Extremal Black Hole and Flux Vacua Attractors
Bellucci, S; Kallosh, R; Marrani, A
2007-01-01
These lectures provide a pedagogical, introductory review of the so-called Attractor Mechanism (AM) at work in two different 4-dimensional frameworks: extremal black holes in N=2 supergravity and N=1 flux compactifications. In the first case, AM determines the stabilization of scalars at the black hole event horizon purely in terms of the electric and magnetic charges, whereas in the second context the AM is responsible for the stabilization of the universal axion-dilaton and of the (complex structure) moduli purely in terms of the RR and NSNS fluxes. Two equivalent approaches to AM, namely the so-called ``criticality conditions'' and ``New Attractor'' ones, are analyzed in detail in both frameworks, whose analogies and differences are discussed. Also a stringy analysis of both frameworks (relying on Hodge-decomposition techniques) is performed, respectively considering Type IIB compactified on $CY_{3}$ and its orientifolded version, associated with $\\frac{CY_{3}\\times T^{2}}{\\mathbb{Z}_{2}}$. Finally, recent...
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Giryavets, Alexander
2004-04-25
We investigate several predictions about the properties of IIB flux vacua on Calabi-Yau orientifolds, by constructing and characterizing a very large set of vacua in a specific example, an orientifold of the Calabi-Yau hypersurface in WP{sub 1,1,1,1,4}{sup 4}. We find support for the prediction of Ashok and Douglas that the density of vacua on moduli space is governed by det(-R-{omega}) where R and {omega} are curvature and Kaehler forms on the moduli space. The conifold point {psi} = 1 on moduli space therefore serves as an attractor, with a significant fraction of the flux vacua contained in a small neighborhood surrounding {psi} = 1. We also study the functional dependence of the number of flux vacua on the D3 charge in the fluxes, finding simple power law growth.
Maxfield, Travis; Robbins, Daniel; Sethi, Savdeep
2013-01-01
Type IIB toroidal orientifolds are among the earliest examples of flux vacua. By applying T-duality, we construct the first examples of massive IIA flux vacua with Minkowski space-times, along with new examples of type IIA flux vacua. The backgrounds are surprisingly simple with no four-form flux at all. They serve as illustrations of the ingredients needed to build type IIA and massive IIA solutions with scale separation. To check that these backgrounds are actually solutions, we formulate the complete set of type II supergravity equations of motion in a very useful form that treats the R-R fields democratically.
Classical Transitions for Flux Vacua
Deskins, J Tate; Yang, I-Sheng
2012-01-01
We present the simplest model for classical transitions in flux vacua. A complex field with a spontaneously broken U(1) symmetry is embedded in $M_2\\times S_1$. We numerically construct different winding number vacua, the vortices interpolating between them, and simulate the collisions of these vortices. We show that classical transitions are generic at large boosts, independent of whether or not vortices miss each other in the compact $S_1$.
Hypermoduli Stabilization, Flux Attractors, and Generating Functions
Larsen, Finn; Robbins, Daniel
2009-01-01
We study stabilization of hypermoduli with emphasis on the effects of generalized fluxes. We find a class of no-scale vacua described by ISD conditions even in the presence of geometric flux. The associated flux attractor equations can be integrated by a generating function with the property that the hypermoduli are determined by a simple extremization principle. We work out several orbifold examples where all vector moduli and many hypermoduli are stabilized, with VEVs given explicitly in terms of fluxes.
Enumerating Flux Vacua With Enhanced Symmetries
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DeWolfe, O.
2004-11-12
We study properties of flux vacua in type IIB string theory in several simple but illustrative models. We initiate the study of the relative frequencies of vacua with vanishing superpotential W = 0 and with certain discrete symmetries. For the models we investigate we also compute the overall rate of growth of the number of vacua as a function of the D3-brane charge associated to the fluxes, and the distribution of vacua on the moduli space. The latter two questions can also be addressed by the statistical theory developed by Ashok, Denef and Douglas, and our results are in good agreement with their predictions. Analysis of the first two questions requires methods which are more number-theoretic in nature. We develop some elementary techniques of this type, which are based on arithmetic properties of the periods of the compactification geometry at the points in moduli space where the flux vacua are located.
Statistics of Flux Vacua for Particle Physics
Watari, Taizan
2015-01-01
Supersymmetric flux compactification of F-theory in the geometric phase yields numerous vacua, and provides an ensemble of low-energy effective theories with different symmetry, matter multiplicity and Lagrangian parameters. Theoretical tools have already been developed so that we can study how the statistics of flux vacua depend on the choice of symmetry and some of Lagrangian parameters. In this article, we estimate the fraction of i) vacua that have a U(1) symmetry for spontaneous R-parity violation, and ii) those that realise ideas which achieve hierarchical eigenvalues of the Yukawa matrices. We also learn a lesson that the number of flux vacua is reduced very much when the unbroken $U(1)_Y$ symmetry is obtained from a non-trivial Mordell--Weil group, while it is not when $U(1)_Y$ is in SU(5) unification. It also turns out that vacua with an approximate U(1) symmetry forms a locus of accumulation points of the flux vacua distribution.
Remarks on scale separation in flux vacua
Gautason, F. F.; Schillo, M.; Van Riet, T.; Williams, M.
2016-03-01
We argue that the Maldacena-Nuñez no-go theorem excluding Minkowski and de Sitter vacua in flux compactifications can be extended to anti-de Sitter (AdS) vacua for which the Kaluza-Klein scale is parametrically smaller than the AdS length scale. In the absence of negative tension sources, scale-separated AdS vacua are ruled out in 11-dimensional supergravity; in 10-dimensional supergravity, we show that such vacua can only arise in conjunction with large dilaton gradients. As a practical application of this observation we demonstrate that the mechanism to resolve O6 singularities in massive type IIA at the classical level is likely not to occur in AdS compactifications with scale separation. We furthermore remark that a compactification to four observable dimensions implies a large cosmological hierarchy.
Flux Vacua Statistics for Two-Parameter Calabi-Yau's
Misra, A
2004-01-01
We study the number of flux vacua for type IIB string theory on an orientifold of the Calabi-Yau expressed as a hypersurface in WCP^4[1,1,2,2,6] by evaluating a suitable integral over the complex-structure moduli space as per the conjecture of Douglas and Ashok. We show that away from the singular conifold locus, one gets the expected power law, and that the (neighborhood) of the conifold locus indeed acts as an attractor in the (complex structure) moduli space. We also study (non)supersymmetric solutions near the conifold locus.
Remarks on scale separation in flux vacua
Gautason, F F; Van Riet, T; Williams, M
2015-01-01
We argue that the Maldacena-Nunez no-go theorem excluding Minkowski and de Sitter vacua in flux compactifications can be extended to exclude anti-de Sitter (AdS) vacua for which the Kaluza-Klein scale is parametrically smaller than the AdS length scale. As a practical application of this observation we demonstrate that the mechanism to resolve O6 singularities in massive type IIA at the classical level is likely not to occur in AdS compactifications with scale separation. We furthermore remark that a compactification to four observable dimensions implies a large cosmological hierarchy.
Generalised Geometry and Flux Vacua
Larfors, Magdalena
2015-01-01
This note discusses the connection between generalised geometry and flux compactifications of string theory. Firstly, we explain in a pedestrian manner how the supersymmetry constraints of type II ${\\mathcal{N}}=1$ flux compactifications can be restated as integrability constraints on certain generalised complex structures. This reformulation uses generalised complex geometry, a mathematical framework that geometrizes the B-field. Secondly, we discuss how exceptional generalised geometry may provide a similar geometrization of the RR fields. Thirdly, we examine the connection between generalised geometry and non-geometry, and finally we present recent developments where generalised geometry is used to construct explicit examples of flux compactifications to flat space.
Metastable Vacua in Flux Compactifications and Their Phenomenology
Lebedev, O; Mambrini, Y; Nilles, H P; Ratz, M; L\\"owen, Val\\'eri; Lebedev, Oleg; Mambrini, Yann; Nilles, Hans Peter; Ratz, Michael
2007-01-01
In the context of flux compactifications, metastable vacua with a small positive cosmological constant are obtained by combining a sector where supersymmetry is broken dynamically with the sector responsible for moduli stabilization, which is known as the F-uplifting. We analyze this procedure in a model-independent way and study phenomenological properties of the resulting vacua.
Statistics of F-theory flux vacua for particle physics
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Watari, Taizan [Kavli Institute for the Physics and Mathematics of the Universe,University of Tokyo, Kashiwa-no-ha 5-1-5, 277-8583 (Japan)
2015-11-10
Supersymmetric flux compactification of F-theory in the geometric phase yields numerous vacua, and provides an ensemble of low-energy effective theories with a variety of symmetry, matter multiplicity and Lagrangian parameters. Theoretical tools have already been developed so that we can study how the statistics of those flux vacua depend on the choice of symmetry and some of the Lagrangian parameters. In this article, we estimate the fraction of i) vacua that have a U(1) symmetry for spontaneous R-parity violation, and ii) those that realise ideas which achieve hierarchical eigenvalues of the Yukawa matrices. We also learn a lesson that the number of flux vacua is reduced very much when the unbroken U(1){sub Y} symmetry is obtained from a non-trivial Mordell-Weil group, while it is not, when U(1){sub Y} is in SU(5) unification. It also turns out to be likely that vacua with an approximate U(1) symmetry form a locus of accumulation points of the flux vacua distribution.
Finding all flux vacua in an explicit example
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Martinez-Pedrera, Danny; Rummel, Markus [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Mehta, Dhagash [Syracuse Univ., NY (United States). Dept. of Physics; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2012-12-15
We explicitly construct all supersymmetric flux vacua of a particular Calabi-Yau compactification of type IIB string theory for a small number of flux carrying cycles and a given D3-brane tadpole. The analysis is performed in the large complex structure region by using the polynomial homotopy continuation method, which allows to find all stationary points of the polynomial equations that characterize the supersymmetric vacuum solutions. The number of vacua as a function of the D3 tadpole is in agreement with statistical studies in the literature. We calculate the available tuning of the cosmological constant from fluxes and extrapolate to scenarios with a larger number of flux carrying cycles. We also verify the range of scales for the moduli and gravitino masses recently found for a single explicit flux choice giving a Kaehler uplifted de Sitter vacuum in the same construction.
The F-theory geometry with most flux vacua
Taylor, Washington; Wang, Yi-Nan
2015-12-01
Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold {M}_{max } gives rise to O({10}^{272,000}) F-theory flux vacua, and that the sum total of the numbers of flux vacua from all other F-theory geometries is suppressed by a relative factor of O({10}^{-3000}) . The fourfold {M}_{max } arises from a generic elliptic fibration over a specific toric threefold base B max, and gives a geometrically non-Higgsable gauge group of E 8 9 × F 4 8 × ( G 2 × SU(2))16, of which we expect some factors to be broken by G-flux to smaller groups. It is not possible to tune an SU(5) GUT group on any further divisors in {M}_{max } , or even an SU(2) or SU(3), so the standard model gauge group appears to arise in this context only from a broken E 8 factor. The results of this paper can either be interpreted as providing a framework for predicting how the standard model arises most naturally in F-theory and the types of dark matter to be found in a typical F-theory compactification, or as a challenge to string theorists to explain why other choices of vacua are not exponentially unlikely compared to F-theory compactifications on {M}_{max }.
Type IIB flux vacua from G-theory II
Candelas, Philip; Damian, Cesar; Larfors, Magdalena; Morales, Jose Francisco
2014-01-01
We find analytic solutions of type IIB supergravity on geometries that locally take the form $\\text{Mink}\\times M_4\\times \\mathbb{C}$ with $M_4$ a generalised complex manifold. The solutions involve the metric, the dilaton, NSNS and RR flux potentials (oriented along the $M_4$) parametrised by functions varying only over $\\mathbb{C}$. Under this assumption, the supersymmetry equations are solved using the formalism of pure spinors in terms of a finite number of holomorphic functions. Alternatively, the solutions can be viewed as vacua of maximally supersymmetric supergravity in six dimensions with a set of scalar fields varying holomorphically over $\\mathbb{C}$. For a class of solutions characterised by up to five holomorphic functions, we outline how the local solutions can be completed to four-dimensional flux vacua of type IIB theory. A detailed study of this global completion for solutions with two holomorphic functions has been carried out in the companion paper [1]. The fluxes of the global solutions ar...
The F-theory geometry with most flux vacua
Taylor, Washington
2015-01-01
Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold ${\\cal M}_{\\rm max}$ gives rise to ${\\cal O} (10^{272,000})$ F-theory flux vacua, and that the sum total of the numbers of flux vacua from all other F-theory geometries is suppressed by a relative factor of ${\\cal O} (10^{-3000})$. The fourfold ${\\cal M}_{\\rm max}$ arises from a generic elliptic fibration over a specific toric threefold base $B_{\\rm max}$, and gives a geometrically non-Higgsable gauge group of $E_8^9 \\times F_4^8 \\times (G_2 \\times SU(2))^{16}$, of which we expect some factors to be broken by G-flux to smaller groups. It is not possible to tune an $SU(5)$ GUT group on any further divisors in ${\\cal M}_{\\rm max}$, or even an $SU(2)$ or $SU(3)$, so the standard model gauge group appears to arise in this context only from a broken $E_8$ factor. The results of this paper can either be interpreted as providing a framework for predicting how the standard model arises most nat...
Type IIA flux compactifications. Vacua, effective theories and cosmological challenges
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Koers, Simon
2009-07-30
In this thesis, we studied a number of type IIA SU(3)-structure compactifications with 06-planes on nilmanifolds and cosets, which are tractable enough to allow for an explicit derivation of the low energy effective theory. In particular we calculated the mass spectrum of the light scalar modes, using N = 1 supergravity techniques. For the torus and the Iwasawa solution, we have also performed an explicit Kaluza-Klein reduction, which led to the same result. For the nilmanifold examples we have found that there are always three unstabilized moduli corresponding to axions in the RR sector. On the other hand, in the coset models, except for SU(2) x SU(2), all moduli are stabilized. We discussed the Kaluza-Klein decoupling for the supersymmetric AdS vacua and found that it requires going to the Nearly-Calabi Yau limited. We searched for non-trivial de Sitter minima in the original flux potential away from the AdS vacuum. Finally, in chapter 7, we focused on a family of three coset spaces and constructed non-supersymmetric vacua on them. (orig.)
Type IIB flux vacua from G-theory I
Candelas, Philip; Damian, Cesar; Larfors, Magdalena; Morales, Jose Francisco
2014-01-01
We construct non-perturbatively exact four-dimensional Minkowski vacua of type IIB string theory with non-trivial fluxes. These solutions are found by gluing together, consistently with U-duality, local solutions of type IIB supergravity on $T^4 \\times \\mathbb{C}$ with the metric, dilaton and flux potentials varying along $\\mathbb{C}$ and the flux potentials oriented along $T^4$. We focus on solutions locally related via U-duality to non-compact Ricci-flat geometries. More general solutions and a complete analysis of the supersymmetry equations are presented in the companion paper [1]. We build a precise dictionary between fluxes in the global solutions and the geometry of an auxiliary $K3$ surface fibered over $\\mathbb{CP}^1$. In the spirit of F-theory, the flux potentials are expressed in terms of locally holomorphic functions that parametrize the complex structure moduli space of the $K3$ fiber in the auxiliary geometry. The brane content is inferred from the monodromy data around the degeneration points o...
Fluxes, hierarchies, and metastable vacua in supersymmetric field theories
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Bruemmer, F.
2008-02-06
This thesis concerns topics both in low-energy effective field theories from type IIB superstring flux compactifications and in four-dimensional, rigidly supersymmetric gauge theories. We introduce flux compactifications with so-called ''warped throat'' regions, which lead to large hierarchies of scales in the effective four-dimensional theory. The correspondence between a particular such throat and a five-dimensional Randall-Sundrum-like model is established. We shown how certain string-theoretic features of the compactification, such as moduli stabilization by fluxes or the presence of an unstabilized Kaehler modulus, are incorporated in the five-dimensional picture. The KKLT construction for metastable de Sitter vacua is reviewed, as well as some possible modifications involving spontaneous F-term supersymmetry breaking. For KKLT-like models with their hidden sector localized inside a throat, the mediation of supersymmetry breaking to the visible sector is investigated. We review the mechanism of mixed modulus-anomaly mediation, and show that there can be additional equally important gravity-mediated contributions. We finally turn to the ISS model of metastable dynamical supersymmetry breaking in four dimensions, and present a renormalizable extension which generates a large hierarchy naturally. We also recapitulate how the ISS model may be obtained from a type IIB superstring model. (orig.)
On flux vacua, SU(n)-structures and generalised complex geometry
Prins, Daniël
2016-01-01
Understanding supersymmetric flux vacua is essential in order to connect string theory to observable physics. In this thesis, flux vacua are studied by making use of two mathematical frameworks: SU(n)-structures and generalised complex geometry. Manifolds with SU(n)-structure are generalisations of Calabi-Yau manifolds. Generalised complex geometry is a geometrical framework that simultaneously generalises complex and symplectic geometry. Classes of flux vacua of type II supergravity and M-theory are given on manifolds with SU(4)-structure. The N= (1,1) type IIA vacua uplift to N=1 M-theory vacua, with four-flux that need not be (2,2) and primitive. Explicit vacua are given on Stenzel space, a non-compact Calabi-Yau. These are then generalised by constructing families of non-CY SU(4)-structures to find vacua on non-symplectic SU(4)-deformed Stenzel spaces. It is shown that the supersymmetry conditions for N = (2,0) type IIB can be rephrased in the language of generalised complex geometry, partially in terms o...
General N=1 supersymmetric flux vacua of massive type IIA string theory.
Behrndt, Klaus; Cvetic, Mirjam
2005-07-08
We derive conditions for the existence of four-dimensional N=1 supersymmetric flux vacua of massive type IIA string theory with general supergravity fluxes turned on. For an SU(3) singlet Killing spinor, we show that such flux vacua exist when the internal geometry is nearly Kähler. The geometry is not warped, all the allowed fluxes are proportional to the mass parameter, and the dilaton is fixed by a ratio of (quantized) fluxes. The four-dimensional cosmological constant, while negative, becomes small in the vacuum with the weak string coupling.
Li, Chunhe; Wang, Erkang; Wang, Jin
2012-05-21
We developed a potential flux landscape theory to investigate the dynamics and the global stability of a chemical Lorenz chaotic strange attractor under intrinsic fluctuations. Landscape was uncovered to have a butterfly shape. For chaotic systems, both landscape and probabilistic flux are crucial to the dynamics of chaotic oscillations. Landscape attracts the system down to the chaotic attractor, while flux drives the coherent motions along the chaotic attractors. Barrier heights from the landscape topography provide a quantitative measure for the robustness of chaotic attractor. We also found that the entropy production rate and phase coherence increase as the molecular numbers increase. Power spectrum analysis of autocorrelation function provides another way to quantify the global stability of chaotic attractor. We further found that limit cycle requires more flux and energy to sustain than the chaotic strange attractor. Finally, by detailed analysis we found that the curl probabilistic flux may provide the origin of the chaotic attractor.
Local models of heterotic flux vacua: spacetime and worldsheet aspects
Energy Technology Data Exchange (ETDEWEB)
Israel, D. [GRECO, Institut d' Astrophysique de Paris, 98bis Bd Arago, 75014 Paris (France); Carlevaro, L. [LAREMA, Universite d' Angers, 2 Bd Lavoisier, 49045 Angers (France); Centre de Physique Theorique, Ecole Polytechnique, 91128 Palaiseau (France)
2011-07-01
We report on some recent progress in understanding heterotic flux compactifications, from a worldsheet perspective mainly. We consider local models consisting in torus fibration over warped Eguchi-Hanson space and non-Kaehler resolved conifold geometries. We analyze the supergravity solutions and define a double-scaling limit of the resolved singularities, defined such that the geometry is smooth and weakly coupled. We show that, remarkably, the heterotic solutions admit solvable worldsheet CFT descriptions in this limit. This allows in particular to understand the important role of worldsheet non-perturbative effects. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
On special geometry of the moduli space of string vacua with fluxes
Hou, Boyu; Yang, Yanhong
2008-01-01
In this paper we construct a special geometry over the moduli space of type II string vacua with both NS and RR fluxes turning on. Depending on what fluxes are turning on we divide into three cases of moduli space of generalized structures. They are respectively generalized Calabi-Yau structures, generalized Calabi-Yau metric structures and ${\\cal N} =1$ generalized string vacua. It is found that the $d d^{\\cal J}$ lemma can be established for all three cases. With the help of the $d d^{\\cal J}$ lemma we identify the moduli space locally as a subspace of $d_{H}$ cohomologies. This leads naturally to the special geometry of the moduli space. It has a flat symplectic structure and a K$\\ddot{\\rm a}$hler metric with the Hitchin functional (modified if RR fluxes are included) the K$\\ddot{\\rm a}$hler potential. Our work is based on previous works of Hitchin and recent works of Gra$\\tilde{\\rm n}$a-Louis-Waldram, Goto, Gualtieri, Yi Li and Tomasiello. The special geometry is useful in flux compactifications of type I...
Explicit de Sitter flux vacua for global string models with chiral matter
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Cicoli, Michele [Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, 40126 Bologna (Italy); INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna (Italy); ICTP, Strada Costiera 11, 34014 Trieste (Italy); Klevers, Denis [Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104-6396 (United States); Krippendorf, Sven [Bethe Center for Theoretical Physics and Physikalisches Institut der Universität Bonn, Nussallee 12, 53115 Bonn (Germany); Mayrhofer, Christoph [Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, 69120 Heidelberg (Germany); Quevedo, Fernando [ICTP, Strada Costiera 11, 34014 Trieste (Italy); DAMTP, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Valandro, Roberto [ICTP, Strada Costiera 11, 34014 Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy)
2014-05-05
We address the open question of performing an explicit stabilisation of all closed string moduli (including dilaton, complex structure and Kähler moduli) in fluxed type IIB Calabi-Yau compactifications with chiral matter. Using toric geometry we construct Calabi-Yau manifolds with del Pezzo singularities. D-branes located at such singularities can support the Standard Model gauge group and matter content or some close extensions. In order to control complex structure moduli stabilisation we consider Calabi-Yau manifolds which exhibit a discrete symmetry that reduces the effective number of complex structure moduli. We calculate the corresponding periods in the symplectic basis of invariant three-cycles and find explicit flux vacua for concrete examples. We compute the values of the flux superpotential and the string coupling at these vacua. Starting from these explicit complex structure solutions, we obtain AdS and dS minima where the Kähler moduli are stabilised by a mixture of D-terms, non-perturbative and perturbative α{sup ′} corrections as in the LARGE Volume Scenario. In the considered example the visible sector lives at a dP{sub 6} singularity which can be higgsed to the phenomenologically interesting class of models at the dP{sub 3} singularity.
Explicit de Sitter flux vacua for global string models with chiral matter
Cicoli, Michele; Klevers, Denis; Krippendorf, Sven; Mayrhofer, Christoph; Quevedo, Fernando; Valandro, Roberto
2014-05-01
We address the open question of performing an explicit stabilisation of all closed string moduli (including dilaton, complex structure and Kähler moduli) in fluxed type IIB Calabi-Yau compactifications with chiral matter. Using toric geometry we construct Calabi-Yau manifolds with del Pezzo singularities. D-branes located at such singularities can support the Standard Model gauge group and matter content or some close extensions. In order to control complex structure moduli stabilisation we consider Calabi-Yau manifolds which exhibit a discrete symmetry that reduces the effective number of complex structure moduli. We calculate the corresponding periods in the symplectic basis of invariant three-cycles and find explicit flux vacua for concrete examples. We compute the values of the flux superpotential and the string coupling at these vacua. Starting from these explicit complex structure solutions, we obtain AdS and dS minima where the Kähler moduli are stabilised by a mixture of D-terms, non-perturbative and perturbative α ' corrections as in the LARGE Volume Scenario. In the considered example the visible sector lives at a dP6 singularity which can be higgsed to the phenomenologically interesting class of models at the dP3 singularity.
Partial SUSY Breaking for Asymmetric Gepner Models and Non-geometric Flux Vacua
Blumenhagen, Ralph; Plauschinn, Erik
2016-01-01
Using the method of simple current extensions, asymmetric Gepner models of Type IIB with N=1 space-time supersymmetry are constructed. The combinatorics of the massless vector fields suggests that these classical Minkowski string vacua provide fully backreacted solutions corresponding to N=1 minima of N=2 gauged supergravity. The latter contain abelian gaugings along the axionic isometries in the hypermultiplet moduli space, and can be considered as Type IIB flux compactifications on Calabi-Yau manifolds equipped with (non-)geometric fluxes. For a particular class of asymmetric Gepner models, we are able to explicitly specify the underlying CICYs and to check necessary conditions for a GSUGRA interpretation. If this conjecture is correct, there exists a large class of exactly solvable non-geometric flux compactifications on CY threefolds.
D-brane networks in flux vacua, generalized cycles and calibrations
Evslin, Jarah; Martucci, Luca
2007-07-01
We consider chains of generalized submanifolds, as defined by Gualtieri in the context of generalized complex geometry, and define a boundary operator that acts on them. This allows us to define generalized cycles and the corresponding homology theory. Gauge invariance demands that D-brane networks on flux vacua must wrap these generalized cycles, while deformations of generalized cycles inside of a certain homology class describe physical processes such as the dissolution of D-branes in higher-dimensional D-branes and MMS-like instantonic transitions. We introduce calibrations that identify the supersymmetric D-brane networks, which minimize their energy inside of the corresponding homology class of generalized cycles. Such a calibration is explicitly presented for type II Script N = 1 flux compactifications to four dimensions. In particular networks of walls and strings in compactifications on warped Calabi-Yau's are treated, with explicit examples on a toroidal orientifold vacuum and on the Klebanov-Strassler geometry.
D-brane networks in flux vacua, generalized cycles and calibrations
Evslin, J; Evslin, Jarah; Martucci, Luca
2007-01-01
We consider chains of generalized submanifolds, as defined by Gualtieri in the context of generalized complex geometry, and define a boundary operator that acts on them. This allows us to define generalized cycles and the corresponding homology theory. Gauge invariance demands that D-brane networks on flux vacua must wrap these generalized cycles, while deformations of generalized cycles inside of a certain homology class describe physical processes such as the dissolution of D-branes in higher-dimensional D-branes and MMS-like instantonic transitions. We introduce calibrations that identify the supersymmetric D-brane networks, which minimize their energy inside of the corresponding homology class of generalized cycles. Such a calibration is explicitly presented for type II N=1 flux compactifications to four dimensions. In particular networks of walls and strings in compactifications on warped Calabi-Yau's are treated, with explicit examples on a toroidal orientifold vacuum and on the Klebanov-Strassler geome...
de Sitter vacua and supersymmetry breaking in six-dimensional flux compactifications
Buchmuller, Wilfried; Dierigl, Markus; Ruehle, Fabian; Schweizer, Julian
2016-07-01
We consider six-dimensional supergravity with Abelian bulk flux compactified on an orbifold. The effective low-energy action can be expressed in terms of N =1 chiral moduli superfields with a gauged shift symmetry. The D -term potential contains two Fayet-Iliopoulos terms which are induced by the flux and by the Green-Schwarz term canceling the gauge anomalies, respectively. The Green-Schwarz term also leads to a correction of the gauge kinetic function which turns out to be crucial for the existence of Minkowski and de Sitter vacua. Moduli stabilization is achieved by the interplay of the D -term and a nonperturbative superpotential. Varying the gauge coupling and the superpotential parameters, the scale of the extra dimensions can range from the GUT scale down to the TeV scale. Supersymmetry is broken by F - and D -terms, and the scale of gravitino, moduli, and modulini masses is determined by the size of the compact dimensions.
de Sitter vacua and supersymmetry breaking in six-dimensional flux compactifications
Buchmuller, Wilfried; Ruehle, Fabian; Schweizer, Julian
2016-01-01
We consider six-dimensional supergravity with Abelian bulk flux compactified on an orbifold. The effective low-energy action can be expressed in terms of N=1 chiral moduli superfields with a gauged shift symmetry. The D-term potential contains two Fayet-Iliopoulos terms which are induced by the flux and by the Green-Schwarz term canceling the gauge anomalies, respectively. The Green-Schwarz term also leads to a correction of the gauge kinetic function which turns out to be crucial for the existence of Minkowski and de Sitter vacua. Moduli stabilization is achieved by the interplay of the D-term and a nonperturbative superpotential. Varying the gauge coupling and the superpotential parameters, the scale of the extra dimensions can range from the GUT scale down to the TeV scale. Supersymmetry is broken by F- and D-terms, and the scale of gravitino, moduli, and modulini masses is determined by the size of the compact dimensions.
Topological effects on string vacua
Loaiza-Brito, Oscar
2011-01-01
We review some topological effects on the construction of string flux-vacua. Specifically we study the effects of brane-flux transitions on the stability of D-branes on a generalized tori compactificaction, the transition that a black hole suffers in a background threaded with fluxes and the connections among some Minkowsky vacua solutions.
3-Cocycles, Non-Associative Star-Products and the Magnetic Paradigm of R-Flux String Vacua
Bakas, Ioannis
2013-01-01
We consider the geometric and non-geometric faces of closed string vacua arising by T-duality from principal torus bundles with constant H-flux and pay attention to their double phase space description encompassing all toroidal coordinates, momenta and their dual on equal footing. We construct a star-product algebra on functions in phase space that is manifestly duality invariant and substitutes for canonical quantization. The 3-cocycles of the Abelian group of translations in double phase space are seen to account for non-associativity of the star-product. We also provide alternative cohomological descriptions of non-associativity and draw analogies with the quantization of point-particles in the field of a Dirac monopole or other distributions of magnetic charge. The magnetic field analogue of the R-flux string model is provided by a constant uniform distribution of magnetic charge in space and non-associativity manifests as breaking of angular symmetry. The Poincare vector comes to rescue angular symmetry ...
Flux vacua in Dirac-Born-Infeld type Einstein-Maxwell theory
Maki, Takuya; Kobayashi, Koichiro; Shiraishi, Kiyoshi
2011-01-01
We study compactification of extra dimensions in a theory of Dirac-Born-Infeld (DBI) type gravity. We investigate the solution for Minkowski spacetime with an $S^{2}$ extra space. The solution is derived by the effective potential method in the presence of the magnetic flux on the extra sphere. We find that, in a certain model, the radius of the extra space has a minimum value independent of the higher-dimensional Newton constant in weak-field limit.
Testing string vacua in the lab. From a hidden CMB to dark forces in flux compactifications
Energy Technology Data Exchange (ETDEWEB)
Cicoli, Michele; Goodsell, Mark; Ringwald, Andreas [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany). Theory Group; Jaeckel, Joerg [Durham Univ. (United Kingdom). Inst. for Particle Physics Phenomenolgy
2011-03-15
We perform a detailed analysis of the phenomenological properties of hidden Abelian gauge bosons with a kinetic mixing with the ordinary photon within type IIB flux compactifications. We study the interplay between moduli stabilisation and the Green-Schwarz mechanism that gives mass to the hidden photon paying particular attention to the role of D-terms. We present two generic classes of explicit Calabi-Yau examples with an isotropic and an anisotropic shape of the extra dimensions showing how the last case turns out to be very promising to make contact with current experiments. In fact, anisotropic compactifications lead naturally to a GeV-scale hidden photon (''dark forces'' that can be searched for in beam dump experiments) for an intermediate string scale; or even to an meV-scale hidden photon (which could lead to a ''hidden CMB'' and can be tested by light-shining-through-a-wall experiments) in the case of TeV-scale strings. (orig.)
Persistent homology and string vacua
Energy Technology Data Exchange (ETDEWEB)
Cirafici, Michele [Center for Mathematical Analysis, Geometry and Dynamical Systems,Instituto Superior Técnico, Universidade de Lisboa,Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Institut des Hautes Études Scientifiques,Le Bois-Marie, 35 route de Chartres, F-91440 Bures-sur-Yvette (France)
2016-03-08
We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by identifying which homological characteristics persist over a long range of scales. We apply these techniques in several contexts. We analyze N=2 vacua by focusing on certain distributions of Calabi-Yau varieties and Landau-Ginzburg models. We then turn to flux compactifications and discuss how we can use topological data analysis to extract physical information. Finally we apply these techniques to certain phenomenologically realistic heterotic models. We discuss the possibility of characterizing string vacua using the topological properties of their distributions.
Cassani, Davide; Marrani, Alessio; Morales, Jose F; Samtleben, Henning
2010-01-01
We apply the techniques of special Kaehler geometry to investigate AdS_4 vacua of general N=2 gauged supergravities underlying flux compactifications of type II theories. We formulate the scalar potential and its extremization conditions in terms of a triplet of prepotentials P_x and their special Kaehler covariant derivatives only, in a form that recalls the potential and the attractor equations of N=2 black holes. We propose a system of first order equations for the P_x which generalize the supersymmetry conditions and yield non-supersymmetric vacua. Special geometry allows us to recast these equations in algebraic form, and we find an infinite class of new N=0 and N=1 AdS_4 solutions, displaying a rich pattern of non-trivial charges associated with NSNS and RR fluxes. Finally, by explicit evaluation of the entropy function on the solutions, we derive a U-duality invariant expression for the cosmological constant and the central charges of the dual CFT's.
Generalized Attractor Points in Gauged Supergravity
Energy Technology Data Exchange (ETDEWEB)
Kachru, Shamit; /Stanford U., Phys. Dept. /SLAC; Kallosh, Renata; /Stanford U., Phys. Dept.; Shmakova, Marina; /KIPAC, Menlo Park /SLAC /Stanford U., Phys. Dept.
2011-08-15
The attractor mechanism governs the near-horizon geometry of extremal black holes in ungauged 4D N=2 supergravity theories and in Calabi-Yau compactifications of string theory. In this paper, we study a natural generalization of this mechanism to solutions of arbitrary 4D N=2 gauged supergravities. We define generalized attractor points as solutions of an ansatz which reduces the Einstein, gauge field, and scalar equations of motion to algebraic equations. The simplest generalized attractor geometries are characterized by non-vanishing constant anholonomy coefficients in an orthonormal frame. Basic examples include Lifshitz and Schroedinger solutions, as well as AdS and dS vacua. There is a generalized attractor potential whose critical points are the attractor points, and its extremization explains the algebraic nature of the equations governing both supersymmetric and non-supersymmetric attractors.
Alonso-Alberca, N; Alonso-Alberca, Natxo; Ortin, Tomas
2002-01-01
We review the definition of (maximally supersymmetric) vacuum in supergravity theories, the currently known vacua in arbitrary dimensions and how the associated supersymmetry algebras can be found. (Invited talk at the Spanish Relativity Meeting (``EREs'') 2002, Mao, Menorca, September 21-23 2002.)
Mirror quintic vacua: hierarchies and inflation
Bizet, Nana Cabo; Zavala, Ivonne
2016-01-01
We study the moduli space of type IIB string theory flux compactifications on the mirror of the CY quintic 3-fold in P4. We focus on the dynamics of the four dimensional moduli space, defined by the axio-dilaton {\\tau} and the complex structure modulus z. The z-plane has critical points, the conifold, the orbifold and the large complex structure with non trivial monodromies. We find the solutions to the Picard-Fuchs equations obeyed by the periods of the CY in the full z-plane as a series expansion in z around the critical points to arbitrary order. This allows us to discard fake vacua, which appear as a result of keeping only the leading order term in the series expansions. Due to monodromies vacua are located at a given sheet in the z-plane. A dS vacuum appears for a set of fluxes. We revisit vacua with hierarchies among the 4D and 6D physical scales close to the conifold point and compare them with those found at leading order in [1, 2]. We explore slow-roll inflationary directions of the scalar potential ...
Mirror quintic vacua: hierarchies and inflation
Bizet, Nana Cabo; Loaiza-Brito, Oscar; Zavala, Ivonne
2016-10-01
We study the moduli space of type IIB string theory flux compactifications on the mirror of the CY quintic 3-fold in P^4 . We focus on the dynamics of the four dimensional moduli space, defined by the axio-dilaton τ and the complex structure modulus z. The z-plane has critical points, the conifold, the orbifold and the large complex structure with non trivial monodromies. We find the solutions to the Picard-Fuchs equations obeyed by the periods of the CY in the full z-plane as a series expansion in z around the critical points to arbitrary order. This allows us to discard fake vacua, which appear as a result of keeping only the leading order term in the series expansions. Due to monodromies vacua are located at a given sheet in the z-plane. A dS vacuum appears for a set of fluxes. We revisit vacua with hierarchies among the 4D and 6D physical scales close to the conifold point and compare them with those found at leading order in [1, 2]. We explore slow-roll inflationary directions of the scalar potential by looking at regions where the multi-field slow-roll parameters ɛ and η are smaller than one. The value of ɛ depends strongly on the approximation of the periods and to achieve a stable value, several orders in the expansion are needed. We do not find realizations of single field axion monodromy inflation. Instead, we find that inflationary regions appear along linear combinations of the four real field directions and for certain configurations of fluxes.
Mirror quintic vacua: hierarchies and inflation
Energy Technology Data Exchange (ETDEWEB)
Bizet, Nana Cabo [Mandelstam Institute for Theoretical Physics, School of Physics,and NITheP, University of the Witwatersrand, WITS 2050, Johannesburg (South Africa); Departamento de Física, Universidad de Guanajuato,Loma del Bosque 103, CP 37150, León, Guanajuato (Mexico); Loaiza-Brito, Oscar [Departamento de Física, Universidad de Guanajuato,Loma del Bosque 103, CP 37150, León, Guanajuato (Mexico); Zavala, Ivonne [Department of Physics, Swansea University, Singleton Park,Swansea, SA2 8PP (United Kingdom)
2016-10-17
We study the moduli space of type IIB string theory flux compactifications on the mirror of the CY quintic 3-fold in ℙ{sup 4}. We focus on the dynamics of the four dimensional moduli space, defined by the axio-dilaton τ and the complex structure modulus z. The z-plane has critical points, the conifold, the orbifold and the large complex structure with non trivial monodromies. We find the solutions to the Picard-Fuchs equations obeyed by the periods of the CY in the full z-plane as a series expansion in z around the critical points to arbitrary order. This allows us to discard fake vacua, which appear as a result of keeping only the leading order term in the series expansions. Due to monodromies vacua are located at a given sheet in the z-plane. A dS vacuum appears for a set of fluxes. We revisit vacua with hierarchies among the 4D and 6D physical scales close to the conifold point and compare them with those found at leading order in http://dx.doi.org/10.1103/PhysRevD.66.106006, http://dx.doi.org/10.1007/JHEP03(2011)119. We explore slow-roll inflationary directions of the scalar potential by looking at regions where the multi-field slow-roll parameters ϵ and η are smaller than one. The value of ϵ depends strongly on the approximation of the periods and to achieve a stable value, several orders in the expansion are needed. We do not find realizations of single field axion monodromy inflation. Instead, we find that inflationary regions appear along linear combinations of the four real field directions and for certain configurations of fluxes.
Membrane Instantons and de Sitter Vacua
Energy Technology Data Exchange (ETDEWEB)
Davidse, Marijn [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands); Saueressig, Frank [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht(Netherlands); Theis, Ulrich [Institute for Theoretical Physics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, D-07743 Jena (Germany); Vandoren, Stefan [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)
2005-09-01
We investigate membrane instanton effects in type-IIA strings compactified on rigid Calabi-Yau manifolds. These effects contribute to the low-energy effective action of the universal hypermultiplet. In the absence of additional fivebrane instantons, the quaternionic geometry of this hypermultiplet is determined by solutions of the three-dimensional Toda equation. We construct solutions describing membrane instantons, and find perfect agreement with the string theory prediction. In the context of flux compactifications we discuss how membrane instantons contribute to the scalar potential and the stabilization of moduli. Finally, we demonstrate the existence of meta-stable de Sitter vacua.
Vacua of the gravitational field
Energy Technology Data Exchange (ETDEWEB)
Compère, Geoffrey; Long, Jiang [Université Libre de Bruxelles and International Solvay Institutes,CP 231, B-1050 Brussels (Belgium)
2016-07-28
The Poincaré invariant vacuum is not unique in quantum gravity. The BMS supertranslation symmetry originally defined at null infinity is spontaneously broken and results in inequivalent Poincaré vacua. In this paper we construct the unique vacua which interpolate between past and future null infinity in BMS gauge and which are entirely characterized by an arbitrary Goldstone boson defined on the sphere which breaks BMS invariance. We show that these vacua contain a defect which carries no Poincaré charges but which generically carries superrotation charges. We argue that there is a huge degeneracy of vacua with multiple defects. We also present the single defect vacua with its canonically conjugated source which can be constructed from a Liouville boson on the stereographic plane. We show that positivity of the energy forces the stress-tensor of the boson to vanish as a boundary condition. Finite superrotations, which turn on the sources, are therefore physically ruled out as canonical transformations around the vacua. Yet, infinitesimal superrotations are external symplectic symmetries which are associated with conserved charges which characterize the Goldstone boson.
Directory of Open Access Journals (Sweden)
Ildefonso M De la Fuente
Full Text Available BACKGROUND: The experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a Systemic Metabolic Structure in the cell, characterized by a set of different enzymatic reactions always locked into active states (metabolic core while the rest of the catalytic processes are only intermittently active. This global metabolic structure was verified for Escherichia coli, Helicobacter pylori and Saccharomyces cerevisiae, and it seems to be a common key feature to all cellular organisms. In concordance with these observations, the cell can be considered a complex metabolic network which mainly integrates a large ensemble of self-organized multienzymatic complexes interconnected by substrate fluxes and regulatory signals, where multiple autonomous oscillatory and quasi-stationary catalytic patterns simultaneously emerge. The network adjusts the internal metabolic activities to the external change by means of flux plasticity and structural plasticity. METHODOLOGY/PRINCIPAL FINDINGS: In order to research the systemic mechanisms involved in the regulation of the cellular enzymatic activity we have studied different catalytic activities of a dissipative metabolic network under different external stimuli. The emergent biochemical data have been analysed using statistical mechanic tools, studying some macroscopic properties such as the global information and the energy of the system. We have also obtained an equivalent Hopfield network using a Boltzmann machine. Our main result shows that the dissipative metabolic network can behave as an attractor metabolic network. CONCLUSIONS/SIGNIFICANCE: We have found that the systemic enzymatic activities are governed by attractors with capacity to store functional metabolic patterns which can be correctly recovered from specific input stimuli. The network attractors regulate the catalytic patterns
Attractor Explosions and Catalyzed Vacuum Decay
Energy Technology Data Exchange (ETDEWEB)
Green, Daniel; Silverstein, Eva; Starr, David
2006-05-05
We present a mechanism for catalyzed vacuum bubble production obtained by combining moduli stabilization with a generalized attractor phenomenon in which moduli are sourced by compact objects. This leads straightforwardly to a class of examples in which the Hawking decay process for black holes unveils a bubble of a different vacuum from the ambient one, generalizing the new endpoint for Hawking evaporation discovered recently by Horowitz. Catalyzed vacuum bubble production can occur for both charged and uncharged bodies, including Schwarzschild black holes for which massive particles produced in the Hawking process can trigger vacuum decay. We briefly discuss applications of this process to the population and stability of metastable vacua.
Asymptotic vacua with higher derivatives
Directory of Open Access Journals (Sweden)
Spiros Cotsakis
2016-04-01
Full Text Available We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Asymptotic vacua with higher derivatives
Energy Technology Data Exchange (ETDEWEB)
Cotsakis, Spiros, E-mail: skot@aegean.gr [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kadry, Seifedine, E-mail: Seifedine.Kadry@aum.edu.kw [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kolionis, Georgios, E-mail: gkolionis@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece); Tsokaros, Antonios, E-mail: atsok@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece)
2016-04-10
We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Metastable vacua and geometric deformations
Amariti, A; Girardello, L; Mariotti, A
2008-01-01
We study the geometric interpretation of metastable vacua for systems of D3 branes at non isolated toric deformable singularities. Using the L^{aba} examples, we investigate the relations between the field theoretic susy breaking and restoration and the complex deformations of the CY singularities.
Ferrara, S; Morales, J F; Samtleben, H
2009-01-01
We apply the entropy formalism to the study of the near-horizon geometry of extremal black p-brane intersections in D>5 dimensional supergravities. The scalar flow towards the horizon is described in terms an effective potential given by the superposition of the kinetic energies of all the forms under which the brane is charged. At the horizon active scalars get fixed to the minima of the effective potential and the entropy function is given in terms of U-duality invariants built entirely out of the black p-brane charges. The resulting entropy function reproduces the central charges of the dual boundary CFT and gives rise to a Bekenstein-Hawking like area law. The results are illustrated in the case of black holes and black string intersections in D=6, 7, 8 supergravities where the effective potentials, attractor equations, moduli spaces and entropy/central charges are worked out in full detail.
Goldstein, Kevin; Nampuri, Suresh
2014-01-01
The product of the areas of the event horizon and the Cauchy horizon of a non-extremal black hole equals the square of the area of the horizon of the black hole obtained from taking the smooth extremal limit. We establish this result for a large class of black holes using the second order equations of motion, black hole thermodynamics, and the attractor mechanism for extremal black holes. This happens even though the area of each horizon generically depends on the moduli, which are asymptotic values of scalar fields. The conformal field theory dual to the BTZ black hole facilitates a microscopic interpretation of the result. In addition, we demonstrate that certain quantities which vanish in the extremal case are zero when integrated over the region between the two horizons. We corroborate these conclusions through an analysis of known solutions.
de Sitter vacua from an anomalous gauge symmetry
Buchmuller, Wilfried; Ruehle, Fabian; Schweizer, Julian
2016-01-01
We find a new class of metastable de Sitter solutions in compactifications of six-dimensional supergravity motivated by type IIB or heterotic string vacua. Two Fayet-Iliopoulos terms of a local U(1) symmetry are generated by magnetic flux and by the Green-Schwarz term canceling the gauge anomalies, respectively. The interplay between the induced D-term and a nonperturbative superpotential stabilizes the moduli and determines the size of the extra dimensions.
De Sitter vacua from an anomalous gauge symmetry
Energy Technology Data Exchange (ETDEWEB)
Buchmuller, Wilfried; Dierigl, Markus; Ruehle, Fabian; Schweizer, Julian
2016-03-15
We find a new class of metastable de Sitter solutions in compactifications of six- dimensional supergravity motivated by type IIB or heterotic string vacua. Two Fayet-Iliopoulos terms of a local U(1) symmetry are generated by magnetic flux and by the Green-Schwarz term canceling the gauge anomalies, respectively. The interplay between the induced D-term, the moduli dependence of the effective gauge coupling, and a nonperturbative superpotential stabilizes the moduli and determines the size of the extra dimensions.
Quantum integrability and supersymmetric vacua
Nekrasov, Nikita A.; Shatashvili, Samson L.
2009-01-01
This is an announcement of some of the results of a longer paper where the supersymmetric vacua of two dimensional N=2 susy gauge theories with matter are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. The correspondence between the Heisenberg spin chain and the two dimensional U(N) theory with fundamental hypermultiplets is reviewed in detail. We demonstrate the isomorphism of the equivariant quantum cohomology of the cotangent bundle to ...
Revisiting constraints on uplifts to de Sitter vacua
Bizet, Nana Cabo
2016-01-01
We revisit the issue of uplifting the potential to de Sitter (dS) vacua in type IIB flux compactifications of Kachru, Kallosh, Linde and Trivedi (KKLT). We shed light on some tension between two constraints on dS vacua in type IIB string theory. One is the well-known and much-discussed constraint which leads to the no-go theorem that can in principle be evaded. The other follows from 4-dimensional Einstein's equations, which has, however, been much less discussed in connection with the former constraint. In addition to the challenges previously posed, it is suggested that the uplifting scenarios, in particular, obstruct the evasion of the no-go theorem more strongly than one might have assumed.
New class of de Sitter vacua in string theory compactifications
Achúcarro, Ana; Ortiz, Pablo; Sousa, Kepa
2016-10-01
String theory contains few known working examples of de Sitter vacua, four-dimensional universes with a positive cosmological constant. A notorious obstacle is the stabilization of a large number—sometimes hundreds—of moduli fields that characterize the compact dimensions. We study the stability of a class of supersymmetric moduli (the complex structure moduli and dilaton in type-IIB flux compactifications) in the regime where the volume of the compact space is large but not exponentially large. We show that, if the number of moduli is very large, random matrix theory provides a new stability condition, a lower bound on the volume. We find a new class of stable vacua where the mass spectrum of these supersymmetric moduli is gapped, without requiring a large mass hierarchy between moduli sectors or any fine-tuning of the superpotential. We provide the first explicit example of this class of vacua in the P[1,1 ,1 ,6 ,9 ] 4 model. A distinguishing feature is that all fermions in the supersymmetric sector are lighter than the gravitino.
A new class of de Sitter vacua in String Theory Compactifications
Achúcarro, Ana; Sousa, Kepa
2015-01-01
We revisit the stability of the complex structure moduli in the large volume regime of type-IIB flux compactifications. We argue that when the volume is not exponentially large, such as in K\\"ahler uplifted dS vacua, the quantum corrections to the tree-level mass spectrum can induce tachyonic instabilities in this sector. We discuss a Random Matrix Theory model for the classical spectrum of the complex structure fields, and derive a new stability bound involving the compactification volume and the (very large) number of moduli. We also present a new class of vacua for this sector where the mass spectrum presents a finite gap, without invoking large supersymmetric masses. At these vacua the complex structure sector is protected from tachyonic instabilities even at non-exponential volumes. A distinguishing feature is that all fermions in this sector are lighter than the gravitino.
