Journal articles: 'Dynamical structure functions'

1

Indumathi, D., and Wei Zhu. "A dynamical model for nuclear structure functions." Zeitschrift für Physik C 74, no. 1 (1997): 119. http://dx.doi.org/10.1007/s002880050375.

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Yuan, Ye, Keith Glover, and Jorge Gonçalves. "On minimal realisations of dynamical structure functions." Automatica 55 (May 2015): 159–64. http://dx.doi.org/10.1016/j.automatica.2015.03.005.

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Glück, M., and E. Reya. "Dynamical QCD evaluation of the photon structure functions." Nuclear Physics B 311, no. 3 (January 1989): 519–26. http://dx.doi.org/10.1016/0550-3213(89)90166-1.

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Golden, Kenneth I., and Gabor J. Kalman. "Dynamical structure functions for charged particle bilayers and superlattices." Journal of Physics A: Mathematical and General 36, no. 22 (May 23, 2003): 5865–75. http://dx.doi.org/10.1088/0305-4470/36/22/306.

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Hohl, M., J. Roth, and H. R. Trebin. "Correlation functions and the dynamical structure factor of quasicrystals." European Physical Journal B 17, no. 4 (October 2000): 595–601. http://dx.doi.org/10.1007/s100510070096.

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Duch, Włodzisław. "Hylomorphism Extended: Dynamical Forms and Minds." Philosophies 3, no. 4 (November 19, 2018): 36. http://dx.doi.org/10.3390/philosophies3040036.

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Physical objects are compounds of matter and form, as stated by Aristotle in his hylomorphism theory. The concept of “form” in this theory refers to physical structures or organizational structures. However, mental processes are not of this kind, they do not change physical arrangement of neurons, but change their states. To cover all natural processes hylomorphism should acknowledge differences between three kinds of forms: Form as physical structure, form as function resulting from organization and interactions between constituent parts, and dynamical form as state transitions that change functions of structures without changing their physical organization. Dynamical forms, patterns of energy activation that change the flow of information without changing the structure of matter, are the key to understand minds of rational animals.

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Shul’ga, N. F., V. V. Syshchenko, A. I. Tarnovsky, and A. Yu Isupov. "Structure of the channeling electrons wave functions under dynamical chaos conditions." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 370 (March 2016): 1–9. http://dx.doi.org/10.1016/j.nimb.2015.12.040.

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Andersson, B. "A string-dynamical description of gluon and ocean quark structure functions." Physics Letters B 277, no. 3 (March 5, 1992): 359–65. http://dx.doi.org/10.1016/0370-2693(92)90758-v.

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Yeung, Enoch, Jongmin Kim, Ye Yuan, Jorge Gonçalves, and Richard M. Murray. "Data-driven network models for genetic circuits from time-series data with incomplete measurements." Journal of The Royal Society Interface 18, no. 182 (September 2021): 20210413. http://dx.doi.org/10.1098/rsif.2021.0413.

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Synthetic gene networks are frequently conceptualized and visualized as static graphs. This view of biological programming stands in stark contrast to the transient nature of biomolecular interaction, which is frequently enacted by labile molecules that are often unmeasured. Thus, the network topology and dynamics of synthetic gene networks can be difficult to verify in vivo or in vitro , due to the presence of unmeasured biological states. Here we introduce the dynamical structure function as a new mesoscopic, data-driven class of models to describe gene networks with incomplete measurements of state dynamics. We develop a network reconstruction algorithm and a code base for reconstructing the dynamical structure function from data, to enable discovery and visualization of graphical relationships in a genetic circuit diagram as time-dependent functions rather than static, unknown weights. We prove a theorem, showing that dynamical structure functions can provide a data-driven estimate of the size of crosstalk fluctuations from an idealized model. We illustrate this idea with numerical examples. Finally, we show how data-driven estimation of dynamical structure functions can explain failure modes in two experimentally implemented genetic circuits, a previously reported in vitro genetic circuit and a new E. coli -based transcriptional event detector.

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Bruin, Nils, and Alexander Molnar. "Minimal models for rational functions in a dynamical setting." LMS Journal of Computation and Mathematics 15 (December 1, 2012): 400–417. http://dx.doi.org/10.1112/s1461157012001131.

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AbstractWe present a practical algorithm to compute models of rational functions with minimal resultant under conjugation by fractional linear transformations. We also report on a search for rational functions of degrees 2 and 3 with rational coefficients that have many integers in a single orbit. We find several minimal quadratic rational functions with eight integers in an orbit and several minimal cubic rational functions with ten integers in an orbit. We also make some elementary observations on possibilities of an analogue of Szpiro’s conjecture in a dynamical setting and on the structure of the set of minimal models for a given rational function.

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Thépaut, Jean-Noël, Philippe Courtier, Gilles Belaud, and Gwendal Lema??tre. "Dynamical structure functions in a four-dimensional variational assimilation: A case study." Quarterly Journal of the Royal Meteorological Society 122, no. 530 (January 1996): 535–61. http://dx.doi.org/10.1002/qj.49712253012.

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Boroun, G. R., B. Rezaei, and J. K. Sarma. "A phenomenological solution small x to the longitudinal structure function dynamical behavior." International Journal of Modern Physics A 29, no. 32 (December 30, 2014): 1450189. http://dx.doi.org/10.1142/s0217751x14501899.

