solid metallic disk with a number of equal size small holes has indicated a gain of 15 dB over the no lens case
Hyperbolic statics in space-time
Pavlov, Dmitry; Kokarev, Sergey
2014-01-01
Based on the concept of material event as an elementary material source that is concentrated on metric sphere of zero radius --- light-cone of Minkowski space-time, we deduce the analog of Coulomb's law for hyperbolic space-time field universally acting between the events of space-time. Collective field that enables interaction of world lines of a pair of particles at rest contains a standard 3-dimensional Coulomb's part and logarithmic addendum. We've found that the Coulomb's part depends on...
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.
Photon gas with hyperbolic dispersion relations
International Nuclear Information System (INIS)
Mohseni, Morteza
2013-01-01
We investigate the density of states for a photon gas confined in a nonmagnetic metamaterial medium in which some components of the permittivity tensor are negative. We study the effect of the resulting hyperbolic dispersion relations on the black body spectral density. We show that for both of the possible wavevector space topologies, the spectral density vanishes at a certain frequency. We obtain the partition function and derive some thermodynamical quantities of the system. To leading order, the results resemble those of a one- or two-dimensional photon gas with an enhanced density of states. (paper)
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.
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.
Different Epidemic Models on Complex Networks
International Nuclear Information System (INIS)
Zhang Haifeng; Small, Michael; Fu Xinchu
2009-01-01
Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can be sorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals' relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemic models on complex networks, and obtain the epidemic threshold for each case. Finally, we present numerical simulations for each case to verify our results.
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.
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…
Computing the Gromov hyperbolicity of a discrete metric space
Fournier, Hervé
2015-01-01
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
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.
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.
Coexistence of critical orbit types in sub-hyperbolic polynomial maps
Poirier, Alfredo
1994-01-01
We establish necessary and sufficient conditions for the realization of mapping schemata as post-critically finite polynomials, or more generally, as post-critically finite polynomial maps from a finite union of copies of the complex numbers {\\bf C} to itself which have degree two or more in each copy. As a consequence of these results we prove a transitivity relation between hyperbolic components in parameter space which was conjectured by Milnor.
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 ...
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.
From complex to simple: interdisciplinary stochastic models
International Nuclear Information System (INIS)
Mazilu, D A; Zamora, G; Mazilu, I
2012-01-01
We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions for certain physical quantities, such as the time dependence of the length of the microtubules, and diffusion coefficients. The second one is a stochastic adsorption model with applications in surface deposition, epidemics and voter systems. We introduce the ‘empty interval method’ and show sample calculations for the time-dependent particle density. These models can serve as an introduction to the field of non-equilibrium statistical physics, and can also be used as a pedagogical tool to exemplify standard statistical physics concepts, such as random walks or the kinetic approach of the master equation. (paper)
Contact Geometry of Hyperbolic Equations of Generic Type
Directory of Open Access Journals (Sweden)
Dennis The
2008-08-01
Full Text Available We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampère (class 6-6, Goursat (class 6-7 and generic (class 7-7 hyperbolic equations, we use Cartan's equivalence method to study the generic case. An intriguing feature of this class of equations is that every generic hyperbolic equation admits at most a nine-dimensional contact symmetry algebra. The nine-dimensional bound is sharp: normal forms for the contact-equivalence classes of these maximally symmetric generic hyperbolic equations are derived and explicit symmetry algebras are presented. Moreover, these maximally symmetric equations are Darboux integrable. An enumeration of several submaximally symmetric (eight and seven-dimensional generic hyperbolic structures is also given.
Layered van der Waals crystals with hyperbolic light dispersion
DEFF Research Database (Denmark)
Gjerding, Morten Niklas; Petersen, R.; Pedersen, T.G.
2017-01-01
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......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...
A SIMULATION MODEL OF THE GAS COMPLEX
Directory of Open Access Journals (Sweden)
Sokolova G. E.
2016-06-01
Full Text Available The article considers the dynamics of gas production in Russia, the structure of sales in the different market segments, as well as comparative dynamics of selling prices on these segments. Problems of approach to the creation of the gas complex using a simulation model, allowing to estimate efficiency of the project and determine the stability region of the obtained solutions. In the presented model takes into account the unit repayment of the loan, allowing with the first year of simulation to determine the possibility of repayment of the loan. The model object is a group of gas fields, which is determined by the minimum flow rate above which the project is cost-effective. In determining the minimum source flow rate for the norm of discount is taken as a generalized weighted average percentage on debt and equity taking into account risk premiums. He also serves as the lower barrier to internal rate of return below which the project is rejected as ineffective. Analysis of the dynamics and methods of expert evaluation allow to determine the intervals of variation of the simulated parameters, such as the price of gas and the exit gas complex at projected capacity. Calculated using the Monte Carlo method, for each random realization of the model simulated values of parameters allow to obtain a set of optimal for each realization of values minimum yield of wells, and also allows to determine the stability region of the solution.
Mechhoud, Sarra; Laleg-Kirati, Taous-Meriem
2016-01-01
In this paper, boundary adaptive estimation of solar radiation in a solar collector plant is investigated. The solar collector is described by a 1D first-order hyperbolic partial differential equation where the solar radiation models the source term
Structured analysis and modeling of complex systems
Strome, David R.; Dalrymple, Mathieu A.
1992-01-01
The Aircrew Evaluation Sustained Operations Performance (AESOP) facility at Brooks AFB, Texas, combines the realism of an operational environment with the control of a research laboratory. In recent studies we collected extensive data from the Airborne Warning and Control Systems (AWACS) Weapons Directors subjected to high and low workload Defensive Counter Air Scenarios. A critical and complex task in this environment involves committing a friendly fighter against a hostile fighter. Structured Analysis and Design techniques and computer modeling systems were applied to this task as tools for analyzing subject performance and workload. This technology is being transferred to the Man-Systems Division of NASA Johnson Space Center for application to complex mission related tasks, such as manipulating the Shuttle grappler arm.
Devasia, Santosh
1996-01-01
A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics is presented. This approach integrates stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics is used (1) to remove non-hyperbolicity which an obstruction to applying stable inversion techniques and (2) to reduce large pre-actuation time needed to apply stable inversion for near non-hyperbolic cases. The method is applied to an example helicopter hover control problem with near non-hyperbolic internal dynamic for illustrating the trade-off between exact tracking and reduction of pre-actuation time.
Directory of Open Access Journals (Sweden)
Robert M. Yamaleev
2013-01-01
Full Text Available The hyperbolic cosines and sines theorems for the curvilinear triangle bounded by circular arcs of three intersecting circles are formulated and proved by using the general complex calculus. The method is based on a key formula establishing a relationship between exponential function and the cross-ratio. The proofs are carried out on Euclidean plane.
Glass Durability Modeling, Activated Complex Theory (ACT)
International Nuclear Information System (INIS)
CAROL, JANTZEN
2005-01-01
The most important requirement for high-level waste glass acceptance for disposal in a geological repository is the chemical durability, expressed as a glass dissolution rate. During the early stages of glass dissolution in near static conditions that represent a repository disposal environment, a gel layer resembling a membrane forms on the glass surface through which ions exchange between the glass and the leachant. The hydrated gel layer exhibits acid/base properties which are manifested as the pH dependence of the thickness and nature of the gel layer. The gel layer has been found to age into either clay mineral assemblages or zeolite mineral assemblages. The formation of one phase preferentially over the other has been experimentally related to changes in the pH of the leachant and related to the relative amounts of Al +3 and Fe +3 in a glass. The formation of clay mineral assemblages on the leached glass surface layers ,lower pH and Fe +3 rich glasses, causes the dissolution rate to slow to a long-term steady state rate. The formation of zeolite mineral assemblages ,higher pH and Al +3 rich glasses, on leached glass surface layers causes the dissolution rate to increase and return to the initial high forward rate. The return to the forward dissolution rate is undesirable for long-term performance of glass in a disposal environment. An investigation into the role of glass stoichiometry, in terms of the quasi-crystalline mineral species in a glass, has shown that the chemistry and structure in the parent glass appear to control the activated surface complexes that form in the leached layers, and these mineral complexes ,some Fe +3 rich and some Al +3 rich, play a role in whether or not clays or zeolites are the dominant species formed on the leached glass surface. The chemistry and structure, in terms of Q distributions of the parent glass, are well represented by the atomic ratios of the glass forming components. Thus, glass dissolution modeling using simple
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
Adaptive aberration correction using a triode hyperbolic electron mirror
International Nuclear Information System (INIS)
Fitzgerald, J.P.S.; Word, R.C.; Koenenkamp, R.
2011-01-01
A converging electron mirror can be used to compensate spherical and chromatic aberrations in an electron microscope. This paper presents an analytical solution to a novel triode (three electrode) hyperbolic mirror as an improvement to the well-known diode (two electrode) hyperbolic mirror for aberration correction. A weakness of the diode mirror is a lack of flexibility in changing the chromatic and spherical aberration coefficients independently without changes in the mirror geometry. In order to remove this limitation, a third electrode can be added. We calculate the optical properties of the resulting triode mirror analytically on the basis of a simple model field distribution. We present the optical properties-the object/image distance, z 0 , and the coefficients of spherical and chromatic aberration, C s and C c , of both mirror types from an analysis of electron trajectories in the mirror field. From this analysis, we demonstrate that while the properties of both designs are similar, the additional parameters in the triode mirror improve the range of aberration that can be corrected. The triode mirror is also able to provide a dynamic adjustment range of chromatic aberration for fixed spherical aberration and focal length, or any permutation of these three parameters. While the dynamic range depends on the values of aberration correction needed, a nominal 10% tuning range is possible for most configurations accompanied by less than 1% change in the other two properties. -- Highlights: → Electrostatic aberration correction for chromatic and spherical aberration in electron optics. → Simultaneous correction of spherical and chromatic aberrations over a wide, adjustable range. → Analytic and quantitative description of correction parameters.
Hyperbolic planforms in relation to visual edges and textures perception.
Directory of Open Access Journals (Sweden)
Pascal Chossat
2009-12-01
Full Text Available We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g., optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in previous work to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.
Landau levels on the hyperbolic plane
International Nuclear Information System (INIS)
Fakhri, H; Shariati, M
2004-01-01
The quantum states of a spinless charged particle on a hyperbolic plane in the presence of a uniform magnetic field with a generalized quantization condition are proved to be the bases of the irreducible Hilbert representation spaces of the Lie algebra u(1, 1). The dynamical symmetry group U(1, 1) with the explicit form of the Lie algebra generators is extracted. It is also shown that the energy has an infinite-fold degeneracy in each of the representation spaces which are allocated to the different values of the magnetic field strength. Based on the simultaneous shift of two parameters, it is also noted that the quantum states realize the representations of Lie algebra u(2) by shifting the magnetic field strength. (letter to the editor)
Landau levels on the hyperbolic plane
Energy Technology Data Exchange (ETDEWEB)
Fakhri, H [Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran 19395-5531 (Iran, Islamic Republic of); Shariati, M [Department of Physics, Khajeh Nassir-Al-Deen Toosi University of Technology, Tehran 15418 (Iran, Islamic Republic of)
2004-11-05
The quantum states of a spinless charged particle on a hyperbolic plane in the presence of a uniform magnetic field with a generalized quantization condition are proved to be the bases of the irreducible Hilbert representation spaces of the Lie algebra u(1, 1). The dynamical symmetry group U(1, 1) with the explicit form of the Lie algebra generators is extracted. It is also shown that the energy has an infinite-fold degeneracy in each of the representation spaces which are allocated to the different values of the magnetic field strength. Based on the simultaneous shift of two parameters, it is also noted that the quantum states realize the representations of Lie algebra u(2) by shifting the magnetic field strength. (letter to the editor)
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.
Resonances for Obstacles in Hyperbolic Space
Hintz, Peter; Zworski, Maciej
2017-12-01
We consider scattering by star-shaped obstacles in hyperbolic space and show that resonances satisfy a universal bound { Im λ ≤ - 1/2 } , which is optimal in dimension 2. In odd dimensions we also show that { Im λ ≤ - μ/ρ } for a universal constant {μ} , where { ρ } is the radius of a ball containing the obstacle; this gives an improvement for small obstacles. In dimensions 3 and higher the proofs follow the classical vector field approach of Morawetz, while in dimension 2 we obtain our bound by working with spaces coming from general relativity. We also show that in odd dimensions resonances of small obstacles are close, in a suitable sense, to Euclidean resonances.
Complex singlet extension of the standard model
International Nuclear Information System (INIS)
Barger, Vernon; McCaskey, Mathew; Langacker, Paul; Ramsey-Musolf, Michael; Shaughnessy, Gabe
2009-01-01
We analyze a simple extension of the standard model (SM) obtained by adding a complex singlet to the scalar sector (cxSM). We show that the cxSM can contain one or two viable cold dark matter candidates and analyze the conditions on the parameters of the scalar potential that yield the observed relic density. When the cxSM potential contains a global U(1) symmetry that is both softly and spontaneously broken, it contains both a viable dark matter candidate and the ingredients necessary for a strong first order electroweak phase transition as needed for electroweak baryogenesis. We also study the implications of the model for discovery of a Higgs boson at the Large Hadron Collider.
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......; CPA and sPC-SAFT. Phase equilibrium and monomer fraction calculations with sPC-SAFT for methanol are used in the thesis to illustrate the importance of parameter estimation when using SAFT. Different parameter sets give similar pure component vapor pressure and liquid density results, whereas very...... association is presented in the thesis, and compared to the corresponding lattice theory. The theory for intramolecular association is then applied in connection with sPC-SAFT for mixtures containing glycol ethers. Calculations with sPC-SAFT (without intramolecular association) are presented for comparison...
The Model of Complex Structure of Quark
Liu, Rongwu
2017-09-01
In Quantum Chromodynamics, quark is known as a kind of point-like fundamental particle which carries mass, charge, color, and flavor, strong interaction takes place between quarks by means of exchanging intermediate particles-gluons. An important consequence of this theory is that, strong interaction is a kind of short-range force, and it has the features of ``asymptotic freedom'' and ``quark confinement''. In order to reveal the nature of strong interaction, the ``bag'' model of vacuum and the ``string'' model of string theory were proposed in the context of quantum mechanics, but neither of them can provide a clear interaction mechanism. This article formulates a new mechanism by proposing a model of complex structure of quark, it can be outlined as follows: (1) Quark (as well as electron, etc) is a kind of complex structure, it is composed of fundamental particle (fundamental matter mass and electricity) and fundamental volume field (fundamental matter flavor and color) which exists in the form of limited volume; fundamental particle lies in the center of fundamental volume field, forms the ``nucleus'' of quark. (2) As static electric force, the color field force between quarks has classical form, it is proportional to the square of the color quantity carried by each color field, and inversely proportional to the area of cross section of overlapping color fields which is along force direction, it has the properties of overlap, saturation, non-central, and constant. (3) Any volume field undergoes deformation when interacting with other volume field, the deformation force follows Hooke's law. (4) The phenomena of ``asymptotic freedom'' and ``quark confinement'' are the result of color field force and deformation force.
The hidden hyperbolic geometry of international trade: World Trade Atlas 1870-2013.
García-Pérez, Guillermo; Boguñá, Marián; Allard, Antoine; Serrano, M Ángeles
2016-09-16
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.
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
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.
Reducing Spatial Data Complexity for Classification Models
International Nuclear Information System (INIS)
Ruta, Dymitr; Gabrys, Bogdan
2007-01-01
Intelligent data analytics gradually becomes a day-to-day reality of today's businesses. However, despite rapidly increasing storage and computational power current state-of-the-art predictive models still can not handle massive and noisy corporate data warehouses. What is more adaptive and real-time operational environment requires multiple models to be frequently retrained which further hinders their use. Various data reduction techniques ranging from data sampling up to density retention models attempt to address this challenge by capturing a summarised data structure, yet they either do not account for labelled data or degrade the classification performance of the model trained on the condensed dataset. Our response is a proposition of a new general framework for reducing the complexity of labelled data by means of controlled spatial redistribution of class densities in the input space. On the example of Parzen Labelled Data Compressor (PLDC) we demonstrate a simulatory data condensation process directly inspired by the electrostatic field interaction where the data are moved and merged following the attracting and repelling interactions with the other labelled data. The process is controlled by the class density function built on the original data that acts as a class-sensitive potential field ensuring preservation of the original class density distributions, yet allowing data to rearrange and merge joining together their soft class partitions. As a result we achieved a model that reduces the labelled datasets much further than any competitive approaches yet with the maximum retention of the original class densities and hence the classification performance. PLDC leaves the reduced dataset with the soft accumulative class weights allowing for efficient online updates and as shown in a series of experiments if coupled with Parzen Density Classifier (PDC) significantly outperforms competitive data condensation methods in terms of classification performance at the
Reducing Spatial Data Complexity for Classification Models
Ruta, Dymitr; Gabrys, Bogdan
2007-11-01
Intelligent data analytics gradually becomes a day-to-day reality of today's businesses. However, despite rapidly increasing storage and computational power current state-of-the-art predictive models still can not handle massive and noisy corporate data warehouses. What is more adaptive and real-time operational environment requires multiple models to be frequently retrained which further hinders their use. Various data reduction techniques ranging from data sampling up to density retention models attempt to address this challenge by capturing a summarised data structure, yet they either do not account for labelled data or degrade the classification performance of the model trained on the condensed dataset. Our response is a proposition of a new general framework for reducing the complexity of labelled data by means of controlled spatial redistribution of class densities in the input space. On the example of Parzen Labelled Data Compressor (PLDC) we demonstrate a simulatory data condensation process directly inspired by the electrostatic field interaction where the data are moved and merged following the attracting and repelling interactions with the other labelled data. The process is controlled by the class density function built on the original data that acts as a class-sensitive potential field ensuring preservation of the original class density distributions, yet allowing data to rearrange and merge joining together their soft class partitions. As a result we achieved a model that reduces the labelled datasets much further than any competitive approaches yet with the maximum retention of the original class densities and hence the classification performance. PLDC leaves the reduced dataset with the soft accumulative class weights allowing for efficient online updates and as shown in a series of experiments if coupled with Parzen Density Classifier (PDC) significantly outperforms competitive data condensation methods in terms of classification performance at the
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
On sampling and modeling complex systems
International Nuclear Information System (INIS)
Marsili, Matteo; Mastromatteo, Iacopo; Roudi, Yasser
2013-01-01
The study of complex systems is limited by the fact that only a few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones to explain the system behavior. In addition, empirical data typically undersample the space of possible states. We study a generic framework where a complex system is seen as a system of many interacting degrees of freedom, which are known only in part, that optimize a given function. We show that the underlying distribution with respect to the known variables has the Boltzmann form, with a temperature that depends on the number of unknown variables. In particular, when the influence of the unknown degrees of freedom on the known variables is not too irregular, the temperature decreases as the number of variables increases. This suggests that models can be predictable only when the number of relevant variables is less than a critical threshold. Concerning sampling, we argue that the information that a sample contains on the behavior of the system is quantified by the entropy of the frequency with which different states occur. This allows us to characterize the properties of maximally informative samples: within a simple approximation, the most informative frequency size distributions have power law behavior and Zipf’s law emerges at the crossover between the under sampled regime and the regime where the sample contains enough statistics to make inferences on the behavior of the system. These ideas are illustrated in some applications, showing that they can be used to identify relevant variables or to select the most informative representations of data, e.g. in data clustering. (paper)
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...
