Sampling saddle points on a free energy surface

NASA Astrophysics Data System (ADS)

Samanta, Amit; Chen, Ming; Yu, Tang-Qing; Tuckerman, Mark; E, Weinan

2014-04-01

Many problems in biology, chemistry, and materials science require knowledge of saddle points on free energy surfaces. These saddle points act as transition states and are the bottlenecks for transitions of the system between different metastable states. For simple systems in which the free energy depends on a few variables, the free energy surface can be precomputed, and saddle points can then be found using existing techniques. For complex systems, where the free energy depends on many degrees of freedom, this is not feasible. In this paper, we develop an algorithm for finding the saddle points on a high-dimensional free energy surface "on-the-fly" without requiring a priori knowledge the free energy function itself. This is done by using the general strategy of the heterogeneous multi-scale method by applying a macro-scale solver, here the gentlest ascent dynamics algorithm, with the needed force and Hessian values computed on-the-fly using a micro-scale model such as molecular dynamics. The algorithm is capable of dealing with problems involving many coarse-grained variables. The utility of the algorithm is illustrated by studying the saddle points associated with (a) the isomerization transition of the alanine dipeptide using two coarse-grained variables, specifically the Ramachandran dihedral angles, and (b) the beta-hairpin structure of the alanine decamer using 20 coarse-grained variables, specifically the full set of Ramachandran angle pairs associated with each residue. For the alanine decamer, we obtain a detailed network showing the connectivity of the minima obtained and the saddle-point structures that connect them, which provides a way to visualize the gross features of the high-dimensional surface.

Saddle point localization of molecular wavefunctions.

PubMed

Mellau, Georg Ch; Kyuberis, Alexandra A; Polyansky, Oleg L; Zobov, Nikolai; Field, Robert W

2016-09-15

The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the eigenstates of the model quartic potential and in the energy levels of the [H, C, N] potential energy surface. We model the spacing of the eigenenergies with the energy dependent classical oscillation frequency decreasing to zero at the saddle point. The eigenstates with the smallest spacing are localized at the saddle point. The analysis of the HCN ↔ HNC isomerization states shows that the eigenstates with small energy spacing relative to the effective (v1, v3, ℓ) bending potentials are highly localized in the bending coordinate at the transition state. These spectroscopically detectable states represent a chemical marker of the transition state in the eigenenergy spectrum. The method developed here provides a basis for modeling characteristic patterns in the eigenenergy spectrum of bound states.

Bifurcation Analysis and Optimal Harvesting of a Delayed Predator-Prey Model

NASA Astrophysics Data System (ADS)

Tchinda Mouofo, P.; Djidjou Demasse, R.; Tewa, J. J.; Aziz-Alaoui, M. A.

A delay predator-prey model is formulated with continuous threshold prey harvesting and Holling response function of type III. Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. The positive invariance of the non-negative orthant is proved and the uniform boundedness of the trajectories. Stability of equilibria is investigated and the existence of some local bifurcations is established: saddle-node bifurcation, Hopf bifurcation. We use optimal control theory to provide the correct approach to natural resource management. Results are also obtained for optimal harvesting. Numerical simulations are given to illustrate the results.

Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection.

PubMed

Cao, Hui; Zhou, Yicang; Ma, Zhien

2013-01-01

A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied. The condition for the global stability of the disease free equilibrium is obtained. The existence of the endemic equilibrium and its stability are investigated. More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation. Sufficient conditions for those bifurcations have been obtained. Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.

Experimental Study of Saddle Point of Attachment in Laminar Juncture Flow

NASA Technical Reports Server (NTRS)

Coon, Michael D.; Tobak, Murray

1995-01-01

An experimental study of laminar horseshoe vortex flows upstream of a cylinder/flat plate juncture has been conducted to verify the existence of saddle-point-of-attachment topologies. In the classical depiction of this flowfield, a saddle point of separation exists on the flat plate upstream of the cylinder, and the boundary layer separates from the surface. Recent computations have indicated that the topology may actually involve a saddle point of attachment on the surface and additional singular points in the flow. Laser light sheet flow visualizations have been performed on the symmetry plane and crossflow planes to identify the saddle-point-of-attachment flowfields. The visualizations reveal that saddle-point-of-attachment topologies occur over a range of Reynolds numbers in both single and multiple vortex regimes. An analysis of the flow topologies is presented that describes the existence and evolution of the singular points in the flowfield.

Electrons at the monkey saddle: a multicritical Lifshitz point

NASA Astrophysics Data System (ADS)

Shtyk, Alex; Goldstein, Garry; Chamon, Claudio

We consider 2D interacting electrons at a monkey saddle with dispersion px3 - 3pxpy2 . Such a dispersion naturally arises at the multicritical Lifshitz point when three van Hove saddles merge in an elliptical umbilic elementary catastrophe, which we show can be realized in biased bilayer graphene. A multicritical Lifshitz point of this kind can be identified by its signature Landau level behavior Em (Bm) 3 / 2 and related oscillations in thermodynamic and transport properties, such as de Haas-van Alphen and Shubnikov-de Haas oscillations, whose period triples as the system crosses the singularity. We show, in the case of a single monkey saddle, that the non-interacting electron fixed point is unstable to interactions under the renormalization group flow, developing either a superconducting instability or non-Fermi liquid features. Biased bilayer graphene, where there are two non-nested monkey saddles at the K and K' points, exhibits an interplay of competing many-body instabilities, namely s-wave superconductivity, ferromagnetism, and spin- and charge-density wave. DOE DE-FG02-06ER46316.

Electrons at the monkey saddle: A multicritical Lifshitz point

NASA Astrophysics Data System (ADS)

Shtyk, A.; Goldstein, G.; Chamon, C.

2017-01-01

We consider two-dimensional interacting electrons at a monkey saddle with dispersion ∝px3-3 pxpy2 . Such a dispersion naturally arises at the multicritical Lifshitz point when three Van Hove saddles merge in an elliptical umbilic elementary catastrophe, which we show can be realized in biased bilayer graphene. A multicritical Lifshitz point of this kind can be identified by its signature Landau level behavior Em∝(Bm ) 3 /2 and related oscillations in thermodynamic and transport properties, such as de Haas-Van Alphen and Shubnikov-de Haas oscillations, whose period triples as the system crosses the singularity. We show, in the case of a single monkey saddle, that the noninteracting electron fixed point is unstable to interactions under the renormalization-group flow, developing either a superconducting instability or non-Fermi-liquid features. Biased bilayer graphene, where there are two non-nested monkey saddles at the K and K' points, exhibits an interplay of competing many-body instabilities, namely, s -wave superconductivity, ferromagnetism, and spin- and charge-density waves.

The Sun-Earth saddle point: characterization and opportunities to test general relativity

NASA Astrophysics Data System (ADS)

Topputo, Francesco; Dei Tos, Diogene A.; Rasotto, Mirco; Nakamiya, Masaki

2018-04-01

The saddle points are locations where the net gravitational accelerations balance. These regions are gathering more attention within the astrophysics community. Regions about the saddle points present clean, close-to-zero background acceleration environments where possible deviations from General Relativity can be tested and quantified. Their location suggests that flying through a saddle point can be accomplished by leveraging highly nonlinear orbits. In this paper, the geometrical and dynamical properties of the Sun-Earth saddle point are characterized. A systematic approach is devised to find ballistic orbits that experience one or multiple passages through this point. A parametric analysis is performed to consider spacecraft initially on L_{1,2} Lagrange point orbits. Sun-Earth saddle point ballistic fly-through trajectories are evaluated and classified for potential use. Results indicate an abundance of short-duration, regular solutions with a variety of characteristics.

Local Bifurcations and Optimal Theory in a Delayed Predator-Prey Model with Threshold Prey Harvesting

NASA Astrophysics Data System (ADS)

Tankam, Israel; Tchinda Mouofo, Plaire; Mendy, Abdoulaye; Lam, Mountaga; Tewa, Jean Jules; Bowong, Samuel

2015-06-01

We investigate the effects of time delay and piecewise-linear threshold policy harvesting for a delayed predator-prey model. It is the first time that Holling response function of type III and the present threshold policy harvesting are associated with time delay. The trajectories of our delayed system are bounded; the stability of each equilibrium is analyzed with and without delay; there are local bifurcations as saddle-node bifurcation and Hopf bifurcation; optimal harvesting is also investigated. Numerical simulations are provided in order to illustrate each result.

Wake-sleep transition as a noisy bifurcation

NASA Astrophysics Data System (ADS)

Yang, Dong-Ping; McKenzie-Sell, Lauren; Karanjai, Angela; Robinson, P. A.

2016-08-01

A recent physiologically based model of the ascending arousal system is used to analyze the dynamics near the transition from wake to sleep, which corresponds to a saddle-node bifurcation at a critical point. A normal form is derived by approximating the dynamics by those of a particle in a parabolic potential well with dissipation. This mechanical analog is used to calculate the power spectrum of fluctuations in response to a white noise drive, and the scalings of fluctuation variance and spectral width are derived versus distance from the critical point. The predicted scalings are quantitatively confirmed by numerical simulations, which show that the variance increases and the spectrum undergoes critical slowing, both in accord with theory. These signals can thus serve as potential precursors to indicate imminent wake-sleep transition, with potential application to safety-critical occupations in transport, air-traffic control, medicine, and heavy industry.

Emphasizing Saddle Points through Game Theory: A Classroom Activity.

ERIC Educational Resources Information Center

Dorrington, Jenny; Jones, Michael A.

2000-01-01

Introduces the necessary game-theoretic background and explains how game-theoretic experiments of the Matching Pennies game can be used as a classroom activity to develop intuition about saddle points. (Author/ASK)

Bifurcation Analysis and Nonlinear Decay of a Tumor in the Presence of an Immune Response

NASA Astrophysics Data System (ADS)

López, Álvaro G.; Seoane, Jesús M.; Sanjuán, Miguel A. F.

2017-12-01

The decay of a planar compact surface that is reduced through its boundary is considered. The interest of this problem lies in the fact that it can represent the destruction of a solid tumor by a population of immune cells. The theory of curves is utilized to derive the rate at which the area of the set decreases. Firstly, the process is represented as a discrete dynamical system. A recurrence equation describing the shrinkage of the area at any step is deduced. Then, a continuum limit is attained to derive an ordinary differential equation that governs the decay of the set. The solutions to the differential equation and its implications are discussed, and numerical simulations are carried out to test the accuracy of the decay law. Finally, the dynamics of a tumor-immune aggregate is inspected using this law and the theory of bifurcations. As the ratio of immune destruction to tumor growth increases, a saddle-node bifurcation stabilizes the tumor-free fixed point.

Integrability and Linearizability of the Lotka-Volterra System with a Saddle Point with Rational Hyperbolicity Ratio

NASA Astrophysics Data System (ADS)

Gravel, Simon; Thibault, Pierre

In this paper, we consider normalizability, integrability and linearizability properties of the Lotka-Volterra system in the neighborhood of a singular point with eigenvalues 1 and - λ. The results are obtained by generalizing and expanding two methods already known: the power expansion of the first integral or of the linearizing transformation and the transformation of the saddle into a node. With these methods we find conditions that are valid for λ∈ R+ or λ∈ Q. These conditions will allow us to find all the integrable and linearizable systems for λ= {p}/{2} and {2}/{p} with p∈ N+.

Practical Methods for the Analysis of Voltage Collapse in Electric Power Systems: a Stationary Bifurcations Viewpoint.

NASA Astrophysics Data System (ADS)

Jean-Jumeau, Rene

1993-03-01

Voltage collapse (VC) is generally caused by either of two types of system disturbances: load variations and contingencies. In this thesis, we study VC resulting from load variations. This is termed static voltage collapse. This thesis deals with this type of voltage collapse in electrical power systems by using a stationary bifurcations viewpoint by associating it with the occurrence of saddle node bifurcations (SNB) in the system. Approximate models are generically used in most VC analyses. We consider the validity of these models for the study of SNB and, thus, of voltage collapse. We justify the use of saddle node bifurcation as a model for VC in power systems. In particular, we prove that this leads to definition of a model and--since load demand is used as a parameter for that model--of a mode of parameterization of that model in order to represent actual power demand variations within the power system network. Ill-conditioning of the set of nonlinear equations defining a dynamical system is a generic occurence near the SNB point. We suggest a reparameterization of the set of nonlinear equations which allows to avoid this problem. A new indicator for the proximity of voltage collapse, the voltage collapse index (VCI), is developed. A new (n + 1)-dimensional set of characteristic equations for the computation of the exact SNB point, replacing the standard (2n + 1)-dimensional one is presented for general parameter -dependent nonlinear dynamical systems. These results are then applied to electric power systems for the analysis and prediction of voltage collapse. The new methods offer the potential of faster computation and greater flexibility. For reasons of theoretical development and clarity, the preceding methodologies are developed under the assumption of the absence of constraints on the system parameters and states, and the full differentiability of the functions defining the power system model. In the latter part of this thesis, we relax these

Singular perturbations and vanishing passage through a turning point

NASA Astrophysics Data System (ADS)

De Maesschalck, P.; Dumortier, F.

The paper deals with planar slow-fast cycles containing a unique generic turning point. We address the question on how to study canard cycles when the slow dynamics can be singular at the turning point. We more precisely accept a generic saddle-node bifurcation to pass through the turning point. It reveals that in this case the slow divergence integral is no longer the good tool to use, but its derivative with respect to the layer variable still is. We provide general results as well as a number of applications. We show how to treat the open problems presented in Artés et al. (2009) [1] and Dumortier and Rousseau (2009) [13], dealing respectively with the graphics DI2a and DF1a from Dumortier et al. (1994) [14].

Classification of the nonlinear dynamics and bifurcation structure of ultrasound contrast agents excited at higher multiples of their resonance frequency

NASA Astrophysics Data System (ADS)

Sojahrood, Amin Jafari; Kolios, Michael C.

2012-07-01

Through numerical simulation of the Hoff model we show that when ultrasound contrast agents (UCAs) are excited at frequencies which are close to integer (m>2) multiples of their natural resonance frequency, the bifurcation structure of the UCA oscillations as a function of pressure may be characterized by 3 general distinct regions. The UCA behavior starts with initial period one oscillations which undergoes a saddle node bifurcation to m coexisting attractors for an acoustic pressure above a threshold, P. Further increasing the pressure above a second threshold P, is followed by a sudden transition to period 1 oscillations.

The Pasinetti-Solow Growth Model with Optimal Saving Behaviour: A Local Bifurcation Analysis

NASA Astrophysics Data System (ADS)

Commendatore, P.; Palmisani, C.

We present a discrete time version of the Pasinetti-Solow economic growth model. Workers and capitalists are assumed to save on the basis of rational choices. Workers face a finite time horizon and base their consumption choices on a life-cycle motive, whereas capitalists behave like an infinitely-lived dynasty. The accumulation of both capitalists' and workers' wealth through time is reduced to a two-dimensional map whose local asymptotic stability properties are studied. Various types of bifurcation emerge (flip, Neimark-Sacker, saddle-node and transcritical): a precondition for chaotic dynamics.

Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow

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

Smith, L. D., E-mail: lachlan.smith@monash.edu; CSIRO Mineral Resources, Clayton, Victoria 3800; Rudman, M.

2016-05-15

Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversalmore » in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.« less

Localized saddle-point search and application to temperature-accelerated dynamics

NASA Astrophysics Data System (ADS)

Shim, Yunsic; Callahan, Nathan B.; Amar, Jacques G.

2013-03-01

We present a method for speeding up temperature-accelerated dynamics (TAD) simulations by carrying out a localized saddle-point (LSAD) search. In this method, instead of using the entire system to determine the energy barriers of activated processes, the calculation is localized by only including a small chunk of atoms around the atoms directly involved in the transition. Using this method, we have obtained N-independent scaling for the computational cost of the saddle-point search as a function of system size N. The error arising from localization is analyzed using a variety of model systems, including a variety of activated processes on Ag(100) and Cu(100) surfaces, as well as multiatom moves in Cu radiation damage and metal heteroepitaxial growth. Our results show significantly improved performance of TAD with the LSAD method, for the case of Ag/Ag(100) annealing and Cu/Cu(100) growth, while maintaining a negligibly small error in energy barriers.

Composite solvers for linear saddle point problems arising from the incompressible Stokes equations with highly heterogeneous viscosity structure

NASA Astrophysics Data System (ADS)

Sanan, P.; Schnepp, S. M.; May, D.; Schenk, O.

2014-12-01

Geophysical applications require efficient forward models for non-linear Stokes flow on high resolution spatio-temporal domains. The bottleneck in applying the forward model is solving the linearized, discretized Stokes problem which takes the form of a large, indefinite (saddle point) linear system. Due to the heterogeniety of the effective viscosity in the elliptic operator, devising effective preconditioners for saddle point problems has proven challenging and highly problem-dependent. Nevertheless, at least three approaches show promise for preconditioning these difficult systems in an algorithmically scalable way using multigrid and/or domain decomposition techniques. The first is to work with a hierarchy of coarser or smaller saddle point problems. The second is to use the Schur complement method to decouple and sequentially solve for the pressure and velocity. The third is to use the Schur decomposition to devise preconditioners for the full operator. These involve sub-solves resembling inexact versions of the sequential solve. The choice of approach and sub-methods depends crucially on the motivating physics, the discretization, and available computational resources. Here we examine the performance trade-offs for preconditioning strategies applied to idealized models of mantle convection and lithospheric dynamics, characterized by large viscosity gradients. Due to the arbitrary topological structure of the viscosity field in geodynamical simulations, we utilize low order, inf-sup stable mixed finite element spatial discretizations which are suitable when sharp viscosity variations occur in element interiors. Particular attention is paid to possibilities within the decoupled and approximate Schur complement factorization-based monolithic approaches to leverage recently-developed flexible, communication-avoiding, and communication-hiding Krylov subspace methods in combination with `heavy' smoothers, which require solutions of large per-node sub-problems, well

Experimental demonstration of the supersonic-subsonic bifurcation in the circular jump: a hydrodynamic white hole.

PubMed

Jannes, G; Piquet, R; Maïssa, P; Mathis, C; Rousseaux, G

2011-05-01

We provide an experimental demonstration that the circular hydraulic jump represents a hydrodynamic white hole or gravitational fountain (the time reverse of a black hole) by measuring the angle of the Mach cone created by an object in the "supersonic" inner flow region. We emphasize the general character of this gravitational analogy by showing theoretically that the white hole horizon constitutes a stationary and spatial saddle-node bifurcation within dynamical-systems theory. We also demonstrate that the inner region has a "superluminal" dispersion relation, that is, that the group velocity of the surface waves increases with frequency, and discuss some possible consequences with respect to the robustness of Hawking radiation. Finally, we point out that our experiment shows a concrete example of a possible "trans-Planckian distortion" of black or white holes. © 2011 American Physical Society

Bursting Types and Bifurcation Analysis in the Pre-Bötzinger Complex Respiratory Rhythm Neuron

NASA Astrophysics Data System (ADS)

Wang, Jing; Lu, Bo; Liu, Shenquan; Jiang, Xiaofang

Many types of neurons and excitable cells could intrinsically generate bursting activity, even in an isolated case, which plays a vital role in neuronal signaling and synaptic plasticity. In this paper, we have mainly investigated bursting types and corresponding bifurcations in the pre-Bötzinger complex respiratory rhythm neuron by using fast-slow dynamical analysis. The numerical simulation results have showed that for some appropriate parameters, the neuron model could exhibit four distinct types of fast-slow bursters. We also explored the bifurcation mechanisms related to these four types of bursters through the analysis of phase plane. Moreover, the first Lyapunov coefficient of the Hopf bifurcation, which can decide whether it is supercritical or subcritical, was calculated with the aid of MAPLE software. In addition, we analyzed the codimension-two bifurcation for equilibria of the whole system and gave a detailed theoretical derivation of the Bogdanov-Takens bifurcation. Finally, we obtained expressions for a fold bifurcation curve, a nondegenerate Hopf bifurcation curve, and a saddle homoclinic bifurcation curve near the Bogdanov-Takens bifurcation point.

Chaos crisis and bistability of self-pulsing dynamics in a laser diode with phase-conjugate feedback

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

Virte, Martin; Karsaklian Dal Bosco, Andreas; Wolfersberger, Delphine

2011-10-15

A laser diode subject to a phase-conjugate optical feedback can exhibit rich nonlinear dynamics and chaos. We report here on two bifurcation mechanisms that appear when increasing the amount of light being fed back to the laser. First, we report on a full suppression of chaos from a crisis induced by a saddle-node bifurcation on self-pulsing, so-called external-cavity-mode solutions (ECMs). Second, the feedback-dependent torus and saddle-node bifurcations on ECMs may be responsible for large regions of bistability between ECMs of different and high (beyond gigahertz) frequencies.

Dynamics of Two Point Vortices in an External Compressible Shear Flow

NASA Astrophysics Data System (ADS)

Vetchanin, Evgeny V.; Mamaev, Ivan S.

2017-12-01

This paper is concerned with a system of equations that describes the motion of two point vortices in a flow possessing constant uniform vorticity and perturbed by an acoustic wave. The system is shown to have both regular and chaotic regimes of motion. In addition, simple and chaotic attractors are found in the system. Attention is given to bifurcations of fixed points of a Poincaré map which lead to the appearance of these regimes. It is shown that, in the case where the total vortex strength changes, the "reversible pitch-fork" bifurcation is a typical scenario of emergence of asymptotically stable fixed and periodic points. As a result of this bifurcation, a saddle point, a stable and an unstable point of the same period emerge from an elliptic point of some period. By constructing and analyzing charts of dynamical regimes and bifurcation diagrams we show that a cascade of period-doubling bifurcations is a typical scenario of transition to chaos in the system under consideration.

Dynamics of a parametrically excited simple pendulum

NASA Astrophysics Data System (ADS)

Depetri, Gabriela I.; Pereira, Felipe A. C.; Marin, Boris; Baptista, Murilo S.; Sartorelli, J. C.

2018-03-01

The dynamics of a parametric simple pendulum submitted to an arbitrary angle of excitation ϕ was investigated experimentally by simulations and analytically. Analytical calculations for the loci of saddle-node bifurcations corresponding to the creation of resonant orbits were performed by applying Melnikov's method. However, this powerful perturbative method cannot be used to predict the existence of odd resonances for a vertical excitation within first order corrections. Yet, we showed that period-3 resonances indeed exist in such a configuration. Two degenerate attractors of different phases, associated with the same loci of saddle-node bifurcations in parameter space, are reported. For tilted excitation, the degeneracy is broken due to an extra torque, which was confirmed by the calculation of two distinct loci of saddle-node bifurcations for each attractor. This behavior persists up to ϕ≈7 π/180 , and for inclinations larger than this, only one attractor is observed. Bifurcation diagrams were constructed experimentally for ϕ=π/8 to demonstrate the existence of self-excited resonances (periods smaller than three) and hidden oscillations (for periods greater than three).

Dynamics of a parametrically excited simple pendulum.

PubMed

Depetri, Gabriela I; Pereira, Felipe A C; Marin, Boris; Baptista, Murilo S; Sartorelli, J C

2018-03-01

The dynamics of a parametric simple pendulum submitted to an arbitrary angle of excitation ϕ was investigated experimentally by simulations and analytically. Analytical calculations for the loci of saddle-node bifurcations corresponding to the creation of resonant orbits were performed by applying Melnikov's method. However, this powerful perturbative method cannot be used to predict the existence of odd resonances for a vertical excitation within first order corrections. Yet, we showed that period-3 resonances indeed exist in such a configuration. Two degenerate attractors of different phases, associated with the same loci of saddle-node bifurcations in parameter space, are reported. For tilted excitation, the degeneracy is broken due to an extra torque, which was confirmed by the calculation of two distinct loci of saddle-node bifurcations for each attractor. This behavior persists up to ϕ≈7π/180, and for inclinations larger than this, only one attractor is observed. Bifurcation diagrams were constructed experimentally for ϕ=π/8 to demonstrate the existence of self-excited resonances (periods smaller than three) and hidden oscillations (for periods greater than three).

Invariants, Attractors and Bifurcation in Two Dimensional Maps with Polynomial Interaction

NASA Astrophysics Data System (ADS)

Hacinliyan, Avadis Simon; Aybar, Orhan Ozgur; Aybar, Ilknur Kusbeyzi

This work will present an extended discrete-time analysis on maps and their generalizations including iteration in order to better understand the resulting enrichment of the bifurcation properties. The standard concepts of stability analysis and bifurcation theory for maps will be used. Both iterated maps and flows are used as models for chaotic behavior. It is well known that when flows are converted to maps by discretization, the equilibrium points remain the same but a richer bifurcation scheme is observed. For example, the logistic map has a very simple behavior as a differential equation but as a map fold and period doubling bifurcations are observed. A way to gain information about the global structure of the state space of a dynamical system is investigating invariant manifolds of saddle equilibrium points. Studying the intersections of the stable and unstable manifolds are essential for understanding the structure of a dynamical system. It has been known that the Lotka-Volterra map and systems that can be reduced to it or its generalizations in special cases involving local and polynomial interactions admit invariant manifolds. Bifurcation analysis of this map and its higher iterates can be done to understand the global structure of the system and the artifacts of the discretization by comparing with the corresponding results from the differential equation on which they are based.

Backward bifurcations, turning points and rich dynamics in simple disease models.

PubMed

Zhang, Wenjing; Wahl, Lindi M; Yu, Pei

2016-10-01

In this paper, dynamical systems theory and bifurcation theory are applied to investigate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous investigations of epidemiology, in-host disease, and autoimmunity. These closely related models display interesting dynamical behaviors including bistability, recurrence, and regular oscillations, each of which has possible clinical or public health implications. In this contribution we elucidate the key role of backward bifurcations in the parameter regimes leading to the behaviors of interest. We demonstrate that backward bifurcations with varied positions of turning points facilitate the appearance of Hopf bifurcations, and the varied dynamical behaviors are then determined by the properties of the Hopf bifurcation(s), including their location and direction. A Maple program developed earlier is implemented to determine the stability of limit cycles bifurcating from the Hopf bifurcation. Numerical simulations are presented to illustrate phenomena of interest such as bistability, recurrence and oscillation. We also discuss the physical motivations for the models and the clinical implications of the resulting dynamics.

Deterministic and stochastic bifurcations in the Hindmarsh-Rose neuronal model

NASA Astrophysics Data System (ADS)

Dtchetgnia Djeundam, S. R.; Yamapi, R.; Kofane, T. C.; Aziz-Alaoui, M. A.

2013-09-01

We analyze the bifurcations occurring in the 3D Hindmarsh-Rose neuronal model with and without random signal. When under a sufficient stimulus, the neuron activity takes place; we observe various types of bifurcations that lead to chaotic transitions. Beside the equilibrium solutions and their stability, we also investigate the deterministic bifurcation. It appears that the neuronal activity consists of chaotic transitions between two periodic phases called bursting and spiking solutions. The stochastic bifurcation, defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value, or under certain condition as the collision of a stochastic attractor with a stochastic saddle, occurs when a random Gaussian signal is added. Our study reveals two kinds of stochastic bifurcation: the phenomenological bifurcation (P-bifurcations) and the dynamical bifurcation (D-bifurcations). The asymptotical method is used to analyze phenomenological bifurcation. We find that the neuronal activity of spiking and bursting chaos remains for finite values of the noise intensity.

Feature-Based Retinal Image Registration Using D-Saddle Feature

PubMed Central

Hasikin, Khairunnisa; A. Karim, Noor Khairiah; Ahmedy, Fatimah

2017-01-01

Retinal image registration is important to assist diagnosis and monitor retinal diseases, such as diabetic retinopathy and glaucoma. However, registering retinal images for various registration applications requires the detection and distribution of feature points on the low-quality region that consists of vessels of varying contrast and sizes. A recent feature detector known as Saddle detects feature points on vessels that are poorly distributed and densely positioned on strong contrast vessels. Therefore, we propose a multiresolution difference of Gaussian pyramid with Saddle detector (D-Saddle) to detect feature points on the low-quality region that consists of vessels with varying contrast and sizes. D-Saddle is tested on Fundus Image Registration (FIRE) Dataset that consists of 134 retinal image pairs. Experimental results show that D-Saddle successfully registered 43% of retinal image pairs with average registration accuracy of 2.329 pixels while a lower success rate is observed in other four state-of-the-art retinal image registration methods GDB-ICP (28%), Harris-PIIFD (4%), H-M (16%), and Saddle (16%). Furthermore, the registration accuracy of D-Saddle has the weakest correlation (Spearman) with the intensity uniformity metric among all methods. Finally, the paired t-test shows that D-Saddle significantly improved the overall registration accuracy of the original Saddle. PMID:29204257

Population collapse to extinction: the catastrophic combination of parasitism and Allee effect.

PubMed

Hilker, Frank M

2010-01-01

Infectious diseases are responsible for the extinction of a number of species. In conventional epidemic models, the transition from endemic population persistence to extirpation takes place gradually. However, if host demographics exhibits a strong Allee effect (AE) (population decline at low densities), extinction can occur abruptly in a catastrophic population crash. This might explain why species suddenly disappear even when they used to persist at high endemic population levels. Mathematically, the tipping point towards population collapse is associated with a saddle-node bifurcation. The underlying mechanism is the simultaneous population size depression and the increase of the extinction threshold due to parasite pathogenicity and Allee effect. Since highly pathogenic parasites cause their own extinction but not that of their host, there can be another saddle-node bifurcation with the re-emergence of two endemic equilibria. The implications for control interventions are discussed, suggesting that effective management may be possible for ℛ(0)≫1.

A method to approximate a closest loadability limit using multiple load flow solutions

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

Yorino, Naoto; Harada, Shigemi; Cheng, Haozhong

A new method is proposed to approximate a closest loadability limit (CLL), or closest saddle node bifurcation point, using a pair of multiple load flow solutions. More strictly, the obtainable points by the method are the stationary points including not only CLL but also farthest and saddle points. An operating solution and a low voltage load flow solution are used to efficiently estimate the node injections at a CLL as well as the left and right eigenvectors corresponding to the zero eigenvalue of the load flow Jacobian. They can be used in monitoring loadability margin, in identification of weak spotsmore » in a power system and in the examination of an optimal control against voltage collapse. Most of the computation time of the proposed method is taken in calculating the load flow solution pair. The remaining computation time is less than that of an ordinary load flow.« less

Bifurcations: Focal Points of Particle Adhesion in Microvascular Networks

PubMed Central

Prabhakarpandian, Balabhaskar; Wang, Yi; Rea-Ramsey, Angela; Sundaram, Shivshankar; Kiani, Mohammad F.; Pant, Kapil

2011-01-01

Objective Particle adhesion in vivo is dependent on microcirculation environment which features unique anatomical (bifurcations, tortuosity, cross-sectional changes) and physiological (complex hemodynamics) characteristics. The mechanisms behind these complex phenomena are not well understood. In this study, we used a recently developed in vitro model of microvascular networks, called Synthetic Microvascular Network, for characterizing particle adhesion patterns in the microcirculation. Methods Synthetic microvascular networks were fabricated using soft lithography processes followed by particle adhesion studies using avidin and biotin-conjugated microspheres. Particle adhesion patterns were subsequently analyzed using CFD based modeling. Results Experimental and modeling studies highlighted the complex and heterogeneous fluid flow patterns encountered by particles in microvascular networks resulting in significantly higher propensity of adhesion (>1.5X) near bifurcations compared to the branches of the microvascular networks. Conclusion Bifurcations are the focal points of particle adhesion in microvascular networks. Changing flow patterns and morphology near bifurcations are the primary factors controlling the preferential adhesion of functionalized particles in microvascular networks. Synthetic microvascular networks provide an in vitro framework for understanding particle adhesion. PMID:21418388

Symmetry-breaking Hopf bifurcations to 1-, 2-, and 3-tori in small-aspect-ratio counterrotating Taylor-Couette flow.

PubMed

Altmeyer, S; Do, Y; Marques, F; Lopez, J M

2012-10-01

The nonlinear dynamics of Taylor-Couette flow in a small-aspect-ratio wide-gap annulus in the counterrotating regime is investigated by solving the full three-dimensional Navier-Stokes equations. The system is invariant under arbitrary rotations about the axis, reflection about the annulus midplane, and time translations. A systematic investigation is presented both in terms of the flow physics elucidated from the numerical simulations and from a dynamical system perspective provided by equivariant normal form theory. The dynamics are primarily associated with the behavior of the jet of angular momentum that emerges from the inner cylinder boundary layer at about the midplane. The sequence of bifurcations as the differential rotation is increased consists of an axisymmetric Hopf bifurcation breaking the reflection symmetry of the basic state leading to an axisymmetric limit cycle with a half-period-flip spatiotemporal symmetry. This undergoes a Hopf bifurcation breaking axisymmetry, leading to quasiperiodic solutions evolving on a 2-torus that is setwise symmetric. These undergo a further Hopf bifurcation, introducing a third incommensurate frequency leading to a 3-torus that is also setwise symmetric. On the 3-torus, as the differential rotation is further increased, a saddle-node-invariant-circle bifurcation takes place, destroying the 3-torus and leaving a pair of symmetrically related 2-tori states on which all symmetries of the system have been broken.

A Codimension-2 Bifurcation Controlling Endogenous Bursting Activity and Pulse-Triggered Responses of a Neuron Model

PubMed Central

Barnett, William H.; Cymbalyuk, Gennady S.

2014-01-01

The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC) curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals–the duration of the burst and the duration of latency to spiking–are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator modeled by a chain of

Bifurcation into functional niches in adaptation.

PubMed

White, Justin S; Adami, Christoph

2004-01-01

One of the central questions in evolutionary biology concerns the dynamics of adaptation and diversification. This issue can be addressed experimentally if replicate populations adapting to identical environments can be investigated in detail. We have studied 501 such replicas using digital organisms adapting to at least two fundamentally different functional niches (survival strategies) present in the same environment: one in which fast replication is the way to live, and another where exploitation of the environment's complexity leads to complex organisms with longer life spans and smaller replication rates. While these two modes of survival are closely analogous to those expected to emerge in so-called r and K selection scenarios respectively, the bifurcation of evolutionary histories according to these functional niches occurs in identical environments, under identical selective pressures. We find that the branching occurs early, and leads to drastic phenotypic differences (in fitness, sequence length, and gestation time) that are permanent and irreversible. This study confirms an earlier experimental effort using microorganisms, in that diversification can be understood at least in part in terms of bifurcations on saddle points leading to peak shifts, as in the picture drawn by Sewall Wright.

Transient spatiotemporal chaos in the Morris-Lecar neuronal ring network.

PubMed

Keplinger, Keegan; Wackerbauer, Renate

2014-03-01

Transient behavior is thought to play an integral role in brain functionality. Numerical simulations of the firing activity of diffusively coupled, excitable Morris-Lecar neurons reveal transient spatiotemporal chaos in the parameter regime below the saddle-node on invariant circle bifurcation point. The neighborhood of the chaotic saddle is reached through perturbations of the rest state, in which few initially active neurons at an effective spatial distance can initiate spatiotemporal chaos. The system escapes from the neighborhood of the chaotic saddle to either the rest state or to a state of pulse propagation. The lifetime of the chaotic transients is manipulated in a statistical sense through a singular application of a synchronous perturbation to a group of neurons.

Spike-adding in parabolic bursters: The role of folded-saddle canards

NASA Astrophysics Data System (ADS)

Desroches, Mathieu; Krupa, Martin; Rodrigues, Serafim

2016-09-01

The present work develops a new approach to studying parabolic bursting, and also proposes a novel four-dimensional canonical and polynomial-based parabolic burster. In addition to this new polynomial system, we also consider the conductance-based model of the Aplysia R15 neuron known as the Plant model, and a reduction of this prototypical biophysical parabolic burster to three variables, including one phase variable, namely the Baer-Rinzel-Carillo (BRC) phase model. Revisiting these models from the perspective of slow-fast dynamics reveals that the number of spikes per burst may vary upon parameter changes, however the spike-adding process occurs in an explosive fashion that involves special solutions called canards. This spike-adding canard explosion phenomenon is analysed by using tools from geometric singular perturbation theory in tandem with numerical bifurcation techniques. We find that the bifurcation structure persists across all considered systems, that is, spikes within the burst are incremented via the crossing of an excitability threshold given by a particular type of canard orbit, namely the true canard of a folded-saddle singularity. However there can be a difference in the spike-adding transitions in parameter space from one case to another, according to whether the process is continuous or discontinuous, which depends upon the geometry of the folded-saddle canard. Using these findings, we construct a new polynomial approximation of the Plant model, which retains all the key elements for parabolic bursting, including the spike-adding transitions mediated by folded-saddle canards. Finally, we briefly investigate the presence of spike-adding via canards in planar phase models of parabolic bursting, namely the theta model by Ermentrout and Kopell.

Bifurcated method and apparatus for floating point addition with decreased latency time

DOEpatents

Farmwald, Paul M.

1987-01-01

Apparatus for decreasing the latency time associated with floating point addition and subtraction in a computer, using a novel bifurcated, pre-normalization/post-normalization approach that distinguishes between differences of floating point exponents.

Small aspect ratio Taylor-Couette flow: onset of a very-low-frequency three-torus state.

PubMed

Lopez, Juan M; Marques, Francisco

2003-09-01

The nonlinear dynamics of Taylor-Couette flow in a small aspect ratio annulus (where the length of the cylinders is half of the annular gap between them) is investigated by numerically solving the full three-dimensional Navier-Stokes equations. The system is invariant to arbitrary rotations about the annulus axis and to a reflection about the annulus half-height, so that the symmetry group is SO(2)xZ2. In this paper, we systematically investigate primary and subsequent bifurcations of the basic state, concentrating on a parameter regime where the basic state becomes unstable via Hopf bifurcations. We derive the four distinct cases for the symmetries of the bifurcated orbit, and numerically find two of these. In the parameter regime considered, we also locate the codimension-two double Hopf bifurcation where these two Hopf bifurcations coincide. Secondary Hopf bifurcations (Neimark-Sacker bifurcations), leading to modulated rotating waves, are subsequently found and a saddle-node-infinite-period bifurcation between a stable (node) and an unstable (saddle) modulated rotating wave is located, which gives rise to a very-low-frequency three-torus. This paper provides the computed example of such a state, along with a comprehensive bifurcation sequence leading to its onset.

Negative Feedback Mediated by Fast Inhibitory Autapse Enhances Neuronal Oscillations Near a Hopf Bifurcation Point

NASA Astrophysics Data System (ADS)

Jia, Bing

One-parameter and two-parameter bifurcations of the Morris-Lecar (ML) neuron model with and without the fast inhibitory autapse, which is a synapse from a neuron onto itself, are investigated. The ML neuron model without autapse manifests an inverse Hopf bifurcation point from firing to a depolarized resting state with high level of membrane potential, with increasing depolarization current. When a fast inhibitory autapse is introduced, a negative feedback or inhibitory current is applied to the ML model. With increasing conductance of the autapse to middle level, the depolarized resting state near the inverse Hopf bifurcation point can change to oscillation and the parameter region of the oscillation becomes wide, which can be well interpreted by the dynamic responses of the depolarized resting state to the inhibitory current stimulus mediated by the autapse. The enlargement of the parameter region of the oscillation induced by the negative feedback presents a novel viewpoint different from the traditional one that inhibitory synapse often suppresses the neuronal oscillation activities. Furthermore, complex nonlinear dynamics such as the coexisting behaviors and codimension-2 bifurcations including the Bautin and cusp bifurcations are acquired. The relationship between the bifurcations and the depolarization block, a physiological concept that indicates a neuron can enter resting state when receiving the depolarization current, is discussed.

Stent-Assisted Coil Embolization of a Symptomatic Renal Artery Aneurysm at a Bifurcation Point.

PubMed

Nassiri, Naiem; Huntress, Lauren A

2017-07-01

Symptomatic renal artery aneurysms at bifurcation points present challenging clinical scenarios rarely amenable to endovascular repair due to concerns regarding parenchymal loss following intervention. Herein, we add to the scant body of literature describing successful endovascular repair of a saccular, symptomatic renal artery aneurysm situated at a bifurcation point. A 52-year-old woman with a 2.5-cm extraparenchymal, saccular, symptomatic left renal artery aneurysm underwent self-expanding stent-assisted detachable platinum microcoil embolization. Complete aneurysm exclusion was achieved with minimal parenchymal loss. There were no perioperative complications, and no evidence of acute kidney injury perioperatively or at 3-month follow-up. Sustained symptomatic relief was achieved. Endovascular therapy can provide safe and effective aneurysm treatment within challenging bifurcated renal artery anatomy. Copyright © 2017 Elsevier Inc. All rights reserved.

Critical Slowing Down Governs the Transition to Neuron Spiking

PubMed Central

Meisel, Christian; Klaus, Andreas; Kuehn, Christian; Plenz, Dietmar

2015-01-01

Many complex systems have been found to exhibit critical transitions, or so-called tipping points, which are sudden changes to a qualitatively different system state. These changes can profoundly impact the functioning of a system ranging from controlled state switching to a catastrophic break-down; signals that predict critical transitions are therefore highly desirable. To this end, research efforts have focused on utilizing qualitative changes in markers related to a system’s tendency to recover more slowly from a perturbation the closer it gets to the transition—a phenomenon called critical slowing down. The recently studied scaling of critical slowing down offers a refined path to understand critical transitions: to identify the transition mechanism and improve transition prediction using scaling laws. Here, we outline and apply this strategy for the first time in a real-world system by studying the transition to spiking in neurons of the mammalian cortex. The dynamical system approach has identified two robust mechanisms for the transition from subthreshold activity to spiking, saddle-node and Hopf bifurcation. Although theory provides precise predictions on signatures of critical slowing down near the bifurcation to spiking, quantitative experimental evidence has been lacking. Using whole-cell patch-clamp recordings from pyramidal neurons and fast-spiking interneurons, we show that 1) the transition to spiking dynamically corresponds to a critical transition exhibiting slowing down, 2) the scaling laws suggest a saddle-node bifurcation governing slowing down, and 3) these precise scaling laws can be used to predict the bifurcation point from a limited window of observation. To our knowledge this is the first report of scaling laws of critical slowing down in an experiment. They present a missing link for a broad class of neuroscience modeling and suggest improved estimation of tipping points by incorporating scaling laws of critical slowing down as a

Critical dynamics of Hopf bifurcations in the corticothalamic system: Transitions from normal arousal states to epileptic seizures.

PubMed

Yang, Dong-Ping; Robinson, P A

2017-04-01

A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form quantitatively to underlying physiology that includes neural dynamics, axonal propagation, and time delays. Thus, a bridge is constructed that enables normal forms to be used to interpret quantitative data. The normal form of the Hopf bifurcations with delays is derived using Hale's theory, the center manifold theorem, and normal form analysis, and it is found to be explicitly expressed in terms of transfer functions and the sensitivity matrix of a reduced open-loop system. It can be applied to understand the effect of each physiological parameter on the critical dynamics and determine whether the Hopf bifurcation is supercritical or subcritical in instabilities that lead to absence and tonic-clonic seizures. Furthermore, the effects of thalamic and cortical nonlinearities on the bifurcation type are investigated, with implications for the roles of underlying physiology. The theoretical predictions about the bifurcation type and the onset dynamics are confirmed by numerical simulations and provide physiologically based criteria for determining bifurcation types from first principles. The results are consistent with experimental data from previous studies, imply that new regimes of seizure transitions may exist in clinical settings, and provide a simplified basis for control-systems interventions. Using the normal form, and the full equations from which it is derived, more complex dynamics, such as quasiperiodic cycles and saddle cycles, are discovered near the critical points of the subcritical Hopf bifurcations.

Critical dynamics of Hopf bifurcations in the corticothalamic system: Transitions from normal arousal states to epileptic seizures

NASA Astrophysics Data System (ADS)

Yang, Dong-Ping; Robinson, P. A.

2017-04-01

A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form quantitatively to underlying physiology that includes neural dynamics, axonal propagation, and time delays. Thus, a bridge is constructed that enables normal forms to be used to interpret quantitative data. The normal form of the Hopf bifurcations with delays is derived using Hale's theory, the center manifold theorem, and normal form analysis, and it is found to be explicitly expressed in terms of transfer functions and the sensitivity matrix of a reduced open-loop system. It can be applied to understand the effect of each physiological parameter on the critical dynamics and determine whether the Hopf bifurcation is supercritical or subcritical in instabilities that lead to absence and tonic-clonic seizures. Furthermore, the effects of thalamic and cortical nonlinearities on the bifurcation type are investigated, with implications for the roles of underlying physiology. The theoretical predictions about the bifurcation type and the onset dynamics are confirmed by numerical simulations and provide physiologically based criteria for determining bifurcation types from first principles. The results are consistent with experimental data from previous studies, imply that new regimes of seizure transitions may exist in clinical settings, and provide a simplified basis for control-systems interventions. Using the normal form, and the full equations from which it is derived, more complex dynamics, such as quasiperiodic cycles and saddle cycles, are discovered near the critical points of the subcritical Hopf bifurcations.

Completely inelastic ball.

PubMed

Gilet, T; Vandewalle, N; Dorbolo, S

2009-05-01

This Rapid Communication presents an analytical study of the bouncing of a completely inelastic ball on a vertically vibrated plate. The interplay of saddle-node and period-doubling bifurcations leads to an intricate structure of the bifurcation diagram with uncommon properties, such as an infinity of bifurcation cascades in a finite range of the control parameter Gamma. A pseudochaotic behavior, consisting in arbitrarily long and complex periodic sequences, is observed through this generic system.

Completely inelastic ball

NASA Astrophysics Data System (ADS)

Gilet, T.; Vandewalle, N.; Dorbolo, S.

2009-05-01

This Rapid Communication presents an analytical study of the bouncing of a completely inelastic ball on a vertically vibrated plate. The interplay of saddle-node and period-doubling bifurcations leads to an intricate structure of the bifurcation diagram with uncommon properties, such as an infinity of bifurcation cascades in a finite range of the control parameter Γ . A pseudochaotic behavior, consisting in arbitrarily long and complex periodic sequences, is observed through this generic system.

Effects of different dispersal patterns on the presence-absence of multiple species

NASA Astrophysics Data System (ADS)

Mohd, Mohd Hafiz; Murray, Rua; Plank, Michael J.; Godsoe, William

2018-03-01

Predicting which species will be present (or absent) across a geographical region remains one of the key problems in ecology. Numerous studies have suggested several ecological factors that can determine species presence-absence: environmental factors (i.e. abiotic environments), interactions among species (i.e. biotic interactions) and dispersal process. While various ecological factors have been considered, less attention has been given to the problem of understanding how different dispersal patterns, in interaction with other factors, shape community assembly in the presence of priority effects (i.e. where relative initial abundances determine the long-term presence-absence of each species). By employing both local and non-local dispersal models, we investigate the consequences of different dispersal patterns on the occurrence of priority effects and coexistence in multi-species communities. In the case of non-local, but short-range dispersal, we observe agreement with the predictions of local models for weak and medium dispersal strength, but disagreement for relatively strong dispersal levels. Our analysis shows the existence of a threshold value in dispersal strength (i.e. saddle-node bifurcation) above which priority effects disappear. These results also reveal a co-dimension 2 point, corresponding to a degenerate transcritical bifurcation: at this point, the transcritical bifurcation changes from subcritical to supercritical with corresponding creation of a saddle-node bifurcation curve. We observe further contrasting effects of non-local dispersal as dispersal distance changes: while very long-range dispersal can lead to species extinctions, intermediate-range dispersal can permit more outcomes with multi-species coexistence than short-range dispersal (or purely local dispersal). Overall, our results show that priority effects are more pronounced in the non-local dispersal models than in the local dispersal models. Taken together, our findings highlight

Bifurcation Analysis on Phase-Amplitude Cross-Frequency Coupling in Neural Networks with Dynamic Synapses

PubMed Central

Sase, Takumi; Katori, Yuichi; Komuro, Motomasa; Aihara, Kazuyuki

2017-01-01

We investigate a discrete-time network model composed of excitatory and inhibitory neurons and dynamic synapses with the aim at revealing dynamical properties behind oscillatory phenomena possibly related to brain functions. We use a stochastic neural network model to derive the corresponding macroscopic mean field dynamics, and subsequently analyze the dynamical properties of the network. In addition to slow and fast oscillations arising from excitatory and inhibitory networks, respectively, we show that the interaction between these two networks generates phase-amplitude cross-frequency coupling (CFC), in which multiple different frequency components coexist and the amplitude of the fast oscillation is modulated by the phase of the slow oscillation. Furthermore, we clarify the detailed properties of the oscillatory phenomena by applying the bifurcation analysis to the mean field model, and accordingly show that the intermittent and the continuous CFCs can be characterized by an aperiodic orbit on a closed curve and one on a torus, respectively. These two CFC modes switch depending on the coupling strength from the excitatory to inhibitory networks, via the saddle-node cycle bifurcation of a one-dimensional torus in map (MT1SNC), and may be associated with the function of multi-item representation. We believe that the present model might have potential for studying possible functional roles of phase-amplitude CFC in the cerebral cortex. PMID:28424606

Experimental Tracking of Limit-Point Bifurcations and Backbone Curves Using Control-Based Continuation

NASA Astrophysics Data System (ADS)

Renson, Ludovic; Barton, David A. W.; Neild, Simon A.

Control-based continuation (CBC) is a means of applying numerical continuation directly to a physical experiment for bifurcation analysis without the use of a mathematical model. CBC enables the detection and tracking of bifurcations directly, without the need for a post-processing stage as is often the case for more traditional experimental approaches. In this paper, we use CBC to directly locate limit-point bifurcations of a periodically forced oscillator and track them as forcing parameters are varied. Backbone curves, which capture the overall frequency-amplitude dependence of the system’s forced response, are also traced out directly. The proposed method is demonstrated on a single-degree-of-freedom mechanical system with a nonlinear stiffness characteristic. Results are presented for two configurations of the nonlinearity — one where it exhibits a hardening stiffness characteristic and one where it exhibits softening-hardening.

Bifurcations and chaos in convection taking non-Fourier heat-flux

NASA Astrophysics Data System (ADS)

Layek, G. C.; Pati, N. C.

2017-11-01

In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C. It also gives a threshold Cattaneo number, CT, above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C, while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map.

Rich Global Dynamics in a Prey-Predator Model with Allee Effect and Density Dependent Death Rate of Predator

NASA Astrophysics Data System (ADS)

Sen, Moitri; Banerjee, Malay

In this work we have considered a prey-predator model with strong Allee effect in the prey growth function, Holling type-II functional response and density dependent death rate for predators. It presents a comprehensive study of the complete global dynamics for the considered system. Especially to see the effect of the density dependent death rate of predator on the system behavior, we have presented the two parametric bifurcation diagrams taking it as one of the bifurcation parameters. In course of that we have explored all possible local and global bifurcations that the system could undergo, namely the existence of transcritical bifurcation, saddle node bifurcation, cusp bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and Bautin bifurcation respectively.

Saddles and dynamics in a solvable mean-field model

NASA Astrophysics Data System (ADS)

Angelani, L.; Ruocco, G.; Zamponi, F.

2003-05-01

We use the saddle-approach, recently introduced in the numerical investigation of simple model liquids, in the analysis of a mean-field solvable system. The investigated system is the k-trigonometric model, a k-body interaction mean field system, that generalizes the trigonometric model introduced by Madan and Keyes [J. Chem. Phys. 98, 3342 (1993)] and that has been recently introduced to investigate the relationship between thermodynamics and topology of the configuration space. We find a close relationship between the properties of saddles (stationary points of the potential energy surface) visited by the system and the dynamics. In particular the temperature dependence of saddle order follows that of the diffusivity, both having an Arrhenius behavior at low temperature and a similar shape in the whole temperature range. Our results confirm the general usefulness of the saddle-approach in the interpretation of dynamical processes taking place in interacting systems.

The dynamics of a harvested predator-prey system with Holling type IV functional response.

PubMed

Liu, Xinxin; Huang, Qingdao

2018-05-31

The paper aims to investigate the dynamical behavior of a predator-prey system with Holling type IV functional response in which both the species are subject to capturing. We mainly consider how the harvesting affects equilibria, stability, limit cycles and bifurcations in this system. We adopt the method of qualitative and quantitative analysis, which is based on the dynamical theory, bifurcation theory and numerical simulation. The boundedness of solutions, the existence and stability of equilibrium points of the system are further studied. Based on the Sotomayor's theorem, the existence of transcritical bifurcation and saddle-node bifurcation are derived. We use the normal form theorem to analyze the Hopf bifurcation. Simulation results show that the first Lyapunov coefficient is negative and a stable limit cycle may bifurcate. Numerical simulations are performed to make analytical studies more complete. This work illustrates that using the harvesting effort as control parameter can change the behaviors of the system, which may be useful for the biological management. Copyright © 2018 Elsevier B.V. All rights reserved.

Relative variances of the cadence frequency of cycling under two differential saddle heights

PubMed Central

Chang, Wen-Dien; Fan Chiang, Chin-Yun; Lai, Ping-Tung; Lee, Chia-Lun; Fang, Sz-Ming

2016-01-01

[Purpose] Bicycle saddle height is a critical factor for cycling performance and injury prevention. The present study compared the variance in cadence frequency after exercise fatigue between saddle heights with 25° and 35° knee flexion. [Methods] Two saddle heights, which were determined by setting the pedal at the bottom dead point with 35° and 25° knee flexion, were used for testing. The relative variances of the cadence frequency were calculated at the end of a 5-minute warm-up period and 5 minutes after inducing exercise fatigue. Comparison of the absolute values of the cadence frequency under the two saddle heights revealed a difference in pedaling efficiency. [Results] Five minutes after inducing exercise fatigue, the relative variances of the cadence frequency for the saddle height with 35° knee flexion was higher than that for the saddle height with 25° knee flexion. [Conclusion] The current finding demonstrated that a saddle height with 25° knee flexion is more appropriate for cyclists than a saddle height with 35° knee flexion. PMID:27065522

Parameter-dependent behaviour of periodic channels in a locus of boundary crisis

NASA Astrophysics Data System (ADS)

Rankin, James; Osinga, Hinke M.

2017-06-01

A boundary crisis occurs when a chaotic attractor outgrows its basin of attraction and suddenly disappears. As previously reported, the locus of a boundary crisis is organised by homo- or heteroclinic tangencies between the stable and unstable manifolds of saddle periodic orbits. In two parameters, such tangencies lead to curves, but the locus of boundary crisis along those curves exhibits gaps or channels, in which other non-chaotic attractors persist. These attractors are stable periodic orbits which themselves can undergo a cascade of period-doubling bifurcations culminating in multi-component chaotic attractors. The canonical diffeomorphic two-dimensional Hénon map exhibits such periodic channels, which are structured in a particular ordered way: each channel is bounded on one side by a saddle-node bifurcation and on the other by a period-doubling cascade to chaos; furthermore, all channels seem to have the same orientation, with the saddle-node bifurcation always on the same side. We investigate the locus of boundary crisis in the Ikeda map, which models the dynamics of energy levels in a laser ring cavity. We find that the Ikeda map features periodic channels with a richer and more general organisation than for the Hénon map. Using numerical continuation, we investigate how the periodic channels depend on a third parameter and characterise how they split into multiple channels with different properties.

Above Saddle-Point Regions of Order in a Sea of Chaos in the Vibrational Dynamics of KCN.

PubMed

Párraga, H; Arranz, F J; Benito, R M; Borondo, F

2018-04-05

The dynamical characteristics of a region of regular vibrational motion in the sea of chaos above the saddle point corresponding to the linear C-N-K configuration is examined in detail. To explain the origin of this regularity, the associated phase space structures were characterized using suitably defined Poincaré surfaces of section, identifying the different resonances between the stretching and bending modes, as a function of excitation energy. The corresponding topology is elucidated by means of periodic orbit analysis.

Topological phase diagram and saddle point singularity in a tunable topological crystalline insulator

DOE PAGES

Neupane, Madhab; Xu, Su-Yang; Sankar, R.; ...

