Directory of Open Access Journals (Sweden)
Yu-Xuan Fu
2018-02-01
Full Text Available 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.
NUMERICAL HOPF BIFURCATION OF DELAY-DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper we consider the numerical solution of some delay differential equations undergoing a Hopf bifurcation. We prove that if the delay differential equations have a Hopf bifurcation point atλ=λ*, then the numerical solution of the equation also has a Hopf bifurcation point atλh =λ* + O(h).
Double Hopf bifurcation in delay differential equations
Directory of Open Access Journals (Sweden)
Redouane Qesmi
2014-07-01
Full Text Available The paper addresses the computation of elements of double Hopf bifurcation for retarded functional differential equations (FDEs with parameters. We present an efficient method for computing, simultaneously, the coefficients of center manifolds and normal forms, in terms of the original FDEs, associated with the double Hopf singularity up to an arbitrary order. Finally, we apply our results to a nonlinear model with periodic delay. This shows the applicability of the methodology in the study of delay models arising in either natural or technological problems.
Hopf bifurcation in an Internet congestion control model
International Nuclear Information System (INIS)
Li Chunguang; Chen Guanrong; Liao Xiaofeng; Yu Juebang
2004-01-01
We consider an Internet model with a single link accessed by a single source, which responds to congestion signals from the network, and study bifurcation of such a system. By choosing the gain parameter as a bifurcation parameter, we prove that Hopf bifurcation occurs. The stability of bifurcating periodic solutions and the direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Finally, a numerical example is given to verify the theoretical analysis
Hopf bifurcation of the stochastic model on business cycle
International Nuclear Information System (INIS)
Xu, J; Wang, H; Ge, G
2008-01-01
A stochastic model on business cycle was presented in thas paper. Simplifying the model through the quasi Hamiltonian theory, the Ito diffusion process was obtained. According to Oseledec multiplicative ergodic theory and singular boundary theory, the conditions of local and global stability were acquired. Solving the stationary FPK equation and analyzing the stationary probability density, the stochastic Hopf bifurcation was explained. The result indicated that the change of parameter awas the key factor to the appearance of the stochastic Hopf bifurcation
Hopf bifurcation for tumor-immune competition systems with delay
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Ping Bi
2014-01-01
Full Text Available In this article, a immune response system with delay is considered, which consists of two-dimensional nonlinear differential equations. The main purpose of this paper is to explore the Hopf bifurcation of a immune response system with delay. The general formula of the direction, the estimation formula of period and stability of bifurcated periodic solution are also given. Especially, the conditions of the global existence of periodic solutions bifurcating from Hopf bifurcations are given. Numerical simulations are carried out to illustrate the the theoretical analysis and the obtained results.
Views on the Hopf bifurcation with respect to voltage instabilities
Energy Technology Data Exchange (ETDEWEB)
Roa-Sepulveda, C A [Universidad de Concepcion, Concepcion (Chile). Dept. de Ingenieria Electrica; Knight, U G [Imperial Coll. of Science and Technology, London (United Kingdom). Dept. of Electrical and Electronic Engineering
1994-12-31
This paper presents a sensitivity study of the Hopf bifurcation phenomenon which can in theory appear in power systems, with reference to the dynamics of the process and the impact of demand characteristics. Conclusions are drawn regarding power levels at which these bifurcations could appear and concern the concept of the imaginary axis as a `hard` limit eigenvalue analyses. (author) 20 refs., 31 figs.
Hopf Bifurcation of Compound Stochastic van der Pol System
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Shaojuan Ma
2016-01-01
Full Text Available Hopf bifurcation analysis for compound stochastic van der Pol system with a bound random parameter and Gaussian white noise is investigated in this paper. By the Karhunen-Loeve (K-L expansion and the orthogonal polynomial approximation, the equivalent deterministic van der Pol system can be deduced. Based on the bifurcation theory of nonlinear deterministic system, the critical value of bifurcation parameter is obtained and the influence of random strength δ and noise intensity σ on stochastic Hopf bifurcation in compound stochastic system is discussed. At last we found that increased δ can relocate the critical value of bifurcation parameter forward while increased σ makes it backward and the influence of δ is more sensitive than σ. The results are verified by numerical simulations.
Adaptive Control of Electromagnetic Suspension System by HOPF Bifurcation
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Aming Hao
2013-01-01
Full Text Available EMS-type maglev system is essentially nonlinear and unstable. It is complicated to design a stable controller for maglev system which is under large-scale disturbance and parameter variance. Theory analysis expresses that this phenomenon corresponds to a HOPF bifurcation in mathematical model. An adaptive control law which adjusts the PID control parameters is given in this paper according to HOPF bifurcation theory. Through identification of the levitated mass, the controller adjusts the feedback coefficient to make the system far from the HOPF bifurcation point and maintain the stability of the maglev system. Simulation result indicates that adjusting proportion gain parameter using this method can extend the state stability range of maglev system and avoid the self-excited vibration efficiently.
An Approach to Robust Control of the Hopf Bifurcation
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Giacomo Innocenti
2011-01-01
Full Text Available The paper illustrates a novel approach to modify the Hopf bifurcation nature via a nonlinear state feedback control, which leaves the equilibrium properties unchanged. This result is achieved by recurring to linear and nonlinear transformations, which lead the system to locally assume the ordinary differential equation representation. Third-order models are considered, since they can be seen as proper representatives of a larger class of systems. The explicit relationship between the control input and the Hopf bifurcation nature is obtained via a frequency approach, that does not need the computation of the center manifold.
The Boundary-Hopf-Fold Bifurcation in Filippov Systems
Efstathiou, Konstantinos; Liu, Xia; Broer, Henk W.
2015-01-01
This paper studies the codimension-3 boundary-Hopf-fold (BHF) bifurcation of planar Filippov systems. Filippov systems consist of at least one discontinuity boundary locally separating the phase space to disjoint components with different dynamics. Such systems find applications in several fields,
Stability and Hopf bifurcation analysis of a new system
International Nuclear Information System (INIS)
Huang Kuifei; Yang Qigui
2009-01-01
In this paper, a new chaotic system is introduced. The system contains special cases as the modified Lorenz system and conjugate Chen system. Some subtle characteristics of stability and Hopf bifurcation of the new chaotic system are thoroughly investigated by rigorous mathematical analysis and symbolic computations. Meanwhile, some numerical simulations for justifying the theoretical analysis are also presented.
Nonintegrability of the unfolding of the fold-Hopf bifurcation
Yagasaki, Kazuyuki
2018-02-01
We consider the unfolding of the codimension-two fold-Hopf bifurcation and prove its meromorphic nonintegrability in the meaning of Bogoyavlenskij for almost all parameter values. Our proof is based on a generalized version of the Morales-Ramis-Simó theory for non-Hamiltonian systems and related variational equations up to second order are used.
Hopf bifurcation formula for first order differential-delay equations
Rand, Richard; Verdugo, Anael
2007-09-01
This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The derivation is accomplished using Lindstedt's perturbation method.
Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation
Abdelkefi, Abdessattar
2013-06-18
In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.
Necessary and sufficient conditions for Hopf bifurcation in tri-neuron equation with a delay
International Nuclear Information System (INIS)
Liu Xiaoming; Liao Xiaofeng
2009-01-01
In this paper, we consider the delayed differential equations modeling three-neuron equations with only a time delay. Using the time delay as a bifurcation parameter, necessary and sufficient conditions for Hopf bifurcation to occur are derived. Numerical results indicate that for this model, Hopf bifurcation is likely to occur at suitable delay parameter values.
Hopf bifurcation and chaos in macroeconomic models with policy lag
International Nuclear Information System (INIS)
Liao Xiaofeng; Li Chuandong; Zhou Shangbo
2005-01-01
In this paper, we consider the macroeconomic models with policy lag, and study how lags in policy response affect the macroeconomic stability. The local stability of the nonzero equilibrium of this equation is investigated by analyzing the corresponding transcendental characteristic equation of its linearized equation. Some general stability criteria involving the policy lag and the system parameter are derived. By choosing the policy lag as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcation. The direction and stability of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Moreover, we show that the government can stabilize the intrinsically unstable economy if the policy lag is sufficiently short, but the system become locally unstable when the policy lag is too long. We also find the chaotic behavior in some range of the policy lag
Hopf bifurcation in a delayed reaction-diffusion-advection population model
Chen, Shanshan; Lou, Yuan; Wei, Junjie
2018-04-01
In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation. The effect of advection on Hopf bifurcation values is also considered, and our results suggest that Hopf bifurcation is more likely to occur when the advection rate increases.
Hopf bifurcation analysis of Chen circuit with direct time delay feedback
International Nuclear Information System (INIS)
Hai-Peng, Ren; Wen-Chao, Li; Ding, Liu
2010-01-01
Direct time delay feedback can make non-chaotic Chen circuit chaotic. The chaotic Chen circuit with direct time delay feedback possesses rich and complex dynamical behaviours. To reach a deep and clear understanding of the dynamics of such circuits described by delay differential equations, Hopf bifurcation in the circuit is analysed using the Hopf bifurcation theory and the central manifold theorem in this paper. Bifurcation points and bifurcation directions are derived in detail, which prove to be consistent with the previous bifurcation diagram. Numerical simulations and experimental results are given to verify the theoretical analysis. Hopf bifurcation analysis can explain and predict the periodical orbit (oscillation) in Chen circuit with direct time delay feedback. Bifurcation boundaries are derived using the Hopf bifurcation analysis, which will be helpful for determining the parameters in the stabilisation of the originally chaotic circuit
Analysis of stability and Hopf bifurcation for a viral infectious model with delay
International Nuclear Information System (INIS)
Sun Chengjun; Cao Zhijie; Lin Yiping
2007-01-01
In this paper, a four-dimensional viral infectious model with delay is considered. The stability of the two equilibria and the existence of Hopf bifurcation are investigated. It is found that there are stability switches and Hopf bifurcations occur when the delay τ passes through a sequence of critical values. Using the normal form theory and center manifold argument [Hassard B, Kazarino D, Wan Y. Theory and applications of Hopf bifurcation. Cambridge: Cambridge University Press; 1981], the explicit formulaes which determine the stability, the direction and the period of bifurcating periodic solutions are derived. Numerical simulations are carried out to illustrate the validity of the main results
Numerical Hopf bifurcation of Runge-Kutta methods for a class of delay differential equations
International Nuclear Information System (INIS)
Wang Qiubao; Li Dongsong; Liu, M.Z.
2009-01-01
In this paper, we consider the discretization of parameter-dependent delay differential equation of the form y ' (t)=f(y(t),y(t-1),τ),τ≥0,y element of R d . It is shown that if the delay differential equation undergoes a Hopf bifurcation at τ=τ * , then the discrete scheme undergoes a Hopf bifurcation at τ(h)=τ * +O(h p ) for sufficiently small step size h, where p≥1 is the order of the Runge-Kutta method applied. The direction of numerical Hopf bifurcation and stability of bifurcating invariant curve are the same as that of delay differential equation.
Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms
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Tao Zhao
2017-01-01
Full Text Available A delayed SEIQRS worm propagation model with different infection rates for the exposed computers and the infectious computers is investigated in this paper. The results are given in terms of the local stability and Hopf bifurcation. Sufficient conditions for the local stability and the existence of Hopf bifurcation are obtained by using eigenvalue method and choosing the delay as the bifurcation parameter. In particular, the direction and the stability of the Hopf bifurcation are investigated by means of the normal form theory and center manifold theorem. Finally, a numerical example is also presented to support the obtained theoretical results.