Supersymmetric vacua in random supergravity
Bachlechner, Thomas C.; Marsh, David; McAllister, Liam; Wrase, Timm
2013-01-01
We determine the spectrum of scalar masses in a supersymmetric vacuum of a general mathcal{N}=1 supergravity theory, with the Kähler potential and superpotential taken to be random functions of N complex scalar fields. We derive a random matrix model for the Hessian matrix and compute the eigenvalue spectrum. Tachyons consistent with the Breitenlohner-Freedman bound are generically present, and although these tachyons cannot destabilize the supersymmetric vacuum, they do influence the likelihood of the existence of an `uplift' to a metastable vacuum with positive cosmological constant. We show that the probability that a supersymmetric AdS vacuum has no tachyons is formally equivalent to the probability of a large fluctuation of the smallest eigenvalue of a certain real Wishart matrix. For normally-distributed matrix entries and any N, this probability is given exactly by P=exp left( {{{{-2{N^2}{{{left| W right|}}^2}}} left/ {{m_{susy}^2}} right.}} right) , with W denoting the superpotential and m susy the supersymmetric mass scale; for more general distributions of the entries, our result is accurate when N ≫ 1. We conclude that for left| W right|gtrsim {{{{m_{susy}}}} left/ {N} right.} , tachyonic instabilities are ubiquitous in configurations obtained by uplifting supersymmetric vacua.
Topology of the Electroweak Vacua
Gripaios, Ben
2016-01-01
In the Standard Model, the electroweak symmetry is broken by a complex, $SU(2)$-doublet Higgs field and the vacuum manifold $SU(2)\\times U(1)/U(1)$ has the topology of a 3-sphere. We remark that there exist alternative effective field theory descriptions that can be fully consistent with existing collider data, but in which the vacuum manifold is homeomorphic to an arbitrary non-trivial principal $U(1)$-bundle over a 2-sphere. These alternatives have non-trivial fundamental group and so lead to topologically-stable electroweak strings. Perhaps the most plausible alternative to $S^3$ is the manifold $\\mathbb{R}P^3$ (with fundamental group $\\mathbb{Z}/2$), since it allows custodial protection of gauge boson masses and their couplings to fermions. Searches for such strings may thus be regarded as independent, and qualitatively different, precision tests of the SM, in that they are (thus far) astrophysical in nature, and test the global topology, rather than the local geometry, of the electroweak vacua.
Vacua and inflation in string theory and supergravity
Energy Technology Data Exchange (ETDEWEB)
Rummel, Markus
2013-07-15
We study the connection between the early and late accelerated expansion of the universe and string theory. In Part I of this thesis, the observational degeneracy between single field models of inflation with canonical kinetic terms and noncanonical kinetic terms, in particular string theory inspired models, is discussed. The 2-point function observables of a given non-canonical theory and its canonical transform that is obtained by matching the inflationary trajectories in phase space are found to match in the case of Dirac-Born-Infeld (DBI) inflation. At the level of the 3-point function observables (non-Gaussianities), we find degeneracy between non-canonical inflation and canonical inflation with a potential that includes a sum of modulated terms. In Part II, we present explicit examples for de Sitter vacua in type IIB string theory. After deriving a sufficient condition for de Sitter vacua in the Kahler uplifting scenario, we show that a globally consistent de Sitter model can be realized on a certain Calabi-Yau manifold. All geometric moduli are stabilized and all known consistency constraints are fulfilled. The complex structure moduli stabilization by fluxes is studied explicitly for a small number of cycles. Extrapolating to a larger number of flux carrying cycles, we verify statistical studies in the literature which show that, in principle, the string landscape can account for a universe with an extremely small cosmological constant.
Black Hole Attractors and Pure Spinors
Energy Technology Data Exchange (ETDEWEB)
Hsu, Jonathan P.; Maloney, Alexander; Tomasiello, Alessandro
2006-02-21
We construct black hole attractor solutions for a wide class of N = 2 compactifications. The analysis is carried out in ten dimensions and makes crucial use of pure spinor techniques. This formalism can accommodate non-Kaehler manifolds as well as compactifications with flux, in addition to the usual Calabi-Yau case. At the attractor point, the charges fix the moduli according to {Sigma}f{sub k} = Im(C{Phi}), where {Phi} is a pure spinor of odd (even) chirality in IIB (A). For IIB on a Calabi-Yau, {Phi} = {Omega} and the equation reduces to the usual one. Methods in generalized complex geometry can be used to study solutions to the attractor equation.
Recurrences of strange attractors
Indian Academy of Sciences (India)
E J Ngamga; A Nandi; R Ramaswamy; M C Romano; M Thiel; J Kurths
2008-06-01
The transitions from or to strange nonchaotic attractors are investigated by recurrence plot-based methods. The techniques used here take into account the recurrence times and the fact that trajectories on strange nonchaotic attractors (SNAs) synchronize. The performance of these techniques is shown for the Heagy-Hammel transition to SNAs and for the fractalization transition to SNAs for which other usual nonlinear analysis tools are not successful.
Cosmography or novel ideas about emergent vacua
Bopp, F W
2010-01-01
Arguments for special emergent vacua which generate fermion and weak boson masses are outlined. Limitations and consequences of the concept are discussed. If confirmed the Australian dipole would give strong support to such a picture. Possible support from preliminatory Fermilab data is discussed and predictions for LHC are presented.
Kaura, P.; Misara, A.
2006-12-01
We look for possible nonsupersymmetric black hole attractor solutions for type II compactification on (the mirror of) CY_3(2,128) expressed as a degree-12 hypersurface in WCP^4[1,1,2,2,6]. In the process, (a) for points away from the conifold locus, we show that the attractors could be connected to an elliptic curve fibered over C^8 which may also be "arithmetic" (in some cases, it is possible to interpret the extremization conditions as an endomorphism involving complex multiplication of an arithmetic elliptic curve), and (b) for points near the conifold locus, we show that the attractors correspond to a version of A_1-singularity in the space Image(Z^6-->R^2/Z_2(embedded in R^3)) fibered over the complex structure moduli space. The potential can be thought of as a real (integer) projection in a suitable coordinate patch of the Veronese map: CP^5-->CP^{20}, fibered over the complex structure moduli space. We also discuss application of the equivalent Kallosh's attractor equations for nonsupersymmetric attractors and show that (a) for points away from the conifold locus, the attractor equations demand that the attractor solutions be independent of one of the two complex structure moduli, and (b) for points near the conifold locus, the attractor equations imply switching off of one of the six components of the fluxes. Both these features are more obvious using the atractor equations than the extremization of the black hole potential.
ATTRACTORS OF NONAUTONOMOUS SCHRODINGER EQUATIONS
Institute of Scientific and Technical Information of China (English)
刘玉荣; 刘曾荣; 郑永爱
2001-01-01
The long-time behaviour of a two-dimensional nonautonomous nonlinear SchrOdinger equation is considered. The existence of uniform attractor is proved and the up per bound of the uniform attractor' s Hausdorff dimension is given.
Hidden attractors in dynamical systems
Dudkowski, Dawid; Jafari, Sajad; Kapitaniak, Tomasz; Kuznetsov, Nikolay V.; Leonov, Gennady A.; Prasad, Awadhesh
2016-06-01
Complex dynamical systems, ranging from the climate, ecosystems to financial markets and engineering applications typically have many coexisting attractors. This property of the system is called multistability. The final state, i.e., the attractor on which the multistable system evolves strongly depends on the initial conditions. Additionally, such systems are very sensitive towards noise and system parameters so a sudden shift to a contrasting regime may occur. To understand the dynamics of these systems one has to identify all possible attractors and their basins of attraction. Recently, it has been shown that multistability is connected with the occurrence of unpredictable attractors which have been called hidden attractors. The basins of attraction of the hidden attractors do not touch unstable fixed points (if exists) and are located far away from such points. Numerical localization of the hidden attractors is not straightforward since there are no transient processes leading to them from the neighborhoods of unstable fixed points and one has to use the special analytical-numerical procedures. From the viewpoint of applications, the identification of hidden attractors is the major issue. The knowledge about the emergence and properties of hidden attractors can increase the likelihood that the system will remain on the most desirable attractor and reduce the risk of the sudden jump to undesired behavior. We review the most representative examples of hidden attractors, discuss their theoretical properties and experimental observations. We also describe numerical methods which allow identification of the hidden attractors.
Bellucci, S; Marrani, A
2008-01-01
We review recent results in the study of attractor horizon geometries (with non-vanishing Bekenstein-Hawking entropy) of dyonic extremal d=4 black holes in supergravity. We focus on N=2, d=4 ungauged supergravity coupled to a number n_{V} of Abelian vector multiplets, outlining the fundamentals of the special Kaehler geometry of the vector multiplets' scalar manifold (of complex dimension n_{V}), and studying the 1/2-BPS attractors, as well as the non-BPS (non-supersymmetric) ones with non-vanishing central charge. For symmetric special Kaehler geometries, we present the complete classification of the orbits in the symplectic representation of the classical U-duality group (spanned by the black hole charge configuration supporting the attractors), as well as of the moduli spaces of non-BPS attractors (spanned by the scalars which are not stabilized at the black hole event horizon). Finally, we report on an analogous classification for N>2-extended, d=4 ungauged supergravities, in which also the 1/N-BPS attrac...
Fermions, wigs, and attractors
Energy Technology Data Exchange (ETDEWEB)
Gentile, L.G.C., E-mail: lgentile@pd.infn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria 15120 (Italy); Dipartimento di Fisica “Galileo Galilei”, Università di Padova, via Marzolo 8, 35131 Padova (Italy); INFN, Sezione di Padova, via Marzolo 8, 35131 Padova (Italy); Grassi, P.A., E-mail: pgrassi@mfn.unipmn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria 15120 (Italy); INFN, Gruppo Collegato di Alessandria, Sezione di Torino (Italy); Marrani, A., E-mail: alessio.marrani@fys.kuleuven.be [ITF KU Leuven, Celestijnenlaan 200D, 3001 Leuven (Belgium); Mezzalira, A., E-mail: andrea.mezzalira@ulb.ac.be [Physique Théorique et Mathématique Université Libre de Bruxelles, C.P. 231, 1050 Bruxelles (Belgium)
2014-05-01
We compute the modifications to the attractor mechanism due to fermionic corrections. In N=2,D=4 supergravity, at the fourth order, we find terms giving rise to new contributions to the horizon values of the scalar fields of the vector multiplets.
A sufficient condition for de Sitter vacua in type IIB string theory
Energy Technology Data Exchange (ETDEWEB)
Rummel, Markus [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2011-07-15
We derive a sufficient condition for realizing meta-stable de Sitter vacua with small positive cosmological constant within type IIB string theory flux compactifications with spontaneously broken supersymmetry. There are a number of 'lamp post' constructions of de Sitter vacua in type IIB string theory and supergravity. We show that one of them - the method of 'Kaehler uplifting' by F-terms from an interplay between non-perturbative effects and the leading {alpha}'-correction - allows for a more general parametric understanding of the existence of de Sitter vacua. The result is a condition on the values of the flux induced superpotential and the topological data of the Calabi-Yau compactification, which guarantees the existence of a meta-stable de Sitter vacuum if met. Our analysis explicitly includes the stabilization of all moduli, i.e. the Kaehler, dilaton and complex structure moduli, by the interplay of the leading perturbative and non-perturbative effects at parametrically large volume. (orig.)
Isolated Minkowski vacua, and stability analysis for an extended brane in the rugby ball
Himmetoǧlu, Burak; Peloso, Marco
2007-06-01
We study a recently proposed model, where a codimension one brane is wrapped around the axis of symmetry of an internal two-dimensional space compactified by a flux. This construction is free from the problems which plague delta-like, codimension two branes, where only tension can be present. In contrast, arbitrary fields can be localized on this extended brane, and their gravitational interaction is standard 4d gravity at large distances. In the first part of this work, we study the de Sitter (dS) vacua of the model. The landscape of these vacua is characterized by discrete points labeled by two integer numbers, related to the flux responsible for the compactification and to the current of a brane field. A Minkowski external space emerges only for a special ratio between these two integers, and it is therefore (topologically) isolated from the nearby dS solutions. In the second part, we show that the Minkowski vacua are stable under the most generic axially-symmetric perturbations, and we argue that this is sufficient to ensure the overall stability.
Inverse Symmetric Inflationary Attractors
Odintsov, S D
2016-01-01
We present a class of inflationary potentials which are invariant under a special symmetry, which depends on the parameters of the models. As we show, in certain limiting cases, the inverse symmetric potentials are qualitatively similar to the $\\alpha$-attractors models, since the resulting observational indices are identical. However, there are some quantitative differences which we discuss in some detail. As we show, some inverse symmetric models always yield results compatible with observations, but this strongly depends on the asymptotic form of the potential at large $e$-folding numbers. In fact when the limiting functional form is identical to the one corresponding to the $\\alpha$-attractors models, the compatibility with the observations is guaranteed. Also we find the relation of the inverse symmetric models with the Starobinsky model and we highlight the differences. In addition, an alternative inverse symmetric model is studied and as we show, not all the inverse symmetric models are viable. Moreove...
Attractors under discretisation
Han, Xiaoying
2017-01-01
This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained – by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes – results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
Gases and vacua handbook of vacuum physics
Beck, A H
2013-01-01
Handbook of Vacuum Physics, Volume 1: Gases and Vacua provides information on the many aspects of vacuum technology, from material on the quantum theoretical aspects of the complex semi-conductors used for thermionic and photo-electric emission to data on the performance of commercially available pumps, gauges, and high-vacuum materials. The handbook satisfies the need of workers using vacuum apparatuses or works on the diverse applications of high-vacuum technology in research and industry. The book is a compilation of long articles prepared by experts in vacuum technology. Sufficient theoret
Generalized geometry of two-dimensional vacua
Rosa, Dario
2013-01-01
We derive the conditions for unbroken supersymmetry for a Mink_2, (2,0) vacuum, arising from Type II supergravity on a compact eight-dimensional manifold M_8. When specialized to internal manifolds enjoying SU(4)xSU(4) structure the resulting system is elegantly rewritten in terms of generalized complex geometry. This particular class of vacua violates the correspondence between supersymmetry conditions and calibrations conditions of D branes (supersymmetry-calibrations correspondence). Our analysis includes and extends previous results about the failure of the supersymmetry-calibrations correspondence, and confirms the existence of a precise relation between such a failure and a subset of the supersymmetry conditions.
Gases and vacua handbook of vacuum physics
Beck, A H
2013-01-01
Handbook of Vacuum Physics, Volume 1: Gases and Vacua presents three major topics, which are the fourth to sixth parts of this volume. These topics are the remarks on units of physical quantities; kinetic theory of gases and gaseous flow; and theory of vacuum diffusion pumps. The first topic aims to present concisely the significance of units of physical quantities, catering the need and interest of those who take measurements and make calculations in different fields of vacuum sciences. The technique and applications of this particular topic are also provided. The second main topic focuses sp
Exophobic quasi-realistic heterotic string vacua
Energy Technology Data Exchange (ETDEWEB)
Assel, Benjamin [Centre de Physique Theorique, Ecole Polytechnique, F-91128 Palaiseau (France); Christodoulides, Kyriakos [Dept. of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL (United Kingdom); Faraggi, Alon E., E-mail: faraggi@amtp.liv.ac.u [Dept. of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL (United Kingdom); Kounnas, Costas [Lab. Physique Theorique, Ecole Normale Superieure, F-75231 Paris 05 (France); Rizos, John [Department of Physics, University of Ioannina, GR45110 Ioannina (Greece)
2010-01-25
We demonstrate the existence of heterotic string vacua that are free of massless exotic fields. The need to break the non-Abelian GUT symmetries in k=1 heterotic string models by Wilson lines, while preserving the GUT embedding of the weak hypercharge and the GUT prediction sin{sup 2}theta{sub w}(M{sub GUT})=3/8, necessarily implies that the models contain states with fractional electric charge. Such states are severely restricted by observations, and must be confined or sufficiently massive and diluted. We construct the first quasi-realistic heterotic string models in which the exotic states do not appear in the massless spectrum, and only exist, as they must, in the massive spectrum. The SO(10) GUT symmetry is broken to the Pati-Salam subgroup. Our PS heterotic string models contain adequate Higgs representations to break the GUT and electroweak symmetry, as well as colour Higgs triplets that can be used for the missing partner mechanism. By statistically sampling the space of Pati-Salam vacua we demonstrate the abundance of quasi-realistic three generation models that are completely free of massless exotics, rendering it plausible that obtaining realistic Yukawa couplings may be possible in this space of models.
Tachyons in classical de Sitter vacua
Junghans, Daniel
2016-06-01
We revisit the possibility of de Sitter vacua and slow-roll inflation in type II string theory at the level of the classical two-derivative supergravity approximation. Previous attempts at explicit constructions were plagued by ubiquitous tachyons with a large η parameter whose origin has not been fully understood so far. In this paper, we determine and explain the tachyons in two setups that are known to admit unstable dS critical points: an SU(3) structure compactification of massive type IIA with O6-planes and an SU(2) structure compactification of type IIB with O5/O7-planes. We explicitly show that the tachyons are always close to, but never fully aligned with the sgoldstino direction in the considered examples and argue that this behavior is explained by a generalized version of a no-go theorem by Covi et al, which holds in the presence of large mixing in the mass matrix between the sgoldstino and the orthogonal moduli. This observation may also provide a useful stability criterion for general dS vacua in supergravity and string theory.
Unity of cosmological inflation attractors.
Galante, Mario; Kallosh, Renata; Linde, Andrei; Roest, Diederik
2015-04-10
Recently, several broad classes of inflationary models have been discovered whose cosmological predictions, in excellent agreement with Planck, are stable with respect to significant modifications of the inflaton potential. Some classes of models are based on a nonminimal coupling to gravity. These models, which we call ξ attractors, describe universal cosmological attractors (including Higgs inflation) and induced inflation models. Another class describes conformal attractors (including Starobinsky inflation and T models) and their generalization to α attractors. The aim of this Letter is to elucidate the common denominator of these attractors: their robust predictions stem from a joint pole of order 2 in the kinetic term of the inflaton field in the Einstein frame formulation prior to switching to the canonical variables. Model-dependent differences only arise at subleading level in the kinetic term. As a final step towards the unification of the different attractors, we introduce a special class of ξ attractors which is fully equivalent to α attractors with the identification α=1+(1/6ξ). While r is generically predicted to be of the order 1/N^{2}, there is no theoretical lower bound on r in this class of models.
Chaotic attractors with separated scrolls
Energy Technology Data Exchange (ETDEWEB)
Bouallegue, Kais, E-mail: kais-bouallegue@yahoo.fr [Department of Electrical Engineering, Higher Institute of Applied Sciences and Technology of Sousse, Sousse (Tunisia)
2015-07-15
This paper proposes a new behavior of chaotic attractors with separated scrolls while combining Julia's process with Chua's attractor and Lorenz's attractor. The main motivation of this work is the ability to generate a set of separated scrolls with different behaviors, which in turn allows us to choose one or many scrolls combined with modulation (amplitude and frequency) for secure communication or synchronization. This set seems a new class of hyperchaos because each element of this set looks like a simple chaotic attractor with one positive Lyapunov exponent, so the cardinal of this set is greater than one. This new approach could be used to generate more general higher-dimensional hyperchaotic attractor for more potential application. Numerical simulations are given to show the effectiveness of the proposed theoretical results.
Metastable Vacua in Deformed N=2 Supersymmetric Models
Halyo, Edi
2009-01-01
We show that supersymmetric Abelian models that are obtained from deformations of those with ${\\cal N}=2$ supersymmetry also contain metastable vacua for a wide range of parameters. The deformations we consider are combinations of masses for charged and singlet fields, a singlet F--term and an anomalous D--term. We find that, in all cases, the nonsupersymmetric vacua are parametrically far from the supersymmetric ones and therefore metastable. Using retrofitting, we show that these metastable vacua may lead to semi--realistic phenomenology.
F-Theory Vacua with $Z_3$ Gauge Symmetry
Cvetič, Mirjam; Klevers, Denis; Piragua, Hernan; Poretschkin, Maximilian
2015-01-01
Discrete gauge groups naturally arise in F-theory compactifications on genus-one fibered Calabi-Yau manifolds. Such geometries appear in families that are parameterized by the Tate-Shafarevich group of the genus-one fibration. While the F-theory compactification on any element of this family gives rise to the same physics, the corresponding M-theory compactifications on these geometries differ and are obtained by a fluxed circle reduction of the former. In this note, we focus on an element of order three in the Tate-Shafarevich group of the general cubic. We discuss how the different M-theory vacua and the associated discrete gauge groups can be obtained by Higgsing of a pair of five-dimensional U(1) symmetries. The Higgs fields arise from vanishing cycles in $I_2$-fibers that appear at certain codimension two loci in the base. We explicitly identify all three curves that give rise to the corresponding Higgs fields. In this analysis the investigation of different resolved phases of the underlying geometry pla...
A new method for finding vacua in string phenomenology
Energy Technology Data Exchange (ETDEWEB)
Gray, James [Institut d' Astrophysique de Paris and APC, Universite de Paris 7, 98 bis, Bd. Arago 75014, Paris (France); He, Yang-Hui [Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP (United Kingdom)]|[Merton College, Oxford, OX1 4JD and Mathematical Institute, Oxford University, Oxford (United Kingdom); Ilderton, Anton [School of Mathematics and Statistics, University of Plymouth, Drake Circus, Plymouth PL4 8AA (United Kingdom); Lukas, Andre [Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP (United Kingdom)
2007-05-15
One of the central problems of string-phenomenology is to find stable vacua in the four dimensional effective theories which result from compactification. We present an algorithmic method to find all of the vacua of any given string-phenomenological system in a huge class. In particular, this paper reviews and then extends hep-th/0606122 to include various nonperturbative effects. These include gaugino condensation and instantonic contributions to the superpotential. (authors)
A New Method for Finding Vacua in String Phenomenology
Gray, J; Ilderton, A; Lukas, A; Gray, James; He, Yang-Hui; Ilderton, Anton; Lukas, Andre
2007-01-01
One of the central problems of string-phenomenology is to find stable vacua in the four dimensional effective theories which result from compactification. We present an algorithmic method to find all of the vacua of any given string-phenomenological system in a huge class. In particular, this paper reviews and then extends hep-th/0606122 to include various non-perturbative effects. These include gaugino condensation and instantonic contributions to the superpotential.
Non-Supersymmetric Stringy Attractors
Dominic, Pramod
2011-01-01
In this paper we examine the stability of non-supersymmetric attractors in type IIA supergravity compactified on a Calabi-Yau manifold, in the presence of sub-leading corrections to the N=$ pre-potential. We study black hole configurations carrying D0-D6 and D0-D4 charges. We consider the O(1) corrections to the pre-potential given by the Euler number of the Calabi-Yau manifold. We argue that such corrections in general can not lift the zero modes for the D0-D6 attractors. However, for the attractors carrying the D0-D4 charges, they affect the zero modes in the vector multiplet sector. We show that, in the presence of such O(1) corrections, the D0-D4 attractors can either be stable or unstable depending on the geometry of the underlying Calabi-Yau manifold, and on the specific values of the charges they carry.
Some properties for the attractors
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
For the continuous flows defined on a topological space,we have discussed some properties for the invariant sets and their domains of influence.We have proved the following open problem posed by C.Conley:an attractor in a locally connected compact Hausdorff invariant set has finitely many components.In the meantime,two necessary and sufficient conditions for a set to be an attractor have been given.
Bajc-Melfo Vacua enable YUMGUTs
Aulakh, Charanjit S
2014-01-01
Bajc-Melfo(\\textbf{BM}) two field ($S,\\phi$) superpotentials define metastable F-term supersymmetry breaking vacua suitable as hidden sectors for calculable and realistic unification models. The undetermined vev $$ of the Polonyi field that breaks Supersymmetry can be fixed either by coupling to N=1 Supergravity or by radiative corrections. \\textbf{BM} hidden sectors extend to symmetric multiplets $(S,\\phi)_{ab}$ of a gauged $O(N_g)$ family symmetry, broken at the GUT scale, so that the $O(N_g)$ charged component vevs $$ are also undetermined before accounting for the $O(N_g)$ D-terms: which fix them by cancellation against D-term contributions from the visible sector. This facilitates Yukawon Ultra Minimal GUTs(YUMGUTs) proposed in \\cite{yukawon} by relieving the visible sector from the need to give null D-terms for the family symmetry $ O(N_g)$. We analyze symmetry breaking and and spectra of the hidden sector fields in the Supergravity resolved case when $N_g=1,2,3$. Besides the Polonyi field $S_s$, most o...
Tachyons in Classical de Sitter Vacua
Junghans, Daniel
2016-01-01
We revisit the possibility of de Sitter vacua and slow-roll inflation in type II string theory at the level of the classical two-derivative supergravity approximation. Previous attempts at explicit constructions were plagued by ubiquitous tachyons with a large $\\eta$ parameter whose origin has not been fully understood so far. In this paper, we determine and explain the tachyons in two setups that are known to admit unstable dS critical points: an SU(3) structure compactification of massive type IIA with O6-planes and an SU(2) structure compactification of type IIB with O5/O7-planes. We explicitly show that the tachyons are always close to, but never fully aligned with the sgoldstino direction in the considered examples and argue that this behavior is explained by a generalized version of a no-go theorem by Covi et al, which holds in the presence of large mixing in the mass matrix between the sgoldstino and the orthogonal moduli. This observation may also provide a useful stability criterion for general dS va...
Inflation, Universality and Attractors
Scalisi, Marco
2016-01-01
In this PhD thesis, we investigate generic features of inflation which are strictly related to fundamental aspects of UV-physics scenarios, such as string theory or supergravity. After a short introduction to standard and inflationary cosmology, we present our research findings. On the one hand, we show that focusing on universality properties of inflation can yield surprisingly stringent bounds on its dynamics. This approach allows us to identify the regime where the inflationary field range is uniquely determined by both the tensor-to-scalar ratio and the spectral index. Then, we derive a novel field-range bound, which is two orders of magnitude stronger than the original one derived by Lyth. On the other hand, we discuss the embedding of inflation in supergravity and prove that non-trivial hyperbolic K\\"ahler geometries induce an attractor for the inflationary observables: the spectral tilt tends automatically to the center of the Planck dome whereas the amount of primordial gravitational waves is directly...
$\\mathcal{N}=1$ AdS$_4$ sourceless vacua in type IIB
Solard, Gautier
2016-01-01
In this paper, we are looking for $\\mathcal{N}=1$, AdS$_4$ sourceless vacua in type IIB. While several examples exist in type IIA , there exists only one example of such vacua in type IIB . Thanks to the framework of generalized geometry we were able to devise a semi-algorithmical method to look for sourceless vacua. We present this method, which can easily be generalized to more complex cases, and give two new sourceless vacua in type IIB.
Destabilizing Tachyonic Vacua at or above the BF Bound
Kanno, Sugumi; Soda, Jiro
2012-01-01
It is well known that tachyonic vacua in an asymptotically Anti-de Sitter (AdS) space-time are classically stable if the mass squared is at or above the Breitenlohner and Freedman (BF) bound. We study the quantum stability of these tachyonic vacua in terms of instantons. We find a series of exact instanton solutions destabilizing tachyonic state at or above the BF bound in asymptotically AdS space. We also give an analytic formula for the decay rate and show that it is finite. Comparing our result with the well-known algebraic condition for the stability, we discuss stability conditions of tachyonic vacua at or above the BF bound.
Spinor-vector duality in heterotic SUSY vacua
Energy Technology Data Exchange (ETDEWEB)
Catelin-Jullien, Tristan [Laboratoire de Physique Theorique, Ecole Normale Superieure, 24 rue Lhomond, F-75231 Paris cedex 05 (France)], E-mail: catelin@lpt.ens.fr; Faraggi, Alon E. [Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL (United Kingdom)], E-mail: alon.faraggi@liv.ac.uk; Kounnas, Costas [Laboratoire de Physique Theorique, Ecole Normale Superieure, 24 rue Lhomond, F-75231 Paris cedex 05 (France)], E-mail: costas.kounnas@lpt.ens.fr; Rizos, John [Department of Physics, University of Ioannina, GR45110 Ioannina (Greece)], E-mail: irizos@uoi.gr
2009-05-01
We elaborate on the recently discovered spinor-vector duality in realistic free fermionic heterotic vacua. We emphasize the interpretation of the freely-acting orbifolds carried out on the six internal dimensions as coordinate-dependent compactifications; they play a central role in the duality, especially because of their ability to break the right-moving superconformal algebra of the space-time supersymmetric heterotic vacua. These considerations lead to a simple and intuitive proof of the spinor-vector duality, and to the formulation of explicit rules to find the dual of a given model. We discuss the interest of such a duality, notably concerning the structure of the space of vacua of superstring theory.
Entanglement entropy of α-vacua in de Sitter space
Kanno, Sugumi; Murugan, Jeff; Shock, Jonathan P.; Soda, Jiro
2014-07-01
We consider the entanglement entropy of a free massive scalar field in the one parameter family of α-vacua in de Sitter space by using a method developed by Maldacena and Pimentel. An α-vacuum can be thought of as a state filled with particles from the point of view of the Bunch-Davies vacuum. Of all the α-vacua we find that the entanglement entropy takes the minimal value in the Bunch-Davies solution. We also calculate the asymptotic value of the Rényi entropy and find that it increases as α increases. We argue these features stem from pair condensation within the non-trivial α-vacua where the pairs have an intrinsic quantum correlation.
Entanglement entropy of $\\alpha$-vacua in de Sitter space
Kanno, Sugumi; Shock, Jonathan P; Soda, Jiro
2014-01-01
We consider the entanglement entropy of a free massive scalar field in the one parameter family of $\\alpha$-vacua in de Sitter space by using a method developed by Maldacena and Pimentel. An $\\alpha$-vacuum can be thought of as a state filled with particles from the point of view of the Bunch-Davies vacuum. Of all the $\\alpha$-vacua we find that the entanglement entropy takes the minimal value in the Bunch-Davies solution. We also calculate the asymptotic value of the R\\'enyi entropy and find that it increases as $\\alpha$ increases. We argue these feature stem from pair condensation within the non-trivial $\\alpha$-vacua where the pairs have an intrinsic quantum correlation.
Moduli Backreaction on Inflationary Attractors
Roest, Diederik; Werkman, Pelle
2016-01-01
We investigate the interplay between moduli dynamics and inflation, focusing on the KKLT-scenario and cosmological $\\alpha$-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for $\\alpha$-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there is a universal supersymmetric minimum where the scalars end up, preventing the decompactification scenario. The observational predictions conform to the universal value of attractors, fully compatible with the Planck data, with possibly a capped number of e-folds due to the interplay with moduli.
Moduli backreaction on inflationary attractors
Roest, Diederik; Scalisi, Marco; Werkman, Pelle
2016-12-01
We investigate the interplay between moduli dynamics and inflation, focusing on the Kachru-Kallosh-Linde-Trivedi scenario and cosmological α -attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for α -attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there is a universal supersymmetric minimum where the scalars end up, preventing the decompactification scenario. The gravitino mass is independent from the inflationary scale with no fine-tuning of the parameters. The observational predictions conform to the universal value of attractors, fully compatible with the Planck data, with possibly a capped number of e -folds due to the interplay with moduli.
Cosmological attractors in massive gravity
Dubovsky, S; Tkachev, I I
2005-01-01
We study Lorentz-violating models of massive gravity which preserve rotations and are invariant under time-dependent shifts of the spatial coordinates. In the linear approximation the Newtonian potential in these models has an extra ``confining'' term proportional to the distance from the source. We argue that during cosmological expansion the Universe may be driven to an attractor point with larger symmetry which includes particular simultaneous dilatations of time and space coordinates. The confining term in the potential vanishes as one approaches the attractor. In the vicinity of the attractor the extra contribution is present in the Friedmann equation which, in a certain range of parameters, gives rise to the cosmic acceleration.
Attractors: architects of network organization?
Mpitsos, G J
2000-05-01
An attractor is defined here informally as a state of activity toward which a system settles. The settling or relaxation process dissipates the effects produced by external perturbations. In neural systems the relaxation process occurs temporally in the responses of each neuron and spatially across the network such that the activity settles into a subset of the available connections. Within limits, the set of neurons toward which the coordinated neural firing settles can be different from one time to another, and a given set of neurons can generate different types of attractor activity, depending on how the input environment activates the network. Findings such as these indicate that though information resides in the details of neuroanatomic structure, the expression of this information is in the dynamics of attractors. As such, attractors are sources of information that can be used not only in adaptive behavior, but also to effect the neural architecture that generates the attractor. The discussion here focuses on the latter possibility. A conjecture is offered to show that the relaxation dynamic of an attractor may 'guide' activity-dependent learning processes in such a way that synaptic strengths, firing thresholds, the physical connections between neurons, and the size of the network are automatically set in an optimal, interrelated fashion. This inter-relatedness among network parameters would not be expected from more classical, 'switchboard' approaches to neural integration. The ideas are discussed within the context of 'pulse-propagated networks' or equivalently as 'spike-activated networks' in which the specific order in time intervals between action potentials carries important information for cooperative activity to emerge among neurons in a network. Though the proposed ideas are forward-looking, being based on preliminary work in biological and artificial networks, they are testable in biological neural networks reconstructed from identified neurons in
On the uniqueness of supersymmetric attractors
Directory of Open Access Journals (Sweden)
Taniya Mandal
2015-10-01
Full Text Available In this paper we discuss the uniqueness of supersymmetric attractors in four-dimensional N=2 supergravity theories coupled to n vector multiplets. We prove that for a given charge configuration the supersymmetry preserving axion free attractors are unique. We generalise the analysis to axionic attractors and state the conditions for uniqueness explicitly. We consider the example of a two-parameter model and find all solutions to the supersymmetric attractor equations and discuss their uniqueness.
Constructing de Sitter vacua in no-scale string models without uplifting
Energy Technology Data Exchange (ETDEWEB)
Covi, Laura [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gomez-Reino, Marta [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Gross, Christian [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Palma, Gonzalo A. [Leiden Univ. (Netherlands). Lorentz Inst. for Theoretical Physics; Scrucca, Claudio A. [Ecole Polytechnique Federale de Lausanne (Switzerland). Inst. de Theorie des Phenomenes Physiques
2008-12-15
We develop a method for constructing metastable de Sitter vacua in N=1 supergravity models describing the no-scale volume moduli sector of Calabi-Yau string compactifications. We consider both heterotic and orientifold models. Our main guideline is the necessary condition for the existence of metastable vacua coming from the Goldstino multiplet, which constrains the allowed scalar geometries and supersymmetry-breaking directions. In the simplest non-trivial case where the volume is controlled by two moduli, this condition simplifies and turns out to be fully characterised by the intersection numbers of the Calabi-Yau manifold. We analyse this case in detail and show that once the metastability condition is satisfied it is possible to reconstruct in a systematic way the local form of the superpotential that is needed to stabilise all the fields. We apply then this procedure to construct some examples of models where the superpotential takes a realistic form allowed by flux backgrounds and gaugino condensation effects, for which a viable vacuum arises without the need of invoking corrections to the Kaehler potential breaking the noscale property or uplifting terms. We finally discuss the prospects of constructing potentially realistic models along these lines. (orig.)
Hyperbolic geometry of cosmological attractors
Carrasco, John Joseph M.; Kallosh, Renata; Linde, Andrei; Roest, Diederik
2015-01-01
Cosmological alpha attractors give a natural explanation for the spectral index n(s) of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r, consistent with all observations, to be measured more precisely in future B-mode experiments. We highlight the crucial ro
Intermittent control of coexisting attractors.
Liu, Yang; Wiercigroch, Marian; Ing, James; Pavlovskaia, Ekaterina
2013-06-28
This paper proposes a new control method applicable for a class of non-autonomous dynamical systems that naturally exhibit coexisting attractors. The central idea is based on knowledge of a system's basins of attraction, with control actions being applied intermittently in the time domain when the actual trajectory satisfies a proximity constraint with regards to the desired trajectory. This intermittent control uses an impulsive force to perturb one of the system attractors in order to switch the system response onto another attractor. This is carried out by bringing the perturbed state into the desired basin of attraction. The method has been applied to control both smooth and non-smooth systems, with the Duffing and impact oscillators used as examples. The strength of the intermittent control force is also considered, and a constrained intermittent control law is introduced to investigate the effect of limited control force on the efficiency of the controller. It is shown that increasing the duration of the control action and/or the number of control actuations allows one to successfully switch between the stable attractors using a lower control force. Numerical and experimental results are presented to demonstrate the effectiveness of the proposed method.
Classification of flipped SU(5) heterotic-string vacua
Faraggi, Alon E.; Rizos, John; Sonmez, Hasan
2014-09-01
We extend the classification of free fermionic heterotic-string vacua to models in which the SO(10) GUT symmetry is reduced at the string level to the flipped SU(5) subgroup. In our classification method the set of boundary condition basis vectors is fixed and the enumeration of string vacua is obtained in terms of the Generalised GSO (GGSO) projection coefficients entering the one-loop partition function. We derive algebraic expressions for the GGSO projections for all the physical states appearing in the sectors generated by the set of basis vectors. This enables the programming of the entire spectrum analysis in a computer code. For that purpose we developed two independent codes, based on FORTRAN95 and JAVA, and all results presented are confirmed by the two independent routines. We perform a statistical sampling in the space of 244∼1013 flipped SU(5) vacua, and scan up to 1012 GGSO configurations. Contrary to the corresponding Pati-Salam classification results, we do not find exophobic flipped SU(5) vacua with an odd number of generations. We study the structure of exotic states appearing in the three generation models, that additionally contain a viable Higgs spectrum, and demonstrate the existence of models in which all the exotic states are confined by a hidden sector non-Abelian gauge symmetry, as well as models that may admit the racetrack mechanism.
Classification of flipped SU(5 heterotic-string vacua
Directory of Open Access Journals (Sweden)
Alon E. Faraggi
2014-09-01
Full Text Available We extend the classification of free fermionic heterotic-string vacua to models in which the SO(10 GUT symmetry is reduced at the string level to the flipped SU(5 subgroup. In our classification method the set of boundary condition basis vectors is fixed and the enumeration of string vacua is obtained in terms of the Generalised GSO (GGSO projection coefficients entering the one-loop partition function. We derive algebraic expressions for the GGSO projections for all the physical states appearing in the sectors generated by the set of basis vectors. This enables the programming of the entire spectrum analysis in a computer code. For that purpose we developed two independent codes, based on FORTRAN95 and JAVA, and all results presented are confirmed by the two independent routines. We perform a statistical sampling in the space of 244∼1013 flipped SU(5 vacua, and scan up to 1012 GGSO configurations. Contrary to the corresponding Pati–Salam classification results, we do not find exophobic flipped SU(5 vacua with an odd number of generations. We study the structure of exotic states appearing in the three generation models, that additionally contain a viable Higgs spectrum, and demonstrate the existence of models in which all the exotic states are confined by a hidden sector non-Abelian gauge symmetry, as well as models that may admit the racetrack mechanism.
Classification of flipped SU(5) heterotic-string vacua
Energy Technology Data Exchange (ETDEWEB)
Faraggi, Alon E., E-mail: alon.faraggi@liv.ac.uk [Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL (United Kingdom); Rizos, John, E-mail: irizos@uoi.gr [Department of Physics, University of Ioannina, GR45110 Ioannina (Greece); Sonmez, Hasan, E-mail: Hasan.Sonmez@liv.ac.uk [Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL (United Kingdom)
2014-09-15
We extend the classification of free fermionic heterotic-string vacua to models in which the SO(10) GUT symmetry is reduced at the string level to the flipped SU(5) subgroup. In our classification method the set of boundary condition basis vectors is fixed and the enumeration of string vacua is obtained in terms of the Generalised GSO (GGSO) projection coefficients entering the one-loop partition function. We derive algebraic expressions for the GGSO projections for all the physical states appearing in the sectors generated by the set of basis vectors. This enables the programming of the entire spectrum analysis in a computer code. For that purpose we developed two independent codes, based on FORTRAN95 and JAVA, and all results presented are confirmed by the two independent routines. We perform a statistical sampling in the space of 2{sup 44}∼10{sup 13} flipped SU(5) vacua, and scan up to 10{sup 12} GGSO configurations. Contrary to the corresponding Pati–Salam classification results, we do not find exophobic flipped SU(5) vacua with an odd number of generations. We study the structure of exotic states appearing in the three generation models, that additionally contain a viable Higgs spectrum, and demonstrate the existence of models in which all the exotic states are confined by a hidden sector non-Abelian gauge symmetry, as well as models that may admit the racetrack mechanism.
Metastable Supersymmetry Breaking Vacua on Abelian Brane Models
Halyo, Edi
2009-01-01
We construct Abelian brane models with metastable vacua which are obtained from deformations of ${\\cal N}=2$ supersymmetric brane configurations. One such model lives on a D4 brane stretched between two displaced and rotated NS5 branes. Another one lives on a D5 brane wrapped on a deformed and fibered $A_2$ singularity.
Unstable attractors induce perpetual synchronization and desynchronization.
Timme, Marc; Wolf, Fred; Geisel, Theo
2003-03-01
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which unstable attractors arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send pulses alternately, resulting in a periodic dynamics of the network. Under the influence of arbitrarily weak noise, this synchronization is followed by a desynchronization of clusters, a phenomenon induced by attractors that are unstable. Perpetual synchronization and desynchronization lead to a switching among attractors. This is explained by the geometrical fact, that these unstable attractors are surrounded by basins of attraction of other attractors, whereas the full measure of their own basin is located remote from the attractor. Unstable attractors do not only exist in these systems, but moreover dominate the dynamics for large networks and a wide range of parameters.
De Boer, J; Hori, K; Keurentjes, A; Morgan, J; Morrison, Douglas Robert Ogston; Sethi, S K; Boer, Jan de; Dijkgraaf, Robbert; Hori, Kentaro; Keurentjes, Arjan; Morgan, John; Morrison, David R.; Sethi, Savdeep
2002-01-01
We study string compactifications with sixteen supersymmetries. The moduli space for these compactifications becomes quite intricate in lower dimensions, partly because there are many different irreducible components. We focus primarily, but not exclusively, on compactifications to seven or more dimensions. These vacua can be realized in a number ways: the perturbative constructions we study include toroidal compactifications of the heterotic/type I strings, asymmetric orbifolds, and orientifolds. In addition, we describe less conventional M and F theory compactifications on smooth spaces. The last class of vacua considered are compactifications on singular spaces with non-trivial discrete fluxes. We find a number of new components in the string moduli space. Contained in some of these components are M theory compactifications with novel kinds of ``frozen'' singularities. We are naturally led to conjecture the existence of new dualities relating spaces with different singular geometries and fluxes. As our stu...
Spin(7) compactifications and 1/4-BPS vacua in heterotic supergravity
Energy Technology Data Exchange (ETDEWEB)
Angus, Stephen [Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS),Daejeon, 34051 Republic of (Korea, Republic of); Matti, Cyril [Department of Mathematics, City University, Northampton Square, London, EC1V 0HB (United Kingdom); Mandelstam Institute for Theoretical Physics, NITheP, andSchool of Physics, University of the Witwatersrand,Johannesburg, WITS 2050 South Africa (South Africa); Svanes, Eirik E. [Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE,Paris, F-75005 (France); CNRS, UMR 7589, LPTHE,Paris, F-75005 (France); Sorbonne Universités, Institut Lagrange de Paris,98 bis Bd Arago, Paris, 75014 (France)
2016-03-25
We continue the investigation into non-maximally symmetric compactifications of the heterotic string. In particular, we consider compactifications where the internal space is allowed to depend on two or more external directions. For preservation of supersymmetry, this implies that the internal space must in general be that of a Spin(7) manifold, which leads to a 1/4-BPS four-dimensional supersymmetric perturbative vacuum breaking all but one supercharge. We find that these solutions allow for internal geometries previously excluded by the domain-wall-type solutions, and hence the resulting four-dimensional superpotential is more generic. In particular, we find an interesting resemblance to the superpotentials that appear in non-geometric flux compactifications of type II string theory. If the vacua are to be used for phenomenological applications, they must be lifted to maximal symmetry by some non-perturbative or higher-order effect.
$Spin(7)$ Compactifications and 1/4-BPS Vacua in Heterotic Supergravity
Angus, Stephen; Svanes, Eirik Eik
2015-01-01
We continue the investigation into non-maximally symmetric compactifications of the heterotic string. In particular, we consider compactifications where the internal space is allowed to depend on two or more external directions. For preservation of supersymmetry, this implies that the internal space must in general be that of a $Spin(7)$ manifold, which leads to a $1/4$-BPS four-dimensional non-supersymmetric perturbative vacuum. We find that these solutions allow for internal geometries previously excluded by the domain-wall-type solutions, and hence the resulting four-dimensional superpotential is more generic. In particular, we find an interesting resemblance to the superpotentials that appear in non-geometric flux compactifications of type II string theory. If the vacua are to be used for phenomenological applications, they must be lifted to a maximally symmetric one by some non-perturbative or higher-order effect.
Detecting variation in chaotic attractors.
Carroll, T L
2011-06-01
If the output of an experiment is a chaotic signal, it may be useful to detect small changes in the signal, but there are a limited number of ways to compare signals from chaotic systems, and most known methods are not robust in the presence of noise. One may calculate dimension or Lyapunov exponents from the signal, or construct a synchronizing model, but all of these are only useful in low noise situations. I introduce a method for detecting small variations in a chaotic attractor based on directly calculating the difference between vector fields in phase space. The differences are found by comparing close strands in phase space, rather than close neighbors. The use of strands makes the method more robust to noise and more sensitive to small attractor differences.
Ceresole, A; Gnecchi, A; Marrani, A
2009-01-01
We examine few simple extremal black hole configurations of N=8, d=4 supergravity. We first elucidate the relation between the BPS Reissner-Nordstrom black hole and the non-BPS Kaluza-Klein dyonic black hole. Their classical entropy, given by the Bekenstein-Hawking formula, can be reproduced via the attractor mechanism by suitable choices of symplectic frame. Then, we display the embedding of the axion-dilaton black hole into N=8 supergravity.
N=2 supergravity models with stable de Sitter vacua
Fré, P; Van Proeyen, A; Fre', Pietro; Trigiante, Mario; Proeyen, Antoine Van
2003-01-01
In the present talk I shall review the construction of N=2 supergravity models exhibiting stable de Sitter vacua. These solutions represent the first instance of stable backgrounds with positive cosmological constant in the framework of extended supergravities (N >=2). After briefly reviewing the role of de Sitter space--times in inflationary cosmology, I shall describe the main ingredients which were necessary for the construction of gauged N=2 supergravity models admitting stable solutions of this kind.
Spinor-vector duality in N=2 heterotic string vacua
Energy Technology Data Exchange (ETDEWEB)
Faraggi, Alon E. [Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL (United Kingdom)], E-mail: faraggi@amtp.liv.ac.uk; Kounnas, Costas [Laboratoire Physique Theorique, Ecole Normale Superieure, F-75231 Paris 05 (France); Rizos, John [Department of Physics, University of Ioannina, GR45110 Ioannina (Greece)
2008-08-11
Classification of the N=1 space-time supersymmetric fermionic Z{sub 2}xZ{sub 2} heterotic-string vacua with symmetric internal shifts, revealed a novel spinor-vector duality symmetry over the entire space of vacua, where the S{sub t}{r_reversible}V duality interchanges the spinor plus anti-spinor representations with vector representations. In this paper we demonstrate that the spinor-vector duality exists also in fermionic Z{sub 2} heterotic string models, which preserve N=2 space-time supersymmetry. In this case the interchange is between spinorial and vectorial representations of the unbroken SO(12) GUT symmetry. We provide a general algebraic proof for the existence of the S{sub t}{r_reversible}V duality map. We present a novel basis to generate the free fermionic models in which the ten-dimensional gauge degrees of freedom are grouped into four groups of four, each generating an SO(8) modular block. In the new basis the GUT symmetries are produced by generators arising from the trivial and non-trivial sectors, and due to the triality property of the SO(8) representations. Thus, while in the new basis the appearance of GUT symmetries is more cumbersome, it may be more instrumental in revealing the duality symmetries that underly the string vacua.
Classification of Flipped SU(5) Heterotic-String Vacua
Faraggi, Alon; Sonmez, Hasan
2014-01-01
We extend the classification of free fermionic heterotic-string vacua to models in which the SO(10) GUT symmetry is reduced at the string level to the flipped SU(5) subgroup. In our classification method the set of boundary condition basis vectors is fixed and the enumeration of string vacua is obtained in terms of the Generalised GSO (GGSO) projection coefficients entering the one-loop partition function. We derive algebraic expressions for the GGSO projections for all the physical states appearing in the sectors generated by the set of basis vectors. This enables the programming of the entire spectrum analysis in a computer code. For that purpose we developed two independent codes, based on FORTRAN95 and JAVA, and all resulted presented are confirmed by the two independent routines. We perform a statistical sampling in the space of 2^{44} ~ 10^{13} flipped SU(5) vacua, and scan up to 10^{12} GGSO configurations. Contrary to the corresponding Pati-Salam classification results, we do not find exophobic flippe...