2015-08-20

Here we report the evolution of the surface electronic structure and surface material properties of a topological crystalline insulator (TCI), Pb 1more » $${-}$$xSnxSe, as a function of various material parameters including composition x, temperature T , and crystal structure. Our spectroscopic data demonstrate the electronic ground-state condition for the saddle point singularity, the tunability of surface chemical potential, and the surface states’ response to circularly polarized light. Our results show that each material parameter can tune the system between the trivial and topological phase in a distinct way, unlike that seen in Bi 2Se 3 and related compounds, leading to a rich topological phase diagram. Our systematic studies of the TCI Pb 1$${-}$$xSnxSe are a valuable materials guide to realize new topological phenomena.« less

Detection of symmetric homoclinic orbits to saddle-centres in reversible systems

NASA Astrophysics Data System (ADS)

Yagasaki, Kazuyuki; Wagenknecht, Thomas

2006-02-01

We present a perturbation technique for the detection of symmetric homoclinic orbits to saddle-centre equilibria in reversible systems of ordinary differential equations. We assume that the unperturbed system has primary, symmetric homoclinic orbits, which may be either isolated or appear in a family, and use an idea similar to that of Melnikov’s method to detect homoclinic orbits in their neighbourhood. This technique also allows us to identify bifurcations of unperturbed or perturbed, symmetric homoclinic orbits. Our technique is of importance in applications such as nonlinear optics and water waves since homoclinic orbits to saddle-centre equilibria describe embedded solitons (ESs) in systems of partial differential equations representing physical models, and except for special cases their existence has been previously studied only numerically using shooting methods and continuation techniques. We apply the general theory to two examples, a four-dimensional system describing ESs in nonlinear optical media and a six-dimensional system which can possess a one-parameter family of symmetric homoclinic orbits in the unperturbed case. For these examples, the analysis is compared with numerical computations and an excellent agreement between both results is found.

Treatment outcomes of saddle nose correction.

PubMed

Hyun, Sang Min; Jang, Yong Ju

2013-01-01

Many valuable classification schemes for saddle nose have been suggested that integrate clinical deformity and treatment; however, there is no consensus regarding the most suitable classification and surgical method for saddle nose correction. To present clinical characteristics and treatment outcome of saddle nose deformity and to propose a modified classification system to better characterize the variety of different saddle nose deformities. The retrospective study included 91 patients who underwent rhinoplasty for correction of saddle nose from April 1, 2003, through December 31, 2011, with a minimum follow-up of 8 months. Saddle nose was classified into 4 types according to a modified classification. Aesthetic outcomes were classified as excellent, good, fair, or poor. Patients underwent minor cosmetic concealment by dorsal augmentation (n = 8) or major septal reconstruction combined with dorsal augmentation (n = 83). Autologous costal cartilages were used in 40 patients (44%), and homologous costal cartilages were used in 5 patients (6%). According to postoperative assessment, 29 patients had excellent, 42 patients had good, 18 patients had fair, and 2 patients had poor aesthetic outcomes. No statistical difference in surgical outcome according to saddle nose classification was observed. Eight patients underwent revision rhinoplasty, owing to recurrence of saddle, wound infection, or warping of the costal cartilage for dorsal augmentation. We introduce a modified saddle nose classification scheme that is simpler and better able to characterize different deformities. Among 91 patients with saddle nose, 20 (22%) had unsuccessful outcomes (fair or poor) and 8 (9%) underwent subsequent revision rhinoplasty. Thus, management of saddle nose deformities remains challenging. 4.

Coupled catastrophes: sudden shifts cascade and hop among interdependent systems

PubMed Central

Barnett, George; D'Souza, Raissa M.

2015-01-01

An important challenge in several disciplines is to understand how sudden changes can propagate among coupled systems. Examples include the synchronization of business cycles, population collapse in patchy ecosystems, markets shifting to a new technology platform, collapses in prices and in confidence in financial markets, and protests erupting in multiple countries. A number of mathematical models of these phenomena have multiple equilibria separated by saddle-node bifurcations. We study this behaviour in its normal form as fast–slow ordinary differential equations. In our model, a system consists of multiple subsystems, such as countries in the global economy or patches of an ecosystem. Each subsystem is described by a scalar quantity, such as economic output or population, that undergoes sudden changes via saddle-node bifurcations. The subsystems are coupled via their scalar quantity (e.g. trade couples economic output; diffusion couples populations); that coupling moves the locations of their bifurcations. The model demonstrates two ways in which sudden changes can propagate: they can cascade (one causing the next), or they can hop over subsystems. The latter is absent from classic models of cascades. For an application, we study the Arab Spring protests. After connecting the model to sociological theories that have bistability, we use socioeconomic data to estimate relative proximities to tipping points and Facebook data to estimate couplings among countries. We find that although protests tend to spread locally, they also seem to ‘hop' over countries, like in the stylized model; this result highlights a new class of temporal motifs in longitudinal network datasets. PMID:26559684

Bifurcation analysis in SIR epidemic model with treatment

NASA Astrophysics Data System (ADS)

Balamuralitharan, S.; Radha, M.

2018-04-01

We investigated the bifurcation analysis of nonlinear system of SIR epidemic model with treatment. It is accepted that the treatment is corresponding to the quantity of infective which is below the limit and steady when the quantity of infective achieves the limit. We analyze about the Transcritical bifurcation which occurs at the disease free equilibrium point and Hopf bifurcation which occurs at endemic equilibrium point. Using MATLAB we show the picture of bifurcation at the disease free equilibrium point.

On the CCN (de)activation nonlinearities

NASA Astrophysics Data System (ADS)

Arabas, Sylwester; Shima, Shin-ichiro

2017-09-01

We take into consideration the evolution of particle size in a monodisperse aerosol population during activation and deactivation of cloud condensation nuclei (CCN). Our analysis reveals that the system undergoes a saddle-node bifurcation and a cusp catastrophe. The control parameters chosen for the analysis are the relative humidity and the particle concentration. An analytical estimate of the activation timescale is derived through estimation of the time spent in the saddle-node bifurcation bottleneck. Numerical integration of the system coupled with a simple air-parcel cloud model portrays two types of activation/deactivation hystereses: one associated with the kinetic limitations on droplet growth when the system is far from equilibrium, and one occurring close to equilibrium and associated with the cusp catastrophe. We discuss the presented analyses in context of the development of particle-based models of aerosol-cloud interactions in which activation and deactivation impose stringent time-resolution constraints on numerical integration.

Solvable model for chimera states of coupled oscillators.

PubMed

Abrams, Daniel M; Mirollo, Rennie; Strogatz, Steven H; Wiley, Daniel A

2008-08-22

Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.

27 CFR 9.203 - Saddle Rock-Malibu.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Saddle Rock-Malibu. 9.203... Saddle Rock-Malibu. (a) Name. The name of the viticultural area described in this section is “Saddle Rock-Malibu”. For purposes of part 4 of this chapter, “Saddle Rock-Malibu” is a term of viticultural...

27 CFR 9.203 - Saddle Rock-Malibu.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Saddle Rock-Malibu. 9.203... Saddle Rock-Malibu. (a) Name. The name of the viticultural area described in this section is “Saddle Rock-Malibu”. For purposes of part 4 of this chapter, “Saddle Rock-Malibu” is a term of viticultural...

27 CFR 9.203 - Saddle Rock-Malibu.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Saddle Rock-Malibu. 9.203... Saddle Rock-Malibu. (a) Name. The name of the viticultural area described in this section is “Saddle Rock-Malibu”. For purposes of part 4 of this chapter, “Saddle Rock-Malibu” is a term of viticultural...

27 CFR 9.203 - Saddle Rock-Malibu.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Saddle Rock-Malibu. 9.203... Saddle Rock-Malibu. (a) Name. The name of the viticultural area described in this section is “Saddle Rock-Malibu”. For purposes of part 4 of this chapter, “Saddle Rock-Malibu” is a term of viticultural...

27 CFR 9.203 - Saddle Rock-Malibu.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2014-04-01 2014-04-01 false Saddle Rock-Malibu. 9.203... Saddle Rock-Malibu. (a) Name. The name of the viticultural area described in this section is “Saddle Rock-Malibu”. For purposes of part 4 of this chapter, “Saddle Rock-Malibu” is a term of viticultural...

The dynamics of phase locking and points of resonance in a forced magnetic oscillator

NASA Astrophysics Data System (ADS)

Bryant, Paul; Jeffries, Carson

1987-03-01

We report data on an experimental system: a forced symmetric oscillator containing a saturable inductor with magnetic hysteresis. It displays a Hopf bifurcation to quasiperiodicity, entrainment horns, and chaos. We study in detail the bifurcations and hysteresis occurring near points of resonance (particularly “ strong resonance”) and show how the observed behavior can be understood using Arnold's theory. Much of the behavior relating to the entrainment horns is explored: period doubling and symmetry breaking bifurcations; homoclinic bifurcations; and crises and other bifurcations taking place at the horn boundaries. Important features of the behavior related to symmetry properties of the oscillator are studied and explained through the concept of a half-cycle map. The system is shown to exhibit a Hopf bifurcation from a phase-locked state to periodic “islands”, similar to those found in Hamiltonian systems. An initialization technique is used to observe the manifolds of saddle orbits and other hidden structure. An unusual differential equation model is developed which is irreversible and generates a noninvertible Poincaré map of the plane. Noninvertibility of this planar map has important effects on the behavior observed. The Poincaré map may also be approximated through experimental measurements, resulting in a planar map with parameter dependence. This model gives good correspondence with the system in a region of the parameter space.

Providing nearest neighbor point-to-point communications among compute nodes of an operational group in a global combining network of a parallel computer

DOEpatents

Archer, Charles J.; Faraj, Ahmad A.; Inglett, Todd A.; Ratterman, Joseph D.

2012-10-23

Methods, apparatus, and products are disclosed for providing nearest neighbor point-to-point communications among compute nodes of an operational group in a global combining network of a parallel computer, each compute node connected to each adjacent compute node in the global combining network through a link, that include: identifying each link in the global combining network for each compute node of the operational group; designating one of a plurality of point-to-point class routing identifiers for each link such that no compute node in the operational group is connected to two adjacent compute nodes in the operational group with links designated for the same class routing identifiers; and configuring each compute node of the operational group for point-to-point communications with each adjacent compute node in the global combining network through the link between that compute node and that adjacent compute node using that link's designated class routing identifier.

Multigrid methods for bifurcation problems: The self adjoint case

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1987-01-01

This paper deals with multigrid methods for computational problems that arise in the theory of bifurcation and is restricted to the self adjoint case. The basic problem is to solve for arcs of solutions, a task that is done successfully with an arc length continuation method. Other important issues are, for example, detecting and locating singular points as part of the continuation process, switching branches at bifurcation points, etc. Multigrid methods have been applied to continuation problems. These methods work well at regular points and at limit points, while they may encounter difficulties in the vicinity of bifurcation points. A new continuation method that is very efficient also near bifurcation points is presented here. The other issues mentioned above are also treated very efficiently with appropriate multigrid algorithms. For example, it is shown that limit points and bifurcation points can be solved for directly by a multigrid algorithm. Moreover, the algorithms presented here solve the corresponding problems in just a few work units (about 10 or less), where a work unit is the work involved in one local relaxation on the finest grid.

Model reduction method using variable-separation for stochastic saddle point problems

NASA Astrophysics Data System (ADS)

Jiang, Lijian; Li, Qiuqi

2018-02-01

In this paper, we consider a variable-separation (VS) method to solve the stochastic saddle point (SSP) problems. The VS method is applied to obtain the solution in tensor product structure for stochastic partial differential equations (SPDEs) in a mixed formulation. The aim of such a technique is to construct a reduced basis approximation of the solution of the SSP problems. The VS method attempts to get a low rank separated representation of the solution for SSP in a systematic enrichment manner. No iteration is performed at each enrichment step. In order to satisfy the inf-sup condition in the mixed formulation, we enrich the separated terms for the primal system variable at each enrichment step. For the SSP problems by regularization or penalty, we propose a more efficient variable-separation (VS) method, i.e., the variable-separation by penalty method. This can avoid further enrichment of the separated terms in the original mixed formulation. The computation of the variable-separation method decomposes into offline phase and online phase. Sparse low rank tensor approximation method is used to significantly improve the online computation efficiency when the number of separated terms is large. For the applications of SSP problems, we present three numerical examples to illustrate the performance of the proposed methods.

On the critical forcing amplitude of forced nonlinear oscillators

NASA Astrophysics Data System (ADS)

Febbo, Mariano; Ji, Jinchen C.

2013-12-01

The steady-state response of forced single degree-of-freedom weakly nonlinear oscillators under primary resonance conditions can exhibit saddle-node bifurcations, jump and hysteresis phenomena, if the amplitude of the excitation exceeds a certain value. This critical value of excitation amplitude or critical forcing amplitude plays an important role in determining the occurrence of saddle-node bifurcations in the frequency-response curve. This work develops an alternative method to determine the critical forcing amplitude for single degree-of-freedom nonlinear oscillators. Based on Lagrange multipliers approach, the proposed method considers the calculation of the critical forcing amplitude as an optimization problem with constraints that are imposed by the existence of locations of vertical tangency. In comparison with the Gröbner basis method, the proposed approach is more straightforward and thus easy to apply for finding the critical forcing amplitude both analytically and numerically. Three examples are given to confirm the validity of the theoretical predictions. The first two present the analytical form for the critical forcing amplitude and the third one is an example of a numerically computed solution.

Flood-inundation maps for the Saddle River from Upper Saddle River Borough to Saddle River Borough, New Jersey, 2013

USGS Publications Warehouse

Watson, Kara M.; Hoppe, Heidi L.

2013-01-01

Digital flood-inundation maps for a 4.1-mile reach of the Saddle River from 0.6 miles downstream from the New Jersey-New York State boundary in Upper Saddle River Borough to 0.2 miles downstream from the East Allendale Road bridge in Saddle River Borough, New Jersey, were created by the U.S. Geological Survey (USGS) in cooperation with the New Jersey Department of Environmental Protection (NJDEP). The inundation maps, which can be accessed through the USGS Flood Inundation Mapping Science Web site at http://water.usgs.gov/osw/flood_inundation/, depict estimates of the areal extent and depth of flooding corresponding to select water levels (stages) at the USGS streamgage 01390450, Saddle River at Upper Saddle River, New Jersey. Current conditions for estimating near real-time areas of inundation using USGS streamgage information may be obtained on the Internet at http://waterdata.usgs.gov/nwis/uv?site_no=01390450. The National Weather Service (NWS) forecasts flood hydrographs at many places that are often collocated with USGS streamgages. NWS-forecasted peak-stage information may be used in conjunction with the maps developed in this study to show predicted areas of flood inundation. In this study, flood profiles were computed for the stream reach by means of a one-dimensional step-backwater model. The model was calibrated by using the most current stage-discharge relations (in effect March 2013) at USGS streamgage 01390450, Saddle River at Upper Saddle River, New Jersey, and documented high-water marks from recent floods. The hydraulic model was then used to determine eight water-surface profiles for flood stages at 0.5-foot (ft) intervals referenced to the streamgage datum, North American Vertical Datum of 1988 (NAVD 88), and ranging from bankfull, 0.5 ft below NWS Action Stage, to the upper extent of the stage-discharge rating which is approximately 1 ft higher than the highest recorded water level at the streamgage. Action Stage is the stage which when reached

Bifurcation of solutions to Hamiltonian boundary value problems

NASA Astrophysics Data System (ADS)

McLachlan, R. I.; Offen, C.

2018-06-01

A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples.

A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

NASA Astrophysics Data System (ADS)

Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

2017-12-01

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

Why do galactic spins flip in the cosmic web? A Theory of Tidal Torques near saddles

NASA Astrophysics Data System (ADS)

Pichon, Christophe; Codis, Sandrine; Pogosyan, Dmitry; Dubois, Yohan; Desjacques, Vincent; Devriendt, Julien

2016-10-01

Filaments of the cosmic web drive spin acquisition of disc galaxies. The point process of filament-type saddle represent best this environment and can be used to revisit the Tidal Torque Theory in the context of an anisotropic peak (saddle) background split. The constrained misalignment between the tidal tensor and the Hessian of the density field generated in the vicinity of filament saddle points simply explains the corresponding transverse and longitudinal point-reflection symmetric geometry of spin distribution. It predicts in particular an azimuthal orientation of the spins of more massive galaxies and spin alignment with the filament for less massive galaxies. Its scale dependence also allows us to relate the transition mass corresponding to the alignment of dark matter halos' spin relative to the direction of their neighboring filament to this geometry, and to predict accordingly it's scaling with the mass of non linearity, as was measured in simulations.

Global bifurcations in fractional-order chaotic systems with an extended generalized cell mapping method

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

Liu, Xiaojun; School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001; Hong, Ling, E-mail: hongling@mail.xjtu.edu.cn

Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7, 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuousmore » change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.« less

Providing full point-to-point communications among compute nodes of an operational group in a global combining network of a parallel computer

DOEpatents

Archer, Charles J; Faraj, Ahmad A; Inglett, Todd A; Ratterman, Joseph D

2013-04-16

Methods, apparatus, and products are disclosed for providing full point-to-point communications among compute nodes of an operational group in a global combining network of a parallel computer, each compute node connected to each adjacent compute node in the global combining network through a link, that include: receiving a network packet in a compute node, the network packet specifying a destination compute node; selecting, in dependence upon the destination compute node, at least one of the links for the compute node along which to forward the network packet toward the destination compute node; and forwarding the network packet along the selected link to the adjacent compute node connected to the compute node through the selected link.

Bifurcations of periodic motion in a three-degree-of-freedom vibro-impact system with clearance

NASA Astrophysics Data System (ADS)

Liu, Yongbao; Wang, Qiang; Xu, Huidong

2017-07-01

The smooth bifurcation and grazing non-smooth bifurcation of periodic motion of a three-degree-of-freedom vibro-impact system with clearance are studied in this paper. Firstly, a periodic solution of vibro-impact system is solved and a six-dimensional Poincaré map is established. Then, for the six-dimensional Poincaré map, the analytic expressions of all eigenvalues of Jacobi matrix with respect to parameters are unavailable. This implies that with application of the classical critical criterion described by the properties of eigenvalues, we have to numerically compute eigenvalues point by point and check their properties to search for the bifurcation points. Such the numerical calculation is a laborious job in the process of determining bifurcation points. To overcome the difficulty that originates from the classical bifurcation criteria, the explicit critical criteria without using eigenvalues calculation of high-dimensional map are applied to determine bifurcation points of Co-dimension-one period doubling bifurcation and Co-dimension-one Neimark-Sacker bifurcation and Co-dimension-two Flip-Neimark-Sacker bifurcation, and then local dynamical behaviors of these bifurcations are analyzed. Moreover, the directions of period doubling bifurcation and Neimark-Sacker bifurcation are analyzed by center manifold reduction theory and normal form approach. Finally, the existence of the grazing periodic motion of the vibro-impact system is analyzed and the grazing bifurcation point is obtained, the discontinuous grazing bifurcation behavior is studied based on the compound normal form map near the grazing point, the discontinuous jumping phenomenon and co-existing multiple solutions near the grazing bifurcation point are revealed.

Chimera states for coupled oscillators.

PubMed

Abrams, Daniel M; Strogatz, Steven H

2004-10-22

Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked oscillators coexist with drifting ones. Discovered two years ago, such "chimera states" are believed to be impossible for locally or globally coupled systems; they are peculiar to the intermediate case of nonlocal coupling. Here we present an exact solution for this state, for a ring of phase oscillators coupled by a cosine kernel. We show that the stable chimera state bifurcates from a spatially modulated drift state, and dies in a saddle-node bifurcation with an unstable chimera state.

A mathematical model of 'Pride and Prejudice'.

PubMed

Rinaldi, Sergio; Rossa, Fabio Della; Landi, Pietro

2014-04-01

A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations.

Providing full point-to-point communications among compute nodes of an operational group in a global combining network of a parallel computer

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

Archer, Charles J.; Faraj, Daniel A.; Inglett, Todd A.

Methods, apparatus, and products are disclosed for providing full point-to-point communications among compute nodes of an operational group in a global combining network of a parallel computer, each compute node connected to each adjacent compute node in the global combining network through a link, that include: receiving a network packet in a compute node, the network packet specifying a destination compute node; selecting, in dependence upon the destination compute node, at least one of the links for the compute node along which to forward the network packet toward the destination compute node; and forwarding the network packet along the selectedmore » link to the adjacent compute node connected to the compute node through the selected link.« less

Double Neimark Sacker bifurcation and torus bifurcation of a class of vibratory systems with symmetrical rigid stops

NASA Astrophysics Data System (ADS)

Luo, G. W.; Chu, Y. D.; Zhang, Y. L.; Zhang, J. G.

2006-11-01

A multidegree-of-freedom system having symmetrically placed rigid stops and subjected to periodic excitation is considered. The system consists of linear components, but the maximum displacement of one of the masses is limited to a threshold value by the symmetrical rigid stops. Repeated impacts usually occur in the vibratory system due to the rigid amplitude constraints. Such models play an important role in the studies of mechanical systems with clearances or gaps. Double Neimark-Sacker bifurcation of the system is analyzed by using the center manifold and normal form method of maps. The period-one double-impact symmetrical motion and homologous disturbed map of the system are derived analytically. A center manifold theorem technique is applied to reduce the Poincaré map to a four-dimensional one, and the normal form map associated with double Neimark-Sacker bifurcation is obtained. The bifurcation sets for the normal-form map are illustrated in detail. Local behavior of the vibratory systems with symmetrical rigid stops, near the points of double Neimark-Sacker bifurcations, is reported by the presentation of results for a three-degree-of-freedom vibratory system with symmetrical stops. The existence and stability of period-one double-impact symmetrical motion are analyzed explicitly. Also, local bifurcations at the points of change in stability are analyzed, thus giving some information on dynamical behavior near the points of double Neimark-Sacker bifurcations. Near the value of double Neimark-Sacker bifurcation there exist period-one double-impact symmetrical motion and quasi-periodic impact motions. The quasi-periodic impact motions are represented by the closed circle and "tire-like" attractor in projected Poincaré sections. With change of system parameters, the quasi-periodic impact motions usually lead to chaos via "tire-like" torus doubling.

Analysis on the crime model using dynamical approach

NASA Astrophysics Data System (ADS)

Mohammad, Fazliza; Roslan, Ummu'Atiqah Mohd

2017-08-01

A research is carried out to analyze a dynamical model of the spread crime system. A Simplified 2-Dimensional Model is used in this research. The objectives of this research are to investigate the stability of the model of the spread crime, to summarize the stability by using a bifurcation analysis and to study the relationship of basic reproduction number, R0 with the parameter in the model. Our results for stability of equilibrium points shows that we have two types of stability, which are asymptotically stable and saddle node. While the result for bifurcation analysis shows that the number of criminally active and incarcerated increases as we increase the value of a parameter in the model. The result for the relationship of R0 with the parameter shows that as the parameter increases, R0 increase too, and the rate of crime increase too.

36 CFR 34.10 - Saddle and pack animals.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 36 Parks, Forests, and Public Property 1 2014-07-01 2014-07-01 false Saddle and pack animals. 34... INTERIOR EL PORTAL ADMINISTRATIVE SITE REGULATIONS § 34.10 Saddle and pack animals. The use of saddle and pack animals is prohibited without a permit from the Superintendent. ...

36 CFR 34.10 - Saddle and pack animals.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 36 Parks, Forests, and Public Property 1 2011-07-01 2011-07-01 false Saddle and pack animals. 34... INTERIOR EL PORTAL ADMINISTRATIVE SITE REGULATIONS § 34.10 Saddle and pack animals. The use of saddle and pack animals is prohibited without a permit from the Superintendent. ...

36 CFR 34.10 - Saddle and pack animals.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 36 Parks, Forests, and Public Property 1 2013-07-01 2013-07-01 false Saddle and pack animals. 34... INTERIOR EL PORTAL ADMINISTRATIVE SITE REGULATIONS § 34.10 Saddle and pack animals. The use of saddle and pack animals is prohibited without a permit from the Superintendent. ...

36 CFR 34.10 - Saddle and pack animals.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 36 Parks, Forests, and Public Property 1 2012-07-01 2012-07-01 false Saddle and pack animals. 34... INTERIOR EL PORTAL ADMINISTRATIVE SITE REGULATIONS § 34.10 Saddle and pack animals. The use of saddle and pack animals is prohibited without a permit from the Superintendent. ...

36 CFR 34.10 - Saddle and pack animals.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 36 Parks, Forests, and Public Property 1 2010-07-01 2010-07-01 false Saddle and pack animals. 34... INTERIOR EL PORTAL ADMINISTRATIVE SITE REGULATIONS § 34.10 Saddle and pack animals. The use of saddle and pack animals is prohibited without a permit from the Superintendent. ...

Bifurcation analysis of a delay reaction-diffusion malware propagation model with feedback control

NASA Astrophysics Data System (ADS)

Zhu, Linhe; Zhao, Hongyong; Wang, Xiaoming

2015-05-01

With the rapid development of network information technology, information networks security has become a very critical issue in our work and daily life. This paper attempts to develop a delay reaction-diffusion model with a state feedback controller to describe the process of malware propagation in mobile wireless sensor networks (MWSNs). By analyzing the stability and Hopf bifurcation, we show that the state feedback method can successfully be used to control unstable steady states or periodic oscillations. Moreover, formulas for determining the properties of the bifurcating periodic oscillations are derived by applying the normal form method and center manifold theorem. Finally, we conduct extensive simulations on large-scale MWSNs to evaluate the proposed model. Numerical evidences show that the linear term of the controller is enough to delay the onset of the Hopf bifurcation and the properties of the bifurcation can be regulated to achieve some desirable behaviors by choosing the appropriate higher terms of the controller. Furthermore, we obtain that the spatial-temporal dynamic characteristics of malware propagation are closely related to the rate constant for nodes leaving the infective class for recovered class and the mobile behavior of nodes.

Self-localized structures in vertical-cavity surface-emitting lasers with external feedback.

PubMed

Paulau, P V; Gomila, D; Ackemann, T; Loiko, N A; Firth, W J

2008-07-01

In this paper, we analyze a model of broad area vertical-cavity surface-emitting lasers subjected to frequency-selective optical feedback. In particular, we analyze the spatio-temporal regimes arising above threshold and the existence and dynamical properties of cavity solitons. We build the bifurcation diagram of stationary self-localized states, finding that branches of cavity solitons emerge from the degenerate Hopf bifurcations marking the homogeneous solutions with maximal and minimal gain. These branches collide in a saddle-node bifurcation, defining a maximum pump current for soliton existence that lies below the threshold of the laser without feedback. The properties of these cavity solitons are in good agreement with those observed in recent experiments.

Estimating turbulent electrovortex flow parameters hear the dynamo cycle bifurcation point

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

Zimin, V.D.; Kolpakov, N.Yu.; Khripchenko, S.Yu.

1988-07-01

Models for estimating turbulent electrovortex flow parameters, derived in earlier studies, were delineated and extended in this paper to express those parameters near the dynamo cycle bifurcation point in a spherical cavity. Toroidal and poloidal fields rising from the induction currents within the liquid metal and their electrovortex interactions were calculated. Toroidal field strengthening by the poloidal electrovortex flow, the first part of the dynamo loop, was determined by the viscous dissipation in the liquid metal. The second part of the loop, in which the toroidal field localized in the liquid metal is converted to a poloidal field and emergesmore » from the sphere, was also established. The dissipative effects near the critical magnetic Reynolds number were estimated.« less

Poster — Thur Eve — 70: Automatic lung bronchial and vessel bifurcations detection algorithm for deformable image registration assessment

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

Labine, Alexandre; Carrier, Jean-François; Bedwani, Stéphane

2014-08-15

Purpose: To investigate an automatic bronchial and vessel bifurcations detection algorithm for deformable image registration (DIR) assessment to improve lung cancer radiation treatment. Methods: 4DCT datasets were acquired and exported to Varian treatment planning system (TPS) EclipseTM for contouring. The lungs TPS contour was used as the prior shape for a segmentation algorithm based on hierarchical surface deformation that identifies the deformed lungs volumes of the 10 breathing phases. Hounsfield unit (HU) threshold filter was applied within the segmented lung volumes to identify blood vessels and airways. Segmented blood vessels and airways were skeletonised using a hierarchical curve-skeleton algorithm basedmore » on a generalized potential field approach. A graph representation of the computed skeleton was generated to assign one of three labels to each node: the termination node, the continuation node or the branching node. Results: 320 ± 51 bifurcations were detected in the right lung of a patient for the 10 breathing phases. The bifurcations were visually analyzed. 92 ± 10 bifurcations were found in the upper half of the lung and 228 ± 45 bifurcations were found in the lower half of the lung. Discrepancies between ten vessel trees were mainly ascribed to large deformation and in regions where the HU varies. Conclusions: We established an automatic method for DIR assessment using the morphological information of the patient anatomy. This approach allows a description of the lung's internal structure movement, which is needed to validate the DIR deformation fields for accurate 4D cancer treatment planning.« less

46 CFR 64.29 - Tank saddles.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 46 Shipping 2 2011-10-01 2011-10-01 false Tank saddles. 64.29 Section 64.29 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) MARINE ENGINEERING MARINE PORTABLE TANKS AND CARGO HANDLING SYSTEMS Standards for an MPT § 64.29 Tank saddles. If a tank is not completely supported by a framework...

46 CFR 64.29 - Tank saddles.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 46 Shipping 2 2013-10-01 2013-10-01 false Tank saddles. 64.29 Section 64.29 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) MARINE ENGINEERING MARINE PORTABLE TANKS AND CARGO HANDLING SYSTEMS Standards for an MPT § 64.29 Tank saddles. If a tank is not completely supported by a framework...

46 CFR 64.29 - Tank saddles.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 46 Shipping 2 2010-10-01 2010-10-01 false Tank saddles. 64.29 Section 64.29 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) MARINE ENGINEERING MARINE PORTABLE TANKS AND CARGO HANDLING SYSTEMS Standards for an MPT § 64.29 Tank saddles. If a tank is not completely supported by a framework...

46 CFR 64.29 - Tank saddles.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 46 Shipping 2 2012-10-01 2012-10-01 false Tank saddles. 64.29 Section 64.29 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) MARINE ENGINEERING MARINE PORTABLE TANKS AND CARGO HANDLING SYSTEMS Standards for an MPT § 64.29 Tank saddles. If a tank is not completely supported by a framework...

46 CFR 64.29 - Tank saddles.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 46 Shipping 2 2014-10-01 2014-10-01 false Tank saddles. 64.29 Section 64.29 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) MARINE ENGINEERING MARINE PORTABLE TANKS AND CARGO HANDLING SYSTEMS Standards for an MPT § 64.29 Tank saddles. If a tank is not completely supported by a framework...

The Taylor saddle effacement: a new technique for correction of saddle nose deformity.

PubMed

Taylor, S Mark; Rigby, Matthew H

2008-02-01

To describe a novel technique, the Taylor saddle effacement (TSE), for correction of saddle nose deformity using autologous grafts from the lower lateral cartilages. A prospective evaluation of six patients, all of whom had the TSE performed. Photographs were taken in combination with completion of a rhinoplasty outcomes questionnaire preoperatively and at 6 months. The questionnaire included a visual analogue scale (VAS) of nasal breathing and a rhinoplasty outcomes evaluation (ROE) of nasal function and esthetics. All six patients had improvement in both their global nasal airflow on the VAS and on their ROE that was statistically significant. The mean preoperative VAS score was 5.8 compared with our postoperative mean of 8.5 of a possible 10. Mean ROE scores improved from 34.7 to 85.5. At 6 months, all patients felt that their nasal appearance had improved. The TSE is a simple and reliable technique for correction of saddle nose deformity. This prospective study has demonstrated improvement in both nasal function and esthetics when it is employed.

Saddled Prominent

Treesearch

Peter A. Rush; Douglas C. Allen

1987-01-01

The saddled prominent, Heterocampa guttivitta (Walker), defoliates hardwoods in the Northeastern United States and Southeastern Canada. Outbreaks of this native insect have occurred in the United States and Canada at intervals of approximately 10 years since they were first recorded in the early 1900's. Populations, characterized by their instability, build...

Deconstructing zero: resurgence, supersymmetry and complex saddles

DOE PAGES

Dunne, Gerald V.; Ünsal, Mithat

2016-12-01

We explain how a vanishing, or truncated, perturbative expansion, such as often arises in semi-classically tractable supersymmetric theories, can nevertheless be related to fluctuations about non-perturbative sectors via resurgence. We also demonstrate that, in the same class of theories, the vanishing of the ground state energy (unbroken supersymmetry) can be attributed to the cancellation between a real saddle and a complex saddle (with hidden topological angle π), and positivity of the ground state energy (broken supersymmetry) can be interpreted as the dominance of complex saddles. In either case, despite the fact that the ground state energy is zero to allmore » orders in perturbation theory, all orders of fluctuations around non-perturbative saddles are encoded in the perturbative E (N, g). Finally, we illustrate these ideas with examples from supersymmetric quantum mechanics and quantum field theory.« less

Bifurcation Analysis Using Rigorous Branch and Bound Methods

NASA Technical Reports Server (NTRS)

Smith, Andrew P.; Crespo, Luis G.; Munoz, Cesar A.; Lowenberg, Mark H.

2014-01-01

For the study of nonlinear dynamic systems, it is important to locate the equilibria and bifurcations occurring within a specified computational domain. This paper proposes a new approach for solving these problems and compares it to the numerical continuation method. The new approach is based upon branch and bound and utilizes rigorous enclosure techniques to yield outer bounding sets of both the equilibrium and local bifurcation manifolds. These sets, which comprise the union of hyper-rectangles, can be made to be as tight as desired. Sufficient conditions for the existence of equilibrium and bifurcation points taking the form of algebraic inequality constraints in the state-parameter space are used to calculate their enclosures directly. The enclosures for the bifurcation sets can be computed independently of the equilibrium manifold, and are guaranteed to contain all solutions within the computational domain. A further advantage of this method is the ability to compute a near-maximally sized hyper-rectangle of high dimension centered at a fixed parameter-state point whose elements are guaranteed to exclude all bifurcation points. This hyper-rectangle, which requires a global description of the bifurcation manifold within the computational domain, cannot be obtained otherwise. A test case, based on the dynamics of a UAV subject to uncertain center of gravity location, is used to illustrate the efficacy of the method by comparing it with numerical continuation and to evaluate its computational complexity.

Stellarator Saddle Coils

NASA Astrophysics Data System (ADS)

Boozer, Allen H.

1999-11-01

Modern stellarators are designed using J. Nuehrenberg’s method of varying Fourier coefficients in the shape of the plasma boundary to maximize a target function. The matrix of second derivatives of the target function at the optimum determines a quality matrix. This matrix gives the degradation in the quality of the configuration as the normal magnetic field is varied on a control surface, which lies on or outside the plasma surface. The task is finding saddle coils that produce the desired configuration in the presence of a given toroidal field. An eigenvector of the quality matrix can be important for two reasons: (1) the normal field that must be produced by the saddles is large or (2) the eigenvalue is large (an island-causing resonant perturbation). The rank of the important part of the quality matrix is the number of important eigenvectors. The current in each saddle coil produces a normal field on the control surface, which can be described by an inductance matrix. The relevant part of the inductance matrix has large eigenvalues. The coils can produce the configuration if the rank of the important part of the quality matrix and its product with the relevant part of the inductance matrix are the same. Existing coil design codes, pioneered by P. Merkel, approximate the quality matrix by the unit matrix. Stellarator flexibility could be enhanced by using a more realistic quality matrix and by using trim coils to balance large eigenvalues.

Border Collision and Smooth Bifurcations in a Family of Linear-Power Maps

NASA Astrophysics Data System (ADS)

Gardini, Laura; Makrooni, Roya

2016-02-01

In this work we describe some properties and bifurcations which occur in a family of linear-power maps typical in Nordmark’ systems. The continuous case has been investigated by many authors since a few years, while the discontinuous case has been considered only recently. In particular, having a vertical asymptote, it gives rise to new kinds of bifurcations. Organizing centers related to codimension-two bifurcation points, due to the intersection of a border collision bifurcation and a smooth fold bifurcation of cycles having a different symbolic sequence are evidenced. It is shown the relevant role played by a codimension-two point existing on any border collision bifurcation curve, and related to the smooth fold bifurcation of cycles with the same symbolic sequence. We recall some of the properties proved up to now, evidencing the rich structure which is still to be understood.

Arctic melt ponds and bifurcations in the climate system

NASA Astrophysics Data System (ADS)

Sudakov, I.; Vakulenko, S. A.; Golden, K. M.

2015-05-01

Understanding how sea ice melts is critical to climate projections. In the Arctic, melt ponds that develop on the surface of sea ice floes during the late spring and summer largely determine their albedo - a key parameter in climate modeling. Here we explore the possibility of a conceptual sea ice climate model passing through a bifurcation point - an irreversible critical threshold as the system warms, by incorporating geometric information about melt pond evolution. This study is based on a bifurcation analysis of the energy balance climate model with ice-albedo feedback as the key mechanism driving the system to bifurcation points.

Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Sun, Jian-Qiao

2016-09-01

The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

Bifurcation theory for finitely smooth planar autonomous differential systems

NASA Astrophysics Data System (ADS)

Han, Maoan; Sheng, Lijuan; Zhang, Xiang

2018-03-01

In this paper we establish bifurcation theory of limit cycles for planar Ck smooth autonomous differential systems, with k ∈ N. The key point is to study the smoothness of bifurcation functions which are basic and important tool on the study of Hopf bifurcation at a fine focus or a center, and of Poincaré bifurcation in a period annulus. We especially study the smoothness of the first order Melnikov function in degenerate Hopf bifurcation at an elementary center. As we know, the smoothness problem was solved for analytic and C∞ differential systems, but it was not tackled for finitely smooth differential systems. Here, we present their optimal regularity of these bifurcation functions and their asymptotic expressions in the finite smooth case.

Bifurcation and Fractal of the Coupled Logistic Map

NASA Astrophysics Data System (ADS)

Wang, Xingyuan; Luo, Chao

The nature of the fixed points of the coupled Logistic map is researched, and the boundary equation of the first bifurcation of the coupled Logistic map in the parameter space is given out. Using the quantitative criterion and rule of system chaos, i.e., phase graph, bifurcation graph, power spectra, the computation of the fractal dimension, and the Lyapunov exponent, the paper reveals the general characteristics of the coupled Logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the coupled Logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) during the process of double-period bifurcation, the system exhibits self-similarity and scale transform invariability in both the parameter space and the phase space. From the research of the attraction basin and Mandelbrot-Julia set of the coupled Logistic map, the following conclusions are indicated: (1) the boundary between periodic and quasiperiodic regions is fractal, and that indicates the impossibility to predict the moving result of the points in the phase plane; (2) the structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.

Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays

PubMed Central

2012-01-01

A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags is mainly studied for its dependency on varying connection strength between populations. Equilibria are identified, and using linear stability analysis, all transitions are determined under which both trivial and non-trivial fixed points lose stability. Periodic solutions arising at some of these bifurcations are numerically studied with a two-parameter bifurcation analysis. PMID:22655859

Basin stability measure of different steady states in coupled oscillators

NASA Astrophysics Data System (ADS)

Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar

2017-04-01

In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis.

Cauda equina syndrome versus saddle embolism.

PubMed

Shaw, A; Anwar, H; Targett, J; Lafferty, K

2008-09-01

We discuss a case of saddle embolism with a clinical presentation similar to cauda equina syndrome in a 79-year-old woman with a history of ischaemic heart disease. Saddle embolus is very rare but one of an array of visceral causes for back and leg pain. This case highlights diagnostic difficulties, particularly in patients with multiple disorders. A high index of suspicion for vascular conditions must be exercised in cases of arterial dysfunction presenting with back pain.

Straight ahead running of a nonlinear car and driver model - new nonlinear behaviours highlighted

NASA Astrophysics Data System (ADS)

Della Rossa, Fabio; Mastinu, Giampiero

2018-05-01

The paper deals with the bifurcation analysis of a validated simple model describing a vehicle+driver running straight ahead. The mechanical model of the car has two degrees of freedom and the related equations of motion contain the nonlinear tyre characteristics. The driver is described by a very simple model. Bifurcation analysis is adopted for characterising straight ahead motion at different speeds for different drivers. A nonlinear sensitivity analysis is performed as a function of the driver's parameters and forward vehicle speed. A wealth of unreferenced bifurcations is discovered both for the understeering (UN) and for the oversteering (OV) vehicle. For the UN vehicle, a supercritical Hopf bifurcation may occur as the forward speed is increased. Also tangent (fold) bifurcations (saddle-node bifurcation of limit cycles) occur as the speed (or disturbance) is further increased. For the OV vehicle, a subcritical Hopf bifurcation occurs as the speed reaches a critical value. The preview distance (a driver's control parameter) plays a fundamental role in straight ahead driving. Either too short or too long preview distances are negative for straight ahead running.

Identifying Septal Support Reconstructions for Saddle Nose Deformity: The Cakmak Algorithm.

PubMed

Cakmak, Ozcan; Emre, Ismet Emrah; Ozkurt, Fazil Emre

2015-01-01

The saddle nose deformity is one of the most challenging problems in nasal surgery with a less predictable and reproducible result than other nasal procedures. The main feature of this deformity is loss of septal support with both functional and aesthetic implications. Most reports on saddle nose have focused on aesthetic improvement and neglected the reestablishment of septal support to improve airway. To explain how the Cakmak algorithm, an algorithm that describes various fixation techniques and grafts in different types of saddle nose deformities, aids in identifying saddle nose reconstructions that restore supportive nasal framework and provide the aesthetic improvements typically associated with procedures to correct saddle nose deformities. This algorithm presents septal support reconstruction of patients with saddle nose deformity based on the experience of the senior author in 206 patients with saddle nose deformity. Preoperative examination, intraoperative assessment, reconstruction techniques, graft materials, and patient evaluation of aesthetic success were documented, and 4 different types of saddle nose deformities were defined. The Cakmak algorithm classifies varying degrees of saddle nose deformity from type 0 to type 4 and helps identify the most appropriate surgical procedure to restore the supportive nasal framework and aesthetic dorsum. Among the 206 patients, 110 women and 96 men, mean (range) age was 39.7 years (15-68 years), and mean (range) of follow-up was 32 months (6-148 months). All but 12 patients had a history of previous nasal surgeries. Application of the Cakmak algorithm resulted in 36 patients categorized with type 0 saddle nose deformities; 79, type 1; 50, type 2; 20, type 3a; 7, type 3b; and 14, type 4. Postoperative photographs showed improvement of deformities, and patient surveys revealed aesthetic improvement in 201 patients and improvement in nasal breathing in 195 patients. Three patients developed postoperative infection

Exploring the Mechanisms of Differentiation, Dedifferentiation, Reprogramming and Transdifferentiation

PubMed Central

Xu, Li; Zhang, Kun; Wang, Jin

2014-01-01

We explored the underlying mechanisms of differentiation, dedifferentiation, reprogramming and transdifferentiation (cell type switchings) from landscape and flux perspectives. Lineage reprogramming is a new regenerative method to convert a matured cell into another cell including direct transdifferentiation without undergoing a pluripotent cell state and indirect transdifferentiation with an initial dedifferentiation-reversion (reprogramming) to a pluripotent cell state. Each cell type is quantified by a distinct valley on the potential landscape with higher probability. We investigated three driving forces for cell fate decision making: stochastic fluctuations, gene regulation and induction, which can lead to cell type switchings. We showed that under the driving forces the direct transdifferentiation process proceeds from a differentiated cell valley to another differentiated cell valley through either a distinct stable intermediate state or a certain series of unstable indeterminate states. The dedifferentiation process proceeds through a pluripotent cell state. Barrier height and the corresponding escape time from the valley on the landscape can be used to quantify the stability and efficiency of cell type switchings. We also uncovered the mechanisms of the underlying processes by quantifying the dominant biological paths of cell type switchings on the potential landscape. The dynamics of cell type switchings are determined by both landscape gradient and flux. The flux can lead to the deviations of the dominant biological paths for cell type switchings from the naively expected landscape gradient path. As a result, the corresponding dominant paths of cell type switchings are irreversible. We also classified the mechanisms of cell fate development from our landscape theory: super-critical pitchfork bifurcation, sub-critical pitchfork bifurcation, sub-critical pitchfork with two saddle-node bifurcation, and saddle-node bifurcation. Our model showed good

Neuronal network model of interictal and recurrent ictal activity

NASA Astrophysics Data System (ADS)

Lopes, M. A.; Lee, K.-E.; Goltsev, A. V.

2017-12-01

We propose a neuronal network model which undergoes a saddle node on an invariant circle bifurcation as the mechanism of the transition from the interictal to the ictal (seizure) state. In the vicinity of this transition, the model captures important dynamical features of both interictal and ictal states. We study the nature of interictal spikes and early warnings of the transition predicted by this model. We further demonstrate that recurrent seizures emerge due to the interaction between two networks.

On the Use of the Main-sequence Knee (Saddle) to Measure Globular Cluster Ages

NASA Astrophysics Data System (ADS)

Saracino, S.; Dalessandro, E.; Ferraro, F. R.; Lanzoni, B.; Origlia, L.; Salaris, M.; Pietrinferni, A.; Geisler, D.; Kalirai, J. S.; Correnti, M.; Cohen, R. E.; Mauro, F.; Villanova, S.; Moni Bidin, C.

2018-06-01

In this paper, we review the operational definition of the so-called main-sequence knee (MS-knee), a feature in the color-magnitude diagram (CMD) occurring at the low-mass end of the MS. The magnitude of this feature is predicted to be independent of age at fixed chemical composition. For this reason, its difference in magnitude with respect to the MS turn-off (MS-TO) point has been suggested as a possible diagnostic to estimate absolute globular cluster (GC) ages. We first demonstrate that the operational definition of the MS-knee currently adopted in the literature refers to the inflection point of the MS (which we here more appropriately named MS-saddle), a feature that is well distinct from the knee and which cannot be used as its proxy. The MS-knee is only visible in near-infrared CMDs, while the MS-saddle can be also detected in optical–NIR CMDs. By using different sets of isochrones, we then demonstrate that the absolute magnitude of the MS-knee varies by a few tenths of a dex from one model to another, thus showing that at the moment stellar models may not capture the full systematic error in the method. We also demonstrate that while the absolute magnitude of the MS-saddle is almost coincident in different models, it has a systematic dependence on the adopted color combinations which is not predicted by stellar models. Hence, it cannot be used as a reliable reference for absolute age determination. Moreover, when statistical and systematic uncertainties are properly taken into account, the difference in magnitude between the MS-TO and the MS-saddle does not provide absolute ages with better accuracy than other methods like the MS-fitting.

MIT-Skywalker: Evaluating comfort of bicycle/saddle seat.

PubMed

Goncalves, Rogerio S; Hamilton, Taya; Daher, Ali R; Hirai, Hiroaki; Krebs, Hermano I

2017-07-01

The MIT-Skywalker is a robotic device developed for the rehabilitation of gait and balance after a neurological injury. This device has been designed based on the concept of a passive walker and provides three distinct training modes: discrete movement, rhythmic movement, and balance training. In this paper, we present our efforts to evaluate the comfort of a bicycle/saddle seat design for the system's novel actuated body weight support device. We employed different bicycle and saddle seats and evaluated comfort using objective and subjective measures. Here we will summarize the results obtained from a study of fifteen healthy subjects and one stroke patient that led to the selection of a saddle seat design for the MIT-Skywalker.

Topology of three-dimensional separated flows

NASA Technical Reports Server (NTRS)

Tobak, M.; Peake, D. J.

1981-01-01

Based on the hypothesis that patterns of skin-friction lines and external streamlines reflect the properties of continuous vector fields, topology rules define a small number of singular points (nodes, saddle points, and foci) that characterize the patterns on the surface and on particular projections of the flow (e.g., the crossflow plane). The restricted number of singular points and the rules that they obey are considered as an organizing principle whose finite number of elements can be combined in various ways to connect together the properties common to all steady three dimensional viscous flows. Introduction of a distinction between local and global properties of the flow resolves an ambiguity in the proper definition of a three dimensional separated flow. Adoption of the notions of topological structure, structural stability, and bifurcation provides a framework to describe how three dimensional separated flows originate and succeed each other as the relevant parameters of the problem are varied.

Homoclinic Bifurcation in an SIQR Model for Childhood Diseases

NASA Astrophysics Data System (ADS)

Wu, Lih-Ing; Feng, Zhilan

2000-11-01

We consider a system of ODEs which describes the transmission dynamics of childhood diseases. A center manifold reduction at a bifurcation point has the normal form x‧=y, y‧=axy+bx2y+O(4), indicating a bifurcation of codimension greater than two. A three-parameter unfolding of the normal form is studied to capture possible complex dynamics of the original system which is subjected to certain constraints on the state space due to biological considerations. It is shown that the perturbed system produces homoclinic bifurcation.

Stochastic bifurcation in a model of love with colored noise

NASA Astrophysics Data System (ADS)

Yue, Xiaokui; Dai, Honghua; Yuan, Jianping

2015-07-01

In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.

Complex behavior in chains of nonlinear oscillators.

PubMed

Alonso, Leandro M

2017-06-01

This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally. The results presented here suggest that in networks composed of many oscillatory units with local interactions, excitability together with balanced interactions is sufficient to give rise to complex emergent features. For values of the parameters where complex behavior occurs, the system also displays a high-dimensional bifurcation where an exponentially large number of equilibria are borne in pairs out of multiple saddle-node bifurcations.

Rotating Saddle Paul Trap.

ERIC Educational Resources Information Center

Rueckner, Wolfgang; And Others

1995-01-01

Describes a demonstration in which a ball is placed in an unstable position on a saddle shape. The ball becomes stable when it is rotated above some threshold angular velocity. The demonstration is a mechanical analog of confining a particle in a "Paul Trap". (DDR)

Do Dogs Know Bifurcations?

ERIC Educational Resources Information Center

Minton, Roland; Pennings, Timothy J.

2007-01-01

When a dog (in this case, Tim Pennings' dog Elvis) is in the water and a ball is thrown downshore, it must choose to swim directly to the ball or first swim to shore. The mathematical analysis of this problem leads to the computation of bifurcation points at which the optimal strategy changes.

Multiple attractors and boundary crises in a tri-trophic food chain.

PubMed

Boer, M P; Kooi, B W; Kooijman, S A

2001-02-01

The asymptotic behaviour of a model of a tri-trophic food chain in the chemostat is analysed in detail. The Monod growth model is used for all trophic levels, yielding a non-linear dynamical system of four ordinary differential equations. Mass conservation makes it possible to reduce the dimension by 1 for the study of the asymptotic dynamic behaviour. The intersections of the orbits with a Poincaré plane, after the transient has died out, yield a two-dimensional Poincaré next-return map. When chaotic behaviour occurs, all image points of this next-return map appear to lie close to a single curve in the intersection plane. This motivated the study of a one-dimensional bi-modal, non-invertible map of which the graph resembles this curve. We will show that the bifurcation structure of the food chain model can be understood in terms of the local and global bifurcations of this one-dimensional map. Homoclinic and heteroclinic connecting orbits and their global bifurcations are discussed also by relating them to their counterparts for a two-dimensional map which is invertible like the next-return map. In the global bifurcations two homoclinic or two heteroclinic orbits collide and disappear. In the food chain model two attractors coexist; a stable limit cycle where the top-predator is absent and an interior attractor. In addition there is a saddle cycle. The stable manifold of this limit cycle forms the basin boundary of the interior attractor. We will show that this boundary has a complicated structure when there are heteroclinic orbits from a saddle equilibrium to this saddle limit cycle. A homoclinic bifurcation to a saddle limit cycle will be associated with a boundary crisis where the chaotic attractor disappears suddenly when a bifurcation parameter is varied. Thus, similar to a tangent local bifurcation for equilibria or limit cycles, this homoclinic global bifurcation marks a region in the parameter space where the top-predator goes extinct. The 'Paradox of

Periodicity and Chaos Amidst Twisting and Folding in Two-Dimensional Maps

NASA Astrophysics Data System (ADS)

Garst, Swier; Sterk, Alef E.

We study the dynamics of three planar, noninvertible maps which rotate and fold the plane. Two maps are inspired by real-world applications whereas the third map is constructed to serve as a toy model for the other two maps. The dynamics of the three maps are remarkably similar. A stable fixed point bifurcates through a Hopf-Neĭmark-Sacker which leads to a countably infinite set of resonance tongues in the parameter plane of the map. Within a resonance tongue a periodic point can bifurcate through a period-doubling cascade. At the end of the cascade we detect Hénon-like attractors which are conjectured to be the closure of the unstable manifold of a saddle periodic point. These attractors have a folded structure which can be explained by means of the concept of critical lines. We also detect snap-back repellers which can either coexist with Hénon-like attractors or which can be formed when the saddle-point of a Hénon-like attractor becomes a source.

Periodic surface structure bifurcation induced by ultrafast laser generated point defect diffusion in GaAs

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

Abere, Michael J.; Yalisove, Steven M.; Torralva, Ben

2016-04-11

The formation of high spatial frequency laser induced periodic surface structures (HSFL) with period <0.3 λ in GaAs after irradiation with femtosecond laser pulses in air is studied. We have identified a point defect generation mechanism that operates in a specific range of fluences in semiconductors between the band-gap closure and ultrafast-melt thresholds that produces vacancy/interstitial pairs. Stress relaxation, via diffusing defects, forms the 350–400 nm tall and ∼90 nm wide structures through a bifurcation process of lower spatial frequency surface structures. The resulting HSFL are predominately epitaxial single crystals and retain the original GaAs stoichiometry.

Motion stability of the magnetic levitation and suspension with YBa2Cu3O7-x high-Tc superconducting bulks and NdFeB magnets

NASA Astrophysics Data System (ADS)

Li, Jipeng; Zheng, Jun; Huang, Huan; Li, Yanxing; Li, Haitao; Deng, Zigang

2017-10-01

The flux pinning effect of YBa2Cu3O7-x high temperature superconducting (HTS) bulk can achieve self-stable levitation over a permanent magnet or magnet array. Devices based on this phenomenon have been widely developed. However, the self-stable flux pinning effect is not unconditional, under disturbances, for example. To disclose the roots of this amazing self-stable levitation phenomenon in theory, mathematical and mechanical calculations using Lyapunov's stability theorem and the Hurwitz criterion were performed under the conditions of magnetic levitation and suspension of HTS bulk near permanent magnets in Halbach array. It is found that the whole dynamical system, in the case of levitation, has only one equilibrium solution, and the singular point is a stable focus. In the general case of suspension, the system has two singular points: one is a stable focus, and the other is an unstable saddle. With the variation of suspension force, the two first-order singular points mentioned earlier will get closer and closer, and finally degenerate to a high-order singular point, which means the stable region gets smaller and smaller, and finally vanishes. According to the center manifold theorem, the high-order singular point is unstable. With the interaction force varying, the HTS suspension dynamical system undergoes a saddle-node bifurcation. Moreover, a deficient damping can also decrease the stable region. These findings, together with existing experiments, could enlighten the improvement of HTS devices with strong anti-interference ability.

Electron bifurcation.

PubMed

Peters, John W; Miller, Anne-Frances; Jones, Anne K; King, Paul W; Adams, Michael Ww

2016-04-01

Electron bifurcation is the recently recognized third mechanism of biological energy conservation. It simultaneously couples exergonic and endergonic oxidation-reduction reactions to circumvent thermodynamic barriers and minimize free energy loss. Little is known about the details of how electron bifurcating enzymes function, but specifics are beginning to emerge for several bifurcating enzymes. To date, those characterized contain a collection of redox cofactors including flavins and iron-sulfur clusters. Here we discuss the current understanding of bifurcating enzymes and the mechanistic features required to reversibly partition multiple electrons from a single redox site into exergonic and endergonic electron transfer paths. Copyright © 2016. Published by Elsevier Ltd.