Global Hopf Bifurcation for a Predator-Prey System with Three Delays
Jiang, Zhichao; Wang, Lin
2017-06-01
In this paper, a delayed predator-prey model is considered. The existence and stability of the positive equilibrium are investigated by choosing the delay τ = τ1 + τ2 as a bifurcation parameter. We see that Hopf bifurcation can occur as τ crosses some critical values. The direction of the Hopf bifurcations and the stability of the bifurcation periodic solutions are also determined by using the center manifold and normal form theory. Furthermore, based on the global Hopf bifurcation theorem for general function differential equations, which was established by J. Wu using fixed point theorem and degree theory methods, the existence of global Hopf bifurcation is investigated. Finally, numerical simulations to support the analytical conclusions are carried out.
Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
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Zizhen Zhang
2013-01-01
Full Text Available A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.
Hopf Bifurcation Control of Subsynchronous Resonance Utilizing UPFC
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Μ. Μ. Alomari
2017-06-01
Full Text Available The use of a unified power flow controller (UPFC to control the bifurcations of a subsynchronous resonance (SSR in a multi-machine power system is introduced in this study. UPFC is one of the flexible AC transmission systems (FACTS where a voltage source converter (VSC is used based on gate-turn-off (GTO thyristor valve technology. Furthermore, UPFC can be used as a stabilizer by means of a power system stabilizer (PSS. The considered system is a modified version of the second system of the IEEE second benchmark model of subsynchronous resonance where the UPFC is added to its transmission line. The dynamic effects of the machine components on SSR are considered. Time domain simulations based on the complete nonlinear dynamical mathematical model are used for numerical simulations. The results in case of including UPFC are compared to the case where the transmission line is conventionally compensated (without UPFC where two Hopf bifurcations are predicted with unstable operating point at wide range of compensation levels. For UPFC systems, it is worth to mention that the operating point of the system never loses stability at all realistic compensation degrees and therefore all power system bifurcations have been eliminated.
Analysis of stability and Hopf bifurcation for a delayed logistic equation
International Nuclear Information System (INIS)
Sun Chengjun; Han Maoan; Lin Yiping
2007-01-01
The dynamics of a logistic equation with discrete delay are investigated, together with the local and global stability of the equilibria. In particular, the conditions under which a sequence of Hopf bifurcations occur at the positive equilibrium are obtained. Explicit algorithm for determining the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are derived by using the theory of normal form and center manifold [Hassard B, Kazarino D, Wan Y. Theory and applications of Hopf bifurcation. Cambridge: Cambridge University Press; 1981.]. Global existence of periodic solutions is also established by using a global Hopf bifurcation result of Wu [Symmetric functional differential equations and neural networks with memory. Trans Amer Math Soc 350:1998;4799-38.
Stability and Hopf bifurcation analysis of a prey-predator system with two delays
International Nuclear Information System (INIS)
Li Kai; Wei Junjie
2009-01-01
In this paper, we have considered a prey-predator model with Beddington-DeAngelis functional response and selective harvesting of predator species. Two delays appear in this model to describe the time that juveniles take to mature. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. The stability and direction of the Hopf bifurcation are determined by applying the normal form method and the center manifold theory. Numerical simulation results are given to support the theoretical predictions.
Hopf bifurcation in love dynamical models with nonlinear couples and time delays
International Nuclear Information System (INIS)
Liao Xiaofeng; Ran Jiouhong
2007-01-01
A love dynamical models with nonlinear couples and two delays is considered. Local stability of this model is studied by analyzing the associated characteristic transcendental equation. We find that the Hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Numerical example is given to illustrate our results
Hopf bifurcation of a free boundary problem modeling tumor growth with two time delays
International Nuclear Information System (INIS)
Xu Shihe
2009-01-01
In this paper, a free boundary problem modeling tumor growth with two discrete delays is studied. The delays respectively represents the time taken for cells to undergo mitosis and the time taken for the cell to modify the rate of cell loss due to apoptosis. We show the influence of time delays on the Hopf bifurcation when one of delays as a bifurcation parameter.
Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays
International Nuclear Information System (INIS)
Song Yongli; Han Maoan; Peng Yahong
2004-01-01
We consider a Lotka-Volterra competition system with two delays. We first investigate the stability of the positive equilibrium and the existence of Hopf bifurcations, and then using the normal form theory and center manifold argument, derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions
Nonresonant Double Hopf Bifurcation in Toxic Phytoplankton-Zooplankton Model with Delay
Yuan, Rui; Jiang, Weihua; Wang, Yong
This paper investigates a toxic phytoplankton-zooplankton model with Michaelis-Menten type phytoplankton harvesting. The model has rich dynamical behaviors. It undergoes transcritical, saddle-node, fold, Hopf, fold-Hopf and double Hopf bifurcation, when the parameters change and go through some of the critical values, the dynamical properties of the system will change also, such as the stability, equilibrium points and the periodic orbit. We first study the stability of the equilibria, and analyze the critical conditions for the above bifurcations at each equilibrium. In addition, the stability and direction of local Hopf bifurcations, and the completion bifurcation set by calculating the universal unfoldings near the double Hopf bifurcation point are given by the normal form theory and center manifold theorem. We obtained that the stable coexistent equilibrium point and stable periodic orbit alternate regularly when the digestion time delay is within some finite value. That is, we derived the pattern for the occurrence, and disappearance of a stable periodic orbit. Furthermore, we calculated the approximation expression of the critical bifurcation curve using the digestion time delay and the harvesting rate as parameters, and determined a large range in terms of the harvesting rate for the phytoplankton and zooplankton to coexist in a long term.
Stability and Hopf Bifurcation for a Delayed SLBRS Computer Virus Model
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Zizhen Zhang
2014-01-01
Full Text Available 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.
Stability and Hopf bifurcation for a delayed SLBRS computer virus model.
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.
Stability and Hopf bifurcation in a simplified BAM neural network with two time delays.
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.
Hopf bifurcation in a environmental defensive expenditures model with time delay
International Nuclear Information System (INIS)
Russu, Paolo
2009-01-01
In this paper a three-dimensional environmental defensive expenditures model with delay is considered. The model is based on the interactions among visitors V, quality of ecosystem goods E, and capital K, intended as accommodation and entertainment facilities, in Protected Areas (PAs). The tourism user fees (TUFs) are used partly as a defensive expenditure and partly to increase the capital stock. The stability and existence of Hopf bifurcation are investigated. It is that stability switches and Hopf bifurcation occurs when the delay t passes through a sequence of critical values, τ 0 . It has been that the introduction of a delay is a destabilizing process, in the sense that increasing the delay could cause the bio-economics to fluctuate. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation are exhibited by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the results.
Hopf bifurcation and chaos from torus breakdown in voltage-mode controlled DC drive systems
International Nuclear Information System (INIS)
Dai Dong; Ma Xikui; Zhang Bo; Tse, Chi K.
2009-01-01
Period-doubling bifurcation and its route to chaos have been thoroughly investigated in voltage-mode and current-mode controlled DC motor drives under simple proportional control. In this paper, the phenomena of Hopf bifurcation and chaos from torus breakdown in a voltage-mode controlled DC drive system is reported. It has been shown that Hopf bifurcation may occur when the DC drive system adopts a more practical proportional-integral control. The phenomena of period-adding and phase-locking are also observed after the Hopf bifurcation. Furthermore, it is shown that the stable torus can breakdown and chaos emerges afterwards. The work presented in this paper provides more complete information about the dynamical behaviors of DC drive systems.
International Nuclear Information System (INIS)
Karaoglu, Esra; Merdan, Huseyin
2014-01-01
Highlights: • A ratio-dependent predator–prey system involving two discrete maturation time delays is studied. • Hopf bifurcations are analyzed by choosing delay parameters as bifurcation parameters. • When a delay parameter passes through a critical value, Hopf bifurcations occur. • The direction of bifurcation, the period and the stability of periodic solution are also obtained. - Abstract: In this paper we give a detailed Hopf bifurcation analysis of a ratio-dependent predator–prey system involving two different discrete delays. By analyzing the characteristic equation associated with the model, its linear stability is investigated. Choosing delay terms as bifurcation parameters the existence of Hopf bifurcations is demonstrated. Stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introduced by Hassard et al. Furthermore, some of the bifurcation properties including direction, stability and period are given. Finally, theoretical results are supported by some numerical simulations
Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay
International Nuclear Information System (INIS)
Ding Yuting; Jiang Weihua; Wang Hongbin
2012-01-01
Highlights: ► We derive the unfolding of a financial system with Hopf-pitchfork bifurcation. ► We show the coexistence of a pair of stable small amplitudes periodic solutions. ► At the same time, also there is a pair of stable large amplitudes periodic solutions. ► Chaos can appear by period-doubling bifurcation far away from Hopf-pitchfork value. ► The study will be useful for interpreting economics phenomena in theory. - Abstract: In this paper, we identify the critical point for a Hopf-pitchfork bifurcation in a nonlinear financial system with delay, and derive the normal form up to third order with their unfolding in original system parameters near the bifurcation point by normal form method and center manifold theory. Furthermore, we analyze its local dynamical behaviors, and show the coexistence of a pair of stable periodic solutions. We also show that there coexist a pair of stable small-amplitude periodic solutions and a pair of stable large-amplitude periodic solutions for different initial values. Finally, we give the bifurcation diagram with numerical illustration, showing that the pair of stable small-amplitude periodic solutions can also exist in a large region of unfolding parameters, and the financial system with delay can exhibit chaos via period-doubling bifurcations as the unfolding parameter values are far away from the critical point of the Hopf-pitchfork bifurcation.
Forced phase-locked response of a nonlinear system with time delay after Hopf bifurcation
International Nuclear Information System (INIS)
Ji, J.C.; Hansen, Colin H.
2005-01-01
The trivial equilibrium of a nonlinear autonomous system with time delay may become unstable via a Hopf bifurcation of multiplicity two, as the time delay reaches a critical value. This loss of stability of the equilibrium is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. The resultant dynamic behaviour of the corresponding nonlinear non-autonomous system in the neighbourhood of the Hopf bifurcation is investigated based on the reduction of the infinite-dimensional problem to a four-dimensional centre manifold. As a result of the interaction between the Hopf bifurcating periodic solutions and the external periodic excitation, a primary resonance can occur in the forced response of the system when the forcing frequency is close to the Hopf bifurcating periodic frequency. The method of multiple scales is used to obtain four first-order ordinary differential equations that determine the amplitudes and phases of the phase-locked periodic solutions. The first-order approximations of the periodic solutions are found to be in excellent agreement with those obtained by direct numerical integration of the delay-differential equation. It is also found that the steady state solutions of the nonlinear non-autonomous system may lose their stability via either a pitchfork or Hopf bifurcation. It is shown that the primary resonance response may exhibit symmetric and asymmetric phase-locked periodic motions, quasi-periodic motions, chaotic motions, and coexistence of two stable motions
Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System
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Jie Ran
2015-01-01
Full Text Available The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.