Qualitative behavior of global solutions to inhomogeneous quasilinear hyperbolic systems
International Nuclear Information System (INIS)
Hsiao, L.
1994-01-01
The emphasis is the influence to the qualitative behavior of solutions caused by the lower order term, which is certain dissipation, in quasilinear hyperbolic systems. Both classical solutions and discontinuous weak solutions are discussed. (author). 12 refs
Infrared hyperbolic metasurface based on nanostructured van der Waals materials
Li, Peining; Dolado, Irene; Alfaro-Mozaz, Francisco Javier; Casanova, Fèlix; Hueso, Luis E.; Liu, Song; Edgar, James H.; Nikitin, Alexey Y.; Vélez, Saül; Hillenbrand, Rainer
2018-02-01
Metasurfaces with strongly anisotropic optical properties can support deep subwavelength-scale confined electromagnetic waves (polaritons), which promise opportunities for controlling light in photonic and optoelectronic applications. We developed a mid-infrared hyperbolic metasurface by nanostructuring a thin layer of hexagonal boron nitride that supports deep subwavelength-scale phonon polaritons that propagate with in-plane hyperbolic dispersion. By applying an infrared nanoimaging technique, we visualize the concave (anomalous) wavefronts of a diverging polariton beam, which represent a landmark feature of hyperbolic polaritons. The results illustrate how near-field microscopy can be applied to reveal the exotic wavefronts of polaritons in anisotropic materials and demonstrate that nanostructured van der Waals materials can form a highly variable and compact platform for hyperbolic infrared metasurface devices and circuits.
Forced oscillation of hyperbolic equations with mixed nonlinearities
Directory of Open Access Journals (Sweden)
Yutaka Shoukaku
2012-04-01
Full Text Available In this paper, we consider the mixed nonlinear hyperbolic equations with forcing term via Riccati inequality. Some sufficient conditions for the oscillation are derived by using Young inequality and integral averaging method.
OSCILLATION OF IMPULSIVE HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION WITH DELAY
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, oscillation properties of the solutions of impulsive hyperbolic equation with delay are investigated via the method of differential inequalities. Sufficient conditions for oscillations of the solutions are established.
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).
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.
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.
Hyperbolic Discounting of the Far-Distant Future
Anchugina, Nina; Ryan, Matthew; Slinko, Arkadii
2017-01-01
We prove an analogue of Weitzman's (1998) famous result that an exponential discounter who is uncertain of the appropriate exponential discount rate should discount the far-distant future using the lowest (i.e., most patient) of the possible discount rates. Our analogous result applies to a hyperbolic discounter who is uncertain about the appropriate hyperbolic discount rate. In this case, the far-distant future should be discounted using the probability-weighted harmonic mean of the possible...
A note on sigular limits to hyperbolic systems
Bianchini, Stefano
2000-01-01
In this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. Under the assumption that the rarefaction curve of the corresponding hyperbolic system are straight lines, we prove the stability of the solution and the convergence to the perturbed system to the unique solution of the limit system for initial data with small total variation.
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 homogeniz......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...
Euler and Navier-Stokes equations on the hyperbolic plane.
Khesin, Boris; Misiolek, Gerard
2012-11-06
We show that nonuniqueness of the Leray-Hopf solutions of the Navier-Stokes equation on the hyperbolic plane (2) observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on (n) whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.
Euler and Navier–Stokes equations on the hyperbolic plane
Khesin, Boris; Misiołek, Gerard
2012-01-01
We show that nonuniqueness of the Leray–Hopf solutions of the Navier–Stokes equation on the hyperbolic plane ℍ2 observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on ℍn whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting. PMID:23091015
Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators
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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.
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.
International Nuclear Information System (INIS)
Yomba, Emmanuel
2008-01-01
With the aid of symbolic computation, we demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schroedinger equations. This system includes the modified Hubbard model and the system of coupled nonlinear Schroedinger derived by Lazarides and Tsironis. Four types of solutions for this system are given explicitly, namely: new bright-bright, new dark-dark, new bright-dark and new dark-bright solitons
Modeling the Structure and Complexity of Engineering Routine Design Problems
Jauregui Becker, Juan Manuel; Wits, Wessel Willems; van Houten, Frederikus J.A.M.
2011-01-01
This paper proposes a model to structure routine design problems as well as a model of its design complexity. The idea is that having a proper model of the structure of such problems enables understanding its complexity, and likewise, a proper understanding of its complexity enables the development
Hyperbolic phonon polaritons in hexagonal boron nitride (Conference Presentation)
Dai, Siyuan; Ma, Qiong; Fei, Zhe; Liu, Mengkun; Goldflam, Michael D.; Andersen, Trond; Garnett, William; Regan, Will; Wagner, Martin; McLeod, Alexander S.; Rodin, Alexandr; Zhu, Shou-En; Watanabe, Kenji; Taniguchi, T.; Dominguez, Gerado; Thiemens, Mark; Castro Neto, Antonio H.; Janssen, Guido C. A. M.; Zettl, Alex; Keilmann, Fritz; Jarillo-Herrero, Pablo; Fogler, Michael M.; Basov, Dmitri N.
2016-09-01
Uniaxial materials whose axial and tangential permittivities have opposite signs are referred to as indefinite or hyperbolic media. While hyperbolic responses are normally achieved with metamaterials, hexagonal boron nitride (hBN) naturally possesses this property due to the anisotropic phonons in the mid-infrared. Using scattering-type scanning near-field optical microscopy, we studied polaritonic phenomena in hBN. We performed infrared nano-imaging of highly confined and low-loss hyperbolic phonon polaritons in hBN. The polariton wavelength was shown to be governed by the hBN thickness according to a linear law persisting down to few atomic layers [1]. Additionally, we carried out the modification of hyperbolic response in meta-structures comprised of a mononlayer graphene deposited on hBN [2]. Electrostatic gating of the top graphene layer allows for the modification of wavelength and intensity of hyperbolic phonon polaritons in bulk hBN. The physics of the modification originates from the plasmon-phonon coupling in the hyperbolic medium. Furthermore, we demonstrated the "hyperlens" for subdiffractional focusing and imaging using a slab of hBN [3]. References [1] S. Dai et al., Science, 343, 1125 (2014). [2] S. Dai et al., Nature Nanotechnology, 10, 682 (2015). [3] S. Dai et al., Nature Communications, 6, 6963 (2015).
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.
Geometry in a dynamical system without space: Hyperbolic Geometry in Kuramoto Oscillator Systems
Engelbrecht, Jan; Chen, Bolun; Mirollo, Renato
Kuramoto oscillator networks have the special property that their time evolution is constrained to lie on 3D orbits of the Möbius group acting on the N-fold torus TN which explains the N - 3 constants of motion discovered by Watanabe and Strogatz. The dynamics for phase models can be further reduced to 2D invariant sets in T N - 1 which have a natural geometry equivalent to the unit disk Δ with hyperbolic metric. We show that the classic Kuramoto model with order parameter Z1 (the first moment of the oscillator configuration) is a gradient flow in this metric with a unique fixed point on each generic 2D invariant set, corresponding to the hyperbolic barycenter of an oscillator configuration. This gradient property makes the dynamics especially easy to analyze. We exhibit several new families of Kuramoto oscillator models which reduce to gradient flows in this metric; some of these have a richer fixed point structure including non-hyperbolic fixed points associated with fixed point bifurcations. Work Supported by NSF DMS 1413020.
Doubly stratified MHD tangent hyperbolic nanofluid flow due to permeable stretched cylinder
Nagendramma, V.; Leelarathnam, A.; Raju, C. S. K.; Shehzad, S. A.; Hussain, T.
2018-06-01
An investigation is exhibited to analyze the presence of heat source and sink in doubly stratified MHD incompressible tangent hyperbolic fluid due to stretching of cylinder embedded in porous space under nanoparticles. To develop the mathematical model of tangent hyperbolic nanofluid, movement of Brownian and thermophoretic are accounted. The established equations of continuity, momentum, thermal and solutal boundary layers are reassembled into sets of non-linear expressions. These assembled expressions are executed with the help of Runge-Kutta scheme with MATLAB. The impacts of sundry parameters are illustrated graphically and the engineering interest physical quantities like skin friction, Nusselt and Sherwood number are examined by computing numerical values. It is clear that the power-law index parameter and curvature parameter shows favorable effect on momentum boundary layer thickness whereas Weissennberg number reveals inimical influence.
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.
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.
Modeling competitive substitution in a polyelectrolyte complex
International Nuclear Information System (INIS)
Peng, B.; Muthukumar, M.
2015-01-01
We have simulated the invasion of a polyelectrolyte complex made of a polycation chain and a polyanion chain, by another longer polyanion chain, using the coarse-grained united atom model for the chains and the Langevin dynamics methodology. Our simulations reveal many intricate details of the substitution reaction in terms of conformational changes of the chains and competition between the invading chain and the chain being displaced for the common complementary chain. We show that the invading chain is required to be sufficiently longer than the chain being displaced for effecting the substitution. Yet, having the invading chain to be longer than a certain threshold value does not reduce the substitution time much further. While most of the simulations were carried out in salt-free conditions, we show that presence of salt facilitates the substitution reaction and reduces the substitution time. Analysis of our data shows that the dominant driving force for the substitution process involving polyelectrolytes lies in the release of counterions during the substitution
Modelling of information processes management of educational complex
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Оксана Николаевна Ромашкова
2014-12-01
Full Text Available This work concerns information model of the educational complex which includes several schools. A classification of educational complexes formed in Moscow is given. There are also a consideration of the existing organizational structure of the educational complex and a suggestion of matrix management structure. Basic management information processes of the educational complex were conceptualized.
Sandpile model for relaxation in complex systems
International Nuclear Information System (INIS)
Vazquez, A.; Sotolongo-Costa, O.; Brouers, F.
1997-10-01
The relaxation in complex systems is, in general, nonexponential. After an initial rapid decay the system relaxes slowly following a long time tail. In the present paper a sandpile moderation of the relaxation in complex systems is analysed. Complexity is introduced by a process of avalanches in the Bethe lattice and a feedback mechanism which leads to slower decay with increasing time. In this way, some features of relaxation in complex systems: long time tails relaxation, aging, and fractal distribution of characteristic times, are obtained by simple computer simulations. (author)
Modeling Complex Chemical Systems: Problems and Solutions
van Dijk, Jan
2016-09-01
Non-equilibrium plasmas in complex gas mixtures are at the heart of numerous contemporary technologies. They typically contain dozens to hundreds of species, involved in hundreds to thousands of reactions. Chemists and physicists have always been interested in what are now called chemical reduction techniques (CRT's). The idea of such CRT's is that they reduce the number of species that need to be considered explicitly without compromising the validity of the model. This is usually achieved on the basis of an analysis of the reaction time scales of the system under study, which identifies species that are in partial equilibrium after a given time span. The first such CRT that has been widely used in plasma physics was developed in the 1960's and resulted in the concept of effective ionization and recombination rates. It was later generalized to systems in which multiple levels are effected by transport. In recent years there has been a renewed interest in tools for chemical reduction and reaction pathway analysis. An example of the latter is the PumpKin tool. Another trend is that techniques that have previously been developed in other fields of science are adapted as to be able to handle the plasma state of matter. Examples are the Intrinsic Low Dimension Manifold (ILDM) method and its derivatives, which originate from combustion engineering, and the general-purpose Principle Component Analysis (PCA) technique. In this contribution we will provide an overview of the most common reduction techniques, then critically assess the pros and cons of the methods that have gained most popularity in recent years. Examples will be provided for plasmas in argon and carbon dioxide.
Modeling the Chemical Complexity in Titan's Atmosphere
Vuitton, Veronique; Yelle, Roger; Klippenstein, Stephen J.; Horst, Sarah; Lavvas, Panayotis
2018-06-01
Titan's atmospheric chemistry is extremely complicated because of the multiplicity of chemical as well as physical processes involved. Chemical processes begin with the dissociation and ionization of the most abundant species, N2 and CH4, by a variety of energy sources, i.e. solar UV and X-ray photons, suprathermal electrons (reactions involving radicals as well as positive and negative ions, all possibly in some excited electronic and vibrational state. Heterogeneous chemistry at the surface of the aerosols could also play a significant role. The efficiency and outcome of these reactions depends strongly on the physical characteristics of the atmosphere, namely pressure and temperature, ranging from 1.5×103 to 10-10 mbar and from 70 to 200 K, respectively. Moreover, the distribution of the species is affected by molecular diffusion and winds as well as escape from the top of the atmosphere and condensation in the lower stratosphere.Photochemical and microphysical models are the keystones of our understanding of Titan's atmospheric chemistry. Their main objective is to compute the distribution and nature of minor chemical species (typically containing up to 6 carbon atoms) and haze particles, respectively. Density profiles are compared to the available observations, allowing to identify important processes and to highlight those that remain to be constrained in the laboratory, experimentally and/or theoretically. We argue that positive ion chemistry is at the origin of complex organic molecules, such as benzene, ammonia and hydrogen isocyanide while neutral-neutral radiative association reactions are a significant source of alkanes. We find that negatively charged macromolecules (m/z ~100) attract the abundant positive ions, which ultimately leads to the formation of the aerosols. We also discuss the possibility that an incoming flux of oxygen from Enceladus, another Saturn's satellite, is responsible for the presence of oxygen-bearing species in Titan's reductive
Modelling the complex dynamics of vegetation, livestock and rainfall ...
African Journals Online (AJOL)
Open Access DOWNLOAD FULL TEXT ... In this paper, we present mathematical models that incorporate ideas from complex systems theory to integrate several strands of rangeland theory in a hierarchical framework. ... Keywords: catastrophe theory; complexity theory; disequilibrium; hysteresis; moving attractors
Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar
2018-05-01
The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.
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.
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.
Generative complexity of Gray-Scott model
Adamatzky, Andrew
2018-03-01
In the Gray-Scott reaction-diffusion system one reactant is constantly fed in the system, another reactant is reproduced by consuming the supplied reactant and also converted to an inert product. The rate of feeding one reactant in the system and the rate of removing another reactant from the system determine configurations of concentration profiles: stripes, spots, waves. We calculate the generative complexity-a morphological complexity of concentration profiles grown from a point-wise perturbation of the medium-of the Gray-Scott system for a range of the feeding and removal rates. The morphological complexity is evaluated using Shannon entropy, Simpson diversity, approximation of Lempel-Ziv complexity, and expressivity (Shannon entropy divided by space-filling). We analyse behaviour of the systems with highest values of the generative morphological complexity and show that the Gray-Scott systems expressing highest levels of the complexity are composed of the wave-fragments (similar to wave-fragments in sub-excitable media) and travelling localisations (similar to quasi-dissipative solitons and gliders in Conway's Game of Life).
One-way spatial integration of hyperbolic equations
Towne, Aaron; Colonius, Tim
2015-11-01
In this paper, we develop and demonstrate a method for constructing well-posed one-way approximations of linear hyperbolic systems. We use a semi-discrete approach that allows the method to be applied to a wider class of problems than existing methods based on analytical factorization of idealized dispersion relations. After establishing the existence of an exact one-way equation for systems whose coefficients do not vary along the axis of integration, efficient approximations of the one-way operator are constructed by generalizing techniques previously used to create nonreflecting boundary conditions. When physically justified, the method can be applied to systems with slowly varying coefficients in the direction of integration. To demonstrate the accuracy and computational efficiency of the approach, the method is applied to model problems in acoustics and fluid dynamics via the linearized Euler equations; in particular we consider the scattering of sound waves from a vortex and the evolution of hydrodynamic wavepackets in a spatially evolving jet. The latter problem shows the potential of the method to offer a systematic, convergent alternative to ad hoc regularizations such as the parabolized stability equations.
Anomalously Weak Scattering in Metal-Semiconductor Multilayer Hyperbolic Metamaterials
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Hao Shen
2015-05-01
Full Text Available In contrast to strong plasmonic scattering from metal particles or structures in metal films, we show that patterns of arbitrary shape fabricated out of multilayer hyperbolic metamaterials become invisible within a chosen band of optical frequencies. This is due to anomalously weak scattering when the in-plane permittivity of the multilayer hyperbolic metamaterials is tuned to match with the surrounding medium. This new phenomenon is described theoretically and demonstrated experimentally by optical characterization of various patterns in Au-Si multilayer hyperbolic metamaterials. This anomalously weak scattering is insensitive to pattern sizes, shapes, and incident angles, and has potential applications in scattering cross-section engineering, optical encryption, low-observable conductive probes, and optoelectric devices.
Hawking into Unruh mapping for embeddings of hyperbolic type
International Nuclear Information System (INIS)
Paston, S A
2015-01-01
We study the conditions of the existence of Hawking into Unruh mapping for hyperbolic (Fronsdal-type) metric embeddings into the Minkowski space, for which timelines are hyperbolas. Many examples are known for global embeddings into the Minkowskian spacetime (GEMS), with such mapping for physically interesting metrics with some symmetry. However, examples of embeddings, both smooth and hyperbolic, for which there is no mapping, were also given. In the present work we prove that Hawking into Unruh mapping takes place for a hyperbolic embedding of an arbitrary metric with a time-like Killing vector and a Killing horizon if the embedding of such type exists and smoothly covers the horizon. At the same time, we do not assume any symmetry (spherical, for example), except the time translational invariance, which corresponds to the existence of a time-like Killing vector. We show that the known examples of the absence of mapping do not satisfy the formulated conditions of its existence. (paper)
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.