Bifurcation structures of a cobweb model with memory and competing technologies

NASA Astrophysics Data System (ADS)

Agliari, Anna; Naimzada, Ahmad; Pecora, Nicolò

2018-05-01

In this paper we study a simple model based on the cobweb demand-supply framework with costly innovators and free imitators. The evolutionary selection between technologies depends on a performance measure which is related to the degree of memory. The resulting dynamics is described by a two-dimensional map. The map has a fixed point which may lose stability either via supercritical Neimark-Sacker bifurcation or flip bifurcation and several multistability situations exist. We describe some sequences of global bifurcations involving attracting and repelling closed invariant curves. These bifurcations, characterized by the creation of homoclinic connections or homoclinic tangles, are described through several numerical simulations. Particular bifurcation phenomena are also observed when the parameters are selected inside a periodicity region.

Hydroelastic effects in the aorta bifurcation zone

NASA Technical Reports Server (NTRS)

Volmir, A. S.; Gersheyn, M. S.; Purinya, B. A.

1980-01-01

The mechanical behavior of the vessels and blood is mathematically analyzed at the point of aortic bifurcation using a homogeneous single layer channel as a model of the aorta. Allowance is made for the fact that the aortic intima is considerably less rigid than the other layers. For analysis of blood flow in the major arteries, the blood is treated as a viscous Newtonian fluid whose movements are described by Navier-Stokes equations and a continuity equation. Blood flow dynamics at the aortic bifurcation are discussed on the basis of the results.

Dynamic behavior of the bray-liebhafsky oscillatory reaction controlled by sulfuric acid and temperature

NASA Astrophysics Data System (ADS)

Pejić, N.; Vujković, M.; Maksimović, J.; Ivanović, A.; Anić, S.; Čupić, Ž.; Kolar-Anić, Lj.

2011-12-01

The non-periodic, periodic and chaotic regimes in the Bray-Liebhafsky (BL) oscillatory reaction observed in a continuously fed well stirred tank reactor (CSTR) under isothermal conditions at various inflow concentrations of the sulfuric acid were experimentally studied. In each series (at any fixed temperature), termination of oscillatory behavior via saddle loop infinite period bifurcation (SNIPER) as well as some kind of the Andronov-Hopf bifurcation is presented. In addition, it was found that an increase of temperature, in different series of experiments resulted in the shift of bifurcation point towards higher values of sulfuric acid concentration.

Positive And Negative Feedback Loops Coupled By Common Transcription Activator And Repressor

NASA Astrophysics Data System (ADS)

Sielewiesiuk, Jan; Łopaciuk, Agata

2015-03-01

Dynamical systems consisting of two interlocked loops with negative and positive feedback have been studied using the linear analysis of stability and numerical solutions. Conditions for saddle-node bifurcation were formulated in a general form. Conditions for Hopf bifurcations were found in a few symmetrical cases. Auto-oscillations, when they exist, are generated by the negative feedback repressive loop. This loop determines the frequency and amplitude of oscillations. The positive feedback loop of activation slightly modifies the oscillations. Oscillations are possible when the difference between Hilll's coefficients of the repression and activation is sufficiently high. The highly cooperative activation loop with a fast turnover slows down or even makes the oscillations impossible. The system under consideration can constitute a component of epigenetic or enzymatic regulation network.

Bifurcation to large period oscillations in physical systems controlled by delay

NASA Astrophysics Data System (ADS)

Erneux, Thomas; Walther, Hans-Otto

2005-12-01

An unusual bifurcation to time-periodic oscillations of a class of delay differential equations is investigated. As we approach the bifurcation point, both the amplitude and the frequency of the oscillations go to zero. The class of delay differential equations is a nonlinear extension of a nonevasive control method and is motivated by a recent study of the foreign exchange rate oscillations. By using asymptotic methods, we determine the bifurcation scaling laws for the amplitude and the period of the oscillations.

19 CFR 148.32 - Vehicles, aircraft, boats, teams and saddle horses taken abroad.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 19 Customs Duties 2 2013-04-01 2013-04-01 false Vehicles, aircraft, boats, teams and saddle horses... for Returning Residents § 148.32 Vehicles, aircraft, boats, teams and saddle horses taken abroad. (a) Admission free of duty. Automobiles and other vehicles, aircraft, boats, teams and saddle horses, together...

19 CFR 148.32 - Vehicles, aircraft, boats, teams and saddle horses taken abroad.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 19 Customs Duties 2 2010-04-01 2010-04-01 false Vehicles, aircraft, boats, teams and saddle horses... for Returning Residents § 148.32 Vehicles, aircraft, boats, teams and saddle horses taken abroad. (a) Admission free of duty. Automobiles and other vehicles, aircraft, boats, teams and saddle horses, together...

19 CFR 148.32 - Vehicles, aircraft, boats, teams and saddle horses taken abroad.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 19 Customs Duties 2 2014-04-01 2014-04-01 false Vehicles, aircraft, boats, teams and saddle horses... for Returning Residents § 148.32 Vehicles, aircraft, boats, teams and saddle horses taken abroad. (a) Admission free of duty. Automobiles and other vehicles, aircraft, boats, teams and saddle horses, together...

19 CFR 148.32 - Vehicles, aircraft, boats, teams and saddle horses taken abroad.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 19 Customs Duties 2 2012-04-01 2012-04-01 false Vehicles, aircraft, boats, teams and saddle horses... for Returning Residents § 148.32 Vehicles, aircraft, boats, teams and saddle horses taken abroad. (a) Admission free of duty. Automobiles and other vehicles, aircraft, boats, teams and saddle horses, together...

19 CFR 148.32 - Vehicles, aircraft, boats, teams and saddle horses taken abroad.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 19 Customs Duties 2 2011-04-01 2011-04-01 false Vehicles, aircraft, boats, teams and saddle horses... for Returning Residents § 148.32 Vehicles, aircraft, boats, teams and saddle horses taken abroad. (a) Admission free of duty. Automobiles and other vehicles, aircraft, boats, teams and saddle horses, together...

Zero-point Energy is Needed in Molecular Dynamics Calculations to Access the Saddle Point for H+HCN→H2CN* and cis/trans-HCNH* on a New Potential Energy Surface.

PubMed

Wang, Xiaohong; Bowman, Joel M

2013-02-12

We calculate the probabilities for the association reactions H+HCN→H2CN* and cis/trans-HCNH*, using quasiclassical trajectory (QCT) and classical trajectory (CT) calculations, on a new global ab initio potential energy surface (PES) for H2CN including the reaction channels. The surface is a linear least-squares fit of roughly 60 000 CCSD(T)-F12b/aug-cc-pVDZ electronic energies, using a permutationally invariant basis with Morse-type variables. The reaction probabilities are obtained at a variety of collision energies and impact parameters. Large differences in the threshold energies in the two types of dynamics calculations are traced to the absence of zero-point energy in the CT calculations. We argue that the QCT threshold energy is the realistic one. In addition, trajectories find a direct pathway to trans-HCNH, even though there is no obvious transition state (TS) for this pathway. Instead the saddle point (SP) for the addition to cis-HCNH is evidently also the TS for direct formation of trans-HCNH.

Decoupling flood and interflood deposits for delta island formation and channel bifurcation

NASA Astrophysics Data System (ADS)

Daniller-Varghese, M. S.; Kim, W.

2016-12-01

Channel islands' size and organization dictate delta networks' morphology. To understand their complex network organization, a single channel island node within that network should be investigated first as the fundamental building block. When a sediment-laden flow enters slack water, it loses momentum and carrying capacity, depositing its sediment. As sediment accumulates, flow moves around it and a mouth bar island develops. We present an experimental investigation of island formation and channel bifurcation using the Sediment Transport and Earth-surface Processes (STEP) basin. We made mouth bar deposits and flow bifurcations in transport-limited turbulent conditions. Time-lapse images, elevation scans on the deltaic surface, and a low-cost particle imaging velocimetry system allow us to characterize the flow and depositional evolution of our experimental islands. Using two flow discharges (0.355 l/s, 6 l/s) and uniform sediment, our experiments have two characteristic advection lengths and corresponding deposit types. One, associated with interflood bedload transport, and the other with flood-suspended transport: proximal low-angle deposits and distal steep deposits, respectively. By varying the frequency of floods (one every 20s-20 mins) while keeping sediment and water mass constant across experiments, we are able to control the time and spatial organization of these two deposit types and examine the effect on bifurcation length and bifurcation incidence time. As the interflood flow deposit and flood deposit accumulate sediment over time, the interflood deposit encroaches onto the flood deposit. Flow is routed from the interflood deposit to the flood deposit but does not have the momentum to uniformly cover it. The flow becomes unsteady, and bifurcates around an island. After the bifurcation, the island's vertical aggradation rate also increases. The experiments suggest that the interaction between deposits stemming from different particle advection lengths is

[The mechanical behavior and biocompatibility of different modern ideas of partial fixed free-end saddle dentures].

PubMed

Lubespere, A; Lebig, A; Jourdan, P

1992-01-01

This research is aimed to check the mechanical holding and the biocompatibility at various conceptions of removable partial dentures with free saddles, constituted from satellite alloys. As a matter of fact, the duality of the supporting surface in this kind of dental prosthesis sets biological problems, that one must try to sort out in the best way. It consists of three in vitro experimentations to point out the type or the types of framework answering in the best way to biomechanical and biological requirements. The very same equipment has been used on that three experimentations adapting it to the needs. It's "a machine to overdrive", imagined into the building of "L'Ecole supérieure d'Aéronautique de Toulouse"; this machine is made of an electric engine with an axis of rotation, of two speed reducers giving a motion, of one turn by second, of a knee-joint converting a rotary motion to an alternating motion, of a lever-arm enclosing supporting the weights, of a needle with a foam point which secure the saddles or the strategic zones, of two supporting mandibular and maxillary framework resin patterns, and on the areas representing the osteo-mucosa support capped uniformly with a compressible silicone material of on millimetre thick, of one dynamometer and of an accurate comparator to check the strength used, and the displacement tested zones. The first part consists in testing the amplitude of the saddle displacement and the mobilization of strategic joining areas from various frameworks used. So we can infer the impact on the mucosa during the function. That is why six types of frameworks have been achieved in Wironit satellite alloy showing mechanical qualities admitted to be excellent and to be subject to very accurate experiment conditions with 30 Kz strength (Lundeen and Gibbs, 1982). The results are interpreted through the reading of histograms which X-AXIS represent the points where motions have been located and the Y-AXIS represent the motion at 1

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

NASA Astrophysics Data System (ADS)

Bonciolini, Giacomo; Ebi, Dominik; Boujo, Edouard; Noiray, Nicolas

2018-03-01

Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the effect of the rate of change of the bifurcation parameter on the tipping points. In this work, we consider a subcritical stochastic Hopf bifurcation under two scenarios: the bifurcation parameter is first changed in a quasi-steady manner and then, with a finite ramping rate. In the latter case, a rate-dependent bifurcation delay is observed and exemplified experimentally using a thermoacoustic instability in a combustion chamber. This delay increases with the rate of change. This leads to a state transition of larger amplitude compared with the one that would be experienced by the system with a quasi-steady change of the parameter. We also bring experimental evidence of a dynamic hysteresis caused by the bifurcation delay when the parameter is ramped back. A surrogate model is derived in order to predict the statistic of these delays and to scrutinize the underlying stochastic dynamics. Our study highlights the dramatic influence of a finite rate of change of bifurcation parameters upon tipping points, and it pinpoints the crucial need of considering this effect when investigating critical transitions.

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

PubMed Central

Noiray, Nicolas

2018-01-01

Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the effect of the rate of change of the bifurcation parameter on the tipping points. In this work, we consider a subcritical stochastic Hopf bifurcation under two scenarios: the bifurcation parameter is first changed in a quasi-steady manner and then, with a finite ramping rate. In the latter case, a rate-dependent bifurcation delay is observed and exemplified experimentally using a thermoacoustic instability in a combustion chamber. This delay increases with the rate of change. This leads to a state transition of larger amplitude compared with the one that would be experienced by the system with a quasi-steady change of the parameter. We also bring experimental evidence of a dynamic hysteresis caused by the bifurcation delay when the parameter is ramped back. A surrogate model is derived in order to predict the statistic of these delays and to scrutinize the underlying stochastic dynamics. Our study highlights the dramatic influence of a finite rate of change of bifurcation parameters upon tipping points, and it pinpoints the crucial need of considering this effect when investigating critical transitions. PMID:29657803

Secondary Channel Bifurcation Geometry: A Multi-dimensional Problem

NASA Astrophysics Data System (ADS)

Gaeuman, D.; Stewart, R. L.

2017-12-01

The construction of secondary channels (or side channels) is a popular strategy for increasing aquatic habitat complexity in managed rivers. Such channels, however, frequently experience aggradation that prevents surface water from entering the side channels near their bifurcation points during periods of relatively low discharge. This failure to maintain an uninterrupted surface water connection with the main channel can reduce the habitat value of side channels for fish species that prefer lotic conditions. Various factors have been proposed as potential controls on the fate of side channels, including water surface slope differences between the main and secondary channels, the presence of main channel secondary circulation, transverse bed slopes, and bifurcation angle. A quantitative assessment of more than 50 natural and constructed secondary channels in the Trinity River of northern California indicates that bifurcations can assume a variety of configurations that are formed by different processes and whose longevity is governed by different sets of factors. Moreover, factors such as bifurcation angle and water surface slope vary with discharge level and are continuously distributed in space, such that they must be viewed as a multi-dimensional field rather than a single-valued attribute that can be assigned to a particular bifurcation.

On the structure of cellular solutions in Rayleigh-Benard-Marangoni flows in small-aspect-ratio containers

NASA Technical Reports Server (NTRS)

Dijkstra, Henk A.

1992-01-01

Multiple steady flow patterns occur in surface-tension/buoyancy-driven convection in a liquid layer heated from below (Rayleigh-Benard-Marangoni flows). Techniques of numerical bifurcation theory are used to study the multiplicity and stability of two-dimensional steady flow patterns (rolls) in rectangular small-aspect-ratio containers as the aspect ratio is varied. For pure Marangoni flows at moderate Biot and Prandtl number, the transitions occurring when paths of codimension 1 singularities intersect determine to a large extent the multiplicity of stable patterns. These transitions also lead, for example, to Hopf bifurcations and stable periodic flows for a small range in aspect ratio. The influence of the type of lateral walls on the multiplicity of steady states is considered. 'No-slip' lateral walls lead to hysteresis effects and typically restrict the number of stable flow patterns (with respect to 'slippery' sidewalls) through the occurrence of saddle node bifurcations. In this way 'no-slip' sidewalls induce a selection of certain patterns, which typically have the largest Nusselt number, through secondary bifurcation.

Codimension-Two Bifurcation, Chaos and Control in a Discrete-Time Information Diffusion Model

NASA Astrophysics Data System (ADS)

Ren, Jingli; Yu, Liping

2016-12-01

In this paper, we present a discrete model to illustrate how two pieces of information interact with online social networks and investigate the dynamics of discrete-time information diffusion model in three types: reverse type, intervention type and mutualistic type. It is found that the model has orbits with period 2, 4, 6, 8, 12, 16, 20, 30, quasiperiodic orbit, and undergoes heteroclinic bifurcation near 1:2 point, a homoclinic structure near 1:3 resonance point and an invariant cycle bifurcated by period 4 orbit near 1:4 resonance point. Moreover, in order to regulate information diffusion process and information security, we give two control strategies, the hybrid control method and the feedback controller of polynomial functions, to control chaos, flip bifurcation, 1:2, 1:3 and 1:4 resonances, respectively, in the two-dimensional discrete system.

Featured Partner: Saddle Creek Logistics Services

EPA Pesticide Factsheets

This EPA fact sheet spotlights Saddle Creek Logistics as a SmartWay partner committed to sustainability in reducing greenhouse gas emissions and air pollution caused by freight transportation, partly by growing its compressed natural gas (CNG) vehicles for

Stability diagram for the forced Kuramoto model.

PubMed

Childs, Lauren M; Strogatz, Steven H

2008-12-01

We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an idealization of many phenomena in physics, chemistry, and biology in which mutual synchronization competes with forced synchronization. In other words, the oscillators in the population try to synchronize with one another while also trying to lock onto an external drive. Previous work on the forced Kuramoto model uncovered two main types of attractors, called forced entrainment and mutual entrainment, but the details of the bifurcations between them were unclear. Here we present a complete bifurcation analysis of the model for a special case in which the infinite-dimensional dynamics collapse to a two-dimensional system. Exact results are obtained for the locations of Hopf, saddle-node, and Takens-Bogdanov bifurcations. The resulting stability diagram bears a striking resemblance to that for the weakly nonlinear forced van der Pol oscillator.

Winner-take-all in a phase oscillator system with adaptation.

PubMed

Burylko, Oleksandr; Kazanovich, Yakov; Borisyuk, Roman

2018-01-11

We consider a system of generalized phase oscillators with a central element and radial connections. In contrast to conventional phase oscillators of the Kuramoto type, the dynamic variables in our system include not only the phase of each oscillator but also the natural frequency of the central oscillator, and the connection strengths from the peripheral oscillators to the central oscillator. With appropriate parameter values the system demonstrates winner-take-all behavior in terms of the competition between peripheral oscillators for the synchronization with the central oscillator. Conditions for the winner-take-all regime are derived for stationary and non-stationary types of system dynamics. Bifurcation analysis of the transition from stationary to non-stationary winner-take-all dynamics is presented. A new bifurcation type called a Saddle Node on Invariant Torus (SNIT) bifurcation was observed and is described in detail. Computer simulations of the system allow an optimal choice of parameters for winner-take-all implementation.

Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks.

PubMed

Wang, Zhen; Campbell, Sue Ann

2017-11-01

We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with Z N symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.

Chimera states in multi-strain epidemic models with temporary immunity

NASA Astrophysics Data System (ADS)

Bauer, Larissa; Bassett, Jason; Hövel, Philipp; Kyrychko, Yuliya N.; Blyuss, Konstantin B.

2017-11-01

We investigate a time-delayed epidemic model for multi-strain diseases with temporary immunity. In the absence of cross-immunity between strains, dynamics of each individual strain exhibit emergence and annihilation of limit cycles due to a Hopf bifurcation of the endemic equilibrium, and a saddle-node bifurcation of limit cycles depending on the time delay associated with duration of temporary immunity. Effects of all-to-all and non-local coupling topologies are systematically investigated by means of numerical simulations, and they suggest that cross-immunity is able to induce a diverse range of complex dynamical behaviors and synchronization patterns, including discrete traveling waves, solitary states, and amplitude chimeras. Interestingly, chimera states are observed for narrower cross-immunity kernels, which can have profound implications for understanding the dynamics of multi-strain diseases.

Lassoing saddle splay and the geometrical control of topological defects

PubMed Central

Tran, Lisa; Lavrentovich, Maxim O.; Beller, Daniel A.; Li, Ningwei; Stebe, Kathleen J.; Kamien, Randall D.

2016-01-01

Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4′-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system’s overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability. PMID:27222582

Lassoing saddle splay and the geometrical control of topological defects

NASA Astrophysics Data System (ADS)

Tran, Lisa; Lavrentovich, Maxim O.; Beller, Daniel A.; Li, Ningwei; Stebe, Kathleen J.; Kamien, Randall D.

2016-06-01

Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4'-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system's overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability.

Saddle Slow Manifolds and Canard Orbits in [Formula: see text] and Application to the Full Hodgkin-Huxley Model.

PubMed

Hasan, Cris R; Krauskopf, Bernd; Osinga, Hinke M

2018-04-19

Many physiological phenomena have the property that some variables evolve much faster than others. For example, neuron models typically involve observable differences in time scales. The Hodgkin-Huxley model is well known for explaining the ionic mechanism that generates the action potential in the squid giant axon. Rubin and Wechselberger (Biol. Cybern. 97:5-32, 2007) nondimensionalized this model and obtained a singularly perturbed system with two fast, two slow variables, and an explicit time-scale ratio ε. The dynamics of this system are complex and feature periodic orbits with a series of action potentials separated by small-amplitude oscillations (SAOs); also referred to as mixed-mode oscillations (MMOs). The slow dynamics of this system are organized by two-dimensional locally invariant manifolds called slow manifolds which can be either attracting or of saddle type.In this paper, we introduce a general approach for computing two-dimensional saddle slow manifolds and their stable and unstable fast manifolds. We also develop a technique for detecting and continuing associated canard orbits, which arise from the interaction between attracting and saddle slow manifolds, and provide a mechanism for the organization of SAOs in [Formula: see text]. We first test our approach with an extended four-dimensional normal form of a folded node. Our results demonstrate that our computations give reliable approximations of slow manifolds and canard orbits of this model. Our computational approach is then utilized to investigate the role of saddle slow manifolds and associated canard orbits of the full Hodgkin-Huxley model in organizing MMOs and determining the firing rates of action potentials. For ε sufficiently large, canard orbits are arranged in pairs of twin canard orbits with the same number of SAOs. We illustrate how twin canard orbits partition the attracting slow manifold into a number of ribbons that play the role of sectors of rotations. The upshot is that we

Hidden imperfect synchronization of wall turbulence.

PubMed

Tardu, Sedat F

2010-03-01

Instantaneous amplitude and phase concept emerging from analytical signal formulation is applied to the wavelet coefficients of streamwise velocity fluctuations in the buffer layer of a near wall turbulent flow. Experiments and direct numerical simulations show both the existence of long periods of inert zones wherein the local phase is constant. These regions are separated by random phase jumps. The local amplitude is globally highly intermittent, but not in the phase locked regions wherein it varies smoothly. These behaviors are reminiscent of phase synchronization phenomena observed in stochastic chaotic systems. The lengths of the constant phase inert (laminar) zones reveal a type I intermittency behavior, in concordance with saddle-node bifurcation, and the periodic orbits of saddle nature recently identified in Couette turbulence. The imperfect synchronization is related to the footprint of coherent Reynolds shear stress producing eddies convecting in the low buffer.

Bifurcation behaviors of synchronized regions in logistic map networks with coupling delay

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

Tang, Longkun, E-mail: tomlk@hqu.edu.cn, E-mail: xqwu@whu.edu.cn; Wu, Xiaoqun, E-mail: tomlk@hqu.edu.cn, E-mail: xqwu@whu.edu.cn; Lu, Jun-an, E-mail: jalu@whu.edu.cn

2015-03-15

Network synchronized regions play an extremely important role in network synchronization according to the master stability function framework. This paper focuses on network synchronous state stability via studying the effects of nodal dynamics, coupling delay, and coupling way on synchronized regions in Logistic map networks. Theoretical and numerical investigations show that (1) network synchronization is closely associated with its nodal dynamics. Particularly, the synchronized region bifurcation points through which the synchronized region switches from one type to another are in good agreement with those of the uncoupled node system, and chaotic nodal dynamics can greatly impede network synchronization. (2) Themore » coupling delay generally impairs the synchronizability of Logistic map networks, which is also dominated by the parity of delay for some nodal parameters. (3) A simple nonlinear coupling facilitates network synchronization more than the linear one does. The results found in this paper will help to intensify our understanding for the synchronous state stability in discrete-time networks with coupling delay.« less

Bifurcations and stability of standing waves in the nonlinear Schrödinger equation on the tadpole graph

NASA Astrophysics Data System (ADS)

Noja, Diego; Pelinovsky, Dmitry; Shaikhova, Gaukhar

2015-07-01

We develop a detailed analysis of edge bifurcations of standing waves in the nonlinear Schrödinger (NLS) equation on a tadpole graph (a ring attached to a semi-infinite line subject to the Kirchhoff boundary conditions at the junction). It is shown in the recent work [7] by using explicit Jacobi elliptic functions that the cubic NLS equation on a tadpole graph admits a rich structure of standing waves. Among these, there are different branches of localized waves bifurcating from the edge of the essential spectrum of an associated Schrödinger operator. We show by using a modified Lyapunov-Schmidt reduction method that the bifurcation of localized standing waves occurs for every positive power nonlinearity. We distinguish a primary branch of never vanishing standing waves bifurcating from the trivial solution and an infinite sequence of higher branches with oscillating behavior in the ring. The higher branches bifurcate from the branches of degenerate standing waves with vanishing tail outside the ring. Moreover, we analyze stability of bifurcating standing waves. Namely, we show that the primary branch is composed by orbitally stable standing waves for subcritical power nonlinearities, while all nontrivial higher branches are linearly unstable near the bifurcation point. The stability character of the degenerate branches remains inconclusive at the analytical level, whereas heuristic arguments based on analysis of embedded eigenvalues of negative Krein signatures support the conjecture of their linear instability at least near the bifurcation point. Numerical results for the cubic NLS equation show that this conjecture is valid and that the degenerate branches become spectrally stable far away from the bifurcation point.

Basic kinematics of the saddle and rider in high-level dressage horses trotting on a treadmill.

PubMed

Byström, A; Rhodin, M; von Peinen, K; Weishaupt, M A; Roepstorff, L

2009-03-01

A comprehensive kinematic description of rider and saddle movements is not yet present in the scientific literature. To describe saddle and rider movements in a group of high-level dressage horses and riders. Seven high-level dressage horses and riders were subjected to kinematic measurements while performing collected trot on a treadmill. For analysis a rigid body model for the saddle and core rider segments, projection angles of the rider's extremities and the neck and trunk of the horse, and distances between markers selected to indicate rider position were used. For a majority of the variables measured it was possible to describe a common pattern for the group. Rotations around the transverse axis (pitch) were generally biphasic for each diagonal. During the first half of stance the saddle rotated anti-clockwise and the rider's pelvis clockwise viewed from the right and the rider's lumbar back extended. During the later part of stance and the suspension phase reverse pitch rotations were observed. Rotations of the saddle and core rider segments around the longitudinal (roll) and vertical axes (yaw) changed direction only around time of contact of each diagonal. The saddles and riders of high-level dressage horses follow a common movement pattern at collected trot. The movements of the saddle and rider are clearly related to the movements of the horse and saddle movements also seem to be influenced by the rider. Knowledge about rider and saddle movements can further our understanding of, and hence possibilities to prevent, orthopaedic injuries related to the exposure of the horse to a rider and saddle.

Multistability in Chua's circuit with two stable node-foci

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

Bao, B. C.; Wang, N.; Xu, Q.

2016-04-15

Only using one-stage op-amp based negative impedance converter realization, a simplified Chua's diode with positive outer segment slope is introduced, based on which an improved Chua's circuit realization with more simpler circuit structure is designed. The improved Chua's circuit has identical mathematical model but completely different nonlinearity to the classical Chua's circuit, from which multiple attractors including coexisting point attractors, limit cycle, double-scroll chaotic attractor, or coexisting chaotic spiral attractors are numerically simulated and experimentally captured. Furthermore, with dimensionless Chua's equations, the dynamical properties of the Chua's system are studied including equilibrium and stability, phase portrait, bifurcation diagram, Lyapunov exponentmore » spectrum, and attraction basin. The results indicate that the system has two symmetric stable nonzero node-foci in global adjusting parameter regions and exhibits the unusual and striking dynamical behavior of multiple attractors with multistability.« less

Three-dimensional separation and reattachment

NASA Technical Reports Server (NTRS)

Peake, D. J.; Tobak, M.

1982-01-01

The separation of three dimensional turbulent boundary layers from the lee of flight vehicles at high angles of attack is investigated. The separation results in dominant, large scale, coiled vortex motions that pass along the body in the general direction of the free stream. In all cases of three dimensional flow separation and reattachment, the assumption of continuous vector fields of skin friction lines and external flow streamlines, coupled with simple laws of topology, provides a flow grammar whose elemental constituents are the singular points: the nodes, spiral nodes (foci), and saddles. The phenomenon of three dimensional separation may be construed as either a local or a global event, depending on whether the skin friction line that becomes a line of separation originates at a node or a saddle point.

Reverse bifurcation and fractal of the compound logistic map

NASA Astrophysics Data System (ADS)

Wang, Xingyuan; Liang, Qingyong

2008-07-01

The nature of the fixed points of the compound logistic map is researched and the boundary equation of the first bifurcation of the map in the parameter space is given out. Using the quantitative criterion and rule of chaotic system, the paper reveal the general features of the compound logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the map may emerge out of double-periodic bifurcation and (2) the chaotic crisis phenomena and the reverse bifurcation are found. At the same time, we analyze the orbit of critical point of the compound logistic map and put forward the definition of Mandelbrot-Julia set of compound logistic map. We generalize the Welstead and Cromer's periodic scanning technology and using this technology construct a series of Mandelbrot-Julia sets of compound logistic map. We investigate the symmetry of Mandelbrot-Julia set and study the topological inflexibility of distributing of period region in the Mandelbrot set, and finds that Mandelbrot set contain abundant information of structure of Julia sets by founding the whole portray of Julia sets based on Mandelbrot set qualitatively.

Hybrid control of the Neimark-Sacker bifurcation in a delayed Nicholson's blowflies equation.

PubMed

Wang, Yuanyuan; Wang, Lisha

In this article, for delayed Nicholson's blowflies equation, we propose a hybrid control nonstandard finite-difference (NSFD) scheme in which state feedback and parameter perturbation are used to control the Neimark-Sacker bifurcation. Firstly, the local stability of the positive equilibria for hybrid control delay differential equation is discussed according to Hopf bifurcation theory. Then, for any step-size, a hybrid control numerical algorithm is introduced to generate the Neimark-Sacker bifurcation at a desired point. Finally, numerical simulation results confirm that the control strategy is efficient in controlling the Neimark-Sacker bifurcation. At the same time, the results show that the NSFD control scheme is better than the Euler control method.

Non-smooth Hopf-type bifurcations arising from impact–friction contact events in rotating machinery

PubMed Central

Mora, Karin; Budd, Chris; Glendinning, Paul; Keogh, Patrick

2014-01-01

We analyse the novel dynamics arising in a nonlinear rotor dynamic system by investigating the discontinuity-induced bifurcations corresponding to collisions with the rotor housing (touchdown bearing surface interactions). The simplified Föppl/Jeffcott rotor with clearance and mass unbalance is modelled by a two degree of freedom impact–friction oscillator, as appropriate for a rigid rotor levitated by magnetic bearings. Two types of motion observed in experiments are of interest in this paper: no contact and repeated instantaneous contact. We study how these are affected by damping and stiffness present in the system using analytical and numerical piecewise-smooth dynamical systems methods. By studying the impact map, we show that these types of motion arise at a novel non-smooth Hopf-type bifurcation from a boundary equilibrium bifurcation point for certain parameter values. A local analysis of this bifurcation point allows us a complete understanding of this behaviour in a general setting. The analysis identifies criteria for the existence of such smooth and non-smooth bifurcations, which is an essential step towards achieving reliable and robust controllers that can take compensating action. PMID:25383034

A bifurcation study to guide the design of a landing gear with a combined uplock/downlock mechanism.

PubMed

Knowles, James A C; Lowenberg, Mark H; Neild, Simon A; Krauskopf, Bernd

2014-12-08

This paper discusses the insights that a bifurcation analysis can provide when designing mechanisms. A model, in the form of a set of coupled steady-state equations, can be derived to describe the mechanism. Solutions to this model can be traced through the mechanism's state versus parameter space via numerical continuation, under the simultaneous variation of one or more parameters. With this approach, crucial features in the response surface, such as bifurcation points, can be identified. By numerically continuing these points in the appropriate parameter space, the resulting bifurcation diagram can be used to guide parameter selection and optimization. In this paper, we demonstrate the potential of this technique by considering an aircraft nose landing gear, with a novel locking strategy that uses a combined uplock/downlock mechanism. The landing gear is locked when in the retracted or deployed states. Transitions between these locked states and the unlocked state (where the landing gear is a mechanism) are shown to depend upon the positions of two fold point bifurcations. By performing a two-parameter continuation, the critical points are traced to identify operational boundaries. Following the variation of the fold points through parameter space, a minimum spring stiffness is identified that enables the landing gear to be locked in the retracted state. The bifurcation analysis also shows that the unlocking of a retracted landing gear should use an unlock force measure, rather than a position indicator, to de-couple the effects of the retraction and locking actuators. Overall, the study demonstrates that bifurcation analysis can enhance the understanding of the influence of design choices over a wide operating range where nonlinearity is significant.

A bifurcation study to guide the design of a landing gear with a combined uplock/downlock mechanism

PubMed Central

Knowles, James A. C.; Lowenberg, Mark H.; Neild, Simon A.; Krauskopf, Bernd

2014-01-01

This paper discusses the insights that a bifurcation analysis can provide when designing mechanisms. A model, in the form of a set of coupled steady-state equations, can be derived to describe the mechanism. Solutions to this model can be traced through the mechanism's state versus parameter space via numerical continuation, under the simultaneous variation of one or more parameters. With this approach, crucial features in the response surface, such as bifurcation points, can be identified. By numerically continuing these points in the appropriate parameter space, the resulting bifurcation diagram can be used to guide parameter selection and optimization. In this paper, we demonstrate the potential of this technique by considering an aircraft nose landing gear, with a novel locking strategy that uses a combined uplock/downlock mechanism. The landing gear is locked when in the retracted or deployed states. Transitions between these locked states and the unlocked state (where the landing gear is a mechanism) are shown to depend upon the positions of two fold point bifurcations. By performing a two-parameter continuation, the critical points are traced to identify operational boundaries. Following the variation of the fold points through parameter space, a minimum spring stiffness is identified that enables the landing gear to be locked in the retracted state. The bifurcation analysis also shows that the unlocking of a retracted landing gear should use an unlock force measure, rather than a position indicator, to de-couple the effects of the retraction and locking actuators. Overall, the study demonstrates that bifurcation analysis can enhance the understanding of the influence of design choices over a wide operating range where nonlinearity is significant. PMID:25484601

Stability of Bifurcating Stationary Solutions of the Artificial Compressible System

NASA Astrophysics Data System (ADS)

Teramoto, Yuka

2018-02-01

The artificial compressible system gives a compressible approximation of the incompressible Navier-Stokes system. The latter system is obtained from the former one in the zero limit of the artificial Mach number ɛ which is a singular limit. The sets of stationary solutions of both systems coincide with each other. It is known that if a stationary solution of the incompressible system is asymptotically stable and the velocity field of the stationary solution satisfies an energy-type stability criterion, then it is also stable as a solution of the artificial compressible one for sufficiently small ɛ . In general, the range of ɛ shrinks when the spectrum of the linearized operator for the incompressible system approaches to the imaginary axis. This can happen when a stationary bifurcation occurs. It is proved that when a stationary bifurcation from a simple eigenvalue occurs, the range of ɛ can be taken uniformly near the bifurcation point to conclude the stability of the bifurcating solution as a solution of the artificial compressible system.

Stability and Hopf bifurcation in a simplified BAM neural network with two time delays.

PubMed

Cao, Jinde; Xiao, Min

2007-03-01

Various local periodic solutions may represent different classes of storage patterns or memory patterns, and arise from the different equilibrium points of neural networks (NNs) by applying Hopf bifurcation technique. In this paper, a bidirectional associative memory NN with four neurons and multiple delays is considered. By applying the normal form theory and the center manifold theorem, analysis of its linear stability and Hopf bifurcation is performed. An algorithm is worked out for determining the direction and stability of the bifurcated periodic solutions. Numerical simulation results supporting the theoretical analysis are also given.

Dark-bright soliton pairs: Bifurcations and collisions

NASA Astrophysics Data System (ADS)

Katsimiga, G. C.; Kevrekidis, P. G.; Prinari, B.; Biondini, G.; Schmelcher, P.

2018-04-01

The statics, stability, and dynamical properties of dark-bright soliton pairs are investigated here, motivated by applications in a homogeneous two-component repulsively interacting Bose-Einstein condensate. One of the intraspecies interaction coefficients is used as the relevant parameter controlling the deviation from the integrable Manakov limit. Two different families of stationary states are identified consisting of dark-bright solitons that are either antisymmetric (out-of-phase) or asymmetric (mass imbalanced) with respect to their bright soliton. Both of the above dark-bright configurations coexist at the integrable limit of equal intra and interspecies repulsions and are degenerate in that limit. However, they are found to bifurcate from it in a transcritical bifurcation. This bifurcation interchanges the stability properties of the bound dark-bright pairs rendering the antisymmetric states unstable and the asymmetric ones stable past the associated critical point (and vice versa before it). Finally, on the dynamical side, it is found that large kinetic energies and thus rapid soliton collisions are essentially unaffected by the intraspecies variation, while cases involving near equilibrium states or breathing dynamics are significantly modified under such a variation.

Loss surface of XOR artificial neural networks

NASA Astrophysics Data System (ADS)

Mehta, Dhagash; Zhao, Xiaojun; Bernal, Edgar A.; Wales, David J.

2018-05-01

Training an artificial neural network involves an optimization process over the landscape defined by the cost (loss) as a function of the network parameters. We explore these landscapes using optimization tools developed for potential energy landscapes in molecular science. The number of local minima and transition states (saddle points of index one), as well as the ratio of transition states to minima, grow rapidly with the number of nodes in the network. There is also a strong dependence on the regularization parameter, with the landscape becoming more convex (fewer minima) as the regularization term increases. We demonstrate that in our formulation, stationary points for networks with Nh hidden nodes, including the minimal network required to fit the XOR data, are also stationary points for networks with Nh+1 hidden nodes when all the weights involving the additional node are zero. Hence, smaller networks trained on XOR data are embedded in the landscapes of larger networks. Our results clarify certain aspects of the classification and sensitivity (to perturbations in the input data) of minima and saddle points for this system, and may provide insight into dropout and network compression.

Saddle-shaped mitral valve annuloplasty rings experience lower forces compared with flat rings.

PubMed

Jensen, Morten O; Jensen, Henrik; Smerup, Morten; Levine, Robert A; Yoganathan, Ajit P; Nygaard, Hans; Hasenkam, J Michael; Nielsen, Sten L

2008-09-30

New insight into the 3D dynamic behavior of the mitral valve has prompted a reevaluation of annuloplasty ring designs. Force balance analysis indicates correlation between annulus forces and stresses in leaflets and chords. Improving this stress distribution can intuitively enhance the durability of mitral valve repair. We tested the hypothesis that saddle-shaped annuloplasty rings have superior uniform systolic force distribution compared with a nonuniform force distribution in flat annuloplasty rings. Sixteen 80-kg pigs had a flat (n=8) or saddle-shaped (n=8) mitral annuloplasty ring implanted. Mitral annulus 3D dynamic geometry was obtained with sonomicrometry before ring insertion. Strain gauges mounted on dedicated D-shaped rigid flat and saddle-shaped annuloplasty rings provided the intraoperative force distribution perpendicular to the annular plane. Average systolic annular height to commissural width ratio before ring implantation was 14.0%+/-1.6%. After flat and saddle shaped ring implantation, the annulus was fixed in the diastolic (9.0%+/-1.0%) and systolic (14.3%+/-1.3%) configuration, respectively (P<0.01). Force accumulation was seen from the anterior (0.72N+/-0.14N) and commissural annular segments (average 1.38N+/-0.27N) of the flat rings. In these segments, the difference between the 2 types of rings was statistically significant (P<0.05). The saddle-shaped annuloplasty rings did not experience forces statistically significantly larger than zero in any annular segments. Saddle-shaped annuloplasty rings provide superior uniform annular force distribution compared to flat rings and appear to represent a configuration that minimizes out-of-plane forces that could potentially be transmitted to leaflets and chords. This may have important implications for annuloplasty ring selections.

A reduction of the saddle vertical force triggers the sit-stand transition in cycling.

PubMed

Costes, Antony; Turpin, Nicolas A; Villeger, David; Moretto, Pierre; Watier, Bruno

2015-09-18

The purpose of the study was to establish the link between the saddle vertical force and its determinants in order to establish the strategies that could trigger the sit-stand transition. We hypothesized that the minimum saddle vertical force would be a critical parameter influencing the sit-stand transition during cycling. Twenty-five non-cyclists were asked to pedal at six different power outputs from 20% (1.6 ± 0.3 W kg(-1)) to 120% (9.6 ± 1.6 W kg(-1)) of their spontaneous sit-stand transition power obtained at 90 rpm. Five 6-component sensors (saddle tube, pedals and handlebars) and a full-body kinematic reconstruction were used to provide the saddle vertical force and other force components (trunk inertial force, hips and shoulders reaction forces, and trunk weight) linked to the saddle vertical force. Minimum saddle vertical force linearly decreased with power output by 87% from a static position on the bicycle (5.30 ± 0.50 N kg(-1)) to power output=120% of the sit-stand transition power (0.68 ± 0.49 N kg(-1)). This decrease was mainly explained by the increase in instantaneous pedal forces from 2.84 ± 0.58 N kg(-1) to 6.57 ± 1.02 N kg(-1) from 20% to 120% of the power output corresponding to the sit-stand transition, causing an increase in hip vertical forces from -0.17 N kg(-1) to 3.29 N kg(-1). The emergence of strategies aiming at counteracting the elevation of the trunk (handlebars and pedals pulling) coincided with the spontaneous sit-stand transition power. The present data suggest that the large decrease in minimum saddle vertical force observed at high pedal reaction forces might trigger the sit-stand transition in cycling. Copyright © 2015 Elsevier Ltd. All rights reserved.

Bifurcation analysis of eight coupled degenerate optical parametric oscillators

NASA Astrophysics Data System (ADS)

Ito, Daisuke; Ueta, Tetsushi; Aihara, Kazuyuki

2018-06-01

A degenerate optical parametric oscillator (DOPO) network realized as a coherent Ising machine can be used to solve combinatorial optimization problems. Both theoretical and experimental investigations into the performance of DOPO networks have been presented previously. However a problem remains, namely that the dynamics of the DOPO network itself can lower the search success rates of globally optimal solutions for Ising problems. This paper shows that the problem is caused by pitchfork bifurcations due to the symmetry structure of coupled DOPOs. Some two-parameter bifurcation diagrams of equilibrium points express the performance deterioration. It is shown that the emergence of non-ground states regarding local minima hampers the system from reaching the ground states corresponding to the global minimum. We then describe a parametric strategy for leading a system to the ground state by actively utilizing the bifurcation phenomena. By adjusting the parameters to break particular symmetry, we find appropriate parameter sets that allow the coherent Ising machine to obtain the globally optimal solution alone.

Controlling the onset of Hopf bifurcation in the Hodgkin-Huxley model

NASA Astrophysics Data System (ADS)

Xie, Yong; Chen, Luonan; Kang, Yan Mei; Aihara, Kazuyuki

2008-06-01

It is a challenging problem to establish safe and simple therapeutic methods for various complicated diseases of the nervous system, particularly dynamical diseases such as epilepsy, Alzheimer’s disease, and Parkinson’s disease. From the viewpoint of nonlinear dynamical systems, a dynamical disease can be considered to be caused by a bifurcation induced by a change in the values of one or more regulating parameter. Therefore, the theory of bifurcation control may have potential applications in the diagnosis and therapy of dynamical diseases. In this study, we employ a washout filter-aided dynamic feedback controller to control the onset of Hopf bifurcation in the Hodgkin-Huxley (HH) model. Specifically, by the control scheme, we can move the Hopf bifurcation to a desired point irrespective of whether the corresponding steady state is stable or unstable. In other words, we are able to advance or delay the Hopf bifurcation, so as to prevent it from occurring in a certain range of the externally applied current. Moreover, we can control the criticality of the bifurcation and regulate the oscillation amplitude of the bifurcated limit cycle. In the controller, there are only two terms: the linear term and the nonlinear cubic term. We show that while the former determines the location of the Hopf bifurcation, the latter regulates the criticality of the Hopf bifurcation. According to the conditions of the occurrence of Hopf bifurcation and the bifurcation stability coefficient, we can analytically deduce the linear term and the nonlinear cubic term, respectively. In addition, we also show that mixed-mode oscillations (MMOs), featuring slow action potential generation, which are frequently observed in both experiments and models of chemical and biological systems, appear in the controlled HH model. It is well known that slow firing rates in single neuron models could be achieved only by type-I neurons. However, the controlled HH model is still classified as a type

Bifurcation theory applied to aircraft motions

NASA Technical Reports Server (NTRS)

Hui, W. H.; Tobak, M.

1985-01-01

Bifurcation theory is used to analyze the nonlinear dynamic stability characteristics of single-degree-of-freedom motions of an aircraft or a flap about a trim position. The bifurcation theory analysis reveals that when the bifurcation parameter, e.g., the angle of attack, is increased beyond a critical value at which the aerodynamic damping vanishes, a new solution representing finite-amplitude periodic motion bifurcates from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solution is stable (supercritical) or unstable (subcritical). For the pitching motion of a flap-plate airfoil flying at supersonic/hypersonic speed, and for oscillation of a flap at transonic speed, the bifurcation is subcritical, implying either that exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop. On the other hand, for the rolling oscillation of a slender delta wing in subsonic flight (wing rock), the bifurcation is found to be supercritical. This and the predicted amplitude of the bifurcation periodic motion are in good agreement with experiments.

Bifurcation theory applied to aircraft motions

NASA Technical Reports Server (NTRS)

Hui, W. H.; Tobak, M.

1985-01-01

The bifurcation theory is used to analyze the nonlinear dynamic stability characteristics of single-degree-of-freedom motions of an aircraft or a flap about a trim position. The bifurcation theory analysis reveals that when the bifurcation parameter, e.g., the angle of attack, is increased beyond a critical value at which the aerodynamic damping vanishes, a new solution representing finite-amplitude periodic motion bifurcates from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solution is stable (supercritical) or unstable (critical). For the pitching motion of a flap-plate airfoil flying at supersonic/hypersonic speed, and for oscillation of a flap at transonic speed, the bifurcation is subcritical, implying either that exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop. On the other hand, for the rolling oscillation of a slender delta wing in subsonic flight (wing rock), the bifurcation is found to be supercritical. This and the predicted amplitude of the bifurcation periodic motion are in good agreement with the experiments.

Exact BPF and FBP algorithms for nonstandard saddle curves.

PubMed

Yu, Hengyong; Zhao, Shiying; Ye, Yangbo; Wang, Ge

2005-11-01

A hot topic in cone-beam CT research is exact cone-beam reconstruction from a general scanning trajectory. Particularly, a nonstandard saddle curve attracts attention, as this construct allows the continuous periodic scanning of a volume-of-interest (VOI). Here we evaluate two algorithms for reconstruction from data collected along a nonstandard saddle curve, which are in the filtered backprojection (FBP) and backprojection filtration (BPF) formats, respectively. Both the algorithms are implemented in a chord-based coordinate system. Then, a rebinning procedure is utilized to transform the reconstructed results into the natural coordinate system. The simulation results demonstrate that the FBP algorithm produces better image quality than the BPF algorithm, while both the algorithms exhibit similar noise characteristics.

Allee’s dynamics and bifurcation structures in von Bertalanffy’s population size functions

NASA Astrophysics Data System (ADS)

Leonel Rocha, J.; Taha, Abdel-Kaddous; Fournier-Prunaret, D.

2018-03-01

The interest and the relevance of the study of the population dynamics and the extinction phenomenon are our main motivation to investigate the induction of Allee Effect in von Bertalanffy’s population size functions. The adjustment or correction factor of rational type introduced allows us to analyze simultaneously strong and weak Allee’s functions and functions with no Allee effect, whose classification is dependent on the stability of the fixed point x = 0. This classification is founded on the concepts of strong and weak Allee’s effects to the population growth rates associated. The transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is verified with the evolution of the rarefaction critical density or Allee’s limit. The existence of cusp points on a fold bifurcation curve is related to this phenomenon of transition on Allee’s dynamics. Moreover, the “foliated” structure of the parameter plane considered is also explained, with respect to the evolution of the Allee limit. The bifurcation analysis is based on the configurations of fold and flip bifurcation curves. The chaotic semistability and the nonadmissibility bifurcation curves are proposed to this family of 1D maps, which allow us to define and characterize the corresponding Allee effect region.

Possibility of Atherosclerosis in an Arterial Bifurcation Model

PubMed Central

Arjmandi-Tash, Omid; Razavi, Seyed Esmail; Zanbouri, Ramin

2011-01-01

Introduction Arterial bifurcations are susceptible locations for formation of atherosclerotic plaques. In the present study, steady blood flow is investigated in a bifurcation model with a non-planar branch. Methods The influence of different bifurcation angles and non-planar branch is demonstrated on wall shear stress (WSS) distribution using three-dimensional Navier–Stokes equations. Results The WSS values are low in two locations at the top and bottom walls of the mother vessels just before the bifurcation, especially for higher bifurcation angles. These regions approach the apex of bifurcation with decreasing the bifurcation angle. The WSS magnitudes approach near to zero at the outer side of bifurcation plane and these locations are separation-prone. By increasing the bifurcation angle, the minimum WSS decreases at the outer side of bifurcation plane but low WSS region squeezes. WSS peaks exist on the inner side of bifurcation plane near the entry section of daughter vessels and these initial peaks drop as bifurcation angle is increased. Conclusion It is concluded that the non-planarity of the daughter vessel lowers the minimum WSS at the outer side of bifurcation and increases the maximum WSS at the inner side. So it seems that the formation of atherosclerotic plaques at bifurcation region in direction of non-planar daughter vessel is more risky. PMID:23678432

A Dynamical Threshold for Cardiac Delayed Afterdepolarization-Mediated Triggered Activity.

PubMed

Liu, Michael B; Ko, Christopher Y; Song, Zhen; Garfinkel, Alan; Weiss, James N; Qu, Zhilin

2016-12-06

Ventricular myocytes are excitable cells whose voltage threshold for action potential (AP) excitation is ∼-60 mV at which I Na is activated to give rise to a fast upstroke. Therefore, for a short stimulus pulse to elicit an AP, a stronger stimulus is needed if the resting potential lies further away from the I Na threshold, such as in hypokalemia. However, for an AP elicited by a long duration stimulus or a diastolic spontaneous calcium release, we observed that the stimulus needed was lower in hypokalemia than in normokalemia in both computer simulations and experiments of rabbit ventricular myocytes. This observation provides insight into why hypokalemia promotes calcium-mediated triggered activity, despite the resting potential lying further away from the I Na threshold. To understand the underlying mechanisms, we performed bifurcation analyses and demonstrated that there is a dynamical threshold, resulting from a saddle-node bifurcation mainly determined by I K1 and I NCX . This threshold is close to the voltage at which I K1 is maximum, and lower than the I Na threshold. After exceeding this dynamical threshold, the membrane voltage will automatically depolarize above the I Na threshold due to the large negative slope of the I K1 -V curve. This dynamical threshold becomes much lower in hypokalemia, especially with respect to calcium, as predicted by our theory. Because of the saddle-node bifurcation, the system can automatically depolarize even in the absence of I Na to voltages higher than the I Ca,L threshold, allowing for triggered APs in single myocytes with complete I Na block. However, because I Na is important for AP propagation in tissue, blocking I Na can still suppress premature ventricular excitations in cardiac tissue caused by calcium-mediated triggered activity. This suppression is more effective in normokalemia than in hypokalemia due to the difference in dynamical thresholds. Copyright © 2016 Biophysical Society. Published by Elsevier Inc

Which System Variables Carry Robust Early Signs of Upcoming Phase Transition? An Ecological Example.

PubMed

Negahbani, Ehsan; Steyn-Ross, D Alistair; Steyn-Ross, Moira L; Aguirre, Luis A

2016-01-01

Growth of critical fluctuations prior to catastrophic state transition is generally regarded as a universal phenomenon, providing a valuable early warning signal in dynamical systems. Using an ecological fisheries model of three populations (juvenile prey J, adult prey A and predator P), a recent study has reported silent early warning signals obtained from P and A populations prior to saddle-node (SN) bifurcation, and thus concluded that early warning signals are not universal. By performing a full eigenvalue analysis of the same system we demonstrate that while J and P populations undergo SN bifurcation, A does not jump to a new state, so it is not expected to carry early warning signs. In contrast with the previous study, we capture a significant increase in the noise-induced fluctuations in the P population, but only on close approach to the bifurcation point; it is not clear why the P variance initially shows a decaying trend. Here we resolve this puzzle using observability measures from control theory. By computing the observability coefficient for the system from the recordings of each population considered one at a time, we are able to quantify their ability to describe changing internal dynamics. We demonstrate that precursor fluctuations are best observed using only the J variable, and also P variable if close to transition. Using observability analysis we are able to describe why a poorly observable variable (P) has poor forecasting capabilities although a full eigenvalue analysis shows that this variable undergoes a bifurcation. We conclude that observability analysis provides complementary information to identify the variables carrying early-warning signs about impending state transition.

Exact BPF and FBP algorithms for nonstandard saddle curves

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

Yu Hengyong; Zhao Shiying; Ye Yangbo

2005-11-15

A hot topic in cone-beam CT research is exact cone-beam reconstruction from a general scanning trajectory. Particularly, a nonstandard saddle curve attracts attention, as this construct allows the continuous periodic scanning of a volume-of-interest (VOI). Here we evaluate two algorithms for reconstruction from data collected along a nonstandard saddle curve, which are in the filtered backprojection (FBP) and backprojection filtration (BPF) formats, respectively. Both the algorithms are implemented in a chord-based coordinate system. Then, a rebinning procedure is utilized to transform the reconstructed results into the natural coordinate system. The simulation results demonstrate that the FBP algorithm produces better imagemore » quality than the BPF algorithm, while both the algorithms exhibit similar noise characteristics.« less

Energized Oxygen : Speiser Current Sheet Bifurcation

NASA Astrophysics Data System (ADS)

George, D. E.; Jahn, J. M.

2017-12-01

A single population of energized Oxygen (O+) is shown to produce a cross-tail bifurcated current sheet in 2.5D PIC simulations of the magnetotail without the influence of magnetic reconnection. Treatment of oxygen in simulations of space plasmas, specifically a magnetotail current sheet, has been limited to thermal energies despite observations of and mechanisms which explain energized ions. We performed simulations of a homogeneous oxygen background, that has been energized in a physically appropriate manner, to study the behavior of current sheets and magnetic reconnection, specifically their bifurcation. This work uses a 2.5D explicit Particle-In-a-Cell (PIC) code to investigate the dynamics of energized heavy ions as they stream Dawn-to-Dusk in the magnetotail current sheet. We present a simulation study dealing with the response of a current sheet system to energized oxygen ions. We establish a, well known and studied, 2-species GEM Challenge Harris current sheet as a starting point. This system is known to eventually evolve and produce magnetic reconnection upon thinning of the current sheet. We added a uniform distribution of thermal O+ to the background. This 3-species system is also known to eventually evolve and produce magnetic reconnection. We add one additional variable to the system by providing an initial duskward velocity to energize the O+. We also traced individual particle motion within the PIC simulation. Three main results are shown. First, energized dawn- dusk streaming ions are clearly seen to exhibit sustained Speiser motion. Second, a single population of heavy ions clearly produces a stable bifurcated current sheet. Third, magnetic reconnection is not required to produce the bifurcated current sheet. Finally a bifurcated current sheet is compatible with the Harris current sheet model. This work is the first step in a series of investigations aimed at studying the effects of energized heavy ions on magnetic reconnection. This work differs

Forces and pressures beneath the saddle during mounting from the ground and from a raised mounting platform.

PubMed

Geutjens, C A; Clayton, H M; Kaiser, L J

2008-03-01

The objective was to use an electronic pressure mat to measure and compare forces and pressures of the saddle on a horse's back when riders mounted from the ground and with the aid of a mounting platform. Ten riders mounted a horse three times each from the ground and from a 35 cm high mounting platform in random order. Total force (summation of forces over all 256 sensors) was measured and compared at specific points on the force-time curve. Total force was usually highest as the rider's right leg was swinging upwards and was correlated with rider mass. When normalized to rider mass, total force and peak pressure were significantly higher when mounting from the ground than from a raised platform (P<0.05). The area of highest pressure was on the right side of the withers in 97% of mounting efforts, confirming the importance of the withers in stabilizing the saddle during mounting.

Node, Node-Link, and Node-Link-Group Diagrams: An Evaluation.