Stability and Hopf Bifurcation Analysis on a Nonlinear Business Cycle Model
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Liming Zhao
2016-01-01
Full Text Available This study begins with the establishment of a three-dimension business cycle model based on the condition of a fixed exchange rate. Using the established model, the reported study proceeds to describe and discuss the existence of the equilibrium and stability of the economic system near the equilibrium point as a function of the speed of market regulation and the degree of capital liquidity and a stable region is defined. In addition, the condition of Hopf bifurcation is discussed and the stability of a periodic solution, which is generated by the Hopf bifurcation and the direction of the Hopf bifurcation, is provided. Finally, a numerical simulation is provided to confirm the theoretical results. This study plays an important role in theoretical understanding of business cycle models and it is crucial for decision makers in formulating macroeconomic policies as detailed in the conclusions of this report.
Hopf bifurcation and chaos in a third-order phase-locked loop
Piqueira, José Roberto C.
2017-01-01
Phase-locked loops (PLLs) are devices able to recover time signals in several engineering applications. The literature regarding their dynamical behavior is vast, specifically considering that the process of synchronization between the input signal, coming from a remote source, and the PLL local oscillation is robust. For high-frequency applications it is usual to increase the PLL order by increasing the order of the internal filter, for guarantying good transient responses; however local parameter variations imply structural instability, thus provoking a Hopf bifurcation and a route to chaos for the phase error. Here, one usual architecture for a third-order PLL is studied and a range of permitted parameters is derived, providing a rule of thumb for designers. Out of this range, a Hopf bifurcation appears and, by increasing parameters, the periodic solution originated by the Hopf bifurcation degenerates into a chaotic attractor, therefore, preventing synchronization.
Hopf Bifurcation of a Delayed Epidemic Model with Information Variable and Limited Medical Resources
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Caijuan Yan
2014-01-01
Full Text Available We consider SIR epidemic model in which population growth is subject to logistic growth in absence of disease. We get the condition for Hopf bifurcation of a delayed epidemic model with information variable and limited medical resources. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. If the basic reproduction ratio ℛ01, we obtain sufficient conditions under which the endemic equilibrium E* of system is locally asymptotically stable. And we also have discussed the stability and direction of Hopf bifurcations. Numerical simulations are carried out to explain the mathematical conclusions.
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.
Wang, Zhen; Wang, Xiaohong; Li, Yuxia; Huang, Xia
2017-12-01
In this paper, the problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed. With the help of the stability theory of fractional-order differential equations and Laplace transforms, several new sufficient conditions, which ensure the stability of the system are derived. Taking the time delay as the bifurcation parameter, Hopf bifurcation is investigated and the critical value of the time delay for the occurrence of Hopf bifurcation is determined. Finally, two representative numerical examples are given to show the effectiveness of the theoretical results.
Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus
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Tao Dong
2012-01-01
Full Text Available By considering that people may immunize their computers with countermeasures in susceptible state, exposed state and using anti-virus software may take a period of time, a computer virus model with time delay based on an SEIR model is proposed. We regard time delay as bifurcating parameter to study the dynamical behaviors which include local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when time delay passes through a sequence of critical value. The linerized model and stability of the bifurcating periodic solutions are also derived by applying the normal form theory and the center manifold theorem. Finally, an illustrative example is also given to support the theoretical results.
Local stability and Hopf bifurcation in small-world delayed networks
International Nuclear Information System (INIS)
Li Chunguang; Chen Guanrong
2004-01-01
The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis
Local stability and Hopf bifurcation in small-world delayed networks
Energy Technology Data Exchange (ETDEWEB)
Li Chunguang E-mail: cgli@uestc.edu.cn; Chen Guanrong E-mail: gchen@ee.cityu.edu.hk
2004-04-01
The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis.
Stability and Hopf Bifurcation of a Reaction-Diffusion Neutral Neuron System with Time Delay
Dong, Tao; Xia, Linmao
2017-12-01
In this paper, a type of reaction-diffusion neutral neuron system with time delay under homogeneous Neumann boundary conditions is considered. By constructing a basis of phase space based on the eigenvectors of the corresponding Laplace operator, the characteristic equation of this system is obtained. Then, by selecting time delay and self-feedback strength as the bifurcating parameters respectively, the dynamic behaviors including local stability and Hopf bifurcation near the zero equilibrium point are investigated when the time delay and self-feedback strength vary. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by using the normal form and the center manifold theorem for the corresponding partial differential equation. Finally, two simulation examples are given to verify the theory.
Si'lnikov chaos and Hopf bifurcation analysis of Rucklidge system
International Nuclear Information System (INIS)
Wang Xia
2009-01-01
A three-dimensional autonomous system - the Rucklidge system is considered. By the analytical method, Hopf bifurcation of Rucklidge system may occur when choosing an appropriate bifurcation parameter. Using the undetermined coefficient method, the existence of heteroclinic and homoclinic orbits in the Rucklidge system is proved, and the explicit and uniformly convergent algebraic expressions of Si'lnikov type orbits are given. As a result, the Si'lnikov criterion guarantees that there exists the Smale horseshoe chaos motion for the Rucklidge system.
On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields
Directory of Open Access Journals (Sweden)
Michail P. Markakis
2016-01-01
Full Text Available The restriction of an n-dimensional nonlinear parametric system on the center manifold is treated via a new proper symbolic form and analytical expressions of the involved quantities are obtained as functions of the parameters by lengthy algebraic manipulations combined with computer assisted calculations. Normal forms regarding degenerate Hopf bifurcations up to codimension 3, as well as the corresponding Lyapunov coefficients and bifurcation portraits, can be easily computed for any system under consideration.
Hopf bifurcation of a ratio-dependent predator-prey system with time delay
International Nuclear Information System (INIS)
Celik, Canan
2009-01-01
In this paper, we consider a ratio dependent predator-prey system with time delay where the dynamics is logistic with the carrying capacity proportional to prey population. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the system based on the normal form approach and the center manifold theory. Finally, we illustrate our theoretical results by numerical simulations.
Stability and Hopf bifurcation in a delayed competitive web sites model
International Nuclear Information System (INIS)
Xiao Min; Cao Jinde
2006-01-01
The delayed differential equations modeling competitive web sites, based on the Lotka-Volterra competition equations, are considered. Firstly, the linear stability is investigated. It is found that there is a stability switch for time delay, and Hopf bifurcation occurs when time delay crosses through a critical value. Then the direction and stability of the bifurcated periodic solutions are determined, using the normal form theory and the center manifold reduction. Finally, some numerical simulations are carried out to illustrate the results found
Hopf bifurcation in a partial dependent predator-prey system with delay
International Nuclear Information System (INIS)
Zhao Huitao; Lin Yiping
2009-01-01
In this paper, a partial dependent predator-prey model with time delay is studied by using the theory of functional differential equation and Hassard's method, the condition on which positive equilibrium exists and Hopf bifurcation occurs are given. Finally, numerical simulations are performed to support the analytical results, and the chaotic behaviors are observed.
Hopf bifurcations in a fractional reaction–diffusion model for the ...
African Journals Online (AJOL)
The phenomenon of hopf bifurcation has been well-studied and applied to many physical situations to explain behaviour of solutions resulting from differential and partial differential equations. This phenomenon is applied to a fractional reaction diffusion model for tumor invasion and development. The result suggests that ...
Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model
DEFF Research Database (Denmark)
Brøns, Morten; Desroches, Mathieu; Krupa, Martin
2015-01-01
In a forest pest model, young trees are distinguished from old trees. The pest feeds on old trees. The pest grows on a fast scale, the young trees on an intermediate scale, and the old trees on a slow scale. A combination of a singular Hopf bifurcation and a “weak return” mechanism, characterized...
Degenerate Hopf bifurcation in a self-exciting Faraday disc dynamo
Indian Academy of Sciences (India)
Weiquan Pan
2017-05-31
May 31, 2017 ... Recently, self-exciting Faraday disk dynamo is also a topic of con- cern [16–20]. ..... Hopf bifurcation. (a) Projected on the x–z plane and (b) pro- ... Key Lab of Com- plex System Optimization and Big Data Processing. (No.
Global Hopf bifurcation analysis on a BAM neural network with delays
Sun, Chengjun; Han, Maoan; Pang, Xiaoming
2007-01-01
A delayed differential equation that models a bidirectional associative memory (BAM) neural network with four neurons is considered. By using a global Hopf bifurcation theorem for FDE and a Bendixon's criterion for high-dimensional ODE, a group of sufficient conditions for the system to have multiple periodic solutions are obtained when the sum of delays is sufficiently large.
Global Hopf bifurcation analysis on a BAM neural network with delays
International Nuclear Information System (INIS)
Sun Chengjun; Han Maoan; Pang Xiaoming
2007-01-01
A delayed differential equation that models a bidirectional associative memory (BAM) neural network with four neurons is considered. By using a global Hopf bifurcation theorem for FDE and a Bendixon's criterion for high-dimensional ODE, a group of sufficient conditions for the system to have multiple periodic solutions are obtained when the sum of delays is sufficiently large
DEFF Research Database (Denmark)
Yang, Li Hui; Xu, Zhao; Østergaard, Jacob
2010-01-01
This paper first presents the Hopf bifurcation analysis for a vector-controlled doubly fed induction generator (DFIG) which is widely used in wind power conversion systems. Using three-phase back-to-back pulse-width-modulated (PWM) converters, DFIG can keep stator frequency constant under variabl...
Directory of Open Access Journals (Sweden)
Huitao Zhao
2013-01-01
Full Text Available A ratio-dependent predator-prey model with two time delays is studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semitrivial equilibrium is addressed. By using the theory of functional equation and Hopf bifurcation, the conditions on which positive equilibrium exists and the quality of Hopf bifurcation are given. Using a global Hopf bifurcation result of Wu (1998 for functional differential equations, the global existence of the periodic solutions is obtained. Finally, an example for numerical simulations is also included.
Xiao, Min; Zheng, Wei Xing; Cao, Jinde
2013-01-01
Recent studies on Hopf bifurcations of neural networks with delays are confined to simplified neural network models consisting of only two, three, four, five, or six neurons. It is well known that neural networks are complex and large-scale nonlinear dynamical systems, so the dynamics of the delayed neural networks are very rich and complicated. Although discussing the dynamics of networks with a few neurons may help us to understand large-scale networks, there are inevitably some complicated problems that may be overlooked if simplified networks are carried over to large-scale networks. In this paper, a general delayed bidirectional associative memory neural network model with n + 1 neurons is considered. By analyzing the associated characteristic equation, the local stability of the trivial steady state is examined, and then the existence of the Hopf bifurcation at the trivial steady state is established. By applying the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction and stability of the bifurcating periodic solution. Furthermore, the paper highlights situations where the Hopf bifurcations are particularly critical, in the sense that the amplitude and the period of oscillations are very sensitive to errors due to tolerances in the implementation of neuron interconnections. It is shown that the sensitivity is crucially dependent on the delay and also significantly influenced by the feature of the number of neurons. Numerical simulations are carried out to illustrate the main results.