Novel features of the nonlinear model arising in nano-ionic currents throughout microtubules
Celik, E.; Bulut, H.; Baskonus, H. M.
2018-05-01
In this manuscript, the modified exp (- Ω (ξ )) -expansion function method is implemented to find the new solutions to the nonlinear differential equation being the transmission line model. We obtain some new solutions to this model such as complex, exponential, trigonometric and hyperbolic functions. We plot the two- and three-dimensional surfaces of each solutions obtained in this manuscript.
Modeling Complex Workflow in Molecular Diagnostics
Gomah, Mohamed E.; Turley, James P.; Lu, Huimin; Jones, Dan
2010-01-01
One of the hurdles to achieving personalized medicine has been implementing the laboratory processes for performing and reporting complex molecular tests. The rapidly changing test rosters and complex analysis platforms in molecular diagnostics have meant that many clinical laboratories still use labor-intensive manual processing and testing without the level of automation seen in high-volume chemistry and hematology testing. We provide here a discussion of design requirements and the results of implementation of a suite of lab management tools that incorporate the many elements required for use of molecular diagnostics in personalized medicine, particularly in cancer. These applications provide the functionality required for sample accessioning and tracking, material generation, and testing that are particular to the evolving needs of individualized molecular diagnostics. On implementation, the applications described here resulted in improvements in the turn-around time for reporting of more complex molecular test sets, and significant changes in the workflow. Therefore, careful mapping of workflow can permit design of software applications that simplify even the complex demands of specialized molecular testing. By incorporating design features for order review, software tools can permit a more personalized approach to sample handling and test selection without compromising efficiency. PMID:20007844
Complex systems modeling by cellular automata
Kroc, J.; Sloot, P.M.A.; Rabuñal Dopico, J.R.; Dorado de la Calle, J.; Pazos Sierra, A.
2009-01-01
In recent years, the notion of complex systems proved to be a very useful concept to define, describe, and study various natural phenomena observed in a vast number of scientific disciplines. Examples of scientific disciplines that highly benefit from this concept range from physics, mathematics,
Modeling pitch perception of complex tones
Houtsma, A.J.M.
1986-01-01
When one listens to a series of harmonic complex tones that have no acoustic energy at their fundamental frequencies, one usually still hears a melody that corresponds to those missing fundamentals. Since it has become evident some two decades ago that neither Helmholtz's difference tone theory nor
Development of neural network model of the multiparametric ...
African Journals Online (AJOL)
The best structure of the model was established for identifying a complex multiparameter object, using the example of statistics for the operation of a ball mill.It was a network with three hidden layers and 50, 35 and 25 neurons in them, with activation functions, respectively by layers - hyperbolic tangent, sigmoid function in 2 ...
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.
Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators
Energy Technology Data Exchange (ETDEWEB)
Semenova, N.; Anishchenko, V. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Zakharova, A.; Schöll, E. [Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, 10623 Berlin (Germany)
2016-06-08
In this work we analyse nonlocally coupled networks of identical chaotic oscillators. We study both time-discrete and time-continuous systems (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of chaotic non-hyperbolic systems and cannot be found in networks of hyperbolic systems. This hypothesis is supported by numerical simulations for hyperbolic and non-hyperbolic cases.
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.
Narrowing the gap between network models and real complex systems
Viamontes Esquivel, Alcides
2014-01-01
Simple network models that focus only on graph topology or, at best, basic interactions are often insufficient to capture all the aspects of a dynamic complex system. In this thesis, I explore those limitations, and some concrete methods of resolving them. I argue that, in order to succeed at interpreting and influencing complex systems, we need to take into account slightly more complex parts, interactions and information flows in our models.This thesis supports that affirmation with five a...
Hyperbolic white noise functional solutions of Wick-type stochastic compound KdV-Burgers equations
International Nuclear Information System (INIS)
Han Xiu; Xie Yingchao
2009-01-01
Variable coefficient and Wick-type stochastic compound KdV-Burgers equations are investigated. By using white noise analysis, Hermite transform and the hyperbolic function method, we obtain a number of Wick versions of hyperbolic white noise functional solutions and hyperbolic function solutions for Wick-type stochastic and variable coefficient compound KdV-Burgers equations, respectively.
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…
Information, complexity and efficiency: The automobile model
Energy Technology Data Exchange (ETDEWEB)
Allenby, B. [Lucent Technologies (United States)]|[Lawrence Livermore National Lab., CA (United States)
1996-08-08
The new, rapidly evolving field of industrial ecology - the objective, multidisciplinary study of industrial and economic systems and their linkages with fundamental natural systems - provides strong ground for believing that a more environmentally and economically efficient economy will be more information intensive and complex. Information and intellectual capital will be substituted for the more traditional inputs of materials and energy in producing a desirable, yet sustainable, quality of life. While at this point this remains a strong hypothesis, the evolution of the automobile industry can be used to illustrate how such substitution may, in fact, already be occurring in an environmentally and economically critical sector.
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.
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.
A novel grid multiwing chaotic system with only non-hyperbolic equilibria
Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le
2018-05-01
The structure of the chaotic attractor of a system is mainly determined by the nonlinear functions in system equations. By using a new saw-tooth wave function and a new stair function, a novel complex grid multiwing chaotic system which belongs to non-Shil'nikov chaotic system with non-hyperbolic equilibrium points is proposed in this paper. It is particularly interesting that the complex grid multiwing attractors are generated by increasing the number of non-hyperbolic equilibrium points, which are different from the traditional methods of realising multiwing attractors by adding the index-2 saddle-focus equilibrium points in double-wing chaotic systems. The basic dynamical properties of the new system, such as dissipativity, phase portraits, the stability of the equilibria, the time-domain waveform, power spectrum, bifurcation diagram, Lyapunov exponents, and so on, are investigated by theoretical analysis and numerical simulations. Furthermore, the corresponding electronic circuit is designed and simulated on the Multisim platform. The Multisim simulation results and the hardware experimental results are in good agreement with the numerical simulations of the same system on Matlab platform, which verify the feasibility of this new grid multiwing chaotic system.
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...
Hierarchical Models of the Nearshore Complex System
National Research Council Canada - National Science Library
Werner, Brad
2004-01-01
.... This grant was termination funding for the Werner group, specifically aimed at finishing up and publishing research related to synoptic imaging of near shore bathymetry, testing models for beach cusp...
Complex models of nodal nuclear data
International Nuclear Information System (INIS)
Dufek, Jan
2011-01-01
During the core simulations, nuclear data are required at various nodal thermal-hydraulic and fuel burnup conditions. The nodal data are also partially affected by thermal-hydraulic and fuel burnup conditions in surrounding nodes as these change the neutron energy spectrum in the node. Therefore, the nodal data are functions of many parameters (state variables), and the more state variables are considered by the nodal data models the more accurate and flexible the models get. The existing table and polynomial regression models, however, cannot reflect the data dependences on many state variables. As for the table models, the number of mesh points (and necessary lattice calculations) grows exponentially with the number of variables. As for the polynomial regression models, the number of possible multivariate polynomials exceeds the limits of existing selection algorithms that should identify a few dozens of the most important polynomials. Also, the standard scheme of lattice calculations is not convenient for modelling the data dependences on various burnup conditions since it performs only a single or few burnup calculations at fixed nominal conditions. We suggest a new efficient algorithm for selecting the most important multivariate polynomials for the polynomial regression models so that dependences on many state variables can be considered. We also present a new scheme for lattice calculations where a large number of burnup histories are accomplished at varied nodal conditions. The number of lattice calculations being performed and the number of polynomials being analysed are controlled and minimised while building the nodal data models of a required accuracy. (author)
Integrated Modeling of Complex Optomechanical Systems
Andersen, Torben; Enmark, Anita
2011-09-01
Mathematical modeling and performance simulation are playing an increasing role in large, high-technology projects. There are two reasons; first, projects are now larger than they were before, and the high cost calls for detailed performance prediction before construction. Second, in particular for space-related designs, it is often difficult to test systems under realistic conditions beforehand, and mathematical modeling is then needed to verify in advance that a system will work as planned. Computers have become much more powerful, permitting calculations that were not possible before. At the same time mathematical tools have been further developed and found acceptance in the community. Particular progress has been made in the fields of structural mechanics, optics and control engineering, where new methods have gained importance over the last few decades. Also, methods for combining optical, structural and control system models into global models have found widespread use. Such combined models are usually called integrated models and were the subject of this symposium. The objective was to bring together people working in the fields of groundbased optical telescopes, ground-based radio telescopes, and space telescopes. We succeeded in doing so and had 39 interesting presentations and many fruitful discussions during coffee and lunch breaks and social arrangements. We are grateful that so many top ranked specialists found their way to Kiruna and we believe that these proceedings will prove valuable during much future work.
Hybrid plasmonic/semiconductor nanoparticle monolayer assemblies as hyperbolic metamaterials
DEFF Research Database (Denmark)
Zhukovsky, Sergei; Ozel, Tuncay; Mutlugun, Evren
2014-01-01
effective permittivity tensor of the structure. This results in increased photonic density of states and strong enhancement of quantum dot luminescence, in line with recent experimental results. Our findings demonstrate that hyperbolic metamaterials can increase the radiative decay rate of emission centers...
Semilinear hyperbolic systems and equations with singular initial data
International Nuclear Information System (INIS)
Gramchev, T.
1991-07-01
We study the weak limits of solutions u ε (t, ·) for ε→0 to semilinear strictly hyperbolic systems and wave equations with initial data u ε (0, ·) approximating a distribution κ, 0 ε (t, ·) for ε→0 exists. 13 refs
A simple finite element method for linear hyperbolic problems
International Nuclear Information System (INIS)
Mu, Lin; Ye, Xiu
2017-01-01
Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.
Classical Liouville action on the sphere with three hyperbolic singularities
Energy Technology Data Exchange (ETDEWEB)
Hadasz, Leszek E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew E-mail: jask@ift.uniwroc.pl
2004-08-30
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.
Classical Liouville action on the sphere with three hyperbolic singularities
Hadasz, Leszek; Jaskólski, Zbigniew
2004-08-01
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.
Classical Liouville action on the sphere with three hyperbolic singularities
International Nuclear Information System (INIS)
Hadasz, Leszek; Jaskolski, Zbigniew
2004-01-01
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory
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
Hyperboles not turning to metaphors : How to explain audience cooperativeness?
van den Hoven, P.J.
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
Discontinuous Galerkin finite element methods for hyperbolic differential equations
van der Vegt, Jacobus J.W.; van der Ven, H.; Boelens, O.J.; Boelens, O.J.; Toro, E.F.
2002-01-01
In this paper a suryey is given of the important steps in the development of discontinuous Galerkin finite element methods for hyperbolic partial differential equations. Special attention is paid to the application of the discontinuous Galerkin method to the solution of the Euler equations of gas
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.
Control of the hyperbolic dispersion of dielectrics by an ultrashort laser pulse
Zhang, Xiaoqin; Wang, Feng; Zhang, Fengshou; Yao, Yugui
2018-01-01
An idea of controlling hyperbolic dispersion of dielectric materials by an ultrashort laser pulse is proposed. Taking the diamond as a concrete example and using time-dependent density functional theory calculations, we show that the permittivity tensor of the material can be effectively tuned by an ultrashort laser pulse, serving as a transient hyperbolic medium with wide working frequency window. With easily tunable laser parameters, the material can even be switched by reversal of both elliptic and hyperbolic for a particular light frequency. Our result points out a route toward transient hyperbolic materials, and it offers methods to achieve tunable hyperbolic dispersion with great potential for ultrafast device applications.
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.)
The sigma model on complex projective superspaces
International Nuclear Information System (INIS)
Candu, Constantin; Mitev, Vladimir; Schomerus, Volker; Quella, Thomas; Saleur, Hubert; USC, Los Angeles, CA
2009-08-01
The sigma model on projective superspaces CP S-1 vertical stroke 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 θ. 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 S-1 vertical stroke 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.)
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...
Spontaneously broken continuous symmetries in hyperbolic (or open) de Sitter spacetime
International Nuclear Information System (INIS)
Ratra, B.
1994-01-01
The functional Schroedinger approach is used to study scalar field theory in hyperbolic (or open) de Sitter spacetime. While on intermediate length scales (small compared to the spatial curvature length scale) the massless minimally coupled scalar field two-point correlation function does have a term that varies logarithmically with scale, as in flat and closed de Sitter spacetime, the spatial curvature tames the infrared behavior of this correlation function at larger scales in the open model. As a result, and contrary to what happens in flat and closed de Sitter spacetime, spontaneously broken continuous symmetries are not restored in open de Sitter spacetime (with more than one spatial dimension)
Hyperbolic orbits of Earth flybys and effects of ungravity-inspired conservative potentials
International Nuclear Information System (INIS)
Bertolami, O; Francisco, F; Gil, P J S
2016-01-01
In this work we take a critical look at the available data on the flyby anomaly and on the current limitations of attempts to develop an explanation. We aim to verify how conservative corrections to gravity could affect the hyperbolic trajectories of Earth flybys. We use ungravity-inspired potentials as illustrative examples and show how the resulting orbital simulations differ from the observed anomaly. We also get constraints on the model parameters from the observed flyby velocity shifts. The conclusion is that no kind of conservative potential can be the cause of the flyby anomaly. (paper)
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.
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
Shippee, Nathan D; Shah, Nilay D; May, Carl R; Mair, Frances S; Montori, Victor M
2012-10-01
To design a functional, patient-centered model of patient complexity with practical applicability to analytic design and clinical practice. Existing literature on patient complexity has mainly identified its components descriptively and in isolation, lacking clarity as to their combined functions in disrupting care or to how complexity changes over time. The authors developed a cumulative complexity model, which integrates existing literature and emphasizes how clinical and social factors accumulate and interact to complicate patient care. A narrative literature review is used to explicate the model. The model emphasizes a core, patient-level mechanism whereby complicating factors impact care and outcomes: the balance between patient workload of demands and patient capacity to address demands. Workload encompasses the demands on the patient's time and energy, including demands of treatment, self-care, and life in general. Capacity concerns ability to handle work (e.g., functional morbidity, financial/social resources, literacy). Workload-capacity imbalances comprise the mechanism driving patient complexity. Treatment and illness burdens serve as feedback loops, linking negative outcomes to further imbalances, such that complexity may accumulate over time. With its components largely supported by existing literature, the model has implications for analytic design, clinical epidemiology, and clinical practice. Copyright © 2012 Elsevier Inc. All rights reserved.
Passengers, Crowding and Complexity : Models for passenger oriented public transport
P.C. Bouman (Paul)
2017-01-01
markdownabstractPassengers, Crowding and Complexity was written as part of the Complexity in Public Transport (ComPuTr) project funded by the Netherlands Organisation for Scientific Research (NWO). This thesis studies in three parts how microscopic data can be used in models that have the potential
Stability of Rotor Systems: A Complex Modelling Approach
DEFF Research Database (Denmark)
Kliem, Wolfhard; Pommer, Christian; Stoustrup, Jakob
1996-01-01
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...
Complex versus simple models: ion-channel cardiac toxicity prediction.
Mistry, Hitesh B
2018-01-01
There is growing interest in applying detailed mathematical models of the heart for ion-channel related cardiac toxicity prediction. However, a debate as to whether such complex models are required exists. Here an assessment in the predictive performance between two established large-scale biophysical cardiac models and a simple linear model B net was conducted. Three ion-channel data-sets were extracted from literature. Each compound was designated a cardiac risk category using two different classification schemes based on information within CredibleMeds. The predictive performance of each model within each data-set for each classification scheme was assessed via a leave-one-out cross validation. Overall the B net model performed equally as well as the leading cardiac models in two of the data-sets and outperformed both cardiac models on the latest. These results highlight the importance of benchmarking complex versus simple models but also encourage the development of simple models.
Complex versus simple models: ion-channel cardiac toxicity prediction
Directory of Open Access Journals (Sweden)
Hitesh B. Mistry
2018-02-01
Full Text Available There is growing interest in applying detailed mathematical models of the heart for ion-channel related cardiac toxicity prediction. However, a debate as to whether such complex models are required exists. Here an assessment in the predictive performance between two established large-scale biophysical cardiac models and a simple linear model Bnet was conducted. Three ion-channel data-sets were extracted from literature. Each compound was designated a cardiac risk category using two different classification schemes based on information within CredibleMeds. The predictive performance of each model within each data-set for each classification scheme was assessed via a leave-one-out cross validation. Overall the Bnet model performed equally as well as the leading cardiac models in two of the data-sets and outperformed both cardiac models on the latest. These results highlight the importance of benchmarking complex versus simple models but also encourage the development of simple models.
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 ...
Surface-complexation models for sorption onto heterogeneous surfaces
International Nuclear Information System (INIS)
Harvey, K.B.
1997-10-01
This report provides a description of the discrete-logK spectrum model, together with a description of its derivation, and of its place in the larger context of surface-complexation modelling. The tools necessary to apply the discrete-logK spectrum model are discussed, and background information appropriate to this discussion is supplied as appendices. (author)
On spin and matrix models in the complex plane
International Nuclear Information System (INIS)
Damgaard, P.H.; Heller, U.M.
1993-01-01
We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution of partition function zeros, and the question of new coupling-constant symmetries of complex-plane spin models. The double-scaling form of matrix models is shown to be exactly equivalent to finite-size scaling of two-dimensional spin systems. This is used to show that the string susceptibility exponents derived from matrix models can be obtained numerically with very high accuracy from the scaling of finite-N partition function zeros in the complex plane. (orig.)
A Framework for Modeling and Analyzing Complex Distributed Systems
National Research Council Canada - National Science Library
Lynch, Nancy A; Shvartsman, Alex Allister
2005-01-01
Report developed under STTR contract for topic AF04-T023. This Phase I project developed a modeling language and laid a foundation for computational support tools for specifying, analyzing, and verifying complex distributed system designs...
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.
Size and complexity in model financial systems
Arinaminpathy, Nimalan; Kapadia, Sujit; May, Robert M.