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In this paper, the evolutions of longitudinal proton structure function have been obtained at small x up to next-to-next-to-leading order using a hard Pomeron behavior. In our paper, evolutions of gluonic as well as heavy longitudinal structure functions have been obtained separately and the total contributions have been calculated. The total longitudinal structure functions have been compared with results of Donnachie–Landshoff (DL) model, Color Dipole (CD) model, kT factorization and H1 data.

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Chernobryvko, Marina V., Konstantin V. Avramov, Valentina N. Romanenko, Tatiana J. Batutina, and Ulan S. Suleimenov. "Dynamic instability of ring-stiffened conical thin-walled rocket fairing in supersonic gas stream." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 1 (June 19, 2015): 55–68. http://dx.doi.org/10.1177/0954406215592171.

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The assumed-modes method is applied to obtain the dynamical model of the ring-stiffened conical shells in a supersonic gas stream. The pressure acting on the shell is described by the piston theory. The displacements of the rings are functions of the shell displacements. The kinetic and the potential energies of the structure are obtained as the functions of the shell displacements. It is suggested the approach to calculate the shell spatial mode, when the shell dynamic stability is lost. The free vibrations of the structures with different numbers of the rings are analyzed. The loss of the structure dynamic stability is investigated.

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Jafarian, Amirhossein, Peter Zeidman, Vladimir Litvak, and Karl Friston. "Structure learning in coupled dynamical systems and dynamic causal modelling." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2160 (October 28, 2019): 20190048. http://dx.doi.org/10.1098/rsta.2019.0048.

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Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill-posed problem that commonly arises when modelling real-world phenomena. In this review, we detail a set of statistical procedures for inferring the structure of nonlinear coupled dynamical systems (structure learning), which has proved useful in neuroscience research. A key focus here is the comparison of competing models of network architectures—and implicit coupling functions—in terms of their Bayesian model evidence. These methods are collectively referred to as dynamic causal modelling. We focus on a relatively new approach that is proving remarkably useful, namely Bayesian model reduction, which enables rapid evaluation and comparison of models that differ in their network architecture. We illustrate the usefulness of these techniques through modelling neurovascular coupling (cellular pathways linking neuronal and vascular systems), whose function is an active focus of research in neurobiology and the imaging of coupled neuronal systems. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

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Marx, D., K. Heinzinger, G. Pálinkás, and I. Bakó. "Structure and Dynamics of NaCl in Methanol. A Molecular Dynamics Study." Zeitschrift für Naturforschung A 46, no. 10 (October 1, 1991): 887–97. http://dx.doi.org/10.1515/zna-1991-1009.

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AbstractA recently developed flexible three-site model for methanol was employed to perform a Molecular Dynamics simulation of a 0.6 molal NaCl solution. The ion-methanol and ion-ion potential functions were derived from ab initio calculations. The structural properties of the solution are discussed on the basis of radial and angular distribution functions, the orientation of the methanol molecules, and their geometrical arrangement in the solvation shells of the ions. The dynamical properties of the solution - like self-diffusion coefficients, hindered translations, librations, and internal vibrations of the methanol molecules - are calculated from various autocorrelation functions.

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Aledo, Juan A., Ali Barzanouni, Ghazaleh Malekbala, Leila Sharifan, and Jose C. Valverde. "On the Periodic Structure of Parallel Dynamical Systems on Generalized Independent Boolean Functions." Mathematics 8, no. 7 (July 3, 2020): 1088. http://dx.doi.org/10.3390/math8071088.

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In this paper, based on previous results on AND-OR parallel dynamical systems over directed graphs, we give a more general pattern of local functions that also provides fixed point systems. Moreover, by considering independent sets, this pattern is also generalized to get systems in which periodic orbits are only fixed points or 2-periodic orbits. The results obtained are also applicable to homogeneous systems. On the other hand, we study the periodic structure of parallel dynamical systems given by the composition of two parallel systems, which are conjugate under an invertible map in which the inverse is equal to the original map. This allows us to prove that the composition of any parallel system on a maxterm (or minterm) Boolean function and its conjugate one by means of the complement map is a fixed point system, when the associated graph is undirected. However, when the associated graph is directed, we demonstrate that the corresponding composition may have points of any period, even if we restrict ourselves to the simplest maxterm OR and the simplest minterm AND. In spite of this general situation, we prove that, when the associated digraph is acyclic, the composition of OR and AND is a fixed point system.

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Rajasekar, S. "Dynamical structure functions at critical bifurcations in a Bonhoeffer-van der Pol equation." Chaos, Solitons & Fractals 7, no. 11 (November 1996): 1799–805. http://dx.doi.org/10.1016/s0960-0779(96)00046-x.

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Fussmann, Gregor F., and Bernd Blasius. "Community response to enrichment is highly sensitive to model structure." Biology Letters 1, no. 1 (March 22, 2005): 9–12. http://dx.doi.org/10.1098/rsbl.2004.0246.