Chaos and Hopf bifurcation of a hybrid ratio-dependent three species food chain
International Nuclear Information System (INIS)
Wang Fengyan; Pang Guoping
2008-01-01
In this paper, we propose and study a model of a hybrid ratio-dependent three species food chain, which is constituted by a hybrid type subsystem of prey and middle-predator and a middle-top predators' subsystem with Holling type-II functional response. We investigate the persistence and Hopf bifurcation of the system. Computer simulations are carried out to explain the mathematical conclusions. The chaotic attractor is obtained for suitable choice of parametric values
Local and global Hopf bifurcation analysis in a neutral-type neuron system with two delays
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.
Directory of Open Access Journals (Sweden)
Carlos Mario Escobar Callejas
2011-12-01
Full Text Available En el presente artículo de investigación se caracteriza el tipo de bifurcación de Hopf que se presenta en el fenómeno de la bifurcación de zip para un sistema tridimensional no lineal de ecuaciones diferenciales que satisface las condiciones planteadas por Butler y Farkas, las cuales modelan la competición de dos especies predadoras por una presa singular que se regenera. Se demuestra que en todas las variedades bidimensionales invariantes del sistema considerado se desarrolla una bifurcación de Hopf supercrítica lo cual es una extensión de algunos resultados sobre el tipo de bifurcación de Hopf que se forma en el fenómeno de la bifurcación de zip en sistema con respuesta funcional del predador del tipo Holling II, [1].This research article characterizes the type of Hopf bifurcation occurring in the Zip bifurcation phenomenon for a non-linear 3D system of differential equations which meets the conditions stated by Butler and Farkas to model competition of two predators struggling for a prey. It is shown that a supercritical Hopf bifurcation is developed in all invariant two-dimensional varieties of the system considered, which is an extension of some results about the kind of Hopf bifurcation which is formed in the Zip bifurcation phenomenon in a system with functional response of the Holling-type predator.
International Nuclear Information System (INIS)
Wang Huijuan; Ren Zhi
2011-01-01
Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion equation. The time delay changes remarkably the oscillation frequency, the intrinsic wave vector, and the intensities of both Turing and Hopf modes. The application of appropriate time delay can control the competition between the Turing and Hopf modes. Analysis shows that individual or both feedbacks can realize the control of the transformation between the Turing and Hopf patterns. Two-dimensional numerical simulations validate the analytical results. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks.
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.
Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks
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 ZN 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.
Stability and Hopf bifurcation on a model for HIV infection of CD4{sup +} T cells with delay
Energy Technology Data Exchange (ETDEWEB)
Wang Xia [College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000 (China)], E-mail: xywangxia@163.com; Tao Youde [College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000 (China); Beijing Institute of Information Control, Beijing 100037 (China); Song Xinyu [College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000 (China) and Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091 (China)], E-mail: xysong88@163.com
2009-11-15
In this paper, a delayed differential equation model that describes HIV infection of CD4{sup +} T cells is considered. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. In succession, using the normal form theory and center manifold argument, we derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions.
Directory of Open Access Journals (Sweden)
Toichiro Asada
2007-01-01
Full Text Available We explore numerically a three-dimensional discrete-time Kaldorian macrodynamic model in an open economy with fixed exchange rates, focusing on the effects of variation of the model parameters, the speed of adjustment of the goods market α, and the degree of capital mobility β on the stability of equilibrium and on the existence of business cycles. We determine the stability region in the parameter space and find that increase of α destabilizes the equilibrium more quickly than increase of β. We determine the Hopf-Neimark bifurcation curve along which business cycles are generated, and discuss briefly the occurrence of Arnold tongues. Bifurcation and Lyapunov exponent diagrams are computed providing information on the emergence, persistence, and amplitude of the cycles and illustrating the complex dynamics involved. Examples of cycles and other attractors are presented. Finally, we discuss a two-dimensional variation of the model related to a “wealth effect,” called model 2, and show that in this case, α does not destabilize the equilibrium more quickly than β, and that a Hopf-Neimark bifurcation curve does not exist in the parameter space, therefore model 2 does not produce cycles.
On control of Hopf bifurcation in time-delayed neural network system
International Nuclear Information System (INIS)
Zhou Shangbo; Liao Xiaofeng; Yu Juebang; Wong Kwokwo
2005-01-01
The control of Hopf bifurcations in neural network systems is studied in this Letter. The asymptotic stability theorem and the relevant corollary for linearized nonlinear dynamical systems are proven. In particular, a novel method for analyzing the local stability of a dynamical system with time-delay is suggested. For the time-delayed system consisting of one or two neurons, a washout filter based control model is proposed and analyzed. By employing the stability theorems derived, we investigate the stability of a control system and state the relevant theorems for choosing the parameters of the stabilized control system
A heterogenous Cournot duopoly with delay dynamics: Hopf bifurcations and stability switching curves
Pecora, Nicolò; Sodini, Mauro
2018-05-01
This article considers a Cournot duopoly model in a continuous-time framework and analyze its dynamic behavior when the competitors are heterogeneous in determining their output decision. Specifically the model is expressed in the form of differential equations with discrete delays. The stability conditions of the unique Nash equilibrium of the system are determined and the emergence of Hopf bifurcations is shown. Applying some recent mathematical techniques (stability switching curves) and performing numerical simulations, the paper confirms how different time delays affect the stability of the economy.
Ferruzzo Correa, Diego P.; Bueno, Átila M.; Castilho Piqueira, José R.
2017-04-01
In this paper we investigate stability conditions for small-amplitude periodic solutions emerging near symmetry-preserving Hopf bifurcations in a time-delayed fully-connected N-node PLL network. The study of this type of systems which includes the time delay between connections has attracted much attention among researchers mainly because the delayed coupling between nodes emerges almost naturally in mathematical modeling in many areas of science such as neurobiology, population dynamics, physiology and engineering. In a previous work it has been shown that symmetry breaking and symmetry preserving Hopf bifurcations can emerge in the parameter space. We analyze the stability along branches of periodic solutions near fully-synchronized Hopf bifurcations in the fixed-point space, based on the reduction of the infinite-dimensional space onto a two-dimensional center manifold in normal form. Numerical results are also presented in order to confirm our analytical results.
Stability switches, Hopf bifurcation and chaos of a neuron model with delay-dependent parameters
International Nuclear Information System (INIS)
Xu, X.; Hu, H.Y.; Wang, H.L.
2006-01-01
It is very common that neural network systems usually involve time delays since the transmission of information between neurons is not instantaneous. Because memory intensity of the biological neuron usually depends on time history, some of the parameters may be delay dependent. Yet, little attention has been paid to the dynamics of such systems. In this Letter, a detailed analysis on the stability switches, Hopf bifurcation and chaos of a neuron model with delay-dependent parameters is given. Moreover, the direction and the stability of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem. It shows that the dynamics of the neuron model with delay-dependent parameters is quite different from that of systems with delay-independent parameters only
Onset of Fast Magnetic Reconnection via Subcritical Bifurcation
Directory of Open Access Journals (Sweden)
ZHIBIN eGUO
2015-04-01
Full Text Available We report a phase transition model for the onset of fast magnetic reconnection. By investigating the joint dynamics of streaming instability(i.e., current driven ion acoustic in this paper and current gradient driven whistler wave {color{blue} {prior to the onset of fast reconnection}}, we show that the nonlinear evolution of current sheet(CS can be described by a Landau-Ginzburg equation. The phase transition from slow reconnection to fast reconnection occurs at a critical thickness, $Delta_csimeq frac{2}{sqrt{pi}}left|frac{v_{the}}{v_c}right|d_e$, where $v_{the}$ is electron thermal velocity and $v_c$ is the velocity threshold of the streaming instability. For current driven ion acoustic, $Delta_c$ is $leq10d_e$. If the thickness of the CS is narrower than $Delta_c$, the CS subcritically bifurcates into a rough state, which facilitates breakage of the CS, and consequently initiates fast reconnection.
International Nuclear Information System (INIS)
Han, Renji; Dai, Binxiang
2017-01-01
Highlights: • We model general two-dimensional reaction-diffusion with nonlocal delay. • The existence of unique positive steady state is studied. • The bilinear form for the proposed system is given. • The existence, direction of Hopf bifurcation are given by symmetry method. - Abstract: A nonlocal delayed reaction-diffusive two-species model with Dirichlet boundary condition and general functional response is investigated in this paper. Based on the Lyapunov–Schmidt reduction, the existence, bifurcation direction and stability of Hopf bifurcating periodic orbits near the positive spatially nonhomogeneous steady-state solution are obtained, where the time delay is taken as the bifurcation parameter. Moreover, the general results are applied to a diffusive Lotka–Volterra type food-limited population model with nonlocal delay effect, and it is found that diffusion and nonlocal delay can also affect the other dynamic behavior of the system by numerical experiments.
Zhao, Huitao; Lu, Mengxia; Zuo, Junmei
2014-01-01
A controlled model for a financial system through washout-filter-aided dynamical feedback control laws is developed, the problem of anticontrol of Hopf bifurcation from the steady state is studied, and the existence, stability, and direction of bifurcated periodic solutions are discussed in detail. The obtained results show that the delay on price index has great influences on the financial system, which can be applied to suppress or avoid the chaos phenomenon appearing in the financial system.
International Nuclear Information System (INIS)
Cliffe, K.A.; Garratt, T.J.; Spence, A.
1992-03-01
This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalised eigenvalue problems arising from mixed finite element discretisations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and can be used in a scheme to determine the stability of steady state solutions and to detect Hopf bifurcations. We introduce a modified Cayley transform of the generalised eigenvalue problem which overcomes a drawback of the usual Cayley transform applied to such problems. Standard iterative methods are then applied to the transformed eigenvalue problem to compute approximations to the eigenvalue of smallest real part. Numerical experiments are performed using a model of double diffusive convection. (author)
Stability and Hopf bifurcation for a business cycle model with expectation and delay
Liu, Xiangdong; Cai, Wenli; Lu, Jiajun; Wang, Yangyang
2015-08-01
According to rational expectation hypothesis, the government will take into account the future capital stock in the process of investment decision. By introducing anticipated capital stock into an economic model with investment delay, we construct a mixed functional differential system including delay and advanced variables. The system is converted to the one containing only delay by variable substitution. The equilibrium point of the system is obtained and its dynamical characteristics such as stability, Hopf bifurcation and its stability and direction are investigated by using the related theories of nonlinear dynamics. We carry out some numerical simulations to confirm these theoretical conclusions. The results indicate that both capital stock's anticipation and investment lag are the certain factors leading to the occurrence of cyclical fluctuations in the macroeconomic system. Moreover, the level of economic fluctuation can be dampened to some extent if investment decisions are made by the reasonable short-term forecast on capital stock.