2012-01-01
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. PMID:23091020
Algebraic computability and enumeration models recursion theory and descriptive complexity
Nourani, Cyrus F
2016-01-01
This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic type...
Modeling of Complex Life Cycle Prediction Based on Cell Division
Directory of Open Access Journals (Sweden)
Fucheng Zhang
2017-01-01
Full Text Available Effective fault diagnosis and reasonable life expectancy are of great significance and practical engineering value for the safety, reliability, and maintenance cost of equipment and working environment. At present, the life prediction methods of the equipment are equipment life prediction based on condition monitoring, combined forecasting model, and driven data. Most of them need to be based on a large amount of data to achieve the problem. For this issue, we propose learning from the mechanism of cell division in the organism. We have established a moderate complexity of life prediction model across studying the complex multifactor correlation life model. In this paper, we model the life prediction of cell division. Experiments show that our model can effectively simulate the state of cell division. Through the model of reference, we will use it for the equipment of the complex life prediction.
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.
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.
Shah, Syed Awais Wahab; Abed-Meraim, Karim; Al-Naffouri, Tareq Y.
2017-01-01
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.
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.
Mathematical Models to Determine Stable Behavior of Complex Systems
Sumin, V. I.; Dushkin, A. V.; Smolentseva, T. E.
2018-05-01
The paper analyzes a possibility to predict functioning of a complex dynamic system with a significant amount of circulating information and a large number of random factors impacting its functioning. Functioning of the complex dynamic system is described as a chaotic state, self-organized criticality and bifurcation. This problem may be resolved by modeling such systems as dynamic ones, without applying stochastic models and taking into account strange attractors.
Hyperbolic projections of siemens 3d-mlc leaf paths
International Nuclear Information System (INIS)
Menzies, N.
2004-01-01
Full text: The Siemens Primus linear accelerator has the option of being fitted with a multi-leaf collimator (3D-MLC) that is marketed as having 'double focus', to achieve a constant dose penumbra for all leaf settings. This is achieved by moving the leaves through arcs (similar to some conventional collimator jaws), as well as shaping the leaf side-faces as divergent planes from the x-ray source. One consequence of the mechanical design of the 3D-MLC is that as individual leaves are moved, their projections from the light / x-ray source to the treatment plane follow paths that are hyperbolic, as shown in the figure below. (The eccentricity of the hyperbola is a function of leaf number / distance from centre.) The trajectories of the MLC leaves were modelled (in a spreadsheet) using geometrical projections of the MLC leaves to the treatment plane, with construction details provided in Siemens documentation. The results were checked against the image of the leaf in the linac light field. This problem belongs to the class of conic sections in mathematics, where the intersection of a plane with both nappes of a double right circular cone results in a hyperbola. The good agreement between the model and the light field image provided confirmation of the MLC construction details. AS/NZS 4434.1:1996 (reproduced from IEC 976:1989) provides specifications for maximum deviation from orthogonality of adjacent edges, which can be interpreted for MLC collimators to parallelism of the direction of leaf travel and the adjacent collimator edge (e.g. Elekta ATS). However for the Siemens 'double focused' MLC, it is demonstrated that the geometrical construction of the MLC militates against the leaf image being used for this kind of test. It is also demonstrated that at last one commercial treatment planning system models the Siemens leaf trajectories linearly. The clinical significance of the error in this model is shown to be negligible. Copyright (2004) Australasian College of
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...
Dynamic complexities in a parasitoid-host-parasitoid ecological model
International Nuclear Information System (INIS)
Yu Hengguo; Zhao Min; Lv Songjuan; Zhu Lili
2009-01-01
Chaotic dynamics have been observed in a wide range of population models. In this study, the complex dynamics in a discrete-time ecological model of parasitoid-host-parasitoid are presented. The model shows that the superiority coefficient not only stabilizes the dynamics, but may strongly destabilize them as well. Many forms of complex dynamics were observed, including pitchfork bifurcation with quasi-periodicity, period-doubling cascade, chaotic crisis, chaotic bands with narrow or wide periodic window, intermittent chaos, and supertransient behavior. Furthermore, computation of the largest Lyapunov exponent demonstrated the chaotic dynamic behavior of the model
Dynamic complexities in a parasitoid-host-parasitoid ecological model
Energy Technology Data Exchange (ETDEWEB)
Yu Hengguo [School of Mathematic and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035 (China); Zhao Min [School of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang 325027 (China)], E-mail: zmcn@tom.com; Lv Songjuan; Zhu Lili [School of Mathematic and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035 (China)
2009-01-15
Chaotic dynamics have been observed in a wide range of population models. In this study, the complex dynamics in a discrete-time ecological model of parasitoid-host-parasitoid are presented. The model shows that the superiority coefficient not only stabilizes the dynamics, but may strongly destabilize them as well. Many forms of complex dynamics were observed, including pitchfork bifurcation with quasi-periodicity, period-doubling cascade, chaotic crisis, chaotic bands with narrow or wide periodic window, intermittent chaos, and supertransient behavior. Furthermore, computation of the largest Lyapunov exponent demonstrated the chaotic dynamic behavior of the model.
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
A marketing mix model for a complex and turbulent environment
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R. B. Mason
2007-12-01
Full Text Available Purpose: This paper is based on the proposition that the choice of marketing tactics is determined, or at least significantly influenced, by the nature of the companys external environment. It aims to illustrate the type of marketing mix tactics that are suggested for a complex and turbulent environment when marketing and the environment are viewed through a chaos and complexity theory lens. Design/Methodology/Approach: Since chaos and complexity theories are proposed as a good means of understanding the dynamics of complex and turbulent markets, a comprehensive review and analysis of literature on the marketing mix and marketing tactics from a chaos and complexity viewpoint was conducted. From this literature review, a marketing mix model was conceptualised. Findings: A marketing mix model considered appropriate for success in complex and turbulent environments was developed. In such environments, the literature suggests destabilising marketing activities are more effective, whereas stabilising type activities are more effective in simple, stable environments. Therefore the model proposes predominantly destabilising type tactics as appropriate for a complex and turbulent environment such as is currently being experienced in South Africa. Implications: This paper is of benefit to marketers by emphasising a new way to consider the future marketing activities of their companies. How this model can assist marketers and suggestions for research to develop and apply this model are provided. It is hoped that the model suggested will form the basis of empirical research to test its applicability in the turbulent South African environment. Originality/Value: Since businesses and markets are complex adaptive systems, using complexity theory to understand how to cope in complex, turbulent environments is necessary, but has not been widely researched. In fact, most chaos and complexity theory work in marketing has concentrated on marketing strategy, with
Generalized complex geometry, generalized branes and the Hitchin sigma model
International Nuclear Information System (INIS)
Zucchini, Roberto
2005-01-01
Hitchin's generalized complex geometry has been shown to be relevant in compactifications of superstring theory with fluxes and is expected to lead to a deeper understanding of mirror symmetry. Gualtieri's notion of generalized complex submanifold seems to be a natural candidate for the description of branes in this context. Recently, we introduced a Batalin-Vilkovisky field theoretic realization of generalized complex geometry, the Hitchin sigma model, extending the well known Poisson sigma model. In this paper, exploiting Gualtieri's formalism, we incorporate branes into the model. A detailed study of the boundary conditions obeyed by the world sheet fields is provided. Finally, it is found that, when branes are present, the classical Batalin-Vilkovisky cohomology contains an extra sector that is related non trivially to a novel cohomology associated with the branes as generalized complex submanifolds. (author)
The arbitrary l continuum states of the hyperbolic molecular potential
Energy Technology Data Exchange (ETDEWEB)
Wei, Gao-Feng, E-mail: fgwei_2000@163.com [School of Physics and Mechatronics Engineering, Xi' an University of Arts and Science, Xi' an 710065 (China); Chen, Wen-Li, E-mail: physwlchen@163.com [Department of Basic Science, Xi' an Peihua University, Xi' an 710065 (China); Dong, Shi-Hai, E-mail: dongsh2@yahoo.com [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, Mexico D.F. 07738 (Mexico); Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001 (United States)
2014-06-27
Within the framework of partial-wave method, we study in this Letter the arbitrary l continuum states of the Schrödinger equation with the hyperbolic molecular potential in terms of an improved approximation to the centrifugal term. We present the normalized radial wave functions and obtain analytical formula of phase shifts. In addition, the corresponding bound states are also discussed by studying the analytical properties of the scattering amplitude. We calculate the energy spectra and scattering phase shifts by the improved, previous approximations and the accurate methods, respectively and find that the improved approximation is better than the previous one since the present results are in better agreement with the accurate ones. - Highlights: • The hyperbolic potential with arbitrary l state is solved. • Improved approximation to centrifugal term is used. • Phase shift formula is derived analytically. • Accurate results are compared with the present results.
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...
Exact moduli space metrics for hyperbolic vortex polygons
International Nuclear Information System (INIS)
Krusch, S.; Speight, J. M.
2010-01-01
Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted as Σ n,m , are spaces of C n -invariant vortex configurations with n single vortices at the vertices of a regular polygon and m=N-n coincident vortices at the polygon's center. The geometric properties of Σ n,m are investigated, and it is found that Σ n,n-1 is isometric to the hyperbolic plane of curvature -(3πn) -1 . The geodesic flow on Σ n,m and a geometrically natural variant of geodesic flow recently proposed by Collie and Tong ['The dynamics of Chern-Simons vortices', Phys. Rev. D Part. Fields Gravit. Cosmol. 78, 065013 (2008);e-print arXiv:hep-th/0805.0602] are analyzed in detail.
Analytical solution of Mori's equation with secant hyperbolic memory
International Nuclear Information System (INIS)
Tankeshwar, K.; Pathak, K.N.
1993-07-01
The equation of motion of the auto-correlation function has been solved analytically using a secant-hyperbolic form of the memory function. The analytical results obtained for the long time expansion together with the short time expansion provide a good description over the whole time domain as judged by their comparison with the numerical solution of Mori's equation of motion. We also find that the time evolution of the auto-correlation function is determined by a single parameter τ which is related to the frequency sum rules up to the fourth order. The auto-correlation function has been found to show simple decaying or oscillatory behaviour depending on whether the parameter τ is greater than or less than some critical values. Similarities as well as differences in time evolution of the auto-correlation have been discussed for exponential, secant-hyperbolic and Gaussian approaches of the memory function. (author). 16 refs, 5 figs
Low-dimensional geometry from euclidean surfaces to hyperbolic knots
Bonahon, Francis
2009-01-01
The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory o...
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...
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...
Operator-Based Preconditioning of Stiff Hyperbolic Systems
International Nuclear Information System (INIS)
Reynolds, Daniel R.; Samtaney, Ravi; Woodward, Carol S.
2009-01-01
We introduce an operator-based scheme for preconditioning stiff components encountered 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 characteristic 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
On the hyperbolicity of Einstein's and other gauge field equations
International Nuclear Information System (INIS)
Friedrich, H.
1985-01-01
It is shown that Einstein's vacuum field equations (respectively the conformal vacuum field equations) in a frame formalism imply a symmetric hyperbolic system of ''reduce'' propagation equations for any choice of coordinate system and frame field (and conformal factor). Certain freely specifiable ''gauge source'' functions occurring in the reduced equations reflect the choice of gauge. Together with the initial data they determine the gauge uniquely. Their choice does not affect the isometry class (conformal class) of a solution of an initial value problem. By the same method symmetric hyperbolic propagation equations are obtained from other gauge field equations, irrespective of the gauge. Using the concept of source functions one finds that Einstein's field equation, considered as second order equations for the metric coefficients, are of wave equation type in any coordinate system. (orig.)
Reassessing Geophysical Models of the Bushveld Complex in 3D
Cole, J.; Webb, S. J.; Finn, C.
2012-12-01
Conceptual geophysical models of the Bushveld Igneous Complex show three possible geometries for its mafic component: 1) Separate intrusions with vertical feeders for the eastern and western lobes (Cousins, 1959) 2) Separate dipping sheets for the two lobes (Du Plessis and Kleywegt, 1987) 3) A single saucer-shaped unit connected at depth in the central part between the two lobes (Cawthorn et al, 1998) Model three incorporates isostatic adjustment of the crust in response to the weight of the dense mafic material. The model was corroborated by results of a broadband seismic array over southern Africa, known as the Southern African Seismic Experiment (SASE) (Nguuri, et al, 2001; Webb et al, 2004). This new information about the crustal thickness only became available in the last decade and could not be considered in the earlier models. Nevertheless, there is still on-going debate as to which model is correct. All of the models published up to now have been done in 2 or 2.5 dimensions. This is not well suited to modelling the complex geometry of the Bushveld intrusion. 3D modelling takes into account effects of variations in geometry and geophysical properties of lithologies in a full three dimensional sense and therefore affects the shape and amplitude of calculated fields. The main question is how the new knowledge of the increased crustal thickness, as well as the complexity of the Bushveld Complex, will impact on the gravity fields calculated for the existing conceptual models, when modelling in 3D. The three published geophysical models were remodelled using full 3Dl potential field modelling software, and including crustal thickness obtained from the SASE. The aim was not to construct very detailed models, but to test the existing conceptual models in an equally conceptual way. Firstly a specific 2D model was recreated in 3D, without crustal thickening, to establish the difference between 2D and 3D results. Then the thicker crust was added. Including the less
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
Detecting topology in a nearly flat hyperbolic universe
Weeks, Jeffrey R.
2002-01-01
Cosmic microwave background data shows the observable universe to be nearly flat, but leaves open the question of whether it is simply or multiply connected. Several authors have investigated whether the topology of a multiply connect hyperbolic universe would be detectable when 0.9 < Omega < 1. However, the possibility of detecting a given topology varies depending on the location of the observer within the space. Recent studies have assumed the observer sits at a favorable location. The pre...
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
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 ...
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.
Symmetric positive differential equations and first order hyperbolic systems
International Nuclear Information System (INIS)
Tangmanee, S.
1981-12-01
We prove that under some conditions the first order hyperbolic system and its associated mixed initial boundary conditions considered, for example, in Kreiss (Math. Comp. 22, 703-704 (1968)) and Kreiss and Gustafsson (Math. Comp. 26, 649-686 (1972)), can be transformed into a symmetric positive system of P.D.E.'s with admissible boundary conditions of Friedrich's type (Comm. Pure Appl. Math 11, 333-418 (1958)). (author)
One-loop effective potential on hyperbolic manifolds
International Nuclear Information System (INIS)
Cognola, G.; Kirsten, K.; Zerbini, S.
1993-01-01
The one-loop effective potential for a scalar field defined on an ultrastatic space-time whose spatial part is a compact hyperbolic manifold is studied using ζ-function regularization for the one-loop effective action. Other possible regularizations are discussed in detail. The renormalization group equations are derived, and their connection with the conformal anomaly is pointed out. The symmetry breaking and the topological mass generation are also discussed
Thermodynamics and stability of hyperbolic charged black holes
International Nuclear Information System (INIS)
Cai Ronggen; Wang Anzhong
2004-01-01
In AdS space the black hole horizon can be a hypersurface with a positive, zero, or negative constant curvature, resulting in different horizon topology. Thermodynamics and stability of black holes in AdS spaces are quite different for different horizon curvatures. In this paper we study thermodynamics and stability of hyperbolic charged black holes with negative constant curvature horizon in the grand canonical ensemble and canonical ensemble, respectively. They include hyperbolic Reissner-Nordstroem black holes in arbitrary dimensions and hyperbolic black holes in the D=5,4,7 gauged supergravities. It is found that associated Gibbs free energies are always negative, which implies that these black hole solutions are globally stable and the black hole phase is dominant in the grand canonical ensemble, but there is a region in the phase space where the black hole is not locally thermodynamically stable with a negative heat capacity for a given gauge potential. In the canonical ensemble, the Helmholtz free energies are not always negative and heat capacities with fixed electric charge are not always positive, which indicates that the Hawking-Page phase transition may happen and black holes are not always locally thermodynamically stable
Optic axis-driven new horizons for hyperbolic metamaterials
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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.
Approximate Treatment of the Dirac Equation with Hyperbolic Potential Function
Durmus, Aysen
2018-03-01
The time independent Dirac equation is solved analytically for equal scalar and vector hyperbolic potential function in the presence of Greene and Aldrich approximation scheme. The bound state energy equation and spinor wave functions expressed by the hypergeometric function have been obtained in detail with asymptotic iteration approach. In order to indicate the accuracy of this different approach proposed to solve second order linear differential equations, we present that in the non-relativistic limit, analytical solutions of the Dirac equation converge to those of the Schrödinger one. We introduce numerical results of the theoretical analysis for hyperbolic potential function. Bound states corresponding to arbitrary values of n and l are reported for potential parameters covering a wide range of interaction. Also, we investigate relativistic vibrational energy spectra of alkali metal diatomic molecules in the different electronic states. It is observed that theoretical vibrational energy values are consistent with experimental Rydberg-Klein-Rees (RKR) results and vibrational energies of NaK, K_2 and KRb diatomic molecules interacting with hyperbolic potential smoothly converge to the experimental dissociation limit D_e=2508cm^{-1}, 254cm^{-1} and 4221cm^{-1}, respectively.
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.
Modeling Complex Nesting Structures in International Business Research
DEFF Research Database (Denmark)
Nielsen, Bo Bernhard; Nielsen, Sabina
2013-01-01
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...
Foundations for Streaming Model Transformations by Complex Event Processing.
Dávid, István; Ráth, István; Varró, Dániel
2018-01-01
Streaming model transformations represent a novel class of transformations to manipulate models whose elements are continuously produced or modified in high volume and with rapid rate of change. Executing streaming transformations requires efficient techniques to recognize activated transformation rules over a live model and a potentially infinite stream of events. In this paper, we propose foundations of streaming model transformations by innovatively integrating incremental model query, complex event processing (CEP) and reactive (event-driven) transformation techniques. Complex event processing allows to identify relevant patterns and sequences of events over an event stream. Our approach enables event streams to include model change events which are automatically and continuously populated by incremental model queries. Furthermore, a reactive rule engine carries out transformations on identified complex event patterns. We provide an integrated domain-specific language with precise semantics for capturing complex event patterns and streaming transformations together with an execution engine, all of which is now part of the Viatra reactive transformation framework. We demonstrate the feasibility of our approach with two case studies: one in an advanced model engineering workflow; and one in the context of on-the-fly gesture recognition.