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Biologists use mathematical functions to model, understand and predict nature. For most biological processes, however, the exact analytical form is not known. This is also true for one of the most basic life processes: the uptake of food or resources. We show that the use of several nearly indistinguishable functions, which can serve as phenomenological descriptors of resource uptake, may lead to alarmingly different dynamical behaviour in a simple community model. More specifically, we demonstrate that the degree of resource enrichment needed to destabilize the community dynamics depends critically on the mathematical nature of the uptake function.

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WADA, RYOICHI, and KAZUTOSHI GOHARA. "FRACTALS AND CLOSURES OF LINEAR DYNAMICAL SYSTEMS EXCITED STOCHASTICALLY BY TEMPORAL INPUTS." International Journal of Bifurcation and Chaos 11, no. 03 (March 2001): 755–79. http://dx.doi.org/10.1142/s0218127401002602.

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Fractals and closures of two-dimensional linear dynamical systems excited by temporal inputs are investigated. The continuous dynamics defined by the set of vector fields in the cylindrical phase space is reduced to the discrete dynamics defined by the set of iterated functions on the Poincaré section. When all iterated functions are contractions, it has already been shown theoretically that a trajectory in the cylindrical phase space converges into an attractive invariant set with a fractal-like structure. Calculating analytically the Lipschitz constants of iterated functions, we show that, under some conditions, noncontractions often appear. However, we numerically show that, even for noncontractions, an attractive invariant set with a fractal-like structure exists. By introducing the interpolating system, we can also show that the set of trajectories in the cylindrical phase space is enclosed by the tube structure whose initial set is the closure of the fractal set on the Poincaré section.

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YANG, HUIJUN. "DEPENDENCE OF HAMILTONIAN CHAOS ON PERTURBATION STRUCTURE." International Journal of Bifurcation and Chaos 03, no. 04 (August 1993): 1013–28. http://dx.doi.org/10.1142/s0218127493000830.

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In this paper, we considered a Hamiltonian dynamical system consisting of a steady wave and a perturbation wave and studied the dependence of spatial patterns of chaos on the perturbation structure (i.e., the wave numbers of the perturbation wave). The system came from the passive wave mixing and transport problem. In order to investigate this dependence, we first did some simple mixing experiments with initially a small blob and calculated the correlation dimensions. Secondly we used Lyapunov exponents to identify the chaotic regions and the invariant tori and computed the histograms or PDFs (Probability Distribution Functions) to characterize the Hamiltonian chaos for different perturbation structure. We found that this dependence was very complicated and the complexity increases with the perturbation structure. This dynamical system became more chaotic with increase in the wave numbers. The fascinating patterns of the Hamiltonian chaos for various perturbation structures were presented. The spatial pattern of chaos on the isentropic surface of the atmosphere was given. Implications of the results of the chaotic wave mixing and transport in climate dynamics, atmospheric chemistry, aeronomy and large scale dynamics of geophysical fluid flows were briefly discussed.

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Bakó, Imre, Tamás Radnai, and Gábor Pálinkás. "Investigation of the Structure of Liquid Pyridine: a Molecular Dynamics Simulation, an RISM, and an X-ray Diffraction Study." Zeitschrift für Naturforschung A 51, no. 7 (July 1, 1996): 859–66. http://dx.doi.org/10.1515/zna-1996-0710.

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Abstract The structure of liquid pyridine is investigated by molecular dynamics simulation and the RISM integral equation methods. The calculated total radial distribution functions (RDF) are compared with the experimental RDF’s, obtained by X-ray diffraction measurement. It is shown that the local structure of liquid pyridine is mainly determined by the dipole-dipole interaction between the molecules. The local order is characterized by the pair distribution functions, angular correlation functions and orientational distributions. Dynamical properties (self-diffusion coefficients, rotational correlation times and reorientational correlation times) calculated on the basis of MD results are in good agreement with experimental data.

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GOHARA, KAZUTOSHI, and ARATA OKUYAMA. "DYNAMICAL SYSTEMS EXCITED BY TEMPORAL INPUTS: FRACTAL TRANSITION BETWEEN EXCITED ATTRACTORS." Fractals 07, no. 02 (June 1999): 205–20. http://dx.doi.org/10.1142/s0218348x99000220.

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This paper presents a framework for dissipative dynamical systems excited by external temporal inputs. We introduce a set {Il} of temporal inputs with finite intervals. The set {Il} defines two other sets of dynamical systems. The first is the set of continuous dynamical systems that are defined by a set {fl} of vector fields on the hyper-cylindrical phase space ℳ. The second is the set of discrete dynamical systems that are defined by a set {gl} of iterated functions on the global Poincaré section Σ. When the inputs are switched stochastically, a trajectory in the space ℳ converges to an attractive invariant set with fractal-like structure. We can analytically prove this result when all of the iterated functions satisfy a contraction property. Even without this property, we can numerically show that an attractive invariant set with fractal-like structure exists.

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Zhang, Huaguang, Yujiao Huang, Tiaoyang Cai, and Zhanshan Wang. "Dynamical stability analysis of delayed recurrent neural networks with ring structure." International Journal of Modern Physics B 28, no. 19 (June 12, 2014): 1450118. http://dx.doi.org/10.1142/s0217979214501185.