International Nuclear Information System (INIS)
Wang Jun-Song; Yuan Rui-Xi; Gao Zhi-Wei; Wang De-Jin
2011-01-01
We study the Hopf bifurcation and the chaos phenomena in a random early detection-based active queue management (RED-AQM) congestion control system with a communication delay. We prove that there is a critical value of the communication delay for the stability of the RED-AQM control system. Furthermore, we show that the system will lose its stability and Hopf bifurcations will occur when the delay exceeds the critical value. When the delay is close to its critical value, we demonstrate that typical chaos patterns may be induced by the uncontrolled stochastic traffic in the RED-AQM control system even if the system is still stable, which reveals a new route to the chaos besides the bifurcation in the network congestion control system. Numerical simulations are given to illustrate the theoretical results. (general)
Complexity and Hopf Bifurcation Analysis on a Kind of Fractional-Order IS-LM Macroeconomic System
Ma, Junhai; Ren, Wenbo
On the basis of our previous research, we deepen and complete a kind of macroeconomics IS-LM model with fractional-order calculus theory, which is a good reflection on the memory characteristics of economic variables, we also focus on the influence of the variables on the real system, and improve the analysis capabilities of the traditional economic models to suit the actual macroeconomic environment. The conditions of Hopf bifurcation in fractional-order system models are briefly demonstrated, and the fractional order when Hopf bifurcation occurs is calculated, showing the inherent complex dynamic characteristics of the system. With numerical simulation, bifurcation, strange attractor, limit cycle, waveform and other complex dynamic characteristics are given; and the order condition is obtained with respect to time. We find that the system order has an important influence on the running state of the system. The system has a periodic motion when the order meets the conditions of Hopf bifurcation; the fractional-order system gradually stabilizes with the change of the order and parameters while the corresponding integer-order system diverges. This study has certain significance to policy-making about macroeconomic regulation and control.
Song, Yongli; Zhang, Tonghua; Tadé, Moses O.
2009-12-01
The dynamical behavior of a delayed neural network with bi-directional coupling is investigated by taking the delay as the bifurcating parameter. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using the theory of functional differential equations. As the propagation time delay in the coupling varies, stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. We also discuss the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. In particular, we obtain that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling, i.e., different ranges of delays correspond to different patterns of neural activities. Numerical simulations are given to illustrate the obtained results and show the existence of bursts in some interval of the time for large enough delay.
Ma, Junhai; Ren, Wenbo; Zhan, Xueli
2017-04-01
Based on the study of scholars at home and abroad, this paper improves the three-dimensional IS-LM model in macroeconomics, analyzes the equilibrium point of the system and stability conditions, focuses on the parameters and complex dynamic characteristics when Hopf bifurcation occurs in the three-dimensional IS-LM macroeconomics system. In order to analyze the stability of limit cycles when Hopf bifurcation occurs, this paper further introduces the first Lyapunov coefficient to judge the limit cycles, i.e. from a practical view of the business cycle. Numerical simulation results show that within the range of most of the parameters, the limit cycle of 3D IS-LM macroeconomics is stable, that is, the business cycle is stable; with the increase of the parameters, limit cycles becomes unstable, and the value range of the parameters in this situation is small. The research results of this paper have good guide significance for the analysis of macroeconomics system.
Stability and Hopf bifurcation in a delayed model for HIV infection of CD4{sup +}T cells
Energy Technology Data Exchange (ETDEWEB)
Cai Liming [Department of Mathematics, Xinyang Normal University, Xinyang, 464000 Henan (China); Beijing Institute of Information Control, Beijing 100037 (China)], E-mail: lmcai06@yahoo.com.cn; Li Xuezhi [Department of Mathematics, Xinyang Normal University, Xinyang, 464000 Henan (China)
2009-10-15
In this paper, we consider a delayed mathematical model for the interactions of HIV infection and CD4{sup +}T cells. We first investigate the existence and stability of the Equilibria. We then study the effect of the time delay on the stability of the infected equilibrium. Criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. Moreover, by applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Finally by using a delay {tau} as a bifurcation parameter, the existence of Hopf bifurcation is also investigated. Numerical simulations are presented to illustrate the analytical results.
Huang, Chengdai; Cao, Jinde; Xiao, Min; Alsaedi, Ahmed; Hayat, Tasawar
2018-04-01
This paper is comprehensively concerned with the dynamics of a class of high-dimension fractional ring-structured neural networks with multiple time delays. Based on the associated characteristic equation, the sum of time delays is regarded as the bifurcation parameter, and some explicit conditions for describing delay-dependent stability and emergence of Hopf bifurcation of such networks are derived. It reveals that the stability and bifurcation heavily relies on the sum of time delays for the proposed networks, and the stability performance of such networks can be markedly improved by selecting carefully the sum of time delays. Moreover, it is further displayed that both the order and the number of neurons can extremely influence the stability and bifurcation of such networks. The obtained criteria enormously generalize and improve the existing work. Finally, numerical examples are presented to verify the efficiency of the theoretical results.
O(2) Hopf bifurcation of viscous shock waves in a channel
Pogan, Alin; Yao, Jinghua; Zumbrun, Kevin
2015-07-01
Extending work of Texier and Zumbrun in the semilinear non-reflection symmetric case, we study O(2) transverse Hopf bifurcation, or "cellular instability", of viscous shock waves in a channel, for a class of quasilinear hyperbolic-parabolic systems including the equations of thermoviscoelasticity. The main difficulties are to (i) obtain Fréchet differentiability of the time- T solution operator by appropriate hyperbolic-parabolic energy estimates, and (ii) handle O(2) symmetry in the absence of either center manifold reduction (due to lack of spectral gap) or (due to nonstandard quasilinear hyperbolic-parabolic form) the requisite framework for treatment by spatial dynamics on the space of time-periodic functions, the two standard treatments for this problem. The latter issue is resolved by Lyapunov-Schmidt reduction of the time- T map, yielding a four-dimensional problem with O(2) plus approximate S1 symmetry, which we treat "by hand" using direct Implicit Function Theorem arguments. The former is treated by balancing information obtained in Lagrangian coordinates with that from associated constraints. Interestingly, this argument does not apply to gas dynamics or magnetohydrodynamics (MHD), due to the infinite-dimensional family of Lagrangian symmetries corresponding to invariance under arbitrary volume-preserving diffeomorphisms.
Singular Hopf bifurcation in a differential equation with large state-dependent delay.
Kozyreff, G; Erneux, T
2014-02-08
We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawtooth oscillations. The dependence of the delay on the solution can be either linear or nonlinear, with at least quadratic dependence. In the former case, an asymptotic connection is made with the Rayleigh oscillator. In the latter, van der Pol's equation is derived for the small-amplitude oscillations. SDD differential equations are currently the subject of intense research in order to establish or amend general theorems valid for constant-delay differential equation, but explicit analytical construction of solutions are rare. This paper illustrates the use of singular perturbation techniques and the unusual way in which solvability conditions can arise for SDD problems with large delays.
Effects of internal noise in mesoscopic chemical systems near Hopf bifurcation
International Nuclear Information System (INIS)
Xiao Tiejun; Ma Juan; Hou Zhonghuai; Xin Houwen
2007-01-01
The effects of internal noise in mesoscopic chemical oscillation systems have been studied analytically, in the parameter region close to the deterministic Hopf bifurcation. Starting from chemical Langevin equations, stochastic normal form equations are obtained, governing the evolution of the radius and phase of the stochastic oscillation. By stochastic averaging, the normal form equation can be solved analytically. Stationary distributions of the radius and auto-correlation functions of the phase variable are obtained. It is shown that internal noise can induce oscillation; even no deterministic oscillation exists. The radius of the noise-induced oscillation (NIO) becomes larger when the internal noise increases, but the correlation time becomes shorter. The trade-off between the strength and regularity of the NIO leads to a clear maximum in its signal-to-noise ratio when the internal noise changes, demonstrating the occurrence of internal noise coherent resonance. Since the intensity of the internal noise is inversely proportional to the system size, the phenomenon also indicates the existence of an optimal system size. These theoretical results are applied to a circadian clock system and excellent agreement with the numerical results is obtained
International Nuclear Information System (INIS)
Agliari, Anna
2006-01-01
In this paper we study some global bifurcations arising in the Puu's oligopoly model when we assume that the producers do not adjust to the best reply but use an adaptive process to obtain at each step the new production. Such bifurcations cause the appearance of a pair of closed invariant curves, one attracting and one repelling, this latter being involved in the subcritical Neimark bifurcation of the Cournot equilibrium point. The aim of the paper is to highlight the relationship between the global bifurcations causing the appearance/disappearance of two invariant closed curves and the homoclinic connections of some saddle cycle, already conjectured in [Agliari A, Gardini L, Puu T. Some global bifurcations related to the appearance of closed invariant curves. Comput Math Simul 2005;68:201-19]. We refine the results obtained in such a paper, showing that the appearance/disappearance of closed invariant curves is not necessarily related to the existence of an attracting cycle. The characterization of the periodicity tongues (i.e. a region of the parameter space in which an attracting cycle exists) associated with a subcritical Neimark bifurcation is also discussed
Li, Chengxian; Liu, Haihong; Zhang, Tonghua; Yan, Fang
2017-12-01
In this paper, a gene regulatory network mediated by small noncoding RNA involving two time delays and diffusion under the Neumann boundary conditions is studied. Choosing the sum of delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of spatially homogeneous and spatially inhomogeneous periodic solutions are investigated by analyzing the corresponding characteristic equation. It is shown that the sum of delays can induce Hopf bifurcation and the diffusion incorporated into the system can effect the amplitude of periodic solutions. Furthermore, the spatially homogeneous periodic solution always exists and the spatially inhomogeneous periodic solution will arise when the diffusion coefficients of protein and mRNA are suitably small. Particularly, the small RNA diffusion coefficient is more robust and its effect on model is much less than protein and mRNA. Finally, the explicit formulae for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by employing the normal form theory and center manifold theorem for partial functional differential equations. Finally, numerical simulations are carried out to illustrate our theoretical analysis.
Noise-induced transitions at a Hopf bifurcation in a first-order delay-differential equation
International Nuclear Information System (INIS)
Longtin, A.
1991-01-01
The influence of colored noise on the Hopf bifurcation in a first-order delay-differential equation (DDE), a model paradigm for nonlinear delayed feedback systems, is considered. First, it is shown, using a stability analysis, how the properties of the DDE depend on the ratio R of system delay to response time. When this ratio is small, the DDE behaves more like a low-dimensional system of ordinary differential equations (ODE's); when R is large, one obtains a singular perturbation limit in which the behavior of the DDE approaches that of a discrete time map. The relative magnitude of the additive and multiplicative noise-induced postponements of the Hopf bifurcation are numerically shown to depend on the ratio R. Although both types of postponements are minute in the large-R limit, they are almost equal due to an equivalence of additive and parametric noise for discrete time maps. When R is small, the multiplicative shift is larger than the additive one at large correlation times, but the shifts are equal for small correlation times. In fact, at constant noise power, the postponement is only slightly affected by the correlation time of the noise, except when the noise becomes white, in which case the postponement drastically decreases. This is a numerical study of the stochastic Hopf bifurcation, in ODE's or DDE's, that looks at the effect of noise correlation time at constant power. Further, it is found that the slope at the fixed point averaged over the stochastic-parameter motion acts, under certain conditions, as a quantitative indicator of oscillation onset in the presence of noise. The problem of how properties of the DDE carry over to ODE's and to maps is discussed, along with the proper theoretical framework in which to study nonequilibrium phase transitions in this class of functional differential equations
Hopf bifurcation in a dynamic IS-LM model with time delay
International Nuclear Information System (INIS)
Neamtu, Mihaela; Opris, Dumitru; Chilarescu, Constantin
2007-01-01
The paper investigates the impact of delayed tax revenues on the fiscal policy out-comes. Choosing the delay as a bifurcation parameter we study the direction and the stability of the bifurcating periodic solutions. We show when the system is stable with respect to the delay. Some numerical examples are given to confirm the theoretical results
Transverse single-file diffusion and enhanced longitudinal diffusion near a subcritical bifurcation
Dessup, Tommy; Coste, Christophe; Saint Jean, Michel
2018-05-01
A quasi-one-dimensional system of repelling particles undergoes a configurational phase transition when the transverse confining potential decreases. Below a threshold, it becomes energetically favorable for the system to adopt one of two staggered raw patterns, symmetric with respect to the system axis. This transition is a subcritical pitchfork bifurcation for short range interactions. As a consequence, the homogeneous zigzag pattern is unstable in a finite zigzag amplitude range [hC 1,hC 2] . We exhibit strong qualitative effects of the subcriticality on the thermal motions of the particles. When the zigzag amplitude is close enough to the limits hC 1 and hC 2, a transverse vibrational soft mode occurs which induces a strongly subdiffusive behavior of the transverse fluctuations, similar to single-file diffusion. On the contrary, the longitudinal fluctuations are enhanced, with a diffusion coefficient which is more than doubled. Conversely, a simple measurement of the thermal fluctuations allows a precise determination of the bifurcation thresholds.