Universal correlators for multi-arc complex matrix models
International Nuclear Information System (INIS)
Akemann, G.
1997-01-01
The correlation functions of the multi-arc complex matrix model are shown to be universal for any finite number of arcs. The universality classes are characterized by the support of the eigenvalue density and are conjectured to fall into the same classes as the ones recently found for the Hermitian model. This is explicitly shown to be true for the case of two arcs, apart from the known result for one arc. The basic tool is the iterative solution of the loop equation for the complex matrix model with multiple arcs, which provides all multi-loop correlators up to an arbitrary genus. Explicit results for genus one are given for any number of arcs. The two-arc solution is investigated in detail, including the double-scaling limit. In addition universal expressions for the string susceptibility are given for both the complex and Hermitian model. (orig.)
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.
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.
Complex groundwater flow systems as traveling agent models
Directory of Open Access Journals (Sweden)
Oliver López Corona
2014-10-01
Full Text Available Analyzing field data from pumping tests, we show that as with many other natural phenomena, groundwater flow exhibits 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.
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
Synchronization Experiments With A Global Coupled Model of Intermediate Complexity
Selten, Frank; Hiemstra, Paul; Shen, Mao-Lin
2013-04-01
In the super modeling approach an ensemble of imperfect models are connected through nudging terms that nudge the solution of each model to the solution of all other models in the ensemble. The goal is to obtain a synchronized state through a proper choice of connection strengths that closely tracks the trajectory of the true system. For the super modeling approach to be successful, the connections should be dense and strong enough for synchronization to occur. In this study we analyze the behavior of an ensemble of connected global atmosphere-ocean models of intermediate complexity. All atmosphere models are connected to the same ocean model through the surface fluxes of heat, water and momentum, the ocean is integrated using weighted averaged surface fluxes. In particular we analyze the degree of synchronization between the atmosphere models and the characteristics of the ensemble mean solution. The results are interpreted using a low order atmosphere-ocean toy model.
Hyperbolic systems with analytic coefficients well-posedness of the Cauchy problem
Nishitani, Tatsuo
2014-01-01
This monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients. Mainly two questions are discussed: (A) Under which conditions on lower order terms is the Cauchy problem well posed? (B) When is the Cauchy problem well posed for any lower order term? For first order two by two systems with two independent variables with real analytic coefficients, we present complete answers for both (A) and (B). For first order systems with real analytic coefficients we prove general necessary conditions for question (B) in terms of minors of the principal symbols. With regard to sufficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contains strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term. We also prove that any hyperbolic system which is close to a hyperbolic system with a nondegenerate characteristic of mu...
Directory of Open Access Journals (Sweden)
Ilija Jegdic
2015-09-01
Full Text Available We consider a two-dimensional Riemann problem for the unsteady transonic small disturbance equation resulting in diverging rarefaction waves. We write the problem in self-similar coordinates and we obtain a mixed type (hyperbolic-elliptic system. Resolving the one-dimensional discontinuities in the far field, where the system is hyperbolic, and using characteristics, we formulate the problem in a semi-hyperbolic patch that is between the hyperbolic and the elliptic regions. A semi-hyperbolic patch is known as a region where one family out of two nonlinear families of characteristics starts on a sonic curve and ends on a transonic shock. We obtain existence of a smooth local solution in this semi-hyperbolic patch and we prove various properties of global smooth solutions based on a characteristic decomposition using directional derivatives.
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.
ANS main control complex three-dimensional computer model development
International Nuclear Information System (INIS)
Cleaves, J.E.; Fletcher, W.M.
1993-01-01
A three-dimensional (3-D) computer model of the Advanced Neutron Source (ANS) main control complex is being developed. The main control complex includes the main control room, the technical support center, the materials irradiation control room, computer equipment rooms, communications equipment rooms, cable-spreading rooms, and some support offices and breakroom facilities. The model will be used to provide facility designers and operations personnel with capabilities for fit-up/interference analysis, visual ''walk-throughs'' for optimizing maintain-ability, and human factors and operability analyses. It will be used to determine performance design characteristics, to generate construction drawings, and to integrate control room layout, equipment mounting, grounding equipment, electrical cabling, and utility services into ANS building designs. This paper describes the development of the initial phase of the 3-D computer model for the ANS main control complex and plans for its development and use
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 ...
A Combination Theorem for Convex Hyperbolic Manifolds, with Applications to Surfaces in 3-Manifolds
Baker, Mark; Cooper, Daryl
2005-01-01
We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, there are finite index subgroups which generate a subgroup that is an amalgamated free product. Constructions of infinite volume hyperbolic n-manifolds are described by gluing lo...
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
How complex does a model need to be to provide useful predictions is a matter of continuous debate across environmental sciences. In the species distributions modelling literature, studies have demonstrated that more complex models tend to provide better fits. However, studies have also shown...... that predictive performance does not always increase with complexity. Testing of species distributions models is challenging because independent data for testing are often lacking, but a more general problem is that model complexity has never been formally described in such studies. Here, we systematically...
Modeling geophysical complexity: a case for geometric determinism
Directory of Open Access Journals (Sweden)
C. E. Puente
2007-01-01
Full Text Available It has been customary in the last few decades to employ stochastic models to represent complex data sets encountered in geophysics, particularly in hydrology. This article reviews a deterministic geometric procedure to data modeling, one that represents whole data sets as derived distributions of simple multifractal measures via fractal functions. It is shown how such a procedure may lead to faithful holistic representations of existing geophysical data sets that, while complementing existing representations via stochastic methods, may also provide a compact language for geophysical complexity. The implications of these ideas, both scientific and philosophical, are stressed.
International Nuclear Information System (INIS)
Graf, U.
1986-01-01
A combination of several numerical methods is used to construct a procedure for effective calculation of complex three-dimensional fluid flow problems. The split coefficient matrix (SCM) method is used so that the differenced equations of the hyperbolic system do not disturb correct signal propagation. The semi-discretisation of the equations of the SCM method is done with the asymmetric, separated region, weighted residual (ASWR) method to give accurate solutions on a relatively coarse mesh. For the resulting system of ordinary differential equations, a general-purpose ordinary differential equation solver is used in conjunction with a method of fractional steps for an economic solution of the large system of linear equations. (orig.) [de
Deterministic ripple-spreading model for complex networks.
Hu, Xiao-Bing; Wang, Ming; Leeson, Mark S; Hines, Evor L; Di Paolo, Ezequiel
2011-04-01
This paper proposes a deterministic complex network model, which is inspired by the natural ripple-spreading phenomenon. The motivations and main advantages of the model are the following: (i) The establishment of many real-world networks is a dynamic process, where it is often observed that the influence of a few local events spreads out through nodes, and then largely determines the final network topology. Obviously, this dynamic process involves many spatial and temporal factors. By simulating the natural ripple-spreading process, this paper reports a very natural way to set up a spatial and temporal model for such complex networks. (ii) Existing relevant network models are all stochastic models, i.e., with a given input, they cannot output a unique topology. Differently, the proposed ripple-spreading model can uniquely determine the final network topology, and at the same time, the stochastic feature of complex networks is captured by randomly initializing ripple-spreading related parameters. (iii) The proposed model can use an easily manageable number of ripple-spreading related parameters to precisely describe a network topology, which is more memory efficient when compared with traditional adjacency matrix or similar memory-expensive data structures. (iv) The ripple-spreading model has a very good potential for both extensions and applications.
International Nuclear Information System (INIS)
Alvi, Kashif
2002-01-01
First-order hyperbolic systems are promising as a basis for numerical integration of Einstein's equations. In previous work, the lapse and shift have typically not been considered part of the hyperbolic system and have been prescribed independently. This can be expensive computationally, especially if the prescription involves solving elliptic equations. Therefore, including the lapse and shift in the hyperbolic system could be advantageous for numerical work. In this paper, two first-order symmetrizable hyperbolic systems are presented that include the lapse and shift as dynamical fields and have only physical characteristic speeds
Directory of Open Access Journals (Sweden)
Yusuf Pandir
2013-01-01
Full Text Available We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE, we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.
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.
Christoforou, Cleopatra; Tzavaras, Athanasios
2017-01-01
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.
Travelling Waves in Hyperbolic Chemotaxis Equations
Xue, Chuan; Hwang, Hyung Ju; Painter, Kevin J.; Erban, Radek
2010-01-01
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.
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.
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.
Predictive modelling of complex agronomic and biological systems.
Keurentjes, Joost J B; Molenaar, Jaap; Zwaan, Bas J
2013-09-01
Biological systems are tremendously complex in their functioning and regulation. Studying the multifaceted behaviour and describing the performance of such complexity has challenged the scientific community for years. The reduction of real-world intricacy into simple descriptive models has therefore convinced many researchers of the usefulness of introducing mathematics into biological sciences. Predictive modelling takes such an approach another step further in that it takes advantage of existing knowledge to project the performance of a system in alternating scenarios. The ever growing amounts of available data generated by assessing biological systems at increasingly higher detail provide unique opportunities for future modelling and experiment design. Here we aim to provide an overview of the progress made in modelling over time and the currently prevalent approaches for iterative modelling cycles in modern biology. We will further argue for the importance of versatility in modelling approaches, including parameter estimation, model reduction and network reconstruction. Finally, we will discuss the difficulties in overcoming the mathematical interpretation of in vivo complexity and address some of the future challenges lying ahead. © 2013 John Wiley & Sons Ltd.
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 \
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…
Modelling, Estimation and Control of Networked Complex Systems
Chiuso, Alessandro; Frasca, Mattia; Rizzo, Alessandro; Schenato, Luca; Zampieri, Sandro
2009-01-01
The paradigm of complexity is pervading both science and engineering, leading to the emergence of novel approaches oriented at the development of a systemic view of the phenomena under study; the definition of powerful tools for modelling, estimation, and control; and the cross-fertilization of different disciplines and approaches. This book is devoted to networked systems which are one of the most promising paradigms of complexity. It is demonstrated that complex, dynamical networks are powerful tools to model, estimate, and control many interesting phenomena, like agent coordination, synchronization, social and economics events, networks of critical infrastructures, resources allocation, information processing, or control over communication networks. Moreover, it is shown how the recent technological advances in wireless communication and decreasing in cost and size of electronic devices are promoting the appearance of large inexpensive interconnected systems, each with computational, sensing and mobile cap...
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...
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.
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.
Uncertainty and validation. Effect of model complexity on uncertainty estimates
International Nuclear Information System (INIS)
Elert, M.
1996-09-01
In the Model Complexity subgroup of BIOMOVS II, models of varying complexity have been applied to the problem of downward transport of radionuclides in soils. A scenario describing a case of surface contamination of a pasture soil was defined. Three different radionuclides with different environmental behavior and radioactive half-lives were considered: Cs-137, Sr-90 and I-129. The intention was to give a detailed specification of the parameters required by different kinds of model, together with reasonable values for the parameter uncertainty. A total of seven modelling teams participated in the study using 13 different models. Four of the modelling groups performed uncertainty calculations using nine different modelling approaches. The models used range in complexity from analytical solutions of a 2-box model using annual average data to numerical models coupling hydrology and transport using data varying on a daily basis. The complex models needed to consider all aspects of radionuclide transport in a soil with a variable hydrology are often impractical to use in safety assessments. Instead simpler models, often box models, are preferred. The comparison of predictions made with the complex models and the simple models for this scenario show that the predictions in many cases are very similar, e g in the predictions of the evolution of the root zone concentration. However, in other cases differences of many orders of magnitude can appear. One example is the prediction of the flux to the groundwater of radionuclides being transported through the soil column. Some issues that have come to focus in this study: There are large differences in the predicted soil hydrology and as a consequence also in the radionuclide transport, which suggests that there are large uncertainties in the calculation of effective precipitation and evapotranspiration. The approach used for modelling the water transport in the root zone has an impact on the predictions of the decline in root
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
The Complexity of Developmental Predictions from Dual Process Models
Stanovich, Keith E.; West, Richard F.; Toplak, Maggie E.
2011-01-01
Drawing developmental predictions from dual-process theories is more complex than is commonly realized. Overly simplified predictions drawn from such models may lead to premature rejection of the dual process approach as one of many tools for understanding cognitive development. Misleading predictions can be avoided by paying attention to several…
Constructive Lower Bounds on Model Complexity of Shallow Perceptron Networks
Czech Academy of Sciences Publication Activity Database
Kůrková, Věra
2018-01-01
Roč. 29, č. 7 (2018), s. 305-315 ISSN 0941-0643 R&D Projects: GA ČR GA15-18108S Institutional support: RVO:67985807 Keywords : shallow and deep networks * model complexity and sparsity * signum perceptron networks * finite mappings * variational norms * Hadamard matrices Subject RIV: IN - Informatics, Computer Science Impact factor: 2.505, year: 2016
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
Kolmogorov complexity, pseudorandom generators and statistical models testing
Czech Academy of Sciences Publication Activity Database
Šindelář, Jan; Boček, Pavel
2002-01-01
Roč. 38, č. 6 (2002), s. 747-759 ISSN 0023-5954 R&D Projects: GA ČR GA102/99/1564 Institutional research plan: CEZ:AV0Z1075907 Keywords : Kolmogorov complexity * pseudorandom generators * statistical models testing Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.341, year: 2002
Framework for Modelling Multiple Input Complex Aggregations for Interactive Installations
DEFF Research Database (Denmark)
Padfield, Nicolas; Andreasen, Troels
2012-01-01
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...
Model-based safety architecture framework for complex systems
Schuitemaker, Katja; Rajabali Nejad, Mohammadreza; Braakhuis, J.G.; Podofillini, 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
A binary logistic regression model with complex sampling design of ...
African Journals Online (AJOL)
2017-09-03
Sep 3, 2017 ... Bi-variable and multi-variable binary logistic regression model with complex sampling design was fitted. .... Data was entered into STATA-12 and analyzed using. SPSS-21. .... lack of access/too far or costs too much. 35. 1.2.
On the general procedure for modelling complex ecological systems
International Nuclear Information System (INIS)
He Shanyu.
1987-12-01
In this paper, the principle of a general procedure for modelling complex ecological systems, i.e. the Adaptive Superposition Procedure (ASP) is shortly stated. The result of application of ASP in a national project for ecological regionalization is also described. (author). 3 refs
The dynamic complexity of a three species food chain model
International Nuclear Information System (INIS)
Lv Songjuan; Zhao Min
2008-01-01
In this paper, a three-species food chain model is analytically investigated on theories of ecology and using numerical simulation. Bifurcation diagrams are obtained for biologically feasible parameters. The results show that the system exhibits rich complexity features such as stable, periodic and chaotic dynamics
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.
International Nuclear Information System (INIS)
Xing Yulong; Shu Chiwang
2006-01-01
Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source term. In our earlier work [J. Comput. Phys. 208 (2005) 206-227; J. Sci. Comput., accepted], we designed a well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, which at the same time maintains genuine high order accuracy for general solutions, to a class of hyperbolic systems with separable source terms including the shallow water equations, the elastic wave equation, the hyperbolic model for a chemosensitive movement, the nozzle flow and a two phase flow model. In this paper, we generalize high order finite volume WENO schemes and Runge-Kutta discontinuous Galerkin (RKDG) finite element methods to the same class of hyperbolic systems to maintain a well-balanced property. Finite volume and discontinuous Galerkin finite element schemes are more flexible than finite difference schemes to treat complicated geometry and adaptivity. However, because of a different computational framework, the maintenance of the well-balanced property requires different technical approaches. After the description of our well-balanced high order finite volume WENO and RKDG schemes, we perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions, the non-oscillatory property for general solutions with discontinuities, and the genuine high order accuracy in smooth regions
Computing with high-resolution upwind schemes for hyperbolic equations
International Nuclear Information System (INIS)
Chakravarthy, S.R.; Osher, S.; California Univ., Los Angeles)
1985-01-01
Computational aspects of modern high-resolution upwind finite-difference schemes for hyperbolic systems of conservation laws are examined. An operational unification is demonstrated for constructing a wide class of flux-difference-split and flux-split schemes based on the design principles underlying total variation diminishing (TVD) schemes. Consideration is also given to TVD scheme design by preprocessing, the extension of preprocessing and postprocessing approaches to general control volumes, the removal of expansion shocks and glitches, relaxation methods for implicit TVD schemes, and a new family of high-accuracy TVD schemes. 21 references
Plasma diagnostics by Abel inversion in hyperbolic geometry
International Nuclear Information System (INIS)
Alhasi, A.S.; Elliott, J.A.
1992-01-01
Plasma confined in the UMIST linear quadrupole adopts a configuration with approximately hyperbolic symmetry. The normal diagnostic is a Langmuir probe, but we have developed an alternative method using optical emission tomography based upon an analytic Abel inversion. Plasma radiance is obtained as a function of a parameter identifying magnetic flux surfaces. The inversion algorithm has been tested using artificial data. Experimentally, the results show that ionizing collisions cause the confined plasma distribution to broaden as the plasma travels through the confining field. This is shown to be a consequence of the approximate incompressibility of the E x B flow. (author)
On the landau levels on the hyperbolic plane
International Nuclear Information System (INIS)
Comtet, A.
1986-04-01
The classical and quantum mechanics of a charged particle moving on the hyperbolic plane in a constant magnetic field is discussed. The underlying SL(2,R) symmetry leads to a general description of various possible trajectories. In contrast with the flat case, it is shown that closed orbits only arise for sufficiently strong fields. At the quantum level a group theoretical approach including both bound and continuum states is presented. It is shown that the semiclassical approximation leads to the exact bound state spectrum. The resolvent and its flat space limit are constructed in closed form
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.
Uncertainty and validation. Effect of model complexity on uncertainty estimates
Energy Technology Data Exchange (ETDEWEB)
Elert, M. [Kemakta Konsult AB, Stockholm (Sweden)] [ed.