Metastable vacua and D-branes at the conifold
Argurio, R; Franco, S; Kachru, S; Argurio, Riccardo; Bertolini, Matteo; Franco, Sebastian; Kachru, Shamit
2007-01-01
We consider quiver gauge theories arising on D-branes at simple Calabi-Yau singularities (quotients of the conifold). These theories have metastable supersymmetry breaking vacua. The field theoretic mechanism is basically the one exhibited by the examples of Intriligator, Seiberg and Shih in SUSY QCD. In a dual description, the SUSY breaking is captured by the presence of anti-branes. In comparison to our earlier related work, the main improvements of the present construction are that we can reach the free magnetic range of the SUSY QCD theory where the existence of the metastable vacua is on firm footing, and we can see explicitly how the small masses for the quark flavors (necessary to the existence of the SUSY breaking vacua) are dynamically stabilized. One crucial mass term is generated by a stringy instanton. Finally, our models naturally incorporate R-symmetry breaking in the non-supersymmetric vacuum, in a way similar to the examples of Kitano, Ooguri and Ookouchi.
An attractor for natural supersymmetry
Cohen, Timothy; Hook, Anson; Torroba, Gonzalo
2012-12-01
We propose an attractor mechanism which generates the more minimal supersymmetric standard model from a broad class of supersymmetry breaking boundary conditions. The hierarchies in the fermion masses and mixings are produced by the same dynamics and a natural weak scale results from gaugino mediation. These features arise from augmenting the standard model with a new SU(3) gauge group under which only the third generation quarks are charged. The theory flows to a strongly interacting fixed point which induces a negative anomalous dimension for the third generation quarks and a positive anomalous dimension for the Higgs. As a result, a split-family natural spectrum and the flavor hierarchies are dynamically generated.
Existence of the atmosphere attractor
Institute of Scientific and Technical Information of China (English)
李建平; 丑纪范
1997-01-01
The global asymptotic behavior of solutions for the equations of large-scale atmospheric motion with the non-stationary external forcing is studied in the infinite-dimensional Hilbert space. Based on the properties of operators of the equations, some energy inequalities and the uniqueness theorem of solutions are obtained. On the assumption that external forces are bounded, the exsitence of the global absorbing set and the atmosphere attractor is proved, and the characteristics of the decay of effect of initial field and the adjustment to the external forcing are revealed. The physical sense of the results is discussed and some ideas about climatic numerical forecast are elucidated.
Energy Technology Data Exchange (ETDEWEB)
Kaura, P. [Indian Institute of Technology Roorkee, Roorkee 247 667, Uttaranchal (India); Misara, A. [Enrico Fermi Institute, University of Chicago, Chicago, IL 60637 (United States)
2006-12-15
We look for possible nonsupersymmetric black hole attractor solutions for type II compactification on (the mirror of) CY{sub 3}(2,128) expressed as a degree-12 hypersurface in WCP{sup 4}[1,1,2,2,6]. In the process, (a) for points away from the conifold locus, we show that the existence of a non-supersymmetric attractor along with a consistent choice of fluxes and extremum values of the complex structure moduli, could be connected to the existence of an elliptic curve fibered over C{sup 8} which may also be ''arithmetic'' (in some cases, it is possible to interpret the extremization conditions for the black-hole superpotential as an endomorphism involving complex multiplication of an arithmetic elliptic curve), and (b) for points near the conifold locus, we show that existence of non-supersymmetric black-hole attractors corresponds to a version of A{sub 1}-singularity in the space Image(Z{sup 6}{yields}R{sup 2}/Z{sub 2}({yields}R{sup 3})) fibered over the complex structure moduli space. The (derivatives of the) effective black hole potential can be thought of as a real (integer) projection in a suitable coordinate patch of the Veronese map: CP{sup 5}{yields}CP{sup 20}, fibered over the complex structure moduli space. We also discuss application of Kallosh's attractor equations (which are equivalent to the extremization of the effective black-hole potential) for nonsupersymmetric attractors and show that (a) for points away from the conifold locus, the attractor equations demand that the attractor solutions be independent of one of the two complex structure moduli, and (b) for points near the conifold locus, the attractor equations imply switching off of one of the six components of the fluxes. Both these features are more obvious using the attractor equations than the extremization of the black hole potential. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
De Sitter vacua and inflation in no-scale string models
Energy Technology Data Exchange (ETDEWEB)
Gross, Christian
2009-09-15
This thesis studies the question of how de Sitter vacua and slow-roll inflation may be realized in string-motivated models. More specifically, we consider 4d N = 1 supergravity theories (without vector multiplets) with Kaehler potentials which are 'no-scale' at leading order. Such theories frequently arise in the moduli sector of string compactifications. We discuss a condition on the scalar geometry (defined by the Kaehler potential) and on the direction of supersymmetry breaking in the scalar manifold, which has to be met in order for the average of the masses of the sGoldstinos to be positive, and hence for metastable vacua to be possible. This condition also turns out to be necessary for the existence of trajectories admitting slow-roll inflation. Its implications for certain scalar manifolds which arise from Calabi-Yau string compactifications are discussed. In particular, for two-moduli models arising from compactifications of heterotic- and type IIB string theory, a simple criterion on the intersection numbers needs to be satisfied for possible de Sitter phases to exist. In addition, we show that subleading corrections breaking the no-scale property may allow the condition on the scalar geometry to be fulfilled, even when it is violated at leading order. Finally, we develop a procedure to construct superpotentials for a given viable Kaehler potential, such that the scalar potential has a realistic local minimum. We propose two-moduli models, with superpotentials which could arise from flux backgrounds and non-perturbative effects, which have a viable vacuum without employing subleading corrections or an uplifting sector. (orig.)
Generalized geometric vacua with eight supercharges
Graña, Mariana
2016-01-01
We investigate compactifications of type II and M-theory down to $AdS_5$ with generic fluxes that preserve eight supercharges, in the framework of Exceptional Generalized Geometry. The geometric data and gauge fields on the internal manifold are encoded in a pair of generalized structures corresponding to the vector and hyper-multiplets of the reduced five-dimensional supergravity. Supersymmetry translates into integrability conditions for these structures, generalizing, in the case of type IIB, the Sasaki-Einstein conditions. We show that the ten and eleven-dimensional type IIB and M-theory Killing-spinor equations specialized to a warped $AdS_5$ background imply the generalized integrability conditions.
Black Hole Attractors in Extended Supergravity
Ferrara, Sergio
2007-01-01
We review some aspects of the attractor mechanism for extremal black holes of (not necessarily supersymmetric) theories coupling Einstein gravity to scalars and Maxwell vector fields. Thence, we consider N=2 and N=8, d=4 supergravities, reporting some recent advances on the moduli spaces associated to BPS and non-BPS attractor solutions supported by charge orbits with non-compact stabilizers.
Non-minimal coupling and inflationary attractors
Yi, Zhu
2016-01-01
We show explicitly how the T-model, E-model and Hilltop inflations are obtained from the general scalar-tensor theory of gravity with arbitrary conformal factors in the strong coupling limit. We argue that $\\xi$ attractors can give any observables $n_s$ and $r$ by this method. The existence of attractors imposes a challenge to distinguish different models.
Strange attractor simulated on a quantum computer
2002-01-01
We show that dissipative classical dynamics converging to a strange attractor can be simulated on a quantum computer. Such quantum computations allow to investigate efficiently the small scale structure of strange attractors, yielding new information inaccessible to classical computers. This opens new possibilities for quantum simulations of various dissipative processes in nature.
de Sitter vacua in N=8 supergravity and slow-roll conditions
Energy Technology Data Exchange (ETDEWEB)
Dall' Agata, G., E-mail: dallagat@pd.infn.it [Dipartimento di Fisica ' Galileo Galilei' , Universita di Padova, Via Marzolo 8, 35131 Padova (Italy); INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova (Italy); Inverso, G. [Dipartimento di Fisica, Universita di Roma ' Tor Vergata' , Via della Ricerca Scientifica, 00133 Roma (Italy); INFN, Sezione di Roma 2, ' Tor Vergata' , Via della Ricerca Scientifica, 00133 Roma (Italy)
2013-01-08
In this Letter we discuss de Sitter vacua in maximal gauged supergravity in 4 dimensions. We show that, using the newly deformed theories introduced in Dall'Agata et al. (2012) [1], we can obtain de Sitter vacua with arbitrarily flat tachyonic directions in the SO(4,4){sub c} models.
Universality in radiative corrections for non-supersymmetric heterotic vacua
Angelantonj, C; Tsulaia, Mirian
2016-01-01
Properties of moduli-dependent gauge threshold corrections in non-supersymmetric heterotic vacua are reviewed. In the absence of space-time supersymmetry these amplitudes are no longer protected and receive contributions from the whole tower of string states, BPS and not. Never-theless, the difference of gauge thresholds for non-Abelian gauge groups displays a remarkable universality property, even when supersymmetry is absent. We present a simple heterotic construction that shares this universal behaviour and expose the necessary conditions on the super-symmetry breaking mechanism for universality to occur.
Asymmetric Orbifolds, Noncommutative Geometry and Type I String Vacua
Blumenhagen, R; Körs, B; Lüst, Dieter; Blumenhagen, Ralph; Goerlich, Lars; Kors, Boris; Lust, Dieter
2000-01-01
We investigate the D-brane contents of asymmetric orbifolds. Using T-dualitywe find that the consistent description of open strings in asymmetric orbifoldsrequires to turn on background gauge fields on the D-branes. Hence open stringsand D-branes in generic asymmetric orbifolds necessarily lead to noncommutativegeometry. We derive the corresponding noncommutative geometry arising on suchD-branes with mixed Neumann-Dirichlet boundary conditions by applying anasymmetric rotation to ordinary D-branes with pure Dirichlet boundaryconditions. As a concrete application of our results we construct asymmetrictype I vacua requiring open strings with mixed boundary conditions for tadpolecancellation.
STU attractors from vanishing concurrence
Lévay, Péter
2010-01-01
Concurrence is an entanglement measure characterizing the {\\it mixed} state bipartite correlations inside of a pure state of an $n$-qubit system. We show that after organizing the charges and the moduli in the STU model of $N=2$, $d=4$ supergravity to a three-qubit state, for static extremal spherically symmetric BPS black hole solutions the vanishing condition for all of the bipartite concurrences on the horizon is equivalent to the attractor equations. As a result of this the macroscopic black hole entropy given by the three-tangle can be reinterpreted as a linear entropy characterizing the {\\it pure} state entanglement for an arbitrary bipartite split. Both for the BPS and non-BPS cases explicit expressions for the concurrences are obtained, with their vanishing on the horizon is demonstrated.
Black Holes: Attractors for Intelligence?
Vidal, Clement
2011-01-01
The Search for Extra-Terrestrial Intelligence (SETI) has so far been unsuccessful and needs additional methods. We introduce a two-dimensional metric for civilization development, using the Kardashev scale of energy increase and the Barrow scale of inward manipulation. To support Barrow's scale limit, we contend with energetic, societal, scientific, computational, and philosophical arguments that black holes are attractors for intelligence. An application of the two-dimensional metric leads to a simple, consistent and observable hypothesis to test the existence of very advanced civilizations. We suggest that some already observed X-Ray binaries may be unnoticed advanced civilizations, of type KII-Bomega. The appendix provides an argumentative map of the paper's main thesis. KEYWORDS: SETI, black holes, Kardashev scale, Barrow scale, star lifting, XRB
Attractor Control Using Machine Learning
Duriez, Thomas; Noack, Bernd R; Cordier, Laurent; Segond, Marc; Abel, Markus
2013-01-01
We propose a general strategy for feedback control design of complex dynamical systems exploiting the nonlinear mechanisms in a systematic unsupervised manner. These dynamical systems can have a state space of arbitrary dimension with finite number of actuators (multiple inputs) and sensors (multiple outputs). The control law maps outputs into inputs and is optimized with respect to a cost function, containing physics via the dynamical or statistical properties of the attractor to be controlled. Thus, we are capable of exploiting nonlinear mechanisms, e.g. chaos or frequency cross-talk, serving the control objective. This optimization is based on genetic programming, a branch of machine learning. This machine learning control is successfully applied to the stabilization of nonlinearly coupled oscillators and maximization of Lyapunov exponent of a forced Lorenz system. We foresee potential applications to most nonlinear multiple inputs/multiple outputs control problems, particulary in experiments.
Instanton Corrected Non-Supersymmetric Attractors
Dominic, Pramod
2010-01-01
We discuss non-supersymmetric attractors with an instanton correction in Type IIA string theory compactified on a Calabi-Yau three-fold at large volume. For a stable non-supersymmetric black hole, the attractor point must minimize the effective black hole potential. We study the supersymmetric as well as non-supersymmetric attractors for the D0-D4 system with instanton corrections. We show that in simple models, like the STU model, the flat directions of the mass matrix can be lifted by a suitable choice of the instanton parameters.
Decaying turbulence and developing chaotic attractors
Bershadskii, A
2016-01-01
Competition between two main attractors of the distributed chaos, one associated with translational symmetry (homogeneity) and another associated with rotational symmetry (isotropy), has been studied in freely decaying turbulence. It is shown that, unlike the case of statistically stationary homogeneous isotropic turbulence, the attractor associated with rotational symmetry (and controlled by Loitsyanskii integral) can dominate turbulent local dynamics in an intermediate stage of the decay, because the attractor associated with translational symmetry (and controlled by Birkhoff-Saffman integral) is still not developed enough. The DNS data have been used in order to support this conclusion.
Quantum Vacua of 2d Maximally Supersymmetric Yang-Mills Theory
Koloğlu, Murat
2016-01-01
We analyze the classical and quantum vacua of 2d $\\mathcal{N}=(8,8)$ supersymmetric Yang-Mills theory with $SU(N)$ and $U(N)$ gauge group, describing the worldvolume interactions of $N$ parallel D1-branes with flat transverse directions $\\mathbb{R}^8$. We claim that the IR limit of the $SU(N)$ theory in the superselection sector labeled $M \\pmod{N}$ --- identified with the internal dynamics of $(M,N)$-string bound states of Type IIB string theory --- is described by the symmetric orbifold $\\mathcal{N}=(8,8)$ sigma model into $(\\mathbb{R}^8)^{D-1}/\\mathbb{S}_D$ when $D=\\gcd(M,N)>1$, and by a single massive vacuum when $D=1$, generalizing the conjectures of E. Witten and others. The full worldvolume theory of the D1-branes is the $U(N)$ theory with an additional $U(1)$ 2-form gauge field $B$ coming from the string theory Kalb-Ramond field. This $U(N)+B$ theory has generalized field configurations, labeled by the $\\mathbb{Z}$-valued generalized electric flux and an independent $\\mathbb{Z}_N$-valued 't Hooft flux...
N=2 vacua in electrically gauged N=4 supergravities
Energy Technology Data Exchange (ETDEWEB)
Horst, Christoph
2013-06-15
In this thesis we study N= 2 vacua in gauged N=4 supergravity theories in fourdimensional spacetime. Using the embedding tensor formalism that describes general consistent magnetic gaugings of an ungauged N=4 matter-coupled supergravity theory in a symplectic frame with SO(1,1) x SO(6,n) off-shell symmetry we formulate necessary conditions for partial supersymmetry breaking and find that the Killing spinor equations can be solved for the embedding tensor components. Subsequently, we show that the classification of theories that allow for vacua with partial supersymmetry amounts to solving a system of purely algebraic quadratic equations. Then, we restrict ourselves to the class of purely electric gaugings and explicitly construct a class of consistent super-Higgs mechanisms and study its properties. In particular, we find that the spectrum fills complete N=2 supermultiplets that are either massless or BPS. Furthermore, we demonstrate that (modulo an abelian Lie algebra) arbitrary unbroken gauge Lie algebras can be realized provided that the number of N=4 vector multiplets is sufficiently large. Finally, we compute the relevant terms of the effective action below the scale of partial supersymmetry breaking and argue that the special Kaehler manifold for the scalars of the N=2 vector multiplets has to be in the unique series of special Kaehler product manifolds.
Spinor-Vector Duality in N=2 Heterotic String Vacua
Faraggi, Alon E; Rizos, John
2007-01-01
Classification of the N=1 space-time supersymmetric fermionic Z2XZ2 heterotic-string vacua with symmetric internal shifts, revealed a novel spinor-vector duality symmetry over the entire space of vacua, where the S_t V duality interchanges the spinor plus anti-spinor representations with vector representations. In this paper we demonstrate that the spinor--vector duality exists also in fermionic Z2 heterotic string models, which preserve N=2 space-time supersymmetry. In this case the interchange is between spinorial and vectorial representations of the unbroken SO(12) GUT symmetry. We provide a general algebraic proof for the existence of the S_t V duality map. We present a novel basis to generate the free fermionic models in which the ten dimensional gauge degrees of freedom are grouped into four groups of four, each generating an SO(8) modular block. In the new basis the GUT symmetries are produced by generators arising from the trivial and non--trivial sectors, and due to the triality property of the SO(...
Non-Abelian magnetized blackholes and unstable attractors
Energy Technology Data Exchange (ETDEWEB)
Mosaffa, A.E. [Institute for Studies in Theoretical Physics and Mathematics (IPM), PO Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail: mosaffa@theory.ipm.ac.ir; Randjbar-Daemi, S. [The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11 34014, Trieste (Italy)], E-mail: seif@ictp.trieste.it; Sheikh-Jabbari, M.M. [Institute for Studies in Theoretical Physics and Mathematics (IPM), PO Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail: jabbari@theory.ipm.ac.ir
2008-01-21
Fluctuations of non-Abelian gauge fields in a background magnetic charge contain 'tachyonic' modes which as we will show cause an instability of the background. We extend this result to the cases where the background charge (flux) is coupled to four-dimensional Einstein gravity and show that the corresponding spherically symmetric geometries, which in the absence of a cosmological constant are of the form of (colored) Reissner-Nordstroem blackholes or the AdS{sub 2}xS{sup 2}, are also unstable unless the flux assumes its smallest allowed value, in which case the configuration is stable. We discuss the relevance of these instabilities to several places in string theory including various string compactifications and the attractor mechanism. Our results for the latter imply that the attractor mechanism shown to work for the extremal Abelian charged blackholes, cannot be applied in a straightforward way to the extremal non-Abelian colored blackholes, with the exception of the minimally charged stable ones.
How chaotic are strange nonchaotic attractors
Glendinning, Paul; Jaeger, Tobias; Keller, Gerhard
2006-01-01
We show that the classic example of quasiperiodically forced maps with strange nonchaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit sensitive dependence on initial conditions, both on the whole phase space and restricted to the attractor. The results also remain valid in more general classes of quasiperiodically forced systems. Further, we include an elementary proof of a classic result by...
A plethora of strange nonchaotic attractors
Indian Academy of Sciences (India)
Surendra Singh Negi; Ramakrishna Ramaswamy
2001-01-01
We show that it is possible to devise a large class of skew-product dynamical systems which have strange nonchaotic attractors (SNAs): the dynamics is asymptotically on fractal attractors and the largest Lyapunov exponent is non-positive. Furthermore, we show that quasiperiodic forcing, which has been a hallmark of essentially all hitherto known examples of such dynamics is not necessary for the creation of SNAs.
Strange Attractors in Drift Wave Turbulence
Energy Technology Data Exchange (ETDEWEB)
J.L.V. Lewandowski
2003-04-25
A multi-grid part-in-cell algorithm for a shearless slab drift wave model with kinetic electrons is presented. The algorithm, which is based on an exact separation of adiabatic and nonadiabatic electron responses, is used to investigate the presence of strange attractors in drift wave turbulence. Although the simulation model has a large number of degrees of freedom, it is found that the strange attractor is low-dimensional and that it is strongly affected by dissipative (collisional) effects.
The ''landscape'' of Pati-Salam heterotic superstring vacua
Energy Technology Data Exchange (ETDEWEB)
Rizos, J. [Theory Division, Physics Department, University of Ioannina, 45110 Ioannina (Greece)
2010-07-15
The main aspects of a recently developed method for classification of heterotic superstring vacua in the Free Fermionic Formulation are presented. Using these techniques we classify a big number of approximately 10{sup 15} heterotic string vacua with Pati-Salam, SU(4) x SU(2){sub L} x SU(2){sub R} gauge symmetry with respect to their main phenomenological features as the number of families, Pati-Salam breaking Higgs, Standard Model Higgs doublets, additional triplets and exotic charge states. We identify an interesting subclass of these vacua, approximately one to one million, whose massless spectrum is completely free of fractionally charge states. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Supersymmetry, attractors and cosmic censorship
Energy Technology Data Exchange (ETDEWEB)
Bellorin, Jorge [Instituto de Fisica Teorica UAM/CSIC, Facultad de Ciencias C-XVI, C.U. Cantoblanco, E-28049 Madrid (Spain)]. E-mail: jorge.bellorin@uam.es; Meessen, Patrick [Instituto de Fisica Teorica UAM/CSIC, Facultad de Ciencias C-XVI, C.U. Cantoblanco, E-28049 Madrid (Spain)]. E-mail: patrick.meessen@cern.ch; Ortin, Tomas [Instituto de Fisica Teorica UAM/CSIC, Facultad de Ciencias C-XVI, C.U. Cantoblanco, E-28049 Madrid (Spain)]. E-mail: tomas.ortin@cern.ch
2007-01-29
We show that requiring unbroken supersymmetry everywhere in black-hole-type solutions of N=2, d=4 supergravity coupled to vector supermultiplets ensures in most cases absence of naked singularities. We formulate three specific conditions which we argue are equivalent to the requirement of global supersymmetry. These three conditions can be related to the absence of sources for NUT charge, angular momentum, scalar hair and negative energy, although the solutions can still have globally defined angular momentum and non-trivial scalar fields, as we show in an explicit example. Furthermore, only the solutions satisfying these requirements seem to have a microscopic interpretation in string theory since only they have supersymmetric sources. These conditions exclude, for instance, singular solutions such as the Kerr-Newman with M=|q|, which fails to be everywhere supersymmetric. We also present a re-derivation of several results concerning attractors in N=2, d=4 theories based on the explicit knowledge of the most general solutions in the timelike class.
Alternative Attractors of Shallow Lakes
Directory of Open Access Journals (Sweden)
Marten Scheffer
2001-01-01
Full Text Available Ponds and shallow lakes can be very clear with abundant submerged plants, or very turbid due to a high concentration of phytoplankton and suspended sediment particles. These strongly contrasting ecosystem states have been found to represent alternative attractors with distinct stabilizing feedback mechanisms. In the turbid state, the development of submerged vegetation is prevented by low underwater light levels. The unprotected sediment frequently is resuspended by wave action and by fish searching for food causing a further decrease of transparency. Since there are no plants that could serve as refuges, zooplankton is grazed down by fish to densities insufficient to control algal blooms. In contrast, the clear state in eutrophic shallow lakes is dominated by aquatic macrophytes. The submerged macrophytes prevent sediment resuspension, take up nutrients from the water, and provide a refuge for zooplankton against fish predation. These processes buffer the impacts of increased nutrient loads until they become too high. Consequently, the response of shallow lakes to eutrophication tends to be catastrophic rather than smooth, and various lakes switch back and forth abruptly between a clear and a turbid state repeatedly without obvious external forcing. Importantly, a switch from a turbid to a stable clear state often can be invoked by means of biomanipulation in the form of a temporary reduction of the fish stock.
An Entropy-Weighted Sum over Non-Perturbative Vacua
Gregori, Andrea
2007-01-01
We discuss how, in a Universe restricted to the causal region connected to the observer, General Relativity implies the quantum nature of physical phenomena and directly leads to a string theory scenario, whose dynamics is ruled by a functional that weights all configurations according to their entropy. The most favoured configurations are those of minimal entropy. Along this class of vacua a four-dimensional space-time is automatically selected; when, at large volume, a description of space-time in terms of classical geometry can be recovered, the entropy-weighted sum reduces to the ordinary Feynman's path integral. What arises is a highly predictive scenario, phenomenologically compatible with the experimental observations and measurements, in which everything is determined in terms of the fundamental constants and the age of the Universe, with no room for freely-adjustable parameters. We discuss how this leads to the known spectrum of particles and interactions. Besides the computation of masses and coupli...
De Sitter Space, Interacting Quantum Field Theory And Alpha Vacua
Goldstein, K
2005-01-01
Inspired by recent evidence for a positive cosmological constant, this thesis considers some of the implications of trying to incorporate approximately seventy percent of the universe, namely dark energy, consistently into quantum field theory on a curved background. Such considerations may have implications for inflation, the understanding of dark energy at the present time and finally the challenging topic of trying to incorporate a positive cosmological constant into string theory. We will mainly examine various aspects of the one parameter family of de Sitter invariant states—the so called α-vacua. On the phenomenological side, not only could such states provide a window into trans-planckian physics through their imprint on the cosmological microwave background (CMB), but they may also be a source of ultra-high energy cosmic rays (UHECR) at the present time. From a purely theoretical perspective, formulating interacting quantum field theory in these states is a challenging problem whic...
Universality of gauge thresholds in non-supersymmetric heterotic vacua
Directory of Open Access Journals (Sweden)
Carlo Angelantonj
2014-09-01
Full Text Available We compute one-loop threshold corrections to non-abelian gauge couplings in four-dimensional heterotic vacua with spontaneously broken N=2→N=0 supersymmetry, obtained as Scherk–Schwarz reductions of six-dimensional K3 compactifications. As expected, the gauge thresholds are no-longer BPS protected, and receive contributions also from the excitations of the RNS sector. Remarkably, the difference of thresholds for non-abelian gauge couplings is BPS saturated and exhibits a universal behaviour independently of the orbifold realisation of K3. Moreover, the thresholds and their difference develop infra-red logarithmic singularities whenever charged BPS-like states, originating from the twisted RNS sector, become massless at special loci in the classical moduli space.
Universality of gauge thresholds in non-supersymmetric heterotic vacua
Energy Technology Data Exchange (ETDEWEB)
Angelantonj, Carlo, E-mail: carlo.angelantonj@unito.it [Dipartimento di Fisica, Università di Torino, and INFN Sezione di Torino, Via P. Giuria 1, 10125 Torino (Italy); Florakis, Ioannis, E-mail: florakis@mppmu.mpg.de [Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München (Germany); Tsulaia, Mirian, E-mail: mirian.tsulaia@canberra.edu.au [Faculty of Education Science Technology and Mathematics, University of Canberra, Bruce ACT 2617 (Australia)
2014-09-07
We compute one-loop threshold corrections to non-abelian gauge couplings in four-dimensional heterotic vacua with spontaneously broken N=2→N=0 supersymmetry, obtained as Scherk–Schwarz reductions of six-dimensional K3 compactifications. As expected, the gauge thresholds are no-longer BPS protected, and receive contributions also from the excitations of the RNS sector. Remarkably, the difference of thresholds for non-abelian gauge couplings is BPS saturated and exhibits a universal behaviour independently of the orbifold realisation of K3. Moreover, the thresholds and their difference develop infra-red logarithmic singularities whenever charged BPS-like states, originating from the twisted RNS sector, become massless at special loci in the classical moduli space.
Supersymmetry breaking metastable vacua in runaway quiver gauge theories
Garcia-Etxebarria, Inaki; Uranga, Angel M
2007-01-01
In this paper we consider quiver gauge theories with fractional branes whose infrared dynamics removes the classical supersymmetric vacua (DSB branes). We show that addition of flavors to these theories (via additional non-compact branes) leads to local meta-stable supersymmetry breaking minima, closely related to those of SQCD with massive flavors. We simplify the study of the one-loop lifting of the accidental classical flat directions by direct computation of the pseudomoduli masses via Feynman diagrams. This new approach allows to obtain analytic results for all these theories. This work extends the results for the $dP_1$ theory in hep-th/0607218. The new approach allows to generalize the computation to general examples of DSB branes, and for arbitrary values of the superpotential couplings.
The Flipped SU(5) String Vacua Classification A Variation Of The SO(10) Breaking Basis Vector
Sonmez, Hasan
2016-01-01
In this paper, an extension of the classification of flipped SU(5) heterotic-string vacua from [1] with a variation of the SO(10) breaking $\\alpha$ basis vector is presented. A statistical sampling in the space of $2^{45}$ flipped SU(5) vacua is explored, where $10^{11}$ GGSO distinct configurations are scanned in comparison to the $10^{12}$ GGSO distinct coefficients scanned in the space of $2^{44}$ vacua in [1]. A JAVA code, akin to the one used for the classification in [1], was implemented to explore these. Results presented here indicate that no three generation exophobic vacua exist, which was also found to be the case in [1] as all odd generations were projected out. This paper will also study the details on the comparison between the two classifications achieved and then reflect on future directions in the quest for finding three generation exophobic flipped SU(5) heterotic-string models.
Energy Technology Data Exchange (ETDEWEB)
Misra, Aalok [Department of Physics, Indian Institute of Technology, Roorkee 247 667, Uttaranchal (India); Physics Department, Theory Unit, CERN, CH-1211 Geneva 23 (Switzerland)], E-mail: aalokfph@iitr.ernet.in; Shukla, Pramod [Department of Physics, Indian Institute of Technology, Roorkee 247 667, Uttaranchal (India)], E-mail: pmathdph@iitr.ernet.in
2008-08-11
We consider two sets of issues in this paper. The first has to do with moduli stabilization, existence of 'area codes' [A. Giryavets, New attractors and area codes, JHEP 0603 (2006) 020, (hep-th/0511215)] and the possibility of getting a non-supersymmetric dS minimum without the addition of D3-bar-branes as in KKLT for type II flux compactifications. The second has to do with the 'inverse problem' [K. Saraikin, C. Vafa, Non-supersymmetric black holes and topological strings, (hep-th/0703214)] and 'fake superpotentials' [A. Ceresole, G. Dall'Agata, Flow equations for non-BPS extremal black holes, JHEP 0703 (2007) 110, (hep-th/0702088)] for extremal (non-)supersymmetric black holes in type II compactifications. We use (orientifold of) a 'Swiss cheese' Calabi-Yau [J.P. Conlon, F. Quevedo, K. Suruliz, Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 0508 (2005) 007, (hep-th/0505076)] expressed as a degree-18 hypersurface in WCP{sup 4}[1,1,1,6,9] in the 'large-volume-scenario' limit [V. Balasubramanian, P. Berglund, J.P. Conlon, F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 0503 (2005) 007, (hep-th/0502058)]. The main result of our paper is that we show that by including non-perturbative {alpha}{sup '} and instanton corrections in the Kaehler potential and superpotential [T.W. Grimm, Non-perturbative corrections and modularity in N=1 type IIB compactifications, (arXiv: 0705.3253 [hep-th])], it may be possible to obtain a large-volume non-supersymmetric dS minimum without the addition of anti-D3 branes a la KKLT. The chosen Calabi-Yau has been of relevance also from the point of other studies of Kaehler moduli stabilization via non-perturbative instanton contributions [F. Denef, M.R. Douglas, B. Florea, Building a better racetrack, JHEP 0406 (2004) 034, (hep-th/0404257)] and non-supersymmetric AdS vacua (and their
GLOBAL ATTRACTOR FOR THE NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES
Institute of Scientific and Technical Information of China (English)
戴正德; 杜先云
2001-01-01
In this paper the authors consider the initial boundary value problems of the generalized nonlinear strain waves in elastic waveguides and prove the existence of global attractors and thefiniteness of the Hausdorff and the fractal dimensions of the attractors.
Homogenization of attractors for a class of nonlinear parabolic equations
Institute of Scientific and Technical Information of China (English)
WANG Guo-lian; ZHANG Xing-you
2004-01-01
The relation between the global attractors Aε for a calss of quasilinear parabolic equations and the global attractor A0for the homogenized equation is discussed, and an explicit error estimate between Aε and A0 is given.
Renormalization group independence of Cosmological Attractors
Fumagalli, Jacopo
2017-06-01
The large class of inflationary models known as α- and ξ-attractors gives identical cosmological predictions at tree level (at leading order in inverse power of the number of efolds). Working with the renormalization group improved action, we show that these predictions are robust under quantum corrections. This means that for all the models considered the inflationary parameters (ns , r) are (nearly) independent on the Renormalization Group flow. The result follows once the field dependence of the renormalization scale, fixed by demanding the leading log correction to vanish, satisfies a quite generic condition. In Higgs inflation (which is a particular ξ-attractor) this is indeed the case; in the more general attractor models this is still ensured by the renormalizability of the theory in the effective field theory sense.
Cosmological Attractor Models and Higher Curvature Supergravity
Cecotti, Sergio
2014-01-01
We study cosmological $\\alpha$-attractors in superconformal/supergravity models, where $\\alpha$ is related to the geometry of the moduli space. For $\\alpha=1$ attractors \\cite{Kallosh:2013hoa} we present a generalization of the previously known manifestly superconformal higher curvature supergravity model \\cite{Cecotti:1987sa}. The relevant standard 2-derivative supergravity with a minimum of two chiral multiplets is shown to be dual to a 4-derivative higher curvature supergravity, where in general one of the chiral superfields is traded for a curvature superfield. There is a degenerate case when both matter superfields become non-dynamical and there is only a chiral curvature superfield, pure higher derivative supergravity. Generic $\\alpha$-models \\cite{Kallosh:2013yoa} interpolate between the attractor point at $\\alpha=0$ and generic chaotic inflation models at large $\\alpha$, in the limit when the inflaton moduli space becomes flat. They have higher derivative duals with the same number of matter fields as...
Generalized Attractors in Five-Dimensional Gauged Supergravity
Inbasekar, Karthik
2012-01-01
In this paper we study study generalized attractors in N=2 gauged supergravity theory in five dimensions coupled to arbitrary number of hyper, vector and tensor multiplets. We look for attractor solutions with constant anholonomy coefficients. By analyzing the equations of motion we derive the attractor potential. We further show that the generalized attractor potential can be obtained from the fermionic shifts. We study some simple examples and show that constant anholonomy gives rise to homogeneous black branes in five dimensions.
Random attractors for asymptotically upper semicompact multivalue random semiflows
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The present paper studied the dynamics of some multivalued random semiflow. The corresponding concept of random attractor for this case was introduced to study asymptotic behavior. The existence of random attractor of multivalued random semiflow was proved under the assumption of pullback asymptotically upper semicompact, and this random attractor is random compact and invariant. Furthermore, if the system has ergodicity, then this random attractor is the limit set of a deterministic bounded set.
Renormalization Group independence of Cosmological Attractors
Fumagalli, Jacopo
2016-01-01
The large class of inflationary models known as $\\alpha$- and $\\xi$-attractors give identical predictions at tree level (at leading order in inverse power of the number of efolds). Working with the renormalization group improved action, we show that these predictions are robust under quantum corrections. This result follows once the field dependence of the renormalization scale, fixed by demanding the leading log correction to vanish, satisfies a quite generic condition. In Higgs inflation this is indeed the case; in the more general attractor models this is still ensured by the renormalizability of the theory in the effective field theory sense.
Erice Lectures on Black Holes and Attractors
Ferrara, Sergio; Marrani, A
2008-01-01
These lectures give an elementary introduction to the subject of four dimensional black holes (BHs) in supergravity and the Attractor Mechanism in the extremal case. Some thermodynamical properties are discussed and some relevant formulae for the critical points of the BH effective potential are given. The case of Maxwell-Einstein-axion-dilaton (super)gravity is discussed in detail. Analogies among BH entropy and multipartite entanglement of qubits in quantum information theory, as well moduli spaces of extremal BH attractors, are also discussed.
Embedding of global attractors and their dynamics
de Moura, Eleonora Pinto; Sánchez-Gabites, Jaime J
2010-01-01
Using shape theory and the concept of cellularity, we show that if $A$ is the global attractor associated with a dissipative partial differential equation in a real Hilbert space $H$ and the set $A-A$ has finite Assouad dimension $d$, then there is an ordinary differential equation in ${\\mathbb R}^{m+1}$, with $m >d$, that has unique solutions and reproduces the dynamics on $A$. Moreover, the dynamical system generated by this new ordinary differential equation has a global attractor $X$ arbitrarily close to $LA$, where $L$ is a homeomorphism from $A$ into ${\\mathbb R}^{m+1}$.
Bubbling and riddling of higher-dimensional attractors
Energy Technology Data Exchange (ETDEWEB)
Kapitaniak, Tomasz; Maistrenko, Yuri; Grebogi, Celso
2003-07-01
We analyze the bifurcation in which one of the unstable periodic orbits embedded in a higher-dimensional chaotic attractor becomes unstable transversely to the attractor. The existence of such local transversal instability may cause the bubbling of the attractor in the invariant manifold or it may cause the riddling of the basin of attraction.
The flux-scaling scenario. De Sitter uplift and axion inflation
Energy Technology Data Exchange (ETDEWEB)
Blumenhagen, Ralph; Damian, Cesar; Herschmann, Daniela; Sun, Rui [Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Muenchen (Germany); Font, Anamaria [Departamento de Fisica, Centro de Fisica Teorica y Computacional, Facultad de Ciencias, Universidad Central de Venezuela, Caracas (Venezuela, Bolivarian Republic of)
2016-06-15
Non-geometric flux-scaling vacua provide promising starting points to realize axion monodromy inflation via the F-term scalar potential. We show that these vacua can be uplifted to Minkowski and de Sitter by adding an D3-brane or a D-term containing geometric and non-geometric fluxes. These uplifted non-supersymmetric models are analyzed with respect to their potential to realize axion monodromy inflation self-consistently. Admitting rational values of the fluxes, we construct examples with the required hierarchy of mass scales. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Sneutrino Inflation with α-attractors
Energy Technology Data Exchange (ETDEWEB)
Kallosh, Renata; Linde, Andrei [Stanford Institute of Theoretical Physics and Department of Physics, Stanford University, Stanford, 94305 CA (United States); Roest, Diederik [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Theoretical Physics Department, CERN, CH-1211 Geneva 23 (Switzerland); Wrase, Timm [Institute for Theoretical Physics, TU Wien, A-1040 Vienna (Austria)
2016-11-22
Sneutrino inflation employs the fermionic partners of the inflaton and stabilizer field as right-handed neutrinos to realize the seesaw mechanism for light neutrino masses. We show that one can improve the latest version of this scenario and its consistency with the Planck data by embedding it in the theory of cosmological α-attractors.
Semicontinuity of attractors for impulsive dynamical systems
Bonotto, E. M.; Bortolan, M. C.; Collegari, R.; Czaja, R.
2016-10-01
In this paper we introduce the concept of collective tube conditions which assures a suitable behaviour for a family of dynamical systems close to impulsive sets. Using the collective tube conditions, we develop the theory of upper and lower semicontinuity of global attractors for a family of impulsive dynamical systems.
Prototypes of attractors in four dimensions
DEFF Research Database (Denmark)
Baier, G.; Thomsen, Jesper Skovhus
1993-01-01
We study an extension of Duffing's equation to three variables with external forcing. Starting from a phase-space preserving chaos, three prototypes of chaotic attractors with a dimension larger than 3 can be derived. We provide examples of hyperchaos and a ''bifractal'' in a four-dimensional how...
Trajectory attractors of equations of mathematical physics
Energy Technology Data Exchange (ETDEWEB)
Vishik, Marko I; Chepyzhov, Vladimir V [Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow (Russian Federation)
2011-08-31
In this survey the method of trajectory dynamical systems and trajectory attractors is described, and is applied in the study of the limiting asymptotic behaviour of solutions of non-linear evolution equations. This method is especially useful in the study of dissipative equations of mathematical physics for which the corresponding Cauchy initial-value problem has a global (weak) solution with respect to the time but the uniqueness of this solution either has not been established or does not hold. An important example of such an equation is the 3D Navier-Stokes system in a bounded domain. In such a situation one cannot use directly the classical scheme of construction of a dynamical system in the phase space of initial conditions of the Cauchy problem of a given equation and find a global attractor of this dynamical system. Nevertheless, for such equations it is possible to construct a trajectory dynamical system and investigate a trajectory attractor of the corresponding translation semigroup. This universal method is applied for various types of equations arising in mathematical physics: for general dissipative reaction-diffusion systems, for the 3D Navier-Stokes system, for dissipative wave equations, for non-linear elliptic equations in cylindrical domains, and for other equations and systems. Special attention is given to using the method of trajectory attractors in approximation and perturbation problems arising in complicated models of mathematical physics. Bibliography: 96 titles.
Large Global Coupled Maps with Multiple Attractors
Carusela, M F; Romanelli, L
1999-01-01
A system of N unidimensional global coupled maps (GCM), which support multiattractors is studied. We analize the phase diagram and some special features of the transitions (volume ratios and characteristic exponents), by controlling the number of elements of the initial partition that are in each basin of attraction. It was found important difference with widely known coupled systems with a single attractor.
ATTRACTORS FOR THE BRUSSELATOR IN RN
Institute of Scientific and Technical Information of China (English)
Han Yongqian; Guo Boling
2007-01-01
We consider the reaction-diffusion system, a model of a certain chemical morphogenetic process and named Brusselator. For the Cauchy problem of this system with nondecaying initial data, the existence and uniqueness of the global solution is established. Moreover, it is proved that this system possesses a global attractor A in the corresponding phase space.
Attractor black holes and quantum distribution functions
Energy Technology Data Exchange (ETDEWEB)
Montanez, S. [Instituto de Fisica Teorica CSIC-UAM, Modulo C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Gomez, C. [Instituto de Fisica Teorica CSIC-UAM, Modulo C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Theory Group, Physics Department, CERN, 1211 Geneva 23 (Switzerland)
2007-05-15
Using the attractor mechanism and the wavefunction interpretation of the topological string partition function on a Calabi Yau threefold M we study the relation between the Bekenstein-Hawking-Wald entropy of BPS Calabi-Yau black holes and quantum distribution functions defined on H{sup 3}(M). We discuss the OSV conjecture in this context. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
The Hyperbolic Geometry of Cosmological Attractors
Carrasco, John Joseph M.; Kallosh, Renata; Linde, Andrei; Roest, Diederik
2015-01-01
Cosmological alpha-attractors give a natural explanation for the spectral index n_s of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r, consistent with all observations, to be measured more precisely in future detection of gravity waves. Their embedding into
Energy Technology Data Exchange (ETDEWEB)
Linde, Andrei [Department of Physics and SITP, Stanford University,Stanford, California 94305 (United States)
2015-05-05
I describe a simple class of α-attractors, generalizing the single-field GL model of inflation in supergravity. The new class of models is defined for 0<α≲1, providing a good match to the present cosmological data. I also present a generalized version of these models which can describe not only inflation but also dark energy and supersymmetry breaking.
Cosmological attractors from alpha-scale supergravity
Roest, Diederik; Scalisi, Marco
2015-01-01
The Planck value of the spectral index can be interpreted as n(s) = 1 - 2/N in terms of the number of e-foldings N. An appealing explanation for this phenomenological observation is provided by alpha-attractors: the inflationary predictions of these supergravity models are fully determined by the cu
The velocities of light in modified QED vacua
Scharnhorst, K
1998-01-01
QED vacua under the influence of external conditions (background fields, finite temperature, boundary conditions) can be considered as dispersive media whose complex behaviour can no longer be described in terms of a single universal vacuum velocity of light c. Beginning in the early 1950's (J.S. Toll), quantum field theoretic investigations have led to considerable insight into the relation between the vacuum structure and the propagation of light. Recent years have witnessed a significant growth of activity in this field of research. After a short overview, two characteristic situations are discussed: the propagation of light in a constant homogeneous magnetic field and in a Casimir vacuum. The latter appears to be particularly interesting because the Casimir vacuum has been found to exhibit modes of the propagation of light with phase and group velocities larger than c in the low frequency domain omega<
Exploring viable vacua of the Z 3-symmetric NMSSM
Beuria, Jyotiranjan; Chattopadhyay, Utpal; Datta, AseshKrishna; Dey, Abhishek
2017-04-01
We explore the vacua of the Z 3-symmetric Next-to-Minimal Supersymmetric Standard Model (NMSSM) and their stability by going beyond the simplistic paradigm that works with a tree-level neutral scalar potential and adheres to some specific flat directions in the field space. We work in the so-called phenomenological NMSSM (pNMSSM) scenario. Also, for our purpose, we adhere to a reasonably `natural' setup by requiring | μ eff| not too large. Key effects are demonstrated by first studying the profiles of this potential under various circumstances of physical interest via a semi-analytical approach. The results thereof are compared to the ones obtained from a dedicated package like Vevacious which further incorporates the thermal effects to the potential. Regions of the pNMSSM parameter space that render the desired symmetry breaking (DSB) vacuum absolutely stable, long- or short-lived (in relation to the age of the Universe) under quantum/thermal tunneling are delineated. Regions that result in the appearance of color and charge breaking (CCB) minima are also presented. It is demonstrated that light singlet scalars along with a light LSP (lightest supersymmetric particle) having an appreciable singlino admixture are compatible with a viable DSB vacuum. Their implications for collider experiments are commented upon.
Lifshitz and Schrodinger Vacua, Superstar Resolution in Gauged Maximal Supergravities
Liu, Hai-Shan
2013-01-01
We consider the subset of gauged maximal supergravities that consists of the SO(n+1) gauge fields A^{ij} and the scalar deformation T^{ij} of the S^n in the spherical reduction of M-theory or type IIB. We focus on the Abelian Cartan subgroup and the diagonal entries of T^{ij}. The resulting theories can be viewed as the STU models with additional hyperscalars. We find that the theories with only one or two such vectors can be generalized naturally to arbitrary dimensions. The same is true for the D=4 or 5 Einstein-Maxwell theory with such a hyperscalar. The gauge fields become massive, determined by stationary points of the hyperscalars a la the analogous Abelian Higgs mechanism. We obtain classes of Lifshitz and Schrodinger vacua in these theories. The scaling exponent z turns out to be rather restricted, taking fractional or irrational numbers. Tweaking the theories by relaxing the mass parameter or making a small change of the superpotential, we find that solutions with z=2 can emerge. In a different appli...
Speed of light in non-trivial vacua
Latorre, J I; Tarrach, Rolf
1994-01-01
We unify all existing results on the change of the speed of low--energy photons due to modifications of the vacuum, finding that it is given by a universal constant times the quotient of the difference of energy densities between the usual and modified vacua over the mass of the electron to the fourth power. Whether photons move faster or slower than c depends only on the lower or higher energy density of the modified vacuum, respectively. Physically, a higher energy density is characterized by the presence of additional particles (real or virtual) in the vacuum whereas a lower one stems from the absence of some virtual modes. We then carry out a systematic study of the speed of propagation of massless particles for several field theories up to two loops on a thermal vacuum. Only low--energy massless particles corresponding to a massive theory show genuine modifications of their speed while remaining massless. All other modifications are mass-related, or running mass-related. We also develop a formalism for t...
Energy Technology Data Exchange (ETDEWEB)
Llibre, Jaume, E-mail: jllibre@mat.uab.cat [Universitat Autònoma de Barcelona, Departament de Matemàtiques (Spain); Valls, Claudia, E-mail: cvalls@math.ist.utl.pt [Universidade de Lisboa, Departamento de Matemática, Instituto Superior Técnico (Portugal)
2017-06-15
For a dynamical system described by a set of autonomous differential equations, an attractor can be either a point, or a periodic orbit, or even a strange attractor. Recently a new chaotic system with only one parameter has been presented where besides a point attractor and a chaotic attractor, it also has a coexisting attractor limit cycle which makes evident the complexity of such a system. We study using analytic tools the dynamics of such system. We describe its global dynamics near the infinity, and prove that it has no Darboux first integrals.
Froggatt, C; Nielsen, H B; Thomas, A
2015-01-01
We argue that the exact degeneracy of vacua in N=1 supergravity can shed light on the smallness of the cosmological constant. The presence of such vacua, which are degenerate to very high accuracy, may also result in small values of the quartic Higgs coupling and its beta function at the Planck scale in the phase in which we live.
Sneutrino Inflation with $\\alpha$-attractors
Kallosh, Renata; Roest, Diederik; Wrase, Timm
2016-01-01
Sneutrino inflation employs the fermionic partners of the inflaton and stabilizer field as right-handed neutrinos to realize the seesaw mechanism for light neutrino masses. A crucial ingredient in existing constructions for sneutrino (multi-)natural inflation is an unbroken discrete shift symmetry. We demonstrate that a similar construction applies to $\\alpha$-attractor models. In this case the hyperbolic geometry protects the neutrino Yukawa couplings to the inflaton field, and the masses of leptons and Higgs fields, from blowing up when the inflaton is super-Planckian. We find that the predictions for $n_s$ and $r$ for $\\alpha$-attractor cosmological models, compatible with the current cosmological data, are preserved in the presence of the neutrino sector.