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In this paper, multistability is discussed for delayed recurrent neural networks with ring structure and multi-step piecewise linear activation functions. Sufficient criteria are obtained to check the existence of multiple equilibria. A lemma is proposed to explore the number and the cross-direction of purely imaginary roots for the characteristic equation, which corresponds to the neural network model. Stability of all of equilibria is investigated. The work improves and extends the existing stability results in the literature. Finally, two examples are given to illustrate the effectiveness of the obtained results.

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Rimanyi, R., and A. Varchenko. "Dynamical Gelfand–Zetlin algebra and equivariant cohomology of grassmannians." Journal of Knot Theory and Its Ramifications 25, no. 12 (October 2016): 1642013. http://dx.doi.org/10.1142/s021821651642013x.

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We consider the rational dynamical quantum group [Formula: see text] and introduce an [Formula: see text]-module structure on [Formula: see text], where [Formula: see text] is the equivariant cohomology algebra [Formula: see text] of the cotangent bundle of the Grassmannian [Formula: see text] with coefficients extended by a suitable ring of rational functions in an additional variable [Formula: see text]. We consider the dynamical Gelfand–Zetlin algebra which is a commutative algebra of difference operators in [Formula: see text]. We show that the action of the Gelfand–Zetlin algebra on [Formula: see text] is the natural action of the algebra [Formula: see text] on [Formula: see text], where [Formula: see text] is the shift operator. The [Formula: see text]-module structure on [Formula: see text] is introduced with the help of dynamical stable envelope maps which are dynamical analogs of the stable envelope maps introduced by Maulik and Okounkov [Quantum Groups and quantum cohomology, preprint (2012) 1–276, arXiv:1211.1287]. The dynamical stable envelope maps are defined in terms of the rational dynamical weight functions introduced in [G. Felder, V. Tarasov and A. Varchenko, Solutions of the elliptic QKZB equations and Bethe ansatz I, in Topics in Singularity Theory V. I. Arnold’s 60th Anniversary Collection, Advances in the Mathematical Sciences, AMS Translations, Series 2, Vol. 180 (AMS, 1997), pp. 45–76.] to construct q-hypergeometric solutions of rational qKZB equations. The cohomology classes in [Formula: see text] induced by the weight functions are dynamical variants of Chern–Schwartz–MacPherson classes of Schubert cells.

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ANDRIES, JOHAN, FABIO BENATTI, MIEKE De COCK, and MARK FANNES. "MULTI-TIME CORRELATIONS IN RELAXING QUANTUM DYNAMICAL SYSTEMS." Reviews in Mathematical Physics 12, no. 07 (July 2000): 921–44. http://dx.doi.org/10.1142/s0129055x00000356.

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In this paper, we consider the long time asymptotics of multi-time correlation functions for quantum dynamical systems that are sufficiently random to relax to a reference state. In particular, the evolution of such systems must have a continuous spectrum. Special attention is paid to general dynamical clustering conditions and their consequences for the structure of fluctuations of temporal averages. This approach is applied to the so-called Powers–Price shifts.

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CHEN, SHYH-LEH, and STEVEN W. SHAW. "A FAST-MANIFOLD APPROACH TO MELNIKOV FUNCTIONS FOR SLOWLY VARYING OSCILLATORS." International Journal of Bifurcation and Chaos 06, no. 08 (August 1996): 1575–78. http://dx.doi.org/10.1142/s021812749600093x.

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A new approach to obtaining the Melnikov function for homoclinic orbits in slowly varying oscillators is proposed. The present method applies the usual two-dimensional Melnikov analysis to the “fast” dynamics of the system which lie on an invariant manifold. It is shown that the resultant Melnikov function is the same as that obtained in the usual way involving distance functions in three dimensions [Wiggins and Holmes, 1987]. This alternative derivation provides some useful insight into the structure of the dynamical system.

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Melcer, Jozef, Daniela Kuchárová, and Mária Kúdelčíková. "Calculation of Characteristics Describing the Properties of Dynamical Systems." Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series. 17, no. 1 (June 1, 2017): 147–54. http://dx.doi.org/10.1515/tvsb-2017-0017.

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Abstract There are characteristics that uniquely define the properties of dynamical systems from the point of its dynamical response. For example, natural frequencies and natural modes or frequency response functions can be assigned to these characteristics. Determination of these characteristics is fixed on the selection of computational model and on the means of structure excitation. This contribution discusses about analysis of such characteristics.

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SIXSMITH, DAVID J. "Dynamical sets whose union with infinity is connected." Ergodic Theory and Dynamical Systems 40, no. 3 (August 10, 2018): 789–98. http://dx.doi.org/10.1017/etds.2018.54.

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Suppose that $f$ is a transcendental entire function. In 2011, Rippon and Stallard showed that the union of the escaping set with infinity is always connected. In this paper we consider the related question of whether the union with infinity of the bounded orbit set, or the bungee set, can also be connected. We give sufficient conditions for these sets to be connected and an example of a transcendental entire function for which all three sets are simultaneously connected. This function lies, in fact, in the Speiser class.It is known that for many transcendental entire functions the escaping set has a topological structure known as a spider’s web. We use our results to give a large class of functions in the Eremenko–Lyubich class for which the escaping set is not a spider’s web. Finally, we give a novel topological criterion for certain sets to be a spider’s web.