1996-09-01
In the Model Complexity subgroup of BIOMOVS II, models of varying complexity have been applied to the problem of downward transport of radionuclides in soils. A scenario describing a case of surface contamination of a pasture soil was defined. Three different radionuclides with different environmental behavior and radioactive half-lives were considered: Cs-137, Sr-90 and I-129. The intention was to give a detailed specification of the parameters required by different kinds of model, together with reasonable values for the parameter uncertainty. A total of seven modelling teams participated in the study using 13 different models. Four of the modelling groups performed uncertainty calculations using nine different modelling approaches. The models used range in complexity from analytical solutions of a 2-box model using annual average data to numerical models coupling hydrology and transport using data varying on a daily basis. The complex models needed to consider all aspects of radionuclide transport in a soil with a variable hydrology are often impractical to use in safety assessments. Instead simpler models, often box models, are preferred. The comparison of predictions made with the complex models and the simple models for this scenario show that the predictions in many cases are very similar, e g in the predictions of the evolution of the root zone concentration. However, in other cases differences of many orders of magnitude can appear. One example is the prediction of the flux to the groundwater of radionuclides being transported through the soil column. Some issues that have come to focus in this study: There are large differences in the predicted soil hydrology and as a consequence also in the radionuclide transport, which suggests that there are large uncertainties in the calculation of effective precipitation and evapotranspiration. The approach used for modelling the water transport in the root zone has an impact on the predictions of the decline in root
On some issues of the modeling and analysis of two phase flow systems
International Nuclear Information System (INIS)
Ndjinga, M.
2007-04-01
Two-fluid and multi-field models are commonly used in the modeling and numerical simulation of two phase flows. They however present several mathematical and numerical difficulties, such as their lack of hyperbolicity or their non trivial Eigen-structure. It is important to understand the well-posedness of such possibly non hyperbolic systems before solving them numerically. For this reason, we study the solutions of systems of first order partial differential equations having a possibly complex Eigen-structure. We then characterise the hyperbolicity of the six equations two-fluid model with interfacial forces having differential expressions such as the interfacial pressure term, virtual mass and lift forces. The study of the characteristic polynomial leads to a diagram representing the location and topology of the non hyperbolic regions. We eventually propose numerous closure laws that make the two-fluid and multi-field models unconditionally hyperbolic. In order to numerically solve the two-fluid and multi-field models equations in a finite volume approach using a Roe type scheme, we propose two new algorithms designed for an efficient computation of the matrix absolute value function. These algorithms are robust as they avoid the computation of the eigenvectors of the argument matrix. The first is based on an iterative approach and converges in a finite number of steps if the eigenvalues are real. The second is faster, and besides can handle the case of complex eigenvalues. Thanks to these new algorithms, it is now possible to solve efficiently the six equations two-fluid model with differential interfacial terms, or the multi-field model with an arbitrary number of fields. We finally show the results of some recent numerical simulations of the six equations two-fluid model and the multi-field model with interfacial forces having a differential expression. (author)
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...
Aoi, Shinya; Tsuchiya, Kazuo; Kokubu, Hiroshi
2016-01-01
Passive dynamic walking is a useful model for investigating the mechanical functions of the body that produce energy-efficient walking. The basin of attraction is very small and thin, and it has a fractal-like shape; this explains the difficulty in producing stable passive dynamic walking. The underlying mechanism that produces these geometric characteristics was not known. In this paper, we consider this from the viewpoint of dynamical systems theory, and we use the simplest walking model to clarify the mechanism that forms the basin of attraction for passive dynamic walking. We show that the intrinsic saddle-type hyperbolicity of the upright equilibrium point in the governing dynamics plays an important role in the geometrical characteristics of the basin of attraction; this contributes to our understanding of the stability mechanism of bipedal walking. PMID:27436971
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
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.
Higher genus correlators for the complex matrix model
International Nuclear Information System (INIS)
Ambjorn, J.; Kristhansen, C.F.; Makeenko, Y.M.
1992-01-01
In this paper, the authors describe an iterative scheme which allows us to calculate any multi-loop correlator for the complex matrix model to any genus using only the first in the chain of loop equations. The method works for a completely general potential and the results contain no explicit reference to the couplings. The genus g contribution to the m-loop correlator depends on a finite number of parameters, namely at most 4g - 2 + m. The authors find the generating functional explicitly up to genus three. The authors show as well that the model is equivalent to an external field problem for the complex matrix model with a logarithmic potential
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.
Deciphering the complexity of acute inflammation using mathematical models.
Vodovotz, Yoram
2006-01-01
Various stresses elicit an acute, complex inflammatory response, leading to healing but sometimes also to organ dysfunction and death. We constructed both equation-based models (EBM) and agent-based models (ABM) of various degrees of granularity--which encompass the dynamics of relevant cells, cytokines, and the resulting global tissue dysfunction--in order to begin to unravel these inflammatory interactions. The EBMs describe and predict various features of septic shock and trauma/hemorrhage (including the response to anthrax, preconditioning phenomena, and irreversible hemorrhage) and were used to simulate anti-inflammatory strategies in clinical trials. The ABMs that describe the interrelationship between inflammation and wound healing yielded insights into intestinal healing in necrotizing enterocolitis, vocal fold healing during phonotrauma, and skin healing in the setting of diabetic foot ulcers. Modeling may help in understanding the complex interactions among the components of inflammation and response to stress, and therefore aid in the development of novel therapies and diagnostics.
Nonlinear model of epidemic spreading in a complex social network.
Kosiński, Robert A; Grabowski, A
2007-10-01
The epidemic spreading in a human society is a complex process, which can be described on the basis of a nonlinear mathematical model. In such an approach the complex and hierarchical structure of social network (which has implications for the spreading of pathogens and can be treated as a complex network), can be taken into account. In our model each individual has one of the four permitted states: susceptible, infected, infective, unsusceptible or dead. This refers to the SEIR model used in epidemiology. The state of an individual changes in time, depending on the previous state and the interactions with other individuals. The description of the interpersonal contacts is based on the experimental observations of the social relations in the community. It includes spatial localization of the individuals and hierarchical structure of interpersonal interactions. Numerical simulations were performed for different types of epidemics, giving the progress of a spreading process and typical relationships (e.g. range of epidemic in time, the epidemic curve). The spreading process has a complex and spatially chaotic character. The time dependence of the number of infective individuals shows the nonlinear character of the spreading process. We investigate the influence of the preventive vaccinations on the spreading process. In particular, for a critical value of preventively vaccinated individuals the percolation threshold is observed and the epidemic is suppressed.
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
2014-12-19
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.
BlenX-based compositional modeling of complex reaction mechanisms
Directory of Open Access Journals (Sweden)
Judit Zámborszky
2010-02-01
Full Text Available Molecular interactions are wired in a fascinating way resulting in complex behavior of biological systems. Theoretical modeling provides a useful framework for understanding the dynamics and the function of such networks. The complexity of the biological networks calls for conceptual tools that manage the combinatorial explosion of the set of possible interactions. A suitable conceptual tool to attack complexity is compositionality, already successfully used in the process algebra field to model computer systems. We rely on the BlenX programming language, originated by the beta-binders process calculus, to specify and simulate high-level descriptions of biological circuits. The Gillespie's stochastic framework of BlenX requires the decomposition of phenomenological functions into basic elementary reactions. Systematic unpacking of complex reaction mechanisms into BlenX templates is shown in this study. The estimation/derivation of missing parameters and the challenges emerging from compositional model building in stochastic process algebras are discussed. A biological example on circadian clock is presented as a case study of BlenX compositionality.
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.
Building Better Ecological Machines: Complexity Theory and Alternative Economic Models
Directory of Open Access Journals (Sweden)
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.
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.
Parametric Linear Hybrid Automata for Complex Environmental Systems Modeling
Directory of Open Access Journals (Sweden)
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.
Transtrum, Mark K; Qiu, Peng
2016-05-01
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.
Big Data Clustering via Community Detection and Hyperbolic Network Embedding in IoT Applications.
Karyotis, Vasileios; Tsitseklis, Konstantinos; Sotiropoulos, Konstantinos; Papavassiliou, Symeon
2018-04-15
In this paper, we present a novel data clustering framework for big sensory data produced by IoT applications. Based on a network representation of the relations among multi-dimensional data, data clustering is mapped to node clustering over the produced data graphs. To address the potential very large scale of such datasets/graphs that test the limits of state-of-the-art approaches, we map the problem of data clustering to a community detection one over the corresponding data graphs. Specifically, we propose a novel computational approach for enhancing the traditional Girvan-Newman (GN) community detection algorithm via hyperbolic network embedding. The data dependency graph is embedded in the hyperbolic space via Rigel embedding, allowing more efficient computation of edge-betweenness centrality needed in the GN algorithm. This allows for more efficient clustering of the nodes of the data graph in terms of modularity, without sacrificing considerable accuracy. In order to study the operation of our approach with respect to enhancing GN community detection, we employ various representative types of artificial complex networks, such as scale-free, small-world and random geometric topologies, and frequently-employed benchmark datasets for demonstrating its efficacy in terms of data clustering via community detection. Furthermore, we provide a proof-of-concept evaluation by applying the proposed framework over multi-dimensional datasets obtained from an operational smart-city/building IoT infrastructure provided by the Federated Interoperable Semantic IoT/cloud Testbeds and Applications (FIESTA-IoT) testbed federation. It is shown that the proposed framework can be indeed used for community detection/data clustering and exploited in various other IoT applications, such as performing more energy-efficient smart-city/building sensing.
Big Data Clustering via Community Detection and Hyperbolic Network Embedding in IoT Applications
Directory of Open Access Journals (Sweden)
Vasileios Karyotis
2018-04-01
Full Text Available In this paper, we present a novel data clustering framework for big sensory data produced by IoT applications. Based on a network representation of the relations among multi-dimensional data, data clustering is mapped to node clustering over the produced data graphs. To address the potential very large scale of such datasets/graphs that test the limits of state-of-the-art approaches, we map the problem of data clustering to a community detection one over the corresponding data graphs. Specifically, we propose a novel computational approach for enhancing the traditional Girvan–Newman (GN community detection algorithm via hyperbolic network embedding. The data dependency graph is embedded in the hyperbolic space via Rigel embedding, allowing more efficient computation of edge-betweenness centrality needed in the GN algorithm. This allows for more efficient clustering of the nodes of the data graph in terms of modularity, without sacrificing considerable accuracy. In order to study the operation of our approach with respect to enhancing GN community detection, we employ various representative types of artificial complex networks, such as scale-free, small-world and random geometric topologies, and frequently-employed benchmark datasets for demonstrating its efficacy in terms of data clustering via community detection. Furthermore, we provide a proof-of-concept evaluation by applying the proposed framework over multi-dimensional datasets obtained from an operational smart-city/building IoT infrastructure provided by the Federated Interoperable Semantic IoT/cloud Testbeds and Applications (FIESTA-IoT testbed federation. It is shown that the proposed framework can be indeed used for community detection/data clustering and exploited in various other IoT applications, such as performing more energy-efficient smart-city/building sensing.
Mathematical modelling of complex contagion on clustered networks
O'sullivan, David J.; O'Keeffe, Gary; Fennell, Peter; Gleeson, James
2015-09-01
The spreading of behavior, such as the adoption of a new innovation, is influenced bythe structure of social networks that interconnect the population. In the experiments of Centola (Science, 2010), adoption of new behavior was shown to spread further and faster across clustered-lattice networks than across corresponding random networks. This implies that the “complex contagion” effects of social reinforcement are important in such diffusion, in contrast to “simple” contagion models of disease-spread which predict that epidemics would grow more efficiently on random networks than on clustered networks. To accurately model complex contagion on clustered networks remains a challenge because the usual assumptions (e.g. of mean-field theory) regarding tree-like networks are invalidated by the presence of triangles in the network; the triangles are, however, crucial to the social reinforcement mechanism, which posits an increased probability of a person adopting behavior that has been adopted by two or more neighbors. In this paper we modify the analytical approach that was introduced by Hebert-Dufresne et al. (Phys. Rev. E, 2010), to study disease-spread on clustered networks. We show how the approximation method can be adapted to a complex contagion model, and confirm the accuracy of the method with numerical simulations. The analytical results of the model enable us to quantify the level of social reinforcement that is required to observe—as in Centola’s experiments—faster diffusion on clustered topologies than on random networks.
Mathematical modelling of complex contagion on clustered networks
Directory of Open Access Journals (Sweden)
David J. P. O'Sullivan
2015-09-01
Full Text Available The spreading of behavior, such as the adoption of a new innovation, is influenced bythe structure of social networks that interconnect the population. In the experiments of Centola (Science, 2010, adoption of new behavior was shown to spread further and faster across clustered-lattice networks than across corresponding random networks. This implies that the complex contagion effects of social reinforcement are important in such diffusion, in contrast to simple contagion models of disease-spread which predict that epidemics would grow more efficiently on random networks than on clustered networks. To accurately model complex contagion on clustered networks remains a challenge because the usual assumptions (e.g. of mean-field theory regarding tree-like networks are invalidated by the presence of triangles in the network; the triangles are, however, crucial to the social reinforcement mechanism, which posits an increased probability of a person adopting behavior that has been adopted by two or more neighbors. In this paper we modify the analytical approach that was introduced by Hebert-Dufresne et al. (Phys. Rev. E, 2010, to study disease-spread on clustered networks. We show how the approximation method can be adapted to a complex contagion model, and confirm the accuracy of the method with numerical simulations. The analytical results of the model enable us to quantify the level of social reinforcement that is required to observe—as in Centola’s experiments—faster diffusion on clustered topologies than on random networks.
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…
On the Growth of the Number of Hyperbolic Gravitational Instantons with respect to Volume
Ratcliffe, John G.; Tschantz, Steven T.
2000-01-01
In this paper, we show that the number of hyperbolic gravitational instantons grows superexponentially with respect to volume. As an application, we show that the Hartle-Hawking wave function for the universe is infinitely peaked at a certain closed hyperbolic 3-manifold.
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...
Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations
Müller, Ingo
2008-12-01
Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. This presentation is based upon the book [1] of which the author of this paper is a co-author. For more details about the motivation and exploitation of the basic principles the interested reader is referred to that reference. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation. Physicists may prefer to appreciate the success of extended thermodynamics in light scattering and to work on the open problems concerning the modification of the Navier-Stokes-Fourier theory in rarefied gases as predicted by extended thermodynamics of 13, 14, and more moments.
Minimality of invariant laminations for partially hyperbolic attractors
International Nuclear Information System (INIS)
Nobili, Felipe
2015-01-01
Let f : M → M be a C 1 -diffeomorphism over a compact boundaryless Riemannian manifold M, and Λ a compact f-invariant subset of M admitting a partially hyperbolic spliting T f Λ = E s ⊕ E c ⊕ E u over the tangent bundle T f Λ. It's known from the Hirsch–Pugh–Shub theory that Λ admits two invariant laminations associated to the extremal bundles E s and E u . These laminations are families of dynamically defined immersed submanifolds of the M tangent, respectively, to the bundles E s and E u at every point in Λ. In this work, we prove that at least one of the invariant laminations of a transitive partially hyperbolic attractor with a one-dimensional center bundle is minimal: the orbit of every leaf intersects Λ densely. This result extends those in Bonatti et al (2002 J. Inst. Math. Jussieu 1 513–41) and Hertz et al (2007 Fields Institute Communications vol 51 (Providence, RI: American Mathematical Society) pp 103–9) about minimal foliations for robustly transitive diffeomorphisms. (paper)
Tangent-Impulse Interception for a Hyperbolic Target
Directory of Open Access Journals (Sweden)
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.
Mixed hyperbolic-second-order-parabolic formulations of general relativity
International Nuclear Information System (INIS)
Paschalidis, Vasileios
2008-01-01
Two new formulations of general relativity are introduced. The first one is a parabolization of the Arnowitt-Deser-Misner formulation and is derived by the addition of combinations of the constraints and their derivatives to the right-hand side of the Arnowitt-Deser-Misner evolution equations. The desirable property of this modification is that it turns the surface of constraints into a local attractor because the constraint propagation equations become second-order parabolic independently of the gauge conditions employed. This system may be classified as mixed hyperbolic--second-order parabolic. The second formulation is a parabolization of the Kidder-Scheel-Teukolsky formulation and is a manifestly mixed strongly hyperbolic--second-order-parabolic set of equations, bearing thus resemblance to the compressible Navier-Stokes equations. As a first test, a stability analysis of flat space is carried out and it is shown that the first modification exponentially damps and smoothes all constraint-violating modes. These systems provide a new basis for constructing schemes for long-term and stable numerical integration of the Einstein field equations.
Demonstrator of atmospheric reentry system with hyperbolic velocity—DASH
Morita, Yasuhiro; Kawaguchi, Jun'ichiro; Inatani, Yoshifumi; Abe, Takashi
2003-01-01
Among a wide variety of challenging projects planned for the coming decade is the MUSES-C mission designed by the ISAS of Japan. Despite huge amount of data collected by the previous interplanetary spacecraft and probes, the origin and evolution of the solar system still remains unveiled due to their limited information. Thus, our concern has been directed toward a sample return to carry sample from an asteroid back to the earth, which will contribute to better understanding of the system. One of the keys to success is considered the reentry technology with hyperbolic velocity, which has not been demonstrated yet. With this as background, the demonstrator of atmospheric reentry system with hyperbolic velocity, DASH, has been given a commitment to demonstrate the high-speed reentry technology, which will be launched in summer of next year by Japan's H-IIA rocket in a piggyback configuration. The spaceship, composed of a reentry capsule and its carrier, will be injected into a geostationary transfer orbit (GTO) and after several revolutions it will deorbit by burn of a solid propellant deorbit motor. The capsule, identical to that of the sample return mission, can experience the targeted level of thermal environment even from the GTO by tracing a specially designed reentry trajectory.
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.
Tuning subwavelength-structured focus in the hyperbolic metamaterials
Pan, Rong; Tang, Zhixiang; Pan, Jin; Peng, Runwu
2016-10-01
In this paper, we have systematically investigated light propagating in the hyperbolic metamaterials (HMMs) covered by a subwavelength grating. Based on the equal-frequency contour analyses, light in the HMM is predicted to propagate along a defined direction because of its hyperbolic dispersion, which is similar to the self-collimating effects in photonic crystals. By using the finite-difference time-domain, numerical simulations demonstrate a subwavelength bright spot at the intersection of the adjacent directional beams. Different from the images in homogeneous media, the magnetic fields and electric fields at the spot are layered, especially for the electric fields Ez that is polarized to the propagating direction, i.e., the layer normal direction. Moreover, the Ez is hollow in the layer plane and is stronger than the other electric field component Ex. Therefore, the whole electric field is structured and its pattern can be tuned by the HMM's effective anisotropic electromagnetic parameters. Our results may be useful for generating subwavelength structured light.