Stability of Bianchi attractors in Gauged Supergravity
Inbasekar, Karthik
2013-01-01
In this paper, we analyse the stability of extremal black brane horizons with homogeneous symmetry in the spatial directions in five dimensional gauged supergravity, under the fluctuations of the scalar fields about their attractor values. We examine the scalar fluctuation equations at the linearised level and demand that the fluctuations vanish as one approaches the horizon. Imposing certain restrictions on the Killing vectors used for gauging we find that the necessary conditions for stability are satisfied only by a subclass of the Bianchi metrics whose symmetry group factorises into a two dimensional Lifshitz symmetry and any homogeneous symmetry group given by the Bianchi classification. We apply these results to a simple example of a gauged supergravity model with one vector multiplet to find the stable attractors.
Gravitational waves in $\\alpha-$attractors
Kumar, K Sravan; Moniz, Paulo Vargas; Das, Suratna
2015-01-01
We study inflation in the $\\alpha-$attractor model under a non-slow-roll dynamics with an ansatz proposed by Gong \\& Sasaki \\cite{Gong:2015ypa} of assuming $N=N\\left(\\phi\\right)$. Under this approach, we construct a class of local shapes of inflaton potential that are different from the T-models. We find this type of inflationary scenario predicts an attractor at $n_{s}\\sim0.967$ and $r\\sim0.00055$. In our approach, the non-slow-roll inflaton dynamics are related to the $\\alpha-$parameter which is the curvature of K\\"ahler geometry in the SUGRA embedding of this model.
Attractor dynamics in local neuronal networks
Directory of Open Access Journals (Sweden)
Jean-Philippe eThivierge
2014-03-01
Full Text Available Patterns of synaptic connectivity in various regions of the brain are characterized by the presence of synaptic motifs, defined as unidirectional and bidirectional synaptic contacts that follow a particular configuration and link together small groups of neurons. Recent computational work proposes that a relay network (two populations communicating via a third, relay population of neurons can generate precise patterns of neural synchronization. Here, we employ two distinct models of neuronal dynamics and show that simulated neural circuits designed in this way are caught in a global attractor of activity that prevents neurons from modulating their response on the basis of incoming stimuli. To circumvent the emergence of a fixed global attractor, we propose a mechanism of selective gain inhibition that promotes flexible responses to external stimuli. We suggest that local neuronal circuits may employ this mechanism to generate precise patterns of neural synchronization whose transient nature delimits the occurrence of a brief stimulus.
Quantum chaotic attractor in a dissipative system
Liu, W V; Schieve, William C.
1997-01-01
A dissipative quantum system is treated here by coupling it with a heat bath of harmonic oscillators. Through quantum Langevin equations and Ehrenfest's theorem, we establish explicitly the quantum Duffing equations with a double-well potential chosen. A quantum noise term appears the only driving force in dynamics. Numerical studies show that the chaotic attractor exists in this system while chaos is certainly forbidden in the classical counterpart.
Dimensions of attractors in pinched skew products
Gröger, M.; Jäger, T.
2011-01-01
We study dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the pointwise dimension and the information dimension are all equal to one, although the box-counting dimension is known to be two. The assertion concerning the pointwise dimension is deduced from the stronger result that the physical measure is rectifiable. Our findi...
Exponential Attractor for a Nonlinear Boussinesq Equation
Institute of Scientific and Technical Information of China (English)
Ahmed Y. Abdallah
2006-01-01
This paper is devoted to prove the existence of an exponential attractor for the semiflow generated by a nonlinear Boussinesq equation. We formulate the Boussinesq equation as an abstract equation in the Hilbert space H20(0, 1) × L2(0, 1). The main step in this research is to show that there exists an absorbing set for the solution semiflow in the Hilbert space H03(0, 1) × H10(0, 1).
Dark Energy density in models with Split Supersymmetry and degenerate vacua
Froggatt, C; Nielsen, H B
2011-01-01
The breakdown of global symmetries, which protect a zero value for the cosmological constant in supergravity (SUGRA) models, may lead to a set of degenerate vacua with broken and unbroken supersymmetry (SUSY) whose vacuum energy densities vanish in the leading approximation. Assuming the degeneracy of vacua with broken and unbroken SUSY originating in the hidden sector, we estimate the value of the cosmological constant. We argue that the observed value of the dark energy density can be reproduced in the Split-SUSY scenario if the SUSY breaking scale is of order of 10^{10} GeV.
Generalised universality of gauge thresholds in heterotic vacua with and without supersymmetry
Directory of Open Access Journals (Sweden)
Carlo Angelantonj
2015-11-01
Full Text Available We study one-loop quantum corrections to gauge couplings in heterotic vacua with spontaneous supersymmetry breaking. Although in non-supersymmetric constructions these corrections are not protected and are typically model dependent, we show how a universal behaviour of threshold differences, typical of supersymmetric vacua, may still persist. We formulate specific conditions on the way supersymmetry should be broken for this to occur. Our analysis implies a generalised notion of threshold universality even in the case of unbroken supersymmetry, whenever extra charged massless states appear at enhancement points in the bulk of moduli space. Several examples with universality, including non-supersymmetric chiral models in four dimensions, are presented.
Comments on A, B, C Chains of Heterotic and Type II Vacua
Candelas, Philip; Rajesh, G; Candelas, Philip; Perevalov, Eugene; Rajesh, Govindan
1997-01-01
We construct, as hypersurfaces in toric varieties, Calabi-Yau manifolds corresponding to F-theory vacua dual to E8*E8 heterotic strings compactified to six dimensions on K3 surfaces with non-semisimple gauge backgrounds. These vacua were studied in the recent work of Aldazabal, Font, Ibanez and Uranga. We extend their results by constructing many more examples, corresponding to enhanced gauge symmetries, by noting that they can be obtained from previously known Calabi-Yau manifolds corresponding to K3 compactification of heterotic strings with simple gauge backgrounds by means of extremal transitions of the conifold type.
Generalised universality of gauge thresholds in heterotic vacua with and without supersymmetry
Angelantonj, Carlo; Tsulaia, Mirian
2015-01-01
We study one-loop quantum corrections to gauge couplings in heterotic vacua with spontaneous supersymmetry breaking. Although in non-supersymmetric constructions these corrections are not protected and are typically model dependent, we show how a universal behaviour of threshold differences, typical of supersymmetric vacua, may still persist. We formulate specific conditions on the way supersymmetry should be broken for this to occur. Our analysis implies a generalised notion of threshold universality even in the case of unbroken supersymmetry, whenever extra charged massless states appear at enhancement points in the bulk of moduli space. Several examples with universality, including non-supersymmetric chiral models in four dimensions, are presented.
Dissipative relativistic standard map: Periodic attractors and basins of attraction
Energy Technology Data Exchange (ETDEWEB)
Lan, Boon Leong [Monash University, School of Engineering, Bandar Sunway, Selangor (Malaysia)], E-mail: lan.boon.leong@eng.monash.edu.my; Yapp, Clarence [Monash University, School of Engineering, Bandar Sunway, Selangor (Malaysia)
2008-09-15
The dissipative relativistic standard map, introduced by Ciubotariu et al. [Ciubotariu C, Badelita L, Stancu V. Chaos in dissipative relativistic standard maps. Chaos, Solitons and Fractals 2002;13:1253-67.], is further studied numerically for small damping in the resonant case. We find that the attractors are all periodic; their basins of attraction have fractal boundaries and are closely interwoven. The number of attractors increases with decreasing damping. For a very small damping, there are thousands of periodic attractors, comprising mostly of the lowest-period attractors of period one or two; the basin of attraction of these lowest-period attractors is significantly larger compared to the basins of the higher-period attractors.
Sourcing Dark Matter and Dark Energy from $\\alpha$-attractors
Mishra, Swagat S.; Sahni, Varun; Shtanov, Yuri(Department of Physics, Taras Shevchenko National University, Kiev, Ukraine)
2017-01-01
Recently, Kallosh and Linde have drawn attention to a new family of superconformal inflationary potentials, subsequently called $\\alpha$-attractors. The $\\alpha$-attractor family can interpolate between a large class of inflationary models. It also has an important theoretical underpinning within the framework of supergravity. We demonstrate that the $\\alpha$-attractors have an even wider appeal since they may describe dark matter and perhaps even dark energy. The dark matter associated with ...
ATTRACTORS FOR DISCRETIZATION OF GINZBURG-LANDAU-BBM EQUATIONS
Institute of Scientific and Technical Information of China (English)
Mu-rong Jiang; Bo-ling Guo
2001-01-01
In this paper, Ginzburg-Landau equation coupled with BBM equationwith periodic initial boundary value conditions are discreted by the finite difference method in spatial direction. Existence of the attractors for the spatially discreted Ginzburg-Landau-BBM equations is proved. For each mesh size, there exist attractors for the discretized system. Moreover, finite Hausdorff and fractal dimensions of the discrete attractors are obtained and the bounds are independent of the mesh sizes.
Symmetry Constraints in Inflation, $\\alpha$-vacua, and the Three Point Function
Shukla, Ashish; Vishal, V
2016-01-01
The Ward identities for conformal symmetries in single field models of inflation are studied in more detail in momentum space. For a class of generalized single field models, where the inflaton action contains arbitrary powers of the scalar and its first derivative, we find that the Ward identities are valid. We also study a one-parameter family of vacua, called $\\alpha$-vacua, which preserve conformal invariance in de Sitter space. We find that the Ward identities, upto contact terms, are met for the three point function of a scalar field in the probe approximation in these vacua. Interestingly, the corresponding non-Gaussian term in the wave function does not satisfy the operator product expansion. For scalar perturbations in inflation, in the $\\alpha$-vacua, we find that the Ward identities are not satisfied. We argue that this is because the back-reaction on the metric of the full quantum stress tensor has not been self-consistently incorporated. We also present a calculation, drawing on techniques from t...
A Farey tail for attractor black holes
de Boer, Jan; Cheng, Miranda C. N.; Dijkgraaf, Robbert; Manschot, Jan; Verlinde, Erik
2006-11-01
The microstates of 4d BPS black holes in IIA string theory compactified on a Calabi-Yau manifold are counted by a (generalized) elliptic genus of a (0,4) conformal field theory. By exploiting a spectral flow that relates states with different charges, and using the Rademacher formula, we find that the elliptic genus has an exact asymptotic expansion in terms of semi-classical saddle-points of the dual supergravity theory. This generalizes the known "Black Hole Farey Tail" of [1] to the case of attractor black holes.
A Farey Tail for Attractor Black Holes
De Boer, J; Dijkgraaf, R; Manschot, J; Verlinde, E; Boer, Jan de; Cheng, Miranda C.N.; Dijkgraaf, Robbert; Manschot, Jan; Verlinde, Erik
2006-01-01
The microstates of 4d BPS black holes in IIA string theory compactified on a Calabi-Yau manifold are counted by a (generalized) elliptic genus of a (0,4) conformal field theory. By exploiting a spectral flow that relates states with different charges, and using the Rademacher formula, we find that the elliptic genus has an exact asymptotic expansion in terms of semi-classical saddle-points of the dual supergravity theory. This generalizes the known "Black Hole Farey Tail" of [1] to the case of attractor black holes.
Dimensions of Attractors in Pinched Skew Products
Gröger, M.; Jäger, T.
2013-05-01
We study dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the pointwise dimension and the information dimension are all equal to one, although the box-counting dimension is known to be two. The assertion concerning the pointwise dimension is deduced from the stronger result that the physical measure is rectifiable. Our findings confirm a conjecture by Ding, Grebogi and Ott from 1989.
Dimensions of attractors in pinched skew products
Gröger, M
2011-01-01
We study dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the pointwise dimension and the information dimension are all equal to one, although the box-counting dimension is known to be two. The assertion concerning the pointwise dimension is deduced from the stronger result that the physical measure is rectifiable. Our findings confirm a conjecture by Ding, Grebogi and Ott from 1989.
3rd School on Attractor Mechanism
SAM 2007; The Attractor Mechanism: Proceedings of the INFN-Laboratori Nazionali di Frascati School 2007
2010-01-01
This book is based upon lectures presented in June 2007 at the INFN-Laboratori Nazionali di Frascati School on Attractor Mechanism, directed by Stefano Bellucci. The symposium included such prestigious lecturers as S. Ferrara, M. Gunaydin, P. Levay, and T. Mohaupt. All lectures were given at a pedagogical, introductory level, which is reflected in the specific "flavor" of this volume. The book also benefits from extensive discussions about, and related reworking of, the various contributions. In addition, this volume contains contributions originating from short presentations of rece
Energy cascade in internal wave attractors
Brouzet, Christophe; Joubaud, Sylvain; Sibgatullin, Ilias; Dauxois, Thierry
2016-01-01
One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique self-consistent experimental and numerical setup that models a cascade of triadic interactions transferring energy from large-scale monochro-matic input to multi-scale internal wave motion. We also provide signatures of a discrete wave turbulence framework for internal waves. Finally, we show how beyond this regime, we have a clear transition to a regime of small-scale high-vorticity events which induce mixing. Introduction.
Hidden attractor in the Rabinovich system, Chua circuits and PLL
Kuznetsov, N. V.; Leonov, G. A.; Mokaev, T. N.; Seledzhi, S. M.
2016-06-01
In this report the existence of hidden attractors in Rabinovich system, phase-locked loop and coupled Chua circuits is considered. It is shown that the existence of hidden attractors may complicate the analysis of the systems and significantly affect the synchronization.
Synchronization in Coupled Oscillators with Two Coexisting Attractors
Institute of Scientific and Technical Information of China (English)
ZHU Han-Han; YANG Jun-Zhong
2008-01-01
Dynamics in coupled Duffing oscillators with two coexisting symmetrical attractors is investigated. For a pair of Dutffng oscillators coupled linearly, the transition to the synchronization generally consists of two steps: Firstly, the two oscillators have to jump onto a same attractor, then they reach synchronization similarly to coupled monostable oscillators. The transition scenarios to the synchronization observed are strongly dependent on initial conditions.
Experimental confirmation of a new reversed butterfly-shaped attractor
Institute of Scientific and Technical Information of China (English)
Liu Ling; Su Yan-Chen; Liu Chong-Xin
2007-01-01
This paper reports a new reverse butterfly-shaped chaotic attractor and its experimental confirmation. Some basic dynamical properties, and chaotic behaviours of this new reverse butterfly attractor are studied. Simulation results support brief theoretical derivations. Furthermore, the system is experimentally confirmed by a simple electronic circuit.
TRAJECTORY ATTRACTORS FOR NONCLASSICAL DIFFUSION EQUATIONS WITH FADING MEMORY
Institute of Scientific and Technical Information of China (English)
Yonghai WANG; Lingzhi WANG
2013-01-01
In this article,we consider the existence of trajectory and global attractors for nonclassical diffusion equations with linear fading memory.For this purpose,we will apply the method presented by Chepyzhov and Miranville [7,8],in which the authors provide some new ideas in describing the trajectory attractors for evolution equations with memory.
THE ATTRACTORS FOR LANDAU-LIFSHITZ-MAXWELL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Guo Boling; Su Fengqiu
2000-01-01
The existence of the attractors of the periodic initial value problem for the Landau-Lifshitz-Maxwell equations in one and two space dimensions is proved. We also get accurate estimates of the upper bounds of Hausdorff and fractal dimensions for the attractors by means of uniform a priori estimates for time and Lyapunov functional method.
Novel Principles and Methods for Computing with Attractors
Directory of Open Access Journals (Sweden)
Horia-Nicolai Teodorescu
2001-08-01
Full Text Available We briefly analyze several issues related to the "computing with attractors" domain. We present a point of view on the topic and several new concepts, methods, and techniques for computing with attractors. We discuss applications where this method may prove useful. We answer several questions related to the usefulness of this computing paradigm.
Adaptive synchronization of neural networks with different attractors
Institute of Scientific and Technical Information of China (English)
Zhang Huaguang; Guan Huanxin; Wang Zhanshan
2007-01-01
This paper aims to present an adaptive control scheme for the synchronization of two classes of uncertain neural networks with different attractors. A new sufficient condition for the global synchronization of two kinds of neural networks with different attractors is derived. The proposed control method is efficient and easy to be implemented. Numerical simulation is used to show the effectiveness of the obtained result.
Effect of resonant-frequency mismatch on attractors.
Wang, Xingang; Lai, Ying-Cheng; Lai, Choy Heng
2006-06-01
Resonant perturbations are effective for harnessing nonlinear oscillators for various applications such as controlling chaos and inducing chaos. Of physical interest is the effect of small frequency mismatch on the attractors of the underlying dynamical systems. By utilizing a prototype of nonlinear oscillators, the periodically forced Duffing oscillator and its variant, we find a phenomenon: resonant-frequency mismatch can result in attractors that are nonchaotic but are apparently strange in the sense that they possess a negative Lyapunov exponent but its information dimension measured using finite numerics assumes a fractional value. We call such attractors pseudo-strange. The transition to pesudo-strange attractors as a system parameter changes can be understood analytically by regarding the system as nonstationary and using the Melnikov function. Our results imply that pseudo-strange attractors are common in nonstationary dynamical systems.
Google matrix, dynamical attractors, and Ulam networks
Shepelyansky, D. L.; Zhirov, O. V.
2010-03-01
We study the properties of the Google matrix generated by a coarse-grained Perron-Frobenius operator of the Chirikov typical map with dissipation. The finite-size matrix approximant of this operator is constructed by the Ulam method. This method applied to the simple dynamical model generates directed Ulam networks with approximate scale-free scaling and characteristics being in certain features similar to those of the world wide web with approximate scale-free degree distributions as well as two characteristics similar to the web: a power-law decay in PageRank that mirrors the decay of PageRank on the world wide web and a sensitivity to the value α in PageRank. The simple dynamical attractors play here the role of popular websites with a strong concentration of PageRank. A variation in the Google parameter α or other parameters of the dynamical map can drive the PageRank of the Google matrix to a delocalized phase with a strange attractor where the Google search becomes inefficient.
Propagation of magnetic vortices using nanocontacts as tunable attractors
Manfrini, M.; Kim, Joo-Von; Petit-Watelot, S.; van Roy, W.; Lagae, L.; Chappert, C.; Devolder, T.
2014-02-01
Magnetic vortices in thin films are in-plane spiral spin configurations with a core in which the magnetization twists out of the film plane. Vortices result from the competition between atomic-scale exchange forces and long-range dipolar interactions. They are often the ground state of magnetic dots, and have applications in medicine, microwave generation and information storage. The compact nature of the vortex core, which is 10-20 nm wide, makes it a suitable probe of magnetism at the nanoscale. However, thus far the positioning of a vortex has been possible only in confined structures, which prevents its transport over large distances. Here we show that vortices can be propagated in an unconstrained system that comprises electrical nanocontacts (NCs). The NCs are used as tunable vortex attractors in a manner that resembles the propelling of space craft with gravitational slingshots. By passing current from the NCs to a ferromagnetic film, circulating magnetic fields are generated, which nucleate the vortex and create a potential well for it. The current becomes spin polarized in the film, and thereby drives the vortex into gyration through spin-transfer torques. The vortex can be guided from one NC to another by tuning attractive strengths of the NCs. We anticipate that NC networks may be used as multiterminal sources of vortices and spin waves (as well as heat, spin and charge flows) to sense the fundamental interactions between physical objects and fluxes of the next-generation spintronic devices.
Gravitino Dark Matter in R-Parity Breaking Vacua
Buchmüller, W; Hamaguchi, K; Ibarra, A; Yanagida, T; Buchmuller, Wilfried; Covi, Laura; Hamaguchi, Koichi; Ibarra, Alejandro; Yanagida, Tsutomu
2007-01-01
We show that in the case of small R-parity and lepton number breaking couplings, primordial nucleosynthesis, thermal leptogenesis and gravitino dark matter are naturally consistent for gravitino masses m_{3/2} \\gsim 5 GeV. We present a model where R-parity breaking is tied to B-L breaking, which predicts the needed small couplings. The metastable next-to-lightest superparticle has a decay length that is typically larger than a few centimeters, with characteristic signatures at the LHC. The photon flux produced by relic gravitino decays may be part of the apparent excess in the extragalactic diffuse gamma-ray flux obtained from the EGRET data for a gravitino mass m_{3/2} \\sim 10 GeV. In this case, a clear signal can be expected from GLAST in the near future.
Cosmological constant in SUGRA models with Planck scale SUSY breaking and degenerate vacua
Froggatt, C D; Nielsen, H B; Thomas, A W
2014-01-01
We argue that the measured value of the cosmological constant, as well as the small values of quartic Higgs self--coupling and the corresponding beta function at the Planck scale, which can be obtained by extrapolating the Standard Model (SM) couplings to high energies, can originate from supergravity (SUGRA) models with degenerate vacua. This scenario is realised if there are at least three exactly degenerate vacua. In the first vacuum, associated with the physical one, local supersymmetry (SUSY) is broken near the Planck scale while the breakdown of the SU(2)_W\\times U(1)_Y symmetry takes place at the electroweak (EW) scale. In the second vacuum local SUSY breaking is induced by gaugino condensation at a scale which is just slightly lower than \\Lambda_{QCD} in the physical vacuum. Finally, in the third vacuum local SUSY and EW symmetry are broken near the Planck scale.
Supersymmetry and R-symmetry Breaking in Meta-stable Vacua at Finite Temperature and Density
Arai, Masato; Sasaki, Shin
2014-01-01
We study a meta-stable supersymmetry-breaking vacuum in a generalized O'Raifeartaigh model at finite temperature and chemical potentials. Fields in the generalized O'Raifeartaigh model possess different R-charges to realize R-symmetry breaking. Accordingly, at finite density and temperature, the chemical potentials have to be introduced in a non-uniform way. Based on the formulation elaborated in our previous work we study the one-loop thermal effective potential including the chemical potentials in the generalized O'Raifeartaigh model. We perform the numerical analysis and find that the R-symmetry breaking vacua, which exist at zero temperature and zero chemical potential, are destabilized for some parameter regions. In addition, we find that there are parameter regions where new R-symmetry breaking vacua are realized even at high temperature by the finite density effects.
Ancillary qubit spectroscopy of vacua in cavity and circuit quantum electrodynamics.
Lolli, Jared; Baksic, Alexandre; Nagy, David; Manucharyan, Vladimir E; Ciuti, Cristiano
2015-05-01
We investigate theoretically how the spectroscopy of an ancillary qubit can probe cavity (circuit) QED ground states containing photons. We consider three classes of systems (Dicke, Tavis-Cummings, and Hopfield-like models), where nontrivial vacua are the result of ultrastrong coupling between N two-level systems and a single-mode bosonic field. An ancillary qubit detuned with respect to the boson frequency is shown to reveal distinct spectral signatures depending on the type of vacua. In particular, the Lamb shift of the ancilla is sensitive to both ground state photon population and correlations. Backaction of the ancilla on the cavity ground state is investigated, taking into account the dissipation via a consistent master equation for the ultrastrong coupling regime. The conditions for high-fidelity measurements are determined.
Dynamics of neural networks with continuous attractors
Fung, C. C. Alan; Wong, K. Y. Michael; Wu, Si
2008-10-01
We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their neutral stability facilitates the tracking performance of a CANN, which is believed to have wide applications in brain functions. We develop a perturbative approach that utilizes the dominant movement of the network stationary states in the state space. We quantify the distortions of the bump shape during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable, and the reaction time to catch up an abrupt change in stimulus.
Oscillatory Attractors: A New Cosmological Phase
Bains, Jasdeep S; Wilczek, Frank
2015-01-01
In expanding FRW spacetimes, it is usually the case that homogeneous scalar fields redshift and their amplitudes approach limiting values: Hubble friction usually ensures that the field relaxes to its minimum energy configuration, which is usually a static configuration. Here we discover a class of relativistic scalar field models in which the attractor behavior is the field oscillating indefinitely, with finite amplitude, in an expanding FRW spacetime, despite the presence of Hubble friction. This is an example of spontaneous breaking of time translation symmetry. We find that the effective equation of state of the field has average value $\\langle w\\rangle=-1$, implying that the field itself could drive an inflationary or dark energy dominated phase. This behavior is reminiscent of ghost condensate models, but in the new models, unlike in the ghost condensate models, the energy-momentum tensor is time dependent, so that these new models embody a more definitive breaking of time translation symmetry. We explo...
The past attractor in inhomogeneous cosmology
Uggla, C; Wainwright, J; Ellis, G F R; Uggla, Claes; Elst, Henk van; Wainwright, John; Ellis, George F R
2003-01-01
We present a general framework for analyzing spatially inhomogeneous cosmological dynamics. It employs Hubble-normalized scale-invariant variables which are defined within the orthonormal frame formalism, and leads to the formulation of Einstein's field equations with a perfect fluid matter source as an autonomous system of evolution equations and constraints. This framework incorporates spatially homogeneous dynamics in a natural way as a special case, thereby placing earlier work on spatially homogeneous cosmology in a broader context, and allows us to draw on experience gained in that field using dynamical systems methods. One of our goals is to provide a precise formulation of the approach to the spacelike initial singularity in cosmological models, described heuristically by Belinski\\v{\\i}, Khalatnikov and Lifshitz. Specifically, we construct an invariant set which we conjecture forms the local past attractor for the evolution equations. We anticipate that this new formulation will provide the basis for ...
Strange Attractor in Immunology of Tumor Growth
Voitikova, M
1997-01-01
The time delayed cytotoxic T-lymphocyte response on the tumor growth has been developed on the basis of discrete approximation (2-dimensional map). The growth kinetic has been described by logistic law with growth rate being the bifurcation parameter. Increase in the growth rate results in instability of the tumor state and causes period-doubling bifurcations in the immune+tumor system. For larger values of tumor growth rate a strange attractor has been observed. The model proposed is able to describe the metastable-state production when time series data of the immune state and the number of tumor cells are irregular and unpredictable. This metastatic disease may be caused not by exterior (medical) factors, but interior density dependent ones.
String vacua with massive boson-fermion degeneracy and non-singular cosmology
Florakis, Ioannis
2011-01-01
We discuss marginal deformations of string vacua with Massive boson-fermion Degeneracy Symmetry (MSDS), in connection to the cosmological evolution of the Universe from an early non-geometrical era. In particular, we discuss recent results on the stringy mechanism that resolves both Hagedorn divergences and the Initial Singularity problem. Based on a talk given at the Workshop on Cosmology & Strings, Corfu Institute, Greece, Sept 10, 2010.
IMPULSIVE CONTROL OF CHAOTIC ATTRACTORS IN NONLINEAR CHAOTIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
马军海; 任彪; 陈予恕
2004-01-01
Based on the study from both domestic and abroad, an impulsive control scheme on chaotic attractors in one kind of chaotic system is presented.By applying impulsive control theory of the universal equation, the asymptotically stable condition of impulsive control on chaotic attractors in such kind of nonlinear chaotic system has been deduced, and with it, the upper bond of the impulse interval for asymptotically stable control was given. Numerical results are presented, which are considered with important reference value for control of chaotic attractors.
How chaotic are strange non-chaotic attractors?
Glendinning, Paul; Jäger, Tobias H.; Keller, Gerhard
2006-09-01
We show that the classic examples of quasiperiodically forced maps with strange non-chaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit sensitive dependence on initial conditions, both on the whole phase space and restricted to the attractor. The results also remain valid in more general classes of quasiperiodically forced systems. Further, we include an elementary proof of a classic result by Glasner and Weiss on sensitive dependence, and we clarify the structure of the attractor in an example with two-dimensional fibres also introduced by Grebogi et al.
Inflationary attractor in Gauss-Bonnet brane cosmology
Meng, X H; Meng, Xin-He; Wang, Peng
2003-01-01
The inflationary attractor properties of the canonical scalar field and Born-Infeld field are investigated in the Randall-Sundrum II scenario with a Gauss-Bonnet term in the bulk action. We find that the inflationary attractor property will always hold for canonical scalar fields for any allowed non-negative Gauss-Bonnet coupling. However, for Born-Infeld field, the Gauss-Bonnet coupling will be highly constrained for the inflationary attractor property to hold. We also briefly discuss the possibility of explaining the suppressed lower multiples and running scalar spectral index simultaneously in the scenario of Gauss-Bonnet brane inflation.
No fermionic wigs for BPS attractors in 5 dimensions
Energy Technology Data Exchange (ETDEWEB)
Gentile, Lorenzo G.C., E-mail: lgentile@pd.infn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria I-15120 (Italy); Dipartimento di Fisica “Galileo Galilei”, Università di Padova, via Marzolo 8, I-35131 Padova (Italy); INFN, Sezione di Padova, via Marzolo 8, I-35131 Padova (Italy); Grassi, Pietro A., E-mail: pgrassi@mfn.unipmn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria I-15120 (Italy); INFN – Gruppo Collegato di Alessandria – Sezione di Torino (Italy); Marrani, Alessio, E-mail: alessio.marrani@fys.kuleuven.be [Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven (Belgium); Mezzalira, Andrea, E-mail: andrea.mezzalira@ulb.ac.be [Physique Théorique et Mathématique, Université Libre de Bruxelles, C.P. 231, B-1050 Bruxelles (Belgium); Sabra, Wafic A., E-mail: ws00@aub.edu.lb [Centre for Advanced Mathematical Sciences and Physics Department, American University of Beirut (Lebanon)
2014-07-30
We analyze the fermionic wigging of 1/2-BPS (electric) extremal black hole attractors in N=2, D=5 ungauged Maxwell–Einstein supergravity theories, by exploiting anti-Killing spinors supersymmetry transformations. Regardless of the specific data of the real special geometry of the manifold defining the scalars of the vector multiplets, and differently from the D=4 case, we find that there are no corrections for the near-horizon attractor value of the scalar fields; an analogous result also holds for 1/2-BPS (magnetic) extremal black string. Thus, the attractor mechanism receives no fermionic corrections in D=5 (at least in the BPS sector)
Random Attractors of Stochastic Non-Newtonian Fluids
Institute of Scientific and Technical Information of China (English)
Chun-xiao GUO; Bo-ling GUO; Yong-qian HAN
2012-01-01
The present paper investigates the asymptotic behavior of solutions for stochastic non-Newtonian fluids in a two-dimensional domain.Firstly,we prove the existence of random attractors AH(ω) in H; Secondly,we prove the existence of random attractors Av(ω) in V.Then we verify regularity of the random attractors by showing that AH(ω) =Av(ω),which implies the smoothing effect of the fluids in the sense that solution becomes eventually more regular than the initial data.
Non-linear fate of internal wave attractors
Scolan, Hélène; Dauxois, Thierry
2013-01-01
We present a laboratory study on the instability of internal wave attractors in a trapezoidal fluid domain filled with uniformly stratified fluid. Energy is injected into the system via standing-wave-type motion of a vertical wall. Attractors are found to be destroyed by parametric subharmonic instability (PSI) via a triadic resonance which is shown to provide a very efficient energy pathway from long to short length scales. This study provides an explanation why attractors may be difficult or impossible to observe in natural systems subject to large amplitude forcing.
Mapping the G-structures and supersymmetric vacua of five-dimensional N=4 supergravity
Energy Technology Data Exchange (ETDEWEB)
Liu, James T; Mahato, Manavendra; Vaman, Diana [Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI 48109-1040 (United States)
2007-03-07
We classify the supersymmetric vacua of N=4, d=5 supergravity in terms of G-structures. We identify three classes of solutions: with R{sup 3}, SU(2) and Id structure. Using the Killing spinor equations, we fully characterize the first two classes and partially solve the latter. With the N=4 graviton multiplet decomposed in terms of N=2 multiplets: the graviton, vector and gravitino multiplets, we obtain new supersymmetric solutions corresponding to turning on fields in the gravitino multiplet. These vacua are described in terms of an SO(5) vector sigma model coupled with gravity, in three or four dimensions. A new feature of these N=4 vacua, which is not seen from an N=2 point of view, is the possibility for preserving more exotic fractions of supersymmetry. We give a few concrete examples of these new supersymmetric (albeit singular) solutions. Additionally, we show how by truncating the N=4, d=5 set of fields to minimal supergravity coupled with one vector multiplet we recover the known two-charge solutions.
Top-quark mass coupling and classification of weakly coupled heterotic superstring vacua
Energy Technology Data Exchange (ETDEWEB)
Rizos, J. [University of Ioannina, Physics Department, Ioannina (Greece)
2014-06-15
The quest for the Standard Model among the huge number of string vacua is usually based on a set of phenomenological criteria related to the massless spectrum of string models. In this work we study criteria associated with interactions in the effective low energy theory and in particular with the presence of the coupling that provides mass to the top quark. Working in the context of the free-fermionic formulation of the heterotic superstring, we demonstrate that, in a big class of phenomenologically promising Z{sub 2} x Z{sub 2} compactifications, these criteria can be expressed entirely in terms of the generalised GSO projection coefficients entering the definition of the models. They are shown to be very efficient in identifying phenomenologically viable vacua, especially in the framework of computer-based search, as they are met by approximately one every 10{sup 4} models. We apply our results in the investigation of a class of supersymmetric Pati-Salam vacua, comprising 10{sup 16} configurations, and we show that when combined with other phenomenological requirements they lead to a relatively small set of about 10{sup 7} Standard Model compatible models that can be fully classified. (orig.)
$AdS_3$ vacua and RG flows in three dimensional gauged supergravities
Gava, Edi; Parinya, K
2010-01-01
We study $AdS_3$ supersymmetric vacua in N=4 and N=8, three dimensional gauged supergravities, with scalar manifolds $(\\frac{SO(4,4)}{SO(4)\\times SO(4)})^2$ and $\\frac{SO(8,8)}{SO(8)\\times SO(8)}$, non-semisimple Chern-Simons gaugings $SO(4)\\ltimes {\\bf R}^6$ and $(SO(4)\\ltimes {\\bf R}^6)^2$, respectively. These are in turn equivalent to SO(4) and $SO(4)\\times SO(4)$ Yang-Mills theories coupled to supergravity. For the N=4 case, we study renormalization group flows between UV and IR $AdS_3$ vacua with the same amount of supersymmetry: in one case, with (3,1) supersymmetry, we can find an analytic solution whereas in another, with (2,0) supersymmetry, we give a numerical solution. In both cases, the flows turn out to be v.e.v. flows, i.e. they are driven by the expectation value of a relevant operator in the dual $SCFT_2$. These provide examples of v.e.v. flows between two $AdS_3$ vacua within a gauged supergravity framework.
Supersymmetric $AdS_6$ vacua in six-dimensional $N=(1,1)$ gauged supergravity
Karndumri, Parinya
2016-01-01
We study fully supersymmetric $AdS_6$ vacua of half-maxi\\-mal $N=(1,1)$ gauged supergravity in six space-time dimensions coupled to $n$ vector multiplets. We show that the existence of $AdS_6$ backgrounds requires that the gauge group is of the form $G'\\times G"\\subset SO(4,n)$ where $G'\\subset SO(3,m)$ and $G"\\subset SO(1,n-m)$. In the $AdS_6$ vacua this gauge group is broken to its maximal compact subgroup $SO(3)\\times H'\\times H"$ where $H'\\subset SO(m)$ and $H"\\subset SO(n-m)$. Furthermore, the $SO(3)$ factor is the R-symmetry gauged by three of the four graviphotons. We further show that the $AdS_6$ vacua have no moduli that preserve all supercharges. This is precisely in agreement with the absence of supersymmetric marginal deformations in holographically dual five-dimensional superconformal field theories.
Algorithms for Finding Small Attractors in Boolean Networks
Directory of Open Access Journals (Sweden)
Hayashida Morihiro
2007-01-01
Full Text Available A Boolean network is a model used to study the interactions between different genes in genetic regulatory networks. In this paper, we present several algorithms using gene ordering and feedback vertex sets to identify singleton attractors and small attractors in Boolean networks. We analyze the average case time complexities of some of the proposed algorithms. For instance, it is shown that the outdegree-based ordering algorithm for finding singleton attractors works in time for , which is much faster than the naive time algorithm, where is the number of genes and is the maximum indegree. We performed extensive computational experiments on these algorithms, which resulted in good agreement with theoretical results. In contrast, we give a simple and complete proof for showing that finding an attractor with the shortest period is NP-hard.
Attractors for stochastic strongly damped plate equations with additive noise
Directory of Open Access Journals (Sweden)
Wenjun Ma
2013-04-01
Full Text Available We study the asymptotic behavior of stochastic plate equations with homogeneous Neumann boundary conditions. We show the existence of an attractor for the random dynamical system associated with the equation.
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...
The attractor of the stochastic generalized Ginzburg-Landau equation
Institute of Scientific and Technical Information of China (English)
GUO BoLing; WANG GuoLian; Li DongLong
2008-01-01
The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system. Then we prove the random system possesses a global random attractor in H01.
RANDOM ATTRACTORS FOR A STOCHASTIC HYDRODYNAMICAL EQUATION IN HEISENBERG PARAMAGNET
Institute of Scientific and Technical Information of China (English)
Guo Boling; Guo Chunxiao; Pu Xueke
2011-01-01
This article studies the asymptotic behaviors of the solution for a stochastic hydrodynamical equation in Heisenberg paramagnet in a two-dimensional periodic domain. We obtain the existence of random attractors in H1.
Features from the non-attractor beginning of inflation
Cai, Yi-Fu; Wang, Dong-Gang; Wang, Ziwei
2016-01-01
We study the effects of the non-attractor initial conditions for the canonical single-field inflation. The non-attractor stage can last only several $e$-folding numbers, and should be followed by hilltop inflation. This two-stage evolution leads to large scale suppression in the primordial power spectrum, which is favored by recent observations. Moreover we give a detailed calculation of primordial non-Guassianity due to the "from non-attractor to slow-roll" transition, and find step features in the local and equilateral shapes. We conclude that a plateau-like inflaton potential with an initial non-attractor phase yields interesting features in both power spectrum and bispectrum.
CMB and reheating constraints to \\alpha-attractor inflationary models
Eshaghi, Mehdi; Riazi, Nematollah; Kiasatpour, Ahmad
2016-01-01
After Planck 2013, a broad class of inflationary models called \\alpha-attractors was developed which has universal observational predictions. For small values of the parameter \\alpha, the models have good consistency with the recent CMB data. In this work, we first calculate analytically (and verify numerically) the predictions of these models for spectral index, n_s and tensor-to-scalar ratio, r and then using BICEP2/Keck 2015 data we impose constraints on \\alpha-attractors. Then, we study the reheating in \\alpha-attractors. The reheating temperature, T_{re} and the number of e-folds during reheating, N_{re} are calculated as functions of n_s. Using these results, we determine the range of free parameter \\alpha for two clasees of \\alpha-attractors which satisfy the constraints of recent CMB data.
The attractor of the stochastic generalized Ginzburg-Landau equation
Institute of Scientific and Technical Information of China (English)
2008-01-01
The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system.Then we prove the random system possesses a global random attractor in H01.
Quasi-attractor dynamics of lambda-phi^4-inflation
Kiselev, V V
2008-01-01
At high e-foldings of expansion, the inflation with the quartic potential exhibits the parametric attractor governed by the slowly running Hubble rate. This quasi-attractor simplifies the analysis of predictions for the inhomogeneity generated by the quantum fluctuations of inflaton. The quartic inflation is still marginally consistent with observations, if one suggests an extended version of tachyonic preheating stage with passing the region of negative potential, for instance.
Finite-dimensional attractors for the Kirchhoff models
Zhijian, Yang
2010-09-01
The paper studies the existence of the finite-dimensional global attractor and exponential attractor for the dynamical system associated with the Kirchhoff models arising in elasto-plastic flow utt-div{|∇u|m -1∇u}-Δut+Δ2u+h(ut)+g(u)=f(x). By using the method of ℓ-trajectories and the operator technique, it proves that under subcritical case, 1≤m
Characterization of Cocycle Attractors for Nonautonomous Reaction-Diffusion Equations
Cardoso, C. A.; Langa, J. A.; Obaya, R.
In this paper, we describe in detail the global and cocycle attractors related to nonautonomous scalar differential equations with diffusion. In particular, we investigate reaction-diffusion equations with almost-periodic coefficients. The associated semiflows are strongly monotone which allow us to give a full characterization of the cocycle attractor. We prove that, when the upper Lyapunov exponent associated to the linear part of the equations is positive, the flow is persistent in the positive cone, and we study the stability and the set of continuity points of the section of each minimal set in the global attractor for the skew product semiflow. We illustrate our result with some nontrivial examples showing the richness of the dynamics on this attractor, which in some situations shows internal chaotic dynamics in the Li-Yorke sense. We also include the sublinear and concave cases in order to go further in the characterization of the attractors, including, for instance, a nonautonomous version of the Chafee-Infante equation. In this last case we can show exponentially forward attraction to the cocycle (pullback) attractors in the positive cone of solutions.
Subdiffusive dynamics of bump attractors: mechanisms and functional roles.
Qi, Yang; Breakspear, Michael; Gong, Pulin
2015-02-01
Bump attractors are localized activity patterns that can self-sustain after stimulus presentation, and they are regarded as the neural substrate for a host of perceptual and cognitive processes. One of the characteristic features of bump attractors is that they are neutrally stable, so that noisy inputs cause them to drift away from their initial locations, severely impairing the accuracy of bump location-dependent neural coding. Previous modeling studies of such noise-induced drifting activity of bump attractors have focused on normal diffusive dynamics, often with an assumption that noisy inputs are uncorrelated. Here we show that long-range temporal correlations and spatial correlations in neural inputs generated by multiple interacting bumps cause them to drift in an anomalous subdiffusive way. This mechanism for generating subdiffusive dynamics of bump attractors is further analyzed based on a generalized Langevin equation. We demonstrate that subdiffusive dynamics can significantly improve the coding accuracy of bump attractors, since the variance of the bump displacement increases sublinearly over time and is much smaller than that of normal diffusion. Furthermore, we reanalyze existing psychophysical data concerning the spread of recalled cue position in spatial working memory tasks and show that its variance increases sublinearly with time, consistent with subdiffusive dynamics of bump attractors. Based on the probability density function of bump position, we also show that the subdiffusive dynamics result in a long-tailed decay of firing rate, greatly extending the duration of persistent activity.
Passive control of chaotic system with multiple strange attractors
Institute of Scientific and Technical Information of China (English)
Song Yun-Zhong; Zhao Guang-Zhou; Qi Dong-Lian
2006-01-01
In this paper we present a new simple controller for a chaotic system, that is, the Newton-Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). The controller design is based on the passive technique. The final structure of this controller for original stabilization has a simple nonlinear feedback form.Using a passive method, we prove the stability of a closed-loop system. Based on the controller derived from the passive principle, we investigate three different kinds of chaotic control of the system, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one,and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the suggested method.
Strange Attractors Characterizing the Osmotic Instability
Tzenov, Stephan I
2014-01-01
In the present paper a simple dynamical model for computing the osmotically driven fluid flow in a variety of complex, non equilibrium situations is derived from first principles. Using the Oberbeck-Boussinesq approximation, the basic equations describing the process of forward osmosis have been obtained. It has been shown that these equations are very similar to the ones used to model the free Rayleigh-Benard convection. The difference is that while in the case of thermal convection the volume expansion is driven by the coefficient of thermal expansion, the key role for the osmotic instability is played by the coefficient of isothermal compressibility. In addition, it has been shown that the osmotic process represents a propagation of standing waves with time-dependent amplitudes and phase velocity, which equals the current velocity of the solvent passing through the semi-permeable membrane. The evolution of the amplitudes of the osmotic waves is exactly following the dynamics of a strange attractor of Loren...
Non-tachyonic semi-realistic non-supersymmetric heterotic-string vacua
Energy Technology Data Exchange (ETDEWEB)
Ashfaque, Johar M.; Athanasopoulos, Panos; Faraggi, Alon E.; Sonmez, Hasan [University of Liverpool, Department of Mathematical Sciences, Liverpool (United Kingdom)
2016-04-15
The heterotic-string models in the free fermionic formulation gave rise to some of the most realistic-string models to date, which possess N = 1 spacetime supersymmetry. Lack of evidence for supersymmetry at the LHC instigated recent interest in non-supersymmetric heterotic-string vacua. We explore what may be learned in this context from the quasi-realistic free fermionic models. We show that constructions with a low number of families give rise to proliferation of a priori tachyon producing sectors, compared to the non-realistic examples, which typically may contain only one such sector. The reason being that in the realistic cases the internal six dimensional space is fragmented into smaller units. We present one example of a quasi-realistic, non-supersymmetric, non-tachyonic, heterotic-string vacuum and compare the structure of its massless spectrum to the corresponding supersymmetric vacuum. While in some sectors supersymmetry is broken explicitly, i.e. the bosonic and fermionic sectors produce massless and massive states, other sectors, and in particular those leading to the chiral families, continue to exhibit Fermi-Bose degeneracy. In these sectors the massless spectrum, as compared to the supersymmetric cases, will only differ in some local or global U(1) charges. We discuss the conditions for obtaining n{sub b} = n{sub f} at the massless level in these models. Our example model contains an anomalous U(1) symmetry, which generates a tadpole diagram at one-loop order in string perturbation theory. We speculate that this tadpole diagram may cancel the corresponding diagram generated by the one-loop non-vanishing vacuum energy and that in this respect the supersymmetric and non-supersymmetric vacua should be regarded on an equal footing. Finally we discuss vacua that contain two supersymmetry generating sectors. (orig.)
Non-tachyonic semi-realistic non-supersymmetric heterotic-string vacua
Ashfaque, Johar M.; Athanasopoulos, Panos; Faraggi, Alon E.; Sonmez, Hasan
2016-04-01
The heterotic-string models in the free fermionic formulation gave rise to some of the most realistic-string models to date, which possess N=1 spacetime supersymmetry. Lack of evidence for supersymmetry at the LHC instigated recent interest in non-supersymmetric heterotic-string vacua. We explore what may be learned in this context from the quasi-realistic free fermionic models. We show that constructions with a low number of families give rise to proliferation of a priori tachyon producing sectors, compared to the non-realistic examples, which typically may contain only one such sector. The reason being that in the realistic cases the internal six dimensional space is fragmented into smaller units. We present one example of a quasi-realistic, non-supersymmetric, non-tachyonic, heterotic-string vacuum and compare the structure of its massless spectrum to the corresponding supersymmetric vacuum. While in some sectors supersymmetry is broken explicitly, i.e. the bosonic and fermionic sectors produce massless and massive states, other sectors, and in particular those leading to the chiral families, continue to exhibit Fermi-Bose degeneracy. In these sectors the massless spectrum, as compared to the supersymmetric cases, will only differ in some local or global U(1) charges. We discuss the conditions for obtaining n_b=n_f at the massless level in these models. Our example model contains an anomalous U(1) symmetry, which generates a tadpole diagram at one-loop order in string perturbation theory. We speculate that this tadpole diagram may cancel the corresponding diagram generated by the one-loop non-vanishing vacuum energy and that in this respect the supersymmetric and non-supersymmetric vacua should be regarded on an equal footing. Finally we discuss vacua that contain two supersymmetry generating sectors.
Kaneko, K
1998-01-01
Strength of attractor is studied by the return rate to itself after perturbations, for a multi-attractor state of a globally coupled map. It is found that fragile (Milnor) attractors have a large basin volume at the partially ordered phase. Such dominance of fragile attractors is understood by robustness of global attraction in the phase space. Change of the attractor strength and basin volume against the parameter and size are studied. In the partially ordered phase, the dynamics is often described as Milnor attractor network, which leads to a new interpretation of chaotic itinerancy. Noise-induced selection of fragile attractors is found that has a sharp dependence on the noise amplitude. Relevance of the observed results to neural dynamics and cell differentiation is also discussed.
On Fayet-Iliopoulos Terms and de Sitter Vacua in Supergravity: Some Easy Pieces
Energy Technology Data Exchange (ETDEWEB)
Catino, Francesca; /Padua U. /INFN, Padua; Villadoro, Giovanni; /SLAC; Zwirner, Fabio; /Padua U. /INFN, Padua
2012-03-27
We clarify a number of issues on Fayet-Iliopoulos (FI) terms in supergravity, keeping the formalism at a minimum and making use of explicit examples. We explain why, if the U(1) vector is massive everywhere in field space, FI terms are not genuine and can always be redefined away or introduced when they are not present. We formulate a simple anomaly-free model with a genuine FI term, a classically stable de Sitter (dS) vacuum and no global symmetries. We explore the relation between N = 2 and N = 1 FI terms by discussing N = 1 truncations of N = 2 models with classically stable dS vacua.
Models with quartic potential of dynamical SUSY breaking in meta-stable vacua
Hirano, Shinji
2007-05-01
We search for models of dynamical SUSY breaking in meta-stable vacua which might have dual string descriptions with a few brane probes. Two models with quartic superpotential are proposed: One of them might be closely related to the dual gauge theory to the flavored Maldacena-Nuñez geometry by Casero, Nuñez, and Paredes with a few additional brane probes corresponding to massive flavors. The other model might be dual to the Klebanov-Strassler geometry with one fractional D3-brane and a few D7-branes as probes.
Models with Quartic Potential of Dynamical SUSY Breaking in Meta-Stable Vacua
Hirano, Shinji
2007-01-01
We search for models of dynamical SUSY breaking in meta-stable vacua which might have dual string descriptions with a few brane probes. Two models with quartic superpotential are proposed: One of them might be closely related to the dual gauge theory to the flavored Maldacena-Nunez geometry by Casero, Nunez, and Paredes with a few additional brane probes corresponding to massive flavors. The other model might be dual to the Klebanov-Strassler geometry with one fractional D3-brane and a few D7-branes as probes.