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Sharif, M., and Z. Yousaf. "Dynamics of spherical stars with structure scalars and R + ϵRn cosmology." Canadian Journal of Physics 93, no. 8 (August 2015): 905–11. http://dx.doi.org/10.1139/cjp-2014-0626.

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We study the role of the R + ϵRn model on the dynamical evolution of radiating anisotropic and shearing viscous relativistic spherical stellar structures. In this context, we calculate modified versions of scalar functions (previously defined by L. Herrera et al. Phys. Rev. D, 79, 064025 (2009). doi:10.1103/PhysRevD.79.064025 ) for the problem under consideration and then associate them with the physical parameters. The Weyl tensor as well as other matter variables with extra curvature terms coming from the model are related and find shear and expansion evolution equations. We conclude that structure scalars along with f(R) degrees of freedom have vital importance in the dynamics of spherical compact systems.

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Basilakos, Spyros. "Cosmic expansion and structure formation in running vacuum cosmologies." Modern Physics Letters A 30, no. 22 (July 3, 2015): 1540031. http://dx.doi.org/10.1142/s0217732315400313.

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We investigate the dynamics of the Friedmann–Lemaître–Robertson–Walker (FLRW) flat cosmological models in which the vacuum energy varies with redshift. A particularly well-motivated model of this type is the so-called quantum field vacuum, in which both kind of terms [Formula: see text] and constant appear in the effective dark energy (DE) density affecting the evolution of the main cosmological functions at the background and perturbation levels. Specifically, it turns out that the functional form of the quantum vacuum endows the vacuum energy of a mild dynamical evolution which could be observed nowadays and appears as dynamical DE. Interestingly, the low-energy behavior is very close to the usual Lambda cold dark matter (ΛCDM) model, but it is by no means identical. Finally, within the framework of the quantum field vacuum we generalize the large scale structure properties, namely growth of matter perturbations, cluster number counts and spherical collapse model.

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OMORI, Luna, Stephanie NIX, and Yukitaka ISHIMOTO. "Study of the relation between the biological structure and fluid dynamical functions of dragonfly wings." Proceedings of the Bioengineering Conference Annual Meeting of BED/JSME 2018.30 (2018): 1I08. http://dx.doi.org/10.1299/jsmebio.2018.30.1i08.

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Zhi-Mei, Lou, Chen Zi-Dong, and Wang Wen-Long. "Poisson structure and Casimir functions for a noncentral dynamical system in four-dimensional phase space." Chinese Physics 14, no. 8 (July 29, 2005): 1483–85. http://dx.doi.org/10.1088/1009-1963/14/8/001.

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FEDRIZZI, MARIO, MICHELE FEDRIZZI, and R. A. MARQUES PEREIRA. "CONSENSUS MODELLING IN GROUP DECISION MAKING: DYNAMICAL APPROACH BASED ON FUZZY PREFERENCES." New Mathematics and Natural Computation 03, no. 02 (July 2007): 219–37. http://dx.doi.org/10.1142/s1793005707000744.

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The. notion of consensus plays an important role in group decision making, particularly when the collective preference structure is generated by a dynamical aggregation process of the single individual preference structures. In this dynamical process of aggregation each single decision maker gradually transforms his/her preference structure by combining it, through iterative weighted averaging, with the preference structures of the remaining decision makers. In this way, the collective decision emerges dynamically as a result of the consensual interaction among the various decision makers in the group. From the point of view of applied mathematics, the models of consensual dynamics stand in the context of multi-agent complex systems, with interactive and nonlinear dynamics. The consensual interaction among the various agents (decision makers) acts on their state variables (the preferences) in order to optimize an appropriate measure of consensus, which can be of type 'hard' (unanimous agreement within the group of decision makers) or 'soft' (partial agreement within the group of decision makers). In this paper, we study the modelling of consensus reaching when the individual testimonies are assumed to be expressed as fuzzy preference relations. Here consensus is meant as the degree to which most of the experts agree on the preferences associated to the most relevant alternatives. First of all we derive a degree of dissensus based on linguistic quantifiers and then we introduce a form of network dynamics in which the quantifiers are represented by scaling functions. Finally, assuming that the decision makers can express their preferences in a more flexible way, i.e. by using triangular fuzzy numbers, we describe the iterative process of opinion transformation towards consensus via the gradient dynamics of a cost function expressed as a linear combination of a dissensus cost function and an inertial cost function.

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Rocha, J. Leonel, Abdel-Kaddous Taha, and D. Fournier-Prunaret. "Dynamical Analysis and Big Bang Bifurcations of 1D and 2D Gompertz's Growth Functions." International Journal of Bifurcation and Chaos 26, no. 11 (October 2016): 1630030. http://dx.doi.org/10.1142/s0218127416300305.

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In this paper, we study the dynamics and bifurcation properties of a three-parameter family of 1D Gompertz's growth functions, which are defined by the population size functions of the Gompertz logistic growth equation. The dynamical behavior is complex leading to a diversified bifurcation structure, leading to the big bang bifurcations of the so-called “box-within-a-box” fractal type. We provide and discuss sufficient conditions for the existence of these bifurcation cascades for 1D Gompertz's growth functions. Moreover, this work concerns the description of some bifurcation properties of a Hénon's map type embedding: a “continuous” embedding of 1D Gompertz's growth functions into a 2D diffeomorphism. More particularly, properties that characterize the big bang bifurcations are considered in relation with this coupling of two population size functions, varying the embedding parameter. The existence of communication areas of crossroad area type or swallowtails are identified for this 2D diffeomorphism.