PubMed

Saket, Bahador; Simonetto, Paolo; Kobourov, Stephen; Börner, Katy

2014-12-01

Effectively showing the relationships between objects in a dataset is one of the main tasks in information visualization. Typically there is a well-defined notion of distance between pairs of objects, and traditional approaches such as principal component analysis or multi-dimensional scaling are used to place the objects as points in 2D space, so that similar objects are close to each other. In another typical setting, the dataset is visualized as a network graph, where related nodes are connected by links. More recently, datasets are also visualized as maps, where in addition to nodes and links, there is an explicit representation of groups and clusters. We consider these three Techniques, characterized by a progressive increase of the amount of encoded information: node diagrams, node-link diagrams and node-link-group diagrams. We assess these three types of diagrams with a controlled experiment that covers nine different tasks falling broadly in three categories: node-based tasks, network-based tasks and group-based tasks. Our findings indicate that adding links, or links and group representations, does not negatively impact performance (time and accuracy) of node-based tasks. Similarly, adding group representations does not negatively impact the performance of network-based tasks. Node-link-group diagrams outperform the others on group-based tasks. These conclusions contradict results in other studies, in similar but subtly different settings. Taken together, however, such results can have significant implications for the design of standard and domain snecific visualizations tools.

Automatic localization of bifurcations and vessel crossings in digital fundus photographs using location regression

NASA Astrophysics Data System (ADS)

Niemeijer, Meindert; Dumitrescu, Alina V.; van Ginneken, Bram; Abrámoff, Michael D.

2011-03-01

Parameters extracted from the vasculature on the retina are correlated with various conditions such as diabetic retinopathy and cardiovascular diseases such as stroke. Segmentation of the vasculature on the retina has been a topic that has received much attention in the literature over the past decade. Analysis of the segmentation result, however, has only received limited attention with most works describing methods to accurately measure the width of the vessels. Analyzing the connectedness of the vascular network is an important step towards the characterization of the complete vascular tree. The retinal vascular tree, from an image interpretation point of view, originates at the optic disc and spreads out over the retina. The tree bifurcates and the vessels also cross each other. The points where this happens form the key to determining the connectedness of the complete tree. We present a supervised method to detect the bifurcations and crossing points of the vasculature of the retina. The method uses features extracted from the vasculature as well as the image in a location regression approach to find those locations of the segmented vascular tree where the bifurcation or crossing occurs (from here, POI, points of interest). We evaluate the method on the publicly available DRIVE database in which an ophthalmologist has marked the POI.

Paleoseismic evidence for late Holocene tectonic deformation along the Saddle mountain fault zone, Southeastern Olympic Peninsula, Washington

USGS Publications Warehouse

Barnett, Elizabeth; Sherrod, Brian; Hughes, Jonathan F.; Kelsey, Harvey M.; Czajkowski, Jessica L.; Walsh, Timothy J.; Contreras, Trevor A.; Schermer, Elizabeth R.; Carson, Robert J.

2015-01-01

Trench and wetland coring studies show that northeast‐striking strands of the Saddle Mountain fault zone ruptured the ground about 1000 years ago, generating prominent scarps. Three conspicuous subparallel fault scarps can be traced for 15 km on Light Detection and Ranging (LiDAR) imagery, traversing the foothills of the southeast Olympic Mountains: the Saddle Mountain east fault, the Saddle Mountain west fault, and the newly identified Sund Creek fault. Uplift of the Saddle Mountain east fault scarp impounded stream flow, forming Price Lake and submerging an existing forest, thereby leaving drowned stumps still rooted in place. Stratigraphy mapped in two trenches, one across the Saddle Mountain east fault and the other across the Sund Creek fault, records one and two earthquakes, respectively, as faulting juxtaposed Miocene‐age bedrock against glacial and postglacial deposits. Although the stratigraphy demonstrates that reverse motion generated the scarps, slip indicators measured on fault surfaces suggest a component of left‐lateral slip. From trench exposures, we estimate the postglacial slip rate to be 0.2  mm/yr and between 0.7 and 3.2  mm/yr during the past 3000 years. Integrating radiocarbon data from this study with earlier Saddle Mountain fault studies into an OxCal Bayesian statistical chronology model constrains the most recent paleoearthquake age of rupture across all three Saddle Mountain faults to 1170–970 calibrated years (cal B.P.), which overlaps with the nearby Mw 7.5 1050–1020 cal B.P. Seattle fault earthquake. An earlier earthquake recorded in the Sund Creek trench exposure, dates to around 3500 cal B.P. The geometry of the Saddle Mountain faults and their near‐synchronous rupture to nearby faults 1000 years ago suggest that the Saddle Mountain fault zone forms a western boundary fault along which the fore‐arc blocks migrate northward in response to margin‐parallel shortening across the Puget Lowland.

Bifurcation in a buoyant horizontal laminar jet

NASA Astrophysics Data System (ADS)

Arakeri, Jaywant H.; Das, Debopam; Srinivasan, J.

2000-06-01

The trajectory of a laminar buoyant jet discharged horizontally has been studied. The experimental observations were based on the injection of pure water into a brine solution. Under certain conditions the jet has been found to undergo bifurcation. The bifurcation of the jet occurs in a limited domain of Grashof number and Reynolds number. The regions in which the bifurcation occurs has been mapped in the Reynolds number Grashof number plane. There are three regions where bifurcation does not occur. The various mechanisms that prevent bifurcation have been proposed.

Stability analysis on an economic epidemiological model with vaccination Pages : - , and.

PubMed

Avusuglo, Wisdom S; Abdella, Kenzu; Feng, Wenying

2017-08-01

In this paper, an economic epidemiological model with vaccination is studied. The stability of the endemic steady-state is analyzed and some bifurcation properties of the system are investigated. It is established that the system exhibits saddle-point and period-doubling bifurcations when adult susceptible individuals are vaccinated. Furthermore, it is shown that susceptible individuals also have the tendency of opting for more number of contacts even if the vaccine is inefficacious and thus causes the disease endemic to increase in the long run. Results from sensitivity analysis with specific disease parameters are also presented. Finally, it is shown that the qualitative behaviour of the system is affected by contact levels.

Bifurcation theory and cardiac arrhythmias

PubMed Central

Karagueuzian, Hrayr S; Stepanyan, Hayk; Mandel, William J

2013-01-01

In this paper we review two types of dynamic behaviors defined by the bifurcation theory that are found to be particularly useful in describing two forms of cardiac electrical instabilities that are of considerable importance in cardiac arrhythmogenesis. The first is action potential duration (APD) alternans with an underlying dynamics consistent with the period doubling bifurcation theory. This form of electrical instability could lead to spatially discordant APD alternans leading to wavebreak and reentrant form of tachyarrhythmias. Factors that modulate the APD alternans are discussed. The second form of bifurcation of importance to cardiac arrhythmogenesis is the Hopf-homoclinic bifurcation that adequately describes the dynamics of the onset of early afterdepolarization (EAD)-mediated triggered activity (Hopf) that may cause ventricular tachycardia and ventricular fibrillation (VT/VF respectively). The self-termination of the triggered activity is compatible with the homoclinic bifurcation. Ionic and intracellular calcium dynamics underlying these dynamics are discussed using available experimental and simulation data. The dynamic analysis provides novel insights into the mechanisms of VT/VF, a major cause of sudden cardiac death in the US. PMID:23459417

Recent perspective on coronary artery bifurcation interventions.

PubMed

Dash, Debabrata

2014-01-01

Coronary bifurcation lesions are frequent in routine practice, accounting for 15-20% of all lesions undergoing percutaneous coronary intervention (PCI). PCI of this subset of lesions is technically challenging and historically has been associated with lower procedural success rates and worse clinical outcomes compared with non-bifurcation lesions. The introduction of drug-eluting stents has dramatically improved the outcomes. The provisional technique of implanting one stent in the main branch remains the default approach in most bifurcation lesions. Selection of the most effective technique for an individual bifurcation is important. The use of two-stent techniques as an intention to treat is an acceptable approach in some bifurcation lesions. However, a large amount of metal is generally left unapposed in the lumen with complex two-stent techniques, which is particularly concerning for the risk of stent thrombosis. New technology and dedicated bifurcation stents may overcome some of the limitations of two-stent techniques and revolutionise the management of bifurcation PCI in the future.

Hopf and Bautin Bifurcation in a Tritrophic Food Chain Model with Holling Functional Response Types III and IV

NASA Astrophysics Data System (ADS)

Castellanos, Víctor; Castillo-Santos, Francisco Eduardo; Dela-Rosa, Miguel Angel; Loreto-Hernández, Iván

In this paper, we analyze the Hopf and Bautin bifurcation of a given system of differential equations, corresponding to a tritrophic food chain model with Holling functional response types III and IV for the predator and superpredator, respectively. We distinguish two cases, when the prey has linear or logistic growth. In both cases we guarantee the existence of a limit cycle bifurcating from an equilibrium point in the positive octant of ℝ3. In order to do so, for the Hopf bifurcation we compute explicitly the first Lyapunov coefficient, the transversality Hopf condition, and for the Bautin bifurcation we also compute the second Lyapunov coefficient and verify the regularity conditions.

Complexes and saddle point structures, vibrational frequencies and relative energies of intermediates for CH2Br + HBr «-» CH3Br + Br

NASA Astrophysics Data System (ADS)

Espinosa-Garcia, J.

Ab initio molecular orbital theory was used to study parts of the reaction between the CH2Br radical and the HBr molecule, and two possibilities were analysed: attack on the hydrogen and attack on the bromine of the HBr molecule. Optimized geometries and harmonic vibrational frequencies were calculated at the second-order Moller-Plesset perturbation theory levels, and comparison with available experimental data was favourable. Then single-point calculations were performed at several higher levels of calculation. In the attack on the hydrogen of HBr, two stationary points were located on the direct hydrogen abstraction reaction path: a very weak hydrogen bonded complex of reactants, C···HBr, close to the reactants, followed by the saddle point (SP). The effects of level of calculation (method + basis set), spin projection, zeropoint energy, thermal corrections (298K), spin-orbit coupling and basis set superposition error (BSSE) on the energy changes were analysed. Taking the reaction enthalpy (298K) as reference, agreement with experiment was obtained only when high correlation energy and large basis sets were used. It was concluded that at room temperature (i.e., with zero-point energy and thermal corrections), when the BSSE was included, the complex disappears and the activation enthalpy (298K) ranges from 0.8kcal mol-1 to 1.4kcal mol-1 above the reactants, depending on the level of calculation. It was concluded also that this result is the balance of a complicated interplay of many factors, which are affected by uncertainties in the theoretical calculations. Finally, another possible complex (X complex), which involves the alkyl radical being attracted to the halogen end of HBr (C···BrH), was explored also. It was concluded that this X complex does not exist at room temperature.

Propagating gene expression fronts in a one-dimensional coupled system of artificial cells

NASA Astrophysics Data System (ADS)

Tayar, Alexandra M.; Karzbrun, Eyal; Noireaux, Vincent; Bar-Ziv, Roy H.

2015-12-01

Living systems employ front propagation and spatiotemporal patterns encoded in biochemical reactions for communication, self-organization and computation. Emulating such dynamics in minimal systems is important for understanding physical principles in living cells and in vitro. Here, we report a one-dimensional array of DNA compartments in a silicon chip as a coupled system of artificial cells, offering the means to implement reaction-diffusion dynamics by integrated genetic circuits and chip geometry. Using a bistable circuit we programmed a front of protein synthesis propagating in the array as a cascade of signal amplification and short-range diffusion. The front velocity is maximal at a saddle-node bifurcation from a bistable regime with travelling fronts to a monostable regime that is spatially homogeneous. Near the bifurcation the system exhibits large variability between compartments, providing a possible mechanism for population diversity. This demonstrates that on-chip integrated gene circuits are dynamical systems driving spatiotemporal patterns, cellular variability and symmetry breaking.

Hysteresis in coral reefs under macroalgal toxicity and overfishing.

PubMed

Bhattacharyya, Joydeb; Pal, Samares

2015-03-01

Macroalgae and corals compete for the available space in coral reef ecosystems.While herbivorous reef fish play a beneficial role in decreasing the growth of macroalgae, macroalgal toxicity and overfishing of herbivores leads to proliferation of macroalgae. The abundance of macroalgae changes the community structure towards a macroalgae-dominated reef ecosystem. We investigate coral-macroalgal phase shifts by means of a continuous time model in a food chain. Conditions for local asymptotic stability of steady states are derived. It is observed that in the presence of macroalgal toxicity and overfishing, the system exhibits hysteresis through saddle-node bifurcation and transcritical bifurcation. We examine the effects of time lags in the liberation of toxins by macroalgae and the recovery of algal turf in response to grazing of herbivores on macroalgae by performing equilibrium and stability analyses of delay-differential forms of the ODE model. Computer simulations have been carried out to illustrate the different analytical results.

Spike-like solitary waves in incompressible boundary layers driven by a travelling wave.

PubMed

Feng, Peihua; Zhang, Jiazhong; Wang, Wei

2016-06-01

Nonlinear waves produced in an incompressible boundary layer driven by a travelling wave are investigated, with damping considered as well. As one of the typical nonlinear waves, the spike-like wave is governed by the driven-damped Benjamin-Ono equation. The wave field enters a completely irregular state beyond a critical time, increasing the amplitude of the driving wave continuously. On the other hand, the number of spikes of solitary waves increases through multiplication of the wave pattern. The wave energy grows in a sequence of sharp steps, and hysteresis loops are found in the system. The wave energy jumps to different levels with multiplication of the wave, which is described by winding number bifurcation of phase trajectories. Also, the phenomenon of multiplication and hysteresis steps is found when varying the speed of driving wave as well. Moreover, the nature of the change of wave pattern and its energy is the stability loss of the wave caused by saddle-node bifurcation.

Bifurcation Analysis and Application for Impulsive Systems with Delayed Impulses

NASA Astrophysics Data System (ADS)

Church, Kevin E. M.; Liu, Xinzhi

In this article, we present a systematic approach to bifurcation analysis of impulsive systems with autonomous or periodic right-hand sides that may exhibit delayed impulse terms. Methods include Lyapunov-Schmidt reduction and center manifold reduction. Both methods are presented abstractly in the context of the stroboscopic map associated to a given impulsive system, and are illustrated by way of two in-depth examples: the analysis of a SIR model of disease transmission with seasonality and unevenly distributed moments of treatment, and a scalar logistic differential equation with a delayed census impulsive harvesting effort. It is proven that in some special cases, the logistic equation can exhibit a codimension two bifurcation at a 1:1 resonance point.

Bifurcation of avoided crossing at an exceptional point in the dispersion of sound and light in locally resonant media

NASA Astrophysics Data System (ADS)

Maznev, A. A.

2018-03-01

The avoided crossing behavior in the interaction of propagating sound or light waves with resonant inclusions is analyzed using a simple model of an acoustic medium containing damped mass-spring oscillators, which is shown to be equivalent to the Lorentz oscillator model in the elementary dispersion theory in optics. Two classes of experimental situations dictating the choice in the analysis of the dispersion relation are identified. If the wavevector is regarded as the independent variable and frequency as a complex function of the wavevector, then the avoided crossing bifurcates at an exceptional point at a certain value of the parameter γβ-1/2 , where γ and β characterize the oscillator damping and interaction strength, respectively. This behavior is not observed if the wavevector is regarded as a complex function of frequency.

The glider balloon: a useful device for the treatment of bifurcation lesions.

PubMed

Briguori, Carlo; Visconti, Gabriella; Donahue, Michael; Chiariello, Giovanni Alfonso; Focaccio, Amelia

2013-10-09

Final kissing balloon dilatation (FKBD) is a recommended final step in case of treatment of bifurcation lesions by two stents approaches. Furthermore, dilatation of the side branch (SB) may be necessary following main vessel (MV) stenting. Occasionally, recrossing the stent struts with a balloon is hampered because the tip hits a stent strut. The Glider (TriReme Medical, Pleasanton, CA) is a dedicated balloon designed for crossing through struts of deployed stents toward a SB. From October 2010 to January 2012, FKBD was attempted in 236 consecutive bifurcation lesions treated in our Institution. FKBD was successfully performed by conventional balloon catheters in 221 (93.5%) lesions (Conventional group). In the remaining 15 (6.5%) lesions, where a conventional balloon failed to cross the stent strut, the Glider balloon was attempted (Glider group). The angle beta (between the axis of the MV after the branch point and the SB axis at the point of divergence) was wider in the Glider group (83±17° versus 65±27°; p=0.032). A trend toward an higher rate of the true bifurcation lesions was observed in the Glider group (93% versus 70.5%; p=0.07). The Glider balloon successfully crossed through MV stent struts toward a SB in 12 patients (80%), whereas failed in the remaining 3 patients. The Glider balloon represents an unique bail-out device which offers an effective rescue strategy for recrossing stent struts during complex bifurcation stenting. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Ecoepidemic predator-prey model with feeding satiation, prey herd behavior and abandoned infected prey.

PubMed

Kooi, Bob W; Venturino, Ezio

2016-04-01

In this paper we analyse a predator-prey model where the prey population shows group defense and the prey individuals are affected by a transmissible disease. The resulting model is of the Rosenzweig-MacArthur predator-prey type with an SI (susceptible-infected) disease in the prey. Modeling prey group defense leads to a square root dependence in the Holling type II functional for the predator-prey interaction term. The system dynamics is investigated using simulations, classical existence and asymptotic stability analysis and numerical bifurcation analysis. A number of bifurcations, such as transcritical and Hopf bifurcations which occur commonly in predator-prey systems will be found. Because of the square root interaction term there is non-uniqueness of the solution and a singularity where the prey population goes extinct in a finite time. This results in a collapse initiated by extinction of the healthy or susceptible prey and thereafter the other population(s). When also a positive attractor exists this leads to bistability similar to what is found in predator-prey models with a strong Allee effect. For the two-dimensional disease-free (i.e. the purely demographic) system the region in the parameter space where bistability occurs is marked by a global bifurcation. At this bifurcation a heteroclinic connection exists between saddle prey-only equilibrium points where a stable limit cycle together with its basin of attraction, are destructed. In a companion paper (Gimmelli et al., 2015) the same model was formulated and analysed in which the disease was not in the prey but in the predator. There we also observed this phenomenon. Here we extend its analysis using a phase portrait analysis. For the three-dimensional ecoepidemic predator-prey system where the prey is affected by the disease, also tangent bifurcations including a cusp bifurcation and a torus bifurcation of limit cycles occur. This leads to new complex dynamics. Continuation by varying one parameter

Experiment Evaluation of Bifurcation in Sands

NASA Technical Reports Server (NTRS)

Alshibi, Khalid A.; Sture, Stein

2000-01-01

The basic principles of bifurcation analysis have been established by several investigators, however several issues remain unresolved, specifically how do stress level, grain size distribution, and boundary conditions affect general bifurcation phenomena in pressure sensitive and dilatant materials. General geometrical and kinematics conditions for moving surfaces of discontinuity was derived and applied to problems of instability of solids. In 1962, the theoretical framework of bifurcation by studying the acceleration waves in elasto-plastic (J2) solids were presented. Bifurcation analysis for more specific forms of constitutive behavior was examined by studying localization in pressure-sensitive, dilatant materials, however, analyses were restricted to plane deformation states only. Bifurcation analyses were presented and applied to predict shear band formations in sand under plane strain condition. The properties of discontinuous bifurcation solutions for elastic-plastic solids under axisymmetric and plane strain loading conditions were studied. The study focused on theory, but also references and comparisons to experiments were made. The current paper includes a presentation of a summary of bifurcation analyses for biaxial and triaxial (axisymmetric) loading conditions. The Coulomb model is implemented using incremental piecewise scheme to predict the constitutive relations and shear band inclination angles. Then, a comprehensive evaluation of bifurcation phenomena is presented based on data from triaxial experiments performed under microgravity conditions aboard the Space Shuttle under very low effective confining pressure (0.05 to 1.30 kPa), in which very high peak friction angles (47 to 75 degrees) and dilatancy angles (30 to 31 degrees) were measured. The evaluation will be extended to include biaxial experiments performed on the same material under low (10 kPa) and moderate (100 kPa) confining pressures. A comparison between the behavior under biaxial and

Small scale exact coherent structures at large Reynolds numbers in plane Couette flow

NASA Astrophysics Data System (ADS)

Eckhardt, Bruno; Zammert, Stefan

2018-02-01

The transition to turbulence in plane Couette flow and several other shear flows is connected with saddle node bifurcations in which fully three-dimensional, nonlinear solutions to the Navier-Stokes equation, so-called exact coherent states (ECS), appear. As the Reynolds number increases, the states undergo secondary bifurcations and their time-evolution becomes increasingly more complex. Their spatial complexity, in contrast, remains limited so that these states cannot contribute to the spatial complexity and cascade to smaller scales expected for higher Reynolds numbers. We here present families of scaling ECS that exist on ever smaller scales as the Reynolds number is increased. We focus in particular on two such families for plane Couette flow, one centered near the midplane and the other close to a wall. We discuss their scaling and localization properties and the bifurcation diagrams. All solutions are localized in the wall-normal direction. In the spanwise and downstream direction, they are either periodic or localized as well. The family of scaling ECS localized near a wall is reminiscent of attached eddies, and indicates how self-similar ECS can contribute to the formation of boundary layer profiles.

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

Zhang, Hailong; Vibration Control Lab, School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042; Zhang, Ning

Magneto-rheological (MR) damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF) MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE) spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phasemore » trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.« less

Spontaneous symmetry breaking due to the trade-off between attractive and repulsive couplings.

PubMed

Sathiyadevi, K; Karthiga, S; Chandrasekar, V K; Senthilkumar, D V; Lakshmanan, M

2017-04-01

Spontaneous symmetry breaking is an important phenomenon observed in various fields including physics and biology. In this connection, we here show that the trade-off between attractive and repulsive couplings can induce spontaneous symmetry breaking in a homogeneous system of coupled oscillators. With a simple model of a system of two coupled Stuart-Landau oscillators, we demonstrate how the tendency of attractive coupling in inducing in-phase synchronized (IPS) oscillations and the tendency of repulsive coupling in inducing out-of-phase synchronized oscillations compete with each other and give rise to symmetry breaking oscillatory states and interesting multistabilities. Further, we provide explicit expressions for synchronized and antisynchronized oscillatory states as well as the so called oscillation death (OD) state and study their stability. If the Hopf bifurcation parameter (λ) is greater than the natural frequency (ω) of the system, the attractive coupling favors the emergence of an antisymmetric OD state via a Hopf bifurcation whereas the repulsive coupling favors the emergence of a similar state through a saddle-node bifurcation. We show that an increase in the repulsive coupling not only destabilizes the IPS state but also facilitates the reentrance of the IPS state.

Stability and Hopf Bifurcation for Two Advertising Systems, Coupled with Delay

NASA Astrophysics Data System (ADS)

Sterpu, Mihaela; Rocşoreanu, Carmen

2007-09-01

Two advertising systems were linearly coupled via the first variable, with time delay. The stability and the Hopf bifurcation corresponding to the symmetric equilibrium point (the origin) in the 4D system are analyzed. Different types of oscillations corresponding to the limit cycles are compared.

Sentinel lymph node biopsy from the vantage point of an oncologic surgeon.

PubMed

Wilson, Lori L

2009-01-01

Sentinel lymph node biopsy has greatly influenced the surgical management of clinically localized primary melanoma. Lymphatic mapping and sentinel lymph node biopsy have been used for the selective management of the draining regional lymph node basin of primary cutaneous melanoma. Oncologic surgeons have adopted this procedure to selectively identify occult nodal status in melanoma patients who are at a higher risk of regional metastasis. The current standard of treatment of tumor-positive sentinel lymph node metastasis is immediate completion lymphadenectomy, but considerable debate surrounds the utility of this procedure. This contribution reviews development, technical aspects, selective management of the lymph node basin, and sentinel lymph node biopsy techniques.

Synchronization transition of a coupled system composed of neurons with coexisting behaviors near a Hopf bifurcation

NASA Astrophysics Data System (ADS)

Jia, Bing

2014-05-01

The coexistence of a resting condition and period-1 firing near a subcritical Hopf bifurcation point, lying between the monostable resting condition and period-1 firing, is often observed in neurons of the central nervous systems. Near such a bifurcation point in the Morris—Lecar (ML) model, the attraction domain of the resting condition decreases while that of the coexisting period-1 firing increases as the bifurcation parameter value increases. With the increase of the coupling strength, and parameter and initial value dependent synchronization transition processes from non-synchronization to compete synchronization are simulated in two coupled ML neurons with coexisting behaviors: one neuron chosen as the resting condition and the other the coexisting period-1 firing. The complete synchronization is either a resting condition or period-1 firing dependent on the initial values of period-1 firing when the bifurcation parameter value is small or middle and is period-1 firing when the parameter value is large. As the bifurcation parameter value increases, the probability of the initial values of a period-1 firing neuron that lead to complete synchronization of period-1 firing increases, while that leading to complete synchronization of the resting condition decreases. It shows that the attraction domain of a coexisting behavior is larger, the probability of initial values leading to complete synchronization of this behavior is higher. The bifurcations of the coupled system are investigated and discussed. The results reveal the complex dynamics of synchronization behaviors of the coupled system composed of neurons with the coexisting resting condition and period-1 firing, and are helpful to further identify the dynamics of the spatiotemporal behaviors of the central nervous system.

78 FR 36164 - Tongass National Forest; Ketchikan-Misty Fiords Ranger District; Alaska; Saddle Lakes Timber Sale...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-06-17

... District; Alaska; Saddle Lakes Timber Sale Environmental Impact Statement AGENCY: Forest Service, USDA... Notice of Intent (NOI) to prepare an Environmental Impact Statement for the Saddle Lakes Timber Sale... management plans documented with a Record of Decision or Decision Notice (reference 36 CFR part 218). This...

The effectiveness of adhesives on the retention of mandibular free end saddle partial dentures: An in vitro study.

PubMed

Quiney, Daniel; Nishio Ayre, Wayne; Milward, Paul

2017-07-01

Existing in vitro methods for testing denture adhesives do not fully replicate the complex oral geometries and environment; and in vivo methods are qualitative, prone to bias and not easily reproducible. The purpose of this study was to develop a novel, quantitative and more accurate model to test the effect of adhesives on the retentive force of mandibular free end saddle partial dentures. An in vitro model was developed based on an anatomically accurate cast of a clinical case. Experimentally, the amount of adhesive was varied (0.2g-1g) and the tensile force required for displacement was measured. Different commercially available adhesives were then tested at the optimum volume using the in vitro model. A 3D finite element model of the denture was used to assess how the forces to induce denture displacement varied according to the position of the force along the saddle length. The mass of adhesive was found to significantly alter retention forces, with 0.4-0.7g being the optimum range for this particular scenario. Use of adhesives significantly improved mandibular free end saddle partial denture retention with the worst performing adhesive increasing retention nine-fold whilst the best performing adhesive increased retention twenty three-fold. The finite element model revealed that 77% more force was required to displace the denture by positioning forces towards the mesial end of the saddle compared to the distal end. An in vitro denture adhesive model was developed, which demonstrated that mass of adhesive plays a significant role in enhancing denture retention and supported the design principle of placing as few teeth as clinically necessary on the distal end of the free end saddles. Limiting the position of teeth on free end saddles to the mesial and mid portion of the saddle will reduce displacements caused by mastication. The movement of mandibular free end saddle partial dentures can be restricted with the use of denture adhesives. Altering the mass of

Nonconvergence to Saddle Boundary Points under Perturbed Reinforcement Learning

DTIC Science & Technology

2012-12-07

of the ODE (12). Note that for some games not all stationary points of the ODE (12) are Nash equilibria. For example, if you consider the Typewriter ...B A 4, 4 2, 2 B 2, 2 3, 3 Table 1: The Typewriter Game. On the other hand, any stationary point in the interior of the probability simplex will... Typewriter Game of Table 1. We observe that it is possible for the process to converge to a pure strategy profile which is not a Nash equilibrium when Ri(α

Detection of bifurcations in noisy coupled systems from multiple time series

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

Williamson, Mark S., E-mail: m.s.williamson@exeter.ac.uk; Lenton, Timothy M.

We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, themore » possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system.« less

Detection of bifurcations in noisy coupled systems from multiple time series

NASA Astrophysics Data System (ADS)

Williamson, Mark S.; Lenton, Timothy M.

2015-03-01

We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, the possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system.

Energetics and monsoon bifurcations

NASA Astrophysics Data System (ADS)

Seshadri, Ashwin K.

2017-01-01

Monsoons involve increases in dry static energy (DSE), with primary contributions from increased shortwave radiation and condensation of water vapor, compensated by DSE export via horizontal fluxes in monsoonal circulations. We introduce a simple box-model characterizing evolution of the DSE budget to study nonlinear dynamics of steady-state monsoons. Horizontal fluxes of DSE are stabilizing during monsoons, exporting DSE and hence weakening the monsoonal circulation. By contrast latent heat addition (LHA) due to condensation of water vapor destabilizes, by increasing the DSE budget. These two factors, horizontal DSE fluxes and LHA, are most strongly dependent on the contrast in tropospheric mean temperature between land and ocean. For the steady-state DSE in the box-model to be stable, the DSE flux should depend more strongly on the temperature contrast than LHA; stronger circulation then reduces DSE and thereby restores equilibrium. We present conditions for this to occur. The main focus of the paper is describing conditions for bifurcation behavior of simple models. Previous authors presented a minimal model of abrupt monsoon transitions and argued that such behavior can be related to a positive feedback called the `moisture advection feedback'. However, by accounting for the effect of vertical lapse rate of temperature on the DSE flux, we show that bifurcations are not a generic property of such models despite these fluxes being nonlinear in the temperature contrast. We explain the origin of this behavior and describe conditions for a bifurcation to occur. This is illustrated for the case of the July-mean monsoon over India. The default model with mean parameter estimates does not contain a bifurcation, but the model admits bifurcation as parameters are varied.

The chaotic saddle of a three degrees of freedom scattering system reconstructed from cross-section data

NASA Astrophysics Data System (ADS)

Drótos, G.; Jung, C.

2016-06-01

The topic of this paper is hyperbolic chaotic scattering in a three degrees of freedom system. We generalize how shadows in the domain of the doubly differential cross-section are found: they are traced out by the appropriately filtered unstable manifolds of the periodic trajectories in the chaotic saddle. These shadows are related to the rainbow singularities in the doubly differential cross-section. As a result of this relation, we discover a method of how to recognize in the cross section a smoothly deformed image of the chaotic saddle, allowing the reconstruction of the symbolic dynamics of the chaotic saddle, its topology and its scaling factors.

High femoral artery bifurcation predicts contralateral high bifurcation: implications for complex percutaneous cardiovascular procedures requiring large caliber and/or dual access.

PubMed

Gupta, Vipul; Feng, Kent; Cheruvu, Pavan; Boyer, Nathan; Yeghiazarians, Yerem; Ports, Thomas A; Zimmet, Jeffrey; Shunk, Kendrick; Boyle, Andrew J

2014-09-01

Recent advances in technology have led to an increase in the use of bilateral femoral artery access and the requirement for large-bore access. Optimal access is in the common femoral artery (CFA), rather than higher (in the external iliac artery) or lower (in one of the branches of the CFA). However, there is a paucity of data in the literature about the relationship between bifurcation level of one CFA and the contralateral CFA. To define the prevalence of high bifurcation of the CFA and the relationship between bifurcation level on both sides, we performed a retrospective analysis of all patients with bilateral femoral angiography. From 4880 femoral angiograms performed at UCSF cardiac catheterization laboratory between 2005-2013, a total of 273 patients had bilateral femoral angiograms. The prevalence of low/normal, high, and very-high femoral bifurcations was 70%, 26%, and 4%, respectively, with no difference between sides. A high or very-high bifurcation significantly increased the likelihood of a high bifurcation on the contralateral side (odds ratio >3.0). Multivariable logistic regression analysis revealed age, gender, self-reported race, height, weight, and body mass index were not predictive of high or very-high bifurcations on either side. In conclusion, high femoral artery bifurcations are common and increase the likelihood of a high bifurcation of the contralateral femoral artery.

Bifurcation-enhanced ultrahigh sensitivity of a buckled cantilever

PubMed Central

An, Sangmin; Kim, Bongsu; Kwon, Soyoung; Moon, Geol; Lee, Manhee

2018-01-01

Buckling, first introduced by Euler in 1744 [Euler L (1744) Opera Omnia I 24:231], a sudden mechanical sideways deflection of a structural member under compressive stress, represents a bifurcation in the solution to the equations of static equilibrium. Although it has been investigated in diverse research areas, such a common nonlinear phenomenon may be useful to devise a unique mechanical sensor that addresses the still-challenging features, such as the enhanced sensitivity and polarization-dependent detection capability. We demonstrate the bifurcation-enhanced sensitive measurement of mechanical vibrations using the nonlinear buckled cantilever tip in ambient conditions. The cantilever, initially buckled with its tip pinned, flips its buckling near the bifurcation point (BP), where the buckled tip becomes softened. The enhanced mechanical sensitivity results from the increasing fluctuations, unlike the typical linear sensors, which facilitate the noise-induced buckling-to-flipping transition of the softened cantilever. This allows the in situ continuous or repeated single-shot detection of the surface acoustic waves of different polarizations without any noticeable wear of the tip. We obtained the sensitivity above 106 V(m/s)−1, a 1,000-fold enhancement over the conventional seismometers. Our results lead to development of mechanical sensors of high sensitivity, reproducibility, and durability, which may be applied to detect, e.g., the directional surface waves on the laboratory as well as the geological scale. PMID:29511105

Malonic acid concentration as a control parameter in the kinetic analysis of the Belousov-Zhabotinsky reaction under batch conditions.

PubMed

Blagojević, Slavica M; Anić, Slobodan R; Cupić, Zeljko D; Pejić, Natasa D; Kolar-Anić, Ljiljana Z

2008-11-28

The influence of the initial malonic acid concentration [MA]0 (8.00 x 10(-3) < or = [MA]0 < or = 4.30 x 10(-2) mol dm(-3)) in the presence of bromate (6.20 x 10(-2) mol dm(-3)), bromide (1.50 x 10(-5) mol dm(-3)), sulfuric acid (1.00 mol dm(-3)) and cerium sulfate (2.50 x 10(-3) mol dm(-3)) on the dynamics and the kinetics of the Belousov-Zhabotinsky (BZ) reactions was examined under batch conditions at 30.0 degrees C. The kinetics of the BZ reaction was analyzed by the earlier proposed method convenient for the examinations of the oscillatory reactions. In the defined region of parameters where oscillograms with only large-amplitude relaxation oscillations appeared, the pseudo-first order of the overall malonic acid decomposition with a corresponding rate constant of 2.14 x 10(-2) min(-1) was established. The numerical results on the dynamics and kinetics of the BZ reaction, carried out by the known skeleton model including the Br2O species, were in good agreement with the experimental ones. The already found saddle node infinite period (SNIPER) bifurcation point in transition from a stable quasi-steady state to periodic orbits and vice versa is confirmed by both experimental and numerical investigations of the system under consideration. Namely, the large-amplitude relaxation oscillations with increasing periods between oscillations in approaching the bifurcation points at the beginning and the end of the oscillatory domain, together with excitability of the stable quasi-steady states in their vicinity are obtained.

Subcritical Hopf Bifurcation and Stochastic Resonance of Electrical Activities in Neuron under Electromagnetic Induction

PubMed Central

Fu, Yu-Xuan; Kang, Yan-Mei; Xie, Yong

2018-01-01

The FitzHugh–Nagumo model is improved to consider the effect of the electromagnetic induction on single neuron. On the basis of investigating the Hopf bifurcation behavior of the improved model, stochastic resonance in the stochastic version is captured near the bifurcation point. It is revealed that a weak harmonic oscillation in the electromagnetic disturbance can be amplified through stochastic resonance, and it is the cooperative effect of random transition between the resting state and the large amplitude oscillating state that results in the resonant phenomenon. Using the noise dependence of the mean of interburst intervals, we essentially suggest a biologically feasible clue for detecting weak signal by means of neuron model with subcritical Hopf bifurcation. These observations should be helpful in understanding the influence of the magnetic field to neural electrical activity. PMID:29467642

Subcritical Hopf Bifurcation and Stochastic Resonance of Electrical Activities in Neuron under Electromagnetic Induction.

PubMed

Fu, Yu-Xuan; Kang, Yan-Mei; Xie, Yong

2018-01-01

The FitzHugh-Nagumo model is improved to consider the effect of the electromagnetic induction on single neuron. On the basis of investigating the Hopf bifurcation behavior of the improved model, stochastic resonance in the stochastic version is captured near the bifurcation point. It is revealed that a weak harmonic oscillation in the electromagnetic disturbance can be amplified through stochastic resonance, and it is the cooperative effect of random transition between the resting state and the large amplitude oscillating state that results in the resonant phenomenon. Using the noise dependence of the mean of interburst intervals, we essentially suggest a biologically feasible clue for detecting weak signal by means of neuron model with subcritical Hopf bifurcation. These observations should be helpful in understanding the influence of the magnetic field to neural electrical activity.

Fractional flow reserve and coronary bifurcation anatomy: a novel quantitative model to assess and report the stenosis severity of bifurcation lesions.

PubMed

Tu, Shengxian; Echavarria-Pinto, Mauro; von Birgelen, Clemens; Holm, Niels R; Pyxaras, Stylianos A; Kumsars, Indulis; Lam, Ming Kai; Valkenburg, Ilona; Toth, Gabor G; Li, Yingguang; Escaned, Javier; Wijns, William; Reiber, Johan H C

2015-04-20

The aim of this study was to develop a new model for assessment of stenosis severity in a bifurcation lesion including its core. The diagnostic performance of this model, powered by 3-dimensional quantitative coronary angiography to predict the functional significance of obstructive bifurcation stenoses, was evaluated using fractional flow reserve (FFR) as the reference standard. Development of advanced quantitative models might help to establish a relationship between bifurcation anatomy and FFR. Patients who had undergone coronary angiography and interventions in 5 European cardiology centers were randomly selected and analyzed. Different bifurcation fractal laws, including Murray, Finet, and HK laws, were implemented in the bifurcation model, resulting in different degrees of stenosis severity. A total of 78 bifurcation lesions in 73 patients were analyzed. In 51 (65%) bifurcations, FFR was measured in the main vessel. A total of 34 (43.6%) interrogated vessels had an FFR≤0.80. Correlation between FFR and diameter stenosis was poor by conventional straight analysis (ρ=-0.23, p<0.001) but significantly improved by bifurcation analyses: the highest by the HK law (ρ=-0.50, p<0.001), followed by the Finet law (ρ=-0.49, p<0.001), and the Murray law (ρ=-0.41, p<0.001). The area under the receiver-operating characteristics curve for predicting FFR≤0.80 was significantly higher by bifurcation analysis compared with straight analysis: 0.72 (95% confidence interval: 0.61 to 0.82) versus 0.60 (95% confidence interval: 0.49 to 0.71; p=0.001). Applying a threshold of ≥50% diameter stenosis, as assessed by the bifurcation model, to predict FFR≤0.80 resulted in 23 true positives, 27 true negatives, 17 false positives, and 11 false negatives. The new bifurcation model provides a comprehensive assessment of bifurcation anatomy. Compared with straight analysis, identification of lesions with preserved FFR values in obstructive bifurcation stenoses was improved

An Emergent Bifurcation Angle on River Deltas

NASA Astrophysics Data System (ADS)

Shaw, J.; Coffey, T.

2017-12-01

Distributary channel bifurcations on river deltas are important features that control water, sediment, and nutrient routing and can dictate large-scale stratigraphic heterogeneity. We use theory originally developed for a special case of tributary networks to understand the dynamics of distributary channel bifurcations. Interestingly, bifurcations in groundwater-fed tributary networks have been shown to evolve dependent on the diffusive flow field outside the network. These networks possess a characteristic bifurcation angle of 72°, due to Laplacian flow in the groundwater flow field near tributary channel tips (gradient2h2=0, where h is water surface elevation). We develop and test the hypothesis that bifurcation angles in distributary channel networks are likewise dictated by the external flow field, in this case the shallow surface water surrounding the subaqueous portion of distributary channel bifurcations in a deltaic setting. We measured 130 unique distributary channel bifurcations in a single experimental delta and in 10 natural deltas, yielding a mean angle of 70.35°±2.59° (95% confidence interval), in line with the theoretical prediction. These data and hydrodynamic scaling arguments convince us that distributary network formation can result simply from the coupling of (Laplacian) extra-channel flow to channels along subaqueous channel networks. The simplicity of this model provides new insight into distributary network formation and its geomorphic and stratigraphic consequences.

Saddle Bag Mountain Research Natural Area: guidebook supplement 34.

Treesearch

Reid Schuller; Ronald L. Exeter

2007-01-01

This guidebook describes the Saddle Bag Mountain Research Natural Area, a 121-ha (300-ac) tract established to represent an old-growth remnant of Pacific silver fir (Abies amabilis) and western hemlock (Tsuga heterophylla) forest in the Oregon Coast Range. Pacific silver fir and noble fir (Abies procera)...

Bifurcation scenarios for bubbling transition.

PubMed

Zimin, Aleksey V; Hunt, Brian R; Ott, Edward

2003-01-01

Dynamical systems with chaos on an invariant submanifold can exhibit a type of behavior called bubbling, whereby a small random or fixed perturbation to the system induces intermittent bursting. The bifurcation to bubbling occurs when a periodic orbit embedded in the chaotic attractor in the invariant manifold becomes unstable to perturbations transverse to the invariant manifold. Generically the periodic orbit can become transversely unstable through a pitchfork, transcritical, period-doubling, or Hopf bifurcation. In this paper a unified treatment of the four types of bubbling bifurcation is presented. Conditions are obtained determining whether the transition to bubbling is soft or hard; that is, whether the maximum burst amplitude varies continuously or discontinuously with variation of the parameter through its critical value. For soft bubbling transitions, the scaling of the maximum burst amplitude with the parameter is derived. For both hard and soft transitions the scaling of the average interburst time with the bifurcation parameter is deduced. Both random (noise) and fixed (mismatch) perturbations are considered. Results of numerical experiments testing our theoretical predictions are presented.

Saddle-nose deformity repair with microplate-adapted costal cartilage.

PubMed

Eren, Fikret; Öksüz, Sinan; Melikoğlu, Cenk; Karagöz, Hüseyin; Ülkür, Ersin

2014-08-01

Nasal deformities affecting the bone and lower two-thirds of the nose due to the loss of septal height and tip support are defined as "saddle-nose" deformity. Reconstruction of a saddle-nose deformity essentially necessitates structural grafting. This article presents an alternative approach for correction of saddle-nose deformity using a microplate and costal cartilage. The results are compared with those of the previously applied costal cartilage repair methods. Between 2004 and 2013, 16 patients were treated with costal cartilage autografts. Of these 16 patients, 7 were treated with a microplate and costal cartilage autograft combination, 4 were treated with a costal cartilage autograft and Kirschner (K)-wire, and 5 were treated with onlay costal cartilage grafts. The mean follow-up periods were 16 months for group treated with microplate-adapted autologous costal cartilage, 12 months for the group treated with K-wire and autologous costal cartilage, and 16 months for the group treated with onlay costal cartilage. The patients treated with K-wire inserted cartilages and the patients treated onlay dorsal costal cartilages encountered complications such as extrusion of the wire and warping, respectively. The seven patients treated with microplate and dorsal onlay costal cartilage graft did not experience any infection, warping, or extrusion complication. The warping tendency of the costal cartilage autograft can be efficiently prevented without a prominent complication risk by using microplate-adapted costal cartilage grafts. This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266 .

Bayesian sensitivity analysis of bifurcating nonlinear models

NASA Astrophysics Data System (ADS)

Becker, W.; Worden, K.; Rowson, J.

2013-01-01

Sensitivity analysis allows one to investigate how changes in input parameters to a system affect the output. When computational expense is a concern, metamodels such as Gaussian processes can offer considerable computational savings over Monte Carlo methods, albeit at the expense of introducing a data modelling problem. In particular, Gaussian processes assume a smooth, non-bifurcating response surface. This work highlights a recent extension to Gaussian processes which uses a decision tree to partition the input space into homogeneous regions, and then fits separate Gaussian processes to each region. In this way, bifurcations can be modelled at region boundaries and different regions can have different covariance properties. To test this method, both the treed and standard methods were applied to the bifurcating response of a Duffing oscillator and a bifurcating FE model of a heart valve. It was found that the treed Gaussian process provides a practical way of performing uncertainty and sensitivity analysis on large, potentially-bifurcating models, which cannot be dealt with by using a single GP, although an open problem remains how to manage bifurcation boundaries that are not parallel to coordinate axes.

Parity bifurcations in trapped multistable phase locked exciton-polariton condensates

NASA Astrophysics Data System (ADS)

Tan, E. Z.; Sigurdsson, H.; Liew, T. C. H.

2018-02-01

We present a theoretical scheme for multistability in planar microcavity exciton-polariton condensates under nonresonant driving. Using an excitation profile resulting in a spatially patterned condensate, we observe organized phase locking which can abruptly reorganize as a result of pump induced instability made possible by nonlinear interactions. For π /2 symmetric systems this reorganization can be regarded as a parity transition and is found to be a fingerprint of multistable regimes existing over a finite range of excitation strengths. The natural degeneracy of the planar equations of motion gives rise to parity bifurcation points where the condensate, as a function of excitation intensity, bifurcates into one of two anisotropic degenerate solutions. Deterministic transitions between multistable states are made possible using controlled nonresonant pulses, perturbing the solution from one attractor to another.

A case study in bifurcation theory

NASA Astrophysics Data System (ADS)

Khmou, Youssef

This short paper is focused on the bifurcation theory found in map functions called evolution functions that are used in dynamical systems. The most well-known example of discrete iterative function is the logistic map that puts into evidence bifurcation and chaotic behavior of the topology of the logistic function. We propose a new iterative function based on Lorentizan function and its generalized versions, based on numerical study, it is found that the bifurcation of the Lorentzian function is of second-order where it is characterized by the absence of chaotic region.

Using Lin's method to solve Bykov's problems

NASA Astrophysics Data System (ADS)

Knobloch, Jürgen; Lamb, Jeroen S. W.; Webster, Kevin N.

2014-10-01

We consider nonwandering dynamics near heteroclinic cycles between two hyperbolic equilibria. The constituting heteroclinic connections are assumed to be such that one of them is transverse and isolated. Such heteroclinic cycles are associated with the termination of a branch of homoclinic solutions, and called T-points in this context. We study codimension-two T-points and their unfoldings in Rn. In our consideration we distinguish between cases with real and complex leading eigenvalues of the equilibria. In doing so we establish Lin's method as a unified approach to (re)gain and extend results of Bykov's seminal studies and related works. To a large extent our approach reduces the study to the discussion of intersections of lines and spirals in the plane. Case (RR): Under open conditions on the eigenvalues, there exist open sets in parameter space for which there exist periodic orbits close to the heteroclinic cycle. In addition, there exist two one-parameter families of homoclinic orbits to each of the saddle points p1 and p2.See Theorem 2.1 and Proposition 2.2 for precise statements and Fig. 2 for bifurcation diagrams. Cases (RC) and (CC): At the bifurcation point μ=0 and for each N≥2, there exists an invariant set S0N close to the heteroclinic cycle on which the first return map is topologically conjugated to a full shift on N symbols. For any fixed N≥2, the invariant set SμN persists for |μ| sufficiently small.In addition, there exist infinitely many transversal and non-transversal heteroclinic orbits connecting the saddle points p1 and p2 in a neighbourhood of μ=0, as well as infinitely many one-parameter families of homoclinic orbits to each of the saddle points.For full statements of the results see Theorem 2.3 and Propositions 2.4, 2.5 and Fig. 3 for bifurcation diagrams. The dynamics near T-points has been studied previously by Bykov [6-10], Glendinning and Sparrow [20], Kokubu [27,28] and Labouriau and Rodrigues [30,31,38]. See also the surveys

True double bifurcation lesions: new application of the self-expandable Axxess stent and review of literature with dedicated bifurcation devices.

PubMed

Borgia, Francesco; Niglio, Tullio; De Luca, Nicola; Di Serafino, Luigi; Esposito, Giovanni; Trimarco, Bruno; Cirillo, Plinio

2018-04-21

Complex coronary artery bifurcation lesions occurred in hard clinical scenarios, such as acute coronary syndromes, may represent a challenge for interventional cardiologists, with not-defined general consensus on treatment. Even if provisional stenting is the most common option used to restore rapidly the coronary branches flow, improvements in industrial technologies and design of new dedicated bifurcation devices might open new modalities of treatment in these complex cases. The Axxess stent (Biosensors Europe SA, Morges, Switzerland) is a self-expanding biolimus-eluting conical V-shape stent, specifically designed to treat "easily" coronary artery bifurcation lesions, with reported favorable long-term clinical results in stable patients compared to a provisional technique. We report for the first time the feasibility to use this device in a case of "true double coronary bifurcation lesion" occurred in the context of acute coronary syndrome. Moreover, we reviewed studies with bifurcation dedicated devices and available cases of "true double bifurcation lesions", underlying advantages/disadvantages of using one device over the others during acute coronary syndrome. Copyright © 2018 Elsevier Inc. All rights reserved.

Stability and Bifurcation of a Fishery Model with Crowley-Martin Functional Response

NASA Astrophysics Data System (ADS)

Maiti, Atasi Patra; Dubey, B.

To understand the dynamics of a fishery system, a nonlinear mathematical model is proposed and analyzed. In an aquatic environment, we considered two populations: one is prey and another is predator. Here both the fish populations grow logistically and interaction between them is of Crowley-Martin type functional response. It is assumed that both the populations are harvested and the harvesting effort is assumed to be dynamical variable and tax is considered as a control variable. The existence of equilibrium points and their local stability are examined. The existence of Hopf-bifurcation, stability and direction of Hopf-bifurcation are also analyzed with the help of Center Manifold theorem and normal form theory. The global stability behavior of the positive equilibrium point is also discussed. In order to find the value of optimal tax, the optimal harvesting policy is used. To verify our analytical findings, an extensive numerical simulation is carried out for this model system.

On the late-time behavior of Virasoro blocks and a classification of semiclassical saddles

NASA Astrophysics Data System (ADS)

Fitzpatrick, A. Liam; Kaplan, Jared

2017-04-01

Recent work has demonstrated that black hole thermodynamics and information loss/restoration in AdS3/CFT2 can be derived almost entirely from the behavior of the Virasoro conformal blocks at large central charge, with relatively little dependence on the precise details of the CFT spectrum or OPE coefficients. Here, we elaborate on the non-perturbative behavior of Virasoro blocks by classifying all `saddles' that can contribute for arbitrary values of external and internal operator dimensions in the semiclassical large central charge limit. The leading saddles, which determine the naive semiclassical behavior of the Virasoro blocks, all decay exponentially at late times, and at a rate that is independent of internal operator dimensions. Consequently, the semiclassical contribution of a finite number of high-energy states cannot resolve a well-known version of the information loss problem in AdS3. However, we identify two infinite classes of sub-leading saddles, and one of these classes does not decay at late times.

Discretization analysis of bifurcation based nonlinear amplifiers

NASA Astrophysics Data System (ADS)

Feldkord, Sven; Reit, Marco; Mathis, Wolfgang

2017-09-01

Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.

Technological parameters of welding of branch saddles to polyethylene pipes at low temperatures

NASA Astrophysics Data System (ADS)

Starostin, N. P.; Vasilieva, M. A.

2017-12-01

The present paper outlines a procedure for determination of dynamics of the temperature field during the welding of the branch saddle to the polyethylene gas pipeline at ambient temperatures below the normative. The analysis is accomplished by the finite element method with the heat of the phase transition taken into account. Methods of the visualization of data sets reveal the possibility of controlling the thermal process by preheating and thermal insulation during welding of the branch saddle to the pipe at low temperatures and the possibility of obtaining the dynamics of the temperature field at which a high-quality welded joint is formed.

Fractal Parameter Space of Lorenz-like Attractors: A Hierarchical Approach

NASA Astrophysics Data System (ADS)

Xing, Tingli; Wojcik, Jeremy; Zaks, Michael A.; Shilnikov, Andrey

2014-12-01

Using bi-parametric sweeping based on symbolic representation we reveal self-similar fractal structures induced by hetero- and homoclinic bifurcations of saddle singularities in the parameter space of two systems with deterministic chaos. We start with the system displaying a few homoclinic bifurcations of higher codimension: resonant saddle, orbitflip and inclination switch that all can give rise to the onset of the Lorenz-type attractor. It discloses a universal unfolding pattern in the case of systems of autonomous ordinary differential equations possessing two-fold symmetry or "Z2-systems" with the characteristic separatrix butterfly. The second system is the classic Lorenz model of 1963, originated in fluid mechanics.

Hero's journey in bifurcation diagram

NASA Astrophysics Data System (ADS)

Monteiro, L. H. A.; Mustaro, P. N.

2012-06-01

The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films.

Dedicated bifurcation stents

PubMed Central

Pillai, Ajith Ananthakrishna; Jayaraman, Balachander

2012-01-01

Bifurcation percutaneous coronary intervention (PCI) is still a difficult call for the interventionist despite advancements in the instrumentation, technical skill and the imaging modalities. With major cardiac events relate to the side-branch (SB) compromise, the concept and practice of dedicated bifurcation stents seems exciting. Several designs of such dedicated stents are currently undergoing trials. This novel concept and pristine technology offers new hope notwithstanding the fact that we need to go a long way in widespread acceptance and practice of these gadgets. Some of these designs even though looks enterprising, the mere complex delivering technique and the demanding knowledge of the exact coronary anatomy makes their routine use challenging. PMID:22572498

Bifurcation analysis of a discrete-time ratio-dependent predator-prey model with Allee Effect

NASA Astrophysics Data System (ADS)

Cheng, Lifang; Cao, Hongjun

2016-09-01

A discrete-time predator-prey model with Allee effect is investigated in this paper. We consider the strong and the weak Allee effect (the population growth rate is negative and positive at low population density, respectively). From the stability analysis and the bifurcation diagrams, we get that the model with Allee effect (strong or weak) growth function and the model with logistic growth function have somewhat similar bifurcation structures. If the predator growth rate is smaller than its death rate, two species cannot coexist due to having no interior fixed points. When the predator growth rate is greater than its death rate and other parameters are fixed, the model can have two interior fixed points. One is always unstable, and the stability of the other is determined by the integral step size, which decides the species coexistence or not in some extent. If we increase the value of the integral step size, then the bifurcated period doubled orbits or invariant circle orbits may arise. So the numbers of the prey and the predator deviate from one stable state and then circulate along the period orbits or quasi-period orbits. When the integral step size is increased to a critical value, chaotic orbits may appear with many uncertain period-windows, which means that the numbers of prey and predator will be chaotic. In terms of bifurcation diagrams and phase portraits, we know that the complexity degree of the model with strong Allee effect decreases, which is related to the fact that the persistence of species can be determined by the initial species densities.

Extreme multiplicity in cylindrical Rayleigh-Bénard convection. II. Bifurcation diagram and symmetry classification

NASA Astrophysics Data System (ADS)

Borońska, Katarzyna; Tuckerman, Laurette S.

2010-03-01

A large number of flows with distinctive patterns have been observed in experiments and simulations of Rayleigh-Bénard convection in a water-filled cylinder whose radius is twice the height. We have adapted a time-dependent pseudospectral code, first, to carry out Newton’s method and branch continuation and, second, to carry out the exponential power method and Arnoldi iteration to calculate leading eigenpairs and determine the stability of the steady states. The resulting bifurcation diagram represents a compromise between the tendency in the bulk toward parallel rolls and the requirement imposed by the boundary conditions that primary bifurcations be toward states whose azimuthal dependence is trigonometric. The diagram contains 17 branches of stable and unstable steady states. These can be classified geometrically as roll states containing two, three, and four rolls; axisymmetric patterns with one or two tori; threefold-symmetric patterns called Mercedes, Mitsubishi, marigold, and cloverleaf; trigonometric patterns called dipole and pizza; and less symmetric patterns called CO and asymmetric three rolls. The convective branches are connected to the conductive state and to each other by 16 primary and secondary pitchfork bifurcations and turning points. In order to better understand this complicated bifurcation diagram, we have partitioned it according to azimuthal symmetry. We have been able to determine the bifurcation-theoretic origin from the conductive state of all the branches observed at high Rayleigh number.

Identification of a mutation that is associated with the saddle tan and black-and-tan phenotypes in Basset Hounds and Pembroke Welsh Corgis.