Head butting sheep: Kink Collisions in the Presence of False Vacua
Ashcroft, Jennifer; Haberichter, Mareike; Nitta, Muneto; Paranjape, M B
2016-01-01
We investigate numerically kink collisions in a $1+1$ dimensional scalar field theory with multiple vacua. The domain wall model we are interested in involves two scalar fields and a potential term built from an asymmetric double well and (double) sine-Gordon potential together with an interaction term. Depending on the initial kink setup and impact velocities, the model allows for a wide range of scattering behaviours. Kinks can repel each other, annihilate, form true or false domain walls and reflect off each other.
Non-commutative and commutative vacua effects in a scalar torsion scenario
Energy Technology Data Exchange (ETDEWEB)
Sheikhahmadi, Haidar, E-mail: h.sh.ahmadi@gmail.com [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of); Aghamohammadi, Ali, E-mail: a.aghamohamadi@iausdj.ac.ir [Sanandaj Branch, Islamic Azad University, Sanandaj (Iran, Islamic Republic of); Saaidi, Khaled, E-mail: ksaaidi@uok.ac.ir [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)
2015-10-07
In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.
Non-commutative and commutative vacua effects in a scalar torsion scenario
Directory of Open Access Journals (Sweden)
Haidar Sheikhahmadi
2015-10-01
Full Text Available In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.
Rainbow vacua of colored higher-spin (A)dS{sub 3} gravity
Energy Technology Data Exchange (ETDEWEB)
Gwak, Seungho; Joung, Euihun; Mkrtchyan, Karapet; Rey, Soo-Jong [School of Physics & Astronomy and Center for Theoretical Physics, Seoul National University,Seoul, 08826 (Korea, Republic of); Gauge, Gravity & Strings, Center for Theoretical Physics of the Universe,Institute for Basic Sciences, Daejeon, 34047 (Korea, Republic of)
2016-05-25
We study the color-decoration of higher-spin (anti)-de Sitter gravity in three dimensions. We show that the rainbow vacua, which we found recently for the colored gravity theory, also pertain in the colored higher-spin theory. The color singlet spin-two plays the role of first fundamental form (metric). The difference is that when spontaneous breaking of color symmetry takes place, the Goldstone modes of massless spin-two combine with all other spins and become the maximal-depth partially massless fields of the highest spin in the theory, forming a Regge trajectory.
The fate of stringy AdS vacua and the WGC
Danielsson, Ulf
2016-01-01
The authors of arXiv:1610.01533 have recently proposed a stronger version of the weak gravity conjecture (WGC), based on which they concluded that all those non-supersymmetric AdS vacua that can be embedded within a constistent theory of quantum gravity necessarily develop instabilities. In this paper we further elaborate on this proposal by arguing that the aforementioned instabilities have a perturbative nature and arise from the crucial interplay between the closed and the open string sectors of the theory.
Fate of stringy AdS vacua and the weak gravity conjecture
Danielsson, Ulf; Dibitetto, Giuseppe
2017-07-01
Ooguri and Vafa [arXiv:1610.01533] have recently proposed a stronger version of the weak gravity conjecture (WGC), based on which they concluded that all those nonsupersymmetric AdS vacua that can be embedded within a consistent theory of quantum gravity necessarily develop instabilities. In this paper we further elaborate on this proposal by arguing that the aforementioned instabilities have a perturbative nature and arise from the crucial interplay between the closed and the open string sectors of the theory.
F-theory duals of nonperturbative heterotic E$_{8}$ x E$_{8}$ vacua in six dimensions
Candelas, Philip; Rajesh, G; Candelas, Philip; Perevalov, Eugene; Rajesh, Govindan
1997-01-01
We present a systematic way of generating F-theory models dual to nonperturbative vacua of heterotic E8xE8 strings compactified on K3, using hypersurfaces in toric varieties. We find a distinction between models with point-like instantons and models with extra tensor multiplets, which is clearly visible in the dual polyhedra of the corresponding Calabi-Yau threefolds on the F-theory side. We conjecture that the point-like instantons signal the appearance of nonperturbative gauge groups in the heterotic models, independent of the distribution of instantons or the presence of tensor multiplets.
The Effective Kahler Potential, Metastable Vacua and R-Symmetry Breaking in O'Raifeartaigh Models
Benjamin, Shermane; Kain, Ben
2010-01-01
Much has been learned about metastable vacua and R-symmetry breaking in O'Raifeartaigh models. Such work has largely been done from the perspective of the superpotential and by including Coleman-Weinberg corrections to the scalar potential. Instead, we consider these ideas from the perspective of the one loop effective Kahler potential. We translate known ideas to this framework and construct convenient formulas for computing individual terms in the expanded effective Kahler potential. We do so for arbitrary R-charge assignments and allow for small R-symmetry violating terms so that both spontaneous and explicit R-symmetry breaking is allowed in our analysis.
Attractors and soak times in artisanal fi shing with traps
Directory of Open Access Journals (Sweden)
Evandro Figueiredo Sebastiani
2009-12-01
Full Text Available Traps are used by artisanal fishers as fishing gear in places where other fishing modalities are impeded or limited. The advantage of this type of fishing modality is the possibility of keeping fish alive and in the case of capturing species of low commercial value or size below the permitted minimum this fishing gear allows the release of such specimens back to nature, resulting in a sustainability aspect to the use of this fishing gear. This study aims to evaluate the effects of different attractors and times of submersion on the efficiency of the traps used. Sardines, shrimps and trash fish were employed as attractors. To evaluate the soak time, two periods were tested: 24 and 96 hours. The sardines, used as the attractor, resulted in a production of 1,296.4 ± 397.4g, significantly superior (p <0.05 to other attractors. In relation to the soak time, the period of 24 hours resulted in an average production of 1,719.2 ± 866.0g, significantly (p <0.05 superior to the period of 96 hours. The results led to the conclusion that to optimize this capture by fishing gear, sardines should be used as the attractor, together with a soak time of 24 hours.
Intersecting Black Attractors in 8D N=1 Supergravity
Laamara, R Ahl; Hassani, F Z; Saidi, E H; Soumail, A A
2010-01-01
We study intersecting extremal black attractors in non chiral 8D N=1 supergravity with moduli space ((SO(2,N))/(SO(2)\\times SO(N)))\\times SO(1,1) and work out explicitly the attractor mechanism for various black p-brane configurations with the typical near horizon geometries AdS_{p+2} \\times S^{m} \\times T^{6-p-m}. We also give the classification of the solutions of the attractor equations in terms of the SO(N-k) subgroups of SO(2)\\times SO(N) symmetry of the moduli space as well as their interpretations in terms of both heterotic string on 2-torus and its type IIA dual. Other features such as non trivial SO(1,7) central charges Z_{{\\mu}_1...{\\mu}_{p}} in 8D N=1 supergravity and their connections to p-form gauge fields are also given. Key Words: 8D Supergravity, Superstring compactifications, Attractor Mechanism, Intersecting Attractors. PACS numbers: 04.70.-s, 11.25.-w, 04.65.+e, 04.70.-s, 04.50.+h, 04.70.Dy
Directory of Open Access Journals (Sweden)
Yin Li
2016-01-01
Full Text Available This paper investigates the existence of random attractor for stochastic Boussinesq equations driven by multiplicative white noises in both the velocity and temperature equations and estimates the Hausdorff dimension of the random attractor.
Upper Semicontinuity of Attractors for a Non-Newtonian Fluid under Small Random Perturbations
Directory of Open Access Journals (Sweden)
Jianxin Luo
2014-01-01
Full Text Available This paper investigates the limiting behavior of attractors for a two-dimensional incompressible non-Newtonian fluid under small random perturbations. Under certain conditions, the upper semicontinuity of the attractors for diminishing perturbations is shown.
Global attractors of a degenerate parabolic equation and their error estimates
Institute of Scientific and Technical Information of China (English)
HU Xiaohong; ZHANG Xingyou
2004-01-01
The existences of the global attractor A? for a degenerate parabolic equation and of the homogenized attractorA0 for the corresponding homogenized equation are studied, and explicit estimates for the distance between A? and A0 are given.
Variety of strange pseudohyperbolic attractors in three-dimensional generalized Hénon maps
Gonchenko, A. S.; Gonchenko, S. V.
2016-12-01
In the present paper we focus on the problem of the existence of strange pseudohyperbolic attractors for three-dimensional diffeomorphisms. Such attractors are genuine strange attractors in that sense that each orbit in the attractor has positive maximal Lyapunov exponent and this property is robust, i.e., it holds for all close systems. We restrict attention to the study of pseudohyperbolic attractors that contain only one fixed point. Then we show that three-dimensional maps may have only 5 different types of such attractors, which we call the discrete Lorenz, figure-8, double-figure-8, super-figure-8, and super-Lorenz attractors. We find the first four types of attractors in three-dimensional generalized Hénon maps of form x ¯ = y, y ¯ = z, z ¯ = Bx + Az + Cy + g(y , z) , where A , B and C are parameters (B is the Jacobian) and g(0 , 0) =g‧(0 , 0) = 0.
Classification of attractors for systems of identical coupled Kuramoto oscillators
Energy Technology Data Exchange (ETDEWEB)
Engelbrecht, Jan R. [Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467 (United States); Mirollo, Renato [Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467 (United States)
2014-03-15
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For N≠3 oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
Classification of attractors for systems of identical coupled Kuramoto oscillators.
Engelbrecht, Jan R; Mirollo, Renato
2014-03-01
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For [Formula: see text] oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
Strange attractors in weakly turbulent Couette-Taylor flow
Brandstater, A.; Swinney, Harry L.
1987-01-01
An experiment is conducted on the transition from quasi-periodic to weakly turbulent flow of a fluid contained between concentric cylinders with the inner cylinder rotating and the outer cylinder at rest. Power spectra, phase-space portraits, and circle maps obtained from velocity time-series data indicate that the nonperiodic behavior observed is deterministic, that is, it is described by strange attractors. Various problems that arise in computing the dimension of strange attractors constructed from experimental data are discussed and it is shown that these problems impose severe requirements on the quantity and accuracy of data necessary for determining dimensions greater than about 5. In the present experiment the attractor dimension increases from 2 at the onset of turbulence to about 4 at a Reynolds number 50-percent above the onset of turbulence.
Coexistence of exponentially many chaotic spin-glass attractors.
Peleg, Y; Zigzag, M; Kinzel, W; Kanter, I
2011-12-01
A chaotic network of size N with delayed interactions which resembles a pseudoinverse associative memory neural network is investigated. For a load α = P/N chaotic network functions as an associative memory of 2P attractors with macroscopic basin of attractions which decrease with α. At finite α, a chaotic spin-glass phase exists, where the number of distinct chaotic attractors scales exponentially with N. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the N chaotic units or freezing with respect to the P patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations.
Separation of attractors in 1-modulus quantum corrected special geometry
Bellucci, S; Marrani, A; Shcherbakov, A
2008-01-01
We study the solutions to the N=2, d=4 Attractor Equations in a dyonic, extremal, static, spherically symmetric and asymptotically flat black hole background, in the simplest case of perturbative quantum corrected cubic Special Kahler geometry consistent with continuous axion-shift symmetry, namely in the 1-modulus Special Kahler geometry described (in a suitable special symplectic coordinate) by the holomorphic Kahler gauge-invariant prepotential F=t^3+i*lambda, with lambda real. By performing computations in the ``magnetic'' charge configuration, we find evidence for interesting phenomena (absent in the classical limit of vanishing lambda). Namely, for a certain range of the quantum parameter lambda we find a ``splitting'' of attractors, i.e. the existence of multiple solutions to the Attractor Equations for fixed supporting charge configuration. This corresponds to the existence of ``area codes'' in the radial evolution of the scalar t, determined by the various disconnected regions of the moduli space, wh...
Structure of attractors for (a,b)-continued fraction transformations
Katok, Svetlana
2010-01-01
We study a two-parameter family of one-dimensional maps and related (a,b)-continued fractions suggested for consideration by Don Zagier. We prove that the associated natural extension maps have attractors with finite rectangular structure for the entire parameter set except for a Cantor-like set of one-dimensional Lebesgue zero measure that we completely describe. We show that the structure of these attractors can be "computed" from the data (a,b), and that for a dense open set of parameters the Reduction theory conjecture holds, i.e. every point is mapped to the attractor after finitely many iterations. We also show how this theory can be applied to the study of invariant measures and ergodic properties of the associated Gauss-like maps.
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)
Possible Effects of Fierz Transformations on Vacua of Some Four-Fermion Interaction Models
Zhou, Bang-Rong
2015-01-01
A theoretical research on possible effects of the Fierz transformations on the ground states (vacua) of some 2-flavor and $N_c$-color four-fermion (quark) interaction models has been systematically conducted. It has been shown that, based on the known criterions of the interplay between the antiquark-quark ($\\bar{q}$-$q$) and diquark ($q$-$q$) condensates, in 4D space-time, for the given $\\bar{q}$-$q$ channel couplings with chiral symmetry and from the heavy gluon exchange, the effects of the Fierz transformations are not enough to change the feature that the models' vacua could only be in the pure $\\bar{q}$-$q$ condensate phases. However, for a given pure scalar $q$-$q$ channel coupling with the strength $H_S$, the Fierz transformations will lead to the nontrivial effect that the model's vacuum could be in the expected $q$-$q$ condensate phase only if $N_c<9$ and $H_S$ is small, and as the increase of $N_c$ and $H_S$, the vacuum will get first in a coexistence phase with $q$-$q$ and $\\bar{q}$-$q$ condensa...
Energy Technology Data Exchange (ETDEWEB)
Herrera-Aguilar, Alfredo [Instituto de FIsica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Edificio C-3, Ciudad Universitaria, Morelia, Mich., CP 58040 (Mexico); Nowakowski, Marek [Departamento de FIsica, Universidad de los Andes, Cra. 1 No 18A-10, Santa Fe de Bogota (Colombia)
2004-02-21
Using the stationary formulation of the toroidally compactified heterotic string theory in terms of a pair of matrix Ernst potentials we consider the four-dimensional truncation of this theory with no U(1) vector fields excited. Imposing one timelike Killing vector permits us to express the stationary effective action as a model in which gravity is coupled to a matrix Ernst potential which, under certain parametrization, allows us to interpret the matter sector of this theory as a double Ernst system. We generate a web of string vacua which are related to each other via a set of discrete symmetries of the effective action (some of them involve S-duality transformations and possess non-perturbative character). Some physical implications of these discrete symmetries are analysed and we find that, in some particular cases, they relate rotating black holes coupled to a dilaton with no Kalb-Ramond field, static black holes with non-trivial dilaton and antisymmetric tensor fields, and rotating and static naked singularities. Further, by applying a nonlinear symmetry, namely, the so-called normalized Harrison transformation, on the seed field configurations corresponding to these neutral backgrounds, we recover the U(1){sup n} Abelian vector sector of the four-dimensional action of the heterotic string, charging in this way the double Ernst system which corresponds to each one of the neutral string vacua, i.e., the stationary and the static black holes and the naked singularities.
Attractors and Dimensions for Discretizations of a NLS Equation with a Non-local Nonlinear Term
Institute of Scientific and Technical Information of China (English)
Shu Qing MA; Qian Shun CHANG
2002-01-01
In this paper we consider a semi-dicretized nonlinear Schrodinger (NLS) equation withlocal integral nonlinearity. It is proved that for each mesh size, there exist attractors for the discretizedsystem. The bounds for the Hausdorff and fractal dimensions of the discrete attractors are obtained,and the various bounds are independent of the mesh sizes. Furthermore, numerical experiments aregiven and many interesting phenomena are observed such as limit cycles, chaotic attractors and aso-called crisis of the chaotic attractors.
Compact Global Chaotic Attractors of Discrete Control Systems
Directory of Open Access Journals (Sweden)
Cheban David
2014-01-01
Full Text Available The paper is dedicated to the study of the problem of existence of compact global chaotic attractors of discrete control systems and to the description of its structure. We consider so called switched systems with discrete time xn+1 = fv(n(xn, where v: Z+ → {1; 2; : : : ;m}. If m≥2 we give sufficient conditions (the family M := {f1; f2; : : : ; fm} of functions is contracting in the extended sense for the existence of a compact global chaotic attractor. We study this problem in the framework of non-autonomous dynamical systems (cocycles
Two Unipolar Terminal-Attractor-Based Associative Memories
Liu, Hua-Kuang; Wu, Chwan-Hwa
1995-01-01
Two unipolar mathematical models of electronic neural network functioning as terminal-attractor-based associative memory (TABAM) developed. Models comprise sets of equations describing interactions between time-varying inputs and outputs of neural-network memory, regarded as dynamical system. Simplifies design and operation of optoelectronic processor to implement TABAM performing associative recall of images. TABAM concept described in "Optoelectronic Terminal-Attractor-Based Associative Memory" (NPO-18790). Experimental optoelectronic apparatus that performed associative recall of binary images described in "Optoelectronic Inner-Product Neural Associative Memory" (NPO-18491).
Analysis, synchronization and circuit design of a novel butterfly attractor
Pehlivan, Ihsan; Moroz, Irene M.; Vaidyanathan, Sundarapandian
2014-09-01
This research paper introduces a novel three-dimensional autonomous system, whose dynamics support periodic and chaotic butterfly attractors as certain parameters vary. A special case of this system, exhibiting reflectional symmetry, is amenable to analytical and numerical analysis. Qualitative properties of the new chaotic system are discussed in detail. Adaptive control laws are derived to achieve global chaotic synchronization of the new chaotic system with unknown parameters. Furthermore, a novel electronic circuit realization of the new chaotic system is presented, examined and realized using Orcad-PSpice program and physical components. The proposed novel butterfly chaotic attractor is very useful for the deliberate generation of chaos in applications.
Chaotic and hyperchaotic attractors of a complex nonlinear system
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Gamal M; Al-Kashif, M A; Farghaly, A A [Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)
2008-02-08
In this paper, we introduce a complex nonlinear hyperchaotic system which is a five-dimensional system of nonlinear autonomous differential equations. This system exhibits both chaotic and hyperchaotic behavior and its dynamics is very rich. Based on the Lyapunov exponents, the parameter values at which this system has chaotic, hyperchaotic attractors, periodic and quasi-periodic solutions and solutions that approach fixed points are calculated. The stability analysis of these fixed points is carried out. The fractional Lyapunov dimension of both chaotic and hyperchaotic attractors is calculated. Some figures are presented to show our results. Hyperchaos synchronization is studied analytically as well as numerically, and excellent agreement is found.
Experimental demonstration of attractor annihilation in a multistable fiber laser
Pisarchik, A. N.; Barmenkov, Yu. O.; Kir'yanov, A. V.
2003-12-01
We report on the experimental open-loop control of generalized multistability in a system with coexisting attractors. The experimental system is an erbium-doped fiber laser with pump modulation of the diode laser. We demonstrate that additional weak harmonic modulation of the diode current annihilates one or two stable limit cycles in the laser. The ability of the method to select a desired state is illustrated through a codimension-two bifurcation diagram in the parameter space of the frequency and amplitude of the control modulation. We identify main resonances on the bifurcation lines (annihilation curves) and evaluate conditions for attractor annihilation.
Strange attractor in the Potts spin glass on hierarchical lattices
Energy Technology Data Exchange (ETDEWEB)
Lima, Washington de [Universidade Federal de Pernambuco, Centro Acadêmico do Agreste, Pernambuco (Brazil); Camelo-Neto, G. [Universidade Federal de Alagoas, Núcleo de Ciências Exatas, Laboratório de Física Teórica e Computacional, CEP 57309-005 Arapiraca, Alagoas (Brazil); Coutinho, S., E-mail: sergio@ufpe.br [Universidade Federal de Pernambuco, Departamento de Física, Laboratório de Física Teórica e Computacional, Cidade Universitária, CEP 50670-901 Recife, Pernambuco (Brazil)
2013-11-29
The spin-glass q-state Potts model on d-dimensional diamond hierarchical lattices is investigated by an exact real space renormalization group scheme. Above a critical dimension d{sub l}(q) for q>2, the coupling constants probability distribution flows to a low-temperature strange attractor or to the high-temperature paramagnetic fixed point, according to the temperature is below or above the critical temperature T{sub c}(q,d). The strange attractor was investigated considering four initial different distributions for q=3 and d=5 presenting strong robustness in shape and temperature interval suggesting a condensed phase with algebraic decay.
Co-existing hidden attractors in a radio-physical oscillator system
DEFF Research Database (Denmark)
Kuznetsov, A. P.; Kuznetsov, S. P.; Mosekilde, Erik
2015-01-01
, this paper describes the formation of several different coexisting sets of hidden attractors, including the simultaneous presence of a pair of coinciding quasiperiodic attractors and of two mutually symmetric chaotic attractors. We follow the dynamics of the system as a function of the basic oscillator...
Institute of Scientific and Technical Information of China (English)
Zheng-de Dai
2002-01-01
In the present paper, the existence of global attractor for dissipative Hamiltonian amplitude equation governing the modulated wave instabilities in E0 is considered. By a decomposition of solution operator, it is shown that the global attractor in E0 is actually equal to a global attractor in E1.
Flipped S U (5 ) string vacua classification: A variation of the S O (10 ) breaking basis vector
Sonmez, Hasan
2016-06-01
In this paper, an extension of the classification of flipped S U (5 ) heterotic-string vacua from Faraggi, Rizos and Sonmez [Nucl. Phys. B886, 202 (2014)] with a variation of the S O (10 ) breaking α basis vector is presented. A statistical sampling in the space of 245 flipped S U (5 ) vacua is explored, where 1011 distinct GGSO projection configurations are scanned in comparison to the 1012 GGSO distinct coefficients scanned in the space of 244 vacua in Faraggi, Rizos and Sonmez. A JAVA code, akin to the one used for the classification in Faraggi, Rizos and Sonmez, was implemented to explore these. Results presented here indicate that no three-generation exophobic vacua exist, which was also found to be the case in Faraggi, Rizos and Sonmez as all odd generations were projected out. This paper will also study the details on the comparison between the two classifications achieved and reflect on the future directions in the quest for finding three-generation exophobic flipped S U (5 ) heterotic-string models.
A non-reward attractor theory of depression.
Rolls, Edmund T
2016-09-01
A non-reward attractor theory of depression is proposed based on the operation of the lateral orbitofrontal cortex and supracallosal cingulate cortex. The orbitofrontal cortex contains error neurons that respond to non-reward for many seconds in an attractor state that maintains a memory of the non-reward. The human lateral orbitofrontal cortex is activated by non-reward during reward reversal, and by a signal to stop a response that is now incorrect. Damage to the human orbitofrontal cortex impairs reward reversal learning. Not receiving reward can produce depression. The theory proposed is that in depression, this lateral orbitofrontal cortex non-reward system is more easily triggered, and maintains its attractor-related firing for longer. This triggers negative cognitive states, which in turn have positive feedback top-down effects on the orbitofrontal cortex non-reward system. Treatments for depression, including ketamine, may act in part by quashing this attractor. The mania of bipolar disorder is hypothesized to be associated with oversensitivity and overactivity in the reciprocally related reward system in the medial orbitofrontal cortex and pregenual cingulate cortex.
Shadow Systems and Attractors in Reaction-Diffusion Equations,
1987-04-01
0 gives some information about the types of singular solutions that can occur at D1 = 0 . Ideally, one would then hope to obtain an attractor AD1,D...for D2 ) d°l and all D1 > 0. This 1’ 2 will involve a very difficult analysis of the existence and stability of large amplitude singular solutions near
Approximating Attractors of Boolean Networks by Iterative CTL Model Checking.
Klarner, Hannes; Siebert, Heike
2015-01-01
This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: "faithfulness" which requires that the oscillating variables of all attractors in a trap space correspond to their dimensions, "univocality" which requires that there is a unique attractor in each trap space, and "completeness" which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal, and complete, which suggests that they are in general good approximations for the asymptotics of Boolean networks.
MAXIMUM-LIKELIHOOD-ESTIMATION OF THE ENTROPY OF AN ATTRACTOR
SCHOUTEN, JC; TAKENS, F; VANDENBLEEK, CM
1994-01-01
In this paper, a maximum-likelihood estimate of the (Kolmogorov) entropy of an attractor is proposed that can be obtained directly from a time series. Also, the relative standard deviation of the entropy estimate is derived; it is dependent on the entropy and on the number of samples used in the est
Uniform attractors of non-autonomous dissipative semilinear wave equations
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The asymptotic long time behaviors of a certain type of non-autonomous dissipative semilinear wave equations are studied. The existence of uniform attractors is proved and their upper bounds for both Hausdorff and Fractal dimensions of uniform are given when the external force satisfies suitable conditions.
Attractor horizons in six-dimensional type IIB supergravity
Energy Technology Data Exchange (ETDEWEB)
Astefanesei, Dumitru, E-mail: dumitru.astefanesei@ucv.cl [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile); Miskovic, Olivera, E-mail: olivera.miskovic@ucv.cl [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile); Olea, Rodrigo, E-mail: rodrigo.olea@unab.cl [Universidad Andres Bello, Departamento de Ciencias Fisicas, Republica 220, Santiago (Chile)
2012-08-14
We consider near horizon geometries of extremal black holes in six-dimensional type IIB supergravity. In particular, we use the entropy function formalism to compute the charges and thermodynamic entropy of these solutions. We also comment on the role of attractor mechanism in understanding the entropy of the Hopf T-dual solutions in type IIA supergravity.
Competition between synaptic depression and facilitation in attractor neural networks.
Torres, J.J.; Cortes, J.M.; Marro, J.; Kappen, H.J.
2007-01-01
We study the effect of competition between short-term synaptic depression and facilitation on the dynamic properties of attractor neural networks, using Monte Carlo simulation and a mean-field analysis. Depending on the balance of depression, facilitation, and the underlying noise, the network displ
Multistability and hidden attractors in a relay system with hysteresis
DEFF Research Database (Denmark)
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Rubanov, Vasily G.
2015-01-01
For nonlinear dynamic systems with switching control, the concept of a "hidden attractor" naturally applies to a stable dynamic state that either (1) coexists with the stable switching cycle or (2), if the switching cycle is unstable, has a basin of attraction that does not intersect with the nei...
Broken scale invariance, α -attractors and vector impurity
Akarsu, Özgür; Boran, Sibel; Kahya, Emre Onur; Özdemir, Neşe; Ozkan, Mehmet
2017-05-01
We show that if the α -attractor model is realized by the spontaneous breaking of the scale symmetry, then the stability and the dynamics of the vector field that gauges the scale symmetry can severely constrain the α -parameter as 5/6universe.
Global attractors for damped abstract nonlinear hyperbolic systems
Pinter, Gabriella Agnes
1997-12-01
This dissertation is concerned with the long time dynamics of a class of damped abstract hyperbolic systems that arise in the study of certain smart material structures, namely elastomers. The term smart material refers to a material capable of both sensing and responding actively to outside excitation. These properties make smart materials a prime canditate for actuation and sensing in next generation control systems. However, modeling and numerically simulating their behavior poses several difficulties. In this work we consider a model for elastomers developed by H. T. Banks, N. J. Lybeck, B. C. Munoz, L. C. Yanyo, formulate this model as an abstract evolution system, and study the long time behavior of its solutions. We remark that the question of existence and uniqueness of solutions for this class of systems is a challenging problem and was only recently solved by H. T. Banks, D. S. Gilliam and V. I. Shubov. Concerning the long time dynamics of the problem, we first prove that the system generates a weak dynamical system, and possesses a weak global attractor. Our main result is the existence of a "strong" dynamical system which has a compact global attractor. With the help of a Lyapunov function we are able to characterize the structure of this attractor. We also give a theorem that guarantees the stability of the global attractor with respect to varying parameters in the system. Our last result concerns the uniform differentiability of the dynamical system.
On the Supersymmetry of Bianchi attractors in Gauged supergravity
Chakrabarty, Bidisha; Samanta, Rickmoy
2016-01-01
Bianchi attractors are near horizon geometries with homogeneous symmetries in the spatial directions. We construct supersymmetric Bianchi attractors in $\\mathcal{N}=2, d=4,5$ gauged supergravity coupled to vector and hypermultiplets. In $d=4$, in the Bianchi I class we construct an electric $1/4$ BPS $AdS_2\\times\\mathbb{R}^2$ geometry. In $d=5$ we consider gauged supergravity with a generic gauging of symmetries of the scalar manifold and the R symmetry. Analyzing the gaugino and hyperino conditions we show that when the fermionic shifts do not vanish there are no supersymmetric Bianchi attractors. When the central charge satisfies an extremization condition, some of the fermionic shifts vanish and supersymmetry requires that the symmetries of the scalar manifold be ungauged. This allows supersymmetric Bianchi attractors sourced by massless gauge fields and a cosmological constant. In the Bianchi I class we show that the anisotropic $AdS_3\\times\\mathbb{R}^2$ solution is $1/2$ BPS. We also construct a new clas...
Recurrence quantification analysis in Liu's attractor
Energy Technology Data Exchange (ETDEWEB)
Balibrea, Francisco [Universidad de Murcia, Departamento de Matematicas, Campus de Espinardo, 30100 Murcia (Spain)], E-mail: balibrea@um.es; Caballero, M. Victoria [Universidad de Murcia, Departamento de Metodos Cuantitativos para la Economia, Campus de Espinardo, 30100 Murcia (Spain)], E-mail: mvictori@um.es; Molera, Lourdes [Universidad de Murcia, Departamento de Metodos Cuantitativos para la Economia, Campus de Espinardo, 30100 Murcia (Spain)
2008-05-15
Recurrence Quantification Analysis is used to detect transitions chaos to periodical states or chaos to chaos in a new dynamical system proposed by Liu et al. This system contains a control parameter in the second equation and was originally introduced to investigate the forming mechanism of the compound structure of the chaotic attractor which exists when the control parameter is zero.
Competition between synaptic depression and facilitation in attractor neural networks.
Torres, J.J.; Cortes, J.M.; Marro, J.; Kappen, H.J.
2007-01-01
We study the effect of competition between short-term synaptic depression and facilitation on the dynamic properties of attractor neural networks, using Monte Carlo simulation and a mean-field analysis. Depending on the balance of depression, facilitation, and the underlying noise, the network displ
Attractor for a Viscous Coupled Camassa-Holm Equation
Directory of Open Access Journals (Sweden)
Tian Lixin
2010-01-01
Full Text Available The global existence of solution to a viscous coupled Camassa-Holm equation with the periodic boundary condition is investigated. We obtain the compact and bounded absorbing set and the existence of the global attractor for the viscous coupled Camassa-Holm equation in by uniform prior estimate.
Non-slow-roll dynamics in $\\alpha-$attractors
Kumar, K Sravan; Moniz, Paulo Vargas; Das, Suratna
2015-01-01
In this paper we consider the $\\alpha-$attractor model and study inflation under a generalization of slow-roll dynamics. We follow the recently proposed Gong \\& Sasaki approach \\cite{Gong:2015ypa} of assuming $N=N\\left(\\phi\\right)$. We relax the requirement of inflaton potential flatness and consider a sufficiently steep one to support 60-efoldings. We find that this type of inflationary scenario predicts an attractor at $n_{s}\\approx0.967$ and $r\\approx5.5\\times10^{-4}$ which are very close to the predictions of the first chaotic inflationary model in supergravity (Goncharov-Linde model) \\cite{Goncharov:1983mw}. We show that even with non-slow-roll dynamics, the $\\alpha-$attractor model is compatible with any value of $r<0.1$. In addition, we emphasize that in this particular inflationary scenario, the standard consistency relation $\\left(r\\simeq-8n_{t}\\right)$ is significantly violated and we find an attractor for tensor tilt at $n_{t}\\approx-0.034$ as $r\\rightarrow0$. Any prominent detection of the ...
Uniform perfectness of the attractor of bi-Lipschitz IFS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we prove that the attractor of C1, α bi-Lipschitz IFS in R is uniformly perfect if it is not a singleton. Then we construct an example to show that this does not hold for C1 bi-Lipschitz IFS in Rn.
Attractors for stochastic lattice dynamical systems with a multiplicative noise
Institute of Scientific and Technical Information of China (English)
Tomás CARABALLO; Kening LU
2008-01-01
In this paper,we consider a stochastic lattice differential equation with diffusive nearest neighbor interaction,a dissipative nonlinear reaction term,and multiplicative white noise at each node.We prove the existence of a compact global random attractor which,pulled back,attracts tempered random bounded sets.
Dynamical movement primitives: learning attractor models for motor behaviors.
Ijspeert, Auke Jan; Nakanishi, Jun; Hoffmann, Heiko; Pastor, Peter; Schaal, Stefan
2013-02-01
Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior (e.g., stable locomotion from a system of coupled oscillators under perceptual guidance). Modeling goal-directed behavior with nonlinear systems is, however, rather difficult due to the parameter sensitivity of these systems, their complex phase transitions in response to subtle parameter changes, and the difficulty of analyzing and predicting their long-term behavior; intuition and time-consuming parameter tuning play a major role. This letter presents and reviews dynamical movement primitives, a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques. The essence of our approach is to start with a simple dynamical system, such as a set of linear differential equations, and transform those into a weakly nonlinear system with prescribed attractor dynamics by means of a learnable autonomous forcing term. Both point attractors and limit cycle attractors of almost arbitrary complexity can be generated. We explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics.
Stabilization of perturbed Boolean network attractors through compensatory interactions
2014-01-01
Background Understanding and ameliorating the effects of network damage are of significant interest, due in part to the variety of applications in which network damage is relevant. For example, the effects of genetic mutations can cascade through within-cell signaling and regulatory networks and alter the behavior of cells, possibly leading to a wide variety of diseases. The typical approach to mitigating network perturbations is to consider the compensatory activation or deactivation of system components. Here, we propose a complementary approach wherein interactions are instead modified to alter key regulatory functions and prevent the network damage from triggering a deregulatory cascade. Results We implement this approach in a Boolean dynamic framework, which has been shown to effectively model the behavior of biological regulatory and signaling networks. We show that the method can stabilize any single state (e.g., fixed point attractors or time-averaged representations of multi-state attractors) to be an attractor of the repaired network. We show that the approach is minimalistic in that few modifications are required to provide stability to a chosen attractor and specific in that interventions do not have undesired effects on the attractor. We apply the approach to random Boolean networks, and further show that the method can in some cases successfully repair synchronous limit cycles. We also apply the methodology to case studies from drought-induced signaling in plants and T-LGL leukemia and find that it is successful in both stabilizing desired behavior and in eliminating undesired outcomes. Code is made freely available through the software package BooleanNet. Conclusions The methodology introduced in this report offers a complementary way to manipulating node expression levels. A comprehensive approach to evaluating network manipulation should take an "all of the above" perspective; we anticipate that theoretical studies of interaction modification
Uenohara, Seiji; Mitsui, Takahito; Hirata, Yoshito; Morie, Takashi; Horio, Yoshihiko; Aihara, Kazuyuki
2013-06-01
We experimentally study strange nonchaotic attractors (SNAs) and chaotic attractors by using a nonlinear integrated circuit driven by a quasiperiodic input signal. An SNA is a geometrically strange attractor for which typical orbits have nonpositive Lyapunov exponents. It is a difficult problem to distinguish between SNAs and chaotic attractors experimentally. If a system has an SNA as a unique attractor, the system produces an identical response to a repeated quasiperiodic signal, regardless of the initial conditions, after a certain transient time. Such reproducibility of response outputs is called consistency. On the other hand, if the attractor is chaotic, the consistency is low owing to the sensitive dependence on initial conditions. In this paper, we analyze the experimental data for distinguishing between SNAs and chaotic attractors on the basis of the consistency.
Continuous attractors of Lotka-Volterra recurrent neural networks with infinite neurons.
Yu, Jiali; Yi, Zhang; Zhou, Jiliu
2010-10-01
Continuous attractors of Lotka-Volterra recurrent neural networks (LV RNNs) with infinite neurons are studied in this brief. A continuous attractor is a collection of connected equilibria, and it has been recognized as a suitable model for describing the encoding of continuous stimuli in neural networks. The existence of the continuous attractors depends on many factors such as the connectivity and the external inputs of the network. A continuous attractor can be stable or unstable. It is shown in this brief that a LV RNN can possess multiple continuous attractors if the synaptic connections and the external inputs are Gussian-like in shape. Moreover, both stable and unstable continuous attractors can coexist in a network. Explicit expressions of the continuous attractors are calculated. Simulations are employed to illustrate the theory.
Bulk supertranslation memories: a concept reshaping the vacua and black holes of general relativity
Compère, Geoffrey
2016-01-01
The memory effect is a prediction of general relativity on the same footing as the existence of gravitational waves. The memory effect is understood at future null infinity as a transition induced by null radiation from a Poincar\\'e vacuum to another vacuum. Those are related by a supertranslation, which is a fundamental symmetry of asymptotically flat spacetimes. In this essay, I argue that finite supertranslation diffeomorphisms should be extended into the bulk spacetime consistently with canonical charge conservation. It then leads to fascinating geometrical features of gravitational Poincar\\'e vacua. I then argue that in the process of black hole merger or gravitational collapse, dramatic but computable memory effects occur. They lead to a final stationary metric which qualitatively deviates from the Schwarzschild metric.
$\\Theta$-Vacua in the Light-Front Quantized Schwinger Model
Srivastava, P P
1996-01-01
The light-front (LF) quantization of the bosonized Schwinger model is discussed in the "continuum formulation". The proposal, successfully used earlier for describing the spontaneous symmetry breaking (SSB) on the LF, of separating first the scalar field into the dynamical condensate and the fluctuation fields before employing the "standard" Dirac method works here as well. The condensate variable, however, is now shown to be a q-number operator in contrast to the case of SSB where it was shown to be a c-number or a background field. The "condensate or Theta-vacua" emerge straightforwardly together with their continuum normalization which avoids the violation of the cluster decomposition property in the theory. Some topics on the "front form" theory are summarized in the Appendices and attention is drawn to the fact that "the theory quantized, say, at equal $x^{+}$ seems already to carry information on equal $x^{-}$ commutators as well".
Study of theta-Vacua in the 2-d O(3) Model
Bögli, Michael; Pepe, Michele; Wiese, Uwe-Jens
2012-01-01
We investigate the continuum limit of the step scaling function in the 2-d O(3) model with different theta-vacua. Since we find a different continuum value of the step scaling function for each value of theta, we can conclude that theta indeed is a relevant parameter of the theory and does not get renormalized non-perturbatively. Furthermore, we confirm the result of the conjectured exact S-matrix theory, which predicts the continuum value at theta = pi. To obtain high precision data, we use a modified Hasenbusch improved estimator and an action with an optimized constraint, which has very small cut-off effects. The optimized constraint action combines the standard action of the 2-d O(3) model with a topological action. The topological action constrains the angle between neighboring spins and is therefore invariant against small deformations of the field.
Protected couplings and BPS dyons in half-maximal supersymmetric string vacua
Directory of Open Access Journals (Sweden)
Guillaume Bossard
2017-02-01
Full Text Available We analyze four- and six-derivative couplings in the low energy effective action of D=3 string vacua with half-maximal supersymmetry. In analogy with an earlier proposal for the (∇Φ4 coupling, we propose that the ∇2(∇Φ4 coupling is given exactly by a manifestly U-duality invariant genus-two modular integral. In the limit where a circle in the internal torus decompactifies, the ∇2(∇Φ4 coupling reduces to the ∇2F4 and R2F2 couplings in D=4, along with an infinite series of corrections of order e−R, from four-dimensional 1/4-BPS dyons whose worldline winds around the circle. Each of these contributions is weighted by a Fourier coefficient of a meromorphic Siegel modular form, explaining and extending standard results for the BPS index of 1/4-BPS dyons.
Protected couplings and BPS dyons in half-maximal supersymmetric string vacua
Bossard, Guillaume; Cosnier-Horeau, Charles; Pioline, Boris
2017-02-01
We analyze four- and six-derivative couplings in the low energy effective action of D = 3 string vacua with half-maximal supersymmetry. In analogy with an earlier proposal for the (∇Φ) 4 coupling, we propose that the ∇2(∇Φ) 4 coupling is given exactly by a manifestly U-duality invariant genus-two modular integral. In the limit where a circle in the internal torus decompactifies, the ∇2(∇Φ) 4 coupling reduces to the ∇2F4 and R2F2 couplings in D = 4, along with an infinite series of corrections of order e-R, from four-dimensional 1/4-BPS dyons whose worldline winds around the circle. Each of these contributions is weighted by a Fourier coefficient of a meromorphic Siegel modular form, explaining and extending standard results for the BPS index of 1/4-BPS dyons.
All homogeneous N=2 M-theory truncations with supersymmetric AdS4 vacua
Cassani, Davide; Varela, Oscar
2012-01-01
We study consistent truncations of M-theory to gauged N=2 supergravity in four dimensions, based on a large class of SU(3)-structures in seven dimensions. We show that the gauging involves isometries of the vector multiplet scalar manifold as well as the Heisenberg algebra and a special isometry of the hyperscalar manifold. As a result, non-abelian gauge groups and new non-trivial scalar potentials are generated. Then we specialize to all homogeneous SU(3)-structures supporting supersymmetric AdS4 vacua. These are the Stiefel manifold V52, the Aloff-Wallach spaces N(k,l), the seven-sphere (seen as SU(4)/SU(3) or Sp(2)/Sp(1)) and the M110 and Q111 coset spaces. For each of these cases, we describe in detail the N=2 model and discuss its peculiarities.
Anomalous U(1)'s in type I string vacua
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios E-mail: antoniad@mail.cern.ch; Kiritsis, Elias E-mail: kiritsis@physics.uoc.gr; Rizos, John E-mail: irizos@cc.uoi.gr
2002-08-19
We perform a systematic string computation of the masses of anomalous U(1) gauge bosons in four-dimensional orientifold vacua, and we study their localization properties in the internal (compactified) space. We find that N=1 supersymmetric sectors yield four-dimensional contributions, localized in the whole six-dimensional internal space, while N=2 sectors give contributions localized in four internal dimensions. As a result, the U(1) gauge fields can be much lighter than the string scale, so that when the latter is at the TeV, they can mediate new non-universal repulsive forces at submillimeter distances much stronger than gravity. We also point out that even U(1)'s which are free of four-dimensional anomalies may acquire non-zero masses as a consequence of six-dimensional anomalies.
On moduli stabilisation and de Sitter vacua in MSSM heterotic orbifolds
Energy Technology Data Exchange (ETDEWEB)
Parameswaran, Susha L. [Uppsala Univ. (Sweden). Dept. of Physics and Astronomy; Ramos-Sanchez, Saul [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Zavala, Ivonne [Bonn Univ. (Germany). Bethe Center for Theoretical Physics and Physikalisches Inst.
2010-09-15
We study the problem of moduli stabilisation in explicit heterotic orbifold compactifications, whose spectra contain the MSSM plus some vector-like exotics that can be decoupled. Considering all the bulk moduli, we obtain the 4D low energy effective action for the compactification, which has contributions from various, computable, perturbative and non-perturbative effects. Hidden sector gaugino condensation and string worldsheet instantons result in a combination of racetrack, KKLT and cusp-form contributions to the superpotential, which lift all the bulk moduli directions. We point out the properties observed in our concrete models, which tend to be missed when only ''generic'' features of a model are assumed. We search for interesting vacua and find several de Sitter solutions, but so far, they all turn out to be unstable. (orig.)
On Moduli Stabilisation and de Sitter Vacua in MSSM Heterotic Orbifolds
Parameswaran, Susha L; Zavala, Ivonne
2010-01-01
We study the problem of moduli stabilisation in explicit heterotic orbifold compactifications, whose spectra contain the MSSM plus some vector-like exotics that can be decoupled. Considering all the bulk moduli, we obtain the 4D low energy effective action for the compactification, which has contributions from various, computable, perturbative and non-perturbative effects. Hidden sector gaugino condensation and string worldsheet instantons result in a combination of racetrack, KKLT and cusp-form contributions to the superpotential, which lift all the bulk moduli directions. We point out the properties observed in our concrete models, which tend to be missed when only "generic" features of a model are assumed. We search for interesting vacua and find several de Sitter solutions, but -- so far -- they all turn out to be unstable.
AdS$_5$ vacua from type IIB supergravity on $T^{1,1}$
Louis, Jan
2016-01-01
We study maximally supersymmetric Anti-de Sitter backgrounds in consistent N=2 truncations of type IIB supergravity compactified on the Sasaki-Einstein manifold $T^{1,1}$. In particular, we focus on truncations that contain fields coming from the nontrivial second and third cohomology forms on $T^{1,1}$. These give rise to N=2 supergravity coupled to two vector- and two hypermultiplets (Betti-vector truncation) or one vector- and three hypermultiplets (Betti-hyper truncation), respectively. We find that both truncations admit AdS$_5$ backgrounds with the gauge group always being broken but containing at least an $U(1)_R$ factor. Moreover, in both cases we show that the moduli space of AdS vacua is nontrivial and of maximal dimension. Finally, we explicitly compute the metrics on these moduli spaces.
Bulk supertranslation memories: A concept reshaping the vacua and black holes of general relativity
Compère, Geoffrey
2016-07-01
The memory effect is a prediction of general relativity on the same footing as the existence of gravitational waves. The memory effect is understood at future null infinity as a transition induced by null radiation from a Poincaré vacuum to another vacuum. Those are related by a supertranslation, which is a fundamental symmetry of asymptotically flat spacetimes. In this paper, I argue that finite supertranslation diffeomorphisms should be extended into the bulk spacetime consistently with canonical charge conservation. It then leads to fascinating geometrical features of gravitational Poincaré vacua. I then argue that in the process of black hole merger or gravitational collapse, dramatic but computable memory effects occur. They lead to a final stationary metric which qualitatively deviates from the Schwarzschild metric.
De Sitter vacua in no-scale supergravities and Calabi-Yau string models
Covi, Laura; Gross, Christian; Louis, Jan; Palma, Gonzalo A; Scrucca, Claudio A
2008-01-01
We perform a general analysis on the possibility of obtaining metastable vacua with spontaneously broken N=1 supersymmetry and non-negative cosmological constant in the moduli sector of string models. More specifically, we study the condition under which the scalar partners of the Goldstino are non-tachyonic, which depends only on the Kahler potential. This condition is not only necessary but also sufficient, in the sense that all of the other scalar fields can be given arbitrarily large positive square masses if the superpotential is suitably tuned. We consider both heterotic and orientifold string compactifications in the large-volume limit and show that the no-scale property shared by these models severely restricts the allowed values for the `sGoldstino' masses in the superpotential parameter space. We find that a positive mass term may be achieved only for certain types of compactifications and specific Goldstino directions. Additionally, we show how subleading corrections to the Kahler potential which b...
Chaotic Attractor Crisis and Climate Sensitivity: a Transfer Operator Approach
Tantet, A.; Lucarini, V.; Lunkeit, F.; Dijkstra, H. A.
2015-12-01
The rough response to a smooth parameter change of some non-chaotic climate models, such as the warm to snowball-Earth transition in energy balance models due to the ice-albedo feedback, can be studied in the framework of bifurcation theory, in particular by analysing the Lyapunov spectrum of fixed points or periodic orbits. However, bifurcation theory is of little help to study the destruction of a chaotic attractor which can occur in high-dimensional General Circulation Models (GCM). Yet, one would expect critical slowing down to occur before the crisis, since, as the system becomes susceptible to the physical instability mechanism responsible for the crisis, it turns out to be less and less resilient to exogenous perturbations and to spontaneous fluctuations due to other types of instabilities on the attractor. The statistical physics framework, extended to nonequilibrium systems, is particularly well suited for the study of global properties of chaotic and stochastic systems. In particular, the semigroup of transfer operators governs the evolution of distributions in phase space and its spectrum characterises both the relaxation rate of distributions to a statistical steady-state and the stability of this steady-state to perturbations. If critical slowing down indeed occurs in the approach to an attractor crisis, the gap in the spectrum of the semigroup of transfer operators is expected to shrink. We show that the chaotic attractor crisis due to the ice-albedo feedback and resulting in a transition from a warm to a snowball-Earth in the Planet Simulator (PlaSim), a GCM of intermediate complexity, is associated with critical slowing down, as observed by the slower decay of correlations before the crisis (cf. left panel). In addition, we demonstrate that this critical slowing down can be traced back to the shrinkage of the gap between the leading eigenvalues of coarse-grained approximations of the transfer operators and that these eigenvalues capture the
Energy Technology Data Exchange (ETDEWEB)
Douglas, Michael R.; Kachru, Shamit
2006-10-24
We review recent work in which compactifications of string and M theory are constructed in which all scalar fields (moduli) are massive, and supersymmetry is broken with a small positive cosmological constant, features needed to reproduce real world physics. We explain how this work implies that there is a ''landscape'' of string/M theory vacua, perhaps containing many candidates for describing real world physics, and present the arguments for and against this idea. We discuss statistical surveys of the landscape, and the prospects for testable consequences of this picture, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking.
Noncommutative Compactifications of Type I Strings on Tori with Magnetic Background Flux
Blumenhagen, R; Körs, B; Lüst, Dieter; Blumenhagen, Ralph; Goerlich, Lars; Kors, Boris; Lust, Dieter
2000-01-01
We construct six- and four-dimensional toroidal compactifications of the Type I string with magnetic flux on the D-branes. The open strings in this background probe a noncommutative internal geometry. Phenomenologically appealing features such as chiral fermions and supersymmetry breaking in the gauge sector are naturally realized by these vacua. We investigate the spectra of such noncommutative string compactifications and in a bottom-up approach discuss the possibility to obtain the standard or some GUT like model.