International Nuclear Information System (INIS)
Zhang Jiangang; Li Xianfeng; Chu Yandong; Yu Jianning; Chang Yingxiang
2009-01-01
In this paper, complex dynamical behavior of a class of centrifugal flywheel governor system is studied. These systems have a rich variety of nonlinear behavior, which are investigated here by numerically integrating the Lagrangian equations of motion. A tiny change in parameters can lead to an enormous difference in the long-term behavior of the system. Bubbles of periodic orbits may also occur within the bifurcation sequence. Hyperchaotic behavior is also observed in cases where two of the Lyapunov exponents are positive, one is zero, and one is negative. The routes to chaos are analyzed using Poincare maps, which are found to be more complicated than those of nonlinear rotational machines. Periodic and chaotic motions can be clearly distinguished by all of the analytical tools applied here, namely Poincare sections, bifurcation diagrams, Lyapunov exponents, and Lyapunov dimensions. This paper proposes a parametric open-plus-closed-loop approach to controlling chaos, which is capable of switching from chaotic motion to any desired periodic orbit. The theoretical work and numerical simulations of this paper can be extended to other systems. Finally, the results of this paper are of practical utility to designers of rotational machines.
DROP TAIL AND RED QUEUE MANAGEMENT WITH SMALL BUFFERS:STABILITY AND HOPF BIFURCATION
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Ganesh Patil
2011-06-01
Full Text Available There are many factors that are important in the design of queue management schemes for routers in the Internet: for example, queuing delay, link utilization, packet loss, energy consumption and the impact of router buffer size. By considering a fluid model for the congestion avoidance phase of Additive Increase Multiplicative Decrease (AIMD TCP, in a small buffer regime, we argue that stability should also be a desirable feature for network performance. The queue management schemes we study are Drop Tail and Random Early Detection (RED. For Drop Tail, the analytical arguments are based on local stability and bifurcation theory. As the buffer size acts as a bifurcation parameter, variations in it can readily lead to the emergence of limit cycles. We then present NS2 simulations to study the effect of changing buffer size on queue dynamics, utilization, window size and packet loss for three different flow scenarios. The simulations corroborate the analysis which highlights that performance is coupled with the notion of stability. Our work suggests that, in a small buffer regime, a simple Drop Tail queue management serves to enhance stability and appears preferable to the much studied RED scheme.
Constructing Hopf bifurcation lines for the stability of nonlinear systems with two time delays
Nguimdo, Romain Modeste
2018-03-01
Although the plethora real-life systems modeled by nonlinear systems with two independent time delays, the algebraic expressions for determining the stability of their fixed points remain the Achilles' heel. Typically, the approach for studying the stability of delay systems consists in finding the bifurcation lines separating the stable and unstable parameter regions. This work deals with the parametric construction of algebraic expressions and their use for the determination of the stability boundaries of fixed points in nonlinear systems with two independent time delays. In particular, we concentrate on the cases for which the stability of the fixed points can be ascertained from a characteristic equation corresponding to that of scalar two-delay differential equations, one-component dual-delay feedback, or nonscalar differential equations with two delays for which the characteristic equation for the stability analysis can be reduced to that of a scalar case. Then, we apply our obtained algebraic expressions to identify either the parameter regions of stable microwaves generated by dual-delay optoelectronic oscillators or the regions of amplitude death in identical coupled oscillators.
A codimension two bifurcation in a railway bogie system
DEFF Research Database (Denmark)
Zhang, Tingting; True, Hans; Dai, Huanyun
2017-01-01
In this paper, a comprehensive analysis is presented to investigate a codimension two bifurcation that exists in a nonlinear railway bogie dynamic system combining theoretical analysis with numerical investigation. By using the running velocity V and the primary longitudinal stiffness (Formula...... coexist in a range of the bifurcation parameters which can lead to jumps in the lateral oscillation amplitude of the railway bogie system. Furthermore, reduce the values of the bifurcation parameters gradually. Firstly, the supercritical Hopf bifurcation turns into a subcritical one with multiple limit...
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.
Castellanos-Rodríguez, Valentina; Campos-Cantón, Eric; Barboza-Gudiño, Rafael; Femat, Ricardo
2017-08-01
The complex oscillatory behavior of a spring-block model is analyzed via the Hopf bifurcation mechanism. The mathematical spring-block model includes Dieterich-Ruina's friction law and Stribeck's effect. The existence of self-sustained oscillations in the transition zone - where slow earthquakes are generated within the frictionally unstable region - is determined. An upper limit for this region is proposed as a function of seismic parameters and frictional coefficients which are concerned with presence of fluids in the system. The importance of the characteristic length scale L, the implications of fluids, and the effects of external perturbations in the complex dynamic oscillatory behavior, as well as in the stationary solution, are take into consideration.
Dessup, Tommy; Coste, Christophe; Saint Jean, Michel
2016-01-01
In this article, we study the effects of white Gaussian additive thermal noise on a subcritical pitchfork bifurcation. We consider a quasi-one-dimensional system of particles that are transversally confined, with short-range (non-Coulombic) interactions and periodic boundary conditions in the longitudinal direction. In such systems, there is a structural transition from a linear order to a staggered row, called the zigzag transition. There is a finite range of transverse confinement stiffnesses for which the stable configuration at zero temperature is a localized zigzag pattern surrounded by aligned particles, which evidences the subcriticality of the bifurcation. We show that these configurations remain stable for a wide temperature range. At zero temperature, the transition between a straight line and such localized zigzag patterns is hysteretic. We have studied the influence of thermal noise on the hysteresis loop. Its description is more difficult than at T =0 K since thermally activated jumps between the two configurations always occur and the system cannot stay forever in a unique metastable state. Two different regimes have to be considered according to the temperature value with respect to a critical temperature Tc(τobs) that depends on the observation time τobs. An hysteresis loop is still observed at low temperature, with a width that decreases as the temperature increases toward Tc(τobs) . In contrast, for T >Tc(τobs) the memory of the initial condition is lost by stochastic jumps between the configurations. The study of the mean residence times in each configuration gives a unique opportunity to precisely determine the barrier height that separates the two configurations, without knowing the complete energy landscape of this many-body system. We also show how to reconstruct the hysteresis loop that would exist at T =0 K from high-temperature simulations.
Bifurcation analysis of a three dimensional system
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Yongwen WANG
2018-04-01
Full Text Available In order to enrich the stability and bifurcation theory of the three dimensional chaotic systems, taking a quadratic truncate unfolding system with the triple singularity equilibrium as the research subject, the existence of the equilibrium, the stability and the bifurcation of the system near the equilibrium under different parametric conditions are studied. Using the method of mathematical analysis, the existence of the real roots of the corresponding characteristic equation under the different parametric conditions is analyzed, and the local manifolds of the equilibrium are gotten, then the possible bifurcations are guessed. The parametric conditions under which the equilibrium is saddle-focus are analyzed carefully by the Cardan formula. Moreover, the conditions of codimension-one Hopf bifucation and the prerequisites of the supercritical and subcritical Hopf bifurcation are found by computation. The results show that the system has abundant stability and bifurcation, and can also supply theorical support for the proof of the existence of the homoclinic or heteroclinic loop connecting saddle-focus and the Silnikov's chaos. This method can be extended to study the other higher nonlinear systems.
Nonlinear dynamics approach of modeling the bifurcation for aircraft wing flutter in transonic speed
DEFF Research Database (Denmark)
Matsushita, Hiroshi; Miyata, T.; Christiansen, Lasse Engbo
2002-01-01
The procedure of obtaining the two-degrees-of-freedom, finite dimensional. nonlinear mathematical model. which models the nonlinear features of aircraft flutter in transonic speed is reported. The model enables to explain every feature of the transonic flutter data of the wind tunnel tests...... conducted at National Aerospace Laboratory in Japan for a high aspect ratio wing. It explains the nonlinear features of the transonic flutter such as the subcritical Hopf bifurcation of a limit cycle oscillation (LCO), a saddle-node bifurcation, and an unstable limit cycle as well as a normal (linear...