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Chu, Miao, Shao Hui Tian, Yan Chao Zhang, and Xiao Chun Pan. "Dynamic Analysis of Three-Dimensional Flexibility of Gear Structure Based on Finite Element Method." Advanced Materials Research 411 (November 2011): 33–37. http://dx.doi.org/10.4028/www.scientific.net/amr.411.33.

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The paper established a three-dimensional flexibility dynamical model of gear structure based on the theory of finite element method. It presented the natural frequency of the gear elastomer and the analytical expression of natural functions and the simulative results. The results showed good agreement. This provided a study method for the vibration analysis of the gear structure body, and established the basis for studying the characteristics of acoustic radiation and the dynamic design of gears.

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Ma, Yian, Qijun Tan, Ruoshi Yuan, Bo Yuan, and Ping Ao. "Potential Function in a Continuous Dissipative Chaotic System: Decomposition Scheme and Role of Strange Attractor." International Journal of Bifurcation and Chaos 24, no. 02 (February 2014): 1450015. http://dx.doi.org/10.1142/s0218127414500151.

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We demonstrate, first in literature, that potential functions can be constructed in a continuous dissipative chaotic system and can be used to reveal its dynamical properties. To attain this aim, a Lorenz-like system is proposed and rigorously proved chaotic for exemplified analysis. We explicitly construct a potential function monotonically decreasing along the system's dynamics, revealing the structure of the chaotic strange attractor. The potential function is not unique for a deterministic system. We also decompose the dynamical system corresponding to a curl-free structure and a divergence-free structure, explaining for the different origins of chaotic attractor and strange attractor. Consequently, reasons for the existence of both chaotic nonstrange attractors and nonchaotic strange attractors are discussed within current decomposition framework.

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Otto, Samuel E., and Clarence W. Rowley. "Koopman Operators for Estimation and Control of Dynamical Systems." Annual Review of Control, Robotics, and Autonomous Systems 4, no. 1 (May 3, 2021): 59–87. http://dx.doi.org/10.1146/annurev-control-071020-010108.

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A common way to represent a system's dynamics is to specify how the state evolves in time. An alternative viewpoint is to specify how functions of the state evolve in time. This evolution of functions is governed by a linear operator called the Koopman operator, whose spectral properties reveal intrinsic features of a system. For instance, its eigenfunctions determine coordinates in which the dynamics evolve linearly. This review discusses the theoretical foundations of Koopman operator methods, as well as numerical methods developed over the past two decades to approximate the Koopman operator from data, for systems both with and without actuation. We pay special attention to ergodic systems, for which especially effective numerical methods are available. For nonlinear systems with an affine control input, the Koopman formalism leads naturally to systems that are bilinear in the state and the input, and this structure can be leveraged for the design of controllers and estimators.

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Meester, Ronald W. J. "An algorithm for calculating critical probabilities and percolation functions in percolation models defined by rotations." Ergodic Theory and Dynamical Systems 9, no. 3 (September 1989): 495–509. http://dx.doi.org/10.1017/s0143385700005137.

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AbstractA class of percolation models on ℤd is developed in which the stochastic structure is provided by means of a d-parameter dynamical system. Of particular interest are those models generated by circle rotations. Unlike for independent models, the critical value and the percolation function can be explicitly calculated. These calculations lead to a conjecture concerning the behaviour of a related dynamical system.

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Cancellara, Donato, Fabio De Angelis, and Vittorio Pasquino. "Finite Element Modelling for Characterizing some Dynamical Properties of a Masonry Building Prototype." Advanced Materials Research 446-449 (January 2012): 3745–52. http://dx.doi.org/10.4028/www.scientific.net/amr.446-449.3745.

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A finite element modelling of a masonry building prototype is illustrated in this paper. A computational analysis describing the dynamic behavior of the structure is presented in order to characterize some dynamical features of the system under the effect of harmonic forces of different intensity. The structure is represented by a two-story masonry building characterized by a regular floor plan. The finite element modelling of the structure intends to reproduce an experimental test of the masonry building subject to a harmonic force input supplied by a vibrodyne. Frequency response functions corresponding to the frequency load inputs are reported for different monitored nodal points of the finite element mesh. In this way by comparison with the experimental results obtained in a parallel study it is possible to suitably assess the calibration of the parameters for characterizing the dynamical behaviour of the masonry structure.

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Carmelo, J. M. P., and P. D. Sacramento. "Exponents of the spectral functions and dynamical structure factor of the 1D Lieb–Liniger Bose gas." Annals of Physics 369 (June 2016): 102–27. http://dx.doi.org/10.1016/j.aop.2016.03.009.

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Fransson, Erik, Mattias Slabanja, Paul Erhart, and Göran Wahnström. "dynasor —A Tool for Extracting Dynamical Structure Factors and Current Correlation Functions from Molecular Dynamics Simulations." Advanced Theory and Simulations 4, no. 2 (January 22, 2021): 2000240. http://dx.doi.org/10.1002/adts.202000240.