Survey of time preference, delay discounting models
Directory of Open Access Journals (Sweden)
John R. Doyle
2013-03-01
Full Text Available The paper surveys over twenty models of delay discounting (also known as temporal discounting, time preference, time discounting, that psychologists and economists have put forward to explain the way people actually trade off time and money. Using little more than the basic algebra of powers and logarithms, I show how the models are derived, what assumptions they are based upon, and how different models relate to each other. Rather than concentrate only on discount functions themselves, I show how discount functions may be manipulated to isolate rate parameters for each model. This approach, consistently applied, helps focus attention on the three main components in any discounting model: subjectively perceived money; subjectively perceived time; and how these elements are combined. We group models by the number of parameters that have to be estimated, which means our exposition follows a trajectory of increasing complexity to the models. However, as the story unfolds it becomes clear that most models fall into a smaller number of families. We also show how new models may be constructed by combining elements of different models. The surveyed models are: Exponential; Hyperbolic; Arithmetic; Hyperboloid (Green and Myerson, Rachlin; Loewenstein and Prelec Generalized Hyperboloid; quasi-Hyperbolic (also known as beta-delta discounting; Benhabib et al's fixed cost; Benhabib et al's Exponential / Hyperbolic / quasi-Hyperbolic; Read's discounting fractions; Roelofsma's exponential time; Scholten and Read's discounting-by-intervals (DBI; Ebert and Prelec's constant sensitivity (CS; Bleichrodt et al.'s constant absolute decreasing impatience (CADI; Bleichrodt et al.'s constant relative decreasing impatience (CRDI; Green, Myerson, and Macaux's hyperboloid over intervals models; Killeen's additive utility; size-sensitive additive utility; Yi, Landes, and Bickel's memory trace models; McClure et al.'s two exponentials; and Scholten and Read's trade
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.
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...
An Ontology for Modeling Complex Inter-relational Organizations
Wautelet, Yves; Neysen, Nicolas; Kolp, Manuel
This paper presents an ontology for organizational modeling through multiple complementary aspects. The primary goal of the ontology is to dispose of an adequate set of related concepts for studying complex organizations involved in a lot of relationships at the same time. In this paper, we define complex organizations as networked organizations involved in a market eco-system that are playing several roles simultaneously. In such a context, traditional approaches focus on the macro analytic level of transactions; this is supplemented here with a micro analytic study of the actors' rationale. At first, the paper overviews enterprise ontologies literature to position our proposal and exposes its contributions and limitations. The ontology is then brought to an advanced level of formalization: a meta-model in the form of a UML class diagram allows to overview the ontology concepts and their relationships which are formally defined. Finally, the paper presents the case study on which the ontology has been validated.
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.
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
Model Complexities of Shallow Networks Representing Highly Varying Functions
Czech Academy of Sciences Publication Activity Database
Kůrková, Věra; Sanguineti, M.
2016-01-01
Roč. 171, 1 January (2016), s. 598-604 ISSN 0925-2312 R&D Projects: GA MŠk(CZ) LD13002 Grant - others:grant for Visiting Professors(IT) GNAMPA-INdAM Institutional support: RVO:67985807 Keywords : shallow networks * model complexity * highly varying functions * Chernoff bound * perceptrons * Gaussian kernel units Subject RIV: IN - Informatics, Computer Science Impact factor: 3.317, year: 2016
Hyperbolic Cosine–Exponentiated Exponential Lifetime Distribution and its Application in Reliability
Directory of Open Access Journals (Sweden)
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.
Nonlocal optical effects on the Goos–Hänchen shifts at multilayered hyperbolic metamaterials
International Nuclear Information System (INIS)
Chen, Chih-Wei; Bian, Tingting; Chiang, Hai-Pang; Leung, P T
2016-01-01
The lateral beam shift of light incident on a multilayered hyperbolic metamaterial (HMM) is investigated using a theoretical model which emphasizes the nonlocal optical response of the indefinite material. By applying an effective local response theory formulated recently in the literature, it is found that nonlocal effects only affect p polarized light in this Goos–Hänchen (GH) shift of the incident beam; leading to a blue-shifted peak for positive shifts at high frequencies and red-shifted dip for negative shifts at low frequencies in the GH shift spectrum. An account for the observed phenomenon is given by referring to the ‘Brewster condition’ for the reflected wave from the HMM. This observation thus provides a relatively direct probe for the nonlocal response of the HMM. (paper)
RDTM solution of Caputo time fractional-order hyperbolic telegraph equation
Directory of Open Access Journals (Sweden)
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.
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.
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......Urbanisation processes are results of a broad variety of actors or actor groups and their behaviour and decisions based on different experiences, knowledge, resources, values etc. The decisions done are often on a micro/individual level but resulting in macro/collective behaviour. In urban research...
Methodology and Results of Mathematical Modelling of Complex Technological Processes
Mokrova, Nataliya V.
2018-03-01
The methodology of system analysis allows us to draw a mathematical model of the complex technological process. The mathematical description of the plasma-chemical process was proposed. The importance the quenching rate and initial temperature decrease time was confirmed for producing the maximum amount of the target product. The results of numerical integration of the system of differential equations can be used to describe reagent concentrations, plasma jet rate and temperature in order to achieve optimal mode of hardening. Such models are applicable both for solving control problems and predicting future states of sophisticated technological systems.
The complex sine-Gordon model on a half line
International Nuclear Information System (INIS)
Tzamtzis, Georgios
2003-01-01
In this thesis, we study the complex sine-Gordon model on a half line. The model in the bulk is an integrable (1+1) dimensional field theory which is U(1) gauge invariant and comprises a generalisation of the sine-Gordon theory. It accepts soliton and breather solutions. By introducing suitably selected boundary conditions we may consider the model on a half line. Through such conditions the model can be shown to remain integrable and various aspects of the boundary theory can be examined. The first chapter serves as a brief introduction to some basic concepts of integrability and soliton solutions. As an example of an integrable system with soliton solutions, the sine-Gordon model is presented both in the bulk and on a half line. These results will serve as a useful guide for the model at hand. The introduction finishes with a brief overview of the two methods that will be used on the fourth chapter in order to obtain the quantum spectrum of the boundary complex sine-Gordon model. In the second chapter the model is properly introduced along with a brief literature review. Different realisations of the model and their connexions are discussed. The vacuum of the theory is investigated. Soliton solutions are given and a discussion on the existence of breathers follows. Finally the collapse of breather solutions to single solitons is demonstrated and the chapter concludes with a different approach to the breather problem. In the third chapter, we construct the lowest conserved currents and through them we find suitable boundary conditions that allow for their conservation in the presence of a boundary. The boundary term is added to the Lagrangian and the vacuum is reexamined in the half line case. The reflection process of solitons from the boundary is studied and the time-delay is calculated. Finally we address the existence of boundary-bound states. In the fourth chapter we study the quantum complex sine-Gordon model. We begin with a brief overview of the theory in
Extending a configuration model to find communities in complex networks
International Nuclear Information System (INIS)
Jin, Di; Hu, Qinghua; He, Dongxiao; Yang, Bo; Baquero, Carlos
2013-01-01
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. (paper)
Grammatical complexity for two-dimensional maps
International Nuclear Information System (INIS)
Hagiwara, Ryouichi; Shudo, Akira
2004-01-01
We calculate the grammatical complexity of the symbol sequences generated from the Henon map and the Lozi map using the recently developed methods to construct the pruning front. When the map is hyperbolic, the language of symbol sequences is regular in the sense of the Chomsky hierarchy and the corresponding grammatical complexity takes finite values. It is found that the complexity exhibits a self-similar structure as a function of the system parameter, and the similarity of the pruning fronts is discussed as an origin of such self-similarity. For non-hyperbolic cases, it is observed that the complexity monotonically increases as we increase the resolution of the pruning front
Grammatical complexity for two-dimensional maps
Energy Technology Data Exchange (ETDEWEB)
Hagiwara, Ryouichi; Shudo, Akira [Department of Physics, Tokyo Metropolitan University, Minami-Ohsawa, Hachioji, Tokyo 192-0397 (Japan)
2004-11-05
We calculate the grammatical complexity of the symbol sequences generated from the Henon map and the Lozi map using the recently developed methods to construct the pruning front. When the map is hyperbolic, the language of symbol sequences is regular in the sense of the Chomsky hierarchy and the corresponding grammatical complexity takes finite values. It is found that the complexity exhibits a self-similar structure as a function of the system parameter, and the similarity of the pruning fronts is discussed as an origin of such self-similarity. For non-hyperbolic cases, it is observed that the complexity monotonically increases as we increase the resolution of the pruning front.
Using model complexes to augment and advance metalloproteinase inhibitor design.
Jacobsen, Faith E; Cohen, Seth M
2004-05-17
The tetrahedral zinc complex [(Tp(Ph,Me))ZnOH] (Tp(Ph,Me) = hydrotris(3,5-phenylmethylpyrazolyl)borate) was combined with 2-thenylmercaptan, ethyl 4,4,4-trifluoroacetoacetate, salicylic acid, salicylamide, thiosalicylic acid, thiosalicylamide, methyl salicylate, methyl thiosalicyliate, and 2-hydroxyacetophenone to form the corresponding [(Tp(Ph,Me))Zn(ZBG)] complexes (ZBG = zinc-binding group). X-ray crystal structures of these complexes were obtained to determine the mode of binding for each ZBG, several of which had been previously studied with SAR by NMR (structure-activity relationship by nuclear magnetic resonance) as potential ligands for use in matrix metalloproteinase inhibitors. The [(Tp(Ph,Me))Zn(ZBG)] complexes show that hydrogen bonding and donor atom acidity have a pronounced effect on the mode of binding for this series of ligands. The results of these studies give valuable insight into how ligand protonation state and intramolecular hydrogen bonds can influence the coordination mode of metal-binding proteinase inhibitors. The findings here suggest that model-based approaches can be used to augment drug discovery methods applied to metalloproteins and can aid second-generation drug design.
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.
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...... approach applying bounds of appropriate Rayleigh quotients. The rotor systems tested are: a simple Laval rotor, a Laval rotor with additional elasticity and damping in the bearings, and a number of rotor systems with complex symmetric 4 x 4 randomly generated matrices.......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...
Surface complexation modeling of zinc sorption onto ferrihydrite.
Dyer, James A; Trivedi, Paras; Scrivner, Noel C; Sparks, Donald L
2004-02-01
A previous study involving lead(II) [Pb(II)] sorption onto ferrihydrite over a wide range of conditions highlighted the advantages of combining molecular- and macroscopic-scale investigations with surface complexation modeling to predict Pb(II) speciation and partitioning in aqueous systems. In this work, an extensive collection of new macroscopic and spectroscopic data was used to assess the ability of the modified triple-layer model (TLM) to predict single-solute zinc(II) [Zn(II)] sorption onto 2-line ferrihydrite in NaNO(3) solutions as a function of pH, ionic strength, and concentration. Regression of constant-pH isotherm data, together with potentiometric titration and pH edge data, was a much more rigorous test of the modified TLM than fitting pH edge data alone. When coupled with valuable input from spectroscopic analyses, good fits of the isotherm data were obtained with a one-species, one-Zn-sorption-site model using the bidentate-mononuclear surface complex, (triple bond FeO)(2)Zn; however, surprisingly, both the density of Zn(II) sorption sites and the value of the best-fit equilibrium "constant" for the bidentate-mononuclear complex had to be adjusted with pH to adequately fit the isotherm data. Although spectroscopy provided some evidence for multinuclear surface complex formation at surface loadings approaching site saturation at pH >/=6.5, the assumption of a bidentate-mononuclear surface complex provided acceptable fits of the sorption data over the entire range of conditions studied. Regressing edge data in the absence of isotherm and spectroscopic data resulted in a fair number of surface-species/site-type combinations that provided acceptable fits of the edge data, but unacceptable fits of the isotherm data. A linear relationship between logK((triple bond FeO)2Zn) and pH was found, given by logK((triple bond FeO)2Znat1g/l)=2.058 (pH)-6.131. In addition, a surface activity coefficient term was introduced to the model to reduce the ionic strength
Modelling of the quenching process in complex superconducting magnet systems
International Nuclear Information System (INIS)
Hagedorn, D.; Rodriguez-Mateos, F.
1992-01-01
This paper reports that the superconducting twin bore dipole magnet for the proposed Large Hadron Collider (LHC) at CERN shows a complex winding structure consisting of eight compact layers each of them electromagnetically and thermally coupled with the others. This magnet is only one part of an electrical circuit; test and operation conditions are characterized by different circuits. In order to study the quenching process in this complex system, design adequate protection schemes, and provide a basis for the dimensioning of protection devices such as heaters, current breakers and dump resistors, a general simulation tool called QUABER has been developed using the analog system analysis program SABER. A complete set of electro-thermal models has been crated for the propagation of normal regions. Any network extension or modification is easy to implement without rewriting the whole set of differential equations
A Primer for Model Selection: The Decisive Role of Model Complexity
Höge, Marvin; Wöhling, Thomas; Nowak, Wolfgang
2018-03-01
Selecting a "best" model among several competing candidate models poses an often encountered problem in water resources modeling (and other disciplines which employ models). For a modeler, the best model fulfills a certain purpose best (e.g., flood prediction), which is typically assessed by comparing model simulations to data (e.g., stream flow). Model selection methods find the "best" trade-off between good fit with data and model complexity. In this context, the interpretations of model complexity implied by different model selection methods are crucial, because they represent different underlying goals of modeling. Over the last decades, numerous model selection criteria have been proposed, but modelers who primarily want to apply a model selection criterion often face a lack of guidance for choosing the right criterion that matches their goal. We propose a classification scheme for model selection criteria that helps to find the right criterion for a specific goal, i.e., which employs the correct complexity interpretation. We identify four model selection classes which seek to achieve high predictive density, low predictive error, high model probability, or shortest compression of data. These goals can be achieved by following either nonconsistent or consistent model selection and by either incorporating a Bayesian parameter prior or not. We allocate commonly used criteria to these four classes, analyze how they represent model complexity and what this means for the model selection task. Finally, we provide guidance on choosing the right type of criteria for specific model selection tasks. (A quick guide through all key points is given at the end of the introduction.)
Spectroscopic studies of molybdenum complexes as models for nitrogenase
International Nuclear Information System (INIS)
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 2 O 4 (cysteine) 2 2- and trans-Mo(N 2 ) 2 (dppe) 2 (dppe = 1,2-bis(diphenylphosphino)ethane). The H 1 and C 13 NMR of solutions of Mo 2 O 4 (cys) 2 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 2 ) 2 (dppe) 2 is described and compared to the EXAFS of MoH 4 (dppe) 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 2 O 4 (cys) 2 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
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.
3D model of amphioxus steroid receptor complexed with estradiol
Energy Technology Data Exchange (ETDEWEB)
Baker, Michael E., E-mail: mbaker@ucsd.edu [Department of Medicine, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0693 (United States); Chang, David J. [Department of Biology, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0693 (United States)
2009-08-28
The origins of signaling by vertebrate steroids are not fully understood. An important advance was the report that an estrogen-binding steroid receptor [SR] is present in amphioxus, a basal chordate with a similar body plan as vertebrates. To investigate the evolution of estrogen-binding to steroid receptors, we constructed a 3D model of amphioxus SR complexed with estradiol. This 3D model indicates that although the SR is activated by estradiol, some interactions between estradiol and human ER{alpha} are not conserved in the SR, which can explain the low affinity of estradiol for the SR. These differences between the SR and ER{alpha} in the steroid-binding domain are sufficient to suggest that another steroid is the physiological regulator of the SR. The 3D model predicts that mutation of Glu-346 to Gln will increase the affinity of testosterone for amphioxus SR and elucidate the evolution of steroid-binding to nuclear receptors.
International Nuclear Information System (INIS)
Bonten, Luc T.C.; Groenenberg, Jan E.; Meesenburg, Henning; Vries, Wim de
2011-01-01
Various dynamic soil chemistry models have been developed to gain insight into impacts of atmospheric deposition of sulphur, nitrogen and other elements on soil and soil solution chemistry. Sorption parameters for anions and cations are generally calibrated for each site, which hampers extrapolation in space and time. On the other hand, recently developed surface complexation models (SCMs) have been successful in predicting ion sorption for static systems using generic parameter sets. This study reports the inclusion of an assemblage of these SCMs in the dynamic soil chemistry model SMARTml and applies this model to a spruce forest site in Solling Germany. Parameters for SCMs were taken from generic datasets and not calibrated. Nevertheless, modelling results for major elements matched observations well. Further, trace metals were included in the model, also using the existing framework of SCMs. The model predicted sorption for most trace elements well. - Highlights: → Surface complexation models can be well applied in field studies. → Soil chemistry under a forest site is adequately modelled using generic parameters. → The model is easily extended with extra elements within the existing framework. → Surface complexation models can show the linkages between major soil chemistry and trace element behaviour. - Surface complexation models with generic parameters make calibration of sorption superfluous in dynamic modelling of deposition impacts on soil chemistry under nature areas.
Energy Technology Data Exchange (ETDEWEB)
Bonten, Luc T.C., E-mail: luc.bonten@wur.nl [Alterra-Wageningen UR, Soil Science Centre, P.O. Box 47, 6700 AA Wageningen (Netherlands); Groenenberg, Jan E. [Alterra-Wageningen UR, Soil Science Centre, P.O. Box 47, 6700 AA Wageningen (Netherlands); Meesenburg, Henning [Northwest German Forest Research Station, Abt. Umweltkontrolle, Sachgebiet Intensives Umweltmonitoring, Goettingen (Germany); Vries, Wim de [Alterra-Wageningen UR, Soil Science Centre, P.O. Box 47, 6700 AA Wageningen (Netherlands)
2011-10-15
Various dynamic soil chemistry models have been developed to gain insight into impacts of atmospheric deposition of sulphur, nitrogen and other elements on soil and soil solution chemistry. Sorption parameters for anions and cations are generally calibrated for each site, which hampers extrapolation in space and time. On the other hand, recently developed surface complexation models (SCMs) have been successful in predicting ion sorption for static systems using generic parameter sets. This study reports the inclusion of an assemblage of these SCMs in the dynamic soil chemistry model SMARTml and applies this model to a spruce forest site in Solling Germany. Parameters for SCMs were taken from generic datasets and not calibrated. Nevertheless, modelling results for major elements matched observations well. Further, trace metals were included in the model, also using the existing framework of SCMs. The model predicted sorption for most trace elements well. - Highlights: > Surface complexation models can be well applied in field studies. > Soil chemistry under a forest site is adequately modelled using generic parameters. > The model is easily extended with extra elements within the existing framework. > Surface complexation models can show the linkages between major soil chemistry and trace element behaviour. - Surface complexation models with generic parameters make calibration of sorption superfluous in dynamic modelling of deposition impacts on soil chemistry under nature areas.