PubMed

Dreger, Dayna L; Parker, Heidi G; Ostrander, Elaine A; Schmutz, Sheila M

2013-01-01

The causative mutation for the black-and-tan (a (t) ) phenotype in dogs was previously shown to be a SINE insertion in the 5' region of Agouti Signaling Protein (ASIP). Dogs with the black-and-tan phenotype, as well as dogs with the saddle tan phenotype, genotype as a (t) /_ at this locus. We have identified a 16-bp duplication (g.1875_1890dupCCCCAGGTCAGAGTTT) in an intron of hnRNP associated with lethal yellow (RALY), which segregates with the black-and-tan phenotype in a group of 99 saddle tan and black-and-tan Basset Hounds and Pembroke Welsh Corgis. In these breeds, all dogs with the saddle tan phenotype had RALY genotypes of +/+ or +/dup, whereas dogs with the black-and-tan phenotype were homozygous for the duplication. The presence of an a (y) /_ fawn or e/e red genotype is epistatic to the +/_ saddle tan genotype. Genotypes from 10 wolves and 1 coyote indicated that the saddle tan (+) allele is the ancestral allele, suggesting that black-and-tan is a modification of saddle tan. An additional 95 dogs from breeds that never have the saddle tan phenotype have all three of the possible RALY genotypes. We suggest that a multi-gene interaction involving ASIP, RALY, MC1R, DEFB103, and a yet-unidentified modifier gene is required for expression of saddle tan.

Plastic buckling. [post-bifurcation and imperfection sensitivity

NASA Technical Reports Server (NTRS)

Hutchinson, J. W.

1974-01-01

The present article is concerned mainly with the post-bifurcation and imperfection-sensitivity aspects of plastic buckling. A simple two-degree-of-freedom model is used to introduce post-bifurcation behavior and a second model illustrates features of the behavior of continuous solids and structures. Hill's bifurcation criterion for a class of three-dimensional solids is applied to the Donnell-Mushtari-Vlasov (DMV) theory of plates and shells. A general treatment of the initial post-bifurcation behavior of plates and shells is given within the context of the DMV theory. This is illustrated by problems involving columns and circular plates under radial compression. Numerical results are given for a column under axial compression, a circular plate under radial compression, and spherical and cylindrical shells.

Double versus single stenting for coronary bifurcation lesions: a meta-analysis.

PubMed

Katritsis, Demosthenes G; Siontis, George C M; Ioannidis, John P A

2009-10-01

Several trials have addressed whether bifurcation lesions require stenting of both the main vessel and side branch, but uncertainty remains on the benefits of such double versus single stenting of the main vessel only. We have conducted a meta-analysis of randomized trials including patients with coronary bifurcation lesions who were randomly selected to undergo percutaneous coronary intervention by either double or single stenting. Six studies (n=1642 patients) were eligible. There was increased risk of myocardial infarction with double stenting (risk ratio, 1.78; P=0.001 by fixed effects; risk ratio, 1.49 with Bayesian meta-analysis). The summary point estimate suggested also an increased risk of stent thrombosis with double stenting, but the difference was not nominally significant given the sparse data (risk ratio, 1.85; P=0.19). No obvious difference was seen for death (risk ratio, 0.81; P=0.66) and target lesion revascularization (risk ratio, 1.09; P=0.67). Stenting of both the main vessel and side branch in bifurcation lesions may increase myocardial infarction and stent thrombosis risk compared with stenting of the main vessel only.

Surface plasma source with saddle antenna radio frequency plasma generator.

PubMed

Dudnikov, V; Johnson, R P; Murray, S; Pennisi, T; Piller, C; Santana, M; Stockli, M; Welton, R

2012-02-01

A prototype RF H(-) surface plasma source (SPS) with saddle (SA) RF antenna is developed which will provide better power efficiency for high pulsed and average current, higher brightness with longer lifetime and higher reliability. Several versions of new plasma generators with small AlN discharge chambers and different antennas and magnetic field configurations were tested in the plasma source test stand. A prototype SA SPS was installed in the Spallation Neutron Source (SNS) ion source test stand with a larger, normal-sized SNS AlN chamber that achieved unanalyzed peak currents of up to 67 mA with an apparent efficiency up to 1.6 mA∕kW. Control experiments with H(-) beam produced by SNS SPS with internal and external antennas were conducted. A new version of the RF triggering plasma gun has been designed. A saddle antenna SPS with water cooling is fabricated for high duty factor testing.

Comment on 'Supersymmetry, PT-symmetry and spectral bifurcation'

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

Bagchi, B., E-mail: bbagchi123@rediffmail.com; Quesne, C., E-mail: cquesne@ulb.ac.be

2011-02-15

We demonstrate that the recent paper by Abhinav and Panigrahi entitled 'Supersymmetry, PT-symmetry and spectral bifurcation' [K. Abhinav, P.K. Panigrahi, Ann. Phys. 325 (2010) 1198], which considers two different types of superpotentials for the PT-symmetric complexified Scarf II potential, fails to take into account the invariance under the exchange of its coupling parameters. As a result, they miss the important point that for unbroken PT-symmetry this potential indeed has two series of real energy eigenvalues, to which one can associate two different superpotentials. This fact was first pointed out by the present authors during the study of complex potentials havingmore » a complex sl(2) potential algebra.« less

Bifurcation and Firing Patterns of the Pancreatic β-Cell

NASA Astrophysics Data System (ADS)

Wang, Jing; Liu, Shenquan; Liu, Xuanliang; Zeng, Yanjun

Using a model of individual isolated pancreatic β-cells, we investigated bifurcation diagrams of interspike intervals (ISIs) and largest Lyapunov exponents (LLE), which clearly demonstrated a wide range of transitions between different firing patterns. The numerical simulation results revealed the effect of different time constants and ion channels on the neuronal discharge rhythm. Furthermore, an individual cell exhibited tonic spiking, square-wave bursting, and tapered bursting. Additionally, several bifurcation phenomena can be observed in this paper, such as period-doubling, period-adding, inverse period-doubling and inverse period-adding scenarios. In addition, we researched the mechanisms underlying two kinds of bursting (tapered and square-wave bursting) by use of fast-slow dynamics analysis. Finally, we analyzed the codimension-two bifurcation of the fast subsystem and studied cusp bifurcation, generalized Hopf (or Bautin) bifurcation and Bogdanov-Takens bifurcation.

Phase slips in oscillatory hair bundles.

PubMed

Roongthumskul, Yuttana; Shlomovitz, Roie; Bruinsma, Robijn; Bozovic, Dolores

2013-04-05

Hair cells of the inner ear contain an active amplifier that allows them to detect extremely weak signals. As one of the manifestations of an active process, spontaneous oscillations arise in fluid immersed hair bundles of in vitro preparations of selected auditory and vestibular organs. We measure the phase-locking dynamics of oscillatory bundles exposed to low-amplitude sinusoidal signals, a transition that can be described by a saddle-node bifurcation on an invariant circle. The transition is characterized by the occurrence of phase slips, at a rate that is dependent on the amplitude and detuning of the applied drive. The resultant staircase structure in the phase of the oscillation can be described by the stochastic Adler equation, which reproduces the statistics of phase slip production.

Conditions and Linear Stability Analysis at the Transition to Synchronization of Three Coupled Phase Oscillators in a Ring

NASA Astrophysics Data System (ADS)

El-Nashar, Hassan F.

2017-06-01

We consider a system of three nonidentical coupled phase oscillators in a ring topology. We explore the conditions that must be satisfied in order to obtain the phases at the transition to a synchrony state. These conditions lead to the correct mathematical expressions of phases that aid to find a simple analytic formula for critical coupling when the oscillators transit to a synchronization state having a common frequency value. The finding of a simple expression for the critical coupling allows us to perform a linear stability analysis at the transition to the synchronization stage. The obtained analytic forms of the eigenvalues show that the three coupled phase oscillators with periodic boundary conditions transit to a synchrony state when a saddle-node bifurcation occurs.

An equation-free approach to agent-based computation: Bifurcation analysis and control of stationary states

NASA Astrophysics Data System (ADS)

Siettos, C. I.; Gear, C. W.; Kevrekidis, I. G.

2012-08-01

We show how the equation-free approach can be exploited to enable agent-based simulators to perform system-level computations such as bifurcation, stability analysis and controller design. We illustrate these tasks through an event-driven agent-based model describing the dynamic behaviour of many interacting investors in the presence of mimesis. Using short bursts of appropriately initialized runs of the detailed, agent-based simulator, we construct the coarse-grained bifurcation diagram of the (expected) density of agents and investigate the stability of its multiple solution branches. When the mimetic coupling between agents becomes strong enough, the stable stationary state loses its stability at a coarse turning point bifurcation. We also demonstrate how the framework can be used to design a wash-out dynamic controller that stabilizes open-loop unstable stationary states even under model uncertainty.

View southwest of concrete saddles and flood walls for demolished ...

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

View southwest of concrete saddles and flood walls for demolished 12-foot pipeline, on west side of West Canada Creek - Trenton Falls Hydroelectric Station, On west bank of West Canada Creek, along Trenton Fally Road, 1.25 miles north of New York Route 28, Trenton Falls, Oneida County, NY

Self-pulsations and excitability in optically injected quantum-dot lasers: Impact of the excited states and spontaneous emission noise

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

Olejniczak, Lukasz; SUPELEC, OPTEL, and LMOPS EA 4423; Panajotov, Krassimir

2010-08-15

We study the dynamics of an optically injected quantum-dot laser accounting for excited states. Mapping of the bifurcations in the plane frequency detuning vs. injection strength shows that the relaxation rate scales the regions of locking and single- and double-period solutions, while the capture rate has a minor effect. Within the regions of time-periodic solutions, close to the saddle-node bifurcation boundary, we identify subregions where the output signal resembles excitable pulses as a result of the bottleneck phenomenon. We show that such emission is determined mainly by fluctuations in the occupation of the excited states. The interpulse time follows anmore » inverse square root scaling law as a function of the detuning. In a deterministic system the pulses are periodic regardless of the detuning, but in the presence of noise, close to the locking region, the interpulse time follows a positively skewed normal distribution. For a fixed frequency detuning, increasing the noise strength can shift the mean of the interpulse time distribution and make the pulsations more periodic.« less

Electron Bifurcation: Thermodynamics and Kinetics of Two-Electron Brokering in Biological Redox Chemistry.

PubMed

Zhang, Peng; Yuly, Jonathon L; Lubner, Carolyn E; Mulder, David W; King, Paul W; Peters, John W; Beratan, David N

2017-09-19

processes of their own. We dissect the thermodynamics and kinetics of electron bifurcation in Nfn and find that the key features of electron bifurcation are (1) spatially separated transfer pathways that diverge from a two-electron donor, (2) one thermodynamically uphill and one downhill redox pathway, with a large negative shift in the donor's reduction potential after departure of the first electron, and (3) electron tunneling and activation factors that enable bifurcation, producing a 1:1 partitioning of electrons onto the two pathways. Electron bifurcation is found in the CO 2 reducing pathways of methanogenic archaea, in the hydrogen pathways of hydrogenases, in the nitrogen fixing pathway of Fix, and in the mitochondrial charge transfer chain of complex III, cytochrome bc 1 . While crossed potentials may offer the biological advantage of producing tightly regulated high energy reactive species, neither kinetic nor thermodynamic considerations mandate crossed potentials to generate successful electron bifurcation. Taken together, the theoretical framework established here, focusing on the underpinning electron tunneling barriers and activation free energies, explains the logic of electron bifurcation that enables energy conversion and conservation in Nfn, points toward bioinspired schemes to execute multielectron redox chemistry, and establishes a roadmap for examining novel electron bifurcation networks in nature.

Congruent Bifurcation Angles in River Delta and Tributary Channel Networks

NASA Astrophysics Data System (ADS)

Coffey, Thomas S.; Shaw, John B.

2017-11-01

We show that distributary channels on river deltas exhibit a mean bifurcation angle that can be understood using theory developed in tributary channel networks. In certain cases, tributary network bifurcation geometries have been demonstrated to be controlled by diffusive groundwater flow feeding incipient bifurcations, producing a characteristic angle of 72∘. We measured 25 unique distributary bifurcations in an experimental delta and 197 bifurcations in 10 natural deltas, yielding a mean angle of 70.4∘±2.6∘ (95% confidence interval) for field-scale deltas and a mean angle of 68.3∘±8.7∘ for the experimental delta, consistent with this theoretical prediction. The bifurcation angle holds for small scales relative to channel width length scales. Furthermore, the experimental data show that the mean angle is 72∘ immediately after bifurcation initiation and remains relatively constant over significant time scales. Although distributary networks do not mirror tributary networks perfectly, the similar control and expression of bifurcation angles suggests that additional morphodynamic insight may be gained from further comparative study.

High incidence of post-dural puncture headache in patients with spinal saddle block induced with Quincke needles for anorectal surgery: a randomised clinical trial.

PubMed

Schmittner, Marc D; Terboven, Tom; Dluzak, Michael; Janke, Andrea; Limmer, Marc E; Weiss, Christel; Bussen, Dieter G; Burmeister, Marc A; Beck, Grietje C

2010-06-01

Spinal saddle block represents nearly the ideal anaesthesia technique for anorectal surgery. Post-dural puncture headache (PDPH) is a dreaded complication but can be decreased by the use of non-cutting spinal needles to rates less than 1%. Though, cutting Quincke type needles are still widely used for economic reasons, leading to a higher rate of PDPH. We performed this study to demonstrate a reduction of PDPH by the use of very small 29-G compared with commonly used 25-G Quincke type spinal needles. Two hundred sixteen adult patients (male/female, 19-83 years, ASA status I-III) were randomised 1:1 to groups, in which either a 25-G or a 29-G Quincke type spinal needle was used for a spinal saddle block. The incidence of PDPH was assessed during 1 week after surgery. Thirty-nine of 216 patients developed PDPH but there was no difference between the two needle sizes (25-G, n = 18/106 vs. 29-G, n = 21/110, p = 0.6870). Women suffered significantly more from PDPH than men (23/86 vs. 16/130, p = 0.0069). Ambulatory patients had a later onset of PDPH than in-patients (24 h [0.5-72] vs. 2 h [0.2-96], p = 0.0002) and the headache was more severe in these patients (NRS 7 [2-10] vs. NRS 3 [1-8], p = 0.0009). The use of 29-G compared with 25-G Quincke needles led to no reduction of PDPH and is considerably higher compared with data from pencil-point needles. The use of non-cutting or pencil-point spinal needles should become the standard for performing spinal saddle block.

Secure message authentication system for node to node network

NASA Astrophysics Data System (ADS)

Sindhu, R.; Vanitha, M. M.; Norman, J.

2017-10-01

The Message verification remains some of the best actual methods for prevent the illegal and dis honored communication after presence progressed to WSNs (Wireless Sensor Networks). Intend for this purpose, several message verification systems must stand established, created on both symmetric key cryptography otherwise public key cryptosystems. Best of them will have some limits for great computational then statement above in count of deficiency of climb ability then flexibility in node settlement occurrence. In a polynomial based system was newly presented for these problems. Though, this system then situations delay will must the dimness of integral limitation firm in the point of polynomial: once the amount of message transferred remains the greater than the limitation then the opponent will completely improve the polynomial approaches. This paper suggests using ECC (Elliptic Curve Cryptography). Though using the node verification the technique in this paper permits some nodes to transfer a limitless amount of messages lacking misery in the limit problem. This system will have the message cause secrecy. Equally theoretic study then model effects show our planned system will be effective than the polynomial based method in positions of calculation then statement above in privacy points though message basis privacy.

Coexistence of multiple bifurcation modes in memristive diode-bridge-based canonical Chua's circuit

NASA Astrophysics Data System (ADS)

Bao, Bocheng; Xu, Li; Wu, Zhimin; Chen, Mo; Wu, Huagan

2018-07-01

Based on a memristive diode bridge cascaded with series resistor and inductor filter, a modified memristive canonical Chua's circuit is presented in this paper. With the modelling of the memristive circuit, a normalised system model is built. Stability analyses of the equilibrium points are performed and bifurcation behaviours are investigated by numerical simulations and hardware experiments. Most extraordinary in the memristive circuit is that within a parameter region, coexisting phenomenon of multiple bifurcation modes is emerged under six sets of different initial values, resulting in the coexistence of four sets of topologically different and disconnected attractors. These coexisting attractors are easily captured by repeatedly switching on and off the circuit power supplies, which well verify the numerical simulations.

Migrated hydrocarbons in exposure of Maastrichtian nonmarine strata near Saddle Mountain, lower Cook Inlet, Alaska

USGS Publications Warehouse

LePain, D.L.; Lillis, P.G.; Helmold, K.P.; Stanley, R.G.

2012-01-01

Magoon and others (1980) described an 83-meter- (272-foot-) thick succession of Maastrichtian (Upper Cretaceous) conglomerate, sandstone, mudstone, and coal exposed on the south side of an unnamed drainage, approximately 3 kilometers (1.8 miles) east of Saddle Mountain in lower Cook Inlet (figs. 1 and 2). The initial significance of this exposure was that it was the first reported occurrence of nonmarine rocks of this age in outcrop in lower Cook Inlet, which helped constrain the Late Cretaceous paleogeography of the area and provided important information on the composition of latest Mesozoic sandstones in the basin. The Saddle Mountain section is thought to be an outcrop analog for Upper Cretaceous nonmarine strata penetrated in the OCS Y-0097 #1 (Raven) well, located approximately 40 kilometers (25 miles) to the south–southeast in Federal waters (fig. 1). Atlantic Richfield Company (ARCO) drilled the Raven well in 1980 and encountered oil-stained rocks and moveable liquid hydrocarbons between the depths of 1,760 and 3,700 feet. Completion reports on file with the Bureau of Ocean Energy Management (BOEM; formerly Bureau of Ocean Energy Management, Regulation and Enforcement, and prior to 2010, U.S. Minerals Management Service) either show flow rates of zero or do not mention flow rates. A fluid analysis report on file with BOEM suggests that a wireline tool sampled some oil beneath a 2,010-foot diesel cushion during the fl ow test of the 3,145–3,175 foot interval, but the recorded fl ow rate was still zero (Kirk Sherwood, written commun., January 9, 2012). Further delineation and evaluation of the apparent accumulation was never performed and the well was plugged and abandoned. As part of a 5-year comprehensive evaluation of the geology and petroleum systems of the Cook Inlet forearc basin, the Alaska Division of Geological & Geophysical Surveys obtained a research permit from the National Park Service to access the relatively poorly understood ‘Saddle

Back in the saddle: large-deviation statistics of the cosmic log-density field

NASA Astrophysics Data System (ADS)

Uhlemann, C.; Codis, S.; Pichon, C.; Bernardeau, F.; Reimberg, P.

2016-08-01

We present a first principle approach to obtain analytical predictions for spherically averaged cosmic densities in the mildly non-linear regime that go well beyond what is usually achieved by standard perturbation theory. A large deviation principle allows us to compute the leading order cumulants of average densities in concentric cells. In this symmetry, the spherical collapse model leads to cumulant generating functions that are robust for finite variances and free of critical points when logarithmic density transformations are implemented. They yield in turn accurate density probability distribution functions (PDFs) from a straightforward saddle-point approximation valid for all density values. Based on this easy-to-implement modification, explicit analytic formulas for the evaluation of the one- and two-cell PDF are provided. The theoretical predictions obtained for the PDFs are accurate to a few per cent compared to the numerical integration, regardless of the density under consideration and in excellent agreement with N-body simulations for a wide range of densities. This formalism should prove valuable for accurately probing the quasi-linear scales of low-redshift surveys for arbitrary primordial power spectra.

Dynamics of bow-tie shaped bursting: Forced pendulum with dynamic feedback.

PubMed

Hongray, Thotreithem; Balakrishnan, Janaki

2016-12-01

A detailed study is performed on the parameter space of the mechanical system of a driven pendulum with damping and constant torque under feedback control. We report an interesting bow-tie shaped bursting oscillatory behaviour, which is exhibited for small driving frequencies, in a certain parameter regime, which has not been reported earlier in this forced system with dynamic feedback. We show that the bursting oscillations are caused because of a transition of the quiescent state to the spiking state by a saddle-focus bifurcation, and because of another saddle-focus bifurcation, which leads to cessation of spiking, bringing the system back to the quiescent state. The resting period between two successive bursts (T rest ) is estimated analytically.

Cross-Disciplinary Analysis of Lymph Node Classification in Lung Cancer on CT Scanning.

PubMed

El-Sherief, Ahmed H; Lau, Charles T; Obuchowski, Nancy A; Mehta, Atul C; Rice, Thomas W; Blackstone, Eugene H

2017-04-01

Accurate and consistent regional lymph node classification is an important element in the staging and multidisciplinary management of lung cancer. Regional lymph node definition sets-lymph node maps-have been created to standardize regional lymph node classification. In 2009, the International Association for the Study of Lung Cancer (IASLC) introduced a lymph node map to supersede all preexisting lymph node maps. Our aim was to study if and how lung cancer specialists apply the IASLC lymph node map when classifying thoracic lymph nodes encountered on CT scans during lung cancer staging. From April 2013 through July 2013, invitations were distributed to all members of the Fleischner Society, Society of Thoracic Radiology, General Thoracic Surgical Club, and the American Association of Bronchology and Interventional Pulmonology to participate in an anonymous online image-based and text-based 20-question survey regarding lymph node classification for lung cancer staging on CT imaging. Three hundred thirty-seven people responded (approximately 25% participation). Respondents consisted of self-reported thoracic radiologists (n = 158), thoracic surgeons (n = 102), and pulmonologists who perform endobronchial ultrasonography (n = 77). Half of the respondents (50%; 95% CI, 44%-55%) reported using the IASLC lymph node map in daily practice, with no significant differences between subspecialties. A disparity was observed between the IASLC definition sets and their interpretation and application on CT scans, in particular for lymph nodes near the thoracic inlet, anterior to the trachea, anterior to the tracheal bifurcation, near the ligamentum arteriosum, between the bronchus intermedius and esophagus, in the internal mammary space, and adjacent to the heart. Use of older lymph node maps and inconsistencies in interpretation and application of definitions in the IASLC lymph node map may potentially lead to misclassification of stage and suboptimal management of lung

Travelling waves and their bifurcations in the Lorenz-96 model

NASA Astrophysics Data System (ADS)

van Kekem, Dirk L.; Sterk, Alef E.

2018-03-01

In this paper we study the dynamics of the monoscale Lorenz-96 model using both analytical and numerical means. The bifurcations for positive forcing parameter F are investigated. The main analytical result is the existence of Hopf or Hopf-Hopf bifurcations in any dimension n ≥ 4. Exploiting the circulant structure of the Jacobian matrix enables us to reduce the first Lyapunov coefficient to an explicit formula from which it can be determined when the Hopf bifurcation is sub- or supercritical. The first Hopf bifurcation for F > 0 is always supercritical and the periodic orbit born at this bifurcation has the physical interpretation of a travelling wave. Furthermore, by unfolding the codimension two Hopf-Hopf bifurcation it is shown to act as an organising centre, explaining dynamics such as quasi-periodic attractors and multistability, which are observed in the original Lorenz-96 model. Finally, the region of parameter values beyond the first Hopf bifurcation value is investigated numerically and routes to chaos are described using bifurcation diagrams and Lyapunov exponents. The observed routes to chaos are various but without clear pattern as n → ∞.

Big Bang Bifurcation Analysis and Allee Effect in Generic Growth Functions

NASA Astrophysics Data System (ADS)

Leonel Rocha, J.; Taha, Abdel-Kaddous; Fournier-Prunaret, D.

2016-06-01

The main purpose of this work is to study the dynamics and bifurcation properties of generic growth functions, which are defined by the population size functions of the generic growth equation. This family of unimodal maps naturally incorporates a principal focus of ecological and biological research: the Allee effect. The analysis of this kind of extinction phenomenon allows to identify a class of Allee’s functions and characterize the corresponding Allee’s effect region and Allee’s bifurcation curve. The bifurcation analysis is founded on the performance of fold and flip bifurcations. The dynamical behavior is rich with abundant complex bifurcation structures, the big bang bifurcations of the so-called “box-within-a-box” fractal type being the most outstanding. Moreover, these bifurcation cascades converge to different big bang bifurcation curves with distinct kinds of boxes, where for the corresponding parameter values several attractors are associated. To the best of our knowledge, these results represent an original contribution to clarify the big bang bifurcation analysis of continuous 1D maps.

Improvements in floating point addition/subtraction operations

DOEpatents

Farmwald, P.M.

1984-02-24

Apparatus is described for decreasing the latency time associated with floating point addition and subtraction in a computer, using a novel bifurcated, pre-normalization/post-normalization approach that distinguishes between differences of floating point exponents.

Predicting bifurcation angle effect on blood flow in the microvasculature.

PubMed

Yang, Jiho; Pak, Y Eugene; Lee, Tae-Rin

2016-11-01

Since blood viscosity is a basic parameter for understanding hemodynamics in human physiology, great amount of research has been done in order to accurately predict this highly non-Newtonian flow property. However, previous works lacked in consideration of hemodynamic changes induced by heterogeneous vessel networks. In this paper, the effect of bifurcation on hemodynamics in a microvasculature is quantitatively predicted. The flow resistance in a single bifurcation microvessel was calculated by combining a new simple mathematical model with 3-dimensional flow simulation for varying bifurcation angles under physiological flow conditions. Interestingly, the results indicate that flow resistance induced by vessel bifurcation holds a constant value of approximately 0.44 over the whole single bifurcation model below diameter of 60μm regardless of geometric parameters including bifurcation angle. Flow solutions computed from this new model showed substantial decrement in flow velocity relative to other mathematical models, which do not include vessel bifurcation effects, while pressure remained the same. Furthermore, when applying the bifurcation angle effect to the entire microvascular network, the simulation results gave better agreements with recent in vivo experimental measurements. This finding suggests a new paradigm in microvascular blood flow properties, that vessel bifurcation itself, regardless of its angle, holds considerable influence on blood viscosity, and this phenomenon will help to develop new predictive tools in microvascular research. Copyright © 2016 Elsevier Inc. All rights reserved.

Bifurcation-based approach reveals synergism and optimal combinatorial perturbation.

PubMed

Liu, Yanwei; Li, Shanshan; Liu, Zengrong; Wang, Ruiqi

2016-06-01

Cells accomplish the process of fate decisions and form terminal lineages through a series of binary choices in which cells switch stable states from one branch to another as the interacting strengths of regulatory factors continuously vary. Various combinatorial effects may occur because almost all regulatory processes are managed in a combinatorial fashion. Combinatorial regulation is crucial for cell fate decisions because it may effectively integrate many different signaling pathways to meet the higher regulation demand during cell development. However, whether the contribution of combinatorial regulation to the state transition is better than that of a single one and if so, what the optimal combination strategy is, seem to be significant issue from the point of view of both biology and mathematics. Using the approaches of combinatorial perturbations and bifurcation analysis, we provide a general framework for the quantitative analysis of synergism in molecular networks. Different from the known methods, the bifurcation-based approach depends only on stable state responses to stimuli because the state transition induced by combinatorial perturbations occurs between stable states. More importantly, an optimal combinatorial perturbation strategy can be determined by investigating the relationship between the bifurcation curve of a synergistic perturbation pair and the level set of a specific objective function. The approach is applied to two models, i.e., a theoretical multistable decision model and a biologically realistic CREB model, to show its validity, although the approach holds for a general class of biological systems.

Defining Electron Bifurcation in the Electron-Transferring Flavoprotein Family.

PubMed

Garcia Costas, Amaya M; Poudel, Saroj; Miller, Anne-Frances; Schut, Gerrit J; Ledbetter, Rhesa N; Fixen, Kathryn R; Seefeldt, Lance C; Adams, Michael W W; Harwood, Caroline S; Boyd, Eric S; Peters, John W

2017-11-01

Electron bifurcation is the coupling of exergonic and endergonic redox reactions to simultaneously generate (or utilize) low- and high-potential electrons. It is the third recognized form of energy conservation in biology and was recently described for select electron-transferring flavoproteins (Etfs). Etfs are flavin-containing heterodimers best known for donating electrons derived from fatty acid and amino acid oxidation to an electron transfer respiratory chain via Etf-quinone oxidoreductase. Canonical examples contain a flavin adenine dinucleotide (FAD) that is involved in electron transfer, as well as a non-redox-active AMP. However, Etfs demonstrated to bifurcate electrons contain a second FAD in place of the AMP. To expand our understanding of the functional variety and metabolic significance of Etfs and to identify amino acid sequence motifs that potentially enable electron bifurcation, we compiled 1,314 Etf protein sequences from genome sequence databases and subjected them to informatic and structural analyses. Etfs were identified in diverse archaea and bacteria, and they clustered into five distinct well-supported groups, based on their amino acid sequences. Gene neighborhood analyses indicated that these Etf group designations largely correspond to putative differences in functionality. Etfs with the demonstrated ability to bifurcate were found to form one group, suggesting that distinct conserved amino acid sequence motifs enable this capability. Indeed, structural modeling and sequence alignments revealed that identifying residues occur in the NADH- and FAD-binding regions of bifurcating Etfs. Collectively, a new classification scheme for Etf proteins that delineates putative bifurcating versus nonbifurcating members is presented and suggests that Etf-mediated bifurcation is associated with surprisingly diverse enzymes. IMPORTANCE Electron bifurcation has recently been recognized as an electron transfer mechanism used by microorganisms to maximize

Defining Electron Bifurcation in the Electron-Transferring Flavoprotein Family

PubMed Central

Garcia Costas, Amaya M.; Poudel, Saroj; Miller, Anne-Frances; Schut, Gerrit J.; Ledbetter, Rhesa N.; Seefeldt, Lance C.; Adams, Michael W. W.

2017-01-01

ABSTRACT Electron bifurcation is the coupling of exergonic and endergonic redox reactions to simultaneously generate (or utilize) low- and high-potential electrons. It is the third recognized form of energy conservation in biology and was recently described for select electron-transferring flavoproteins (Etfs). Etfs are flavin-containing heterodimers best known for donating electrons derived from fatty acid and amino acid oxidation to an electron transfer respiratory chain via Etf-quinone oxidoreductase. Canonical examples contain a flavin adenine dinucleotide (FAD) that is involved in electron transfer, as well as a non-redox-active AMP. However, Etfs demonstrated to bifurcate electrons contain a second FAD in place of the AMP. To expand our understanding of the functional variety and metabolic significance of Etfs and to identify amino acid sequence motifs that potentially enable electron bifurcation, we compiled 1,314 Etf protein sequences from genome sequence databases and subjected them to informatic and structural analyses. Etfs were identified in diverse archaea and bacteria, and they clustered into five distinct well-supported groups, based on their amino acid sequences. Gene neighborhood analyses indicated that these Etf group designations largely correspond to putative differences in functionality. Etfs with the demonstrated ability to bifurcate were found to form one group, suggesting that distinct conserved amino acid sequence motifs enable this capability. Indeed, structural modeling and sequence alignments revealed that identifying residues occur in the NADH- and FAD-binding regions of bifurcating Etfs. Collectively, a new classification scheme for Etf proteins that delineates putative bifurcating versus nonbifurcating members is presented and suggests that Etf-mediated bifurcation is associated with surprisingly diverse enzymes. IMPORTANCE Electron bifurcation has recently been recognized as an electron transfer mechanism used by microorganisms to

Dynamics of self-sustained asynchronous-irregular activity in random networks of spiking neurons with strong synapses

PubMed Central

Kriener, Birgit; Enger, Håkon; Tetzlaff, Tom; Plesser, Hans E.; Gewaltig, Marc-Oliver; Einevoll, Gaute T.

2014-01-01

Random networks of integrate-and-fire neurons with strong current-based synapses can, unlike previously believed, assume stable states of sustained asynchronous and irregular firing, even without external random background or pacemaker neurons. We analyze the mechanisms underlying the emergence, lifetime and irregularity of such self-sustained activity states. We first demonstrate how the competition between the mean and the variance of the synaptic input leads to a non-monotonic firing-rate transfer in the network. Thus, by increasing the synaptic coupling strength, the system can become bistable: In addition to the quiescent state, a second stable fixed-point at moderate firing rates can emerge by a saddle-node bifurcation. Inherently generated fluctuations of the population firing rate around this non-trivial fixed-point can trigger transitions into the quiescent state. Hence, the trade-off between the magnitude of the population-rate fluctuations and the size of the basin of attraction of the non-trivial rate fixed-point determines the onset and the lifetime of self-sustained activity states. During self-sustained activity, individual neuronal activity is moreover highly irregular, switching between long periods of low firing rate to short burst-like states. We show that this is an effect of the strong synaptic weights and the finite time constant of synaptic and neuronal integration, and can actually serve to stabilize the self-sustained state. PMID:25400575

Dynamics of self-sustained asynchronous-irregular activity in random networks of spiking neurons with strong synapses.

PubMed

Kriener, Birgit; Enger, Håkon; Tetzlaff, Tom; Plesser, Hans E; Gewaltig, Marc-Oliver; Einevoll, Gaute T

2014-01-01

Random networks of integrate-and-fire neurons with strong current-based synapses can, unlike previously believed, assume stable states of sustained asynchronous and irregular firing, even without external random background or pacemaker neurons. We analyze the mechanisms underlying the emergence, lifetime and irregularity of such self-sustained activity states. We first demonstrate how the competition between the mean and the variance of the synaptic input leads to a non-monotonic firing-rate transfer in the network. Thus, by increasing the synaptic coupling strength, the system can become bistable: In addition to the quiescent state, a second stable fixed-point at moderate firing rates can emerge by a saddle-node bifurcation. Inherently generated fluctuations of the population firing rate around this non-trivial fixed-point can trigger transitions into the quiescent state. Hence, the trade-off between the magnitude of the population-rate fluctuations and the size of the basin of attraction of the non-trivial rate fixed-point determines the onset and the lifetime of self-sustained activity states. During self-sustained activity, individual neuronal activity is moreover highly irregular, switching between long periods of low firing rate to short burst-like states. We show that this is an effect of the strong synaptic weights and the finite time constant of synaptic and neuronal integration, and can actually serve to stabilize the self-sustained state.

Evaluation of the impact of carotid artery bifurcation angle on hemodynamics by use of computational fluid dynamics: a simulation and volunteer study.

PubMed

Saho, Tatsunori; Onishi, Hideo

2016-07-01

In this study, we evaluated the hemodynamics of carotid artery bifurcation with various geometries using simulated and volunteer models based on magnetic resonance imaging (MRI). Computational fluid dynamics (CFD) was analyzed by use of OpenFOAM. The velocity distribution, streamline, and wall shear stress (WSS) were evaluated in a simulated model with known bifurcation angles (30°, 40°, 50°, 60°, derived from patients' data) and in three-dimensional (3D) healthy volunteer models. Separated flow was observed at the outer side of the bifurcation, and large bifurcation models represented upstream transfer of the point. Local WSS values at the outer bifurcation [both simulated (<30 Pa) and volunteer (<50 Pa) models] were lower than those in the inner region (>100 Pa). The bifurcation angle had a significant negative correlation with the WSS value (p<0.05). The results of this study show that the carotid artery bifurcation angle is related to the WSS value. This suggests that hemodynamic stress can be estimated based on the carotid artery geometry. The construction of a clinical database for estimation of developing atherosclerosis is warranted.

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

NASA Astrophysics Data System (ADS)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.

PubMed

Goto, Hayato

2016-02-22

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

PubMed Central

Goto, Hayato

2016-01-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

NASA Astrophysics Data System (ADS)

Goto, Hayato

2016-02-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Codimension-Two Bifurcation Analysis in DC Microgrids Under Droop Control

NASA Astrophysics Data System (ADS)

Lenz, Eduardo; Pagano, Daniel J.; Tahim, André P. N.

This paper addresses local and global bifurcations that may appear in electrical power systems, such as DC microgrids, which recently has attracted interest from the electrical engineering society. Most sources in these networks are voltage-type and operate in parallel. In such configuration, the basic technique for stabilizing the bus voltage is the so-called droop control. The main contribution of this work is a codimension-two bifurcation analysis of a small DC microgrid considering the droop control gain and the power processed by the load as bifurcation parameters. The codimension-two bifurcation set leads to practical rules for achieving a robust droop control design. Moreover, the bifurcation analysis also offers a better understanding of the dynamics involved in the problem and how to avoid possible instabilities. Simulation results are presented in order to illustrate the bifurcation analysis.

A financial market model with two discontinuities: Bifurcation structures in the chaotic domain

NASA Astrophysics Data System (ADS)

Panchuk, Anastasiia; Sushko, Iryna; Westerhoff, Frank

2018-05-01

We continue the investigation of a one-dimensional piecewise linear map with two discontinuity points. Such a map may arise from a simple asset-pricing model with heterogeneous speculators, which can help us to explain the intricate bull and bear behavior of financial markets. Our focus is on bifurcation structures observed in the chaotic domain of the map's parameter space, which is associated with robust multiband chaotic attractors. Such structures, related to the map with two discontinuities, have been not studied before. We show that besides the standard bandcount adding and bandcount incrementing bifurcation structures, associated with two partitions, there exist peculiar bandcount adding and bandcount incrementing structures involving all three partitions. Moreover, the map's three partitions may generate intriguing bistability phenomena.

Fractional noise destroys or induces a stochastic bifurcation

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

Yang, Qigui, E-mail: qgyang@scut.edu.cn; Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn; School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640

2013-12-15

Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.

The stability and slow dynamics of spot patterns in the 2D Brusselator model: The effect of open systems and heterogeneities

NASA Astrophysics Data System (ADS)

Tzou, J. C.; Ward, M. J.

2018-06-01

Spot patterns, whereby the activator field becomes spatially localized near certain dynamically-evolving discrete spatial locations in a bounded multi-dimensional domain, is a common occurrence for two-component reaction-diffusion (RD) systems in the singular limit of a large diffusivity ratio. In previous studies of 2-D localized spot patterns for various specific well-known RD systems, the domain boundary was assumed to be impermeable to both the activator and inhibitor, and the reaction-kinetics were assumed to be spatially uniform. As an extension of this previous theory, we use formal asymptotic methods to study the existence, stability, and slow dynamics of localized spot patterns for the singularly perturbed 2-D Brusselator RD model when the domain boundary is only partially impermeable, as modeled by an inhomogeneous Robin boundary condition, or when there is an influx of inhibitor across the domain boundary. In our analysis, we will also allow for the effect of a spatially variable bulk feed term in the reaction kinetics. By applying our extended theory to the special case of one-spot patterns and ring patterns of spots inside the unit disk, we provide a detailed analysis of the effect on spot patterns of these three different sources of heterogeneity. In particular, when there is an influx of inhibitor across the boundary of the unit disk, a ring pattern of spots can become pinned to a ring-radius closer to the domain boundary. Under a Robin condition, a quasi-equilibrium ring pattern of spots is shown to exhibit a novel saddle-node bifurcation behavior in terms of either the inhibitor diffusivity, the Robin constant, or the ambient background concentration. A spatially variable bulk feed term, with a concentrated source of "fuel" inside the domain, is shown to yield a saddle-node bifurcation structure of spot equilibria, which leads to qualitatively new spot-pinning behavior. Results from our asymptotic theory are validated from full numerical

Saddle clamp assembly

NASA Technical Reports Server (NTRS)

Belrose, Charles R. (Inventor)

1994-01-01

A saddle clamp assembly is presented. The assembly is comprised of a hollow cylindrical body centered about a longitudinal axis and being diametrically split into semicircular top and bottom sections. Each section has a pair of connection flanges, at opposite ends, that project radially outward. A pair of bolts are retained on the top section flanges and are threadable into nuts retained on the bottom section flanges. A base member is anchored to a central underside portion of the bottom clamp body section and has a pair of connection tabs positioned beneath the bottom clamp body section connection flanges on opposite sides of the clamp axis. A pair of bolts are retained on the base member connection tabs and are threadable into a pair of nuts retainable on a support structure. The connection tab and connection flanges on each side of the clamp body are axially offset in a manner permitting downward installation/removable tool access to the lower bolts past the connection flanges. An elongated retention tether is used to connect the top clamp body section to the balance of the clamp assembly. This prevents loss of the top clamp body section when it is removed from the bottom clamp body section.

Three-Dimensional, Laminar Flow Past a Short, Surface-Mounted Cylinder

NASA Astrophysics Data System (ADS)

Liakos, Anastasios; Malamataris, Nikolaos

2016-11-01

The topology and evolution of three-dimensional flow past a cylinder of slenderness ratio SR = 1 mounted in a wind tunnel is examined for 0 . 1 <= Re <= 325 (based on the diameter of the cylinder) where steady-state solutions have been obtained. Direct numerical simulations were computed using an in-house parallel finite element code. Results indicate that symmetry breaking occurs at Re = 1 , while the first prominent structure is a horseshoe vortex downstream from the cylinder. At Re = 150 , two foci are observed, indicating the formation of two tornadolike vortices downstream. Concurrently, another horseshoe vortex is formed upstream from the cylinder. For higher Reynolds numbers, the flow downstream is segmented to upper and lower parts, whereas the topology of the flow on the solid boundaries remains unaltered. Pressure distributions show that pressure, the key physical parameter in the flow, decreases everywhere except immediately upstream from the cylinder. In addition, creation of critical points from saddle-node-type bifurcations occur when the streamwise component of the pressure gradient changes sign. Finally, at Re = 325 , an additional horseshoe vorrtex is formed at the wake of the cylinder

Shunt-Enhanced, Lead-Driven Bifurcation of Epilayer GaAs based EEC Sensor Responsivity

NASA Astrophysics Data System (ADS)

Solin, Stuart; Werner, Fletcher

2015-03-01

The results reported here explore the geometric optimization of room-temperature EEC sensor responsivity to applied bias by exploring contact geometry and location. The EEC sensor structure resembles that of a MESFET, but the measurement technique and operation distinguish the EEC sensor significantly; the EEC sensor employs a four-point resistance measurement as opposed to a two-point source-drain measurement and is operated under both forward and reverse bias. Under direct forward bias, the sensor distinguishes itself from a traditional FET by allowing current to be injected from the gate, referred to as a shunt, into the active layer. We show that the observed bifurcation in EEC sensor response to direct reverse bias depends critically on measurement lead location. A dramatic enhancement in responsivity is achieved via a modification of the shunt geometry. A maximum percent change of 130,856% of the four-point resistance was achieved under a direct reverse bias of -1V using an enhanced shunt design, a 325 fold increase over the conventional EEC square shunt design. This result was accompanied by an observed bifurcation in sensor response, driven by a rotation of the four-point measurement leads. S. A. S is a co-founder of and has a financial interest in PixelEXX, a start-up company whose mission is to market imaging arrays.

Bifurcations on Potential Energy Surfaces of Organic Reactions

PubMed Central

Ess, Daniel H.; Wheeler, Steven E.; Iafe, Robert G.; Xu, Lai; Çelebi-Ölçüm, Nihan; Houk, K. N.

2009-01-01

A single transition state may lead to multiple intermediates or products if there is a post-transition state reaction path bifurcation. These bifurcations arise when there are sequential transition states with no intervening energy minimum. For such systems, the shape of the potential energy surface and dynamic effects control selectivity rather than transition state energetics. This minireview covers recent investigations of organic reactions exhibiting reaction pathway bifurcations. Such phenomena are surprisingly general and affect experimental observables such as kinetic isotope effects and product distributions. PMID:18767086

Bifurcation of self-folded polygonal bilayers

NASA Astrophysics Data System (ADS)

Abdullah, Arif M.; Braun, Paul V.; Hsia, K. Jimmy

2017-09-01

Motivated by the self-assembly of natural systems, researchers have investigated the stimulus-responsive curving of thin-shell structures, which is also known as self-folding. Self-folding strategies not only offer possibilities to realize complicated shapes but also promise actuation at small length scales. Biaxial mismatch strain driven self-folding bilayers demonstrate bifurcation of equilibrium shapes (from quasi-axisymmetric doubly curved to approximately singly curved) during their stimulus-responsive morphing behavior. Being a structurally instable, bifurcation could be used to tune the self-folding behavior, and hence, a detailed understanding of this phenomenon is appealing from both fundamental and practical perspectives. In this work, we investigated the bifurcation behavior of self-folding bilayer polygons. For the mechanistic understanding, we developed finite element models of planar bilayers (consisting of a stimulus-responsive and a passive layer of material) that transform into 3D curved configurations. Our experiments with cross-linked Polydimethylsiloxane samples that change shapes in organic solvents confirmed our model predictions. Finally, we explored a design scheme to generate gripper-like architectures by avoiding the bifurcation of stimulus-responsive bilayers. Our research contributes to the broad field of self-assembly as the findings could motivate functional devices across multiple disciplines such as robotics, artificial muscles, therapeutic cargos, and reconfigurable biomedical devices.

Periodic or chaotic bursting dynamics via delayed pitchfork bifurcation in a slow-varying controlled system

NASA Astrophysics Data System (ADS)

Yu, Yue; Zhang, Zhengdi; Han, Xiujing

2018-03-01

In this work, we aim to demonstrate the novel routes to periodic and chaotic bursting, i.e., the different bursting dynamics via delayed pitchfork bifurcations around stable attractors, in the classical controlled Lü system. First, by computing the corresponding characteristic polynomial, we determine where some critical values about bifurcation behaviors appear in the Lü system. Moreover, the transition mechanism among different stable attractors has been introduced including homoclinic-type connections or chaotic attractors. Secondly, taking advantage of the above analytical results, we carry out a study of the mechanism for bursting dynamics in the Lü system with slowly periodic variation of certain control parameter. A distinct delayed supercritical pitchfork bifurcation behavior can be discussed when the control item passes through bifurcation points periodically. This delayed dynamical behavior may terminate at different parameter areas, which leads to different spiking modes around different stable attractors (equilibriums, limit cycles, or chaotic attractors). In particular, the chaotic attractor may appear by Shilnikov connections or chaos boundary crisis, which leads to the occurrence of impressive chaotic bursting oscillations. Our findings enrich the study of bursting dynamics and deepen the understanding of some similar sorts of delayed bursting phenomena. Finally, some numerical simulations are included to illustrate the validity of our study.

Stability and instability of axisymmetric droplets in thermocapillary-driven thin films

NASA Astrophysics Data System (ADS)

Nicolaou, Zachary G.

2018-03-01

The stability of compactly supported, axisymmetric droplet states is considered for driven thin viscous films evolving on two-dimensional surfaces. Stability is assessed using Lyapunov energy methods afforded by the Cahn-Hilliard variational form of the governing equation. For general driving forces, a criterion on the gradient of profiles at the boundary of their support (their contact slope) is shown to be a necessary condition for stability. Additional necessary and sufficient conditions for stability are established for a specific driving force corresponding to a thermocapillary-driven film. It is found that only droplets of sufficiently short height that satisfy the contact slope criterion are stable. This destabilization of droplets with increasing height is characterized as a saddle-node bifurcation between a branch of tall, unstable droplets and a branch of short, stable droplets.

Solar Coronal Loop Dynamics Near the Null Point Above Active Region NOAA 2666

NASA Astrophysics Data System (ADS)

Filippov, B.

2018-06-01

We analyse observations of a saddle-like structure in the corona above the western limb of the Sun on 2017 July 18. The structure was clearly outlined by coronal loops with typical coronal temperature no more than 1 MK. The dynamics of loops showed convergence towards the centre of the saddle in the vertical direction and divergence in the horizontal direction. The event is a clear example of smooth coronal magnetic field reconnection. No heating manifestations in the reconnection region or magnetically connected areas were observed. Potential magnetic field calculations, which use as the boundary condition the SDO/HMI magnetogram taken on July 14, showed the presence of a null point at the height of 122 arcsec above the photosphere just at the centre of the saddle structure. The shape of field lines fits the fan-spine magnetic configuration above NOAA 2666.

Signatures of bifurcation on quantum correlations: Case of the quantum kicked top

NASA Astrophysics Data System (ADS)

Bhosale, Udaysinh T.; Santhanam, M. S.

2017-01-01

Quantum correlations reflect the quantumness of a system and are useful resources for quantum information and computational processes. Measures of quantum correlations do not have a classical analog and yet are influenced by classical dynamics. In this work, by modeling the quantum kicked top as a multiqubit system, the effect of classical bifurcations on measures of quantum correlations such as the quantum discord, geometric discord, and Meyer and Wallach Q measure is studied. The quantum correlation measures change rapidly in the vicinity of a classical bifurcation point. If the classical system is largely chaotic, time averages of the correlation measures are in good agreement with the values obtained by considering the appropriate random matrix ensembles. The quantum correlations scale with the total spin of the system, representing its semiclassical limit. In the vicinity of trivial fixed points of the kicked top, the scaling function decays as a power law. In the chaotic limit, for large total spin, quantum correlations saturate to a constant, which we obtain analytically, based on random matrix theory, for the Q measure. We also suggest that it can have experimental consequences.

Application of a Saddle-Type Eddy Current Sensor in Steel Ball Surface-Defect Inspection

PubMed Central

Zhong, Mingming; Xie, Fengqin; Cao, Maoyong

2017-01-01

Steel ball surface-defect inspection was performed by using a new saddle-type eddy current sensor (SECS), which included a saddle coil and a signal conditioning circuit. The saddle coil was directly wound on the steel ball’s outer bracket in a semi-circumferential direction. Driven by a friction wheel, the test steel ball rotated in a one-dimensional direction, such that the steel ball surface was fully scanned by the SECS. There were two purposes for using the SECS in the steel ball inspection system: one was to reduce the complexity of the unfolding wheel of the surface deployment mechanism, and the other was to reduce the difficulty of sensor processing and installation. Experiments were carried out on bearing steel balls in diameter of 8 mm with three types of representative and typical defects by using the SECS, and the results showed that the inspection system can detect surface defects as small as 0.05 mm in width and 0.1 mm in depth with high-repetition detection accuracy, and the detection efficiency of 5 pcs/s, which meet the requirement for inspecting ISO grade 10 bearing steel balls. The feasibility of detecting steel ball surface defects by SECS was verified. PMID:29206154

Application of a Saddle-Type Eddy Current Sensor in Steel Ball Surface-Defect Inspection.

PubMed

Zhang, Huayu; Zhong, Mingming; Xie, Fengqin; Cao, Maoyong

2017-12-05

Steel ball surface-defect inspection was performed by using a new saddle-type eddy current sensor (SECS), which included a saddle coil and a signal conditioning circuit. The saddle coil was directly wound on the steel ball's outer bracket in a semi-circumferential direction. Driven by a friction wheel, the test steel ball rotated in a one-dimensional direction, such that the steel ball surface was fully scanned by the SECS. There were two purposes for using the SECS in the steel ball inspection system: one was to reduce the complexity of the unfolding wheel of the surface deployment mechanism, and the other was to reduce the difficulty of sensor processing and installation. Experiments were carried out on bearing steel balls in diameter of 8 mm with three types of representative and typical defects by using the SECS, and the results showed that the inspection system can detect surface defects as small as 0.05 mm in width and 0.1 mm in depth with high-repetition detection accuracy, and the detection efficiency of 5 pcs/s, which meet the requirement for inspecting ISO grade 10 bearing steel balls. The feasibility of detecting steel ball surface defects by SECS was verified.

Sediment oxygen demand in the Saddle River and Salem River watersheds, New Jersey, July-August 2008

USGS Publications Warehouse

Heckathorn, Heather A.; Gibs, Jacob

2010-01-01

Many factors, such as river depth and velocity, biochemical oxygen demand, and algal productivity, as well as sediment oxygen demand, can affect the concentration of dissolved oxygen in the water column. Measurements of sediment oxygen demand, in conjunction with those of other water-column water-quality constituents, are useful for quantifying the mechanisms that affect in-stream dissolved-oxygen concentrations. Sediment-oxygen-demand rates are also needed to develop and calibrate a water-quality model being developed for the Saddle River and Salem River Basins in New Jersey to predict dissolved-oxygen concentrations. This report documents the methods used to measure sediment oxygen demand in the Saddle River and Salem River watersheds along with the rates of sediment oxygen demand that were obtained during this investigation. In July and August 2008, sediment oxygen demand was measured in situ in the Saddle River and Salem River watersheds. In the Saddle River Basin, sediment oxygen demand was measured twice at two sites and once at a third location; in the Salem River Basin, sediment oxygen demand was measured three times at two sites and once at a third location. In situ measurements of sediment oxygen demand in the Saddle River and Salem River watersheds ranged from 0.8 to 1.4 g/m2d (grams per square meter per day) and from 0.6 to 7.1 g/m2d at 20 degrees Celsius, respectively. Except at one site in this study, rates of sediment oxygen demand generally were low. The highest rate of sediment oxygen demand measured during this investigation, 7.1 g/m2d, which occurred at Courses Landing in the Salem River Basin, may be attributable to the consumption of oxygen by a large amount of organic matter (54 grams per kilogram as organic carbon) in the streambed sediments or to potential error during data collection. In general, sediment oxygen demand increased with the concentration of organic carbon in the streambed sediments. Repeated measurements made 6 to 7 days apart

Stalk Phase Formation: Effects of Dehydration and Saddle Splay Modulus

PubMed Central

Kozlovsky, Yonathan; Efrat, Avishay; Siegel, David A.; Kozlov, Michael M.

2004-01-01

One of the earliest lipid intermediates forming in the course of membrane fusion is the lipid stalk. Although many aspects of the stalk hypothesis were elaborated theoretically and confirmed by experiments it remained unresolved whether stalk formation is always an energy consuming process or if there are conditions where the stalks are energetically favorable and form spontaneously resulting in an equilibrium stalk phase. Motivated by a recent breakthrough experiments we analyze the physical factors determining the spontaneous stalk formation. We show that this process can be driven by interplay between two factors: the elastic energy of lipid monolayers including a contribution of the saddle splay deformation and the energy of hydration repulsion acting between apposing membranes. We analyze the dependence of stalk formation on the saddle splay (Gaussian) modulus of the lipid monolayers and estimate the values of this modulus based on the experimentally established phase boundary between the lamellar and the stalk phases. We suggest that fusion proteins can induce stalk formation just by bringing the membranes into close contact, and accumulating, at least locally, a sufficiently large energy of the hydration repulsion. PMID:15454446

Miocene−Pleistocene deformation of the Saddle Mountains: Implications for seismic hazard in central Washington, USA

USGS Publications Warehouse

Staisch, Lydia; Kelsey, Harvey; Sherrod, Brian; Möller, Andreas; Paces, James B.; Blakely, Richard J.; Styron, Richard

2017-01-01

The Yakima fold province, located in the backarc of the Cascadia subduction zone, is a region of active strain accumulation and deformation distributed across a series of fault-cored folds. The geodetic network in central Washington has been used to interpret large-scale N-S shortening and westward-increasing strain; however, geodetic data are unable to resolve shortening rates across individual structures in this low-strain-rate environment. Resolving fault geometries, slip rates, and timing of faulting in the Yakima fold province is critically important to seismic hazard assessment for nearby infrastructure and population centers.The Saddle Mountains anticline is one of the most prominent Yakima folds. It is unique within the Yakima fold province in that the syntectonic strata of the Ringold Formation are preserved and provide a record of deformation and drainage reorganization. Here, we present new stratigraphic columns, U-Pb zircon tephra ages, U-series caliche ages, and geophysical modeling that constrain two line-balanced and retrodeformed cross sections. These new constraints indicate that the Saddle Mountains anticline has accommodated 1.0−1.3 km of N-S shortening since 10 Ma, that shortening increases westward along the anticline, and that the average slip rate has increased 6-fold since 6.8 Ma. Provenance analysis suggests that the source terrane for the Ringold Formation was similar to that of the modern Snake River Plain. Using new slip rates and structural constraints, we calculate the strain accumulation time, interpretable as a recurrence interval, for earthquakes on the Saddle Mountains fault and find that large-magnitude earthquakes could rupture along the Saddle Mountains fault every 2−11 k.y.