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Pakdaman, K., T. Nomura, S. Sato, and E. Bagarinao. "Reconstructing Bifurcation Diagrams of Dynamical Systems Using Measured Time Series." Methods of Information in Medicine 39, no. 02 (2000): 146–49. http://dx.doi.org/10.1055/s-0038-1634278.

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Abstract:We present an algorithm for reconstructing the bifurcation structure of a dynamical system from time series. The method consists in finding a parameterized predictor function whose bifurcation structure is similar to that of the given system. Nonlinear autoregressive (NAR) models with polynomial terms are employed as predictor functions. The appropriate terms in the NAR models are obtained using a fast orthogonal search scheme. This scheme eliminates the problem of multiparameter optimization and makes the approach robust to noise. The algorithm is applied to the reconstruction of the bifurcation diagram (BD) of a neuron model from the simulated membrane potential waveforms. The reconstructed BD captures the different behaviors of the given system. Moreover, the algorithm also works well even for a limited number of time series.

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YURI, MICHIKO. "Zeta functions for certain non-hyperbolic systems and topological Markov approximations." Ergodic Theory and Dynamical Systems 18, no. 6 (December 1998): 1589–612. http://dx.doi.org/10.1017/s0143385798117972.

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We study dynamical (Artin–Mazur–Ruelle) zeta functions for piecewise invertible multi-dimensional maps. In particular, we direct our attention to non-hyperbolic systems admitting countable generating definite partitions which are not necessarily Markov but satisfy the finite range structure (FRS) condition. We define a version of Gibbs measure (weak Gibbs measure) and by using it we establish an analogy with thermodynamic formalism for specific cases, i.e. a characterization of the radius of convergence in terms of pressure. The FRS condition leads us to nice countable state symbolic dynamics and allows us to realize it as towers over Markov systems. The Markov approximation method then gives a product formula of zeta functions for certain weighted functions.

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Sharif, M., and H. Ismat Fatima. "Evolution of axially symmetric systems and f(G) gravity." International Journal of Modern Physics D 26, no. 10 (August 20, 2017): 1750109. http://dx.doi.org/10.1142/s0218271817501097.

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This paper explores evolution of dissipative axially symmetric collapsing fluid under the dark effects of [Formula: see text] gravity. We formulate the dynamical variables and study the effects of dark sources in pressure anisotropy as well as heat dissipation. The structure scalars (scalar functions) as well as their role in the dynamics of source are investigated. Finally, we develop heat transport equation to examine the thermodynamic aspect and a set of equations governing the evolution of dynamical variables. It is concluded that dark sources affect thermodynamics of the system, evolution of kinematical quantities as well as density inhomogeneity.

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Beuther, H., Y. Wang, J. Soler, H. Linz, J. Henshaw, E. Vazquez-Semadeni, G. Gomez, et al. "Dynamical cloud formation traced by atomic and molecular gas." Astronomy & Astrophysics 638 (June 2020): A44. http://dx.doi.org/10.1051/0004-6361/202037950.

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Context. Atomic and molecular cloud formation is a dynamical process. However, kinematic signatures of these processes are still observationally poorly constrained. Aims. We identify and characterize the cloud formation signatures in atomic and molecular gas. Methods. Targeting the cloud-scale environment of the prototypical infrared dark cloud G28.3, we employed spectral line imaging observations of the two atomic lines HI and [CI] as well as molecular lines observations in 13CO in the 1–0 and 3–2 transitions. The analysis comprises investigations of the kinematic properties of the different tracers, estimates of the mass flow rates, velocity structure functions, a histogram of oriented gradients (HOG) study, and comparisons to simulations. Results. The central infrared dark cloud (IRDC) is embedded in a more diffuse envelope of cold neutral medium traced by HI self-absorption and molecular gas. The spectral line data as well as the HOG and structure function analysis indicate a possible kinematic decoupling of the HI from the other gas compounds. Spectral analysis and position–velocity diagrams reveal two velocity components that converge at the position of the IRDC. Estimated mass flow rates appear rather constant from the cloud edge toward the center. The velocity structure function analysis is consistent with gas flows being dominated by the formation of hierarchical structures. Conclusions. The observations and analysis are consistent with a picture where the IRDC G28.3 is formed at the center of two converging gas flows. While the approximately constant mass flow rates are consistent with a self-similar, gravitationally driven collapse of the cloud, external compression (e.g., via spiral arm shocks or supernova explosions) cannot be excluded yet. Future investigations should aim at differentiating the origin of such converging gas flows.

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Ruffing, Andreas. "Differential representations of dynamical oscillator symmetries in discrete Hilbert space." Discrete Dynamics in Nature and Society 5, no. 2 (2000): 97–106. http://dx.doi.org/10.1155/s1026022600000455.

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As a very important example for dynamical symmetries in the context ofq-generalized quantum mechanics the algebraaa†−q−2a†a=1is investigated. It represents the oscillator symmetrySUq(1,1)and is regarded as a commutation phenomenon of theq-Heisenberg algebra which provides a discrete spectrum of momentum and space,i.e., a discrete Hilbert space structure. Generalizedq-Hermite functions and systems of creation and annihilation operators are derived. The classical limitq→1is investigated. Finally theSUq(1,1)algebra is represented by the dynamical variables of theq-Heisenberg algebra.