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.
Dynamics in stationary, non-globally hyperbolic spacetimes
Energy Technology Data Exchange (ETDEWEB)
Seggev, Itai [Enrico Fermi Institute and Department of Physics, University of Chicago, 5640 S Ellis Avenue, Chicago, IL 60637 (United States)
2004-06-07
Classically, the dynamics of a scalar field in a non-globally hyperbolic spacetime is ill-posed. Previously, a prescription was given for defining dynamics in static spacetimes in terms of a second-order operator acting on a Hilbert space defined on static slices. The present work extends this result by giving a similar prescription for defining dynamics in stationary spacetimes obeying certain mild assumptions. The prescription is defined in terms of a first-order operator acting on a different Hilbert space from that used in the static prescription. It preserves the important properties of the earlier prescription: the formal solution agrees with the Cauchy evolution within the domain of dependence, and smooth data of compact support always give rise to smooth solutions. In the static case, the first-order formalism agrees with the second-order formalism (using specifically the Friedrichs extension). Applications to field quantization are also discussed.
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...... with the nanoparticles. It is predicted that the super absorption properties of HMM show up when exceedingly large amounts of high-k modes are excited by strong plasmonic resonances. In the case that the coupling interface is formed by non-resonance scatterers, there is almost the same enhancement in the absorption...
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.
Solutions of hyperbolic equations with the CIP-BS method
International Nuclear Information System (INIS)
Utsumi, Takayuki; Koga, James; Yamagiwa, Mitsuru; Yabe, Takashi; Aoki, Takayuki
2004-01-01
In this paper, we show that a new numerical method, the Constrained Interpolation Profile - Basis Set (CIP-BS) method, can solve general hyperbolic equations efficiently. This method uses a simple polynomial basis set that is easily extendable to any desired higher-order accuracy. The interpolating profile is chosen so that the subgrid scale solution approaches the local real solution owing to the constraints from the spatial derivatives of the master equations. Then, introducing scalar products, the linear and nonlinear partial differential equations are uniquely reduced to the ordinary differential equations for values and spatial derivatives at the grid points. The method gives stable, less diffusive, and accurate results. It is successfully applied to the continuity equation, the Burgers equation, the Korteweg-de Vries equation, and one-dimensional shock tube problems. (author)
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...
Spectral approach to homogenization of hyperbolic equations with periodic coefficients
Dorodnyi, M. A.; Suslina, T. A.
2018-06-01
In L2 (Rd ;Cn), we consider selfadjoint strongly elliptic second order differential operators Aε with periodic coefficients depending on x / ε, ε > 0. We study the behavior of the operators cos (Aε1/2 τ) and Aε-1/2 sin (Aε1/2 τ), τ ∈ R, for small ε. Approximations for these operators in the (Hs →L2)-operator norm with a suitable s are obtained. The results are used to study the behavior of the solution vε of the Cauchy problem for the hyperbolic equation ∂τ2 vε = -Aεvε + F. General results are applied to the acoustics equation and the system of elasticity theory.
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.
Optimized difference schemes for multidimensional hyperbolic partial differential equations
Directory of Open Access Journals (Sweden)
Adrian Sescu
2009-04-01
Full Text Available In numerical solutions to hyperbolic partial differential equations in multidimensions, in addition to dispersion and dissipation errors, there is a grid-related error (referred to as isotropy error or numerical anisotropy that affects the directional dependence of the wave propagation. Difference schemes are mostly analyzed and optimized in one dimension, wherein the anisotropy correction may not be effective enough. In this work, optimized multidimensional difference schemes with arbitrary order of accuracy are designed to have improved isotropy compared to conventional schemes. The derivation is performed based on Taylor series expansion and Fourier analysis. The schemes are restricted to equally-spaced Cartesian grids, so the generalized curvilinear transformation method and Cartesian grid methods are good candidates.
Geometry through history Euclidean, hyperbolic, and projective geometries
Dillon, Meighan I
2018-01-01
Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...
Optimal control for parabolic-hyperbolic system with time delay
International Nuclear Information System (INIS)
Kowalewski, A.
1985-07-01
In this paper we consider an optimal control problem for a system described by a linear partial differential equation of the parabolic-hyperbolic type with time delay in the state. The right-hand side of this equation and the initial conditions are not continuous functions usually, but they are measurable functions belonging to L 2 or Lsup(infinity) spaces. Therefore, the solution of this equation is given by a certain Sobolev space. The time delay in the state is constant, but it can be also a function of time. The control time T is fixed in our problem. Making use of the Milutin-Dubovicki theorem, necessary and sufficient conditions of optimality with the quadratic performance functional and constrained control are derived for the Dirichlet problem. The flow chart of the algorithm which can be used in the numerical solving of certain optimization problems for distributed systems is also presented. (author)
Inflation with hyperbolic potential in the braneworld model
Indian Academy of Sciences (India)
BK21 Division of Advanced Research and Education in Physics, Hanyang University, ... high energy perhaps was available shortly after the Big Bang. ... fits the supernovae data very well, allowing for −2.4 < ωφ < −1 at 95% confidence.
On a hyperbolic system arising in liquid crystals modeling
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Rocca, E.; Schimperna, G.; Zarnescu, A.
2018-01-01
Roč. 15, č. 1 (2018), s. 15-35 ISSN 0219-8916 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : dissipative solution * liquid crystal * weak-strong uniqueness Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.940, year: 2016 https://www.worldscientific.com/doi/abs/10.1142/S0219891618500029
Diffusion models for mixtures using a stiff dissipative hyperbolic formalism
Boudin , Laurent; Grec , Bérénice; Pavan , Vincent
2018-01-01
In this article, we are interested in a system of uid equations for mixtures with a sti relaxation term of Maxwell-Stefan diusion type. We use the formalism developed by Chen, Levermore, Liu in [4] to obtain a limit system of Fick type where the species velocities tend to align to a bulk velocity when the relaxation parameter remains small.
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.
Multiagent model and mean field theory of complex auction dynamics
International Nuclear Information System (INIS)
Chen, Qinghua; Wang, Yougui; Huang, Zi-Gang; Lai, Ying-Cheng
2015-01-01
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. (paper)
Complex Coronary Hemodynamics - Simple Analog Modelling as an Educational Tool.
Parikh, Gaurav R; Peter, Elvis; Kakouros, Nikolaos
2017-01-01
Invasive coronary angiography remains the cornerstone for evaluation of coronary stenoses despite there being a poor correlation between luminal loss assessment by coronary luminography and myocardial ischemia. This is especially true for coronary lesions deemed moderate by visual assessment. Coronary pressure-derived fractional flow reserve (FFR) has emerged as the gold standard for the evaluation of hemodynamic significance of coronary artery stenosis, which is cost effective and leads to improved patient outcomes. There are, however, several limitations to the use of FFR including the evaluation of serial stenoses. In this article, we discuss the electronic-hydraulic analogy and the utility of simple electrical modelling to mimic the coronary circulation and coronary stenoses. We exemplify the effect of tandem coronary lesions on the FFR by modelling of a patient with sequential disease segments and complex anatomy. We believe that such computational modelling can serve as a powerful educational tool to help clinicians better understand the complexity of coronary hemodynamics and improve patient care.
On problems with displacement in boundary conditions for hyperbolic equation
Directory of Open Access Journals (Sweden)
Elena A. Utkina
2016-03-01
Full Text Available We consider three problems for hyperbolic equation on a plane in the characteristic domain. In these problems at least one of the conditions of the Goursat problem is replaced by nonlocal condition on the relevant characteristic. Non-local conditions are the linear combinations of the normal derivatives at points on opposite characteristics. In case of replacement of one condition we solve the problem by reduction to the Goursat problem for which it exists and is unique. To find the unknown Goursat condition author receives the integral equation, rewrite it in operational form and finds its unique solvability cases. To prove the unique solvability of the equation, the author shows the continuous linear operator and the fact, that some degree of the resulting operator is a contraction mapping. It is known that in this case the required Goursat condition can be written as Neumann series. We considered in detail only one of the tasks, but for both the unique solvability theorems are formulated. If the two conditions are changed, the uniqueness of the solution on the assumption that it exists, is proved by the method of a priori estimates. For this purpose, the inner product and the norm in $L_2$ are used. As a result, the conditions were obtained for the coefficients of a hyperbolic equation that ensure the uniqueness of the solution. An example is given, confirming that these conditions are essential. Namely, constructed an equation whose coefficients do not satisfy the conditions of the last theorem, given the conditions on the characteristics and nontrivial solution is built.
Rybalova, Elena; Semenova, Nadezhda; Strelkova, Galina; Anishchenko, Vadim
2017-06-01
We study the transition from coherence (complete synchronization) to incoherence (spatio-temporal chaos) in ensembles of nonlocally coupled chaotic maps with nonhyperbolic and hyperbolic attractors. As basic models of a partial element we use the Henon map and the Lozi map. We show that the transition to incoherence in a ring of coupled Henon maps occurs through the appearance of phase and amplitude chimera states. An ensemble of coupled Lozi maps demonstrates the coherence-incoherence transition via solitary states and no chimera states are observed in this case.
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......-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...
Wenchi Jin; Hong S. He; Frank R. Thompson
2016-01-01
Process-based forest ecosystem models vary from simple physiological, complex physiological, to hybrid empirical-physiological models. Previous studies indicate that complex models provide the best prediction at plot scale with a temporal extent of less than 10 years, however, it is largely untested as to whether complex models outperform the other two types of models...
Modelling study of sea breezes in a complex coastal environment
Cai, X.-M.; Steyn, D. G.
This study investigates a mesoscale modelling of sea breezes blowing from a narrow strait into the lower Fraser valley (LFV), British Columbia, Canada, during the period of 17-20 July, 1985. Without a nudging scheme in the inner grid, the CSU-RAMS model produces satisfactory wind and temperature fields during the daytime. In comparison with observation, the agreement indices for surface wind and temperature during daytime reach about 0.6 and 0.95, respectively, while the agreement indices drop to 0.4 at night. In the vertical, profiles of modelled wind and temperature generally agree with tethersonde data collected on 17 and 19 July. The study demonstrates that in late afternoon, the model does not capture the advection of an elevated warm layer which originated from land surfaces outside of the inner grid. Mixed layer depth (MLD) is calculated from model output of turbulent kinetic energy field. Comparison of MLD results with observation shows that the method generates a reliable MLD during the daytime, and that accurate estimates of MLD near the coast require the correct simulation of wind conditions over the sea. The study has shown that for a complex coast environment like the LFV, a reliable modelling study depends not only on local surface fluxes but also on elevated layers transported from remote land surfaces. This dependence is especially important when local forcings are weak, for example, during late afternoon and at night.
Physical modelling of flow and dispersion over complex terrain
Cermak, J. E.
1984-09-01
Atmospheric motion and dispersion over topography characterized by irregular (or regular) hill-valley or mountain-valley distributions are strongly dependent upon three general sets of variables. These are variables that describe topographic geometry, synoptic-scale winds and surface-air temperature distributions. In addition, pollutant concentration distributions also depend upon location and physical characteristics of the pollutant source. Overall fluid-flow complexity and variability from site to site have stimulated the development and use of physical modelling for determination of flow and dispersion in many wind-engineering applications. Models with length scales as small as 1:12,000 have been placed in boundary-layer wind tunnels to study flows in which forced convection by synoptic winds is of primary significance. Flows driven primarily by forces arising from temperature differences (gravitational or free convection) have been investigated by small-scale physical models placed in an isolated space (gravitational convection chamber). Similarity criteria and facilities for both forced and gravitational-convection flow studies are discussed. Forced-convection modelling is illustrated by application to dispersion of air pollutants by unstable flow near a paper mill in the state of Maryland and by stable flow over Point Arguello, California. Gravitational-convection modelling is demonstrated by a study of drainage flow and pollutant transport from a proposed mining operation in the Rocky Mountains of Colorado. Other studies in which field data are available for comparison with model data are reviewed.
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
Animal Models of Lymphangioleiomyomatosis (LAM) and Tuberous Sclerosis Complex (TSC)
2010-01-01
Abstract Animal models of lymphangioleiomyomatosis (LAM) and tuberous sclerosis complex (TSC) are highly desired to enable detailed investigation of the pathogenesis of these diseases. Multiple rats and mice have been generated in which a mutation similar to that occurring in TSC patients is present in an allele of Tsc1 or Tsc2. Unfortunately, these mice do not develop pathologic lesions that match those seen in LAM or TSC. However, these Tsc rodent models have been useful in confirming the two-hit model of tumor development in TSC, and in providing systems in which therapeutic trials (e.g., rapamycin) can be performed. In addition, conditional alleles of both Tsc1 and Tsc2 have provided the opportunity to target loss of these genes to specific tissues and organs, to probe the in vivo function of these genes, and attempt to generate better models. Efforts to generate an authentic LAM model are impeded by a lack of understanding of the cell of origin of this process. However, ongoing studies provide hope that such a model will be generated in the coming years. PMID:20235887
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.
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
a Range Based Method for Complex Facade Modeling
Adami, A.; Fregonese, L.; Taffurelli, L.
2011-09-01
3d modelling of Architectural Heritage does not follow a very well-defined way, but it goes through different algorithms and digital form according to the shape complexity of the object, to the main goal of the representation and to the starting data. Even if the process starts from the same data, such as a pointcloud acquired by laser scanner, there are different possibilities to realize a digital model. In particular we can choose between two different attitudes: the mesh and the solid model. In the first case the complexity of architecture is represented by a dense net of triangular surfaces which approximates the real surface of the object. In the other -opposite- case the 3d digital model can be realized by the use of simple geometrical shapes, by the use of sweeping algorithm and the Boolean operations. Obviously these two models are not the same and each one is characterized by some peculiarities concerning the way of modelling (the choice of a particular triangulation algorithm or the quasi-automatic modelling by known shapes) and the final results (a more detailed and complex mesh versus an approximate and more simple solid model). Usually the expected final representation and the possibility of publishing lead to one way or the other. In this paper we want to suggest a semiautomatic process to build 3d digital models of the facades of complex architecture to be used for example in city models or in other large scale representations. This way of modelling guarantees also to obtain small files to be published on the web or to be transmitted. The modelling procedure starts from laser scanner data which can be processed in the well known way. Usually more than one scan is necessary to describe a complex architecture and to avoid some shadows on the facades. These have to be registered in a single reference system by the use of targets which are surveyed by topography and then to be filtered in order to obtain a well controlled and homogeneous point cloud of
A RANGE BASED METHOD FOR COMPLEX FACADE MODELING
Directory of Open Access Journals (Sweden)
A. Adami
2012-09-01
Full Text Available 3d modelling of Architectural Heritage does not follow a very well-defined way, but it goes through different algorithms and digital form according to the shape complexity of the object, to the main goal of the representation and to the starting data. Even if the process starts from the same data, such as a pointcloud acquired by laser scanner, there are different possibilities to realize a digital model. In particular we can choose between two different attitudes: the mesh and the solid model. In the first case the complexity of architecture is represented by a dense net of triangular surfaces which approximates the real surface of the object. In the other -opposite- case the 3d digital model can be realized by the use of simple geometrical shapes, by the use of sweeping algorithm and the Boolean operations. Obviously these two models are not the same and each one is characterized by some peculiarities concerning the way of modelling (the choice of a particular triangulation algorithm or the quasi-automatic modelling by known shapes and the final results (a more detailed and complex mesh versus an approximate and more simple solid model. Usually the expected final representation and the possibility of publishing lead to one way or the other. In this paper we want to suggest a semiautomatic process to build 3d digital models of the facades of complex architecture to be used for example in city models or in other large scale representations. This way of modelling guarantees also to obtain small files to be published on the web or to be transmitted. The modelling procedure starts from laser scanner data which can be processed in the well known way. Usually more than one scan is necessary to describe a complex architecture and to avoid some shadows on the facades. These have to be registered in a single reference system by the use of targets which are surveyed by topography and then to be filtered in order to obtain a well controlled and
A subsurface model of the beaver meadow complex
Nash, C.; Grant, G.; Flinchum, B. A.; Lancaster, J.; Holbrook, W. S.; Davis, L. G.; Lewis, S.
2015-12-01
Wet meadows are a vital component of arid and semi-arid environments. These valley spanning, seasonally inundated wetlands provide critical habitat and refugia for wildlife, and may potentially mediate catchment-scale hydrology in otherwise "water challenged" landscapes. In the last 150 years, these meadows have begun incising rapidly, causing the wetlands to drain and much of the ecological benefit to be lost. The mechanisms driving this incision are poorly understood, with proposed means ranging from cattle grazing to climate change, to the removal of beaver. There is considerable interest in identifying cost-effective strategies to restore the hydrologic and ecological conditions of these meadows at a meaningful scale, but effective process based restoration first requires a thorough understanding of the constructional history of these ubiquitous features. There is emerging evidence to suggest that the North American beaver may have had a considerable role in shaping this landscape through the building of dams. This "beaver meadow complex hypothesis" posits that as beaver dams filled with fine-grained sediments, they became large wet meadows on which new dams, and new complexes, were formed, thereby aggrading valley bottoms. A pioneering study done in Yellowstone indicated that 32-50% of the alluvial sediment was deposited in ponded environments. The observed aggradation rates were highly heterogeneous, suggesting spatial variability in the depositional process - all consistent with the beaver meadow complex hypothesis (Polvi and Wohl, 2012). To expand on this initial work, we have probed deeper into these meadow complexes using a combination of geophysical techniques, coring methods and numerical modeling to create a 3-dimensional representation of the subsurface environments. This imaging has given us a unique view into the patterns and processes responsible for the landforms, and may shed further light on the role of beaver in shaping these landscapes.