Behavior of an aeroelastic system beyond critical point of instability

NASA Astrophysics Data System (ADS)

Sekar, T. Chandra; Agarwal, Ravindra; Mandal, Alakesh Chandra; Kushari, Abhijit

2017-11-01

Understanding the behavior of an aeroelastic system beyond the critical point is essential for effective implementation of any active control scheme since the control system design depends on the type of instability (bifurcation) the system encounters. Previous studies had found the aeroelastic system to enter into chaos beyond the point of instability. In the present work, an attempt has been made to carry out an experimental study on an aeroelastic model placed in a wind tunnel, to understand the behavior of aerodynamics around a wing section undergoing classical flutter. Wind speed was increased from zero until the model encountered flutter. Pressure at various locations along the surface of wing and acceleration at multiple points on the wing were measured in real time for the entire duration of experiment. A Leading Edge Separation Bubble (LSB) was observed beyond the critical point. The growing strength of the LSB with increasing wind speed was found to alter the aerodynamic moment acting on the system, which forced the system to enter into a second bifurcation. Based on the nature of the response, the system appears to undergo periodic doubling bifurcation rather than Hopf-bifurcation, resulting in chaotic motion. Eliminating the LSB can help in preventing the system from entering chaos. Any active flow control scheme that can avoid or counter the formation of leading edge separation bubble can be a potential solution to control the classical flutter.

Bifurcating fronts for the Taylor-Couette problem in infinite cylinders

NASA Astrophysics Data System (ADS)

Hărăguş-Courcelle, M.; Schneider, G.

We show the existence of bifurcating fronts for the weakly unstable Taylor-Couette problem in an infinite cylinder. These fronts connect a stationary bifurcating pattern, here the Taylor vortices, with the trivial ground state, here the Couette flow. In order to show the existence result we improve a method which was already used in establishing the existence of bifurcating fronts for the Swift-Hohenberg equation by Collet and Eckmann, 1986, and by Eckmann and Wayne, 1991. The existence proof is based on spatial dynamics and center manifold theory. One of the difficulties in applying center manifold theory comes from an infinite number of eigenvalues on the imaginary axis for vanishing bifurcation parameter. But nevertheless, a finite dimensional reduction is possible, since the eigenvalues leave the imaginary axis with different velocities, if the bifurcation parameter is increased. In contrast to previous work we have to use normalform methods and a non-standard cut-off function to obtain a center manifold which is large enough to contain the bifurcating fronts.

Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate

NASA Astrophysics Data System (ADS)

Ren, Jingli; Yuan, Qigang

2017-08-01

A three dimensional microbial continuous culture model with a restrained microbial growth rate is studied in this paper. Two types of dilution rates are considered to investigate the dynamic behaviors of the model. For the unforced system, fold bifurcation and Hopf bifurcation are detected, and numerical simulations reveal that the system undergoes degenerate Hopf bifurcation. When the system is periodically forced, bifurcation diagrams for periodic solutions of period-one and period-two are given by researching the Poincaré map, corresponding to different bifurcation cases in the unforced system. Stable and unstable quasiperiodic solutions are obtained by Neimark-Sacker bifurcation with different parameter values. Periodic solutions of various periods can occur or disappear and even change their stability, when the Poincaré map of the forced system undergoes Neimark-Sacker bifurcation, flip bifurcation, and fold bifurcation. Chaotic attractors generated by a cascade of period doublings and some phase portraits are given at last.

Time-periodic solutions of driven-damped trimer granular crystals

DOE PAGES

Charalampidis, E. G.; Li, F.; Chong, C.; ...

2015-01-01

In this work, we consider time-periodic structures of granular crystals consisting of alternate chrome steel (S) and tungsten carbide (W) spherical particles where each unit cell follows the pattern of a 2:1 trimer: S-W-S. The configuration at the left boundary is driven by a harmonic in-time actuation with given amplitude and frequency while the right one is a fixed wall. Similar to the case of a dimer chain, the combination of dissipation, driving of the boundary, and intrinsic nonlinearity leads to complex dynamics. For fixed driving frequencies in each of the spectral gaps, we find that the nonlinear surface modesmore » and the states dictated by the linear drive collide in a saddle-node bifurcation as the driving amplitude is increased, beyond which the dynamics of the system becomes chaotic. While the bifurcation structure is similar for solutions within the first and second gap, those in the first gap appear to be less robust. We also conduct a continuation in driving frequency, where it is apparent that the nonlinearity of the system results in a complex bifurcation diagram, involving an intricate set of loops of branches, especially within the spectral gap. The theoretical findings are qualitatively corroborated by the experimental full-field visualization of the time-periodic structures.« less

Cis-dicarbonyl binding at cobalt and iron porphyrins with saddle-shape conformation.

PubMed

Seufert, Knud; Bocquet, Marie-Laure; Auwärter, Willi; Weber-Bargioni, Alexander; Reichert, Joachim; Lorente, Nicolás; Barth, Johannes V

2011-02-01

Diatomic molecules attached to complexed iron or cobalt centres are important in many biological processes. In natural systems, metallotetrapyrrole units carry respiratory gases or provide sensing and catalytic functions. Conceiving synthetic model systems strongly helps to determine the pertinent chemical foundations for such processes, with recent work highlighting the importance of the prosthetic groups' conformational flexibility as an intricate variable affecting their functional properties. Here, we present simple model systems to investigate, at the single molecule level, the interaction of carbon monoxide with saddle-shaped iron- and cobalt-porphyrin conformers, which have been stabilized as two-dimensional arrays on well-defined surfaces. Using scanning tunnelling microscopy we identified a novel bonding scheme expressed in tilted monocarbonyl and cis-dicarbonyl configurations at the functional metal-macrocycle unit. Modelling with density functional theory revealed that the weakly bonded diatomic carbonyl adduct can effectively bridge specific pyrrole groups with the metal atom as a result of the pronounced saddle-shape conformation of the porphyrin cage.

Bifurcation physics of magnetic islands and stochasticity explored by heat pulse propagation studies in toroidal plasmas

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

Ida, K.; Kobayashi, T.; Yoshinuma, M.

Bifurcation physics of the magnetic island was investigated using the heat pulse propagation technique produced by the modulation of electron cyclotron heating. There are two types of bifurcation phenomena observed in LHD and DIII-D. One is a bifurcation of the magnetic topology between nested and stochastic fields. The nested state is characterized by the bi-directional (inward and outward) propagation of the heat pulse with slow propagation speed. The stochastic state is characterized by the fast propagation of the heat pulse with electron temperature flattening. The other bifurcation is between magnetic island with larger thermal diffusivity and that with smaller thermalmore » diffusivity. The damping of toroidal flow is observed at the O-point of the magnetic island both in helical plasmas and in tokamak plasmas during a mode locking phase with strong flow shears at the boundary of the magnetic island. Associated with the stochastization of the magnetic field, the abrupt damping of toroidal flow is observed in LHD. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. Lastly, this observation suggests that this flow damping is due to the change in the non-diffusive term of momentum transport.« less

Bifurcation physics of magnetic islands and stochasticity explored by heat pulse propagation studies in toroidal plasmas

DOE PAGES

Ida, K.; Kobayashi, T.; Yoshinuma, M.; ...

2016-07-29

Bifurcation physics of the magnetic island was investigated using the heat pulse propagation technique produced by the modulation of electron cyclotron heating. There are two types of bifurcation phenomena observed in LHD and DIII-D. One is a bifurcation of the magnetic topology between nested and stochastic fields. The nested state is characterized by the bi-directional (inward and outward) propagation of the heat pulse with slow propagation speed. The stochastic state is characterized by the fast propagation of the heat pulse with electron temperature flattening. The other bifurcation is between magnetic island with larger thermal diffusivity and that with smaller thermalmore » diffusivity. The damping of toroidal flow is observed at the O-point of the magnetic island both in helical plasmas and in tokamak plasmas during a mode locking phase with strong flow shears at the boundary of the magnetic island. Associated with the stochastization of the magnetic field, the abrupt damping of toroidal flow is observed in LHD. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. Lastly, this observation suggests that this flow damping is due to the change in the non-diffusive term of momentum transport.« less

Effects of Bifurcations on Aft-Fan Engine Nacelle Noise

NASA Technical Reports Server (NTRS)

Nark, Douglas M.; Farassat, Fereidoun; Pope, D. Stuart; Vatsa, Veer N.

2004-01-01

Aft-fan engine nacelle noise is a significant factor in the increasingly important issue of aircraft community noise. The ability to predict such noise within complex duct geometries is a valuable tool in studying possible noise attenuation methods. A recent example of code development for such predictions is the ducted fan noise propagation and radiation code CDUCT-LaRC. This work focuses on predicting the effects of geometry changes (i.e. bifurcations, pylons) on aft fan noise propagation. Beginning with simplified geometries, calculations show that bifurcations lead to scattering of acoustic energy into higher order modes. In addition, when circumferential mode number and the number of bifurcations are properly commensurate, bifurcations increase the relative importance of the plane wave mode near the exhaust plane of the bypass duct. This is particularly evident when the bypass duct surfaces include acoustic treatment. Calculations involving more complex geometries further illustrate that bifurcations and pylons clearly affect modal content, in both propagation and radiation calculations. Additionally, results show that consideration of acoustic radiation results may provide further insight into acoustic treatment effectiveness for situations in which modal decomposition may not be straightforward. The ability of CDUCT-LaRC to handle complex (non-axisymmetric) multi-block geometries, as well as axially and circumferentially segmented liners, allows investigation into the effects of geometric elements (bifurcations, pylons).

Stability boundaries for command augmentation systems

NASA Technical Reports Server (NTRS)

Shrivastava, P. C.

1987-01-01

The Stability Augmentation System (SAS) is a special case of the Command Augmentation System (CAS). Control saturation imposes bounds on achievable commands. The state equilibrium depends only on the open loop dynamics and control deflection. The control magnitude to achieve a desired command equilibrium is independent of the feedback gain. A feedback controller provides the desired response, maintains the system equilibrium under disturbances, but it does not affect the equilibrium values of states and control. The saturation boundaries change with commands, but the location of the equilibrium points in the saturated region remains unchanged. Nonzero command vectors yield saturation boundaries that are asymmetric with respect to the state equilibrium. Except for the saddle point case with MCE control law, the stability boundaries change with commands. For the cases of saddle point and unstable nodes, the region of stability decreases with increasing command magnitudes.

Characterisation of Feature Points in Eye Fundus Images

NASA Astrophysics Data System (ADS)

Calvo, D.; Ortega, M.; Penedo, M. G.; Rouco, J.

The retinal vessel tree adds decisive knowledge in the diagnosis of numerous opthalmologic pathologies such as hypertension or diabetes. One of the problems in the analysis of the retinal vessel tree is the lack of information in terms of vessels depth as the image acquisition usually leads to a 2D image. This situation provokes a scenario where two different vessels coinciding in a point could be interpreted as a vessel forking into a bifurcation. That is why, for traking and labelling the retinal vascular tree, bifurcations and crossovers of vessels are considered feature points. In this work a novel method for these retinal vessel tree feature points detection and classification is introduced. The method applies image techniques such as filters or thinning to obtain the adequate structure to detect the points and sets a classification of these points studying its environment. The methodology is tested using a standard database and the results show high classification capabilities.

Dorsal Failures: From Saddle Deformity to Pollybeak.

PubMed

Hamilton, Grant S

2018-06-01

The nasal dorsum is an important component of a rhinoplasty and may be the primary motivation for seeking surgery. The nasal dorsum is a complex three-dimensional shape that is shrouded by local anesthetic and edema during surgery. This makes an accurate assessment of the surgical changes challenging. Complications related to dorsal modification include imbalances from over- or underresection of the structures of the nasal dorsum, inadequate or overaugmentation, an open-roof deformity, pollybeak, saddle nose, inverted-V, warped cartilage, visible grafts, contour problems, graft malposition, and extrusion. This review will discuss the common problems that can occur with dorsal modification during rhinoplasty. Thieme Medical Publishers 333 Seventh Avenue, New York, NY 10001, USA.

Amphibian sacculus and the forced Kuramoto model with intrinsic noise and frequency dispersion

NASA Astrophysics Data System (ADS)

Ji, Seung; Bozovic, Dolores; Bruinsma, Robijn

2018-04-01

The amphibian sacculus (AS) is an end organ that specializes in the detection of low-frequency auditory and vestibular signals. In this paper, we propose a model for the AS in the form of an array of phase oscillators with long-range coupling, subject to a steady load that suppresses spontaneous oscillations. The array is exposed to significant levels of frequency dispersion and intrinsic noise. We show that such an array can be a sensitive and robust subthreshold detector of low-frequency stimuli, though without significant frequency selectivity. The effects of intrinsic noise and frequency dispersion are contrasted. Intermediate levels of intrinsic noise greatly enhance the sensitivity through stochastic resonance. Frequency dispersion, on the other hand, only degrades detection sensitivity. However, frequency dispersion can play a useful role in terms of the suppression of spontaneous activity. As a model for the AS, the array parameters are such that the system is poised near a saddle-node bifurcation on an invariant circle. However, by a change of array parameters, the same system also can be poised near an emergent Andronov-Hopf bifurcation and thereby function as a frequency-selective detector.

The Hindmarsh-Rose neuron model: bifurcation analysis and piecewise-linear approximations.

PubMed

Storace, Marco; Linaro, Daniele; de Lange, Enno

2008-09-01

This paper provides a global picture of the bifurcation scenario of the Hindmarsh-Rose model. A combination between simulations and numerical continuations is used to unfold the complex bifurcation structure. The bifurcation analysis is carried out by varying two bifurcation parameters and evidence is given that the structure that is found is universal and appears for all combinations of bifurcation parameters. The information about the organizing principles and bifurcation diagrams are then used to compare the dynamics of the model with that of a piecewise-linear approximation, customized for circuit implementation. A good match between the dynamical behaviors of the models is found. These results can be used both to design a circuit implementation of the Hindmarsh-Rose model mimicking the diversity of neural response and as guidelines to predict the behavior of the model as well as its circuit implementation as a function of parameters. (c) 2008 American Institute of Physics.

Bifurcations of 2-Periodic Nonautonomous Stunted Tent Systems

NASA Astrophysics Data System (ADS)

Silva, L.; Rocha, J. Leonel; Silva, M. T.

2017-06-01

In this paper, we will consider a family of 2-periodic nonautonomous dynamical systems, generated by the alternate iteration of two stunted tent maps and study its bifurcation skeleton. We will describe the bifurcation phenomena along and around the bones accomplished with the combinatorial data furnished by the respective symbolic dynamics.

Bifurcation of rupture path by linear and cubic damping force

NASA Astrophysics Data System (ADS)

Dennis L. C., C.; Chew X., Y.; Lee Y., C.

2014-06-01

Bifurcation of rupture path is studied for the effect of linear and cubic damping. Momentum equation with Rayleigh factor was transformed into ordinary differential form. Bernoulli differential equation was obtained and solved by the separation of variables. Analytical or exact solutions yielded the bifurcation was visible at imaginary part when the wave was non dispersive. For the dispersive wave, bifurcation of rupture path was invisible.

Bifurcation, chaos, and scan instability in dynamic atomic force microscopy

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

Cantrell, John H., E-mail: john.h.cantrell@nasa.gov; Cantrell, Sean A., E-mail: scantrell@nlsanalytics.com

The dynamical motion at any point on the cantilever of an atomic force microscope can be expressed quite generally as a superposition of simple harmonic oscillators corresponding to the vibrational modes allowed by the cantilever shape. Central to the dynamical equations is the representation of the cantilever-sample interaction force as a polynomial expansion with coefficients that account for the interaction force “stiffness,” the cantilever-to-sample energy transfer, and the displacement amplitude of cantilever oscillation. Renormalization of the cantilever beam model shows that for a given cantilever drive frequency cantilever dynamics can be accurately represented by a single nonlinear mass-spring model withmore » frequency-dependent stiffness and damping coefficients [S. A. Cantrell and J. H. Cantrell, J. Appl. Phys. 110, 094314 (2011)]. Application of the Melnikov method to the renormalized dynamical equation is shown to predict a cascade of period doubling bifurcations with increasing cantilever drive force that terminates in chaos. The threshold value of the drive force necessary to initiate bifurcation is shown to depend strongly on the cantilever setpoint and drive frequency, effective damping coefficient, nonlinearity of the cantilever-sample interaction force, and the displacement amplitude of cantilever oscillation. The model predicts the experimentally observed interruptions of the bifurcation cascade for cantilevers of sufficiently large stiffness. Operational factors leading to the loss of image quality in dynamic atomic force microscopy are addressed, and guidelines for optimizing scan stability are proposed using a quantitative analysis based on system dynamical parameters and choice of feedback loop parameter.« less

The Absence of Sensory Axon Bifurcation Affects Nociception and Termination Fields of Afferents in the Spinal Cord

PubMed Central

Tröster, Philip; Haseleu, Julia; Petersen, Jonas; Drees, Oliver; Schmidtko, Achim; Schwaller, Frederick; Lewin, Gary R.; Ter-Avetisyan, Gohar; Winter, York; Peters, Stefanie; Feil, Susanne; Feil, Robert; Rathjen, Fritz G.; Schmidt, Hannes

2018-01-01

A cGMP signaling cascade composed of C-type natriuretic peptide, the guanylyl cyclase receptor Npr2 and cGMP-dependent protein kinase I (cGKI) controls the bifurcation of sensory axons upon entering the spinal cord during embryonic development. However, the impact of axon bifurcation on sensory processing in adulthood remains poorly understood. To investigate the functional consequences of impaired axon bifurcation during adult stages we generated conditional mouse mutants of Npr2 and cGKI (Npr2fl/fl;Wnt1Cre and cGKIKO/fl;Wnt1Cre) that lack sensory axon bifurcation in the absence of additional phenotypes observed in the global knockout mice. Cholera toxin labeling in digits of the hind paw demonstrated an altered shape of sensory neuron termination fields in the spinal cord of conditional Npr2 mouse mutants. Behavioral testing of both sexes indicated that noxious heat sensation and nociception induced by chemical irritants are impaired in the mutants, whereas responses to cold sensation, mechanical stimulation, and motor coordination are not affected. Recordings from C-fiber nociceptors in the hind limb skin showed that Npr2 function was not required to maintain normal heat sensitivity of peripheral nociceptors. Thus, the altered behavioral responses to noxious heat found in Npr2fl/fl;Wnt1Cre mice is not due to an impaired C-fiber function. Overall, these data point to a critical role of axonal bifurcation for the processing of pain induced by heat or chemical stimuli. PMID:29472841

Partial synchronization of relaxation oscillators with repulsive coupling in autocatalytic integrate-and-fire model and electrochemical experiments

NASA Astrophysics Data System (ADS)

Kori, Hiroshi; Kiss, István Z.; Jain, Swati; Hudson, John L.

2018-04-01

Experiments and supporting theoretical analysis are presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation, where the coupling is repulsive in the electrode potential. While attractive coupling generates phase clusters and desynchronized states, repulsive coupling results in synchronized oscillations. The experiments are interpreted with a phenomenological model that captures the waveform of the oscillations (exponential increase) followed by a refractory period. The globally coupled autocatalytic integrate-and-fire model predicts the development of partially synchronized states that occur through attracting heteroclinic cycles between out-of-phase two-cluster states. Similar behavior can be expected in many other systems where the oscillations occur close to a saddle-loop bifurcation, e.g., with Morris-Lecar neurons.

Modelling landslide liquefaction, mobility bifurcation and the dynamics of the 2014 Oso disaster

USGS Publications Warehouse

Iverson, Richard M.; George, David L.

2016-01-01

Some landslides move slowly or intermittently downslope, but others liquefy during the early stages of motion, leading to runaway acceleration and high-speed runout across low-relief terrain. Mechanisms responsible for this disparate behaviour are represented in a two-phase, depth-integrated, landslide dynamics model that melds principles from soil mechanics, granular mechanics and fluid mechanics. The model assumes that gradually increasing pore-water pressure causes slope failure to nucleate at the weakest point on a basal slip surface in a statically balanced mass. Failure then spreads to adjacent regions as a result of momentum exchange. Liquefaction is contingent on pore-pressure feedback that depends on the initial soil state. The importance of this feedback is illustrated by using the model to study the dynamics of a disastrous landslide that occurred near Oso, Washington, USA, on 22 March 2014. Alternative simulations of the event reveal the pronounced effects of a landslide mobility bifurcation that occurs if the initial void ratio of water-saturated soil equals the lithostatic, critical-state void ratio. They also show that the tendency for bifurcation increases as the soil permeability decreases. The bifurcation implies that it can be difficult to discriminate conditions that favour slow landsliding from those that favour liquefaction and long runout.

Bifurcation and Spike Adding Transition in Chay-Keizer Model

NASA Astrophysics Data System (ADS)

Lu, Bo; Liu, Shenquan; Liu, Xuanliang; Jiang, Xiaofang; Wang, Xiaohui

Electrical bursting is an activity which is universal in excitable cells such as neurons and various endocrine cells, and it encodes rich physiological information. As burst delay identifies that the signal integration has reached the threshold at which it can generate an action potential, the number of spikes in a burst may have essential physiological implications, and the transition of bursting in excitable cells is associated with the bifurcation phenomenon closely. In this paper, we focus on the transition of the spike count per burst of the pancreatic β-cells within a mathematical model and bifurcation phenomenon in the Chay-Keizer model, which is utilized to simulate the pancreatic β-cells. By the fast-slow dynamical bifurcation analysis and the bi-parameter bifurcation analysis, the local dynamics of the Chay-Keizer system around the Bogdanov-Takens bifurcation is illustrated. Then the variety of the number of spikes per burst is discussed by changing the settings of a single parameter and bi-parameter. Moreover, results on the number of spikes within a burst are summarized in ISIs (interspike intervals) sequence diagrams, maximum and minimum, and the number of spikes under bi-parameter value changes.

Saddle-shaped reticulate Nummulites from Early Oligocene rocks of Khari area, SW Kutch, India

NASA Astrophysics Data System (ADS)

Sengupta, S.; Sarkar, Sampa; Mukhopadhyay, S.

2011-04-01

Saddle-shaped reticulate Nummulites from the Early Oligocene rocks of Khari area, SW Kutch, India is reported here for the first time. Unusual shape of this Nummulites is due to the curved nature of the coiling plane, indicating space constrained postembryonic test growth. With regular development of chambers, septa and septal filaments, the saddle-shaped Nummulites constitutes the third morphotype of N. cf. fichteli Michelotti form A. Other morphotypes of the species reported earlier include inflated lenticular and conical tests. Multiple morphotypes of N. cf. fichteli form A indicates varied test growth in response to substrate conditions. Morphological variability exhibited by N. cf. fichteli form A from Kutch and some Early Oligocene reticulate Nummulites from the Far East are comparable. This faunal suite is morphologically distinct from the contemporary reticulate Nummulites of the European localities.

Bifurcation of elastic solids with sliding interfaces

NASA Astrophysics Data System (ADS)

Bigoni, D.; Bordignon, N.; Piccolroaz, A.; Stupkiewicz, S.

2018-01-01

Lubricated sliding contact between soft solids is an interesting topic in biomechanics and for the design of small-scale engineering devices. As a model of this mechanical set-up, two elastic nonlinear solids are considered jointed through a frictionless and bilateral surface, so that continuity of the normal component of the Cauchy traction holds across the surface, but the tangential component is null. Moreover, the displacement can develop only in a way that the bodies in contact do neither detach, nor overlap. Surprisingly, this finite strain problem has not been correctly formulated until now, so this formulation is the objective of the present paper. The incremental equations are shown to be non-trivial and different from previously (and erroneously) employed conditions. In particular, an exclusion condition for bifurcation is derived to show that previous formulations based on frictionless contact or `spring-type' interfacial conditions are not able to predict bifurcations in tension, while experiments-one of which, ad hoc designed, is reported-show that these bifurcations are a reality and become possible when the correct sliding interface model is used. The presented results introduce a methodology for the determination of bifurcations and instabilities occurring during lubricated sliding between soft bodies in contact.

2D bifurcations and Newtonian properties of memristive Chua's circuits

NASA Astrophysics Data System (ADS)

Marszalek, W.; Podhaisky, H.

2016-01-01

Two interesting properties of Chua's circuits are presented. First, two-parameter bifurcation diagrams of Chua's oscillatory circuits with memristors are presented. To obtain various 2D bifurcation images a substantial numerical effort, possibly with parallel computations, is needed. The numerical algorithm is described first and its numerical code for 2D bifurcation image creation is available for free downloading. Several color 2D images and the corresponding 1D greyscale bifurcation diagrams are included. Secondly, Chua's circuits are linked to Newton's law φ ''= F(t,φ,φ')/m with φ=\\text{flux} , constant m > 0, and the force term F(t,φ,φ') containing memory terms. Finally, the jounce scalar equations for Chua's circuits are also discussed.

Study on Nonlinear Lateral Parameter Bifurcation Characteristic of Soft Footbridge

NASA Astrophysics Data System (ADS)

Chen, Zhou; Deng, De-Yuan; Yan, Quan-Sheng; Lu, Jin-Zhong; Lu, Jian-Xin

2018-03-01

With the trend of large span in the development of footbridge, its nonlinear characteristic is more and more obvious. Bifurcation has a great influence on the nonstationary trivial solution and its boundary stability of nonlinear vibration. Based on the Millennium Bridge in London, this paper deduces its nonlinear transverse vibration equation. Also, the method of Galerkin and multi-scale method is used to obtain the judgment condition of nonstationary trivial stability. Based on the bifurcation theory, the influence of nonlinear behavior on nontrivial solution as well as its stability is studied in the paper under two situations, a 1 ‑ σ bifurcation and a 1 ‑ ζ2 bifurcation of parameter plane respectively.

Critical fluctuations near the pitchfork bifurcations of period-doubling maps

NASA Astrophysics Data System (ADS)

Noble, Andrew; Karimeddiny, Saba; Hastings, Alan; Machta, Jonathan

2015-03-01

Period-doubling maps, such as the logistic map, have been a subject of intense study in both physics and biology. The period-doubling route to chaos proceeds through a sequence of supercritical pitchfork bifurcations. Here, motivated by applications to population ecology, we investigate the asymptotic behavior of period-doubling bifurcations subject to environmental or demographic noise. We demonstrate, analytically, that fluctuations in the vicinity of each noisy pitchfork bifurcation are described by finite-size mean-field theory. Our results establish an exact correspondence between the bifurcations of far-from-equilibrium systems and the mean-field critical phenomena of equilibrium systems. This material is based upon work supported by the National Science Foundation under INSPIRE Grant No. 1344187.

Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Delay

NASA Astrophysics Data System (ADS)

Pal, Nikhil; Samanta, Sudip; Biswas, Santanu; Alquran, Marwan; Al-Khaled, Kamel; Chattopadhyay, Joydev

In the present paper, we study the effect of gestation delay on a tri-trophic food chain model with Holling type-II functional response. The essential mathematical features of the proposed model are analyzed with the help of equilibrium analysis, stability analysis, and bifurcation theory. Considering time-delay as the bifurcation parameter, the Hopf-bifurcation analysis is carried out around the coexisting equilibrium. The direction of Hopf-bifurcation and the stability of the bifurcating periodic solutions are determined by applying the normal form theory and center manifold theorem. We observe that if the magnitude of the delay is increased, the system loses stability and shows limit cycle oscillations through Hopf-bifurcation. The system also shows the chaotic dynamics via period-doubling bifurcation for further enhancement of time-delay. Our analytical findings are illustrated through numerical simulations.

Emergence of the bifurcation structure of a Langmuir-Blodgett transfer model

NASA Astrophysics Data System (ADS)

Köpf, Michael H.; Thiele, Uwe

2014-11-01

We explore the bifurcation structure of a modified Cahn-Hilliard equation that describes a system that may undergo a first-order phase transition and is kept permanently out of equilibrium by a lateral driving. This forms a simple model, e.g., for the deposition of stripe patterns of different phases of surfactant molecules through Langmuir-Blodgett transfer. Employing continuation techniques the bifurcation structure is numerically investigated using the non-dimensional transfer velocity as the main control parameter. It is found that the snaking structure of steady front states is intertwined with a large number of branches of time-periodic solutions that emerge from Hopf or period-doubling bifurcations and end in global bifurcations (sniper and homoclinic). Overall the bifurcation diagram has a harp-like appearance. This is complemented by a two-parameter study in non-dimensional transfer velocity and domain size (as a measure of the distance to the phase transition threshold) that elucidates through which local and global codimension 2 bifurcations the entire harp-like structure emerges.

Stability of River Bifurcations from Bedload to Suspended Load Dominated Conditions

NASA Astrophysics Data System (ADS)

de Haas, T.; Kleinhans, M. G.

2010-12-01

Bifurcations (also called diffluences) are as common as confluences in braided and anabranched rivers, and more common than confluences on alluvial fans and deltas where the network is essentially distributary. River bifurcations control the partitioning of both water and sediment through these systems with consequences for immediate river and coastal management and long-term evolution. Their stability is poorly understood and seems to differ between braided rivers, meandering river plains and deltas. In particular, it is the question to what extent the division of flow is asymmetrical in stable condition, where highly asymmetrical refers to channel closure and avulsion. Recent work showed that bifurcations in gravel bed braided rivers become more symmetrical with increasing sediment mobility, whereas bifurcations in a lowland sand delta become more asymmetrical with increasing sediment mobility. This difference is not understood and our objective is to resolve this issue. We use a one-dimensional network model with Y-shaped bifurcations to explore the parameter space from low to high sediment mobility. The model solves gradually varied flow, bedload transport and morphological change in a straightforward manner. Sediment is divided at the bifurcation including the transverse slope effect and the spiral flow effect caused by bends at the bifurcation. Width is evolved whilst conserving mass of eroded or built banks with the bed balance. The bifurcations are perturbed from perfect symmetry either by a subtle gradient advantage for one branch or a gentle bend at the bifurcation. Sediment transport was calculated with and without a critical threshold for sediment motion. Sediment mobility, determined in the upstream channel, was varied in three different ways to isolate the causal factor: by increasing discharge, increasing channel gradient and decreasing particle size. In reality the sediment mobility is mostly determined by particle size: gravel bed rivers are near

The use of multiple time point dynamic positron emission tomography/computed tomography in patients with oral/head and neck cancer does not predictably identify metastatic cervical lymph nodes.

PubMed

Carlson, Eric R; Schaefferkoetter, Josh; Townsend, David; McCoy, J Michael; Campbell, Paul D; Long, Misty

2013-01-01

To determine whether the time course of 18-fluorine fluorodeoxyglucose (18F-FDG) activity in multiple consecutively obtained 18F-FDG positron emission tomography (PET)/computed tomography (CT) scans predictably identifies metastatic cervical adenopathy in patients with oral/head and neck cancer. It is hypothesized that the activity will increase significantly over time only in those lymph nodes harboring metastatic cancer. A prospective cohort study was performed whereby patients with oral/head and neck cancer underwent consecutive imaging at 9 time points with PET/CT from 60 to 115 minutes after injection with (18)F-FDG. The primary predictor variable was the status of the lymph nodes based on dynamic PET/CT imaging. Metastatic lymph nodes were defined as those that showed an increase greater than or equal to 10% over the baseline standard uptake values. The primary outcome variable was the pathologic status of the lymph node. A total of 2,237 lymph nodes were evaluated histopathologically in the 83 neck dissections that were performed in 74 patients. A total of 119 lymph nodes were noted to have hypermetabolic activity on the 90-minute (static) portion of the study and were able to be assessed by time points. When we compared the PET/CT time point (dynamic) data with the histopathologic analysis of the lymph nodes, the sensitivity, specificity, positive predictive value, negative predictive value, and accuracy were 60.3%, 70.5%, 66.0%, 65.2%, and 65.5%, respectively. The use of dynamic PET/CT imaging does not permit the ablative surgeon to depend only on the results of the PET/CT study to determine which patients will benefit from neck dissection. As such, we maintain that surgeons should continue to rely on clinical judgment and maintain a low threshold for executing neck dissection in patients with oral/head and neck cancer, including those patients with N0 neck designations. Copyright © 2013 American Association of Oral and Maxillofacial Surgeons. Published

Computational analysis of microbubble flows in bifurcating airways: role of gravity, inertia, and surface tension.

PubMed

Chen, Xiaodong; Zielinski, Rachel; Ghadiali, Samir N

2014-10-01

Although mechanical ventilation is a life-saving therapy for patients with severe lung disorders, the microbubble flows generated during ventilation generate hydrodynamic stresses, including pressure and shear stress gradients, which damage the pulmonary epithelium. In this study, we used computational fluid dynamics to investigate how gravity, inertia, and surface tension influence both microbubble flow patterns in bifurcating airways and the magnitude/distribution of hydrodynamic stresses on the airway wall. Direct interface tracking and finite element techniques were used to simulate bubble propagation in a two-dimensional (2D) liquid-filled bifurcating airway. Computational solutions of the full incompressible Navier-Stokes equation were used to investigate how inertia, gravity, and surface tension forces as characterized by the Reynolds (Re), Bond (Bo), and Capillary (Ca) numbers influence pressure and shear stress gradients at the airway wall. Gravity had a significant impact on flow patterns and hydrodynamic stress magnitudes where Bo > 1 led to dramatic changes in bubble shape and increased pressure and shear stress gradients in the upper daughter airway. Interestingly, increased pressure gradients near the bifurcation point (i.e., carina) were only elevated during asymmetric bubble splitting. Although changes in pressure gradient magnitudes were generally more sensitive to Ca, under large Re conditions, both Re and Ca significantly altered the pressure gradient magnitude. We conclude that inertia, gravity, and surface tension can all have a significant impact on microbubble flow patterns and hydrodynamic stresses in bifurcating airways.

Shells, orbit bifurcations, and symmetry restorations in Fermi systems

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

Magner, A. G., E-mail: magner@kinr.kiev.ua; Koliesnik, M. V.; Arita, K.

The periodic-orbit theory based on the improved stationary-phase method within the phase-space path integral approach is presented for the semiclassical description of the nuclear shell structure, concerning themain topics of the fruitful activity ofV.G. Soloviev. We apply this theory to study bifurcations and symmetry breaking phenomena in a radial power-law potential which is close to the realistic Woods–Saxon one up to about the Fermi energy. Using the realistic parametrization of nuclear shapes we explain the origin of the double-humped fission barrier and the asymmetry in the fission isomer shapes by the bifurcations of periodic orbits. The semiclassical origin of themore » oblate–prolate shape asymmetry and tetrahedral shapes is also suggested within the improved periodic-orbit approach. The enhancement of shell structures at some surface diffuseness and deformation parameters of such shapes are explained by existence of the simple local bifurcations and new non-local bridge-orbit bifurcations in integrable and partially integrable Fermi-systems. We obtained good agreement between the semiclassical and quantum shell-structure components of the level density and energy for several surface diffuseness and deformation parameters of the potentials, including their symmetry breaking and bifurcation values.« less

Bifurcation analysis of a heterogeneous traffic flow model

NASA Astrophysics Data System (ADS)

Wang, Yu-Qing; Yan, Bo-Wen; Zhou, Chao-Fan; Li, Wei-Kang; Jia, Bin

2018-03-01

In this work, a heterogeneous traffic flow model coupled with the periodic boundary condition is proposed. Based on the previous models, a heterogeneous system composed of more than one kind of vehicles is considered. By bifurcation analysis, bifurcation patterns of the heterogeneous system are discussed in three situations in detail and illustrated by diagrams of bifurcation patterns. Besides, the stability analysis of the heterogeneous system is performed to test its anti-interference ability. The relationship between the number of vehicles and the stability is obtained. Furthermore, the attractor analysis is applied to investigate the nature of the heterogeneous system near its steady-state neighborhood. Phase diagrams of the process of the heterogeneous system from initial state to equilibrium state are intuitively presented.

Role of Unchannelized Flow in Determining Bifurcation Angle in Distributary Channel Networks

NASA Astrophysics Data System (ADS)

Coffey, T.

2016-02-01

Distributary channel bifurcations on river deltas are important features in both actively prograding river deltas and in lithified deltas within the stratigraphic record. Attributes of distributary channels have long been thought to be defined by flow velocity, grain size and channel aspect ratio where the channel enters the basin. Interestingly, bifurcations in groundwater-fed tributary networks have been shown to grow and bifurcate independent of flow within the exposed channel network. These networks possess a characteristic bifurcation angle of 72°, based on Laplacian flow (water surface concavity equals zero) in the groundwater flow field near tributary channel tips. Based on the tributary channel model, we develop and test the hypothesis that bifurcation angles in distributary channels are likewise dictated by the external flow field, in this case the surface water surrounding the subaqueous portion of distributary channel tips in a deltaic setting. We measured 64 unique distributary bifurcations in an experimental delta, yielding a characteristic angle of 70.2°±2.2° (95% confidence interval), in line with the theoretical prediction for tributary channels. This similarity between bifurcation angles suggests that (A) flow directly outside of the distributary network is Laplacian, (B) the external flow field controls the bifurcation dynamics of distributary channels, and (C) that flow within the channel plays a secondary role in network dynamics.

Local and global Hopf bifurcation analysis in a neutral-type neuron system with two delays

NASA Astrophysics Data System (ADS)

Lv, Qiuyu; Liao, Xiaofeng

2018-03-01

In recent years, neutral-type differential-difference equations have been applied extensively in the field of engineering, and their dynamical behaviors are more complex than that of the delay differential-difference equations. In this paper, the equations used to describe a neutral-type neural network system of differential difference equation with two delays are studied (i.e. neutral-type differential equations). Firstly, by selecting τ1, τ2 respectively as a parameter, we provide an analysis about the local stability of the zero equilibrium point of the equations, and sufficient conditions of asymptotic stability for the system are derived. Secondly, by using the theory of normal form and applying the theorem of center manifold introduced by Hassard et al., the Hopf bifurcation is found and some formulas for deciding the stability of periodic solutions and the direction of Hopf bifurcation are given. Moreover, by applying the theorem of global Hopf bifurcation, the existence of global periodic solution of the system is studied. Finally, an example is given, and some computer numerical simulations are taken to demonstrate and certify the correctness of the presented results.

TQ-bifurcations in discrete dynamical systems: Analysis of qualitative rearrangements of the oscillation mode

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

Makarenko, A. V., E-mail: avm.science@mail.ru

A new class of bifurcations is defined in discrete dynamical systems, and methods for their diagnostics and the analysis of their properties are presented. The TQ-bifurcations considered are implemented in discrete mappings and are related to the qualitative rearrangement of the shape of trajectories in an extended space of states. Within the demonstration of the main capabilities of the toolkit, an analysis is carried out of a logistic mapping in a domain to the right of the period-doubling limit point. Five critical values of the parameter are found for which the geometric structure of the trajectories of the mapping experiencesmore » a qualitative rearrangement. In addition, an analysis is carried out of the so-called “trace map,” which arises in the problems of quantum-mechanical description of various properties of discrete crystalline and quasicrystalline lattices.« less

Modified jailed balloon technique for bifurcation lesions.

PubMed

Saito, Shigeru; Shishido, Koki; Moriyama, Noriaki; Ochiai, Tomoki; Mizuno, Shingo; Yamanaka, Futoshi; Sugitatsu, Kazuya; Tobita, Kazuki; Matsumi, Junya; Tanaka, Yutaka; Murakami, Masato

2017-12-04

We propose a new systematic approach in bifurcation lesions, modified jailed balloon technique (M-JBT), and report the first clinical experience. Side branch occlusion brings with a serious complication and occurs in more than 7.0% of cases during bifurcation stenting. A jailed balloon (JB) is introduced into the side branch (SB), while a stent is placed in the main branch (MB) as crossing SB. The size of the JB is half of the MB stent size. While the proximal end of JB attaching to MB stent, both stent and JB are simultaneously inflated with same pressure. JB is removed and then guidewires are recrossed. Kissing balloon dilatation (KBD) and/or T and protrusion (TAP) stenting are applied as needed. Between February 2015 and February 2016, 233 patients (254 bifurcation lesions including 54 left main trunk disease) underwent percutaneous coronary intervention (PCI) using this technique. Procedure success was achieved in all cases. KBD was performed for 183 lesions and TAP stenting was employed for 31 lesions. Occlusion of SV was not observed in any of the patients. Bench test confirmed less deformity of MB stent in M-JBT compared with conventional-JBT. This is the first report for clinical experiences by using modified jailed balloon technique. This novel M-JBT is safe and effective in the preservation of SB patency during bifurcation stenting. © 2017 Wiley Periodicals, Inc.

Three-dimensional motion and deformation of a red blood cell in bifurcated microvessels

NASA Astrophysics Data System (ADS)

Ye, Ting; Peng, Lina; Li, Yu

2018-02-01

Microvessels are generally not simple straight tubes, but rather they continually bifurcate (namely, diverging bifurcation) and merge with other microvessels (namely, converging bifurcation). This paper presents a simulation study on the three-dimensional motion and deformation of a red blood cell (RBC) in a bifurcated microvessel with both diverging and converging bifurcations. The motion of the fluids inside and outside of the RBC is modeled by smooth dissipative particle dynamics. The RBC membrane is modeled as a triangular network, having the ability to not only resist the stretching and bending deformations, but also to conserve the RBC volume and surface area. The bifurcation configurations have been studied, including the bifurcated angle and the branch diameter, as well as the RBC properties, including the initial shape, shear modulus, and bending modulus. The simulation results show that the RBC deformation can be divided into five stages, when the RBC flows through a diverging-converging bifurcated microvessel. In these five stages, the RBCs have similar deformation trends but different deformation indices, subject to different bifurcation configurations or different RBC properties. If the shear modulus is large enough, the RBC membrane presents several folds; if the bending modulus is large enough, the RBC loses the symmetry completely with the long shape. These results are helpful in understanding the motion and deformation of healthy or unhealthy cells in blood microcirculation.

Modifying PASVART to solve singular nonlinear 2-point boundary problems

NASA Technical Reports Server (NTRS)

Fulton, James P.

1988-01-01

To study the buckling and post-buckling behavior of shells and various other structures, one must solve a nonlinear 2-point boundary problem. Since closed-form analytic solutions for such problems are virtually nonexistent, numerical approximations are inevitable. This makes the availability of accurate and reliable software indispensable. In a series of papers Lentini and Pereyra, expanding on the work of Keller, developed PASVART: an adaptive finite difference solver for nonlinear 2-point boundary problems. While the program does produce extremely accurate solutions with great efficiency, it is hindered by a major limitation. PASVART will only locate isolated solutions of the problem. In buckling problems, the solution set is not unique. It will contain singular or bifurcation points, where different branches of the solution set may intersect. Thus, PASVART is useless precisely when the problem becomes interesting. To resolve this deficiency we propose a modification of PASVART that will enable the user to perform a more complete bifurcation analysis. PASVART would be combined with the Thurston bifurcation solution: as adaptation of Newton's method that was motivated by the work of Koiter 3 are reinterpreted in terms of an iterative computational method by Thurston.

Comparison of saddle, lumbar epidural and caudal blocks on anal sphincter tone: A prospective, randomized study.

PubMed

Shon, Yoon-Jung; Huh, Jin; Kang, Sung-Sik; Bae, Seung-Kil; Kang, Ryeong-Ah; Kim, Duk-Kyung

2016-10-01

Objective To compare the effects of saddle, lumbar epidural and caudal blocks on anal sphincter tone using anorectal manometry. Methods Patients undergoing elective anorectal surgery with regional anaesthesia were divided randomly into three groups and received a saddle (SD), lumbar epidural (LE), or caudal (CD) block. Anorectal manometry was performed before and 30 min after each regional block. The degree of motor blockade of the anal sphincter was compared using the maximal resting pressure (MRP) and the maximal squeezing pressure (MSP). Results The study analysis population consisted of 49 patients (SD group, n = 18; LE group, n = 16; CD group, n = 15). No significant differences were observed in the percentage inhibition of the MRP among the three regional anaesthetic groups. However, percentage inhibition of the MSP was significantly greater in the SD group (83.6 ± 13.7%) compared with the LE group (58.4 ± 19.8%) and the CD group (47.8 ± 16.9%). In all groups, MSP was reduced significantly more than MRP after each regional block. Conclusions Saddle block was more effective than lumbar epidural or caudal block for depressing anal sphincter tone. No differences were detected between lumbar epidural and caudal blocks.

The appearance, motion, and disappearance of three-dimensional magnetic null points

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

Murphy, Nicholas A., E-mail: namurphy@cfa.harvard.edu; Parnell, Clare E.; Haynes, Andrew L.

2015-10-15

While theoretical models and simulations of magnetic reconnection often assume symmetry such that the magnetic null point when present is co-located with a flow stagnation point, the introduction of asymmetry typically leads to non-ideal flows across the null point. To understand this behavior, we present exact expressions for the motion of three-dimensional linear null points. The most general expression shows that linear null points move in the direction along which the magnetic field and its time derivative are antiparallel. Null point motion in resistive magnetohydrodynamics results from advection by the bulk plasma flow and resistive diffusion of the magnetic field,more » which allows non-ideal flows across topological boundaries. Null point motion is described intrinsically by parameters evaluated locally; however, global dynamics help set the local conditions at the null point. During a bifurcation of a degenerate null point into a null-null pair or the reverse, the instantaneous velocity of separation or convergence of the null-null pair will typically be infinite along the null space of the Jacobian matrix of the magnetic field, but with finite components in the directions orthogonal to the null space. Not all bifurcating null-null pairs are connected by a separator. Furthermore, except under special circumstances, there will not exist a straight line separator connecting a bifurcating null-null pair. The motion of separators cannot be described using solely local parameters because the identification of a particular field line as a separator may change as a result of non-ideal behavior elsewhere along the field line.« less

The anatomy of the bifurcated neural spine and its occurrence within Tetrapoda.

PubMed

Woodruff, D Cary

2014-09-01

Vertebral neural spine bifurcation has been historically treated as largely restrictive to sauropodomorph dinosaurs; wherein it is inferred to be an adaptation in response to the increasing weight from the horizontally extended cervical column. Because no extant terrestrial vertebrates have massive, horizontally extended necks, extant forms with large cranial masses were examined for the presence of neural spine bifurcation. Here, I report for the first time on the soft tissue surrounding neural spine bifurcation in a terrestrial quadruped through the dissection of three Ankole-Watusi cattle. With horns weighing up to a combined 90 kg, the Ankole-Watusi is unlike any other breed of cattle in terms of cranial weight and presence of neural spine bifurcation. Using the Ankole-Watusi as a model, it appears that neural spine bifurcation plays a critical role in supporting a large mobile weight adjacent to the girdles. In addition to neural spine bifurcation being recognized within nonavian dinosaurs, this vertebral feature is also documented within many members of temnospondyls, captorhinids, seymouriamorphs, diadectomorphs, Aves, marsupials, artiodactyls, perissodactyls, and Primates, amongst others. This phylogenetic distribution indicates that spine bifurcation is more common than previously thought, and that this vertebral adaptation has contributed throughout the evolutionary history of tetrapods. Neural spine bifurcation should now be recognized as an anatomical component adapted by some vertebrates to deal with massive, horizontal, mobile weights adjacent the girdles. © 2014 Wiley Periodicals, Inc.

Tunable strength saddle-point contacts impact on quantum rings transmission

NASA Astrophysics Data System (ADS)

González, J. J.; Diago-Cisneros, L.

2016-09-01

A particular subject of investigation is the role of several sadle-point contact (QPC) parameters on the scattering properties of an Aharonov-Bohm-Aharonov-Casher quantum ring (QR) under Rashba-type spin orbit interaction. We discuss the interplay of the conductance with the confinement strengths and height of the QPC, which yields new and tunable harmonic and non-harmonics patterns, while one manipulates these constriction parameters. This phenomenology may be of utility to implement a novel way to modulate spin interference effects in semiconducting QRs, providing an appealing test-platform for spintronics applications.

Andreas Acrivos Dissertation Prize Lecture: Stability of inviscid flows from bifurcation diagrams exploiting a variational argument

NASA Astrophysics Data System (ADS)

Luzzatto-Fegiz, Paolo

2011-11-01

Steady fluid solutions play a special role in the dynamics of a flow: stable states may be realized in practice, while unstable ones may act as attractors. Unfortunately, determining stability is often a process far more laborious than finding steady states; indeed, even for simple vortex or wave flows, stability properties have often been the subject of debate. We consider here a stability idea originating with Lord Kelvin (1876), which involves using the second variation of the energy, δ2 E , to establish bounds on a perturbation. However, for numerically obtained flows, computing δ2 E explicitly is often not feasible. To circumvent this issue, Saffman & Szeto (1980) proposed an argument linking changes in δ2 E to turning points in a bifurcation diagram, for families of steady flows. Later work has shown that this argument is unreliable; the two key issues are associated with the absence of a formal turning-point theory, and with the inability to detect bifurcations (Dritschel 1995, and references therein). In this work, we build on ideas from bifurcation theory, and link turning points in a velocity-impulse diagram to changes in δ2 E ; in addition, this diagram delivers the direction of the change of δ2 E , thereby providing information as to whether stability is gained or lost. To detect hidden solution branches, we introduce to these fluid problems concepts from imperfection theory. The resulting approach, involving ``imperfect velocity-impulse'' diagrams, leads us to new and surprising results for a wide range of fundamental vortex and wave flows; we mention here the calculation of the first steady vortices without any symmetry, and the uncovering of the complete solution structure for vortex pairs. In addition, we find precise agreement with available results from linear stability analysis. Doctoral work advised by C.H.K. Williamson at Cornell University.

An experimental investigation of bubble splitting through multiple bifurcations

NASA Astrophysics Data System (ADS)

Bull, Joseph L.; Eshpuniyani, Brijesh; Fowlkes, J. Brian

2004-11-01

A bench top vascular bifurcation model is used to investigate the splitting of long bubbles in a series of liquid-filled bifurcations. These experiments are motivated by a gas embolotherapy technique for the potential treatment of cancer by using gas emboli to infarct tumors. The gas bubbles originate as perfluorocarbon droplets that are small enough to pass through capillaries and are injected into the bloodstream. Low intensity ultrasound is used to track their motion, and they are vaporized at the desired location for treatment via high intensity ultrasound to produce gas bubbles whose volumes are approximately 125 to 150 times the droplet volume. Achieving complete tumor necrosis requires infarction of most of the tumor. Understanding the transport and splitting of the gas bubbles, which can be long enough to extend through more than one bifurcation, is necessary to design delivery strategies. The current experiments investigate the behavior of a bubble as it passes through a series of two geometrically symmetric bifurcations, for different values of effective Bond number, which depends on gravity and the positioning of the bifurcation, capillary number, and bubble volume. The experiments are designed to match the Reynolds, Bond and capillary numbers to the physiological values for arterioles, and to provide guidance in achieving uniform tumor infarction. This work is supported by NSF grant BES-0301278 and NIH grant EB003541-01.

Magnetic navigation system assisted stenting of coronary bifurcation lesions.

PubMed

Simsek, Cihan; Magro, Michael; Patterson, Mark S; Onuma, Yoshinobu; Ciampichetti, Isabella; van Weenen, Sander; van Domburg, Ron T; Serruys, Patrick W; Boersma, Eric; van Geuns, Robert-Jan

2011-03-01

Magnetic guidewire assisted percutaneous coronary interventions (MPCI) could have certain advantages in coronary bifurcation lesions. We aimed to report the angiographic characteristics of the bifurcation lesions, as well as the procedural and clinical outcomes of the MPCI patients. The lesion characteristics and the treatment effect were assessed by performing diagnostic and quantitative coronary angiography with dedicated bifurcation software. A total of 76 patients (age 65 years, 78% male) were assigned to undergo MPCI, in which two-thirds of the lesions were located in LAD/D1. Fifty-seven out of 78 lesions (73%) had a diseased side branch and complex stenting techniques were used in the majority of the lesions (64%). All 59/78 (76%) fenestration attempts were successfully performed and only 13 dedicated bifurcation stents were implanted. The average acute gain in minimal luminal diameter was 1.08±0.81 mm, 0.80±0.70 mm and 0.59±0.56 mm for the proximal, distal and side branch, respectively. The procedural success was 69% with a procedure time of 107±43 minutes, fluoroscopy time of 34±24 minutes and contrast use of 338±136 ml. At a mean of 1.8-years follow-up, 15 patients (20%) had a cardiac event. MPCI is associated with good angiographic, fenestration and procedural success rates in the treatment of coronary bifurcation lesions.

Dynamics of the seasonal variation of the North Equatorial Current bifurcation

NASA Astrophysics Data System (ADS)

Chen, Zhaohui; Wu, Lixin

2011-02-01

The dynamics of the seasonal variation of the North Equatorial Current (NEC) bifurcation is studied using a 1.5-layer nonlinear reduced-gravity Pacific basin model and a linear, first-mode baroclinic Rossby wave model. The model-simulated bifurcation latitude exhibits a distinct seasonal cycle with the southernmost latitude in June and the northernmost latitude in November, consistent with observational analysis. It is found that the seasonal migration of the NEC bifurcation latitude (NBL) not only is determined by wind locally in the tropics, as suggested in previous studies, but is also significantly intensified by the extratropical wind through coastal Kelvin waves. The model further demonstrates that the amplitude of the NEC bifurcation is also associated with stratification. A strong (weak) stratification leads to a fast (slow) phase speed of first-mode baroclinic Rossby waves, and thus large (small) annual range of the bifurcation latitude. Therefore, it is expected that in a warm climate the NBL should have a large range of annual migration.

Usefulness of Corsair microcatheter to cross stent struts in bifurcation lesions.

PubMed

Fujimoto, Yoshihide; Iwata, Yo; Yamamoto, Masashi; Kobayashi, Yoshio

2014-01-01

Side branch compromise after stenting in bifurcation lesions is a matter of concern. It may happen that even low-profile balloon catheters do not cross stent struts after rewiring. The Corsair catheter is a hybrid catheter that has features of a microcatheter and a support catheter. The present study evaluated usefulness of the Corsair catheter to facilitate advancing a low-profile balloon catheter through stent struts in bifurcation lesions. After rewiring, low-profile balloon catheters failed to cross stent struts of 29 bifurcation lesions. The Corsair microcatheter successfully crossed stent struts in all lesions except one (97 %) where a stent was implanted to treat in-stent restenosis (stent-in-stent). Low-profile balloon catheters were able to advance into the side branch of all bifurcation lesions where the Corsair microcatheter crossed stent struts. In conclusion, the Corsair microcatheter may be utilized if low-profile balloon catheters are unable to cross stent struts in bifurcation lesions.

Complex bifurcation patterns in a discrete predator-prey model with periodic environmental modulation

NASA Astrophysics Data System (ADS)

Harikrishnan, K. P.

2018-02-01

We consider the simplest model in the family of discrete predator-prey system and introduce for the first time an environmental factor in the evolution of the system by periodically modulating the natural death rate of the predator. We show that with the introduction of environmental modulation, the bifurcation structure becomes much more complex with bubble structure and inverse period doubling bifurcation. The model also displays the peculiar phenomenon of coexistence of multiple limit cycles in the domain of attraction for a given parameter value that combine and finally gets transformed into a single strange attractor as the control parameter is increased. To identify the chaotic regime in the parameter plane of the model, we apply the recently proposed scheme based on the correlation dimension analysis. We show that the environmental modulation is more favourable for the stable coexistence of the predator and the prey as the regions of fixed point and limit cycle in the parameter plane increase at the expense of chaotic domain.

Anatomic Distribution of Fluorodeoxyglucose-Avid Para-aortic Lymph Nodes in Patients With Cervical Cancer

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

Takiar, Vinita; Fontanilla, Hiral P.; Eifel, Patricia J.