Global attractor for a class of Kirchhoff models
Zhijian, Yang; Baoxia, Jin
2009-03-01
The paper studies the longtime behavior of solutions to the initial boundary value problem (IBVP) for a class of Kirchhoff models arising in elastoplastic flow utt-div{|∇u|m -1∇u}-Δut+Δ2u+h(ut)+g(u)=f(x). By combining the decomposition idea with the operate technique, it proves that under rather mild conditions, the dynamical system associated with above-mentioned IBVP possesses in different phase spaces a global attractor which is connected, respectively. For application, the fact shows that for the concerned elastoplastic flow the permanent regime (global attractor) can be observed when the excitation starts from any bounded set in phase space.
A Hyperchaotic Attractor with Multiple Positive Lyapunov Exponents
Institute of Scientific and Technical Information of China (English)
HU Guo-Si
2009-01-01
There are many hyperchaotic systems,but few systems can generate hyperchaotic attractors with more than three PLEs(positive Lyapunov exponents).A new hyperchaotic system,constructed by adding an approximate time-delay state feedback to a five-dimensional hyperchaotic system,is presented.With the increasing number of phase-shift units used in this system,the number of PLEs also steadily increases.Hyperchaotic attractors with 25 PLEs can be generated by this system with 32 phase-shift units.The sum of the PLEs will reach the maximum value when 23 phase-shift units are used.A simple electronic circuit,consisting of 16 operational amplifiers and two analogy multipliers,is presented for confirming hyperchaos of order 5,i.e.,with 5 PLEs.
Strong Attractors in Stochastic Adaptive Networks: Emergence and Characterization
Santos, Augusto Almeida; Krishnan, Ramayya; Moura, José M F
2016-01-01
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical systems, on the edges of a graph, exhibits \\emph{good} convergence properties, in particular, we prove a strong-stability result: a subset of binary matrices or graphs -- characterized by certain compatibility properties -- is a global almost sure attractor of the family of stochastic dynamical systems. To illustrate finer properties of the corresponding strong attractor, we present some simulation results that capture, e.g., the conspicuous phenomenon of emergence and downfall of leaders in social networks.
Generating multi-double-scroll attractors via nonautonomous approach
Energy Technology Data Exchange (ETDEWEB)
Hong, Qinghui; Xie, Qingguo, E-mail: qgxie@mail.hust.edu.cn [Wuhan National Laboratory for Optoelectronics, Wuhan 430074 (China); Shen, Yi; Wang, Xiaoping [School of Automation, Huazhong University of Science and Technology, Wuhan 430074 (China)
2016-08-15
It is a common phenomenon that multi-scroll attractors are realized by introducing the various nonlinear functions with multiple breakpoints in double scroll chaotic systems. Differently, we present a nonautonomous approach for generating multi-double-scroll attractors (MDSA) without changing the original nonlinear functions. By using the multi-level-logic pulse excitation technique in double scroll chaotic systems, MDSA can be generated. A Chua's circuit, a Jerk circuit, and a modified Lorenz system are given as designed example and the Matlab simulation results are presented. Furthermore, the corresponding realization circuits are designed. The Pspice results are in agreement with numerical simulation results, which verify the availability and feasibility of this method.
Perpetual points and hidden attractors in dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Dudkowski, Dawid, E-mail: dawid.dudkowski@p.lodz.pl [Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz (Poland); Prasad, Awadhesh [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India); Kapitaniak, Tomasz [Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz (Poland)
2015-10-23
We discuss the use of perpetual points for tracing the hidden and the rare attractors of dynamical systems. The analysis of perpetual points and their co-existence due to the parameters values is presented and the impact of these points on the behavior of the systems is shown. The results are obtained for single as well as coupled externally excited van der Pol–Duffing oscillators. The presented results can be generalized to other systems having different dynamics. - Highlights: • Computation of perpetual points in forced nonlinear dynamical systems. • Locating the hidden and rare attractors using perpetual points. • Analysis of states and different types of synchronization in coupled systems. • Understanding the complexity in coupled and uncoupled forced van der Pol–Duffing oscillator.
Inflationary Attractors and Perturbation Spectra in Generally Coupled Gravity
Amendola, L; Occhionero, F; Amendola, Luca; Bellisai, Diego; Occhionero, Franco; Observatory, Rome Astronomical
1993-01-01
A generic outcome of theories with scalar-tensor coupling is the existence of inflationary attractors, either power-law or de Sitter. The fluctuations arising during this phase are Gaussian and their spectrum depends on the wavenumber $k$ according to the power-law $k^{1/(1-p)}$, where $p$ is the inflationary power-law exponent. We investigate to which extent these properties depend on the coupling function and on the potential. We find the class of models in which viable attractors exist. Within this class, we find that the cosmic expansion and the scaling of the fluctuation spectrum are independent of the coupling function. Further, the analytical solution of the Fokker-Planck equation shows that the deviations from Gaussianity are negligible.
A Riemann-Hilbert approach to rotating attractors
Câmara, M. C.; Cardoso, G. L.; Mohaupt, T.; Nampuri, S.
2017-06-01
We construct rotating extremal black hole and attractor solutions in gravity theories by solving a Riemann-Hilbert problem associated with the Breitenlohner-Maison linear system. By employing a vectorial Riemann-Hilbert factorization method we explicitly factorize the corresponding monodromy matrices, which have second order poles in the spectral parameter. In the underrotating case we identify elements of the Geroch group which implement Harrison-type transformations which map the attractor geometries to interpolating rotating black hole solutions. The factorization method we use yields an explicit solution to the linear system, from which we do not only obtain the spacetime solution, but also an explicit expression for the master potential encoding the potentials of the infinitely many conserved currents which make this sector of gravity integrable.
Logical Attractors: a Boolean Approach to the Dynamics of Psychosis
Kupper, Z.; Hoffmann, H.
A Boolean modeling approach to attractors in the dynamics of psychosis is presented: Kinetic Logic, originating from R. Thomas, describes systems on an intermediate level between a purely verbal, qualitative description and a description using nonlinear differential equations. With this method we may model impact, feedback and temporal evolution, as well as analyze the resulting attractors. In our previous research the method has been applied to general and more specific questions in the dynamics of psychotic disorders. In this paper a model is introduced that describes different dynamical patterns of chronic psychosis in the context of vocational rehabilitation. It also shows to be useful in formulating and exploring possible treatment strategies. Finally, some of the limitations and benefits of Kinetic Logic as a modeling tool for psychology and psychiatry are discussed.
A chaotic attractor in timing noise from the Vela pulsar?
Harding, Alice K.; Shinbrot, Troy; Cordes, James M.
1990-01-01
Fourteen years of timing residual data from the Vela pulsar have been analyzed in order to determine if a chaotic dynamical process is the origin of timing noise. Using the correlation sum technique, a dimension of about 1.5 is obtained. This low dimension indicates underlying structure in the phase residuals which may be evidence for a chaotic attractor. It is therefore possible that nonlinear dynamics intrinsic to the spin-down may be the cause of the timing noise in the Vela pulsar. However, it has been found that the stimulated random walks in frequency and frequency derivative often used to model pulsar timing noise also have low fractal dimension, using the same analysis technique. Recent work suggesting that random processes with steep power spectra can mimic strange attractors seems to be confirmed in the case of these random walks. It appears that the correlation sum estimator for dimension is unable to distinguish between chaotic and random processes.
Emerging attractors and the transition from dissipative to conservative dynamics.
Rodrigues, Christian S; de Moura, Alessandro P S; Grebogi, Celso
2009-08-01
The topological structure of basin boundaries plays a fundamental role in the sensitivity to the final state in chaotic dynamical systems. Herewith we present a study on the dynamics of dissipative systems close to the Hamiltonian limit, emphasizing the increasing number of periodic attractors, and on the structural changes in their basin boundaries as the dissipation approaches zero. We show numerically that a power law with nontrivial exponent describes the growth of the total number of periodic attractors as the damping is decreased. We also establish that for small scales the dynamics is governed by effective dynamical invariants, whose measure depends not only on the region of the phase space but also on the scale under consideration. Therefore, our results show that the concept of effective invariants is also relevant for dissipative systems.
Generating multi-double-scroll attractors via nonautonomous approach
Hong, Qinghui; Xie, Qingguo; Shen, Yi; Wang, Xiaoping
2016-08-01
It is a common phenomenon that multi-scroll attractors are realized by introducing the various nonlinear functions with multiple breakpoints in double scroll chaotic systems. Differently, we present a nonautonomous approach for generating multi-double-scroll attractors (MDSA) without changing the original nonlinear functions. By using the multi-level-logic pulse excitation technique in double scroll chaotic systems, MDSA can be generated. A Chua's circuit, a Jerk circuit, and a modified Lorenz system are given as designed example and the Matlab simulation results are presented. Furthermore, the corresponding realization circuits are designed. The Pspice results are in agreement with numerical simulation results, which verify the availability and feasibility of this method.
Stability and Multiscroll Attractors of Control Systems via the Abscissa
Directory of Open Access Journals (Sweden)
Edgar-Cristian Díaz-González
2017-01-01
Full Text Available We present an approach to generate multiscroll attractors via destabilization of piecewise linear systems based on Hurwitz matrix in this paper. First we present some results about the abscissa of stability of characteristic polynomials from linear differential equations systems; that is, we consider Hurwitz polynomials. The starting point is the Gauss–Lucas theorem, we provide lower bounds for Hurwitz polynomials, and by successively decreasing the order of the derivative of the Hurwitz polynomial one obtains a sequence of lower bounds. The results are extended in a straightforward way to interval polynomials; then we apply the abscissa as a measure to destabilize Hurwitz polynomial for the generation of a family of multiscroll attractors based on a class of unstable dissipative systems (UDS of affine linear type.
Perpetual points and hidden attractors in dynamical systems
Dudkowski, Dawid; Prasad, Awadhesh; Kapitaniak, Tomasz
2015-10-01
We discuss the use of perpetual points for tracing the hidden and the rare attractors of dynamical systems. The analysis of perpetual points and their co-existence due to the parameters values is presented and the impact of these points on the behavior of the systems is shown. The results are obtained for single as well as coupled externally excited van der Pol-Duffing oscillators. The presented results can be generalized to other systems having different dynamics.
CONCEPTUAL ANALYSIS AND RANDOM ATTRACTOR FOR DISSIPATIVE RANDOM DYNAMICAL SYSTEMS
Institute of Scientific and Technical Information of China (English)
Li Yuhong; Zdzistaw Brze(z)niak; Zhou Jianzhong
2008-01-01
The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems (RDS), which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS.
Chaotically spiking attractors in suspended mirror optical cavities
Marino, Francesco
2010-01-01
A high-finesse suspended mirror Fabry-Perot cavity is experimentally studied in a regime where radiation pressure and photothermal effect are both relevant. The competition between these phenomena, operating at different time scales, produces unobserved dynamical scenarios where an initial Hopf instability is followed by the birth of small-amplitude chaotic attractors which erratically but deterministically trigger optical spikes. The observed dynamical regimes are well reproduced by a detailed physical model of the system.
Attractors of magnetohydrodynamic flows in an Alfvenic state
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel; Sanz, Javier [Departamento de Analisis Matematico, Universidad de Valladolid, Valladolid (Spain)
1999-08-13
We present a simplified form of the magnetohydrodynamic system which describes the evolution of a plasma where the small-scale velocity and magnetic field are aligned in the form of Alfven waves, such as happens in several turbulent situations. Bounds on the dimension of the global attractor are found, and are shown to be an improvement of the standard ones for the full magnetohydrodynamic equations. (author)
Attractors and chaos of electron dynamics in electromagnetic standing wave
Esirkepov, Timur Zh; Koga, James K; Kando, Masaki; Kondo, Kiminori; Rosanov, Nikolay N; Korn, Georg; Bulanov, Sergei V
2014-01-01
The radiation reaction radically influences the electron motion in an electromagnetic standing wave formed by two super-intense counter-propagating laser pulses. Depending on the laser intensity and wavelength, either classical or quantum mode of radiation reaction prevail, or both are strong. When radiation reaction dominates, electron motion evolves to limit cycles and strange attractors. This creates a new framework for high energy physics experiments on an interaction of energetic charged particle beams and colliding super-intense laser pulses.
Global attractors and extinction dynamics of cyclically competing species
Rulands, Steffen; Zielinski, Alejandro; Frey, Erwin
2013-05-01
Transitions to absorbing states are of fundamental importance in nonequilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three cyclically interacting species. The interaction scheme comprises both direct competition between species as in the cyclic Lotka-Volterra model, and separated selection and reproduction processes as in the May-Leonard model. We show that the dynamic processes leading to the transient maintenance of biodiversity are closely linked to attractors of the nonlinear dynamics for the overall species’ concentrations. The characteristics of these global attractors change qualitatively at certain threshold values of the mobility and depend on the relative strength of the different types of competition between species. They give information about the scaling of extinction times with the system size and thereby the stability of biodiversity. We define an effective free energy as the negative logarithm of the probability to find the system in a specific global state before reaching one of the absorbing states. The global attractors then correspond to minima of this effective energy landscape and determine the most probable values for the species’ global concentrations. As in equilibrium thermodynamics, qualitative changes in the effective free energy landscape indicate and characterize the underlying nonequilibrium phase transitions. We provide the complete phase diagrams for the population dynamics and give a comprehensive analysis of the spatio-temporal dynamics and routes to extinction in the respective phases.
Unstable periodic orbits and attractor of the barotropic ocean model
Directory of Open Access Journals (Sweden)
E. Kazantsev
1998-01-01
Full Text Available A numerical method for detection of unstable periodic orbits on attractors of nonlinear models is proposed. The method requires similar techniques to data assimilation. This fact facilitates its implementation for geophysical models. This method was used to find numerically several low-period orbits for the barotropic ocean model in a square. Some numerical particularities of application of this method are discussed. Knowledge of periodic orbits of the model helps to explain some of these features like bimodality of probability density functions (PDF of principal parameters. These PDFs have been reconstructed as weighted averages of periodic orbits with weights proportional to the period of the orbit and inversely proportional to the sum of positive Lyapunov exponents. The fraction of time spent in the vicinity of each periodic orbit has been compared with its instability characteristics. The relationship between these values shows the 93% correlation. The attractor dimension of the model has also been approximated as a weighted average of local attractor dimensions in vicinities of periodic orbits.
Pattern Selection in Network of Coupled Multi-Scroll Attractors.
Li, Fan; Ma, Jun
2016-01-01
Multi-scroll chaotic attractor makes the oscillator become more complex in dynamic behaviors. The collective behaviors of coupled oscillators with multi-scroll attractors are investigated in the regular network in two-dimensional array, which the local kinetics is described by an improved Chua circuit. A feasible scheme of negative feedback with diversity is imposed on the network to stabilize the spatial patterns. Firstly, the Chua circuit is improved by replacing the nonlinear term with Sine function to generate infinite aquariums so that multi-scroll chaotic attractors could be generated under appropriate parameters, which could be detected by calculating the Lyapunov exponent in the parameter region. Furthermore, negative feedback with different gains (D1, D2) is imposed on the local square center area A2 and outer area A1 of the network, it is found that spiral wave, target wave could be developed in the network under appropriate feedback gain with diversity and size of controlled area. Particularly, homogeneous state could be reached after synchronization by selecting appropriate feedback gain and controlled size in the network. Finally, the distribution for statistical factors of synchronization is calculated in the two-parameter space to understand the transition of pattern region. It is found that developed spiral waves, target waves often are associated with smaller factor of synchronization. These results show that emergence of sustained spiral wave and continuous target wave could be effective for further suppression of spatiotemporal chaos in network by generating stable pacemaker completely.
Pattern Selection in Network of Coupled Multi-Scroll Attractors.
Directory of Open Access Journals (Sweden)
Fan Li
Full Text Available Multi-scroll chaotic attractor makes the oscillator become more complex in dynamic behaviors. The collective behaviors of coupled oscillators with multi-scroll attractors are investigated in the regular network in two-dimensional array, which the local kinetics is described by an improved Chua circuit. A feasible scheme of negative feedback with diversity is imposed on the network to stabilize the spatial patterns. Firstly, the Chua circuit is improved by replacing the nonlinear term with Sine function to generate infinite aquariums so that multi-scroll chaotic attractors could be generated under appropriate parameters, which could be detected by calculating the Lyapunov exponent in the parameter region. Furthermore, negative feedback with different gains (D1, D2 is imposed on the local square center area A2 and outer area A1 of the network, it is found that spiral wave, target wave could be developed in the network under appropriate feedback gain with diversity and size of controlled area. Particularly, homogeneous state could be reached after synchronization by selecting appropriate feedback gain and controlled size in the network. Finally, the distribution for statistical factors of synchronization is calculated in the two-parameter space to understand the transition of pattern region. It is found that developed spiral waves, target waves often are associated with smaller factor of synchronization. These results show that emergence of sustained spiral wave and continuous target wave could be effective for further suppression of spatiotemporal chaos in network by generating stable pacemaker completely.
Effective field theory of non-attractor inflation
Energy Technology Data Exchange (ETDEWEB)
Akhshik, Mohammad [Department of Physics, Sharif University of Technology,Tehran (Iran, Islamic Republic of); School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P. O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Firouzjahi, Hassan [School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P. O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Jazayeri, Sadra [Department of Physics, Sharif University of Technology,Tehran (Iran, Islamic Republic of)
2015-07-29
We present the model-independent studies of non attractor inflation in the context of effective field theory (EFT) of inflation. Within the EFT approach two independent branches of non-attractor inflation solutions are discovered in which a near scale-invariant curvature perturbation power spectrum is generated from the interplay between the variation of sound speed and the second slow roll parameter η. The first branch captures and extends the previously studied models of non-attractor inflation in which the curvature perturbation is not frozen on super-horizon scales and the single field non-Gaussianity consistency condition is violated. We present the general expression for the amplitude of local-type non-Gaussianity in this branch. The second branch is new in which the curvature perturbation is frozen on super-horizon scales and the single field non-Gaussianity consistency condition does hold in the squeezed limit. Depending on the model parameters, the shape of bispectrum in this branch changes from an equilateral configuration to a folded configuration while the amplitude of non-Gaussianity is less than unity.
High-dimensional chaotic and attractor systems a comprehensive introduction
Ivancevic, Vladimir G
2007-01-01
This is a graduate–level monographic textbook devoted to understanding, prediction and control of high–dimensional chaotic and attractor systems of real life. The objective of the book is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high–dimensional chaotic and attractor dynamics. The book has nine Chapters. The first Chapter gives a textbook-like introduction into the low-dimensional attractors and chaos. This Chapter has an inspirational character, similar to other books on nonlinear dynamics and deterministic chaos. The second Chapter deals with Smale’s topological transformations of stretching, squeezing and folding (of the system’s phase–space), developed for the purpose of chaos theory. The third Chapter is devoted to Poincaré's 3-body problem and basic techniques of chaos control, mostly of Ott-Grebogi-Yorke type. The fourth Chapter is a review of both Landau’s and topological phase transition theory, as w...
Wave attractors and the asymptotic dissipation rate of tidal disturbances
Ogilvie, G I
2005-01-01
Linear waves in bounded inviscid fluids do not generally form normal modes with regular eigenfunctions. Examples are provided by inertial waves in a rotating fluid contained in a spherical annulus, and internal gravity waves in a stratified fluid contained in a tank with a non-rectangular cross-section. For wave frequencies in the ranges of interest, the inviscid linearized equations are spatially hyperbolic and their characteristic rays are typically focused on to wave attractors. When these systems experience periodic forcing, for example of tidal origin, the response of the fluid can become localized in the neighbourhood of a wave attractor. In this paper I define a prototypical problem of this form and construct analytically the long-term response to a periodic body force in the asymptotic limit of small viscosity. The vorticity of the fluid is localized in a detached shear layer close to the wave attractor in such a way that the total rate of dissipation of energy is asymptotically independent of the vis...
The Potential and Flux Landscape Theory of Ecology
Zhang, Kun; Wang, Erkang; Wang, Jin
2014-01-01
The species in ecosystems are mutually interacting and self sustainable stable for a certain period. Stability and dynamics are crucial for understanding the structure and the function of ecosystems. We developed a potential and flux landscape theory of ecosystems to address these issues. We show that the driving force of the ecological dynamics can be decomposed to the gradient of the potential landscape and the curl probability flux measuring the degree of the breaking down of the detailed balance (due to in or out flow of the energy to the ecosystems). We found that the underlying intrinsic potential landscape is a global Lyapunov function monotonically going down in time and the topology of the landscape provides a quantitative measure for the global stability of the ecosystems. We also quantified the intrinsic energy, the entropy, the free energy and constructed the non-equilibrium thermodynamics for the ecosystems. We studied several typical and important ecological systems: the predation, competition, mutualism and a realistic lynx-snowshoe hare model. Single attractor, multiple attractors and limit cycle attractors emerge from these studies. We studied the stability and robustness of the ecosystems against the perturbations in parameters and the environmental fluctuations. We also found that the kinetic paths between the multiple attractors do not follow the gradient paths of the underlying landscape and are irreversible because of the non-zero flux. This theory provides a novel way for exploring the global stability, function and the robustness of ecosystems. PMID:24497975
The potential and flux landscape theory of ecology.
Directory of Open Access Journals (Sweden)
Li Xu
Full Text Available The species in ecosystems are mutually interacting and self sustainable stable for a certain period. Stability and dynamics are crucial for understanding the structure and the function of ecosystems. We developed a potential and flux landscape theory of ecosystems to address these issues. We show that the driving force of the ecological dynamics can be decomposed to the gradient of the potential landscape and the curl probability flux measuring the degree of the breaking down of the detailed balance (due to in or out flow of the energy to the ecosystems. We found that the underlying intrinsic potential landscape is a global Lyapunov function monotonically going down in time and the topology of the landscape provides a quantitative measure for the global stability of the ecosystems. We also quantified the intrinsic energy, the entropy, the free energy and constructed the non-equilibrium thermodynamics for the ecosystems. We studied several typical and important ecological systems: the predation, competition, mutualism and a realistic lynx-snowshoe hare model. Single attractor, multiple attractors and limit cycle attractors emerge from these studies. We studied the stability and robustness of the ecosystems against the perturbations in parameters and the environmental fluctuations. We also found that the kinetic paths between the multiple attractors do not follow the gradient paths of the underlying landscape and are irreversible because of the non-zero flux. This theory provides a novel way for exploring the global stability, function and the robustness of ecosystems.
Wang, Chunhua; Liu, Xiaoming; Xia, Hu
2017-03-01
In this paper, two kinds of novel ideal active flux-controlled smooth multi-piecewise quadratic nonlinearity memristors with multi-piecewise continuous memductance function are presented. The pinched hysteresis loop characteristics of the two memristor models are verified by building a memristor emulator circuit. Using the two memristor models establish a new memristive multi-scroll Chua's circuit, which can generate 2N-scroll and 2N+1-scroll chaotic attractors without any other ordinary nonlinear function. Furthermore, coexisting multi-scroll chaotic attractors are found in the proposed memristive multi-scroll Chua's circuit. Phase portraits, Lyapunov exponents, bifurcation diagrams, and equilibrium point analysis have been used to research the basic dynamics of the memristive multi-scroll Chua's circuit. The consistency of circuit implementation and numerical simulation verifies the effectiveness of the system design.
An efficient approach of attractor calculation for large-scale Boolean gene regulatory networks.
He, Qinbin; Xia, Zhile; Lin, Bin
2016-11-07
Boolean network models provide an efficient way for studying gene regulatory networks. The main dynamics of a Boolean network is determined by its attractors. Attractor calculation plays a key role for analyzing Boolean gene regulatory networks. An approach of attractor calculation was proposed in this study, which improved the predecessor-based approach. Furthermore, the proposed approach combined with the identification of constant nodes and simplified Boolean networks to accelerate attractor calculation. The proposed algorithm is effective to calculate all attractors for large-scale Boolean gene regulatory networks. If the average degree of the network is not too large, the algorithm can get all attractors of a Boolean network with dozens or even hundreds of nodes.
Wang, Bixiang
2012-01-01
We study pullback attractors of non-autonomous non-compact dynamical systems generated by differential equations with non-autonomous deterministic as well as stochastic forcing terms. We first introduce the concepts of pullback attractors and asymptotic compactness for such systems. We then prove a sufficient and necessary condition for existence of pullback attractors. We also introduce the concept of complete orbits for this sort of systems and use these special solutions to characterize the structures of pullback attractors. For random systems containing periodic deterministic forcing terms, we show the pullback attractors are also periodic. As an application of the abstract theory, we prove the existence of a unique pullback attractor for Reaction-Diffusion equations on $\\R^n$ with both deterministic and random external terms. Since Sobolev embeddings are not compact on unbounded domains, the uniform estimates on the tails of solutions are employed to establish the asymptotic compactness of solutions.
Continuous or discrete attractors in neural circuits? A self-organized switch at maximal entropy
Bernacchia, Alberto
2007-01-01
A recent experiment suggests that neural circuits may alternatively implement continuous or discrete attractors, depending on the training set up. In recurrent neural network models, continuous and discrete attractors are separately modeled by distinct forms of synaptic prescriptions (learning rules). Here, we report a solvable network model, endowed with Hebbian synaptic plasticity, which is able to learn either discrete or continuous attractors, depending on the frequency of presentation of stimuli and on the structure of sensory coding. A continuous attractor is learned when experience matches sensory coding, i.e. when the distribution of experienced stimuli matches the distribution of preferred stimuli of neurons. In that case, there is no processing of sensory information and neural activity displays maximal entropy. If experience goes beyond sensory coding, processing is initiated and the continuous attractor is destabilized into a set of discrete attractors.
Kimoto, Tomoyuki; Uezu, Tatsuya; Okada, Masato
2008-12-01
We study a neural network model for the inferior temporal cortex, in terms of finite memory loading and sparse coding. We show that an uncorrelated Hopfield-type attractor and some correlated attractors have multiple stability, and examine the retrieval dynamics for these attractors when the initial state is set to a noise-degraded memory pattern. Then, we show that there is a critical initial overlap: that is, the system converges to the correlated attractor when the noise level is large, and otherwise to the Hopfield-type attractor. Furthermore, we study the time course of the correlation between the correlated attractors in the retrieval dynamics. On the basis of these theoretical results, we resolve the controversy regarding previous physiologic experimental findings regarding neuron properties in the inferior temporal cortex and propose a new experimental paradigm.
Attractors for strongly damped wave equations with nonlinear hyperbolic dynamic boundary conditions
Jameson Graber, P.; Shomberg, Joseph L.
2016-04-01
We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying operator is analytic, α >0 , or only of Gevrey class, α =0 . We establish the existence of a global attractor for each α \\in ≤ft[0,1\\right], and we show that the family of global attractors is upper-semicontinuous as α \\to 0. Furthermore, for each α \\in ≤ft[0,1\\right] , we show the existence of a weak exponential attractor. A weak exponential attractor is a finite dimensional compact set in the weak topology of the phase space. This result ensures the corresponding global attractor also possesses finite fractal dimension in the weak topology; moreover, the dimension is independent of the perturbation parameter α. In both settings, attractors are found under minimal assumptions on the nonlinear terms.
Noise-induced attractor annihilation in the delayed feedback logistic map
Energy Technology Data Exchange (ETDEWEB)
Pisarchik, A.N., E-mail: apisarch@cio.mx [Centro de Investigaciones en Optica, Loma del Bosque 115, Leon, Guanajuato (Mexico); Centre for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, 28223 Pozuelo de Alarcon, Madrid (Spain); Martínez-Zérega, B.E. [Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Diaz de Leon 1144, Paseos de la Montaña, Lagos de Moreno, Jalisco 47460 (Mexico)
2013-12-06
We study dynamics of the bistable logistic map with delayed feedback, under the influence of white Gaussian noise and periodic modulation applied to the variable. This system may serve as a model to describe population dynamics under finite resources in noisy environment with seasonal fluctuations. While a very small amount of noise has no effect on the global structure of the coexisting attractors in phase space, an intermediate noise totally eliminates one of the attractors. Slow periodic modulation enhances the attractor annihilation.
Discontinuous bifurcation and coexistence of attractors in a piecewise linear map with a gap
Institute of Scientific and Technical Information of China (English)
Qu Shi-Xian; Lu Yong-Zhi; Zhang Lin; He Da-Ren
2008-01-01
Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are induced by different mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically.
Ge, Hao; Qian, Hong
2012-06-01
Landscape is one of the key notions in literature on biological processes and physics of complex systems with both deterministic and stochastic dynamics. The large deviation theory (LDT) provides a possible mathematical basis for the scientists' intuition. In terms of Freidlin-Wentzell's LDT, we discuss explicitly two issues in singularly perturbed stationary diffusion processes arisen from nonlinear differential equations: (1) For a process whose corresponding ordinary differential equation has a stable limit cycle, the stationary solution exhibits a clear separation of time scales: an exponential terms and an algebraic prefactor. The large deviation rate function attains its minimum zero on the entire stable limit cycle, while the leading term of the prefactor is inversely proportional to the velocity of the non-uniform periodic oscillation on the cycle. (2) For dynamics with multiple stable fixed points and saddles, there is in general a breakdown of detailed balance among the corresponding attractors. Two landscapes, a local and a global, arise in LDT, and a Markov jumping process with cycle flux emerges in the low-noise limit. A local landscape is pertinent to the transition rates between neighboring stable fixed points; and the global landscape defines a nonequilibrium steady state. There would be nondifferentiable points in the latter for a stationary dynamics with cycle flux. LDT serving as the mathematical foundation for emergent landscapes deserves further investigations.
Finite-dimensional attractors for the Kirchhoff models with critical exponents
Zhijian, Yang
2012-03-01
The paper studies the existence of the finite-dimensional global attractor and exponential attractor for the dynamical system associated with the Kirchhoff models utt - ∇ . {|∇u|m - 1∇u} - Δut + Δ2u + h(ut) + g(u) = f(x). It proves that for the subcritical and critical cases: 1
An efficient algorithm for computing attractors of synchronous and asynchronous Boolean networks.
Directory of Open Access Journals (Sweden)
Desheng Zheng
Full Text Available Biological networks, such as genetic regulatory networks, often contain positive and negative feedback loops that settle down to dynamically stable patterns. Identifying these patterns, the so-called attractors, can provide important insights for biologists to understand the molecular mechanisms underlying many coordinated cellular processes such as cellular division, differentiation, and homeostasis. Both synchronous and asynchronous Boolean networks have been used to simulate genetic regulatory networks and identify their attractors. The common methods of computing attractors are that start with a randomly selected initial state and finish with exhaustive search of the state space of a network. However, the time complexity of these methods grows exponentially with respect to the number and length of attractors. Here, we build two algorithms to achieve the computation of attractors in synchronous and asynchronous Boolean networks. For the synchronous scenario, combing with iterative methods and reduced order binary decision diagrams (ROBDD, we propose an improved algorithm to compute attractors. For another algorithm, the attractors of synchronous Boolean networks are utilized in asynchronous Boolean translation functions to derive attractors of asynchronous scenario. The proposed algorithms are implemented in a procedure called geneFAtt. Compared to existing tools such as genYsis, geneFAtt is significantly [Formula: see text] faster in computing attractors for empirical experimental systems.The software package is available at https://sites.google.com/site/desheng619/download.
An Efficient Algorithm for Computing Attractors of Synchronous And Asynchronous Boolean Networks
Zheng, Desheng; Yang, Guowu; Li, Xiaoyu; Wang, Zhicai; Liu, Feng; He, Lei
2013-01-01
Biological networks, such as genetic regulatory networks, often contain positive and negative feedback loops that settle down to dynamically stable patterns. Identifying these patterns, the so-called attractors, can provide important insights for biologists to understand the molecular mechanisms underlying many coordinated cellular processes such as cellular division, differentiation, and homeostasis. Both synchronous and asynchronous Boolean networks have been used to simulate genetic regulatory networks and identify their attractors. The common methods of computing attractors are that start with a randomly selected initial state and finish with exhaustive search of the state space of a network. However, the time complexity of these methods grows exponentially with respect to the number and length of attractors. Here, we build two algorithms to achieve the computation of attractors in synchronous and asynchronous Boolean networks. For the synchronous scenario, combing with iterative methods and reduced order binary decision diagrams (ROBDD), we propose an improved algorithm to compute attractors. For another algorithm, the attractors of synchronous Boolean networks are utilized in asynchronous Boolean translation functions to derive attractors of asynchronous scenario. The proposed algorithms are implemented in a procedure called geneFAtt. Compared to existing tools such as genYsis, geneFAtt is significantly faster in computing attractors for empirical experimental systems. Availability The software package is available at https://sites.google.com/site/desheng619/download. PMID:23585840
MAXIMAL ATTRACTORS OF CLASSICAL SOLUTIONS FOR REACTION DIFFUSION EQUATIONS WITH DISPERSION
Institute of Scientific and Technical Information of China (English)
Li Yanling; Ma Yicheng
2005-01-01
The paper first deals with the existence of the maximal attractor of classical solution for reaction diffusion equation with dispersion, and gives the sup-norm estimate for the attractor. This estimate is optimal for the attractor under Neumann boundary condition. Next, the same problem is discussed for reaction diffusion system with uniformly contracting rectangle, and it reveals that the maximal attractor of classical solution for such system in the whole space is only necessary to be established in some invariant region.Finally, a few examples of application are given.
On the Moduli Space of non-BPS Attractors for N=2 Symmetric Manifolds
Ferrara, Sergio
2007-01-01
We study the ``flat'' directions of non-BPS extremal black hole attractors for N=2, d=4 supergravities whose vector multiplets' scalar manifold is endowed with homogeneous symmetric special Kahler geometry. The non-BPS attractors with non-vanishing central charge have a moduli space described by real special geometry (and thus related to the d=5 parent theory), whereas the moduli spaces of non-BPS attractors with vanishing central charge are certain Kahler homogeneous symmetric manifolds. The moduli spaces of the non-BPS attractors of the corresponding N=2, d=5 theories are also indicated, and shown to be rank-1 homogeneous symmetric manifolds.
Finding the attractor of anger: bridging the gap between dynamic concepts and empirical data.
Hoeksma, Jan B; Oosterlaan, Jaap; Schipper, Eline; Koot, Hans
2007-08-01
Although it accounts for the prototypical course of emotions, the attractor concept has hardly ever been used empirically. Authors applied Empirical Differential Equations (EDE) to frequent (hourly) anger ratings to find the attractor of anger. The attractor concept, its neurological basis, and EDE are explained. The attractor of anger follows an underdamped oscillator, and is affected by the capacity to inhibit prepotent responses. Anger accelerates less fast when inhibitory control increases. Results stress the internal dynamics of emotions, and help to bridge the gap between concepts from dynamic systems theory and empirical data.
QCD $\\theta$-vacua from the chiral limit to the quenched limit
Mameda, Kazuya
2014-01-01
We investigate the dependence of the QCD vacuum structure on $\\theta$-angle and quark mass, using the Veneziano$-$Di-Vecchia model. Although the Veneziano$-$Di-Vecchia model is a chiral effective model, it contains the topological property of the pure Yang$-$Mills theory. It is shown that within this model, the ground state energies for all $\\theta$ are continuous functions of quark mass from the chiral limit to the quenched limit, including the first order phase transition at $\\theta = \\pi$ for arbitrary finite mass. Besides, based on this effective model, we discuss (i) how the ground state depends on quark mass, and (ii) why the phase transition at $\\theta = \\pi$ is caused both in the chiral and quenched limit. In order to analyze the relation between quark mass and $\\theta$-vacua, we calculate chiral condensate as a function of quark mass. We also give a unified understanding of the phase transitions at $\\theta = \\pi$ in the chiral and quenched limit, making reference to the metastable states included inn...
Global Fluctuation Spectra in Big Crunch/Big Bang String Vacua
Craps, B; Craps, Ben; Ovrut, Burt A.
2004-01-01
We study Big Crunch/Big Bang cosmologies that correspond to exact world-sheet superconformal field theories of type II strings. The string theory spacetime contains a Big Crunch and a Big Bang cosmology, as well as additional ``whisker'' asymptotic and intermediate regions. Within the context of free string theory, we compute, unambiguously, the scalar fluctuation spectrum in all regions of spacetime. Generically, the Big Crunch fluctuation spectrum is altered while passing through the bounce singularity. The change in the spectrum is characterized by a function $\\Delta$, which is momentum and time-dependent. We compute $\\Delta$ explicitly and demonstrate that it arises from the whisker regions. The whiskers are also shown to lead to ``entanglement'' entropy in the Big Bang region. Finally, in the Milne orbifold limit of our superconformal vacua, we show that $\\Delta\\to 1$ and, hence, the fluctuation spectrum is unaltered by the Big Crunch/Big Bang singularity. We comment on, but do not attempt to resolve, su...
Decoupling and de Sitter Vacua in Approximate No-Scale Supergravities
Marsh, M C David; Wrase, Timm
2014-01-01
We study ${\\cal N}=1$ supergravity with $N>1$ chiral superfields in which one of the fields has a K\\"ahler potential of exact no-scale type. Such systems admit de Sitter (dS) solutions in which supersymmetry is predominantly broken by the no-scale field, with only a small contribution to the breaking coming from the other fields. Metastable dS vacua of this type were recently shown to be achievable by the finetuning of an $N\\times N$ sub-matrix of the Hessian matrix at the critical point. We show that perturbatively small deformations of the no-scale Minkowski vacuum into dS are only possible when the spectrum of the no-scale vacuum, besides the no-scale field, contain an additional massless mode. The no-scale structure allows for a decoupling of $N-2$ fields, and metastability can be achieved by the tuning of ${\\cal O}(N^0)$ parameters. We illustrate this scenario in several examples, and derive a geometric condition for its realisation in type IIB string theory. Supergravities in which the complex structure...
de Sitter vacua in no-scale supergravities and Calabi-Yau string models
Energy Technology Data Exchange (ETDEWEB)
Covi, L. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]|[Warsaw Univ. (Poland). Inst. of Theoretical Physics; Gomez-Reino, M. [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Gross, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Louis, J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Hamburg Univ. (Germany). Zentrum fuer Mathematische Physik; Palma, G.A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Scrucca, C.A. [Ecole Polytechnique Federale de Lausanne (Switzerland). Inst. de Th. des Phen. Phys.
2008-04-15
We perform a general analysis on the possibility of obtaining metastable vacua with spontaneously broken N = 1 supersymmetry and non-negative cosmological constant in the moduli sector of string models. More specifically, we study the condition under which the scalar partners of the Goldstino are non-tachyonic, which depends only on the Kaehler potential. This condition is not only necessary but also sufficient, in the sense that all of the other scalar fields can be given arbitrarily large positive square masses if the superpotential is suitably tuned. We consider both heterotic and orientifold string compactifications in the large-volume limit and show that the no-scale property shared by these models severely restricts the allowed values for the 'sGoldstino' masses in the superpotential parameter space. We find that a positive mass term may be achieved only for certain types of compactifications and specific Goldstino directions. Additionally, we show how subleading corrections to the Kaehler potential which break the no-scale property may allow to lift these masses. (orig.)
Lifshitz and Schrödinger vacua, superstar resolution in gauged maximal supergravities
Liu, Hai-Shan; Lü, H.
2014-02-01
We consider the subset of gauged maximal supergravities that consists of the SO( n + 1) gauge fields A ij and the scalar deformation T ij of the S n in the spherical reduction of M-theory or type IIB. We focus on the Abelian Cartan subgroup and the diagonal entries of T ij . The resulting theories can be viewed as the STU models with additional hyperscalars. We find that the theories with only one or two such vectors can be generalized naturally to arbitrary dimensions. The same is true for the D = 4 or 5 Einstein-Maxwell theory with such a hyperscalar. The gauge fields become massive, determined by stationary points of the hyperscalars a la the analogous Abelian Higgs mechanism. We obtain classes of Lifshitz and Schrödinger vacua in these theories. The scaling exponent z turns out to be rather restricted, taking fractional or irrational numbers. Tweaking the theories by relaxing the mass parameter or making a small change of the superpotential, we find that solutions with z = 2 can emerge. In a different application, we find that the resolution of superstar singularity in the STU models by using bubbling-AdS solitons can be generalized to arbitrary dimensions in our theories. In particular, we obtain the smooth AdS solitons that can be viewed as the resolution of the Reissner-Nordstrøm superstars in general dimensions.
Unruh effect in vacua with anisotropic scaling: Applications to multilayer graphene
Energy Technology Data Exchange (ETDEWEB)
Katsnelson, M.I. [Radboud University Nijmegen, Institute for Molecules and Materials, Heyndaalseweg 135, NL-6525AJ Nijmegen (Netherlands); Volovik, G.E. [Low Temperature Laboratory, School of Science and Technology, Aalto University, P.O. Box 15100, FI-00076 Aalto (Finland); L. D. Landau Institute for Theoretical Physics, Kosygina 2, 119334 Moscow (Russian Federation); Zubkov, M.A., E-mail: zubkov@itep.ru [ITEP, B.Cheremushkinskaya 25, Moscow, 117259 (Russian Federation)
2013-09-15
We extend the calculation of the Unruh effect to the universality classes of quantum vacua obeying topologically protected invariance under anisotropic scaling r→br, t→b{sup z}t. Two situations are considered. The first one is related to the accelerated detector which detects the electron–hole pairs. The second one is related to the system in external electric field, when the electron–hole pairs are created due to the Schwinger process. As distinct from the Unruh effect in relativistic systems (where z=1) the calculated radiation is not thermal, but has properties of systems in the vicinity of quantum criticality. The vacuum obeying anisotropic scaling can be realized, in particular, in multilayer graphene with the rhombohedral stacking. Opportunities of the experimental realization of the Unruh effect in this situation are discussed. -- Highlights: •Unruh effect in the system with anisotropic scaling (multilayer graphene) is investigated. •The accelerated detector is considered which detects the electron–hole pairs. •The system in external electric field is considered as the “accelerated vacuum”. •Unruh effect in the nonrelativistic case differs from that of the relativistic case.
Hematopoietic differentiation: a coordinated dynamical process towards attractor stable states
Directory of Open Access Journals (Sweden)
Rossi Simona
2010-06-01
Full Text Available Abstract Background The differentiation process, proceeding from stem cells towards the different committed cell types, can be considered as a trajectory towards an attractor of a dynamical process. This view, taking into consideration the transcriptome and miRNome dynamics considered as a whole, instead of looking at few 'master genes' driving the system, offers a novel perspective on this phenomenon. We investigated the 'differentiation trajectories' of the hematopoietic system considering a genome-wide scenario. Results We developed serum-free liquid suspension unilineage cultures of cord blood (CB CD34+ hematopoietic progenitor cells through erythroid (E, megakaryocytic (MK, granulocytic (G and monocytic (Mo pathways. These cultures recapitulate physiological hematopoiesis, allowing the analysis of almost pure unilineage precursors starting from initial differentiation of HPCs until terminal maturation. By analyzing the expression profile of protein coding genes and microRNAs in unilineage CB E, MK, G and Mo cultures, at sequential stages of differentiation and maturation, we observed a coordinated, fully interconnected and scalable character of cell population behaviour in both transcriptome and miRNome spaces reminiscent of an attractor-like dynamics. MiRNome and transcriptome space differed for a still not terminally committed behaviour of microRNAs. Conclusions Consistent with their roles, the transcriptome system can be considered as the state space of a cell population, while the continuously evolving miRNA space corresponds to the tuning system necessary to reach the attractor. The behaviour of miRNA machinery could be of great relevance not only for the promise of reversing the differentiated state but even for tumor biology.
Is attentional blink a byproduct of neocortical attractors?
Directory of Open Access Journals (Sweden)
David N Silverstein
2011-05-01
Full Text Available This study proposes a computational model for attentional blink or blink of the mind, a phenomenon where a human subject misses perception of a later expected visual pattern as two expected visual patterns are presented less than 500 ms apart. A neocortical patch modeled as an attractor network is stimulated with a sequence of 14 patterns 100 ms apart, two of which are expected targets. Patterns that become active attractors are considered recognized. A neocortical patch is represented as a square matrix of hypercolumns, each containing a set of minicolumns with synaptic connections within and across both minicolumns and hypercolumns. Each minicolumn consists of locally connected layer 2/3 pyramidal cells with interacting basket cells and layer 4 pyramidal cells for input stimulation. All neurons are implemented using the Hodgkin-Huxley multi-compartmental cell formalism and include calcium dynamics, and they interact via saturating and depressing AMPA / NMDA and GABAA synapses. Stored patterns are encoded with global connectivity of minicolumns across hypercolumns and active patterns compete as the result of lateral inhibition in the network. Stored patterns were stimulated over time intervals to create attractor interference measurable with synthetic spike traces. This setup corresponds with item presentations in human visual attentional blink studies. Stored target patterns were depolarized while distractor patterns where hyperpolarized to represent expectation of items in working memory. Additionally, studies on the inhibitory effect of benzodiazopines on attentional blink in human subjects were compared with neocortical simulations where the GABAA receptor conductance and decay time were increased. Simulations showed increases in the attentional blink duration, agreeing with observations in human studies.
Experimental exploration of the optomechanical attractor diagram and its dynamics
Buters, Frank M; Heeck, Kier; Weaver, Matthew J; Pepper, Brian; de Man, Sven; Bouwmeester, Dirk
2015-01-01
We demonstrate experimental exploration of the attractor diagram of an optomechanical system where the optical forces compensate for the mechanical losses. In this case stable self-induced oscillations occur but only for specific mirror amplitudes and laser detunings. We demonstrate that we can amplify the mechanical mode to an amplitude 500 times larger than the thermal amplitude at 300K. The lack of unstable or chaotic motion allows us to manipulate our system into a non-trivial steady state and explore the dynamics of self-induced oscillations in great detail.
Exploring strange nonchaotic attractors through Jacobian elliptic functions
Energy Technology Data Exchange (ETDEWEB)
GarcIa-Hoz, A Martinez [Departamento de Fisica Aplicada, Escuela Universitaria Politecnica, Universidad de Castilla La Mancha, E-13400 Almaden (Ciudad Real) (Spain); Chacon, R, E-mail: rchacon@unex.es [Departamento de Fisica Aplicada, Escuela de IngenierIas Industriales, Universidad de Extremadura, Apartado Postal 382, E-06006 Badajoz (Spain)
2011-11-15
We demonstrate the effectiveness of Jacobian elliptic functions (JEFs) for inquiring into the reshaping effect of quasiperiodic forces in nonlinear nonautonomous systems exhibiting strange nonchaotic attractors (SNAs). Specifically, we characterize analytically and numerically some reshaping-induced transitions starting from SNAs in the context of quasiperiodically forced systems. We found similar scenarios of SNAs from the analysis of two representative examples: a quasiperiodically forced damped pendulum and a two-dimensional map. This clearly well-suited and advantageous use of the JEFs, which in their own right lie at the heart of nonlinear physics, may encourage students at intermediate university levels to study them in depth.
Synchronization of two 3-scroll hyperchaotic attractors using wavelet transform
Institute of Scientific and Technical Information of China (English)
Li Jian; Zhou Jiliu; Wang Yong; Zhi Yong
2006-01-01
The synchronization of two 3-scroll hyperchaotic attractors is realized based on wavelet transform and single variables' feedback. In the transmitter, one signal is decomposed by wavelet transform and the detailed information is removed, then the component with low frequency is reconstructed and sent into the channel. In the receiver, the received signal is used as the feedback signal to realize the synchronization of two chaotic systems. Using this synchronous method, the transmitting signal is transported in compressible way, the system resource is saved, furthermore, because the transported signal is not a whole chaotic signal, the performance of security of the system is improved.
Chaotic attractor transforming control of hybrid Lorenz-Chen system
Institute of Scientific and Technical Information of China (English)
Qi Dong-Lian; Wang Qiao; Gu Hong
2008-01-01
Based on passive theory, this paper studies a hybrid chaotic dynamical system from the mathematics perspective to implement the control of system stabilization.According to the Jacobian matrix of the nonlinear system, the stabilization control region is gotten.The controller is designed to stabilize fast the minimum phase Lorenz-Chen chaotic system after equivalently transforming from chaotic system to passive system. The simulation results show that the system not only can be controlled at the different equilibria, but also can be transformed between the different chaotic attractors.
Observational constraints on the generalized $\\alpha$ attractor model
Shahalam, M; Myrzakul, Shynaray; Wang, Anzhong
2016-01-01
We study the generalized $\\alpha$ attractor model in context of late time cosmic acceleration; the model interpolates between freezing and thawing dark energy models. In the slow roll regime, the originally potential is modified whereas the modification ceases in the asymptotic regime and the effective potential behaves as quadratic. In our setting, field rolls slowly around the present epoch and mimics dark matter in future. We put observational constraints on the model parameters for which we use an integrated data base (SN+Hubble+BAO+CMB) for carrying out the data analysis.