Nonlinear stability, bifurcation and resonance in granular plane Couette flow
Shukla, Priyanka; Alam, Meheboob
2010-11-01
A weakly nonlinear stability theory is developed to understand the effect of nonlinearities on various linear instability modes as well as to unveil the underlying bifurcation scenario in a two-dimensional granular plane Couette flow. The relevant order parameter equation, the Landau-Stuart equation, for the most unstable two-dimensional disturbance has been derived using the amplitude expansion method of our previous work on the shear-banding instability.ootnotetextShukla and Alam, Phys. Rev. Lett. 103, 068001 (2009). Shukla and Alam, J. Fluid Mech. (2010, accepted). Two types of bifurcations, Hopf and pitchfork, that result from travelling and stationary linear instabilities, respectively, are analysed using the first Landau coefficient. It is shown that the subcritical instability can appear in the linearly stable regime. The present bifurcation theory shows that the flow is subcritically unstable to disturbances of long wave-lengths (kx˜0) in the dilute limit, and both the supercritical and subcritical states are possible at moderate densities for the dominant stationary and traveling instabilities for which kx=O(1). We show that the granular plane Couette flow is prone to a plethora of resonances.ootnotetextShukla and Alam, J. Fluid Mech. (submitted, 2010)
Energy Technology Data Exchange (ETDEWEB)
Pandey, Vikas; Singh, Suneet, E-mail: suneet.singh@iitb.ac.in
2017-04-15
Highlights: • Non-linear stability analysis of nuclear reactor is carried out. • Global and local stability boundaries are drawn in the parameter space. • Globally stable, bi-stable, and unstable regions have been demarcated. • The identification of the regions is verified by numerical simulations. - Abstract: Nonlinear stability study of the neutron coupled thermal hydraulics instability has been carried out by several researchers for boiling water reactors (BWRs). The focus of these studies has been to identify subcritical and supercritical Hopf bifurcations. Supercritical Hopf bifurcation are soft or safe due to the fact that stable limit cycles arise in linearly unstable region; linear and global stability boundaries are same for this bifurcation. It is well known that the subcritical bifurcations can be considered as hard or dangerous due to the fact that unstable limit cycles (nonlinear phenomena) exist in the (linearly) stable region. The linear stability leads to a stable equilibrium in such regions, only for infinitesimally small perturbations. However, finite perturbations lead to instability due to the presence of unstable limit cycles. Therefore, it is evident that the linear stability analysis is not sufficient to understand the exact stability characteristics of BWRs. However, the effect of these bifurcations on the stability boundaries has been rarely discussed. In the present work, the identification of global stability boundary is demonstrated using simplified models. Here, five different models with different thermal hydraulics feedback have been investigated. In comparison to the earlier works, current models also include the impact of adding the rate of change in temperature on void reactivity as well as effect of void reactivity on rate of change of temperature. Using the bifurcation analysis of these models the globally stable region in the parameter space has been identified. The globally stable region has only stable solutions and
International Nuclear Information System (INIS)
Pandey, Vikas; Singh, Suneet
2017-01-01
Highlights: • Non-linear stability analysis of nuclear reactor is carried out. • Global and local stability boundaries are drawn in the parameter space. • Globally stable, bi-stable, and unstable regions have been demarcated. • The identification of the regions is verified by numerical simulations. - Abstract: Nonlinear stability study of the neutron coupled thermal hydraulics instability has been carried out by several researchers for boiling water reactors (BWRs). The focus of these studies has been to identify subcritical and supercritical Hopf bifurcations. Supercritical Hopf bifurcation are soft or safe due to the fact that stable limit cycles arise in linearly unstable region; linear and global stability boundaries are same for this bifurcation. It is well known that the subcritical bifurcations can be considered as hard or dangerous due to the fact that unstable limit cycles (nonlinear phenomena) exist in the (linearly) stable region. The linear stability leads to a stable equilibrium in such regions, only for infinitesimally small perturbations. However, finite perturbations lead to instability due to the presence of unstable limit cycles. Therefore, it is evident that the linear stability analysis is not sufficient to understand the exact stability characteristics of BWRs. However, the effect of these bifurcations on the stability boundaries has been rarely discussed. In the present work, the identification of global stability boundary is demonstrated using simplified models. Here, five different models with different thermal hydraulics feedback have been investigated. In comparison to the earlier works, current models also include the impact of adding the rate of change in temperature on void reactivity as well as effect of void reactivity on rate of change of temperature. Using the bifurcation analysis of these models the globally stable region in the parameter space has been identified. The globally stable region has only stable solutions and
Bifurcations and chaos in convection taking non-Fourier heat-flux
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.
Travelling waves and their bifurcations in the Lorenz-96 model
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 → ∞.
Beer bottle whistling: a stochastic Hopf bifurcation
Boujo, Edouard; Bourquard, Claire; Xiong, Yuan; Noiray, Nicolas
2017-11-01
Blowing in a bottle to produce sound is a popular and yet intriguing entertainment. We reproduce experimentally the common observation that the bottle ``whistles'', i.e. produces a distinct tone, for large enough blowing velocity and over a finite interval of blowing angle. For a given set of parameters, the whistling frequency stays constant over time while the acoustic pressure amplitude fluctuates. Transverse oscillations of the shear layer in the bottle's neck are clearly identified with time-resolved particle image velocimetry (PIV) and proper orthogonal decomposition (POD). To account for these observations, we develop an analytical model of linear acoustic oscillator (the air in the bottle) subject to nonlinear stochastic forcing (the turbulent jet impacting the bottle's neck). We derive a stochastic differential equation and, from the associated Fokker-Planck equation and the measured acoustic pressure signals, we identify the model's parameters with an adjoint optimization technique. Results are further validated experimentally, and allow us to explain (i) the occurrence of whistling in terms of linear instability, and (ii) the amplitude of the limit cycle as a competition between linear growth rate, noise intensity, and nonlinear saturation. E. B. and N. N. acknowledge support by Repower and the ETH Zurich Foundation.
Stability and bifurcation of a discrete BAM neural network model with delays
International Nuclear Information System (INIS)
Zheng Baodong; Zhang Yang; Zhang Chunrui
2008-01-01
A map modelling a discrete bidirectional associative memory neural network with delays is investigated. Its dynamics is studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Numerical simulation is performed to verify the analytical results
Rehren, K. -H.
1996-01-01
Weak C* Hopf algebras can act as global symmetries in low-dimensional quantum field theories, when braid group statistics prevents group symmetries. Possibilities to construct field algebras with weak C* Hopf symmetry from a given theory of local observables are discussed.
Stability and bifurcation analysis in a delayed SIR model
International Nuclear Information System (INIS)
Jiang Zhichao; Wei Junjie
2008-01-01
In this paper, a time-delayed SIR model with a nonlinear incidence rate is considered. The existence of Hopf bifurcations at the endemic equilibrium is established by analyzing the distribution of the characteristic values. A explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory. Numerical simulations to support the analytical conclusions are carried out
International Nuclear Information System (INIS)
Mishra, A.M.; Paul, S.; Singh, S.; Panday, V.
2015-01-01
In this paper the two-phase flow instability analysis of multiple heated channels with various inclinations is studied. In addition, the bifurcation analysis is also carried out to capture the nonlinear dynamics of the system and to identify the regions in parameter space for which subcritical and supercritical bifurcations exist. In order to carry out the analysis, the system is mathematically represented by nonlinear Partial Differential Equation (PDE) for mass, momentum and energy in single as well as two-phase region. Then converted into Ordinary Differential Equation (ODE) using weighted residual method. Also, coupling equation is being used under the assumption that pressure drop in each channel is the same and the total mass flow rate is equal to sum of the individual mass flow rates. The homogeneous equilibrium model is used for the analysis. Stability Map is obtained in terms of phase change number (Npch) and Subcooling Number (Nsb) by solving a set of nonlinear, coupled algebraic equations obtained at equilibrium using Newton Raphson Method. MATLAB Code is verified by comparing it with results obtained by Matcont (Open source software) under same parametric values. Numerical simulations of the time-dependent, nonlinear ODEs are carried out for selected points in the operating parameter space to obtain the actual damped and growing oscillations in the channel inlet flow velocity which confirms the stability region across the stability map. Generalized Hopf (GH) points are observed for different inclinations, they are also points for subcritical and supercritical bifurcations. (authors)
Discretization analysis of bifurcation based nonlinear amplifiers
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.
International Nuclear Information System (INIS)
Huang Hualin; Li Libin; Ye Yu
2004-07-01
We study pointed graded self-dual Hopf algebras with a help of the dual Gabriel theorem for pointed Hopf algebras. Quivers of such Hopf algebras are said to be self-dual. An explicit classification of self-dual Hopf quivers is obtained. We also prove that finite dimensional coradically graded pointed self-dual Hopf algebras are generated by group-like and skew-primitive elements as associative algebras. This partially justifies a conjecture of Andruskiewitsch and Schneider and may help to classify finite dimensional self-dual pointed Hopf algebras
Hypercrater Bifurcations, Attractor Coexistence, and Unfolding in a 5D Model of Economic Dynamics
Directory of Open Access Journals (Sweden)
Toichiro Asada
2011-01-01
Full Text Available Complex dynamical features are explored in a discrete interregional macrodynamic model proposed by Asada et al., using numerical methods. The model is five-dimensional with four parameters. The results demonstrate patterns of dynamical behaviour, such as bifurcation processes and coexistence of attractors, generated by high-dimensional discrete systems. In three cases of two-dimensional parameter subspaces the stability of equilibrium region is determined and its boundaries, the flip and Neimark-Hopf bifurcation curves, are identified by means of necessary coefficient criteria. In the first case closed invariant curves (CICs are found to occur through 5D-crater-type bifurcations, and for certain ranges of parameter values a stable equilibrium coexists with an unstable CIC associated with the subcritical bifurcation, as well as with an outer stable CIC. A remarkable feature of the second case is the coexistence of two attracting CICs outside the stability region. In both these cases the related hysteresis effects are illustrated by numerical simulations. In the third case a remarkable feature is the apparent unfolding of an attracting CIC before it evolves to a chaotic attractor. Examples of CICs and chaotic attractors are given in subspaces of phase space.
Bifurcation analysis and stability design for aircraft longitudinal motion with high angle of attack
Directory of Open Access Journals (Sweden)
Xin Qi
2015-02-01
Full Text Available Bifurcation analysis and stability design for aircraft longitudinal motion are investigated when the nonlinearity in flight dynamics takes place severely at high angle of attack regime. To predict the special nonlinear flight phenomena, bifurcation theory and continuation method are employed to systematically analyze the nonlinear motions. With the refinement of the flight dynamics for F-8 Crusader longitudinal motion, a framework is derived to identify the stationary bifurcation and dynamic bifurcation for high-dimensional system. Case study shows that the F-8 longitudinal motion undergoes saddle node bifurcation, Hopf bifurcation, Zero-Hopf bifurcation and branch point bifurcation under certain conditions. Moreover, the Hopf bifurcation renders series of multiple frequency pitch oscillation phenomena, which deteriorate the flight control stability severely. To relieve the adverse effects of these phenomena, a stabilization control based on gain scheduling and polynomial fitting for F-8 longitudinal motion is presented to enlarge the flight envelope. Simulation results validate the effectiveness of the proposed scheme.
Khechiba, Khaled; Mamou, Mahmoud; Hachemi, Madjid; Delenda, Nassim; Rebhi, Redha
2017-06-01
The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau-Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.
Codimension-2 bifurcations of the Kaldor model of business cycle
International Nuclear Information System (INIS)
Wu, Xiaoqin P.
2011-01-01
Research highlights: → The conditions are given such that the characteristic equation may have purely imaginary roots and double zero roots. → Purely imaginary roots lead us to study Hopf and Bautin bifurcations and to calculate the first and second Lyapunov coefficients. → Double zero roots lead us to study Bogdanov-Takens (BT) bifurcation. → Bifurcation diagrams for Bautin and BT bifurcations are obtained by using the normal form theory. - Abstract: In this paper, complete analysis is presented to study codimension-2 bifurcations for the nonlinear Kaldor model of business cycle. Sufficient conditions are given for the model to demonstrate Bautin and Bogdanov-Takens (BT) bifurcations. By computing the first and second Lyapunov coefficients and performing nonlinear transformation, the normal forms are derived to obtain the bifurcation diagrams such as Hopf, homoclinic and double limit cycle bifurcations. Some examples are given to confirm the theoretical results.
Bifurcation Analysis of the QI 3-D Four-Wing Chaotic System
International Nuclear Information System (INIS)
Sun, Y.; Qi, G.; Wang, Z.; Wyk, B.J. van
2010-01-01
This paper analyzes the pitchfork and Hopf bifurcations of a new 3-D four-wing quadratic autonomous system proposed by Qi et al. The center manifold technique is used to reduce the dimensions of this system. The pitchfork and Hopf bifurcations of the system are theoretically analyzed. The influence of system parameters on other bifurcations are also investigated. The theoretical analysis and simulations demonstrate the rich dynamics of the system. (authors)
Bifurcations of Tumor-Immune Competition Systems with Delay
Directory of Open Access Journals (Sweden)
Ping Bi
2014-01-01
Full Text Available A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. General formulas for the direction, period, and stability of the bifurcated periodic solutions are given for codimension one and codimension two bifurcations, including Hopf bifurcation, steady-state bifurcation, and B-T bifurcation. Numerical examples and simulations are given to illustrate the bifurcations analysis and obtained results.