Purpose: Conformal treatment of para-aortic lymph nodes (PAN) in cervical cancer allows dose escalation and reduces normal tissue toxicity. Currently, data documenting the precise location of involved PAN are lacking. We define the spatial distribution of this high-risk nodal volume by analyzing fluorodeoxyglucose (FDG)-avid lymph nodes (LNs) on positron emission tomography/computed tomography (PET/CT) scans in patients with cervical cancer. Methods and Materials: We identified 72 PANs on pretreatment PET/CT of 30 patients with newly diagnosed stage IB-IVA cervical cancer treated with definitive chemoradiation. LNs were classified as left-lateral para-aortic (LPA), aortocaval (AC), or right paracaval (RPC). Distances from the LNmore » center to the closest vessel and adjacent vertebral body were calculated. Using deformable image registration, nodes were mapped to a template computed tomogram to provide a visual impression of nodal frequencies and anatomic distribution. Results: We identified 72 PET-positive para-aortic lymph nodes (37 LPA, 32 AC, 3 RPC). All RPC lymph nodes were in the inferior third of the para-aortic region. The mean distance from aorta for all lymph nodes was 8.3 mm (range, 3-17 mm), and from the inferior vena cava was 5.6 mm (range, 2-10 mm). Of the 72 lymph nodes, 60% were in the inferior third, 36% were in the middle third, and 4% were in the upper third of the para-aortic region. In all, 29 of 30 patients also had FDG-avid pelvic lymph nodes. Conclusions: A total of 96% of PET positive nodes were adjacent to the aorta; PET positive nodes to the right of the IVC were rare and were all located distally, within 3 cm of the aortic bifurcation. Our findings suggest that circumferential margins around the vessels do not accurately define the nodal region at risk. Instead, the anatomical extent of the nodal basin should be contoured on each axial image to provide optimal coverage of the para-aortic nodal compartment.« less

Statistical prescission point model of fission fragment angular distributions

NASA Astrophysics Data System (ADS)

John, Bency; Kataria, S. K.

1998-03-01

In light of recent developments in fission studies such as slow saddle to scission motion and spin equilibration near the scission point, the theory of fission fragment angular distribution is examined and a new statistical prescission point model is developed. The conditional equilibrium of the collective angular bearing modes at the prescission point, which is guided mainly by their relaxation times and population probabilities, is taken into account in the present model. The present model gives a consistent description of the fragment angular and spin distributions for a wide variety of heavy and light ion induced fission reactions.

Resilience and tipping points of an exploited fish population over six decades.

PubMed

Vasilakopoulos, Paraskevas; Marshall, C Tara

2015-05-01

Complex natural systems with eroded resilience, such as populations, ecosystems and socio-ecological systems, respond to small perturbations with abrupt, discontinuous state shifts, or critical transitions. Theory of critical transitions suggests that such systems exhibit fold bifurcations featuring folded response curves, tipping points and alternate attractors. However, there is little empirical evidence of fold bifurcations occurring in actual complex natural systems impacted by multiple stressors. Moreover, resilience of complex systems to change currently lacks clear operational measures with generic application. Here, we provide empirical evidence for the occurrence of a fold bifurcation in an exploited fish population and introduce a generic measure of ecological resilience based on the observed fold bifurcation attributes. We analyse the multivariate development of Barents Sea cod (Gadus morhua), which is currently the world's largest cod stock, over six decades (1949-2009), and identify a population state shift in 1981. By plotting a multivariate population index against a multivariate stressor index, the shift mechanism was revealed suggesting that the observed population shift was a nonlinear response to the combined effects of overfishing and climate change. Annual resilience values were estimated based on the position of each year in relation to the fitted attractors and assumed tipping points of the fold bifurcation. By interpolating the annual resilience values, a folded stability landscape was fit, which was shaped as predicted by theory. The resilience assessment suggested that the population may be close to another tipping point. This study illustrates how a multivariate analysis, supported by theory of critical transitions and accompanied by a quantitative resilience assessment, can clarify shift mechanisms in data-rich complex natural systems. © 2014 John Wiley & Sons Ltd.

Role of Unchannelized Flow in Determining Bifurcation Angle in Distributary Channel Networks

NASA Astrophysics Data System (ADS)

Coffey, T.

2016-12-01

Distributary channel bifurcations on river deltas are important features in both modern systems, where the channels control water, sediment, and nutrient routing, and in ancient deltas, where the channel networks can dictate large-scale stratigraphic heterogeneity. Geometric features of distributary channels, such as channel dimensions and network structure, have long been thought to be defined by factors such as flow velocity, grain size, or channel aspect ratio where the channel enters the basin. We use theory originally developed for tributary networks fed by groundwater seepage to understand the dynamics of distributary channel bifurcations. Interestingly, bifurcations in groundwater-fed tributary networks have been shown to evolve dependent on the diffusive flow patterns around the channel network. These networks possess a characteristic bifurcation angle of 72°, due to Laplacian flow (gradient2h2=0, where h is water surface elevation) in the groundwater flow field near tributary channel tips. We develop and test the hypothesis that bifurcation angles in distributary channel networks are likewise dictated by the external flow field, in this case the shallow surface water surrounding the subaqueous portion of distributary channel bifurcations in a deltaic setting. We measured 130 unique distributary channel bifurcations in a single experimental delta and in 10 natural deltas, yielding a mean angle of 70.35°±2.59° (95% confidence interval), in line with the theoretical prediction. This similarity implies that flow outside of the distributary channel network is also Laplacian, which we use scaling arguments to justify. We conclude that the dynamics of the unchannelized flow control bifurcation formation in distributary networks.

Message propagation in the network based on node credibility

NASA Astrophysics Data System (ADS)

Nian, Fuzhong; Dang, Zhongkai

2018-04-01

In the propagation efficiency point of view, the node credibility is introduced in this paper. For the message receiver, the node would partially believe the message according to the credibility of the propagator. For a node, the credibility is variable. The more the true message spread, the higher the credibility, and vice versa, the credibility becomes smaller. Based on the idea, a new network was established with the node credibility. Finally, a comparing experiment between the fully trusted network and the network with the node credibility was implemented. The results indicate that the spread effect of messages is better in the network with the node credibility.

Anomalous neuronal responses to fluctuated inputs

NASA Astrophysics Data System (ADS)

Hosaka, Ryosuke; Sakai, Yutaka

2015-10-01

The irregular firing of a cortical neuron is thought to result from a highly fluctuating drive that is generated by the balance of excitatory and inhibitory synaptic inputs. A previous study reported anomalous responses of the Hodgkin-Huxley neuron to the fluctuated inputs where an irregularity of spike trains is inversely proportional to an input irregularity. In the current study, we investigated the origin of these anomalous responses with the Hindmarsh-Rose neuron model, map-based models, and a simple mixture of interspike interval distributions. First, we specified the parameter regions for the bifurcations in the Hindmarsh-Rose model, and we confirmed that the model reproduced the anomalous responses in the dynamics of the saddle-node and subcritical Hopf bifurcations. For both bifurcations, the Hindmarsh-Rose model shows bistability in the resting state and the repetitive firing state, which indicated that the bistability was the origin of the anomalous input-output relationship. Similarly, the map-based model that contained bistability reproduced the anomalous responses, while the model without bistability did not. These results were supported by additional findings that the anomalous responses were reproduced by mimicking the bistable firing with a mixture of two different interspike interval distributions. Decorrelation of spike trains is important for neural information processing. For such spike train decorrelation, irregular firing is key. Our results indicated that irregular firing can emerge from fluctuating drives, even weak ones, under conditions involving bistability. The anomalous responses, therefore, contribute to efficient processing in the brain.

A ryanodine receptor-dependent Ca(i)(2+) asymmetry at Hensen's node mediates avian lateral identity.

PubMed

Garic-Stankovic, Ana; Hernandez, Marcos; Flentke, George R; Zile, Maija H; Smith, Susan M

2008-10-01

In mouse, the establishment of left-right (LR) asymmetry requires intracellular calcium (Ca(i)(2+)) enrichment on the left of the node. The use of Ca(i)(2+) asymmetry by other vertebrates, and its origins and relationship to other laterality effectors are largely unknown. Additionally, the architecture of Hensen's node raises doubts as to whether Ca(i)(2+) asymmetry is a broadly conserved mechanism to achieve laterality. We report here that the avian embryo uses a left-side enriched Ca(i)(2+) asymmetry across Hensen's node to govern its lateral identity. Elevated Ca(i)(2+) was first detected along the anterior node at early HH4, and its emergence and left-side enrichment by HH5 required both ryanodine receptor (RyR) activity and extracellular calcium, implicating calcium-induced calcium release (CICR) as the novel source of the Ca(i)(2+). Targeted manipulation of node Ca(i)(2+) randomized heart laterality and affected nodal expression. Bifurcation of the Ca(i)(2+) field by the emerging prechordal plate may permit the independent regulation of LR Ca(i)(2+) levels. To the left of the node, RyR/CICR and H(+)V-ATPase activity sustained elevated Ca(i)(2+). On the right, Ca(i)(2+) levels were actively repressed through the activities of H(+)K(+) ATPase and serotonin-dependent signaling, thus identifying a novel mechanism for the known effects of serotonin on laterality. Vitamin A-deficient quail have a high incidence of situs inversus hearts and had a reversed calcium asymmetry. Thus, Ca(i)(2+) asymmetry across the node represents a more broadly conserved mechanism for laterality among amniotes than had been previously believed.

Calcification at orifices of aortic arch branches is a reliable and significant marker of stenosis at carotid bifurcation and intracranial arteries.

PubMed

Yamada, Shigeki; Hashimoto, Kenji; Ogata, Hideki; Watanabe, Yoshihiko; Oshima, Marie; Miyake, Hidenori

2014-02-01

Simple rating scale for calcification in the cervical arteries and the aortic arch on multi-detector computed tomography angiography (MDCTA) was evaluated its reliability and validity. Additionally, we investigated where is the most representative location for evaluating the calcification risk of carotid bifurcation stenosis and atherosclerotic infarction in the overall cervical arteries covering from the aortic arch to the carotid bifurcation. The aortic arch and cervical arteries among 518 patients (292 men, 226 women) were evaluated the extent of calcification using a 4-point grading scale for MDCTA. Reliability, validity and the concomitant risk with vascular stenosis and atherosclerotic infarction were assessed. Calcification was most frequently observed in the aortic arch itself, the orifices from the aortic arch, and the carotid bifurcation. Compared with the bilateral carotid bifurcations, the aortic arch itself had a stronger inter-observer agreement for the calcification score (Fleiss' kappa coefficients; 0.77), but weaker associations with stenosis and atherosclerotic infarction. Calcification at the orifices of the aortic arch branches had a stronger inter-observer agreement (0.74) and enough associations with carotid bifurcation stenosis and intracranial stenosis. In addition, the extensive calcification at the orifices from the aortic arch was significantly associated with atherosclerotic infarction, similar to the calcification at the bilateral carotid bifurcations. The orifices of the aortic arch branches were the novel representative location of the aortic arch and overall cervical arteries for evaluating the calcification extent. Thus, calcification at the aortic arch should be evaluated with focus on the orifices of 3 main branches. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

The Hunt Opinion Model—An Agent Based Approach to Recurring Fashion Cycles

PubMed Central

Apriasz, Rafał; Krueger, Tyll; Marcjasz, Grzegorz; Sznajd-Weron, Katarzyna

2016-01-01

We study a simple agent-based model of the recurring fashion cycles in the society that consists of two interacting communities: “snobs” and “followers” (or “opinion hunters”, hence the name of the model). Followers conform to all other individuals, whereas snobs conform only to their own group and anticonform to the other. The model allows to examine the role of the social structure, i.e. the influence of the number of inter-links between the two communities, as well as the role of the stability of links. The latter is accomplished by considering two versions of the same model—quenched (parameterized by fraction L of fixed inter-links) and annealed (parameterized by probability p that a given inter-link exists). Using Monte Carlo simulations and analytical treatment (the latter only for the annealed model), we show that there is a critical fraction of inter-links, above which recurring cycles occur. For p ≤ 0.5 we derive a relation between parameters L and p that allows to compare both models and show that the critical value of inter-connections, p*, is the same for both versions of the model (annealed and quenched) but the period of a fashion cycle is shorter for the quenched model. Near the critical point, the cycles are irregular and a change of fashion is difficult to predict. For the annealed model we also provide a deeper theoretical analysis. We conjecture on topological grounds that the so-called saddle node heteroclinic bifurcation appears at p*. For p ≥ 0.5 we show analytically the existence of the second critical value of p, for which the system undergoes Hopf’s bifurcation. PMID:27835679

The Hunt Opinion Model-An Agent Based Approach to Recurring Fashion Cycles.

PubMed

Apriasz, Rafał; Krueger, Tyll; Marcjasz, Grzegorz; Sznajd-Weron, Katarzyna

2016-01-01

We study a simple agent-based model of the recurring fashion cycles in the society that consists of two interacting communities: "snobs" and "followers" (or "opinion hunters", hence the name of the model). Followers conform to all other individuals, whereas snobs conform only to their own group and anticonform to the other. The model allows to examine the role of the social structure, i.e. the influence of the number of inter-links between the two communities, as well as the role of the stability of links. The latter is accomplished by considering two versions of the same model-quenched (parameterized by fraction L of fixed inter-links) and annealed (parameterized by probability p that a given inter-link exists). Using Monte Carlo simulations and analytical treatment (the latter only for the annealed model), we show that there is a critical fraction of inter-links, above which recurring cycles occur. For p ≤ 0.5 we derive a relation between parameters L and p that allows to compare both models and show that the critical value of inter-connections, p*, is the same for both versions of the model (annealed and quenched) but the period of a fashion cycle is shorter for the quenched model. Near the critical point, the cycles are irregular and a change of fashion is difficult to predict. For the annealed model we also provide a deeper theoretical analysis. We conjecture on topological grounds that the so-called saddle node heteroclinic bifurcation appears at p*. For p ≥ 0.5 we show analytically the existence of the second critical value of p, for which the system undergoes Hopf's bifurcation.

Bifurcated helical core equilibrium states in tokamaks

NASA Astrophysics Data System (ADS)

Cooper, W. A.; Chapman, I. T.; Schmitz, O.; Turnbull, A. D.; Tobias, B. J.; Lazarus, E. A.; Turco, F.; Lanctot, M. J.; Evans, T. E.; Graves, J. P.; Brunetti, D.; Pfefferlé, D.; Reimerdes, H.; Sauter, O.; Halpern, F. D.; Tran, T. M.; Coda, S.; Duval, B. P.; Labit, B.; Pochelon, A.; Turnyanskiy, M. R.; Lao, L.; Luce, T. C.; Buttery, R.; Ferron, J. R.; Hollmann, E. M.; Petty, C. C.; van Zeeland, M.; Fenstermacher, M. E.; Hanson, J. M.; Lütjens, H.

2013-07-01

Tokamaks with weak to moderate reversed central shear in which the minimum inverse rotational transform (safety factor) qmin is in the neighbourhood of unity can trigger bifurcated magnetohydrodynamic equilibrium states, one of which is similar to a saturated ideal internal kink mode. Peaked prescribed pressure profiles reproduce the ‘snake’ structures observed in many tokamaks which has led to a novel explanation of the snake as a bifurcated equilibrium state. Snake equilibrium structures are computed in simulations of the tokamak à configuration variable (TCV), DIII-D and mega amp spherical torus (MAST) tokamaks. The internal helical deformations only weakly modulate the plasma-vacuum interface which is more sensitive to ripple and resonant magnetic perturbations. On the other hand, the external perturbations do not alter the helical core deformation in a significant manner. The confinement of fast particles in MAST simulations deteriorate with the amplitude of the helical core distortion. These three-dimensional bifurcated solutions constitute a paradigm shift that motivates the applications of tools developed for stellarator research in tokamak physics investigations.

Dynamical importance of van der Waals saddle and excited potential surface in C(1D)+D2 complex-forming reaction

PubMed Central

Shen, Zhitao; Ma, Haitao; Zhang, Chunfang; Fu, Mingkai; Wu, Yanan; Bian, Wensheng; Cao, Jianwei

2017-01-01

Encouraged by recent advances in revealing significant effects of van der Waals wells on reaction dynamics, many people assume that van der Waals wells are inevitable in chemical reactions. Here we find that the weak long-range forces cause van der Waals saddles in the prototypical C(1D)+D2 complex-forming reaction that have very different dynamical effects from van der Waals wells at low collision energies. Accurate quantum dynamics calculations on our highly accurate ab initio potential energy surfaces with van der Waals saddles yield cross-sections in close agreement with crossed-beam experiments, whereas the same calculations on an earlier surface with van der Waals wells produce much smaller cross-sections at low energies. Further trajectory calculations reveal that the van der Waals saddle leads to a torsion then sideways insertion reaction mechanism, whereas the well suppresses reactivity. Quantum diffraction oscillations and sharp resonances are also predicted based on our ground- and excited-state potential energy surfaces. PMID:28094253

Bubble transport in bifurcations

NASA Astrophysics Data System (ADS)

Bull, Joseph; Qamar, Adnan

2017-11-01

Motivated by a developmental gas embolotherapy technique for cancer treatment, we examine the transport of bubbles entrained in liquid. In gas embolotherapy, infarction of tumors is induced by selectively formed vascular gas bubbles that originate from acoustic vaporization of vascular droplets. In the case of non-functionalized droplets with the objective of vessel occlusion, the bubbles are transported by flow through vessel bifurcations, where they may split prior to eventually reach vessels small enough that they become lodged. This splitting behavior affects the distribution of bubbles and the efficacy of flow occlusion and the treatment. In these studies, we investigated bubble transport in bifurcations using computational and theoretical modeling. The model reproduces the variety of experimentally observed splitting behaviors. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Maximum shear stresses were found to decrease with increasing Reynolds number. The initial bubble length was found to affect the splitting behavior in the presence of gravitational asymmetry. This work was supported by NIH Grant R01EB006476.

Input-output relation and energy efficiency in the neuron with different spike threshold dynamics.

PubMed

Yi, Guo-Sheng; Wang, Jiang; Tsang, Kai-Ming; Wei, Xi-Le; Deng, Bin

2015-01-01

Neuron encodes and transmits information through generating sequences of output spikes, which is a high energy-consuming process. The spike is initiated when membrane depolarization reaches a threshold voltage. In many neurons, threshold is dynamic and depends on the rate of membrane depolarization (dV/dt) preceding a spike. Identifying the metabolic energy involved in neural coding and their relationship to threshold dynamic is critical to understanding neuronal function and evolution. Here, we use a modified Morris-Lecar model to investigate neuronal input-output property and energy efficiency associated with different spike threshold dynamics. We find that the neurons with dynamic threshold sensitive to dV/dt generate discontinuous frequency-current curve and type II phase response curve (PRC) through Hopf bifurcation, and weak noise could prohibit spiking when bifurcation just occurs. The threshold that is insensitive to dV/dt, instead, results in a continuous frequency-current curve, a type I PRC and a saddle-node on invariant circle bifurcation, and simultaneously weak noise cannot inhibit spiking. It is also shown that the bifurcation, frequency-current curve and PRC type associated with different threshold dynamics arise from the distinct subthreshold interactions of membrane currents. Further, we observe that the energy consumption of the neuron is related to its firing characteristics. The depolarization of spike threshold improves neuronal energy efficiency by reducing the overlap of Na(+) and K(+) currents during an action potential. The high energy efficiency is achieved at more depolarized spike threshold and high stimulus current. These results provide a fundamental biophysical connection that links spike threshold dynamics, input-output relation, energetics and spike initiation, which could contribute to uncover neural encoding mechanism.

Input-output relation and energy efficiency in the neuron with different spike threshold dynamics

PubMed Central

Yi, Guo-Sheng; Wang, Jiang; Tsang, Kai-Ming; Wei, Xi-Le; Deng, Bin

2015-01-01

Neuron encodes and transmits information through generating sequences of output spikes, which is a high energy-consuming process. The spike is initiated when membrane depolarization reaches a threshold voltage. In many neurons, threshold is dynamic and depends on the rate of membrane depolarization (dV/dt) preceding a spike. Identifying the metabolic energy involved in neural coding and their relationship to threshold dynamic is critical to understanding neuronal function and evolution. Here, we use a modified Morris-Lecar model to investigate neuronal input-output property and energy efficiency associated with different spike threshold dynamics. We find that the neurons with dynamic threshold sensitive to dV/dt generate discontinuous frequency-current curve and type II phase response curve (PRC) through Hopf bifurcation, and weak noise could prohibit spiking when bifurcation just occurs. The threshold that is insensitive to dV/dt, instead, results in a continuous frequency-current curve, a type I PRC and a saddle-node on invariant circle bifurcation, and simultaneously weak noise cannot inhibit spiking. It is also shown that the bifurcation, frequency-current curve and PRC type associated with different threshold dynamics arise from the distinct subthreshold interactions of membrane currents. Further, we observe that the energy consumption of the neuron is related to its firing characteristics. The depolarization of spike threshold improves neuronal energy efficiency by reducing the overlap of Na+ and K+ currents during an action potential. The high energy efficiency is achieved at more depolarized spike threshold and high stimulus current. These results provide a fundamental biophysical connection that links spike threshold dynamics, input-output relation, energetics and spike initiation, which could contribute to uncover neural encoding mechanism. PMID:26074810

Numerical simulation of magnetic nanoparticles targeting in a bifurcation vessel

NASA Astrophysics Data System (ADS)

Larimi, M. M.; Ramiar, A.; Ranjbar, A. A.

2014-08-01

Guiding magnetic iron oxide nanoparticles with the help of an external magnetic field to its target is the principle behind the development of super paramagnetic iron oxide nanoparticles (SPIONs) as novel drug delivery vehicles. The present paper is devoted to study on MDT (Magnetic Drug Targeting) technique by particle tracking in the presence of magnetic field in a bifurcation vessel. The blood flow in bifurcation is considered incompressible, unsteady and Newtonian. The flow analysis applies the time dependent, two dimensional, incompressible Navier-Stokes equations for Newtonian fluids. The Lagrangian particle tracking is performed to estimate particle behavior under influence of imposed magnetic field gradients along the bifurcation. According to the results, the magnetic field increased the volume fraction of particle in target region, but in vessels with high Reynolds number, the efficiency of MDT technique is very low. Also the results showed that in the bifurcation vessels with lower angles, wall shear stress is higher and consequently the risk of the vessel wall rupture increases.

Small-bubble transport and splitting dynamics in a symmetric bifurcation.

PubMed

Qamar, Adnan; Warnez, Matthew; Valassis, Doug T; Guetzko, Megan E; Bull, Joseph L

2017-08-01

Simulations of small bubbles traveling through symmetric bifurcations are conducted to garner information pertinent to gas embolotherapy, a potential cancer treatment. Gas embolotherapy procedures use intra-arterial bubbles to occlude tumor blood supply. As bubbles pass through bifurcations in the blood stream nonhomogeneous splitting and undesirable bioeffects may occur. To aid development of gas embolotherapy techniques, a volume of fluid method is used to model the splitting process of gas bubbles passing through artery and arteriole bifurcations. The model reproduces the variety of splitting behaviors observed experimentally, including the bubble reversal phenomenon. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Small bubbles, having initial length less than twice the vessel diameter, were found unlikely to split in the presence of gravitational asymmetry. Maximum shear stresses were found to decrease exponentially with increasing Reynolds number. Vortex-induced shearing near the bifurcation is identified as a possible mechanism for endothelial cell damage.

Stability of low aspect ratio inverted flags and rods in a uniform flow

NASA Astrophysics Data System (ADS)

Huertas-Cerdeira, Cecilia; Sader, John E.; Gharib, Morteza

2016-11-01

Cantilevered elastic plates and rods in an inverted configuration, where the leading edge is free to move and the trailing edge is clamped, undergo complex dynamics when subjected to a uniform flow. The stability of low aspect ratio inverted plates and rods is theoretically examined, showing that it is markedly different from that of their large aspect ratio counterpart. In the limit of zero aspect ratio, the undeflected equilibrium position is found to be stable for all wind speeds. A saddle-node bifurcation emerges at finite wind speed, giving rise to a strongly deflected stable and a weakly deflected unstable equilibria. This theory is compared to experimental measurements, where good agreement is found. This research was supported by a Grant of the Gordon and Betty Moore Foundation, the Australian Research Council Grants scheme and a "la Caixa" Fellowship Grant for Post-Graduate Studies of "la Caixa" Banking Foundation.

A Practice-Oriented Bifurcation Analysis for Pulse Energy Converters: A Stability Margin

NASA Astrophysics Data System (ADS)

Kolokolov, Yury; Monovskaya, Anna

The popularity of systems of pulse energy conversion (PEC-systems) for practical applications is due to the heightened efficiency of energy conversion processes with comparatively simple realizations. Nevertheless, a PEC-system represents a nonlinear object with a variable structure, and the bifurcation analysis remains the basic tool to describe PEC dynamics evolution. The paper is devoted to the discussion on whether the scientific viewpoint on the natural nonlinear dynamics evolution can be involved in practical applications. We focus on the problems connected with stability boundaries of an operating regime. The results of both small-signal analysis and computational bifurcation analysis are considered in the parametrical space in comparison with the results of the experimental identification of the zonal heterogeneity of the operating process. This allows to propose an adapted stability margin as a sufficiently safe distance before the point after which the operating process begins to lose the stability. Such stability margin can extend the permissible operating domain in the parametrical space at the expense of using cause-and-effect relations in the context of natural regularities of nonlinear dynamics. Reasoning and discussion are based on the experimental and computational results for a synchronous buck converter with a pulse-width modulation. The presented results can be useful, first of all, for PEC-systems with significant variation of equivalent inductance and/or capacity. We believe that the discussion supports a viewpoint by which the contemporary methods of the computational and experimental bifurcation analyses possess both analytical abilities and experimental techniques for promising solutions which could be practice-oriented for PEC-systems.

Chiral interface at the finite temperature transition point of QCD

NASA Technical Reports Server (NTRS)

Frei, Z.; Patkos, A.

1990-01-01

The domain wall between coexisting chirally symmetric and broken symmetry regions is studied in a saddle point approximation to the effective three-flavor sigma model. In the chiral limit the surface tension varies in the range ((40 to -50)MeV)(exp 3). The width of the domain wall is estimated to be approximately or equal to 4.5 fm.

Monolithic diffraction-limited 976-nm laser based on saddle-shaped photo darkening-free Yb-doped fiber

NASA Astrophysics Data System (ADS)

Aleshkina, Svetlana S.; Lipatov, Denis S.; Levchenko, Andrei E.; Medvedkov, Oleg I.; Bobkov, Konstantin K.; Bubnov, Mikhail M.; Guryanov, Alexei N.; Likhachev, Mikhail E.

2018-02-01

Monolithic 976 nm laser design based on a newly developed saddle-shaped Yb-doped fiber has been proposed. The fiber has central single-mode part with core diameter of about 12 μm and ultra-thin square-shaped clad with side of about 42x42 μm. At the both ends of the saddle-shaped fiber the core and the clad sizes were adiabatically increased up to 20/(70x70) μm and the fiber could be spliced with standard (80..125 μm clad) passive fibers using commercially available equipment. Single-mode laser at 976 nm based on the developed fiber has been fabricated and photodarkening-free operation with output power of 10.6 W, which is the record high for all-fiber laser schemes, has been demonstrated.

Analyses of bifurcation of reaction pathways on a global reaction route map: A case study of gold cluster Au5

NASA Astrophysics Data System (ADS)

Harabuchi, Yu; Ono, Yuriko; Maeda, Satoshi; Taketsugu, Tetsuya

2015-07-01

A global reaction route map is generated for Au5 by the anharmonic downward distortion following method in which 5 minima and 14 transition states (TSs) are located. Through vibrational analyses in the 3N - 7 (N = 5) dimensional space orthogonal to the intrinsic reaction coordinate (IRC), along all the IRCs, four IRCs are found to have valley-ridge transition (VRT) points on the way where a potential curvature changes its sign from positive to negative in a direction orthogonal to the IRC. The detailed mechanisms of bifurcations related to the VRTs are discussed by surveying a landscape of the global reaction route map, and the connectivity of VRT points and minima is clarified. Branching of the products through bifurcations is confirmed by ab initio molecular dynamics simulations starting from the TSs. A new feature of the reaction pathways, unification, is found and discussed.

Comparative Analysis of Sequential Proximal Optimizing Technique Versus Kissing Balloon Inflation Technique in Provisional Bifurcation Stenting: Fractal Coronary Bifurcation Bench Test.

PubMed

Finet, Gérard; Derimay, François; Motreff, Pascal; Guerin, Patrice; Pilet, Paul; Ohayon, Jacques; Darremont, Olivier; Rioufol, Gilles

2015-08-24

This study used a fractal bifurcation bench model to compare 6 optimization sequences for coronary bifurcation provisional stenting, including 1 novel sequence without kissing balloon inflation (KBI), comprising initial proximal optimizing technique (POT) + side-branch inflation (SBI) + final POT, called "re-POT." In provisional bifurcation stenting, KBI fails to improve the rate of major adverse cardiac events. Proximal geometric deformation increases the rate of in-stent restenosis and target lesion revascularization. A bifurcation bench model was used to compare KBI alone, KBI after POT, KBI with asymmetric inflation pressure after POT, and 2 sequences without KBI: initial POT plus SBI, and initial POT plus SBI with final POT (called "re-POT"). For each protocol, 5 stents were tested using 2 different drug-eluting stent designs: that is, a total of 60 tests. Compared with the classic KBI-only sequence and those associating POT with modified KBI, the re-POT sequence gave significantly (p < 0.05) better geometric results: it reduced SB ostium stent-strut obstruction from 23.2 ± 6.0% to 5.6 ± 8.3%, provided perfect proximal stent apposition with almost perfect circularity (ellipticity index reduced from 1.23 ± 0.02 to 1.04 ± 0.01), reduced proximal area overstretch from 24.2 ± 7.6% to 8.0 ± 0.4%, and reduced global strut malapposition from 40 ± 6.2% to 2.6 ± 1.4%. In comparison with 5 other techniques, the re-POT sequence significantly optimized the final result of provisional coronary bifurcation stenting, maintaining circular geometry while significantly reducing SB ostium strut obstruction and global strut malapposition. These experimental findings confirm that provisional stenting may be optimized more effectively without KBI using re-POT. Copyright © 2015 American College of Cardiology Foundation. Published by Elsevier Inc. All rights reserved.

THEMIS two‐point measurements of the cross‐tail current density: A thick bifurcated current sheet in the near‐Earth plasma sheet

PubMed Central

2015-01-01

Abstract The basic properties of the near‐Earth current sheet from 8 RE to 12 RE were determined based on Time History of Events and Macroscale Interactions during Substorms (THEMIS) observations from 2007 to 2013. Ampere's law was used to estimate the current density when the locations of two spacecraft were suitable for the calculation. A total of 3838 current density observations were obtained to study the vertical profile. For typical solar wind conditions, the current density near (off) the central plane of the current sheet ranged from 1 to 2 nA/m2 (1 to 8 nA/m2). All the high current densities appeared off the central plane of the current sheet, indicating the formation of a bifurcated current sheet structure when the current density increased above 2 nA/m2. The median profile also showed a bifurcated structure, in which the half thickness was about 3 RE. The distance between the peak of the current density and the central plane of the current sheet was 0.5 to 1 RE. High current densities above 4 nA/m2 were observed in some cases that occurred preferentially during substorms, but they also occurred in quiet times. In contrast to the commonly accepted picture, these high current densities can form without a high solar wind dynamic pressure. In addition, these high current densities can appear in two magnetic configurations: tail‐like and dipolar structures. At least two mechanisms, magnetic flux depletion and new current system formation during the expansion phase, other than plasma sheet compression are responsible for the formation of the bifurcated current sheets. PMID:27722039

Bifurcation structure of localized states in the Lugiato-Lefever equation with anomalous dispersion

NASA Astrophysics Data System (ADS)

Parra-Rivas, P.; Gomila, D.; Gelens, L.; Knobloch, E.

2018-04-01

The origin, stability, and bifurcation structure of different types of bright localized structures described by the Lugiato-Lefever equation are studied. This mean field model describes the nonlinear dynamics of light circulating in fiber cavities and microresonators. In the case of anomalous group velocity dispersion and low values of the intracavity phase detuning these bright states are organized in a homoclinic snaking bifurcation structure. We describe how this bifurcation structure is destroyed when the detuning is increased across a critical value, and determine how a bifurcation structure known as foliated snaking emerges.

IDIS Small Bodies and Dust Node

NASA Astrophysics Data System (ADS)

de Sanctis, M. C.; Capria, M. T.; Carraro, F.; Fonte, S.; Giacomini, L.; Turrini, D.

2009-04-01

The EuroPlaNet information service provides access to lists of researchers, laboratories and data archives relevant to many aspects of planetary and space physics. Information can be accessed through EuroPlaNet website or, for advanced searches, via web-services available at the different thematic nodes. The goal of IDIS is to provide easy-to-use access to resources like people, laboratories, modeling activities and data archives related to planetary sciences. The development of IDIS is an international effort started under the European Commission's 6th Framework Programme and which will expand its capabilities during the 7th Framework Programme, as part of the Capacities Specific Programme/Research Infrastructures. IDIS is complemented by a set of other EuroPlaNet web-services maintained under the responsibility of separate institutions. Each activity maintains its own web-portal with cross-links pointing to the other elements of EuroPlaNet. General access is provided via the EuroPlaNet Homepage. IDIS is not a repository of original data but rather supports the access to various data sources. The final goal of IDIS is to provide Virtual Observatory tools for the access to data from laboratory measurements and ground- and spaced-based observations to modeling results, allowing the combination of as divergent data sources as feasible. IDIS is built around four scientific nodes located in different European countries. Each node deals with a subset of the disciplines related to planetary sciences and, working in cooperation with international experts in these fields, provides a wealth of information to the international planetary science community. The EuroPlaNet IDIS thematic node "Small Bodies and Dust Node" is hosted by the Istituto di Fisica dello Spazio Interplanetario and is established in close cooperation with the Istituto di Astrofisica Spaziale. Both these institutes are part of the Istituto Nazionale di Astrofisica (INAF). The IDIS Small Bodies and Dust

Stability and Hopf Bifurcation for a Delayed SLBRS Computer Virus Model

PubMed Central

Yang, Huizhong

2014-01-01

By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative example is also presented to testify our analytical results. PMID:25202722

Stability and Hopf bifurcation for a delayed SLBRS computer virus model.

PubMed

Zhang, Zizhen; Yang, Huizhong

2014-01-01

By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative example is also presented to testify our analytical results.

On bifurcation delay: An alternative approach using Geometric Singular Perturbation Theory

NASA Astrophysics Data System (ADS)

Hsu, Ting-Hao

2017-02-01

To explain the phenomenon of bifurcation delay, which occurs in planar systems of the form x ˙ = ɛf (x , z , ɛ), z ˙ = g (x , z , ɛ) z, where f (x , 0 , 0) > 0 and g (x , 0 , 0) changes sign at least once on the x-axis, we use the Exchange Lemma in Geometric Singular Perturbation Theory to track the limiting behavior of the solutions. Using the trick of extending dimension to overcome the degeneracy at the turning point, we show that the limiting attracting and repulsion points are given by the well-known entry-exit function, and the minimum of z on the trajectory is of order exp ⁡ (- 1 / ɛ). Also we prove smoothness of the return map up to arbitrary finite order in ɛ.

Bifurcation of potential vorticity gradients across the Southern Hemisphere stratospheric polar vortex

NASA Astrophysics Data System (ADS)

Conway, Jonathan; Bodeker, Greg; Cameron, Chris

2018-06-01

The wintertime stratospheric westerly winds circling the Antarctic continent, also known as the Southern Hemisphere polar vortex, create a barrier to mixing of air between middle and high latitudes. This dynamical isolation has important consequences for export of ozone-depleted air from the Antarctic stratosphere to lower latitudes. The prevailing view of this dynamical barrier has been an annulus compromising steep gradients of potential vorticity (PV) that create a single semi-permeable barrier to mixing. Analyses presented here show that this barrier often displays a bifurcated structure where a double-walled barrier exists. The bifurcated structure manifests as enhanced gradients of PV at two distinct latitudes - usually on the inside and outside flanks of the region of highest wind speed. Metrics that quantify the bifurcated nature of the vortex have been developed and their variation in space and time has been analysed. At most isentropic levels between 395 and 850 K, bifurcation is strongest in mid-winter and decreases dramatically during spring. From August onwards a distinct structure emerges, where elevated bifurcation remains between 475 and 600 K, and a mostly single-walled barrier occurs at other levels. While bifurcation at a given level evolves from month to month, and does not always persist through a season, interannual variations in the strength of bifurcation display coherence across multiple levels in any given month. Accounting for bifurcation allows the region of reduced mixing to be better characterised. These results suggest that improved understanding of cross-vortex mixing requires consideration of the polar vortex not as a single mixing barrier but as a barrier with internal structure that is likely to manifest as more complex gradients in trace gas concentrations across the vortex barrier region.

Research on centrality of urban transport network nodes

NASA Astrophysics Data System (ADS)

Wang, Kui; Fu, Xiufen

2017-05-01

Based on the actual data of urban transport in Guangzhou, 19,150 bus stations in Guangzhou (as of 2014) are selected as nodes. Based on the theory of complex network, the network model of Guangzhou urban transport is constructed. By analyzing the degree centrality index, betweenness centrality index and closeness centrality index of nodes in the network, the level of centrality of each node in the network is studied. From a different point of view to determine the hub node of Guangzhou urban transport network, corresponding to the city's key sites and major transfer sites. The reliability of the network is determined by the stability of some key nodes (transport hub station). The research of network node centralization can provide a theoretical basis for the rational allocation of urban transport network sites and public transport system planning.

Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system

NASA Astrophysics Data System (ADS)

Liu, Shuang; Zhao, Shuang-Shuang; Sun, Bao-Ping; Zhang, Wen-Ming

2014-09-01

Hopf bifurcation and chaos of a nonlinear electromechanical coupling relative rotation system are studied in this paper. Considering the energy in air-gap field of AC motor, the dynamical equation of nonlinear electromechanical coupling relative rotation system is deduced by using the dissipation Lagrange equation. Choosing the electromagnetic stiffness as a bifurcation parameter, the necessary and sufficient conditions of Hopf bifurcation are given, and the bifurcation characteristics are studied. The mechanism and conditions of system parameters for chaotic motions are investigated rigorously based on the Silnikov method, and the homoclinic orbit is found by using the undetermined coefficient method. Therefore, Smale horseshoe chaos occurs when electromagnetic stiffness changes. Numerical simulations are also given, which confirm the analytical results.

Stochastic bifurcations in the nonlinear parallel Ising model.

PubMed

Bagnoli, Franco; Rechtman, Raúl

2016-11-01

We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.

Risk factors for saddle-related skin lesions on elephants used in the tourism industry in Thailand.

PubMed

Magda, Scarlett; Spohn, Olivia; Angkawanish, Taweepoke; Smith, Dale A; Pearl, David L

2015-05-19

Lesions related to working conditions and improper saddle design are a concern for a variety of working animals including elephants. The objectives of the present study were to determine the prevalence of cutaneous lesions in anatomic regions (i.e., neck, girth, back, tail) in contact with saddle-related equipment among elephants in Thailand working in the tourism industry, and to identify potential risk factors associated with these lesions. Data for this cross-sectional study were collected between May 2007 and July 2007 on 194 elephants from 18 tourism camps across Thailand. There was a high prevalence (64.4 %; 95 % CI 57.3 - 71.2) of active lesions, most often located on the back region. Using multilevel multivariable logistic regression modelling containing a random intercept for camp we identified the following risk factors: increasing elephant age, the use of rice sacks as padding material in contact with the skin, and the provision of a break for the elephants. Working hours had a quadratic relationship with the log odds of an active lesion where the probability of an active lesion initially increased with the number of working hours per day and then declined possibly reflecting a "healthy worker" bias where only animals without lesions continue to be able to work these longer hours. While we recognize that the cross-sectional nature of the study posed some inferential limitations, our results offer several potential intervention points for the prevention of these lesions. Specifically, we recommend the following until longitudinal studies can be conducted: increased monitoring of older elephants and the back region of all elephants, working less than 6 hours per day, and the avoidance of rice sacks as padding material in contact with skin.

The integrable case of Adler-van Moerbeke. Discriminant set and bifurcation diagram

NASA Astrophysics Data System (ADS)

Ryabov, Pavel E.; Oshemkov, Andrej A.; Sokolov, Sergei V.

2016-09-01

The Adler-van Moerbeke integrable case of the Euler equations on the Lie algebra so(4) is investigated. For the L- A pair found by Reyman and Semenov-Tian-Shansky for this system, we explicitly present a spectral curve and construct the corresponding discriminant set. The singularities of the Adler-van Moerbeke integrable case and its bifurcation diagram are discussed. We explicitly describe singular points of rank 0, determine their types, and show that the momentum mapping takes them to self-intersection points of the real part of the discriminant set. In particular, the described structure of singularities of the Adler-van Moerbeke integrable case shows that it is topologically different from the other known integrable cases on so(4).

Stability and bifurcation analysis of a generalized scalar delay differential equation.

PubMed

Bhalekar, Sachin

2016-08-01

This paper deals with the stability and bifurcation analysis of a general form of equation D(α)x(t)=g(x(t),x(t-τ)) involving the derivative of order α ∈ (0, 1] and a constant delay τ ≥ 0. The stability of equilibrium points is presented in terms of the stability regions and critical surfaces. We provide a necessary condition to exist chaos in the system also. A wide range of delay differential equations involving a constant delay can be analyzed using the results proposed in this paper. The illustrative examples are provided to explain the theory.

Technique and results of femoral bifurcation endarterectomy by eversion.

PubMed

Dufranc, Julie; Palcau, Laura; Heyndrickx, Maxime; Gouicem, Djelloul; Coffin, Olivier; Felisaz, Aurélien; Berger, Ludovic

2015-03-01

This study evaluated, in a contemporary prospective series, the safety and efficacy of femoral endarterectomy using the eversion technique and compared our results with results obtained in the literature for the standard endarterectomy with patch closure. Between 2010 and 2012, 121 patients (76% male; mean age, 68.7 years; diabetes, 28%; renal insufficiency, 20%) underwent 147 consecutive femoral bifurcation endarterectomies using the eversion technique, associating or not inflow or outflow concomitant revascularization. The indications were claudication in 89 procedures (60%) and critical limb ischemia in 58 (40%). Primary, primary assisted, and secondary patency of the femoral bifurcation, clinical improvement, limb salvage, and survival were assessed using Kaplan-Meier life-table analysis. Factors associated with those primary end-points were evaluated with univariate analysis. The technical success of eversion was of 93.2%. The 30-day mortality was 0%, and the complication rate was 8.2%; of which, half were local and benign. Median follow-up was 16 months (range, 1.6-31.2 months). Primary, primary assisted, and secondary patencies were, respectively, 93.2%, 97.2%, and 98.6% at 2 years. Primary, primary assisted, and secondary maintenance of clinical improvement were, respectively, 79.9%, 94.6%, and 98.6% at 2 years. The predictive factors for clinical degradation were clinical stage (Rutherford category 5 or 6, P = .024), platelet aggregation inhibitor treatment other than clopidogrel (P = .005), malnutrition (P = .025), and bad tibial runoff (P = .0016). A reintervention was necessary in 18.3% of limbs at 2 years: 2% involving femoral bifurcation, 6.1% inflow improvement, and 9.5% outflow improvement. The risk factors of reintervention were platelet aggregation inhibitor (other than clopidogrel, P = .049) and cancer (P = .011). Limb preservation at 2 years was 100% in the claudicant population. Limb salvage was 88.6% in the critical limb ischemia population

SU-E-T-157: Evaluation and Comparison of Doses to Pelvic Lymph Nodes and to Point B with 3D Image Guided Treatment Planning for High Dose Brachytherapy for Treatment of Cervical Cancer

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

Bhandare, N.

2014-06-01

Purpose: To estimate and compare the doses received by the obturator, external and internal iliac lymph nodes and point Methods: CT-MR fused image sets of 15 patients obtained for each of 5 fractions of HDR brachytherapy using tandem and ring applicator, were used to generate treatment plans optimized to deliver a prescription dose to HRCTV-D90 and to minimize the doses to organs at risk (OARs). For each set of image, target volume (GTV, HRCTV) OARs (Bladder, Rectum, Sigmoid), and both left and right pelvic lymph nodes (obturator, external and internal iliac lymph nodes) were delineated. Dose-volume histograms (DVH) were generatedmore » for pelvic nodal groups (left and right obturator group, internal and external iliac chains) Per fraction DVH parameters used for dose comparison included dose to 100% volume (D100), and dose received by 2cc (D2cc), 1cc (D1cc) and 0.1 cc (D0.1cc) of nodal volume. Dose to point B was compared with each DVH parameter using 2 sided t-test. Pearson correlation were determined to examine relationship of point B dose with nodal DVH parameters. Results: FIGO clinical stage varied from 1B1 to IIIB. The median pretreatment tumor diameter measured on MRI was 4.5 cm (2.7– 6.4cm).The median dose to bilateral point B was 1.20 Gy ± 0.12 or 20% of the prescription dose. The correlation coefficients were all <0.60 for all nodal DVH parameters indicating low degree of correlation. Only 2 cc of obturator nodes was not significantly different from point B dose on t-test. Conclusion: Dose to point B does not adequately represent the dose to any specific pelvic nodal group. When using image guided 3D dose-volume optimized treatment nodal groups should be individually identified and delineated to obtain the doses received by pelvic nodes.« less

Bifurcation of finitely deformed thick-walled electroelastic cylindrical tubes subject to a radial electric field

NASA Astrophysics Data System (ADS)

Melnikov, Andrey; Ogden, Ray W.

2018-06-01

This paper is concerned with the bifurcation analysis of a pressurized electroelastic circular cylindrical tube with closed ends and compliant electrodes on its curved boundaries. The theory of small incremental electroelastic deformations superimposed on a finitely deformed electroelastic tube is used to determine those underlying configurations for which the superimposed deformations do not maintain the perfect cylindrical shape of the tube. First, prismatic bifurcations are examined and solutions are obtained which show that for a neo-Hookean electroelastic material prismatic modes of bifurcation become possible under inflation. This result contrasts with that for the purely elastic case for which prismatic bifurcation modes were found only for an externally pressurized tube. Second, axisymmetric bifurcations are analyzed, and results for both neo-Hookean and Mooney-Rivlin electroelastic energy functions are obtained. The solutions show that in the presence of a moderate electric field the electroelastic tube becomes more susceptible to bifurcation, i.e., for fixed values of the axial stretch axisymmetric bifurcations become possible at lower values of the circumferential stretches than in the corresponding problems in the absence of an electric field. As the magnitude of the electric field increases, however, the possibility of bifurcation under internal pressure becomes restricted to a limited range of values of the axial stretch and is phased out completely for sufficiently large electric fields. Then, axisymmetric bifurcation is only possible under external pressure.

Flow topology of rare back flow events and critical points in turbulent channels and toroidal pipes

NASA Astrophysics Data System (ADS)

Chin, C.; Vinuesa, R.; Örlü, R.; Cardesa, J. I.; Noorani, A.; Schlatter, P.; Chong, M. S.

2018-04-01

A study of the back flow events and critical points in the flow through a toroidal pipe at friction Reynolds number Re τ ≈ 650 is performed and compared with the results in a turbulent channel flow at Re τ ≈ 934. The statistics and topological properties of the back flow events are analysed and discussed. Conditionally-averaged flow fields in the vicinity of the back flow event are obtained, and the results for the torus show a similar streamwise wall-shear stress topology which varies considerably for the spanwise wall-shear stress when compared to the channel flow. The comparison between the toroidal pipe and channel flows also shows fewer back flow events and critical points in the torus. This cannot be solely attributed to differences in Reynolds number, but is a clear effect of the secondary flow present in the toroidal pipe. A possible mechanism is the effect of the secondary flow present in the torus, which convects momentum from the inner to the outer bend through the core of the pipe, and back from the outer to the inner bend through the pipe walls. In the region around the critical points, the skin-friction streamlines and vorticity lines exhibit similar flow characteristics with a node and saddle pair for both flows. These results indicate that back flow events and critical points are genuine features of wall-bounded turbulence, and are not artifacts of specific boundary or inflow conditions in simulations and/or measurement uncertainties in experiments.

Stability and Hopf bifurcation for a regulated logistic growth model with discrete and distributed delays

NASA Astrophysics Data System (ADS)

Fang, Shengle; Jiang, Minghui

2009-12-01

In this paper, we investigate the stability and Hopf bifurcation of a new regulated logistic growth with discrete and distributed delays. By choosing the discrete delay τ as a bifurcation parameter, we prove that the system is locally asymptotically stable in a range of the delay and Hopf bifurcation occurs as τ crosses a critical value. Furthermore, explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived by normal form theorem and center manifold argument. Finally, an illustrative example is also given to support the theoretical results.

Cutting Balloon Angioplasty in the Treatment of Short Infrapopliteal Bifurcation Disease.

PubMed

Iezzi, Roberto; Posa, Alessandro; Santoro, Marco; Nestola, Massimiliano; Contegiacomo, Andrea; Tinelli, Giovanni; Paolini, Alessandra; Flex, Andrea; Pitocco, Dario; Snider, Francesco; Bonomo, Lorenzo

2015-08-01

To evaluate the safety, feasibility, and effectiveness of cutting balloon angioplasty in the management of infrapopliteal bifurcation disease. Between November 2010 and March 2013, 23 patients (mean age 69.6±9.01 years, range 56-89; 16 men) suffering from critical limb ischemia were treated using cutting balloon angioplasty (single cutting balloon, T-shaped double cutting balloon, or double kissing cutting balloon technique) for 47 infrapopliteal artery bifurcation lesions (16 popliteal bifurcation and 9 tibioperoneal bifurcation) in 25 limbs. Follow-up consisted of clinical examination and duplex ultrasonography at 1 month and every 3 months thereafter. All treatments were technically successful. No 30-day death or adverse events needing treatment were registered. No flow-limiting dissection was observed, so no stent implantation was necessary. The mean postprocedure minimum lumen diameter and acute gain were 0.28±0.04 and 0.20±0.06 cm, respectively, with a residual stenosis of 0.04±0.02 cm. Primary and secondary patency rates were estimated as 89.3% and 93.5% at 6 months and 77.7% and 88.8% at 12 months, respectively; 1-year primary and secondary patency rates of the treated bifurcation were 74.2% and 87.0%, respectively. The survival rate estimated by Kaplan-Meier analysis was 82.5% at 1 year. Cutting balloon angioplasty seems to be a safe and effective tool in the routine treatment of short/ostial infrapopliteal bifurcation lesions, avoiding procedure-related complications, overcoming the limitations of conventional angioplasty, and improving the outcome of catheter-based therapy. © The Author(s) 2015.

Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions

NASA Astrophysics Data System (ADS)

Barnett, William A.; Duzhak, Evgeniya Aleksandrovna

2008-06-01

Grandmont [J.M. Grandmont, On endogenous competitive business cycles, Econometrica 53 (1985) 995-1045] found that the parameter space of the most classical dynamic models is stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with many forms of multiperiodic dynamics in between. The econometric implications of Grandmont’s findings are particularly important, if bifurcation boundaries cross the confidence regions surrounding parameter estimates in policy-relevant models. Stratification of a confidence region into bifurcated subsets seriously damages robustness of dynamical inferences. Recently, interest in policy in some circles has moved to New-Keynesian models. As a result, in this paper we explore bifurcation within the class of New-Keynesian models. We develop the econometric theory needed to locate bifurcation boundaries in log-linearized New-Keynesian models with Taylor policy rules or inflation-targeting policy rules. Central results needed in this research are our theorems on the existence and location of Hopf bifurcation boundaries in each of the cases that we consider.

On the late-time behavior of Virasoro blocks and a classification of semiclassical saddles

DOE PAGES

Fitzpatrick, A. Liam; Kaplan, Jared

2017-04-12

Recent work has demonstrated that black hole thermodynamics and information loss/restoration in AdS 3/CFT 2 can be derived almost entirely from the behavior of the Virasoro conformal blocks at large central charge, with relatively little dependence on the precise details of the CFT spectrum or OPE coefficients. Here, we elaborate on the non-perturbative behavior of Virasoro blocks by classifying all ‘saddles’ that can contribute for arbitrary values of external and internal operator dimensions in the semiclassical large central charge limit. The leading saddles, which determine the naive semiclassical behavior of the Virasoro blocks, all decay exponentially at late times, andmore » at a rate that is independent of internal operator dimensions. Consequently, the semiclassical contribution of a finite number of high-energy states cannot resolve a well-known version of the information loss problem in AdS 3. Furthermore, we identify two infinite classes of sub-leading saddles, and one of these classes does not decay at late times.« less

Dirac node arcs in PtSn 4

DOE PAGES

Wu, Yun; Wang, Lin -Lin; Mun, Eundeok; ...

2016-04-04

In topological quantum materials 1,2,3 the conduction and valence bands are connected at points or along lines in the momentum space. A number of studies have demonstrated that several materials are indeed Dirac/Weyl semimetals 4,5,6,7,8. However, there is still no experimental confirmation of materials with line nodes, in which the Dirac nodes form closed loops in the momentum space 2,3. Here we report the discovery of a novel topological structure—Dirac node arcs—in the ultrahigh magnetoresistive material PtSn 4 using laser-based angle-resolved photoemission spectroscopy data and density functional theory calculations. Unlike the closed loops of line nodes, the Dirac node arcmore » structure arises owing to the surface states and resembles the Dirac dispersion in graphene that is extended along a short line in the momentum space. Here, we propose that this reported Dirac node arc structure is a novel topological state that provides an exciting platform for studying the exotic properties of Dirac fermions.« less

Dynamic bifurcation and strange nonchaos in a two-frequency parametrically driven nonlinear oscillator

NASA Astrophysics Data System (ADS)

Premraj, D.; Suresh, K.; Palanivel, J.; Thamilmaran, K.

2017-09-01

A periodically forced series LCR circuit with Chua's diode as a nonlinear element exhibits slow passage through Hopf bifurcation. This slow passage leads to a delay in the Hopf bifurcation. The delay in this bifurcation is a unique quantity and it can be predicted using various numerical analysis. We find that when an additional periodic force is added to the system, the delay in bifurcation becomes chaotic which leads to an unpredictability in bifurcation delay. Further, we study the bifurcation of the periodic delay to chaotic delay in the slow passage effect through strange nonchaotic delay. We also report the occurrence of strange nonchaotic dynamics while varying the parameter of the additional force included in the system. We observe that the system exhibits a hitherto unknown dynamical transition to a strange nonchaotic attractor. With the help of Lyapunov exponent, we explain the new transition to strange nonchaotic attractor and its mechanism is studied by making use of rational approximation theory. The birth of SNA has also been confirmed numerically, using Poincaré maps, phase sensitivity exponent, the distribution of finite-time Lyapunov exponents and singular continuous spectrum analysis.

Microbubble transport through a bifurcating vessel network with pulsatile flow.

PubMed

Valassis, Doug T; Dodde, Robert E; Esphuniyani, Brijesh; Fowlkes, J Brian; Bull, Joseph L

2012-02-01

Motivated by two-phase microfluidics and by the clinical applications of air embolism and a developmental gas embolotherapy technique, experimental and theoretical models of microbubble transport in pulsatile flow are presented. The one-dimensional time-dependent theoretical model is developed from an unsteady Bernoulli equation that has been modified to include viscous and unsteady effects. Results of both experiments and theory show that roll angle (the angle the plane of the bifurcating network makes with the horizontal) is an important contributor to bubble splitting ratio at each bifurcation within the bifurcating network. When compared to corresponding constant flow, pulsatile flow was shown to produce insignificant changes to the overall splitting ratio of the bubble despite the order one Womersley numbers, suggesting that bubble splitting through the vasculature could be modeled adequately with a more modest constant flow model. However, bubble lodging was affected by the flow pulsatility, and the effects of pulsatile flow were evident in the dependence of splitting ratio of bubble length. The ability of bubbles to remain lodged after reaching a steady state in the bifurcations is promising for the effectiveness of gas embolotherapy to occlude blood flow to tumors, and indicates the importance of understanding where lodging will occur in air embolism. The ability to accurately predict the bubble dynamics in unsteady flow within a bifurcating network is demonstrated and suggests the potential for bubbles in microfluidics devices to encode information in both steady and unsteady aspects of their dynamics.

Analysis of non-Newtonian effects within an aorta-iliac bifurcation region.