Attractors and chaos of electron dynamics in electromagnetic standing waves
Energy Technology Data Exchange (ETDEWEB)
Esirkepov, Timur Zh. [QuBS, Japan Atomic Energy Agency, Kizugawa, Kyoto 619-0215 (Japan); Bulanov, Stepan S. [University of California, Berkeley, CA 94720 (United States); Koga, James K.; Kando, Masaki; Kondo, Kiminori [QuBS, Japan Atomic Energy Agency, Kizugawa, Kyoto 619-0215 (Japan); Rosanov, Nikolay N. [Vavilov State Optical Institute, Saint-Petersburg 199034 (Russian Federation); Korn, Georg [ELI Beamline Facility, Institute of Physics, Czech Academy of Sciences, Prague 18221 (Czech Republic); Bulanov, Sergei V., E-mail: bulanov.sergei@jaea.go.jp [QuBS, Japan Atomic Energy Agency, Kizugawa, Kyoto 619-0215 (Japan)
2015-09-25
In an electromagnetic standing wave formed by two super-intense colliding laser pulses, radiation reaction totally modifies the electron motion. The quantum corrections to the electron motion and the radiation reaction force can be independently small or large, depending on the laser intensity and wavelength, thus dividing the parameter space into 4 domains. The electron motion evolves to limit cycles and strange attractors when radiation reaction dominates. This creates a new framework for high energy physics experiments on the interaction of energetic charged particle beams and colliding super-intense laser pulses.
Universal fractional map and cascade of bifurcations type attractors.
Edelman, M
2013-09-01
We modified the way in which the Universal Map is obtained in the regular dynamics to derive the Universal α-Family of Maps depending on a single parameter α>0, which is the order of the fractional derivative in the nonlinear fractional differential equation describing a system experiencing periodic kicks. We consider two particular α-families corresponding to the Standard and Logistic Maps. For fractional αbifurcations from regular to chaotic motion in regular dynamics corresponding fractional systems demonstrate a new type of attractors--cascade of bifurcations type trajectories.
Inflationary α-attractors and F(R)-gravity
Kuiroukidis, A.
2017-09-01
We consider a generic class of the so-called inflationary α-attractor models and compute the cosmological observables in the Einstein and Jordan frames of the corresponding F(R)-gravity theory. We find that the two sets coincide (to within errors from the use of the slow-roll approximation) for moderate and large values of the number of e-foldings N, which is the novel result of this paper, generalizing previous results on the subject (see e.g. Ref. 24). We briefly comment on the possible generalizations of these results.
A novel strange attractor and its dynamic analysis
Directory of Open Access Journals (Sweden)
Zhongtang Wu
2014-03-01
Full Text Available In this paper, not only a novel three-dimensional autonomous strange attractor is proposed, but also an idea to generate a more complex chaotic system was introduced. Of particular interest is that this novel system has complex phase diagram, big positive Lyapunov exponent and broad frequency spectrum. With either analytical or numerical methods, basic properties of the system, such as dynamical behaviors (time history and phase diagrams, Poincáre mapping, bifurcation diagram and Lyapunov exponents are investigated to observe chaotic motions. The obtained results clearly show that this is a new chaotic system which has good application prospects.
Generalized Pole Inflation: Hilltop, Natural, and Chaotic Inflationary Attractors
Terada, Takahiro
2016-01-01
A new paradigm for inflationary model building appeared recently, in which inflationary observables are determined by the structure of a pole in the inflaton kinetic term rather than the shape of the inflaton potential. We comprehensively study this framework with an arbitrary order of the pole taking into account possible additional poles in the kinetic term or in the potential. Depending on the setup, the canonical potential becomes the form of hilltop or plateau models, variants of natural inflation, or monomial or polynomial chaotic inflation. We demonstrate attractor behavior of these models and compute corrections from the additional poles to the inflationary observables.
Attractors and chaos of electron dynamics in electromagnetic standing waves
Esirkepov, Timur Zh.; Bulanov, Stepan S.; Koga, James K.; Kando, Masaki; Kondo, Kiminori; Rosanov, Nikolay N.; Korn, Georg; Bulanov, Sergei V.
2015-09-01
In an electromagnetic standing wave formed by two super-intense colliding laser pulses, radiation reaction totally modifies the electron motion. The quantum corrections to the electron motion and the radiation reaction force can be independently small or large, depending on the laser intensity and wavelength, thus dividing the parameter space into 4 domains. The electron motion evolves to limit cycles and strange attractors when radiation reaction dominates. This creates a new framework for high energy physics experiments on the interaction of energetic charged particle beams and colliding super-intense laser pulses.
Li, X Y; Yang, G W; Zheng, D S; Guo, W S; Hung, W N N
2015-01-01
Genetic regulatory networks are the key to understanding biochemical systems. One condition of the genetic regulatory network under different living environments can be modeled as a synchronous Boolean network. The attractors of these Boolean networks will help biologists to identify determinant and stable factors. Existing methods identify attractors based on a random initial state or the entire state simultaneously. They cannot identify the fixed length attractors directly. The complexity of including time increases exponentially with respect to the attractor number and length of attractors. This study used the bounded model checking to quickly locate fixed length attractors. Based on the SAT solver, we propose a new algorithm for efficiently computing the fixed length attractors, which is more suitable for large Boolean networks and numerous attractors' networks. After comparison using the tool BooleNet, empirical experiments involving biochemical systems demonstrated the feasibility and efficiency of our approach.
FINITE DIMENSION OF GLOBAL ATTRACTORS FOR DISSIPATIVE EQUATIONS GOVERNING MODULATED WAVE
Institute of Scientific and Technical Information of China (English)
YangLin; DaiZhengde
2003-01-01
The finite dimension of the global attractors for the systems of the perturbed and unperturbed dissipative Hamiltonian amplitude equations governing modulated wave are investigated, An interesting result is also obtained that the upper bound of the dimension of the global attractor for the perturbed equation is independent of ε.
Institute of Scientific and Technical Information of China (English)
ZHONG CHENGKUI; SUN CHUNYOU; NIU MINGFEI
2005-01-01
By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attractor for some nonlinear reaction-diffusion equations with some distribution derivatives in inhomogeneous terms is obtained.
Sustainability as global attractor: the greening of the 2008 Beijing Olympics
Mol, A.P.J.
2010-01-01
If one interprets sustainability as an attractor, it means that across time and place notions and ideas of sustainability structure, order and pattern institutions and practices. One can effectively explore the idea that sustainability is turning into a global attractor through mega events. As high
Attractors of multivalued semiflows generated by differential inclusions and their approximations
Directory of Open Access Journals (Sweden)
Alexei V. Kapustian
2000-01-01
Full Text Available We prove the existence of global compact attractors for differential inclusions and obtain some results concerning the continuity and upper semicontinuity of the attractors for approximating and perturbed inclusions. Applications are given to a model of regional economic growth.
Random sampling versus exact enumeration of attractors in random Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Berdahl, Andrew; Shreim, Amer; Sood, Vishal; Paczuski, Maya; Davidsen, Joern [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Alberta (Canada)], E-mail: aberdahl@phas.ucalgary.ca
2009-04-15
We clarify the effect different sampling methods and weighting schemes have on the statistics of attractors in ensembles of random Boolean networks (RBNs). We directly measure the cycle lengths of attractors and the sizes of basins of attraction in RBNs using exact enumeration of the state space. In general, the distribution of attractor lengths differs markedly from that obtained by randomly choosing an initial state and following the dynamics to reach an attractor. Our results indicate that the former distribution decays as a power law with exponent 1 for all connectivities K>1 in the infinite system size limit. In contrast, the latter distribution decays as a power law only for K=2. This is because the mean basin size grows linearly with the attractor cycle length for K>2, and is statistically independent of the cycle length for K=2. We also find that the histograms of basin sizes are strongly peaked at integer multiples of powers of two for K<3.
Generation and control of multi-scroll chaotic attractors in fractional order systems
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Wajdi M. [Department of Electrical and Computer Engineering, University of Sharjah, P.O. Box 27272, Sharjah (United Arab Emirates)] e-mail: wajdi@sharjah.ac.ae
2005-08-01
The objective of this paper is twofold: on one hand we demonstrate the generation of multi-scroll attractors in fractional order chaotic systems. Then, we design state feedback controllers to eliminate chaos from the system trajectories. It is demonstrated that modifying the underlying nonlinearity of the fractional chaotic system results in the birth of multiple chaotic attractors, thus forming the so called multi-scroll attractors. The presence of chaotic behavior is evidenced by a positive largest Lyapunov exponent computed for the output time series. We investigate generation and control of multi-scroll attractors in two different models, both of which are fractional order and chaotic: an electronic oscillator, and a mechanical 'jerk' model. The current findings extend previously reported results on generation of n-scroll attractors from the domain of integer order to the domain of fractional order chaotic systems, and addresses the issue of controlling such chaotic behaviors. Our investigations are validated through numerical simulations.
Required criteria for recognizing new types of chaos: Application to the ``cord'' attractor
Letellier, Christophe; Aguirre, Luis A.
2012-03-01
After suggesting criteria to recognize a new system and a new attractor—and to make a distinction between them—the paper details the topological analysis of the “cord” attractor. This attractor, which resembles a cord between two leaves, is produced by a three-dimensional system that is obtained after a modification of the Lorenz-84 model for the global atmospheric circulation [L. A. Aguirre and C. Letellier, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.83.066209 83, 066209 (2011)]. The nontrivial topology of the attractor is described in terms of a template that corresponds to a reverse horseshoe, that is, to a spiral Rössler attractor with negative and positive global π twists. Due to its particular structure and to the fact that such a system has two variables from which the dynamics is poorly observable, this attractor qualifies as a challenging benchmark in nonlinear dynamics.
ILP/SMT-Based Method for Design of Boolean Networks Based on Singleton Attractors.
Kobayashi, Koichi; Hiraishi, Kunihiko
2014-01-01
Attractors in gene regulatory networks represent cell types or states of cells. In system biology and synthetic biology, it is important to generate gene regulatory networks with desired attractors. In this paper, we focus on a singleton attractor, which is also called a fixed point. Using a Boolean network (BN) model, we consider the problem of finding Boolean functions such that the system has desired singleton attractors and has no undesired singleton attractors. To solve this problem, we propose a matrix-based representation of BNs. Using this representation, the problem of finding Boolean functions can be rewritten as an Integer Linear Programming (ILP) problem and a Satisfiability Modulo Theories (SMT) problem. Furthermore, the effectiveness of the proposed method is shown by a numerical example on a WNT5A network, which is related to melanoma. The proposed method provides us a basic method for design of gene regulatory networks.
Sensory feedback in a bump attractor model of path integration.
Poll, Daniel B; Nguyen, Khanh; Kilpatrick, Zachary P
2016-04-01
Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.
Strange Non-Chaotic Attractors in Quasiperiodically Forced Circle Maps
Jäger, Tobias
2009-07-01
The occurrence of strange non-chaotic attractors (SNA) in quasiperiodically forced systems has attracted considerable interest over the last two decades, in particular since it provides a rich class of examples for the possibility of complicated dynamics in the absence of chaos. Their existence was first described by Millions̆c̆ikov (and later by Vinograd and also Herman) for quasiperiodic {SL(2, {mathbb R})} -cocycles and by Grebogi et al (and later Keller) for so-called pinched skew products. However, except for these two particular classes there are still hardly any rigorous results on the topic, despite a large number of numerical studies confirming the widespread existence of SNA in quasiperiodically forced systems. Here, we prove the existence of SNA in quasiperiodically forced circle maps under rather general conditions, which can be stated in terms of {{mathcal C}^1} -estimates. As a consequence, we obtain the existence of SNA for parameter sets of positive measure in suitable parameter families. These SNA carry the unique physical measure of the system, which determines the behaviour of Lebesgue-almost all initial conditions. Finally, we show that the dynamics are minimal in the considered situations. The results apply in particular to a forced version of the Arnold circle map. For this example, we also describe how the first Arnold tongue collapses and looses its regularity due to the presence of strange non-chaotic attractors and a related unbounded mean motion property.
Attractor scenarios and superluminal signals in k-essence cosmology
Kang, Jin U; Winitzki, Sergei
2007-01-01
Cosmological scenarios with k-essence are invoked in order to explain the observed late-time acceleration of the universe. These scenarios avoid the need for fine-tuned initial conditions (the "coincidence problem") because of the attractor-like dynamics of the k-essence field \\phi. It was recently shown that all k-essence scenarios with Lagrangians p=L(X)/\\phi^2, necessarily involve an epoch where perturbations of \\phi propagate faster than light (the "no-go theorem"). We carry out a comprehensive study of attractor-like cosmological solutions ("trackers") involving a k-essence scalar field \\phi and another matter component. The result of this study is a complete classification of k-essence Lagrangians that admit asymptotically stable tracking solutions, among all Lagrangians of the form p=K(\\phi)L(X) . Using this classification, we select the class of models that describe the late-time acceleration and avoid the coincidence problem through the tracking mechanism. An analogous "no-go theorem" still holds for...
Characterization of chaotic attractors under noise: A recurrence network perspective
Jacob, Rinku; Harikrishnan, K. P.; Misra, R.; Ambika, G.
2016-12-01
We undertake a detailed numerical investigation to understand how the addition of white and colored noise to a chaotic time series changes the topology and the structure of the underlying attractor reconstructed from the time series. We use the methods and measures of recurrence plot and recurrence network generated from the time series for this analysis. We explicitly show that the addition of noise obscures the property of recurrence of trajectory points in the phase space which is the hallmark of every dynamical system. However, the structure of the attractor is found to be robust even upto high noise levels of 50%. An advantage of recurrence network measures over the conventional nonlinear measures is that they can be applied on short and non stationary time series data. By using the results obtained from the above analysis, we go on to analyse the light curves from a dominant black hole system and show that the recurrence network measures are capable of identifying the nature of noise contamination in a time series.
The effective Kaehler potential, metastable vacua and R-symmetry breaking in O'Raifeartaigh models
Energy Technology Data Exchange (ETDEWEB)
Benjamin, Shermane; Freund, Christopher [Department of Physics and Astronomy, Rowan University, 201 Mullica Hill Road, Glassboro, NJ 08028 (United States); Kain, Ben, E-mail: kain@rowan.ed [Department of Physics and Astronomy, Rowan University, 201 Mullica Hill Road, Glassboro, NJ 08028 (United States)
2011-01-21
Much has been learned about metastable vacua and R-symmetry breaking in O'Raifeartaigh models. Such work has largely been done from the perspective of the superpotential and by including Coleman-Weinberg corrections to the scalar potential. Instead, we consider these ideas from the perspective of the one loop effective Kaehler potential. We translate known ideas to this framework and construct convenient formulas for computing individual terms in the expanded effective Kaehler potential. We do so for arbitrary R-charge assignments and allow for small R-symmetry violating terms so that both spontaneous and explicit R-symmetry breaking is allowed in our analysis.
Tracking dynamics of two-dimensional continuous attractor neural networks
Fung, C. C. Alan; Wong, K. Y. Michael; Wu, Si
2009-12-01
We introduce an analytically solvable model of two-dimensional continuous attractor neural networks (CANNs). The synaptic input and the neuronal response form Gaussian bumps in the absence of external stimuli, and enable the network to track external stimuli by its translational displacement in the two-dimensional space. Basis functions of the two-dimensional quantum harmonic oscillator in polar coordinates are introduced to describe the distortion modes of the Gaussian bump. The perturbative method is applied to analyze its dynamics. Testing the method by considering the network behavior when the external stimulus abruptly changes its position, we obtain results of the reaction time and the amplitudes of various distortion modes, with excellent agreement with simulation results.
Attractor switching by neural control of chaotic neurodynamics.
Pasemann, F; Stollenwerk, N
1998-11-01
Chaotic attractors of discrete-time neural networks include infinitely many unstable periodic orbits, which can be stabilized by small parameter changes in a feedback control. Here we explore the control of unstable periodic orbits in a chaotic neural network with only two neurons. Analytically, a local control algorithm is derived on the basis of least squares minimization of the future deviations between actual system states and the desired orbit. This delayed control allows a consistent neural implementation, i.e. the same types of neurons are used for chaotic and controlling modules. The control signal is realized with one layer of neurons, allowing selective switching between different stabilized periodic orbits. For chaotic modules with noise, random switching between different periodic orbits is observed.
A 5-D hyperchaotic Rikitake dynamo system with hidden attractors
Vaidyanathan, S.; Pham, V.-T.; Volos, C. K.
2015-07-01
This paper presents a 5-D hyperchaotic Rikitake dynamo system with three positive Lyapunov exponents which is derived by adding two state feedback controls to the famous 3-D Rikitake two-disk dynamo system. It is noted that the proposed hyperchaotic system has no equilibrium points and hence it exhibits hidden attractors. In addition, the qualitative properties, as well as the adaptive synchronization of the hyperchaotic Rikitake dynamo system with unknown system parameters, are discussed in details. The main results are proved using Lyapunov stability theory and numerical simulations are shown using MATLAB. Moreover, an electronic circuit realization in SPICE has been detailed to confirm the feasibility of the theoretical 5-D hyperchaotic Rikitake dynamo model.
Late time attractors of some varying Chaplygin gas cosmological models
Khurshudyan, M
2015-01-01
Varying Chaplygin gas is one of the dark fluids actively studied in modern cosmology. It does belong to the group of the fluids which has an explicitly given EoS. From the other hand phase space does contain all possible states of the system. Therefore, phase space analysis of the cosmological models does allow to understand qualitative behavior and estimate required characteristics of the models. Phase space analysis is a convenient approach to study a cosmological model, because we do not need to solve a system of differential equations for a given initial conditions, instead, we need to deal with appropriate algebraic equations. The goal of this paper is to find late time attractors for the cosmological models, where a varying Chaplygin gas is one of the components of the large sale universe. We will pay our attention to some non linear interacting models.
Broken Scale Invariance, Alpha-Attractors and Vector Impurity
Akarsu, Ozgur; Kahya, Emre O; Ozdemir, Nese; Ozkan, Mehmet
2016-01-01
We show that if the {\\alpha}-attractor model is realized by the spontaneous breaking of the scale symmetry, then the stability and the dynamics of the vector field that gauges the scale symmetry severely constrains the {\\alpha}-parameter as 5/6 < {\\alpha} < 1, restricting the inflationary predictions in a very tiny region in the n_s vs r plane that are in great agreement with the latest Planck data. Although the different values of {\\alpha} do not make a tangible difference for n_s and r, they provide radically different scenarios for the post-inflationary dynamics which determines the standard BBN processes and the large scale isotropy of the universe.
Fast, parallel and secure cryptography algorithm using Lorenz's attractor
Marco, Anderson Gonçalves; Bruno, Odemir Martinez; 10.1142/S0129183110015166
2012-01-01
A novel cryptography method based on the Lorenz's attractor chaotic system is presented. The proposed algorithm is secure and fast, making it practical for general use. We introduce the chaotic operation mode, which provides an interaction among the password, message and a chaotic system. It ensures that the algorithm yields a secure codification, even if the nature of the chaotic system is known. The algorithm has been implemented in two versions: one sequential and slow and the other, parallel and fast. Our algorithm assures the integrity of the ciphertext (we know if it has been altered, which is not assured by traditional algorithms) and consequently its authenticity. Numerical experiments are presented, discussed and show the behavior of the method in terms of security and performance. The fast version of the algorithm has a performance comparable to AES, a popular cryptography program used commercially nowadays, but it is more secure, which makes it immediately suitable for general purpose cryptography ...
Strange attractor of Henon map and its basin
Institute of Scientific and Technical Information of China (English)
曹永罗
1995-01-01
In this paper, Henon map is considered. For a positive measure set of parameters (a, b), we construct a trapping region G of topologically transitive strange attractor Aa,b for Ta,b, and prove that Aa,b= ∩n≥0Ta,bnG, and the basin B(Aa,b) of Aa,b is exactly the union of domain whose boundary is contained in w5(p) ∪wu(p) and ws(p). Therefore, that the conjecture posed by Benedicks and Carleson about the basin of strange attactor is true is proved. Furthermore, B(Aa,b) is simply connected and path-connected, w4(p2) is contained in the attainable boundary set of B(Aa,b) (where p2 is another hyperbolic fixed point of Ta,b).
Navigating cancer network attractors for tumor-specific therapy
DEFF Research Database (Denmark)
Creixell, Pau; Schoof, Erwin; Erler, Janine Terra
2012-01-01
Cells employ highly dynamic signaling networks to drive biological decision processes. Perturbations to these signaling networks may attract cells to new malignant signaling and phenotypic states, termed cancer network attractors, that result in cancer development. As different cancer cells reach...... these malignant states by accumulating different molecular alterations, uncovering these mechanisms represents a grand challenge in cancer biology. Addressing this challenge will require new systems-based strategies that capture the intrinsic properties of cancer signaling networks and provide deeper...... understanding of the processes by which genetic lesions perturb these networks and lead to disease phenotypes. Network biology will help circumvent fundamental obstacles in cancer treatment, such as drug resistance and metastasis, empowering personalized and tumor-specific cancer therapies....
Strange Attractors in Multipath propagation Detection and characterisation
Tannous, C; Angus, A G
2001-01-01
Multipath propagation of radio waves in indoor/outdoor environments shows a highly irregular behavior as a function of time. Typical modeling of this phenomenon assumes the received signal is a stochastic process composed of the superposition of various altered replicas of the transmitted one, their amplitudes and phases being drawn from specific probability densities. We set out to explore the hypothesis of the presence of deterministic chaos in signals propagating inside various buildings at the University of Calgary. The correlation dimension versus embedding dimension saturates to a value between 3 and 4 for various antenna polarizations. The full Liapunov spectrum calculated contains two positive exponents and yields through the Kaplan-Yorke conjecture the same dimension obtained from the correlation sum. The presence of strange attractors in multipath propagation hints to better ways to predict the behaviour of the signal and better methods to counter the effects of interference. The use of Neural Netwo...
Excessive attractor instability accounts for semantic priming in schizophrenia.
Directory of Open Access Journals (Sweden)
Itamar Lerner
Full Text Available One of the most pervasive findings in studies of schizophrenics with thought disorders is their peculiar pattern of semantic priming, which presumably reflects abnormal associative processes in the semantic system of these patients. Semantic priming is manifested by faster and more accurate recognition of a word-target when preceded by a semantically related prime, relative to an unrelated prime condition. Compared to control, semantic priming in schizophrenics is characterized by reduced priming effects at long prime-target Stimulus Onset Asynchrony (SOA and, sometimes, augmented priming at short SOA. In addition, unlike controls, schizophrenics consistently show indirect (mediated priming (such as from the prime 'wedding' to the target 'finger', mediated by 'ring'. In a previous study, we developed a novel attractor neural network model with synaptic adaptation mechanisms that could account for semantic priming patterns in healthy individuals. Here, we examine the consequences of introducing attractor instability to this network, which is hypothesized to arise from dysfunctional synaptic transmission known to occur in schizophrenia. In two simulated experiments, we demonstrate how such instability speeds up the network's dynamics and, consequently, produces the full spectrum of priming effects previously reported in patients. The model also explains the inconsistency of augmented priming results at short SOAs using directly related pairs relative to the consistency of indirect priming. Further, we discuss how the same mechanism could account for other symptoms of the disease, such as derailment ('loose associations' or the commonly seen difficulty of patients in utilizing context. Finally, we show how the model can statistically implement the overly-broad wave of spreading activation previously presumed to characterize thought-disorders in schizophrenia.
How organisms do the right thing: The attractor hypothesis
Emlen, J.M.; Freeman, D.C.; Mills, A.; Graham, J.H.
1998-01-01
Neo-Darwinian theory is highly successful at explaining the emergence of adaptive traits over successive generations. However, there are reasons to doubt its efficacy in explaining the observed, impressively detailed adaptive responses of organisms to day-to-day changes in their surroundings. Also, the theory lacks a clear mechanism to account for both plasticity and canalization. In effect, there is a growing sentiment that the neo-Darwinian paradigm is incomplete, that something more than genetic structure, mutation, genetic drift, and the action of natural selection is required to explain organismal behavior. In this paper we extend the view of organisms as complex self-organizing entities by arguing that basic physical laws, coupled with the acquisitive nature of organisms, makes adaptation all but tautological. That is, much adaptation is an unavoidable emergent property of organisms' complexity and, to some a significant degree, occurs quite independently of genomic changes wrought by natural selection. For reasons that will become obvious, we refer to this assertion as the attractor hypothesis. The arguments also clarify the concept of "adaptation." Adaptation across generations, by natural selection, equates to the (game theoretic) maximization of fitness (the success with which one individual produces more individuals), while self-organizing based adaptation, within generations, equates to energetic efficiency and the matching of intake and biosynthesis to need. Finally, we discuss implications of the attractor hypothesis for a wide variety of genetical and physiological phenomena, including genetic architecture, directed mutation, genetic imprinting, paramutation, hormesis, plasticity, optimality theory, genotype-phenotype linkage and puncuated equilibrium, and present suggestions for tests of the hypothesis. ?? 1998 American Institute of Physics.
On the Stability of Non-Supersymmetric Quantum Attractors in String Theory
Dominic, Pramod
2011-01-01
We study four dimensional non-supersymmetric attractors in type IIA string theory in the presence of sub-leading corrections to the prepotential. For a given Calabi-Yau manifold, the D0-D4 system admits an attractor point in the moduli space which is uniquely specified by the black hole charges. The perturbative corrections to the prepotential do not change the number of massless directions in the black hole effective potential. We further study non-supersymmetric D0-D6 black holes in the presence of sub-leading corrections. In this case the space of attractor points define a hypersurface in the moduli space.
Synthesis of n-scroll attractors using saturated functions from high-level simulation
Muñoz-Pacheco, J.-M.; Tlelo-Cuautle, E.
2008-02-01
Modeling and simulation of a chaotic oscillator based on saturated nonlinear functions (SNLFs) are presented for the synthesis of n-scrolls attractors. First, the oscillator is simulated at the electronic system level by applying state variables and piecewise-linear approximation. Second, the dynamic ranges are scaled to control the breaking points and slopes within practical values. Additionally, the frequency scaling of n-scrolls attractors is performed. Finally, the SNLF is synthesized using operational amplifiers to generate 2, 3, 4, 5 and 6-scrolls attractors. Theoretical results are confirmed by SPICE simulations to show the usefulness of the proposed synthesis approach.
Synthesis of n-scroll attractors using saturated functions from high-level simulation
Energy Technology Data Exchange (ETDEWEB)
Munoz-Pacheco, J-M; Tlelo-Cuautle, E [Department of Electronics, INAOE, Luis Enrique Erro No. 1, Tonantzintla, Puebla, 72840 (Mexico)], E-mail: mpacheco@inaoep.mx, E-mail: e.tlelo@ieee.org
2008-02-15
Modeling and simulation of a chaotic oscillator based on saturated nonlinear functions (SNLFs) are presented for the synthesis of n-scrolls attractors. First, the oscillator is simulated at the electronic system level by applying state variables and piecewise-linear approximation. Second, the dynamic ranges are scaled to control the breaking points and slopes within practical values. Additionally, the frequency scaling of n-scrolls attractors is performed. Finally, the SNLF is synthesized using operational amplifiers to generate 2, 3, 4, 5 and 6-scrolls attractors. Theoretical results are confirmed by SPICE simulations to show the usefulness of the proposed synthesis approach.
Stochastic sensitivity analysis of the attractors for the randomly forced Ricker model with delay
Energy Technology Data Exchange (ETDEWEB)
Bashkirtseva, Irina; Ryashko, Lev
2014-11-14
Stochastically forced regular attractors (equilibria, cycles, closed invariant curves) of the discrete-time nonlinear systems are studied. For the analysis of noisy attractors, a unified approach based on the stochastic sensitivity function technique is suggested and discussed. Potentialities of the elaborated theory are demonstrated in the parametric analysis of the stochastic Ricker model with delay nearby Neimark–Sacker bifurcation. - Highlights: • Stochastically forced regular attractors of the discrete-time nonlinear systems are studied. • Unified approach based on the stochastic sensitivity function technique is suggested. • Potentialities of the elaborated theory are demonstrated. • Parametric analysis of the stochastic Ricker model with delay is given.
Fluxes, Tadpoles and Holography for N=1 Super Yang Mills
Gómez, C; Resco, P; Gomez, Cesar; Montanez, Sergio; Resco, Pedro
2004-01-01
We study non perturbative superpotentials for N=1 super Yang Mills from the point of view of large $N$ dualities. Starting with open topological strings we work out the relation between the closed string sector dilaton tadpole, which appears in the annulus amplitude, and NSNS fluxes in the closed string dual on the resolved conifold. For the mirror closed string dual version on the deformed conifold we derive, for a non vanishing $G_{3}$ form, the $N$ supersymmetric vacua and the transformations of $G_{3}$ through domain walls. Finally, as an extension of Fischler Susskind mechanism we find a direct relation between the dilaton tadpole and the geometric warping factors induced by the gravitational backreaction of NSNS fluxes.
Distribution of the number of generations in flux compactifications
Braun, Andreas P.; Watari, Taizan
2014-12-01
Flux compactification of string theory generates an ensemble with a large number of vacua, called the landscape. By using the statistics of various properties of low-energy effective theories in the string landscape, one can therefore hope to provide a scientific foundation to the notion of naturalness. This article discusses how to answer such questions of practical interest by using flux compactification of F-theory. It is found that the distribution is approximately in a factorized form given by distribution on the choice of 7-brane gauge group, that on the number of generations Ngen and that on effective coupling constants. The distribution on Ngen is approximately Gaussian for the range |Ngen|≲10 . The statistical cost of higher-rank gauge group is also discussed.
Distribution of the Number of Generations in Flux Compactifications
Braun, Andreas P
2014-01-01
Flux compactification of string theory generates an ensemble with a large number of vacua called the landscape. By using the statistics of various properties of low-energy effective theories in the string landscape, one can therefore hope to provide a scientific foundation to the notion of naturalness. This article discusses how to answer such questions of practical interest by using flux compactification of F-theory. It is found that the distribution is approximately in a factorized form given by the distribution of the choice of 7-brane gauge group, that of the number of generations $N_{\\rm gen}$ and that of effective coupling constants. The distribution of $N_{\\rm gen}$ is approximately Gaussian for the range $|N_{\\rm gen}| \\lesssim 10$. The statistical cost of higher-rank gauge groups is also discussed.
Global attractors and their Hausdorff dimensions for a class of Kirchhoff models
Zhijian, Yang
2010-03-01
This paper studies the existence, regularity, and Hausdorff dimensions of global attractors for a class of Kirchhoff models arising in elastoplastic flow utt-div{|∇u|m -1∇u}-Δut+Δ2u+h(ut)+g(u)=f(x). It proves that under rather mild conditions, the dynamical system associated with above-mentioned models possesses in phase space X a global attractor which has further regularity in Xσ1(↪↪X) and has finite Hausdorff dimension. For application, the fact shows that for the concerned elastoplastic flow the permanent regime (global attractor) can be observed when the excitation starts from any bounded set in phase space, and the dimension of the attractor, that is, the number of degree of freedom of the turbulent phenomenon and thus the level of complexity concerning the flow, is finite.
State space parsimonious reconstruction of attractor produced by an electronic oscillator
Aguirre, Luis A.; Freitas, Ubiratan S.; Letellier, Christophe; Sceller, Lois Le; Maquet, Jean
2000-02-01
This work discusses the reconstruction, from a set of real data, of a chaotic attractor produced by a well-known electronic oscillator, Chua's circuit. The mathematical representation used is a nonlinear differential equation of the polynomial type. One of the contributions of the present study is that structure selection techniques have been applied to help determine the regressors in the model. Models of the chaotic attractor obtained with and without structure selection were compared. The main differences between structure-selected models and complete structure models are: i) the former are more parsimonious that the latter, ii) fixed-point symmetry is guaranteed for the former, iii) for structure-selected models a trivial fixed point is also guaranteed, and iv) the former set of models produce attractors that are topologically closer to the original attractor than those produced by the complete structure models.
Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model
Ovsyannikov, I. I.; Turaev, D. V.
2017-01-01
We give an analytic (free of computer assistance) proof of the existence of a classical Lorenz attractor for an open set of parameter values of the Lorenz model in the form of Yudovich-Morioka-Shimizu. The proof is based on detection of a homoclinic butterfly with a zero saddle value and rigorous verification of one of the Shilnikov criteria for the birth of the Lorenz attractor; we also supply a proof for this criterion. The results are applied in order to give an analytic proof for the existence of a robust, pseudohyperbolic strange attractor (the so-called discrete Lorenz attractor) for an open set of parameter values in a 4-parameter family of 3D Henon-like diffeomorphisms.
Poret, Arnaud; Boissel, Jean-Pierre
2014-12-01
Target identification aims at identifying biomolecules whose function should be therapeutically altered to cure the considered pathology. An algorithm for in silico target identification using Boolean network attractors is proposed. It assumes that attractors correspond to phenotypes produced by the modeled biological network. It identifies target combinations which allow disturbed networks to avoid attractors associated with pathological phenotypes. The algorithm is tested on a Boolean model of the mammalian cell cycle and its applications are illustrated on a Boolean model of Fanconi anemia. Results show that the algorithm returns target combinations able to remove attractors associated with pathological phenotypes and then succeeds in performing the proposed in silico target identification. However, as with any in silico evidence, there is a bridge to cross between theory and practice. Nevertheless, it is expected that the algorithm is of interest for target identification.
Institute of Scientific and Technical Information of China (English)
Zhao Caidi; Jia Xiaolin; Yang Xinbo
2011-01-01
This paper is joint with [27].The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces.
H 2-regularity random attractors of stochastic non-Newtonian fluids with multiplicative noise
Institute of Scientific and Technical Information of China (English)
Chun-xiao GUO; Bo-ling GUO; Hui YANG
2014-01-01
In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H 2-regularity random attractor.
Global periodic attractor of a class of third-order phase-locked loop
Institute of Scientific and Technical Information of China (English)
林源渠
1997-01-01
The uniform boundedness and existence of a global periodic attractor for a third-order phase-locked loop with general phase detector characteristics and frequency modulation input is proved under some parametric conditions.
de Moura FA; Tirnakli; Lyra
2000-11-01
For a family of logisticlike maps, we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space. We found that the phase-space volume occupied by the ensemble W(t) depicts a power-law decay with log-periodic oscillations reflecting the multifractal character of the critical attractor. We explore the parametric dependence of the power-law exponent and the amplitude of the log-periodic oscillations with the attractor's fractal dimension governed by the inflection of the map near its extremal point. Further, we investigate the temporal evolution of W(t) for the circle map whose critical attractor is dense. In this case, we found W(t) to exhibit a rich pattern with a slow logarithmic decay of the lower bounds. These results are discussed in the context of nonextensive Tsallis entropies.
Attractors for the Ginzburg—Landau—BBM Equations in an Unbounded Domain
Institute of Scientific and Technical Information of China (English)
BolingGUO; MurongJIANG
1998-01-01
In this paper,the long time behavior of the global solutions of the Ginzburg-Landau equation coupled with BBM equation in an unbounded domain is considered,The existence of the maximal attractor is obtained.
Institute of Scientific and Technical Information of China (English)
ALI M.; SAHA L.M.
2005-01-01
A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring trajectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1＞0) or not (λ1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an altemative method to calculate λ1has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.
Global attractor and finite dimensionality for a class of dissipative equations of BBM's type
1998-01-01
In this work we study the Cauchy problem for a class of nonlinear dissipative equations of Benjamin-Bona-Mahony's type. We discuss the existence of a global attractor and estimate its Hausdorff and fractal dimensions.
Global attractor and finite dimensionality for a class of dissipative equations of BBM's type
Directory of Open Access Journals (Sweden)
M.A. Astaburuaga
1998-10-01
Full Text Available In this work we study the Cauchy problem for a class of nonlinear dissipative equations of Benjamin-Bona-Mahony's type. We discuss the existence of a global attractor and estimate its Hausdorff and fractal dimensions.
Cortez, Vasco; Medina, Pablo; Goles, Eric; Zarama, Roberto; Rica, Sergio
2015-01-01
Statistical properties, fluctuations and probabilistic arguments are shown to explain the robust dynamics of the Schelling's social segregation model. With the aid of probability density functions we characterize the attractors for multiple external parameters and conditions. We discuss the role of the initial states and we show that, indeed, the system evolves towards well defined attractors. Finally, we provide probabilistic arguments to explain quantitatively the observed behavior.
Exponential Attractor for the Boussinesq Equation with Strong Damping and Clamped Boundary Condition
Fan Geng; Ruizhai Li; Xiaojun Zhang; Xiangyu Ge
2016-01-01
The paper studies the existence of exponential attractor for the Boussinesq equation with strong damping and clamped boundary condition utt-Δu+Δ2u-Δut-Δg(u)=f(x). The main result is concerned with nonlinearities g(u) with supercritical growth. In that case, we construct a bounded absorbing set with further regularity and obtain quasi-stability estimates. Then the exponential attractor is established in natural energy space V2×H.
A Search for Strange Attractors in the Saturation of Middle Atmosphere Gravity Waves
1990-09-01
attractor in surface pressure data, sunshine *duration data and 500 mb zonal wave amplitude data. In a later study 17 (Fraedrich, 1987), he examined...difference in the latter finding. Fraedrich (1986) repeated these calculations for a 30 year record of the number of daily sunshine hours. Again, the...greater if the attractor were of higher dimensions which is very likely. Six hours is practically an eternity for the phenomena we are considering in the
The open-plus-closed loop (OPCL) method for chaotic systems with multiple strange attractors
Institute of Scientific and Technical Information of China (English)
Song Yun-Zhong
2007-01-01
Based on the open-plus-closed-loop (OPCL) control method a systematic and comprehensive controller is presented in this paper for a chaotic system, that is, the Newton-Leipnik equation with two strange attractors: the upper attractor(UA) and the lower attractor (LA). Results show that the final structure of the suggested controller for stabilization has a simple linear feedback form. To keep the integrity of the suggested approach, the globality proof of the basins of entrainment is also provided. In virtue of the OPCL technique, three different kinds of chaotic controls of the system are investigated, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one; and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the proposed means.
Models of Innate Neural Attractors and Their Applications for Neural Information Processing.
Solovyeva, Ksenia P; Karandashev, Iakov M; Zhavoronkov, Alex; Dunin-Barkowski, Witali L
2015-01-01
In this work we reveal and explore a new class of attractor neural networks, based on inborn connections provided by model molecular markers, the molecular marker based attractor neural networks (MMBANN). Each set of markers has a metric, which is used to make connections between neurons containing the markers. We have explored conditions for the existence of attractor states, critical relations between their parameters and the spectrum of single neuron models, which can implement the MMBANN. Besides, we describe functional models (perceptron and SOM), which obtain significant advantages over the traditional implementation of these models, while using MMBANN. In particular, a perceptron, based on MMBANN, gets specificity gain in orders of error probabilities values, MMBANN SOM obtains real neurophysiological meaning, the number of possible grandma cells increases 1000-fold with MMBANN. MMBANN have sets of attractor states, which can serve as finite grids for representation of variables in computations. These grids may show dimensions of d = 0, 1, 2,…. We work with static and dynamic attractor neural networks of the dimensions d = 0 and 1. We also argue that the number of dimensions which can be represented by attractors of activities of neural networks with the number of elements N = 10(4) does not exceed 8.
MODELS OF INNATE NEURAL ATTRACTORS AND THEIR APPLICATIONS FOR NEURALINFORMATION PROCESSING
Directory of Open Access Journals (Sweden)
Ksenia P. Solovyeva
2016-01-01
Full Text Available In this work we reveal and explore a new class of attractor neural networks, based on inborn connections provided by model molecular markers, the molecular marker based attractor neural networks (MMBANN. Each set of markers has a metric, which is used to make connections between neurons containing the markers. We have explored conditions for the existence of attractor states, critical relations between their parameters and the spectrum of single neuron models, which can implement the MMBANN. Besides, we describe functional models (perceptron and SOM, which obtain significant advantages over the traditional implementation of these models, while using MMBANN. In particular, a perceptron, based on MMBANN, gets specificity gain in orders of error probabilities values, MMBANN SOM obtains real neurophysiological meaning, the number of possible grandma cells increases 1000-fold with MMBANN. MMBANN have sets of attractor states, which can serve as finite grids for representation of variables in computations. These grids may show dimensions of d = 0, 1, 2, ... We work with static and dynamic attractor neural networks of the dimensions d = 0 and d = 1. We also argue that the number of dimensions which can be represented by attractors of activities of neural networks with the number of elements N=104 does not exceed 8.
Directory of Open Access Journals (Sweden)
J.E. Camargo-Molina
2014-10-01
Full Text Available We re-evaluate the constraints on the parameter space of the minimal supersymmetric standard model from tunneling to charge- and/or color-breaking minima, taking into account thermal corrections. We pay particular attention to the region known as the Natural MSSM, where the masses of the scalar partners of the top quarks are within an order of magnitude or so of the electroweak scale. These constraints arise from the interaction between these scalar tops and the Higgs fields, which allows the possibility of parameter points having deep charge- and color-breaking true vacua. In addition to requiring that our electroweak-symmetry-breaking, yet QCD- and electromagnetism-preserving vacuum has a sufficiently long lifetime at zero temperature, also demanding stability against thermal tunneling further restricts the allowed parameter space.
Energy Technology Data Exchange (ETDEWEB)
Camargo-Molina, J.E., E-mail: jose.camargo@physik.uni-wuerzburg.de [Institut für Theoretische Physik und Astronomie, Universität Würzburg, Am Hubland, 97074 Würzburg (Germany); Garbrecht, B., E-mail: garbrecht@tum.de [Physik Department T70, Technische Universität München, 85748 Garching (Germany); O' Leary, B., E-mail: ben.oleary@physik.uni-wuerzburg.de [Institut für Theoretische Physik und Astronomie, Universität Würzburg, Am Hubland, 97074 Würzburg (Germany); Porod, W., E-mail: porod@physik.uni-wuerzburg.de [Institut für Theoretische Physik und Astronomie, Universität Würzburg, Am Hubland, 97074 Würzburg (Germany); Staub, F., E-mail: fnstaub@th.physik.uni-bonn.de [Bethe Center for Theoretical Physics and Physikalisches Institut der Universität Bonn, 53115 Bonn (Germany)
2014-10-07
We re-evaluate the constraints on the parameter space of the minimal supersymmetric standard model from tunneling to charge- and/or color-breaking minima, taking into account thermal corrections. We pay particular attention to the region known as the Natural MSSM, where the masses of the scalar partners of the top quarks are within an order of magnitude or so of the electroweak scale. These constraints arise from the interaction between these scalar tops and the Higgs fields, which allows the possibility of parameter points having deep charge- and color-breaking true vacua. In addition to requiring that our electroweak-symmetry-breaking, yet QCD- and electromagnetism-preserving vacuum has a sufficiently long lifetime at zero temperature, also demanding stability against thermal tunneling further restricts the allowed parameter space.
Constraints on \\alpha-attractor inflation and reheating
Ueno, Yoshiki
2016-01-01
We investigate a constraint on reheating followed by alpha-attractor-type inflation (the E-model and T-model) from an observation of the spectral index n_s. When the energy density of the universe is dominated by an energy component with the cosmic equation-of-state parameter w_{re} during reheating, its e-folding number N_{re} and the reheating temperature T_{re} are bounded depending on w_{re}. When the reheating epoch consists of two phases, where the energy density of the universe is dominated by uniform inflaton field oscillations in the first phase and by relativistic non-thermalised particles in the second phase, we find a constraint on the e-folding number of the first oscillation phase, N_{sc}, depending the parameters of the inflaton potential. For the simplest perturbative reheating scenario, we find the lower bound for a coupling constant of inflaton decay in the E-model and T-model depending on the model parameters. We also find a constraint on the $\\alpha$ parameter, \\alpha\\simgt 0.01, for the T...
Seven-disk manifold, α -attractors, and B modes
Ferrara, Sergio; Kallosh, Renata
2016-12-01
Cosmological α -attractor models in N =1 supergravity are based on the hyperbolic geometry of a Poincaré disk with the radius square R2=3 α . The predictions for the B modes, r ≈3 α 4/N2, depend on moduli space geometry and are robust for a rather general class of potentials. Here we notice that starting with M theory compactified on a 7-manifold with G2 holonomy, with a special choice of Betti numbers, one can obtain d =4 , N =1 supergravity with the rank 7 scalar coset [S/L (2 ) S O (2 ) ]7. In a model where these seven unit size Poincaré disks have identified moduli one finds that 3 α =7 . Assuming that the moduli space geometry of the phenomenological models is inherited from this version of M theory, one would predict r ≈10-2 for N =53 e -foldings. We also describe the related maximal supergravity and M/string theory models leading to preferred values 3 α =1 , 2, 3, 4, 5, 6, 7.
The Radiative Kicked Oscillator A Stochastic Web or Chaotic Attractor ?
Ashkenazy, Yu
1999-01-01
A relativistic charged particle moving in a uniform magnetic field and kicked by an electric field is considered. Under the assumption of small magnetic field, an iterative map is developed. We consider both the case in which no radiation is assumed and the radiative case, using the Lorentz-Dirac equation to describe the motion. Comparison between the non-radiative case and the radiative case shows that in both cases one can observe a stochastic web structure for weak magnetic fields, and, although there are global differences in the result of the map, that both cases are qualitatively similar in their small scale behavior. We also develop an iterative map for strong magnetic fields. In that case the web structure no longer exists; it is replaced by a rich chaotic behavior. It is shown that the particle does not diffuse to infinite energy; it is limited by the boundaries of an attractor (the boundaries are generally much smaller than light velocity). Bifurcation occurs, converging rapidly to Feigenbaum's univ...
Attractor dynamics of network UP states in the neocortex
Cossart, Rosa; Aronov, Dmitriy; Yuste, Rafael
2003-05-01
The cerebral cortex receives input from lower brain regions, and its function is traditionally considered to be processing that input through successive stages to reach an appropriate output. However, the cortical circuit contains many interconnections, including those feeding back from higher centres, and is continuously active even in the absence of sensory inputs. Such spontaneous firing has a structure that reflects the coordinated activity of specific groups of neurons. Moreover, the membrane potential of cortical neurons fluctuates spontaneously between a resting (DOWN) and a depolarized (UP) state, which may also be coordinated. The elevated firing rate in the UP state follows sensory stimulation and provides a substrate for persistent activity, a network state that might mediate working memory. Using two-photon calcium imaging, we reconstructed the dynamics of spontaneous activity of up to 1,400 neurons in slices of mouse visual cortex. Here we report the occurrence of synchronized UP state transitions (`cortical flashes') that occur in spatially organized ensembles involving small numbers of neurons. Because of their stereotyped spatiotemporal dynamics, we conclude that network UP states are circuit attractors-emergent features of feedback neural networks that could implement memory states or solutions to computational problems.
Persistent dynamic attractors in activity patterns of cultured neuronal networks
Wagenaar, Daniel A.; Nadasdy, Zoltan; Potter, Steve M.
2006-05-01
Three remarkable features of the nervous system—complex spatiotemporal patterns, oscillations, and persistent activity—are fundamental to such diverse functions as stereotypical motor behavior, working memory, and awareness. Here we report that cultured cortical networks spontaneously generate a hierarchical structure of periodic activity with a strongly stereotyped population-wide spatiotemporal structure demonstrating all three fundamental properties in a recurring pattern. During these “superbursts,” the firing sequence of the culture periodically converges to a dynamic attractor orbit. Precursors of oscillations and persistent activity have previously been reported as intrinsic properties of the neurons. However, complex spatiotemporal patterns that are coordinated in a large population of neurons and persist over several hours—and thus are capable of representing and preserving information—cannot be explained by known oscillatory properties of isolated neurons. Instead, the complexity of the observed spatiotemporal patterns implies large-scale self-organization of neurons interacting in a precise temporal order even in vitro, in cultures usually considered to have random connectivity.
Domain Walls and Flux Tubes in N=2 SQCD D-Brane Prototypes
Shifman, M
2003-01-01
This paper could have been entitled "D branes and strings from flesh and blood." We study field theoretic prototypes of D branes/strings. To this end we consider (2+1)-dimensional domain walls in (3+1)-dimensional N=2 SQCD with SU(2) gauge group and two quark flavors in the fundamental representation. This theory is perturbed by a small mass term of the adjoint matter which, in the leading order in the mass parameter, does not break N=2 supersymmetry, and reduces to a (generalized) Fayet-Iliopoulos term in the effective low-energy N=2 SQED. We find 1/2 BPS-saturated domain wall solution interpolating between two quark vacua at weak coupling, and show that this domain wall localizes a U(1) gauge field. To make contact with the brane/string picture we consider the Abrikosov-Nielsen-Olesen magnetic flux tube in one of two quark vacua and demonstrate that it can end on the domain wall. We find an explicit 1/4 BPS-saturated solution for the wall/flux tube junction. We verify that the end point of the flux tube on ...
Wurdeman, Shane R; Myers, Sara A; Stergiou, Nicholas
2013-04-01
The amputation and subsequent prosthetic rehabilitation of a lower leg affects gait. Dynamical systems theory would predict the use of a prosthetic device should alter the functional attractor dynamics to which the system self-organizes. Therefore, the purpose of this study was to compare the largest Lyapunov exponent (a nonlinear tool for assessing attractor dynamics) for amputee gait compared to healthy non-amputee individuals. Fourteen unilateral, transtibial amputees and fourteen healthy, non-amputee individuals ambulated on a treadmill at preferred, self-selected walking speed. Our results showed that the sound hip (p = 0.013), sound knee (p = 0.05), and prosthetic ankle (p = 0.023) have significantly greater largest Lyapunov exponents than healthy non-amputees. Furthermore, the prosthetic ankle has a significantly greater (p = 0.0.17) largest Lyapunov exponent than the sound leg ankle. These findings indicate attractor states for amputee gait with increased divergence. The increased attractor divergence seems to coincide with decreased ability for motor control between the natural rhythms of the individual and those of the prosthetic device. Future work should consider the impact of different prostheses and rehabilitation on the attractor dynamics.