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Rajaraman, Arvind. "Correlation functions of massless interacting scalar fields in de Sitter space." International Journal of Modern Physics A 30, no. 26 (September 18, 2015): 1550173. http://dx.doi.org/10.1142/s0217751x15501730.

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In this paper, we examine the behavior of correlation functions for a massless scalar field in de Sitter space with a quartic interaction. We find that two-loop corrections are relevant, and the resummation of these corrections generates a complicated structure whereby high momentum modes stay massless while low momentum modes develop a dynamical mass.

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Schwenk, C. F., and B. M. Rode. "Ab initio QM/MM MD simulations of the hydrated Ca2+ ion." Pure and Applied Chemistry 76, no. 1 (January 1, 2004): 37–47. http://dx.doi.org/10.1351/pac200476010037.

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The comparison of two different combined quantum mechanical (QM)/molecular mechanical (MM) simulations treating the quantum mechanical region at Hartree-Fock (HF) and B3-LYP density functional theory (DFT) level allowed us to determine structural and dynamical properties of the hydrated calcium ion. The structure is discussed in terms of radial distribution functions, coordination number distributions, and various angular distributions and the dynamical properties, as librations and vibrations, reorientational times and mean residence times were evaluated by means of velocity autocorrelation functions. The QM/MM molecular dynamics (MD) simulation results prove an eightfold-coordinated complex to be the dominant species, yielding average coordination numbers of 7.9 in the HF and 8.0 in the DFT case. Structural and dynamical results show higher rigidity of the hydrate complex using DFT. The high instability of calcium ion's hydration shell allows the observation of water-exchange processes between first and second hydration shell and shows that the mean lifetimes of water molecules in this first shell (<100 ps) have been strongly overestimated by conclusions from experimental data.

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Nie, Xiaobing, Jinde Cao, and Shumin Fei. "Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions." Abstract and Applied Analysis 2014 (2014): 1–20. http://dx.doi.org/10.1155/2014/901519.

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We investigate the existence and dynamical behaviors of multiple equilibria for competitive neural networks with a class of general Mexican-hat-type activation functions. The Mexican-hat-type activation functions are not monotonously increasing, and the structure of neural networks with Mexican-hat-type activation functions is totally different from those with sigmoidal activation functions or nondecreasing saturated activation functions, which have been employed extensively in previous multistability papers. By tracking the dynamics of each state component and applying fixed point theorem and analysis method, some sufficient conditions are presented to study the multistability and instability, including the total number of equilibria, their locations, and local stability and instability. The obtained results extend and improve the very recent works. Two illustrative examples with their simulations are given to verify the theoretical analysis.

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PRIGOGINE, ILYA. "WHY IRREVERSIBILITY? THE FORMULATION OF CLASSICAL AND QUANTUM MECHANICS FOR NONINTEGRABLE SYSTEMS." International Journal of Bifurcation and Chaos 05, no. 01 (February 1995): 3–16. http://dx.doi.org/10.1142/s0218127495000028.

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Nonintegrable Poincaré systems with continuous spectrum (so-called Large Poincaré Systems, LPS) lead to the appearance of diffusive terms in the framework of dynamics. These terms break time symmetry. They lead, therefore, to limitations to classical trajectory dynamics and of wave functions. These diffusive terms correspond to well-defined classes of dynamical processes (i.e., so-called “vacuum-vacuum” transitions). The diffusive effects are amplified in situations corresponding to persistent interactions. As a result, we have to include already in the fundamental dynamical description the two aspects, probability and irreversibility, which are so conspicuous on the macroscopic level. We have to formulate both classical and quantum mechanics on the Liouville level of probability distributions (or density matrices). For integrable systems, we recover the usual formulations of classical or quantum mechanics. Instead of being irreducible concepts, which cannot be further analyzed, trajectories and wave functions appear as special solutions of the Liouville-von Neumann equations. This extension of classical and quantum dynamics permits us to unify the two concepts of nature we inherited from the 19th century, based on the one hand on dynamical time-reversible laws and on the other on an evolutionary view associated to entropy. It leads also to a unified formulation of quantum theory avoiding the conventional dual structure based on Schrödinger’s equation on the one hand, and on the “collapse” of the wave function on the other. A dynamical interpretation is given to processes such as decoherence or approach to equilibrium without any appeal to extra dynamic considerations (such as the many-world theory, coarse graining or averaging over the environment). There is a striking parallelism between classical and quantum theory. For LPS we have, in general, both a “collapse” of trajectories and of wave functions for LPS. In both cases, we need a generalized formulation of dynamics in terms of probability distributions or density matrices. Since the beginning of this century, we know that classical mechanics had to be generalized to take into account the existence of universal constants. We now see that classical as well as quantum mechanics also have to be extended to include unstable dynamical systems such as LPS. As a result, we achieve a new formulation of "laws of physics" dealing no more with certitudes but with probabilities. The formulation is appropriate to describe an open, evolving universe.

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Journal articles on the topic 'Dynamical structure functions'

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