PubMed

Iasiello, Marcello; Vafai, Kambiz; Andreozzi, Assunta; Bianco, Nicola

2017-11-07

The geometry of the arteries at or near arterial bifurcation influences the blood flow field, which is an important factor affecting arteriogenesis. The blood can act sometimes as a non-Newtonian fluid. However, many studies have argued that for large and medium arteries, the blood flow can be considered to be Newtonian. In this work a comprehensive investigation of non-Newtonian effects on the blood fluid dynamic behavior in an aorta-iliac bifurcation is presented. The aorta-iliac geometry is reconstructed with references to the values reported in Shah et al. (1978); the 3D geometrical model consists of three filleted cylinders of different diameters. Governing equations with the appropriate boundary conditions are solved with a finite-element code. Different rheological models are used for the blood flow through the lumen and detailed comparisons are presented for the aorta-iliac bifurcation. Results are presented in terms of the velocity profiles in the bifurcation zone and Wall Shear Stress (WSS) for different sides of the bifurcation both for male and female geometries, showing that the Newtonian fluid assumption can be made without any particular loss in terms of accuracy with respect to the other more complex rheological models. Copyright © 2017 Elsevier Ltd. All rights reserved.

Backward Bifurcation in a Cholera Model: A Case Study of Outbreak in Zimbabwe and Haiti

NASA Astrophysics Data System (ADS)

Sharma, Sandeep; Kumari, Nitu

In this paper, a nonlinear deterministic model is proposed with a saturated treatment function. The expression of the basic reproduction number for the proposed model was obtained. The global dynamics of the proposed model was studied using the basic reproduction number and theory of dynamical systems. It is observed that proposed model exhibits backward bifurcation as multiple endemic equilibrium points exist when R0 < 1. The existence of backward bifurcation implies that making R0 < 1 is not enough for disease eradication. This, in turn, makes it difficult to control the spread of cholera in the community. We also obtain a unique endemic equilibria when R0 > 1. The global stability of unique endemic equilibria is performed using the geometric approach. An extensive numerical study is performed to support our analytical results. Finally, we investigate two major cholera outbreaks, Zimbabwe (2008-09) and Haiti (2010), with the help of the present study.

Bifurcation and Control in a Singular Phytoplankton-Zooplankton-Fish Model with Nonlinear Fish Harvesting and Taxation

NASA Astrophysics Data System (ADS)

Meng, Xin-You; Wu, Yu-Qian

In this paper, a delayed differential algebraic phytoplankton-zooplankton-fish model with taxation and nonlinear fish harvesting is proposed. In the absence of time delay, the existence of singularity induced bifurcation is discussed by regarding economic interest as bifurcation parameter. A state feedback controller is designed to eliminate singularity induced bifurcation. Based on Liu’s criterion, Hopf bifurcation occurs at the interior equilibrium when taxation is taken as bifurcation parameter and is more than its corresponding critical value. In the presence of time delay, by analyzing the associated characteristic transcendental equation, the interior equilibrium loses local stability when time delay crosses its critical value. What’s more, the direction of Hopf bifurcation and stability of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem, and nonlinear state feedback controller is designed to eliminate Hopf bifurcation. Furthermore, Pontryagin’s maximum principle has been used to obtain optimal tax policy to maximize the benefit as well as the conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical analysis.

Implementation of a digital evaluation platform to analyze bifurcation based nonlinear amplifiers

NASA Astrophysics Data System (ADS)

Feldkord, Sven; Reit, Marco; Mathis, Wolfgang

2016-09-01

Recently, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have become a focus of attention, especially in the modeling of the mammalian hearing organ. In general, to gain deeper insights in the input-output behavior, the analysis of bifurcation based amplifiers requires a flexible framework to exchange equations and adjust certain parameters. A DSP implementation is presented which is capable to analyze various amplifier systems. Amplifiers based on the Andronov-Hopf and Neimark-Sacker bifurcations are implemented and compared exemplarily. It is shown that the Neimark-Sacker system remarkably outperforms the Andronov-Hopf amplifier regarding the CPU usage. Nevertheless, both show a similar input-output behavior over a wide parameter range. Combined with an USB-based control interface connected to a PC, the digital framework provides a powerful instrument to analyze bifurcation based amplifiers.

Cascades of alternating pitchfork and flip bifurcations in H-bridge inverters

NASA Astrophysics Data System (ADS)

Avrutin, Viktor; Zhusubaliyev, Zhanybai T.; Mosekilde, Erik

2017-04-01

Power electronic DC/AC converters (inverters) play an important role in modern power engineering. These systems are also of considerable theoretical interest because their dynamics is influenced by the presence of two vastly different forcing frequencies. As a consequence, inverter systems may be modeled in terms of piecewise smooth maps with an extremely high number of switching manifolds. We have recently shown that models of this type can demonstrate a complicated bifurcation structure associated with the occurrence of border collisions. Considering the example of a PWM H-bridge single-phase inverter, the present paper discusses a number of unusual phenomena that can occur in piecewise smooth maps with a very large number of switching manifolds. We show in particular how smooth (pitchfork and flip) bifurcations may form a macroscopic pattern that stretches across the overall bifurcation structure. We explain the observed bifurcation phenomena, show under which conditions they occur, and describe them quantitatively by means of an analytic approximation.

Delay-induced stochastic bifurcations in a bistable system under white noise

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

Sun, Zhongkui, E-mail: sunzk@nwpu.edu.cn; Fu, Jin; Xu, Wei

2015-08-15

In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochasticmore » P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.« less

Monitoring populations of saddled prominent (Lepidoptera: Notodontidae) with pheromone-baited traps.

PubMed

Spear-O'Mara, Jennifer; Allen, Douglas C

2007-04-01

Field trials with three types of pheromone traps were performed in eight northern hardwood stands in northern New York state to develop a population-monitoring tool for the saddled prominent, Heterocampa guttivitta (Walker) (Lepidoptera: Notodontidae). Lure specificity and the relationship between pheromone trap catch and subsequent egg density were examined. A study of moth emergence in relation to temperature was designed to determine whether moth activity throughout the flight season can be predicted using a growing degree-day (DD) model. Pherocon 1C wing traps were significantly more effective than the green Unitrap bucket style. Catch was not affected by position when traps were > or =20 m from an opening (road), and lures were specific to saddled prominent. Lure specificity was examined using green Multipher bucket traps, which effectively attracted and held moths. In the first year of the study, number of viable eggs per 10 leaf clusters was significantly correlated (r2 = 0.59) with average moth catch/trap in pheromone-baited Pherocon traps. When differences in stand density (basal area) and relative abundance of sugar maple (percentage of total stems per hectare), the principle host, were accounted for, the multiple regression model also was significant and r2 = 0. 83. Neither model, however, was significant the second year. Using a base temperature of 5.5 degrees C and on-site temperature data, the peak of moth flight occurred at 316 +/- 8 DD and end of flight occurred at 533 +/- 9 DD.

Mechanistic insights into energy conservation by flavin-based electron bifurcation.

PubMed

Lubner, Carolyn E; Jennings, David P; Mulder, David W; Schut, Gerrit J; Zadvornyy, Oleg A; Hoben, John P; Tokmina-Lukaszewska, Monika; Berry, Luke; Nguyen, Diep M; Lipscomb, Gina L; Bothner, Brian; Jones, Anne K; Miller, Anne-Frances; King, Paul W; Adams, Michael W W; Peters, John W

2017-06-01

The recently realized biochemical phenomenon of energy conservation through electron bifurcation provides biology with an elegant means to maximize utilization of metabolic energy. The mechanism of coordinated coupling of exergonic and endergonic oxidation-reduction reactions by a single enzyme complex has been elucidated through optical and paramagnetic spectroscopic studies revealing unprecedented features. Pairs of electrons are bifurcated over more than 1 volt of electrochemical potential by generating a low-potential, highly energetic, unstable flavin semiquinone and directing electron flow to an iron-sulfur cluster with a highly negative potential to overcome the barrier of the endergonic half reaction. The unprecedented range of thermodynamic driving force that is generated by flavin-based electron bifurcation accounts for unique chemical reactions that are catalyzed by these enzymes.

Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models

NASA Astrophysics Data System (ADS)

Giona, M.; Brasiello, A.; Crescitelli, S.

2015-11-01

One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.

High-resolution mapping of bifurcations in nonlinear biochemical circuits

NASA Astrophysics Data System (ADS)

Genot, A. J.; Baccouche, A.; Sieskind, R.; Aubert-Kato, N.; Bredeche, N.; Bartolo, J. F.; Taly, V.; Fujii, T.; Rondelez, Y.

2016-08-01

Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.

Symmetry-breaking bifurcations and enhanced mixing in microfluidic cross-slots

NASA Astrophysics Data System (ADS)

Poole, Rob; Haward, Simon; Oliveira, Paulo; Alves, Manuel

2014-11-01

We investigate, both experimentally and numerically, a new subcritical bifurcation phenomenon for a Newtonian fluid flowing through three-dimensional cross-slot geometries. At low Reynolds numbers the flow remains steady and symmetric. For the case of square inlets and outlets, at a critical Reynolds number of approximately 40 (based on average velocity) a pitchfork bifurcation is observed beyond which the unstable symmetrical solution is replaced by a pair of steady asymmetric solutions. Sensitivity of this critical Reynolds number to the initial conditions of the simulation, resulting in a small degree of hysteresis, suggests a subcritical instability. At higher flowrates the flow becomes unsteady. The effects of channel aspect ratio are investigated on the critical conditions and excellent agreement is found between three-dimensional finite volume simulations and flow visualisation experiments in microfluidic channels. Finally we suggest this new flow bifurcation could be an effective method of enhancing mixing in microfluidic channels as significant increases in mixing quality are observed beyond the bifurcation. This enhancement occurs at flowrates more than a factor of two smaller than those observed in the well-known T-channel micromixer.

Bifurcation structure of successive torus doubling

NASA Astrophysics Data System (ADS)

Sekikawa, Munehisa; Inaba, Naohiko; Yoshinaga, Tetsuya; Tsubouchi, Takashi

2006-01-01

The authors discuss the “embryology” of successive torus doubling via the bifurcation theory, and assert that the coupled map of a logistic map and a circle map has a structure capable of generating infinite number of torus doublings.

Topological bifurcations in a model society of reasonable contrarians

NASA Astrophysics Data System (ADS)

Bagnoli, Franco; Rechtman, Raúl

2013-12-01

People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion, which denotes a social norm. Such reasonable contrarian behavior is often considered a mark of independent thought and can be a useful strategy in financial markets. We present the opinion dynamics of a society of reasonable contrarian agents. The model is a cellular automaton of Ising type, with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms. We introduce the entropy of the collective variable as a way of comparing deterministic (mean-field) and probabilistic (simulations) bifurcation diagrams. In the mean-field approximation the model exhibits bifurcations and a chaotic phase, interpreted as coherent oscillations of the whole society. However, in a one-dimensional spatial arrangement one observes incoherent oscillations and a constant average. In simulations on Watts-Strogatz networks with a small-world effect the mean-field behavior is recovered, with a bifurcation diagram that resembles the mean-field one but where the rewiring probability is used as the control parameter. Similar bifurcation diagrams are found for scale-free networks, and we are able to compute an effective connectivity for such networks.

Topological bifurcations in a model society of reasonable contrarians.

PubMed

Bagnoli, Franco; Rechtman, Raúl

2013-12-01

People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion, which denotes a social norm. Such reasonable contrarian behavior is often considered a mark of independent thought and can be a useful strategy in financial markets. We present the opinion dynamics of a society of reasonable contrarian agents. The model is a cellular automaton of Ising type, with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms. We introduce the entropy of the collective variable as a way of comparing deterministic (mean-field) and probabilistic (simulations) bifurcation diagrams. In the mean-field approximation the model exhibits bifurcations and a chaotic phase, interpreted as coherent oscillations of the whole society. However, in a one-dimensional spatial arrangement one observes incoherent oscillations and a constant average. In simulations on Watts-Strogatz networks with a small-world effect the mean-field behavior is recovered, with a bifurcation diagram that resembles the mean-field one but where the rewiring probability is used as the control parameter. Similar bifurcation diagrams are found for scale-free networks, and we are able to compute an effective connectivity for such networks.

A mass-conservation-based approach to predicting river mouth channel bifurcations

NASA Astrophysics Data System (ADS)

Shaw, J.; McElroy, B. J.; Miller, K. L.

2015-12-01

Channel bifurcation is an important process in fluvio-deltaic morphodynamics and resulting stratigraphic architecture of prograding river deltas. We develop and test a new theory for the formation of channel bifurcations based on fluid mass conservation and system-averaged transport conditions rather than local hydrodynamics. We built 29 experimental deltas under a variety of boundary conditions to examine the inception and growth of bars and channel bifurcations. From the initial condition of water and sediment entering a still basin of uniform depth as a wall-bounded turbulent jet, delta growth begins with the formation of a lunate bar as predicted by the hydrodynamics of jet spreading. However, the lunate bar diverts water and sediment laterally causing the bar to widen into a radially symmetric sediment "apron" extending uniformly from the channel axis to the flume walls. This apron is stable to perturbations, and its distal limit progrades basinward while maintaining a roughly constant flow depth of ~10 times the median grain diameter (H=2-3 mm). Bar formation and channel bifurcation occur on top of the apron at the distance where shear stress applied by radially-averaged flow velocity falls below the threshold of sediment motion. Our model predicts that the distance to the first channel bifurcation should scale with water discharge, scale inversely with flow depth over the apron, and scale with median grain diameter to the negative one half.

Seepage Bifurcation as a Critical Process

NASA Astrophysics Data System (ADS)

Yi, R.; Rothman, D.

2015-12-01

Channel networks form beautiful and surprisingly intricate geometries, yet diligently evade comprehensive mathematical understanding. Work in recent years has shed light on this problem. Networks driven by seepage flow, in particular, have been shown to grow in a field that can be described by the Laplace equation, providing us with an understanding of valley growth and shape. However, the process by which such networks branch to form these ramified shapes is yet a mystery. We focus our attention on a highly ramified seepage valley network in Bristol, Florida. We study the behavior of flux to valley heads as a function of valley length, and use this result to motivate our discussion of branch formation. We then hypothesize that a critical groundwater flux demarcates a transition point where topographic diffusion is overcome by branching processes, and we present network-wide flux calculations, cosmogenic data, and simulation to support our claim. Our results ultimately suggest a mechanism for seepage bifurcation, and inform our understanding of pattern formation in river networks.

Mechanistic insights into energy conservation by flavin-based electron bifurcation

DOE PAGES

Lubner, Carolyn E.; Jennings, David P.; Mulder, David W.; ...

2017-04-10

The recently realized biochemical phenomenon of energy conservation through electron bifurcation provides biology with an elegant means to maximize utilization of metabolic energy. The mechanism of coordinated coupling of exergonic and endergonic oxidation-reduction reactions by a single enzyme complex has been elucidated through optical and paramagnetic spectroscopic studies revealing unprecedented features. Pairs of electrons are bifurcated over more than 1 volt of electrochemical potential by generating a low-potential, highly energetic, unstable flavin semiquinone and directing electron flow to an iron-sulfur cluster with a highly negative potential to overcome the barrier of the endergonic half reaction. As a result, the unprecedentedmore » range of thermodynamic driving force that is generated by flavin-based electron bifurcation accounts for unique chemical reactions that are catalyzed by these enzymes.« less

Mechanistic insights into energy conservation by flavin-based electron bifurcation

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

Lubner, Carolyn E.; Jennings, David P.; Mulder, David W.

The recently realized biochemical phenomenon of energy conservation through electron bifurcation provides biology with an elegant means to maximize utilization of metabolic energy. The mechanism of coordinated coupling of exergonic and endergonic oxidation-reduction reactions by a single enzyme complex has been elucidated through optical and paramagnetic spectroscopic studies revealing unprecedented features. Pairs of electrons are bifurcated over more than 1 volt of electrochemical potential by generating a low-potential, highly energetic, unstable flavin semiquinone and directing electron flow to an iron-sulfur cluster with a highly negative potential to overcome the barrier of the endergonic half reaction. As a result, the unprecedentedmore » range of thermodynamic driving force that is generated by flavin-based electron bifurcation accounts for unique chemical reactions that are catalyzed by these enzymes.« less

Bifurcation in epigenetics: Implications in development, proliferation, and diseases

NASA Astrophysics Data System (ADS)

Jost, Daniel

2014-01-01

Cells often exhibit different and stable phenotypes from the same DNA sequence. Robustness and plasticity of such cellular states are controlled by diverse transcriptional and epigenetic mechanisms, among them the modification of biochemical marks on chromatin. Here, we develop a stochastic model that describes the dynamics of epigenetic marks along a given DNA region. Through mathematical analysis, we show the emergence of bistable and persistent epigenetic states from the cooperative recruitment of modifying enzymes. We also find that the dynamical system exhibits a critical point and displays, in the presence of asymmetries in recruitment, a bifurcation diagram with hysteresis. These results have deep implications for our understanding of epigenetic regulation. In particular, our study allows one to reconcile within the same formalism the robust maintenance of epigenetic identity observed in differentiated cells, the epigenetic plasticity of pluripotent cells during differentiation, and the effects of epigenetic misregulation in diseases. Moreover, it suggests a possible mechanism for developmental transitions where the system is shifted close to the critical point to benefit from high susceptibility to developmental cues.

Real-Time Spaceborne Synthetic Aperture Radar Float-Point Imaging System Using Optimized Mapping Methodology and a Multi-Node Parallel Accelerating Technique

PubMed Central

Li, Bingyi; Chen, Liang; Yu, Wenyue; Xie, Yizhuang; Bian, Mingming; Zhang, Qingjun; Pang, Long

2018-01-01

With the development of satellite load technology and very large-scale integrated (VLSI) circuit technology, on-board real-time synthetic aperture radar (SAR) imaging systems have facilitated rapid response to disasters. A key goal of the on-board SAR imaging system design is to achieve high real-time processing performance under severe size, weight, and power consumption constraints. This paper presents a multi-node prototype system for real-time SAR imaging processing. We decompose the commonly used chirp scaling (CS) SAR imaging algorithm into two parts according to the computing features. The linearization and logic-memory optimum allocation methods are adopted to realize the nonlinear part in a reconfigurable structure, and the two-part bandwidth balance method is used to realize the linear part. Thus, float-point SAR imaging processing can be integrated into a single Field Programmable Gate Array (FPGA) chip instead of relying on distributed technologies. A single-processing node requires 10.6 s and consumes 17 W to focus on 25-km swath width, 5-m resolution stripmap SAR raw data with a granularity of 16,384 × 16,384. The design methodology of the multi-FPGA parallel accelerating system under the real-time principle is introduced. As a proof of concept, a prototype with four processing nodes and one master node is implemented using a Xilinx xc6vlx315t FPGA. The weight and volume of one single machine are 10 kg and 32 cm × 24 cm × 20 cm, respectively, and the power consumption is under 100 W. The real-time performance of the proposed design is demonstrated on Chinese Gaofen-3 stripmap continuous imaging. PMID:29495637

[Technical points of laparoscopic splenic hilar lymph node dissection--The original intention of CLASS-04 research design].

PubMed

Huang, Changming; Lin, Mi

2018-02-25

According to Japanese gastric cancer treatment guidelines, the standard operation for locally advanced upper third gastric cancer is the total gastrectomy with D2 lymphadenectomy, which includes the dissection of the splenic hilar lymph nodes. With the development of minimally invasive ideas and surgical techniques, laparoscopic spleen-preserving splenic hilar lymph node dissection is gradually accepted. It needs high technical requirements and should be carried out by surgeons with rich experience of open operation and skilled laparoscopic techniques. Based on being familiar with the anatomy of splenic hilum, we should choose a reasonable surgical approach and standardized operating procedure. A favorable left-sided approach is used to perform the laparoscopic spleen-preserving splenic hilar lymph node dissection in Department of Gastric Surgery, Fujian Medical University Union Hospital. This means that the membrane of the pancreas is separated at the superior border of the pancreatic tail in order to reach the posterior pancreatic space, revealing the end of the splenic vessels' trunk. The short gastric vessels are severed at their roots. This enables complete removal of the splenic hilar lymph nodes and stomach. At the same time, based on the rich clinical practice of laparoscopic gastric cancer surgery, we have summarized an effective operating procedure called Huang's three-step maneuver. The first step is the dissection of the lymph nodes in the inferior pole region of the spleen. The second step is the dissection of the lymph nodes in the trunk of splenic artery region. The third step is the dissection of the lymph nodes in the superior pole region of the spleen. It simplifies the procedure, reduces the difficulty of the operation, improves the efficiency of the operation, and ensures the safety of the operation. To further explore the safety of laparoscopic spleen-preserving splenic hilar lymph node dissection for locally advanced upper third gastric cancer

Bifurcation and Nonlinear Oscillations.

DTIC Science & Technology

1980-09-28

Structural stability and bifurcation theory. pp. 549-560 in Dinamical Systems (Ed. MI. Peixoto), Academic Press, 1973. [211 J. Sotomayor, Generic one...Dynamical Systems Brown University ELECTP" 71, Providence, R. I. 02912 1EC 2 4 1980j //C -*)’ Septabe-4., 1980 / -A + This research was supported in...problems are discussed. The first one deals with the characterization of the flow for a periodic planar system which is the perturbation of an autonomous

Cardiovascular microbubble transport in vessel bifurcations with pulsatile flow: experimental model and theory

NASA Astrophysics Data System (ADS)

Valassis, Doug; Dodde, Robert; Eshpuniyani, Brijesh; Fowlkes, J. Brian; Bull, Joseph

2008-11-01

The behavior of long gas bubbles suspended in liquid flowing through successive bifurcations was investigated experimentally and theoretically as a model of cardiovascular bubble transport in gas embolotherapy. In this developmental cancer therapy, perflurocarbon droplets are vaporized in the vasculature and travel through a bifurcating network of vessels before lodging. The homogeneity of tumor necrosis is directly correlated with the transport and lodging of the emboli. An experimental model was used to explore the effects of flow pulsatility, frequency, gravity, and bifurcation roll angle on bubble splitting and lodging. At a bifurcation roll angle of 45-degrees, the most distinct difference in splitting ratios between three physiologic frequencies (1, 1.5, 2 Hz) was observed. As roll angle increased, lodged bubble volume in the first generation channel increased while bubble volume beyond the second bifurcation proportionately decreased. A corresponding time-dependent one-dimensional theoretical model was also developed. The results elucidate the effects of pulsatile flow and suggest the potential of gas embolotherapy to occlude blood flow to tumors.

Von Bertalanffy's dynamics under a polynomial correction: Allee effect and big bang bifurcation

NASA Astrophysics Data System (ADS)

Leonel Rocha, J.; Taha, A. K.; Fournier-Prunaret, D.

2016-02-01

In this work we consider new one-dimensional populational discrete dynamical systems in which the growth of the population is described by a family of von Bertalanffy's functions, as a dynamical approach to von Bertalanffy's growth equation. The purpose of introducing Allee effect in those models is satisfied under a correction factor of polynomial type. We study classes of von Bertalanffy's functions with different types of Allee effect: strong and weak Allee's functions. Dependent on the variation of four parameters, von Bertalanffy's functions also includes another class of important functions: functions with no Allee effect. The complex bifurcation structures of these von Bertalanffy's functions is investigated in detail. We verified that this family of functions has particular bifurcation structures: the big bang bifurcation of the so-called “box-within-a-box” type. The big bang bifurcation is associated to the asymptotic weight or carrying capacity. This work is a contribution to the study of the big bang bifurcation analysis for continuous maps and their relationship with explosion birth and extinction phenomena.

Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics

NASA Astrophysics Data System (ADS)

Drogoul, Audric; Veltz, Romain

2017-02-01

In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived [De Masi et al., J. Stat. Phys. 158, 866-902 (2015) and Fournier and löcherbach, Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)] mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation. The second stems from the simulation of the full mean field. Finally, the last evidence comes from the simulation of the network for a large number of neurons. We provide a "recipe" to find such bifurcation which nicely complements the works in De Masi et al. [J. Stat. Phys. 158, 866-902 (2015)] and Fournier and löcherbach [Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)]. This suggests in return to revisit theoretically these mean field equations from a dynamical point of view. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronization in excitatory globally pulse-coupled networks.

Phase transitions in tumor growth VI: Epithelial-Mesenchymal transition

NASA Astrophysics Data System (ADS)

Guerra, A.; Rodriguez, D. J.; Montero, S.; Betancourt-Mar, J. A.; Martin, R. R.; Silva, E.; Bizzarri, M.; Cocho, G.; Mansilla, R.; Nieto-Villar, J. M.

2018-06-01

Herewith we discuss a network model of the epithelial-mesenchymal transition (EMT) based on our previous proposed framework. The EMT appears as a "first order" phase transition process, analogous to the transitions observed in the chemical-physical field. Chiefly, EMT should be considered a transition characterized by a supercritical Andronov-Hopf bifurcation, with the emergence of limit cycle and, consequently, a cascade of saddle-foci Shilnikov's bifurcations. We eventually show that the entropy production rate is an EMT-dependent function and, as such, its formalism reminds the van der Waals equation.

Endodontic-periodontic bifurcation lesions: a novel treatment option.

PubMed

Lin, Shaul; Tillinger, Gabriel; Zuckerman, Offer

2008-05-01

The purpose of this preliminary clinical report is to suggest a novel treatment modality for periodontal bifurcation lesions of endodontic origin. The study consisted of 11 consecutive patients who presented with periodontal bifurcation lesions of endodontic origin (endo-perio lesions). All patients were followed-up for at least 12 months. Treatment included calcium hydroxide with iodine-potassium iodide placed in the root canals for 90 days followed by canal sealing with gutta-percha and cement during a second stage. Dentin bonding was used to seal the furcation floor to prevent the ingress of bacteria and their by-products to the furcation root area through the accessory canals. A radiographic examination showed complete healing of the periradicular lesion in all patients. Probing periodontal pocket depths decreased to 2 to 4 mm (mean 3.5 mm), and resolution of the furcation involvement was observed in post-operative clinical evaluations. The suggested treatment of endo-perio lesions may result in complete healing. Further studies are warranted. This treatment method improves both the disinfection of the bifurcation area and the healing process in endodontically treated teeth considered to be hopeless.

Cellular instability in rapid directional solidification - Bifurcation theory

NASA Technical Reports Server (NTRS)

Braun, R. J.; Davis, S. H.

1992-01-01

Merchant and Davis performed a linear stability analysis on a model for the directional solidification of a dilute binary alloy valid for all speeds. The analysis revealed that nonequilibrium segregation effects modify the Mullins and Sekerka cellular mode, whereas attachment kinetics has no effect on these cells. In this paper, the nonlinear stability of the steady cellular mode is analyzed. A Landau equation is obtained that determines the amplitude of the cells. The Landau coefficient here depends on both nonequilibrium segregation effects and attachment kinetics. This equation gives the ranges of parameters for subcritical bifurcation (jump transition) or supercritical bifurcation (smooth transition) to cells.

Estimation of distributed Fermat-point location for wireless sensor networking.

PubMed

Huang, Po-Hsian; Chen, Jiann-Liang; Larosa, Yanuarius Teofilus; Chiang, Tsui-Lien

2011-01-01

This work presents a localization scheme for use in wireless sensor networks (WSNs) that is based on a proposed connectivity-based RF localization strategy called the distributed Fermat-point location estimation algorithm (DFPLE). DFPLE applies triangle area of location estimation formed by intersections of three neighboring beacon nodes. The Fermat point is determined as the shortest path from three vertices of the triangle. The area of estimated location then refined using Fermat point to achieve minimum error in estimating sensor nodes location. DFPLE solves problems of large errors and poor performance encountered by localization schemes that are based on a bounding box algorithm. Performance analysis of a 200-node development environment reveals that, when the number of sensor nodes is below 150, the mean error decreases rapidly as the node density increases, and when the number of sensor nodes exceeds 170, the mean error remains below 1% as the node density increases. Second, when the number of beacon nodes is less than 60, normal nodes lack sufficient beacon nodes to enable their locations to be estimated. However, the mean error changes slightly as the number of beacon nodes increases above 60. Simulation results revealed that the proposed algorithm for estimating sensor positions is more accurate than existing algorithms, and improves upon conventional bounding box strategies.

Quantum coordinated multi-point communication based on entanglement swapping

NASA Astrophysics Data System (ADS)

Du, Gang; Shang, Tao; Liu, Jian-wei

2017-05-01

In a quantum network, adjacent nodes can communicate with each other point to point by using pre-shared Einsten-Podolsky-Rosen (EPR) pairs, and furthermore remote nodes can establish entanglement channels by using quantum routing among intermediate nodes. However, with the rapid development of quantum networks, the demand of various message transmission among nodes inevitably emerges. In order to realize this goal and extend quantum networks, we propose a quantum coordinated multi-point communication scheme based on entanglement swapping. The scheme takes full advantage of EPR pairs between adjacent nodes and performs multi-party entanglement swapping to transmit messages. Considering various demands of communication, all nodes work cooperatively to realize different message transmission modes, including one to many, many to one and one to some. Scheme analysis shows that the proposed scheme can flexibly organize a coordinated group and efficiently use EPR resources, while it meets basic security requirement under the condition of coordinated communication.

Stratified rotating Boussinesq equations in geophysical fluid dynamics: Dynamic bifurcation and periodic solutions

NASA Astrophysics Data System (ADS)

Hsia, Chun-Hsiung; Ma, Tian; Wang, Shouhong

2007-06-01

The main objective of this article is to study the dynamics of the stratified rotating Boussinesq equations, which are a basic model in geophysical fluid dynamics. First, for the case where the Prandtl number is greater than 1, a complete stability and bifurcation analysis near the first critical Rayleigh number is carried out. Second, for the case where the Prandtl number is smaller than 1, the onset of the Hopf bifurcation near the first critical Rayleigh number is established, leading to the existence of nontrivial periodic solutions. The analysis is based on a newly developed bifurcation and stability theory for nonlinear dynamical systems (both finite and infinite dimensional) by two of the authors [T. Ma and S. Wang, Bifurcation Theory and Applications, World Scientific Series on Nonlinear Sciences Vol. 53 (World Scientific, Singapore, 2005)].

Stress-mediated Allee effects can cause the sudden collapse of honey bee colonies.

PubMed

Booton, Ross D; Iwasa, Yoh; Marshall, James A R; Childs, Dylan Z

2017-05-07

The recent rapid decline in global honey bee populations could have significant implications for ecological systems, economics and food security. No single cause of honey bee collapse has yet to be identified, although pesticides, mites and other pathogens have all been shown to have a sublethal effect. We present a model of a functioning bee hive and introduce external stress to investigate the impact on the regulatory processes of recruitment to the forager class, social inhibition and the laying rate of the queen. The model predicts that constant density-dependent stress acting through an Allee effect on the hive can result in sudden catastrophic switches in dynamical behaviour and the eventual collapse of the hive. The model proposes that around a critical point the hive undergoes a saddle-node bifurcation, and that a small increase in model parameters can have irreversible consequences for the entire hive. We predict that increased stress levels can be counteracted by a higher laying rate of the queen, lower levels of forager recruitment or lower levels of natural mortality of foragers, and that increasing social inhibition can not maintain the colony under high levels of stress. We lay the theoretical foundation for sudden honey bee collapse in order to facilitate further experimental and theoretical consideration. Copyright © 2017 Elsevier Ltd. All rights reserved.

Incidence and location of lymph node metastases in patients undergoing radical cystectomy for clinical non-muscle invasive bladder cancer: results from a prospective lymph node mapping study.

PubMed

Bruins, Harman M; Skinner, Eila C; Dorin, Ryan P; Ahmadi, Hamed; Djaladat, Hooman; Miranda, Gus; Cai, Jie; Daneshmand, Siamak

2014-01-01

The objective of this study is to investigate the incidence and location of lymph node metastases (LNMs) in patients undergoing radical cystectomy (RC) and lymph node dissection (LND) for clinical non-muscle invasive bladder cancer (NMIBC). Prospectively collected data of 637 patients who underwent RC and 'superextended' LND with intent-to-cure for urothelial carcinoma of the bladder between 2002 and 2008 were examined. Inclusion criteria were (a) clinical stage Ta, Tis-only, or T1, (b) muscle presence at diagnostic transurethral resection in clinical T1 patients, (c) no prior diagnosis of ≥ T2 disease, (d) no neoadjuvant therapy, and (e) lymphatic tissue sample submitted from all 13 predesignated locations. Lymph node mapping was performed in all patients to determine the location of metastatic lymph nodes. Median follow-up time was 4.7 years. Recurrence-free survival and overall survival were reported. A total of 114 patients were included of whom 9 patients (7.9%) had LNM. Stratified by clinical stage, LNM was present in 6/67 (9.0%) patients with cT1, 3/25 (12.0%) patients with cTis-only, and none of the 22 patients with cTa. Of the 9 node-positive patients (33.3%), 3 had LNM proximal to the aortic bifurcation. No skip metastases were found. After RC, 27 patients (23.7%) were upstaged to muscle invasive disease; of whom 16.7% had cT1, 2.6% had cTa, and 4.4% had cTis-only. Of the remaining 87 patients with pathologic NMIBC, 1 patient (1.1%) had LNM, limited to the true pelvis. Five-year RFS was 82.3%, 81.5%, and 62.0% in patients with pathologic NMIBC, clinical NMIBC, and pathologic muscle invasive bladder cancer, respectively. Routine LND is important in patients with cT1 and cTis-only bladder cancer, but may have limited value in patients with cTa. LNM beyond the boundaries of a standard LND occurred in up to one-third of node-positive patients. In the absence of skip metastases, however, performing a standard LND would correctly identify all node

Turing-Hopf bifurcations in a predator-prey model with herd behavior, quadratic mortality and prey-taxis

NASA Astrophysics Data System (ADS)

Liu, Xia; Zhang, Tonghua; Meng, Xinzhu; Zhang, Tongqian

2018-04-01

In this paper, we propose a predator-prey model with herd behavior and prey-taxis. Then, we analyze the stability and bifurcation of the positive equilibrium of the model subject to the homogeneous Neumann boundary condition. By using an abstract bifurcation theory and taking prey-tactic sensitivity coefficient as the bifurcation parameter, we obtain a branch of stable nonconstant solutions bifurcating from the positive equilibrium. Our results show that prey-taxis can yield the occurrence of spatial patterns.

The possibility of a tipping point in the Arctic sea ice cover, and associated early-warning signals

NASA Astrophysics Data System (ADS)

Jastamin Steene, Rebekka

2017-04-01

As the Arctic sea ice has become one of the primer indicators of global climate change, with a seemingly accelerated loss in both ice extent and volume the latest decades, the existence of a tipping point related to the Arctic sea ice cover has been widely debated. Several observed and potential abrupt transitions in the climate system may be interpreted as bifurcations in randomly driven dynamical systems. This means that a system approaching a bifurcation point shifts from one stable state to another, and we say that the system is subject to a critical transition. As the equilibrium states become unstable in the vicinity of a bifurcation point the characteristic relaxation times increases, and the system is said to experience a "critical slowing down". This makes it plausible to observe so called early-warning signals (EWS) when approaching a critical transition. In the Arctic non-linear mechanisms like the temperature response of the ice-albedo feedback can potentially cause a sudden shift to an ice-free Arctic Ocean. Using bifurcation theory and potential analyses we examine time series of observational data of the Arctic sea ice, investigating the possibility of multiple states in the behavior of the ice cover. We further debate whether a shift between states is irreversible, and whether it can be preluded by early-warning signals.

Bifurcating Particle Swarms in Smooth-Walled Fractures

NASA Astrophysics Data System (ADS)

Pyrak-Nolte, L. J.; Sun, H.

2010-12-01

Particle swarms can occur naturally or from industrial processes where small liquid drops containing thousands to millions of micron-size to colloidal-size particles are released over time from seepage or leaks into fractured rock. The behavior of these particle swarms as they fall under gravity are affected by particle interactions as well as interactions with the walls of the fractures. In this paper, we present experimental results on the effect of fractures on the cohesiveness of the swarm and the formation of bifurcation structures as they fall under gravity and interact with the fracture walls. A transparent cubic sample (100 mm x 100 mm x 100 mm) containing a synthetic fracture with uniform aperture distributions was optically imaged to quantify the effect of confinement within fractures on particle swarm formation, swarm velocity, and swarm geometry. A fracture with a uniform aperture distribution was fabricated from two polished rectangular prisms of acrylic. A series of experiments were performed to determine how swarm movement and geometry are affected as the walls of the fracture are brought closer together from 50 mm to 1 mm. During the experiments, the fracture was fully saturated with water. We created the swarms using two different particle sizes in dilute suspension (~ 1.0% by mass). The particles were 3 micron diameter fluorescent polymer beads and 25 micron diameter soda-lime glass beads. Experiments were performed using swarms that ranged in size from 5 µl to 60 µl. The swarm behavior was imaged using an optical fluorescent imaging system composed of a CCD camera illuminated by a 100 mW diode-pumped doubled YAG laser. As a swarm falls in an open-tank of water, it forms a torroidal shape that is stable as long as no ambient or background currents exist in the water tank. When a swarm is released into a fracture with an aperture less than 5 mm, the swarm forms the torroidal shape but it is distorted because of the presence of the walls. The

Cops or Robbers — a Bistable Society

NASA Astrophysics Data System (ADS)

Kułakowski, K.

The norm game described by Axelrod in 1985 was recently treated with the master equation formalism. Here we discuss the equations, where (i) those who break the norm cannot punish and those who punish cannot break the norm, (ii) the tendency to punish is suppressed if the majority breaks the norm. The second mechanism is new. For some values of the parameters the solution shows the saddle-point bifurcation. Then, two stable solutions are possible, where the majority breaks the norm or the majority punishes. This means, that the norm breaking can be discontinuous, when measured in the social scale. The bistable character is reproduced also with new computer simulations on the Erdös-Rényi directed network.

Experimental Study of Flow in a Bifurcation

NASA Astrophysics Data System (ADS)

Fresconi, Frank; Prasad, Ajay

2003-11-01

An instability known as the Dean vortex occurs in curved pipes with a longitudinal pressure gradient. A similar effect is manifest in the flow in a converging or diverging bifurcation, such as those found in the human respiratory airways. The goal of this study is to characterize secondary flows in a bifurcation. Particle image velocimetry (PIV) and laser-induced fluorescence (LIF) experiments were performed in a clear, plastic model. Results show the strength and migration of secondary vortices. Primary velocity features are also presented along with dispersion patterns from dye visualization. Unsteadiness, associated with a hairpin vortex, was also found at higher Re. This work can be used to assess the dispersion of particles in the lung. Medical delivery systems and pollution effect studies would profit from such an understanding.

Numerical continuation and bifurcation analysis in aircraft design: an industrial perspective.

PubMed

Sharma, Sanjiv; Coetzee, Etienne B; Lowenberg, Mark H; Neild, Simon A; Krauskopf, Bernd

2015-09-28

Bifurcation analysis is a powerful method for studying the steady-state nonlinear dynamics of systems. Software tools exist for the numerical continuation of steady-state solutions as parameters of the system are varied. These tools make it possible to generate 'maps of solutions' in an efficient way that provide valuable insight into the overall dynamic behaviour of a system and potentially to influence the design process. While this approach has been employed in the military aircraft control community to understand the effectiveness of controllers, the use of bifurcation analysis in the wider aircraft industry is yet limited. This paper reports progress on how bifurcation analysis can play a role as part of the design process for passenger aircraft. © 2015 The Author(s).

Flood-inundation maps for the Saddle River from Rochelle Park to Lodi, New Jersey, 2012

USGS Publications Warehouse

Hoppe, Heidi L.; Watson, Kara M.

2012-01-01

Digital flood-inundation maps for a 2.75-mile reach of the Saddle River from 0.2 mile upstream from the Interstate 80 bridge in Rochelle Park to 1.5 miles downstream from the U.S. Route 46 bridge in Lodi, New Jersey, were created by the U.S. Geological Survey (USGS) in cooperation with the New Jersey Department of Environmental Protection (NJDEP). The inundation maps, which can be accessed through the USGS Flood Inundation Mapping Science Web site at http://water.usgs.gov/osw/flood_inundation, depict estimates of the areal extent and depth of flooding corresponding to selected water levels (stages) at the USGS streamgage at Saddle River at Lodi, New Jersey (station 01391500). Current conditions for estimating near real-time areas of inundation using USGS streamgage information may be obtained on the Internet at http://waterdata.usgs.gov/nwis/uv?site_no=01391500. The National Weather Service (NWS) forecasts flood hydrographs at many places that are often collocated with USGS streamgages. NWS-forecasted peak-stage information may be used in conjunction with the maps developed in this study to show predicted areas of flood inundation. In this study, flood profiles were computed for the stream reach by means of a one-dimensional step-backwater model. The model was calibrated using the most current stage-discharge relations at the Saddle River at Lodi, New Jersey streamgage and documented high-water marks from recent floods. The hydraulic model was then used to determine 11 water-surface profiles for flood stages at the Saddle River streamgage at 1-ft intervals referenced to the streamgage datum, North American Vertical Datum of 1988 (NAVD 88), and ranging from bankfull, 0.5 ft below NWS Action Stage, to the extent of the stage-discharge rating, which is approximately 1 ft higher than the highest recorded water level at the streamgage. Action Stage is the stage which when reached by a rising stream the NWS or a partner needs to take some type of mitigation action in

Bifurcation parameters of a reflected shock wave in cylindrical channels of different roughnesses

NASA Astrophysics Data System (ADS)

Penyazkov, O.; Skilandz, A.

2018-03-01

To investigate the effect of bifurcation on the induction time in cylindrical shock tubes used for chemical kinetic experiments, one should know the parameters of the bifurcation structure of a reflected shock wave. The dynamics and parameters of the shock wave bifurcation, which are caused by reflected shock wave-boundary layer interactions, are studied experimentally in argon, in air, and in a hydrogen-nitrogen mixture for Mach numbers M = 1.3-3.5 in a 76-mm-diameter shock tube without any ramp. Measurements were taken at a constant gas density behind the reflected shock wave. Over a wide range of experimental conditions, we studied the axial projection of the oblique shock wave and the pressure distribution in the vicinity of the triple Mach configuration at 50, 150, and 250 mm from the endwall, using side-wall schlieren and pressure measurements. Experiments on a polished shock tube and a shock tube with a surface roughness of 20 {μ }m Ra were carried out. The surface roughness was used for initiating small-scale turbulence in the boundary layer behind the incident shock wave. The effect of small-scale turbulence on the homogenization of the transition zone from the laminar to turbulent boundary layer along the shock tube perimeter was assessed, assuming its influence on a subsequent stabilization of the bifurcation structure size versus incident shock wave Mach number, as well as local flow parameters behind the reflected shock wave. The influence of surface roughness on the bifurcation development and pressure fluctuations near the wall, as well as on the Mach number, at which the bifurcation first develops, was analyzed. It was found that even small additional surface roughness can lead to an overshoot in pressure growth by a factor of two, but it can stabilize the bifurcation structure along the shock tube perimeter.

Impact of leakage delay on bifurcation in high-order fractional BAM neural networks.

PubMed

Huang, Chengdai; Cao, Jinde

2018-02-01

The effects of leakage delay on the dynamics of neural networks with integer-order have lately been received considerable attention. It has been confirmed that fractional neural networks more appropriately uncover the dynamical properties of neural networks, but the results of fractional neural networks with leakage delay are relatively few. This paper primarily concentrates on the issue of bifurcation for high-order fractional bidirectional associative memory(BAM) neural networks involving leakage delay. The first attempt is made to tackle the stability and bifurcation of high-order fractional BAM neural networks with time delay in leakage terms in this paper. The conditions for the appearance of bifurcation for the proposed systems with leakage delay are firstly established by adopting time delay as a bifurcation parameter. Then, the bifurcation criteria of such system without leakage delay are successfully acquired. Comparative analysis wondrously detects that the stability performance of the proposed high-order fractional neural networks is critically weakened by leakage delay, they cannot be overlooked. Numerical examples are ultimately exhibited to attest the efficiency of the theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Gap structure in Fe-based superconductors with accidental nodes: The role of hybridization

NASA Astrophysics Data System (ADS)

Hinojosa, Alberto; Chubukov, Andrey V.

2015-06-01

We study the effects of hybridization between the two electron pockets in Fe-based superconductors with s -wave gap with accidental nodes. We argue that hybridization reconstructs the Fermi surfaces and also induces an additional interpocket pairing component. We analyze how these two effects modify the gap structure by tracing the position of the nodal points of the energy dispersions in the superconducting state. We find three possible outcomes. In the first, the nodes simply shift their positions in the Brillouin zone; in the second, the nodes merge and disappear, in which case the gap function has either equal or opposite signs on the electron pockets; in the third, a new set of nodal points emerges, doubling the original number of nodes.

Control-based continuation: Bifurcation and stability analysis for physical experiments

NASA Astrophysics Data System (ADS)

Barton, David A. W.

2017-02-01

Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The idea is to apply the method of numerical continuation to a feedback-controlled physical experiment such that the control becomes non-invasive. Since in an experiment it is not (generally) possible to set the state of the system directly, the control target becomes a proxy for the state. Control-based continuation enables the systematic investigation of the bifurcation structure of a physical system, much like if it was numerical model. However, stability information (and hence bifurcation detection and classification) is not readily available due to the presence of stabilising feedback control. This paper uses a periodic auto-regressive model with exogenous inputs (ARX) to approximate the time-varying linearisation of the experiment around a particular periodic orbit, thus providing the missing stability information. This method is demonstrated using a physical nonlinear tuned mass damper.

Bifurcation Analysis and Chaos Control in a Modified Finance System with Delayed Feedback

NASA Astrophysics Data System (ADS)

Yang, Jihua; Zhang, Erli; Liu, Mei

2016-06-01

We investigate the effect of delayed feedback on the finance system, which describes the time variation of the interest rate, for establishing the fiscal policy. By local stability analysis, we theoretically prove the existences of Hopf bifurcation and Hopf-zero bifurcation. By using the normal form method and center manifold theory, we determine the stability and direction of a bifurcating periodic solution. Finally, we give some numerical solutions, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable equilibrium or periodic orbit.

Bifurcation analysis of nephron pressure and flow regulation

NASA Astrophysics Data System (ADS)

Barfred, Mikael; Mosekilde, Erik; Holstein-Rathlou, Niels-Henrik

1996-09-01

One- and two-dimensional continuation techniques are applied to study the bifurcation structure of a model of renal flow and pressure control. Integrating the main physiological mechanisms by which the individual nephron regulates the incoming blood flow, the model describes the interaction between the tubuloglomerular feedback and the response of the afferent arteriole. It is shown how a Hopf bifurcation leads the system to perform self-sustained oscillations if the feedback gain becomes sufficiently strong, and how a further increase of this parameter produces a folded structure of overlapping period-doubling cascades. Similar phenomena arise in response to increasing blood pressure. The numerical analyses are supported by existing experimental results on anesthetized rats.

Cervical lymph node diseases in children

PubMed Central

Lang, Stephan; Kansy, Benjamin

2014-01-01

The lymph nodes are an essential part of the body’s immune system and as such are affected in many infectious, autoimmune, metabolic and malignant diseases. The cervical lymph nodes are particularly important because they are the first drainage stations for key points of contact with the outside world (mouth/throat/nose/eyes/ears/respiratory system) – a critical aspect especially among children – and can represent an early clinical sign in their exposed position on a child’s slim neck. Involvement of the lymph nodes in multiple conditions is accompanied by a correspondingly large number of available diagnostic procedures. In the interests of time, patient wellbeing and cost, a careful choice of these must be made to permit appropriate treatment. The basis of diagnostic decisions is a detailed anamnesis and clinical examination. Sonography also plays an important role in differential diagnosis of lymph node swelling in children and is useful in answering one of the critical diagnostic questions: is there a suspicion of malignancy? If so, full dissection of the most conspicuous lymph node may be necessary to obtain histological confirmation. Diagnosis and treatment of childhood cervical lymph node disorders present the attending pediatric and ENT physicians with some particular challenges. The spectrum of differential diagnoses and the varying degrees of clinical relevance – from banal infections to malignant diseases – demand a clear and considered approach to the child’s individual clinical presentation. Such an approach is described in the following paper. PMID:25587368

Numerical modelling of flow through foam's node.

PubMed

Anazadehsayed, Abdolhamid; Rezaee, Nastaran; Naser, Jamal

2017-10-15

In this work, for the first time, a three-dimensional model to describe the dynamics of flow through geometric Plateau border and node components of foam is presented. The model involves a microscopic-scale structure of one interior node and four Plateau borders with an angle of 109.5 from each other. The majority of the surfaces in the model make a liquid-gas interface where the boundary condition of stress balance between the surface and bulk is applied. The three-dimensional Navier-Stoke equation, along with continuity equation, is solved using the finite volume approach. The numerical results are validated against the available experimental results for the flow velocity and resistance in the interior nodes and Plateau borders. A qualitative illustration of flow in a node in different orientations is shown. The scaled resistance against the flow for different liquid-gas interface mobility is studied and the geometrical characteristics of the node and Plateau border components of the system are compared to investigate the Plateau border and node dominated flow regimes numerically. The findings show the values of the resistance in each component, in addition to the exact point where the flow regimes switch. Furthermore, a more accurate effect of the liquid-gas interface on the foam flow, particularly in the presence of a node in the foam network is obtained. The comparison of the available numerical results with our numerical results shows that the velocity of the node-PB system is lower than the velocity of single PB system for mobile interfaces. That is owing to the fact that despite the more relaxed geometrical structure of the node, constraining effect of merging and mixing of flow and increased viscous damping in the node component result in the node-dominated regime. Moreover, we obtain an accurate updated correlation for the dependence of the scaled average velocity of the node-Plateau border system on the liquid-gas interface mobility described by

Sarcoidal granuloma developing not only at the entry site of industrial lubricating oil, but also at a regional lymph node and entry points of venepuncture.

PubMed

Kogushi, Hazuki; Egawa, Kiyofumi; Ono, Tomomichi

2006-01-01

We describe a 40-year-old male who presented with sarcoidal granulomas not only at the entry site of an industrial lubricating oil containing silicone in the right thumb, but also in a regional lymph node and at the entry points of venepuncture in both forearms. Laboratory tests and chest X-ray showed no evidence of sarcoidosis. 2006 S. Karger AG, Basel

Nomogram for prediction of level 2 axillary lymph node metastasis in proven level 1 node-positive breast cancer patients.

PubMed

Jiang, Yanlin; Xu, Hong; Zhang, Hao; Ou, Xunyan; Xu, Zhen; Ai, Liping; Sun, Lisha; Liu, Caigang

2017-09-22

The current management of the axilla in level 1 node-positive breast cancer patients is axillary lymph node dissection regardless of the status of the level 2 axillary lymph nodes. The goal of this study was to develop a nomogram predicting the probability of level 2 axillary lymph node metastasis (L-2-ALNM) in patients with level 1 axillary node-positive breast cancer. We reviewed the records of 974 patients with pathology-confirmed level 1 node-positive breast cancer between 2010 and 2014 at the Liaoning Cancer Hospital and Institute. The patients were randomized 1:1 and divided into a modeling group and a validation group. Clinical and pathological features of the patients were assessed with uni- and multivariate logistic regression. A nomogram based on independent predictors for the L-2-ALNM identified by multivariate logistic regression was constructed. Independent predictors of L-2-ALNM by the multivariate logistic regression analysis included tumor size, Ki-67 status, histological grade, and number of positive level 1 axillary lymph nodes. The areas under the receiver operating characteristic curve of the modeling set and the validation set were 0.828 and 0.816, respectively. The false-negative rates of the L-2-ALNM nomogram were 1.82% and 7.41% for the predicted probability cut-off points of < 6% and < 10%, respectively, when applied to the validation group. Our nomogram could help predict L-2-ALNM in patients with level 1 axillary lymph node metastasis. Patients with a low probability of L-2-ALNM could be spared level 2 axillary lymph node dissection, thereby reducing postoperative morbidity.

Ozone Uptake During Inspiratory Flow in a Model of the Larynx, Trachea and Primary Bronchial Bifurcation

PubMed Central

Padaki, Amit; Ultman, James S.; Borhan, Ali

2009-01-01

Three-dimensional simulations of the transport and uptake of a reactive gas such as O3 were compared between an idealized model of the larynx, trachea, and first bifurcation and a second “control” model in which the larynx was replaced by an equivalent, cylindrical, tube segment. The Navier-Stokes equations, Spalart-Allmaras turbulence equation, and convection-diffusion equation were implemented at conditions reflecting inhalation into an adult human lung. Simulation results were used to analyze axial velocity, turbulent viscosity, local fractional uptake, and regional uptake. Axial velocity data revealed a strong laryngeal jet with a reattachment point in the proximal trachea. Turbulent viscosity data indicated that jet turbulence occurred only at high Reynolds numbers and was attenuated by the first bifurcation. Local fractional uptake data affirmed hotspots previously reported at the first carina, and suggested additional hotspots at the glottal constriction and jet reattachment point in the proximal trachea. These laryngeal effects strongly depended on inlet Reynolds number, with maximal effects (approaching 15%) occurring at maximal inlet flow rates. While the increase in the regional uptake caused by the larynx subsided by the end of the model, the effect of the larynx on cumulative uptake persisted further downstream. These results suggest that with prolonged exposure to a reactive gas, entire regions of the larynx and proximal trachea could show signs of tissue injury. PMID:22949744

Impact adding bifurcation in an autonomous hybrid dynamical model of church bell

NASA Astrophysics Data System (ADS)

Brzeski, P.; Chong, A. S. E.; Wiercigroch, M.; Perlikowski, P.

2018-05-01

In this paper we present the bifurcation analysis of the yoke-bell-clapper system which corresponds to the biggest bell "Serce Lodzi" mounted in the Cathedral Basilica of St Stanislaus Kostka, Lodz, Poland. The mathematical model of the system considered in this work has been derived and verified based on measurements of dynamics of the real bell. We perform numerical analysis both by direct numerical integration and path-following method using toolbox ABESPOL (Chong, 2016). By introducing the active yoke the position of the bell-clapper system with respect to the yoke axis of rotation can be easily changed and it can be used to probe the system dynamics. We found a wide variety of periodic and non-periodic solutions, and examined the ranges of coexistence of solutions and transitions between them via different types of bifurcations. Finally, a new type of bifurcation induced by a grazing event - an "impact adding bifurcation" has been proposed. When it occurs, the number of impacts between the bell and the clapper is increasing while the period of the system's motion stays the same.

Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations.

PubMed

Miranda, Rodrigo A; Rempel, Erico L; Chian, Abraham C-L; Seehafer, Norbert; Toledo, Benjamin A; Muñoz, Pablo R

2013-09-01

We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.

Automatic detection of lung vessel bifurcation in thoracic CT images

NASA Astrophysics Data System (ADS)

Maduskar, Pragnya; Vikal, Siddharth; Devarakota, Pandu

2011-03-01

Computer-aided diagnosis (CAD) systems for detection of lung nodules have been an active topic of research for last few years. It is desirable that a CAD system should generate very low false positives (FPs) while maintaining high sensitivity. This work aims to reduce the number of false positives occurring at vessel bifurcation point. FPs occur quite frequently on vessel branching point due to its shape which can appear locally spherical due to the intrinsic geometry of intersecting tubular vessel structures combined with partial volume effects and soft tissue attenuation appearance surrounded by parenchyma. We propose a model-based technique for detection of vessel branching points using skeletonization, followed by branch-point analysis. First we perform vessel structure enhancement using a multi-scale Hessian filter to accurately segment tubular structures of various sizes followed by thresholding to get binary vessel structure segmentation [6]. A modified Reebgraph [7] is applied next to extract the critical points of structure and these are joined by a nearest neighbor criterion to obtain complete skeletal model of vessel structure. Finally, the skeletal model is traversed to identify branch points, and extract metrics including individual branch length, number of branches and angle between various branches. Results on 80 sub-volumes consisting of 60 actual vessel-branching and 20 solitary solid nodules show that the algorithm identified correctly vessel branching points for 57 sub-volumes (95% sensitivity) and misclassified 2 nodules as vessel branch. Thus, this technique has potential in explicit identification of vessel branching points for general vessel analysis, and could be useful in false positive reduction in a lung CAD system.