Lunkenheimer, Erika S; Hollenstein, Tom; Wang, Jun; Shields, Ann M
2012-07-01
Familial emotion socialization practices relate to children's emotion regulation (ER) skills in late childhood, however, we have more to learn about how the context and structure of these interactions relates to individual differences in children's ER. The present study examined flexibility and attractors in family emotion socialization patterns in three different conversational contexts and their relation to ER in 8-12 year olds. Flexibility was defined as dispersion across the repertoire of discrete emotion words and emotion socialization functions (emotion coaching, dismissing, and elaboration) in family conversation, whereas attractors were defined as the average duration per visit to each of these three emotion socialization functions using state space grid analysis. It was hypothesized that higher levels of flexibility in emotion socialization would buffer children's ER from the presence of maladaptive attractors, or the absence of adaptive attractors, in family emotion conversation. Flexibility was generally adaptive, related to children's higher ER across all contexts, and also buffered children from maladaptive attractors in select situations. Findings suggest that the study of dynamic interaction patterns in context may reveal adaptive versus maladaptive socialization processes in the family that can inform basic and applied research on children's regulatory problems.
Chaotic inflation limits for non-minimal models with a Starobinsky attractor
Mosk, Benjamin
2014-01-01
We investigate inflationary attractor points by analyzing non-minimally coupled single field inflation models in two opposite limits; the `flat' limit in which the first derivative of the conformal factor is small and the `steep' limit, in which the first derivative of the conformal factor is large. We consider a subset of models that yield Starobinsky inflation in the steep conformal factor, strong coupling, limit and demonstrate that they result in chaotic inflation in the opposite flat, weak coupling, limit. The suppression of higher order powers of the inflaton field in the potential is shown to be related to the flatness condition on the conformal factor. We stress that the chaotic attractor behaviour in the weak coupling limit is of a different, less universal, character than the Starobinsky attractor. Agreement with the COBE normalisation cannot be obtained in both attractor limits at the same time and in the chaotic attractor limit the scale of inflation depends on the details of the conformal factor,...
Liu, Tianyu; Jiao, Licheng; Ma, Wenping; Shang, Ronghua
2017-03-01
In this paper, an improved quantum-behaved particle swarm optimization (CL-QPSO), which adopts a new collaborative learning strategy to generate local attractors for particles, is proposed to solve nonlinear numerical problems. Local attractors, which directly determine the convergence behavior of particles, play an important role in quantum-behaved particle swarm optimization (QPSO). In order to get a promising and efficient local attractor for each particle, a collaborative learning strategy is introduced to generate local attractors in the proposed algorithm. Collaborative learning strategy consists of two operators, namely orthogonal operator and comparison operator. For each particle, orthogonal operator is used to discover the useful information that lies in its personal and global best positions, while comparison operator is used to enhance the particle's ability of jumping out of local optima. By using a probability parameter, the two operators cooperate with each other to generate local attractors for particles. A comprehensive comparison of CL-QPSO with some state-of-the-art evolutionary algorithms on nonlinear numeric optimization functions demonstrates the effectiveness of the proposed algorithm.
Structure and evolution of strange attractors in non-elastic triangular billiards
Arroyo, Aubin; Sanders, David P
2011-01-01
We study pinball billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls are non-elastic: the outgoing angle with the normal vector to the boundary is a uniform factor $\\lambda < 1$ smaller than the incoming angle. This leads to contraction in phase space for the discrete-time dynamics between consecutive collisions, and hence to attractors of zero Lebesgue measure, which are almost always fractal strange attractors with chaotic dynamics, due to the presence of an expansion mechanism. We study the structure of these strange attractors and their evolution as the contraction parameter $\\lambda$ is varied. For $\\lambda$ in the interval (0, 1/3), we prove rigorously that the attractor has the structure of a Cantor set times an interval, whereas for larger values of $\\lambda$ the billiard dynamics gives rise to nonaccessible regions in phase space. For $\\lambda$ close to 1, the attractor splits into three transitive components, the basins of attraction of which have fra...
A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous system
Institute of Scientific and Technical Information of China (English)
Dong En-Zeng; Chen Zai-Ping; Chen Zeng-Qiang; Yuan Zhu-Zhi
2009-01-01
This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms, and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis, the Hopf bifurcation processes are proved to arise at certain equilibrium points. Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours; the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies.Finally, an analog electronic circuit is designed to physically realize the chaotic system; the existence of four-wing chaotic attractor is verified by the analog circuit realization.
The Chaotic Attractor Analysis of DJIA Based on Manifold Embedding and Laplacian Eigenmaps
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Xiaohua Song
2016-01-01
Full Text Available By using the techniques of Manifold Embedding and Laplacian Eigenmaps, a novel strategy has been proposed in this paper to detect the chaos of Dow Jones Industrial Average. Firstly, the chaotic attractor of financial time series is assumed to lie on a low-dimensional manifold that is embedded into a high-dimensional Euclidean space. Then, an improved phase space reconstruction method and a nonlinear dimensionality reduction method are introduced to help reveal the structure of the chaotic attractor. Next, the empirical study on the financial time series of Dow Jones Industrial Average shows that there exists an attractor which lies on a manifold constructed by the time sequence of Moving average convergence divergence; finally, Determinism Test, Poincaré section, and translation analysis are used as test approaches to prove both whether it is a chaos and how it works.
Design and implementation of grid multi-scroll fractional-order chaotic attractors.
Chen, Liping; Pan, Wei; Wu, Ranchao; Tenreiro Machado, J A; Lopes, António M
2016-08-01
This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most. Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.
Institute of Scientific and Technical Information of China (English)
Yu Fei; Wang Chun-Hua; Yin Jin-Wen; Xu Hao
2011-01-01
In this paper,we propose a novel four-dimensional autonomous chaotic system.Of particular interest is that this novel system can generate one-,two,three- and four-wing chaotic attractors with the variation of a single parameter,and the multi-wing type of the chaotic attractors can be displayed in all directions.The system is simple with a large positive Lyapunov exponent and can exhibit some interesting and complicated dynamical behaviours.Basic dynamical properties of the four-dimensional chaotic system,such as equilibrium points,the Poincaré map,the bifurcation diagram and the Lyapunov exponents are investigated by using either theoretical analysis or numerical method.Finally,a circuit is designed for the implementation of the multi-wing chaotic attractors.The electronic workbench observations are in good agreement with the numerical simulation results.
The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System.
Li, Yongjun; Wei, Xiaona; Zhang, Yanhong
2016-01-01
First, for a process {U(t, τ)∣t ≥ τ}, we introduce a new concept, called the weak D-pullback exponential attractor, which is a family of sets {ℳ(t)∣t ≤ T}, for any T ∈ ℝ, satisfying the following: (i) ℳ(t) is compact, (ii) ℳ(t) is positively invariant, that is, U(t, τ)ℳ(τ) ⊂ ℳ(t), and (iii) there exist k, l > 0 such that dist(U(t, τ)B(τ), ℳ(t)) ≤ ke (-(t-τ)); that is, ℳ(t) pullback exponential attracts B(τ). Then we give a method to obtain the existence of weak D-pullback exponential attractors for a process. As an application, we obtain the existence of weak D-pullback exponential attractor for reaction diffusion equation in H 0 (1) with exponential growth of the external force.
Design and implementation of grid multi-scroll fractional-order chaotic attractors
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Chen, Liping, E-mail: lip-chenhut@126.com; Pan, Wei [School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009 (China); Wu, Ranchao [School of Mathematics, Anhui University, Hefei 230039 (China); Tenreiro Machado, J. A. [Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249-015 Porto (Portugal); Lopes, António M. [UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto (Portugal)
2016-08-15
This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most. Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.
Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys
Institute of Scientific and Technical Information of China (English)
Pierluigi COLLI; Michel FR(E)MOND; Elisabetta ROCCA; Ken SHIRAKAWA
2006-01-01
In this note, we consider a Frémond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely,we generalize the paper [12] dealing with the one-dimensional case. First, we show the existence of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the non-autonomous case by the limiting global attractor.
Non-BPS Attractors in 5d and 6d Extended Supergravity
Andrianopoli, L; Marrani, A; Trigiante, M
2008-01-01
We connect the attractor equations of a certain class of N=2, d=5 supergravities with their (1,0), d=6 counterparts, by relating the moduli space of non-BPS d=5 black hole/black string attractors to the moduli space of extremal dyonic black string d=6 non-BPS attractors. For d = 5 real special symmetric spaces and for N = 4,6,8 theories, we explicitly compute the flat directions of the black object potential corresponding to vanishing eigenvalues of its Hessian matrix. In the case N = 4, we study the relation to the (2,0), d=6 theory. We finally describe the embedding of the N=2, d=5 magic models in N=8, d=5 supergravity as well as the interconnection among the corresponding charge orbits.
Existence of the solutions and the attractors for the large-scale atmospheric equations
Institute of Scientific and Technical Information of China (English)
HUANG; Haiyang; GUO; Boling
2006-01-01
In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik's definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations.The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.
On the control of the chaotic attractors of the 2-d Navier-Stokes equations.
Smaoui, Nejib; Zribi, Mohamed
2017-03-01
The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, Re. Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.
Direct numerical simulations of an inertial wave attractor in linear and nonlinear regimes
Jouve, Laurène
2014-01-01
In a uniformly rotating fluid, inertial waves propagate along rays that are inclined to the rotation axis by an angle that depends on the wave frequency. In closed domains, multiple reflections from the boundaries may cause inertial waves to focus on to particular structures known as wave attractors. Such structures have previously been studied from a theoretical point of view, in laboratory experiments, in linear numerical calculations and in some recent numerical simulations. In the present paper, two-dimensional direct numerical simulations of an inertial wave attractor are presented. In the linear regime, we first recover the results of the linear calculations and asymptotic theory of Ogilvie (2005) who considered a prototypical problem involving the focusing of linear internal waves into a narrow beam centred on a wave attractor in a steady state. The velocity profile of the beam and its scalings with the Ekman number, as well as the asymptotic value of the dissipation rate, are found to be in agreement ...
Willie, Robert
2016-09-01
In this paper, we study a model system of equations of the time dependent Ginzburg-Landau equations of superconductivity in a Lorentz gauge, in scale of Hilbert spaces E^{α } with initial data in E^{β } satisfying 3α + β ≥ N/2, where N=2,3 is such that the spatial domain of the equations [InlineEquation not available: see fulltext.]. We show in the asymptotic dynamics of the equations, well-posedness of the dynamical system for a global exponential attractor {{U}}subset E^{α } compact in E^{β } if α >β , uniform differentiability of orbits on the attractor in E0\\cong L2, and the existence of an explicit finite bounding estimate on the fractal dimension of the attractor yielding that its Hausdorff dimension is as well finite. Uniform boundedness in (0,∞ )× Ω of solutions in E^{1/2}\\cong H1(Ω ) is in addition investigated.
Attractors and the attraction basins of discrete-time cellular neural networks
Institute of Scientific and Technical Information of China (English)
Ma Runnian; Xi Youmin
2005-01-01
The dynamic behavior of discrete-time cellular neural networks(DTCNN), which is strict with zero threshold value, is mainly studied in asynchronous mode and in synchronous mode. In general, a k-attractor of DTCNN is not a convergent point.But in this paper, it is proved that a k-attractor is a convergent point if the strict DTCNN satisfies some conditions. The attraction basin of the strict DTCNN is studied, one example is given to illustrate the previous conclusions to be wrong, and several results are presented. The obtained results on k-attractor and attraction basin not only correct the previous results, but also provide a theoretical foundation of performance analysis and new applications of the DTCNN.
Controllable V-Shape Multi-Scroll Butterfly Attractor: System and Circuit Implementation
Zidan, Mohammed A.
2012-07-23
In this paper, a new controllable V-shape multiscroll attractor is presented, where a variety of symmetrical and unsymmetrical attractors with a variable number of scrolls can be controlled using new staircase nonlinear function and the parameters of the system. This attractor can be used to generate random signals with a variety of symbol distribution. Digital implementation of the proposed generator is also presented using a Xilinx Virtex® 4 Field Programmable Gate Array and experimental results are provided. The digital realization easily fits into a small area (<1.5% of the total area) and expresses a high throughput (4.3 Gbit/sec per state variable). © 2012 World Scientific Publishing Company.
Radiation reaction induced spiral attractors in ultra-intense colliding laser beams
Gong, Z; Shou, Y R; Qiao, B; Chen, C E; Xu, F R; He, X T; Yan, X Q
2016-01-01
The radiation reaction effects on electron dynamics in counter-propagating circularly polarized laser beams are investigated through the linearization theorem and the results are in great agreement with numeric solutions. For the first time, the properties of fixed points in electron phase-space were analyzed with linear stability theory, showing that center nodes will become attractors if the classical radiation reaction is considered. Electron dynamics are significantly affected by the properties of the fixed points and the electron phase-space densities are found to be increasing exponentially near the attractors. The density growth rates are derived theoretically and further verified by particle-in-cell simulations, which can be detected in experiments to explore the effects of radiation reaction qualitatively. The attractor can also facilitate to realize a series of nanometer-scaled flying electron slices via adjusting the colliding laser frequencies.
The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System
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Yongjun Li
2016-01-01
Full Text Available First, for a process U(t,τ∣t≥τ, we introduce a new concept, called the weak D-pullback exponential attractor, which is a family of sets M(t∣t≤T, for any T∈R, satisfying the following: (i M(t is compact, (ii M(t is positively invariant, that is, U(t,τM(τ⊂M(t, and (iii there exist k,l>0 such that dist(U(t,τB(τ,M(t≤ke-(t-τ; that is, M(t pullback exponential attracts B(τ. Then we give a method to obtain the existence of weak D-pullback exponential attractors for a process. As an application, we obtain the existence of weak D-pullback exponential attractor for reaction diffusion equation in H01 with exponential growth of the external force.
Roach, James; Sander, Leonard; Zochowski, Michal
Auto-associative memory is the ability to retrieve a pattern from a small fraction of the pattern and is an important function of neural networks. Within this context, memories that are stored within the synaptic strengths of networks act as dynamical attractors for network firing patterns. In networks with many encoded memories, some attractors will be stronger than others. This presents the problem of how networks switch between attractors depending on the situation. We suggest that regulation of neuronal spike-frequency adaptation (SFA) provides a universal mechanism for network-wide attractor selectivity. Here we demonstrate in a Hopfield type attractor network that neurons minimal SFA will reliably activate in the pattern corresponding to a local attractor and that a moderate increase in SFA leads to the network to converge to the strongest attractor state. Furthermore, we show that on long time scales SFA allows for temporal sequences of activation to emerge. Finally, using a model of cholinergic modulation within the cortex we argue that dynamic regulation of attractor preference by SFA could be critical for the role of acetylcholine in attention or for arousal states in general. This work was supported by: NSF Graduate Research Fellowship Program under Grant No. DGE 1256260 (JPR), NSF CMMI 1029388 (MRZ) and NSF PoLS 1058034 (MRZ & LMS).
A signature of attractor dynamics in the CA3 region of the hippocampus.
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César Rennó-Costa
2014-05-01
Full Text Available The notion of attractor networks is the leading hypothesis for how associative memories are stored and recalled. A defining anatomical feature of such networks is excitatory recurrent connections. These "attract" the firing pattern of the network to a stored pattern, even when the external input is incomplete (pattern completion. The CA3 region of the hippocampus has been postulated to be such an attractor network; however, the experimental evidence has been ambiguous, leading to the suggestion that CA3 is not an attractor network. In order to resolve this controversy and to better understand how CA3 functions, we simulated CA3 and its input structures. In our simulation, we could reproduce critical experimental results and establish the criteria for identifying attractor properties. Notably, under conditions in which there is continuous input, the output should be "attracted" to a stored pattern. However, contrary to previous expectations, as a pattern is gradually "morphed" from one stored pattern to another, a sharp transition between output patterns is not expected. The observed firing patterns of CA3 meet these criteria and can be quantitatively accounted for by our model. Notably, as morphing proceeds, the activity pattern in the dentate gyrus changes; in contrast, the activity pattern in the downstream CA3 network is attracted to a stored pattern and thus undergoes little change. We furthermore show that other aspects of the observed firing patterns can be explained by learning that occurs during behavioral testing. The CA3 thus displays both the learning and recall signatures of an attractor network. These observations, taken together with existing anatomical and behavioral evidence, make the strong case that CA3 constructs associative memories based on attractor dynamics.
Non-Abelian Magnetized Blackholes and Unstable Attractors
Mosaffa, A. E.; Randjbar-Daemi, S.; Sheikh-Jabbari, M. M.
2006-01-01
Fluctuations of non-Abelian gauge fields in a background magnetic flux contain tachyonic modes and hence the background is unstable. We extend these results to the cases where the background flux is coupled to Einstein gravity and show that the corresponding spherically symmetric geometries, which in the absence of a cosmological constant are of the form of Reissner-Nordstrom blackholes or the AdS_2xS^2, are also unstable. We discuss the relevance of these instabilities to several places in s...
Łukaszewicz, Grzegorz
2012-01-01
We consider a two-dimensional nonstationary Navier-Stokes shear flow with a subdifferential boundary condition on a part of the boundary of the flow domain, namely, with a boundary driving subject to the Tresca law. There exists a unique global in time solution of the considered problem which is governed by a variational inequality. Our aim is to prove the existence of a global attractor of a finite fractional dimension and of an exponential attractor for the associated semigroup. We use the method of $l$-trajectories. This research is motivated by a problem from lubrication theory.
Maximal Attractors for the m-Dimensional Cahn-Hilliard System
Institute of Scientific and Technical Information of China (English)
Wei Nian ZHANG
2004-01-01
In this paper we discuss maximal attractors of the m-dimensional Cahn-Hilliard System in the product spaces (L2(Ω))m and (H2(Ω))m in terms of D. Henry's general theory and from the viewpoint of compactness and absorptivity of semigroups as R. Temam did. After giving the existence and uniqueness of global solutions, we technically restrict our discussion to some subspaces, give estimates with a new graph norm, and obtain the existence of maximal attractors and some properties of them.
Modeling multi-agent self-organization through the lens of higher order attractor dynamics
DEFF Research Database (Denmark)
Butner, Jonathan E.; Wiltshire, Travis; Munion, A.K.
2017-01-01
's behavior. We present four examples that differ in the number of variables used to depict the attractor dynamics (1, 2, and 6) and range from simulated to non-simulated data sources. We demonstrate that this is a flexible method that advances scientific study of SCD in a variety of multi-agent systems....... of attractor dynamic patterns. The advantage of this approach is that we are able to quantify the self-organized dynamics that agents exhibit, link these dynamics back to activity from individual agents, and relate it to other variables central to understanding the coordinative functionality of a system...
Hidden attractors in a chaotic system with an exponential nonlinear term
Pham, V.-T.; Vaidyanathan, S.; Volos, C. K.; Jafari, S.
2015-07-01
Studying systems with hidden attractors is new attractive research direction because of its practical and threoretical importance. A novel system with an exponential nonlinear term, which can exhibit hidden attractors, is proposed in this work. Although new system possesses no equilibrium points, it displays rich dynamical behaviors, like chaos. By calculating Lyapunov exponents and bifurcation diagram, the dynamical behaviors of such system are discovered. Moreover, two important features of a chaotic system, the possibility of synchronization and the feasibility of the theoretical model, are also presented by introducing an adaptive synchronization scheme and designing a digital hardware platform-based emulator.
Existence and regularity of a global attractor for doubly nonlinear parabolic equations
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Abderrahmane El Hachimi
2002-05-01
Full Text Available In this paper we consider a doubly nonlinear parabolic partial differential equation $$ frac{partial eta (u}{partial t}-Delta _{p}u+f(x,t,u=0 quad hbox{in }Omega imesmathbb{R}^{+}, $$ with Dirichlet boundary condition and initial data given. We prove the existence of a global compact attractor by using a dynamical system approach. Under additional conditions on the nonlinearities $Beta$, $f$, and on $p$, we prove more regularity for the global attractor and obtain stabilization results for the solutions.
Rank One Strange Attractors in Periodically Kicked Predator-Prey System with Time-Delay
Yang, Wenjie; Lin, Yiping; Dai, Yunxian; Zhao, Huitao
2016-06-01
This paper is devoted to the study of the problem of rank one strange attractor in a periodically kicked predator-prey system with time-delay. Our discussion is based on the theory of rank one maps formulated by Wang and Young. Firstly, we develop the rank one chaotic theory to delayed systems. It is shown that strange attractors occur when the delayed system undergoes a Hopf bifurcation and encounters an external periodic force. Then we use the theory to the periodically kicked predator-prey system with delay, deriving the conditions for Hopf bifurcation and rank one chaos along with the results of numerical simulations.
INFN-Laboratori Nazionali di Frascati School on the Attractor Mechanism 2009
4th School on Attractor Mechanism : Supersymmetric Gravity and Black Holes
2013-01-01
This book is based upon lectures presented in the summer of 2009 at the INFN-Laboratori Nazionali di Frascati School on Attractor Mechanism, directed by Stefano Bellucci. The symposium included such prestigious lecturers as S. Ferrara, G. Dall'Agata, J.F. Morales, J. Simón and M. Trigiante. All lectures were given at a pedagogical, introductory level, which is reflected in the specific "flavor" of this volume. The book also benefits from extensive discussions about, and the related reworking of, the various contributions. It is the fifth volume in a series of books on the general topics of supersymmetry, supergravity, black holes and the attractor mechanism.
Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains
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Qiuying Lu
2014-01-01
Full Text Available We prove the existence of a pullback attractor in L2(ℝn for the stochastic Ginzburg-Landau equation with additive noise on the entire n-dimensional space ℝn. We show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system. We demonstrate that the system possesses a unique D-random attractor, for which the asymptotic compactness is established by the method of uniform estimates on the tails of its solutions.
Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains
Brzeźniak, Z.; Caraballo, T.; Langa, J. A.; Li, Y.; Łukaszewicz, G.; Real, J.
We show that the stochastic flow generated by the 2-dimensional Stochastic Navier-Stokes equations with rough noise on a Poincaré-like domain has a unique random attractor. One of the technical problems associated with the rough noise is overcomed by the use of the corresponding Cameron-Martin (or reproducing kernel Hilbert) space. Our results complement the result by Brzeźniak and Li (2006) [10] who showed that the corresponding flow is asymptotically compact and also generalize Caraballo et al. (2006) [12] who proved existence of a unique attractor for the time-dependent deterministic Navier-Stokes equations.
Exponential attractors for a Cahn-Hilliard model in bounded domains with permeable walls
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Ciprian G. Gal
2006-11-01
Full Text Available In a previous article [7], we proposed a model of phase separation in a binary mixture confined to a bounded region which may be contained within porous walls. The boundary conditions were derived from a mass conservation law and variational methods. In the present paper, we study the problem further. Using a Faedo-Galerkin method, we obtain the existence and uniqueness of a global solution to our problem, under more general assumptions than those in [7]. We then study its asymptotic behavior and prove the existence of an exponential attractor (and thus of a global attractor with finite dimension.
U.S. Geological Survey, Department of the Interior — Methane (CH4) flux is the net rate of methane exchange between an ecosystem and the atmosphere. Data of this variable were generated by the USGS LandCarbon project...
Inertial Wave Excitation and Wave Attractors in an Annular Tank: DNS
Klein, Marten; Ghasemi, Abouzar; Harlander, Uwe; Will, Andreas
2014-05-01
Rotation is the most relevant aspect of geophysical fluid dynamics, manifesting itself by the Coriolis force. Small perturbations to the state of rigid body rotation can excite inertial waves (waves restored by Coriolis force) with frequencies in the range 0 kinematic viscosity ν. The whole vessel rotates with a mean angular velocity Ω0 around its axis of symmetry. Ekman numbers investigated are 1 ≠« E = ν(Ω0H2)-1 ≥ 10-5. Similarly to [1-5] we perturb the system by longitudinal libration, Ω(t) = Ω0(1 + ɛsinωt), where ω > 0 denotes the frequency and 0 < ɛ < 1 the amplitude of libration. Three-dimensional direct numerical simulations (3-D DNS) of the set-up were conducted in order to resolve different excitation mechanisms. We used an incompressible Navier-Stokes solver with the equations formulated for volume fluxes in generalized curvilinear coordinates. Under some constraints the scheme conserves three quantities of Hamiltonian mechanics: mass, momentum and kinetic energy. To separate between possible excitation mechanisms we investigated configurations that cannot be accessed in the laboratory, e.g., axially periodic geometries and cases with libration of different walls. For ɛ ≤ 0.3 we found qualitative agreement of wave attractor patterns obtained by numerical simulations, ray tracing and measurements in the laboratory for all libration frequencies investigated. We adapted boundary layer theory for the librating walls to estimate inertial wave excitation, in particular, the relation to libration frequency and amplitude, as well as the effect of the inclination angle α of the frustum. By comparison with numerical simulations we found that wave energy in the bulk obeys a similar dependency on frequency as the energy in the boundary layer over the librating wall. References [1] A. Tilgner, Phys. Rev. E (1999), vol. 59(2), pp. 1769-1794. [2] J. Boisson, C. Lamriben, L. R. M. Maas, P.-P. Cortet and F. Moisy, Phys. Fluids (2012), vol. 24, 076602
Global attractor for the Kirchhoff type equation with a strong dissipation
Zhijian, Yang; Yunqing, Wang
The paper studies the longtime behavior of the Kirchhoff type equation with a strong dissipation u-M(‖∇u‖2)Δu-Δu+h(u)+g(u)=f(x). It proves that the related continuous semigroup S(t) possesses in the phase space with low regularity a global attractor which is connected. And an example is shown.
Detecting small attractors of large Boolean networks by function-reduction-based strategy.
Zheng, Qiben; Shen, Liangzhong; Shang, Xuequn; Liu, Wenbin
2016-04-01
Boolean networks (BNs) are widely used to model gene regulatory networks and to design therapeutic intervention strategies to affect the long-term behaviour of systems. A central aim of Boolean-network analysis is to find attractors that correspond to various cellular states, such as cell types or the stage of cell differentiation. This problem is NP-hard and various algorithms have been used to tackle it with considerable success. The idea is that a singleton attractor corresponds to n consistent subsequences in the truth table. To find these subsequences, the authors gradually reduce the entire truth table of Boolean functions by extending a partial gene activity profile (GAP). Not only does this process delete inconsistent subsequences in truth tables, it also directly determines values for some nodes not extended, which means it can abandon the partial GAPs that cannot lead to an attractor as early as possible. The results of simulation show that the proposed algorithm can detect small attractors with length p = 4 in BNs of up to 200 nodes with average indegree K = 2.
Lorenz, HW; Nusse, HE
Goodwin's nonlinear accelerator model with periodic investment outlays is reconsidered and used as an economic example of the emergence of complex motion in nonlinear dynamical systems. In addition to chaotic attractors, the model can possess coexisting attracting periodic orbits or simple
DEFF Research Database (Denmark)
Isaeva, Olga B.; Kuznetsov, Sergey P.; Mosekilde, Erik
2011-01-01
The paper proposes an approach to constructing feasible examples of dynamical systems with hyperbolic chaotic attractors based on the successive transfer of excitation between two pairs of self-oscillators that are alternately active. An angular variable that measures the relations of the current...
Lerner, Itamar; Bentin, Shlomo; Shriki, Oren
2012-01-01
Localist models of spreading activation (SA) and models assuming distributed representations offer very different takes on semantic priming, a widely investigated paradigm in word recognition and semantic memory research. In this study, we implemented SA in an attractor neural network model with distributed representations and created a unified…
From Cellular Attractor Selection to Adaptive Signal Control for Traffic Networks.
Tian, Daxin; Zhou, Jianshan; Sheng, Zhengguo; Wang, Yunpeng; Ma, Jianming
2016-03-14
The management of varying traffic flows essentially depends on signal controls at intersections. However, design an optimal control that considers the dynamic nature of a traffic network and coordinates all intersections simultaneously in a centralized manner is computationally challenging. Inspired by the stable gene expressions of Escherichia coli in response to environmental changes, we explore the robustness and adaptability performance of signalized intersections by incorporating a biological mechanism in their control policies, specifically, the evolution of each intersection is induced by the dynamics governing an adaptive attractor selection in cells. We employ a mathematical model to capture such biological attractor selection and derive a generic, adaptive and distributed control algorithm which is capable of dynamically adapting signal operations for the entire dynamical traffic network. We show that the proposed scheme based on attractor selection can not only promote the balance of traffic loads on each link of the network but also allows the global network to accommodate dynamical traffic demands. Our work demonstrates the potential of bio-inspired intelligence emerging from cells and provides a deep understanding of adaptive attractor selection-based control formation that is useful to support the designs of adaptive optimization and control in other domains.
Quasi-periodic Henon-like attractors in the Lorenz-84 climate model with seasonal forcing
Broer, HW; Vitolo, R; Simo, C; Dumortier, F; Broer, H; Mawhin, J; Vanderbauwhede, A; Lunel, SV
2005-01-01
A class of strange attractors is described, occurring in a low-dimensional model of general atmospheric circulation. The differential equations of the system are subject to periodic forcing, where the period is one year - as suggested by Lorenz in 1984. The dynamics of the system is described in ter
RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH MULTIPLICATIVE NOISE
Institute of Scientific and Technical Information of China (English)
Zhao Caidi; Li Yongsheng; Zhou Shengfan
2011-01-01
This article proves that the random dynamical system generated by a two- dimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.
Analytical estimates of efficiency of attractor neural networks with inborn connections
Directory of Open Access Journals (Sweden)
Solovyeva Ksenia
2016-01-01
Full Text Available The analysis is restricted to the features of neural networks endowed to the latter by the inborn (not learned connections. We study attractor neural networks in which for almost all operation time the activity resides in close vicinity of a relatively small number of attractor states. The number of the latter, M, is proportional to the number of neurons in the neural network, N, while the total number of the states in it is 2N. The unified procedure of growth/fabrication of neural networks with sets of all attractor states with dimensionality d=0 and d=1, based on model molecular markers, is studied in detail. The specificity of the networks (d=0 or d=1 depends on topology (i.e., the set of distances between elements which can be provided to the set of molecular markers by their physical nature. The neural networks parameters estimates and trade-offs for them in attractor neural networks are calculated analytically. The proposed mechanisms reveal simple and efficient ways of implementation in artificial as well as in natural neural networks of multiplexity, i.e. of using activity of single neurons in representation of multiple values of the variables, which are operated by the neural systems. It is discussed how the neuronal multiplexity provides efficient and reliable ways of performing functional operations in the neural systems.
The necessity for a time local dimension in systems with time-varying attractors
DEFF Research Database (Denmark)
Særmark, Knud H; Ashkenazy, Y; Levitan, J;
1997-01-01
We show that a simple non-linear system for ordinary differential equations may possess a time-varying attractor dimension. This indicates that it is infeasible to characterize EEG and MEG time series with a single time global dimension. We suggest another measure for the description of non...
Global attractors of non-autonomous quasi-homogeneous dynamical systems
Directory of Open Access Journals (Sweden)
David N. Cheban
2002-01-01
Full Text Available It is shown that non-autonomous quasi-homogeneous dynamical systems admit a compact global attractor. The general results obtained here are applied to differential equations both in finite dimensional spaces and in infinite dimensional spaces, such as ordinary differential equations in Banach space and some types of evolutional partial differential equations.
On coincidence problem and attractor solutions in ELKO dark energy model
Sadjadi, H Mohseni
2011-01-01
We study the critical points of a Universe dominated by ELKO spinor field dark energy and a barotropic matter in an almost general case. The coincidence problem and attractor solutions are discussed and it is shown the coincidence problem can not be alleviated in this model.
Lerner, Itamar; Bentin, Shlomo; Shriki, Oren
2012-01-01
Localist models of spreading activation (SA) and models assuming distributed representations offer very different takes on semantic priming, a widely investigated paradigm in word recognition and semantic memory research. In this study, we implemented SA in an attractor neural network model with distributed representations and created a unified…
From Cellular Attractor Selection to Adaptive Signal Control for Traffic Networks
Tian, Daxin; Zhou, Jianshan; Sheng, Zhengguo; Wang, Yunpeng; Ma, Jianming
2016-03-01
The management of varying traffic flows essentially depends on signal controls at intersections. However, design an optimal control that considers the dynamic nature of a traffic network and coordinates all intersections simultaneously in a centralized manner is computationally challenging. Inspired by the stable gene expressions of Escherichia coli in response to environmental changes, we explore the robustness and adaptability performance of signalized intersections by incorporating a biological mechanism in their control policies, specifically, the evolution of each intersection is induced by the dynamics governing an adaptive attractor selection in cells. We employ a mathematical model to capture such biological attractor selection and derive a generic, adaptive and distributed control algorithm which is capable of dynamically adapting signal operations for the entire dynamical traffic network. We show that the proposed scheme based on attractor selection can not only promote the balance of traffic loads on each link of the network but also allows the global network to accommodate dynamical traffic demands. Our work demonstrates the potential of bio-inspired intelligence emerging from cells and provides a deep understanding of adaptive attractor selection-based control formation that is useful to support the designs of adaptive optimization and control in other domains.
Dynamics of warped flux compactifications with backreacting anti-branes
Junghans, Daniel
2014-01-01
We revisit the effective low-energy dynamics of the volume modulus in warped flux compactifications with anti-D3-branes in order to analyze the prospects for meta-stable de Sitter vacua and brane inflation along the lines of KKLT/KKLMMT. At the level of the 10d supergravity solution, anti-branes in flux backgrounds with opposite charge are known to source singular terms in the energy densities of the bulk fluxes, which led to a debate on the consistency of such constructions in string theory. A straightforward yet non-trivial check of the singular solution is to verify that its dimensional reduction in the large-volume limit reproduces the 4d low-energy dynamics expected from known results where the anti-branes are treated as a probe. Taking into account the anti-brane backreaction in the effective scalar potential, we find that both the volume scaling and the coefficient of the anti-brane uplift term are in exact agreement with the probe potential if the singular fluxes satisfy a certain near-brane boundary ...
Interpolating from Bianchi attractors to Lifshitz and AdS spacetimes
Energy Technology Data Exchange (ETDEWEB)
Kachru, Shamit [SITP, Department of Physics and Theory Group, SLAC, Stanford University,Stanford, CA 94305 (United States); Kundu, Nilay [Tata Institute for Fundamental Research, Mumbai 400005 (India); Saha, Arpan [Indian Institute of Technology - Bombay,Powai, Mumbai (India); Samanta, Rickmoy; Trivedi, Sandip P. [Tata Institute for Fundamental Research, Mumbai 400005 (India)
2014-03-17
We construct classes of smooth metrics which interpolate from Bianchi attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or AdS{sub 2}×S{sup 3} geometries in the UV. While we do not obtain these metrics as solutions of Einstein gravity coupled to a simple matter field theory, we show that the matter sector stress-energy required to support these geometries (via the Einstein equations) does satisfy the weak, and therefore also the null, energy condition. Since Lifshitz or AdS{sub 2}×S{sup 3} geometries can in turn be connected to AdS{sub 5} spacetime, our results show that there is no barrier, at least at the level of the energy conditions, for solutions to arise connecting these Bianchi attractor geometries to AdS{sub 5} spacetime. The asymptotic AdS{sub 5} spacetime has no non-normalizable metric deformation turned on, which suggests that furthermore, the Bianchi attractor geometries can be the IR geometries dual to field theories living in flat space, with the breaking of symmetries being either spontaneous or due to sources for other fields. Finally, we show that for a large class of flows which connect two Bianchi attractors, a C-function can be defined which is monotonically decreasing from the UV to the IR as long as the null energy condition is satisfied. However, except for special examples of Bianchi attractors (including AdS space), this function does not attain a finite and non-vanishing constant value at the end points.
Directory of Open Access Journals (Sweden)
Yijin Zhang
2013-01-01
Full Text Available This work is concerned with the random dynamics of two-dimensional stochastic Boussinesq system with dynamical boundary condition. The white noises affect the system through a dynamical boundary condition. Using a method based on the theory of omega-limit compactness of a random dynamical system, we prove that the L2-random attractor for the generated random dynamical system is exactly the H1-random attractor. This improves a recent conclusion derived by Brune et al. on the existence of the L2-random attractor for the same system.
On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes
Energy Technology Data Exchange (ETDEWEB)
Chatzistavrakidis, A. [Institute of Nuclear Physics, NCSR Demokritos, 15310 Athens (Greece); Physics Department, National Technical University, Zografou Campus, 15780 Athens (Greece); Steinacker, H. [Department of Physics, University of Vienna, Boltzmanngasse 5, 1090 Wien (Austria); Zoupanos, G. [Physics Department, National Technical University, Zografou Campus, 15780 Athens (Greece)
2010-06-15
We consider certain vacua of four-dimensional SU(N) gauge theory with the same field content as the N=4 supersymmetric Yang-Mills theory, resulting from potentials which break the N=4 supersymmetry as well as its global SO(6) symmetry down to SO(3) x SO(3). We show that the theory behaves at intermediate scales as Yang-Mills theory on M{sup 4} x S{sub L}{sup 2} x S{sub R}{sup 2}, where the extra dimensions are fuzzy spheres with magnetic fluxes. We determine in particular the structure of the zero modes due to the fluxes, which leads to low-energy mirror models. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
A flux-scaling scenario for high-scale moduli stabilization in string theory
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Ralph Blumenhagen
2015-08-01
Full Text Available Tree-level moduli stabilization via geometric and non-geometric fluxes in type IIB orientifolds on Calabi–Yau manifolds is investigated. The focus is on stable non-supersymmetric minima, where all moduli are fixed except for some massless axions. The scenario includes the purely axionic orientifold-odd moduli. A set of vacua allowing for parametric control over the moduli vacuum expectation values and their masses is presented, featuring a specific scaling with the fluxes. Uplift mechanisms and supersymmetry breaking soft masses on MSSM-like D7-branes are discussed as well. This scenario provides a complete effective framework for realizing the idea of F-term axion monodromy inflation in string theory. It is argued that, with all masses close to the Planck and GUT scales, one is confronted with working at the threshold of controlling all mass hierarchies.
A flux-scaling scenario for high-scale moduli stabilization in string theory
Energy Technology Data Exchange (ETDEWEB)
Blumenhagen, Ralph [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München (Germany); Font, Anamaría [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München (Germany); Arnold Sommerfeld Center for Theoretical Physics, LMU, Theresienstr. 37, 80333 München (Germany); Fuchs, Michael [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München (Germany); Herschmann, Daniela, E-mail: herschma@mpp.mpg.de [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München (Germany); Plauschinn, Erik [Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova (Italy); INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova (Italy); Sekiguchi, Yuta; Wolf, Florian [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München (Germany); Arnold Sommerfeld Center for Theoretical Physics, LMU, Theresienstr. 37, 80333 München (Germany)
2015-08-15
Tree-level moduli stabilization via geometric and non-geometric fluxes in type IIB orientifolds on Calabi–Yau manifolds is investigated. The focus is on stable non-supersymmetric minima, where all moduli are fixed except for some massless axions. The scenario includes the purely axionic orientifold-odd moduli. A set of vacua allowing for parametric control over the moduli vacuum expectation values and their masses is presented, featuring a specific scaling with the fluxes. Uplift mechanisms and supersymmetry breaking soft masses on MSSM-like D7-branes are discussed as well. This scenario provides a complete effective framework for realizing the idea of F-term axion monodromy inflation in string theory. It is argued that, with all masses close to the Planck and GUT scales, one is confronted with working at the threshold of controlling all mass hierarchies.
Laboratory and numerical simulation of internal wave attractors and their instability.
Brouzet, Christophe; Dauxois, Thierry; Ermanyuk, Evgeny; Joubaud, Sylvain; Sibgatullin, Ilias
2015-04-01
Internal wave attractors are formed as result of focusing of internal gravity waves in a confined domain of stably stratified fluid due to peculiarities of reflections properties [1]. The energy injected into domain due to external perturbation, is concentrated along the path formed by the attractor. The existence of attractors was predicted theoretically and proved both experimentally and numerically [1-4]. Dynamics of attractors is greatly influenced by geometrical focusing, viscous dissipation and nonlinearity. The experimental setup features Schmidt number equal to 700 which impose constraints on resolution in numerical schemes. Also for investigation of stability on large time intervals (about 1000 periods of external forcing) numerical viscosity may have significant impact. For these reasons, we have chosen spectral element method for investigation of this problem, what allows to carefully follow the nonlinear dynamics. We present cross-comparison of experimental observations and numerical simulations of long-term behavior of wave attractors. Fourier analysis and subsequent application of Hilbert transform are used for filtering of spatial components of internal-wave field [5]. The observed dynamics shows a complicated coupling between the effects of local instability and global confinement of the fluid domain. The unstable attractor is shown to act as highly efficient mixing box providing the efficient energy pathway from global-scale excitation to small-scale wave motions and mixing. Acknowledgement, IS has been partially supported by Russian Ministry of Education and Science (agreement id RFMEFI60714X0090) and Russian Foundation for Basic Research, grant N 15-01-06363. EVE gratefully acknowledges his appointment as a Marie Curie incoming fellow at Laboratoire de physique ENS de Lyon. This work has been partially supported by the ONLITUR grant (ANR-2011-BS04-006-01) and achieved thanks to the resources of PSMN from ENS de Lyon 1. Maas, L. R. M. & Lam, F
Kinetic attractor phase diagrams of active nematic suspensions: the dilute regime.
Forest, M Gregory; Wang, Qi; Zhou, Ruhai
2015-08-28
Large-scale simulations by the authors of the kinetic-hydrodynamic equations for active polar nematics revealed a variety of spatio-temporal attractors, including steady and unsteady, banded (1d) and cellular (2d) spatial patterns. These particle scale activation-induced attractors arise at dilute nanorod volume fractions where the passive equilibrium phase is isotropic, whereas all previous model simulations have focused on the semi-dilute, nematic equilibrium regime and mostly on low-moment orientation tensor and polarity vector models. Here we extend our previous results to complete attractor phase diagrams for active nematics, with and without an explicit polar potential, to map out novel spatial and dynamic transitions, and to identify some new attractors, over the parameter space of dilute nanorod volume fraction and nanorod activation strength. The particle-scale activation parameter corresponds experimentally to a tunable force dipole strength (so-called pushers with propulsion from the rod tail) generated by active rod macromolecules, e.g., catalysis with the solvent phase, ATP-induced propulsion, or light-activated propulsion. The simulations allow 2d spatial variations in all flow and orientational variables and full spherical orientational degrees of freedom; the attractors correspond to numerical integration of a coupled system of 125 nonlinear PDEs in 2d plus time. The phase diagrams with and without the polar interaction potential are remarkably similar, implying that polar interactions among the rodlike particles are not essential to long-range spatial and temporal correlations in flow, polarity, and nematic order. As a general rule, above a threshold, low volume fractions induce 1d banded patterns, whereas higher yet still dilute volume fractions yield 2d patterns. Again as a general rule, varying activation strength at fixed volume fraction induces novel dynamic transitions. First, stationary patterns saturate the instability of the isotropic
Energy Technology Data Exchange (ETDEWEB)
Guo, Kong-Ming, E-mail: kmguo@xidian.edu.cn [School of Electromechanical Engineering, Xidian University, P.O. Box 187, Xi' an 710071 (China); Jiang, Jun, E-mail: jun.jiang@mail.xjtu.edu.cn [State Key Laboratory for Strength and Vibration, Xi' an Jiaotong University, Xi' an 710049 (China)
2014-07-04
To apply stochastic sensitivity function method, which can estimate the probabilistic distribution of stochastic attractors, to non-autonomous dynamical systems, a 1/N-period stroboscopic map for a periodic motion is constructed in order to discretize the continuous cycle into a discrete one. In this way, the sensitivity analysis of a cycle for discrete map can be utilized and a numerical algorithm for the stochastic sensitivity analysis of periodic solutions of non-autonomous nonlinear dynamical systems under stochastic disturbances is devised. An external excited Duffing oscillator and a parametric excited laser system are studied as examples to show the validity of the proposed method. - Highlights: • A method to analyze sensitivity of stochastic periodic attractors in non-autonomous dynamical systems is proposed. • Probabilistic distribution around periodic attractors in an external excited Φ{sup 6} Duffing system is obtained. • Probabilistic distribution around a periodic attractor in a parametric excited laser system is determined.
Directory of Open Access Journals (Sweden)
Gui Mu
2013-01-01
Full Text Available The existence of the exponential attractors for coupled Ginzburg-Landau equations describing Bose-Einstein condensates and nonlinear optical waveguides and cavities with periodic initial boundary is obtained by showing Lipschitz continuity and the squeezing property.
Energy Technology Data Exchange (ETDEWEB)
Márquez, Bicky A., E-mail: bmarquez@ivic.gob.ve; Suárez-Vargas, José J., E-mail: jjsuarez@ivic.gob.ve; Ramírez, Javier A. [Centro de Física, Instituto Venezolano de Investigaciones Científicas, km. 11 Carretera Panamericana, Caracas 1020-A (Venezuela, Bolivarian Republic of)
2014-09-01
Controlled transitions between a hierarchy of n-scroll attractors are investigated in a nonlinear optoelectronic oscillator. Using the system's feedback strength as a control parameter, it is shown experimentally the transition from Van der Pol-like attractors to 6-scroll, but in general, this scheme can produce an arbitrary number of scrolls. The complexity of every state is characterized by Lyapunov exponents and autocorrelation coefficients.
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale
Energy Technology Data Exchange (ETDEWEB)
Maslennikov, Oleg V.; Nekorkin, Vladimir I. [Institute of Applied Physics of RAS, Nizhny Novgorod (Russian Federation)
2016-07-15
In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.
Rohde, G K; Nichols, J M; Bucholtz, F
2008-03-01
We consider the problem of detection and estimation of chaotic signals in the presence of white Gaussian noise. Traditionally this has been a difficult problem since generalized likelihood ratio tests are difficult to implement due to the chaotic nature of the signals of interest. Based on Poincare's recurrence theorem we derive an algorithm for approximating a chaotic time series with unknown initial conditions. The algorithm approximates signals using elements carefully chosen from a dictionary constructed based on the chaotic signal's attractor. We derive a detection approach based on the signal estimation algorithm and show, with simulated data, that the new approach can outperform other methods for chaotic signal detection. Finally, we describe how the attractor based detection scheme can be used in a secure binary digital communications protocol.
Attractors of derivative complex Ginzburg-Landau equation in unbounded domains
Institute of Scientific and Technical Information of China (English)
GUO Boling; HAN Yongqian
2007-01-01
The Ginzburg-Landau-type complex equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. In this paper, the derivative complex Ginzburg- Landau (DCGL) equation in an unbounded domain ΩС R2 is studied. We extend the Gagliardo-Nirenberg inequality to the weighted Sobolev spaces introduced by S. V. Zelik. Applied this Gagliardo-Nirenberg inequality of the weighted Sobolev spaces and based on the technique for the semi-linear system of parabolic equations which has been developed by M. A. Efendiev and S. V. Zelik, the global attractor in the corresponding phase space is constructed, the upper bound of its Kolmogorov's ε-entropy is obtained, and the spatial chaos of the attractor for DCGL equation in R2 is detailed studied.
Piecewise affine models of chaotic attractors: The Rössler and Lorenz systems
Amaral, Gleison F. V.; Letellier, Christophe; Aguirre, Luis Antonio
2006-03-01
This paper proposes a procedure by which it is possible to synthesize Rössler [Phys. Lett. A 57, 397-398 (1976)] and Lorenz [J. Atmos. Sci. 20, 130-141 (1963)] dynamics by means of only two affine linear systems and an abrupt switching law. Comparison of different (valid) switching laws suggests that parameters of such a law behave as codimension one bifurcation parameters that can be changed to produce various dynamical regimes equivalent to those observed with the original systems. Topological analysis is used to characterize the resulting attractors and to compare them with the original attractors. The paper provides guidelines that are helpful to synthesize other chaotic dynamics by means of switching affine linear systems.
6d → 5d → 4d reduction of BPS attractors in flat gauged supergravities
Directory of Open Access Journals (Sweden)
Kiril Hristov
2015-08-01
This is achieved starting from the BPS black string in 6d with an AdS3×S3 attractor and taking two different routes to arrive at a 1/2 BPS AdS2×S2 attractor of a non-BPS black hole in 4d N=2 flat gauged supergravity. The two inequivalent routes interchange the order of KK reduction on AdS3 and SS reduction on S3. We also find the commutator between the two operations after performing a duality transformation: on the level of the theory the result is the exchange of electric with magnetic gaugings; on the level of the solution we find a flip of the quartic invariant I4 to −I4.
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale.
Maslennikov, Oleg V; Nekorkin, Vladimir I
2016-07-01
In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.