Hopf algebras in noncommutative geometry
International Nuclear Information System (INIS)
Varilly, Joseph C.
2001-10-01
We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)
Li, Li; Xu, Jian
Time delay is inevitable in unidirectionally coupled drive-free vibratory gyroscope system. The effect of time delay on the gyroscope system is studied in this paper. To this end, amplitude death and Hopf bifurcation induced by small time delay are first investigated by analyzing the related characteristic equation. Then, the direction of Hopf bifurcations and stability of Hopf-bifurcating periodic oscillations are determined by calculating the normal form on the center manifold. Next, spatiotemporal patterns of these Hopf-bifurcating periodic oscillations are analyzed by using the symmetric bifurcation theory of delay differential equations. Finally, it is found that numerical simulations agree with the associated analytic results. These phenomena could be induced although time delay is very small. Therefore, it is shown that time delay is an important factor which influences the sensitivity and accuracy of the gyroscope system and cannot be neglected during the design and manufacture.
Bifurcation routes and economic stability
Czech Academy of Sciences Publication Activity Database
Vošvrda, Miloslav
2001-01-01
Roč. 8, č. 14 (2001), s. 43-59 ISSN 1212-074X R&D Projects: GA ČR GA402/00/0439; GA ČR GA402/01/0034; GA ČR GA402/01/0539 Institutional research plan: AV0Z1075907 Keywords : macroeconomic stability * foreign investment phenomenon * the Hopf bifurcation Subject RIV: AH - Economics
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2017-01-01
Full Text Available Hopf bifurcation for an SEIRS-V model with delays on the transmission of worms in a wireless sensor network is investigated. We focus on existence of the Hopf bifurcation by regarding the diverse delay as a bifurcation parameter. The results show that propagation of worms in the wireless sensor network can be controlled when the delay is suitably small under some certain conditions. Then, we study properties of the Hopf bifurcation by using the normal form theory and center manifold theorem. Finally, we give a numerical example to support the theoretical results.
International Nuclear Information System (INIS)
Ding Xiaohua; Su Huan; Liu Mingzhu
2008-01-01
The paper analyzes a discrete second-order, nonlinear delay differential equation with negative feedback. The characteristic equation of linear stability is solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The existence of local Hopf bifurcations is investigated, and the direction and stability of periodic solutions bifurcating from the Hopf bifurcation of the discrete model are determined by the Hopf bifurcation theory of discrete system. Finally, some numerical simulations are performed to illustrate the analytical results found
Bifurcation theory for finitely smooth planar autonomous differential systems
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.
Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate
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.
Bifurcation analysis in delayed feedback Jerk systems and application of chaotic control
International Nuclear Information System (INIS)
Zheng Baodong; Zheng Huifeng
2009-01-01
Jerk systems with delayed feedback are considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associated characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, the stability and direction of the Hopf bifurcation are determined by applying the normal form method and center manifold theorem. Finally, the application to chaotic control is investigated, and some numerical simulations are carried out to illustrate the obtained results.
Stability and bifurcation analysis in a kind of business cycle model with delay
International Nuclear Information System (INIS)
Zhang Chunrui; Wei Junjie
2004-01-01
A kind of business cycle model with delay is considered. Firstly, the linear stability of the model is studied and bifurcation set is drawn in the appropriate parameter plane. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Then the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived, using the normal form method and center manifold theorem. Finally, a group conditions to guarantee the global existence of periodic solutions is given, and numerical simulations are performed to illustrate the analytical results found
Hopf algebras and topological recursion
International Nuclear Information System (INIS)
Esteves, João N
2015-01-01
We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293–309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347–452). (paper)
Bifurcations of a class of singular biological economic models
International Nuclear Information System (INIS)
Zhang Xue; Zhang Qingling; Zhang Yue
2009-01-01
This paper studies systematically a prey-predator singular biological economic model with time delay. It shows that this model exhibits two bifurcation phenomena when the economic profit is zero. One is transcritical bifurcation which changes the stability of the system, and the other is singular induced bifurcation which indicates that zero economic profit brings impulse, i.e., rapid expansion of the population in biological explanation. On the other hand, if the economic profit is positive, at a critical value of bifurcation parameter, the system undergoes a Hopf bifurcation, i.e., the increase of delay destabilizes the system and bifurcates into small amplitude periodic solution. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results obtained here. In addition, we study numerically that the system undergoes a saddle-node bifurcation when the bifurcation parameter goes through critical value of positive economic profit.
Bifurcation of the spin-wave equations
International Nuclear Information System (INIS)
Cascon, A.; Koiller, J.; Rezende, S.M.
1990-01-01
We study the bifurcations of the spin-wave equations that describe the parametric pumping of collective modes in magnetic media. Mechanisms describing the following dynamical phenomena are proposed: (i) sequential excitation of modes via zero eigenvalue bifurcations; (ii) Hopf bifurcations followed (or not) by Feingenbaum cascades of period doubling; (iii) local and global homoclinic phenomena. Two new organizing center for routes to chaos are identified; in the classification given by Guckenheimer and Holmes [GH], one is a codimension-two local bifurcation, with one pair of imaginary eigenvalues and a zero eigenvalue, to which many dynamical consequences are known; secondly, global homoclinic bifurcations associated to splitting of separatrices, in the limit where the system can be considered a Hamiltonian subjected to weak dissipation and forcing. We outline what further numerical and algebraic work is necessary for the detailed study following this program. (author)
Hopf Structures on Standard Young Tableaux
International Nuclear Information System (INIS)
Loday, Jean-Louis; Popov, Todor
2010-01-01
We review the Poirier-Reutenauer Hopf structure on Standard Young Tableaux and show that it is a distinguished member of a family of Hopf structures. The family in question is related to deformed parastatistics.
The formal theory of Hopf algebras part II: the case of Hopf algebras ...
African Journals Online (AJOL)
The category HopfR of Hopf algebras over a commutative unital ring R is analyzed with respect to its categorical properties. The main results are: (1) For every ring R the category HopfR is locally presentable, it is coreflective in the category of bialgebras over R, over every R-algebra there exists a cofree Hopf algebra. (2) If ...
On period doubling bifurcations of cycles and the harmonic balance method
International Nuclear Information System (INIS)
Itovich, Griselda R.; Moiola, Jorge L.
2006-01-01
This works attempts to give quasi-analytical expressions for subharmonic solutions appearing in the vicinity of a Hopf bifurcation. Starting with well-known tools as the graphical Hopf method for recovering the periodic branch emerging from classical Hopf bifurcation, precise frequency and amplitude estimations of the limit cycle can be obtained. These results allow to attain approximations for period doubling orbits by means of harmonic balance techniques, whose accuracy is established by comparison of Floquet multipliers with continuation software packages. Setting up a few coefficients, the proposed methodology yields to approximate solutions that result from a second period doubling bifurcation of cycles and to extend the validity limits of the graphical Hopf method
Coxeter groups and Hopf algebras
Aguiar, Marcelo
2011-01-01
An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructing and studying many of these objects as well as new ones. The first three chapters introduce the necessary backgrou
Bifurcation Behavior Analysis in a Predator-Prey Model
Directory of Open Access Journals (Sweden)
Nan Wang
2016-01-01
Full Text Available A predator-prey model is studied mathematically and numerically. The aim is to explore how some key factors influence dynamic evolutionary mechanism of steady conversion and bifurcation behavior in predator-prey model. The theoretical works have been pursuing the investigation of the existence and stability of the equilibria, as well as the occurrence of bifurcation behaviors (transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation, which can deduce a standard parameter controlled relationship and in turn provide a theoretical basis for the numerical simulation. Numerical analysis ensures reliability of the theoretical results and illustrates that three stable equilibria will arise simultaneously in the model. It testifies the existence of Bogdanov-Takens bifurcation, too. It should also be stressed that the dynamic evolutionary mechanism of steady conversion and bifurcation behavior mainly depend on a specific key parameter. In a word, all these results are expected to be of use in the study of the dynamic complexity of ecosystems.
Bifurcation structure of a model of bursting pancreatic cells
DEFF Research Database (Denmark)
Mosekilde, Erik; Lading, B.; Yanchuk, S.
2001-01-01
. The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n + 1)-spike bursting...... behavior is born, slightly overlapping with a subcritical period-doubling bifurcation in which n-spike bursting behavior loses its stability.......One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other...
Hopf Bifurcation in a Cobweb Model with Discrete Time Delays
Directory of Open Access Journals (Sweden)
Luca Gori
2014-01-01
Full Text Available We develop a cobweb model with discrete time delays that characterise the length of production cycle. We assume a market comprised of homogeneous producers that operate as adapters by taking the (expected profit-maximising quantity as a target to adjust production and consumers with a marginal willingness to pay captured by an isoelastic demand. The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1 if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2 if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle is high enough.
Generalized exclusion and Hopf algebras
International Nuclear Information System (INIS)
Yildiz, A
2002-01-01
We propose a generalized oscillator algebra at the roots of unity with generalized exclusion and we investigate the braided Hopf structure. We find that there are two solutions: these are the generalized exclusions of the bosonic and fermionic types. We also discuss the covariance properties of these oscillators
Bifurcation structure of a model of bursting pancreatic cells
DEFF Research Database (Denmark)
Mosekilde, Erik; Lading, B.; Yanchuk, S.
2001-01-01
One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other. The transit......One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other....... The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n + 1)-spike bursting...
Codimension-two bifurcation analysis on firing activities in Chay neuron model
International Nuclear Information System (INIS)
Duan Lixia; Lu Qishao
2006-01-01
Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing
Codimension-two bifurcation analysis on firing activities in Chay neuron model
Energy Technology Data Exchange (ETDEWEB)
Duan Lixia [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China); Lu Qishao [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China)]. E-mail: qishaolu@hotmail.com
2006-12-15
Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing.
Bifurcation scenarios for bubbling transition.
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.
Global Bifurcation of a Novel Computer Virus Propagation Model
Directory of Open Access Journals (Sweden)
Jianguo Ren
2014-01-01
Full Text Available In a recent paper by J. Ren et al. (2012, a novel computer virus propagation model under the effect of the antivirus ability in a real network is established. The analysis there only partially uncovers the dynamics behaviors of virus spread over the network in the case where around bifurcation is local. In the present paper, by mathematical analysis, it is further shown that, under appropriate parameter values, the model may undergo a global B-T bifurcation, and the curves of saddle-node bifurcation, Hopf bifurcation, and homoclinic bifurcation are obtained to illustrate the qualitative behaviors of virus propagation. On this basis, a collection of policies is recommended to prohibit the virus prevalence. To our knowledge, this is the first time the global bifurcation has been explored for the computer virus propagation. Theoretical results and corresponding suggestions may help us suppress or eliminate virus propagation in the network.
Hopf solitons in the AFZ model
International Nuclear Information System (INIS)
Gillard, Mike
2011-01-01
The Aratyn–Ferreira–Zimerman (AFZ) model is a conformal field theory in three-dimensional space. It has solutions that are topological solitons classified by an integer-valued Hopf index. There exist infinitely many axial solutions which have been found analytically. Static axial, knot and linked solitons are found numerically using a modified volume preserving flow for Hopf index one to eight, allowing for comparison with other Hopf soliton models. Solutions include a static trefoil knot at Hopf index five. A one-parameter family of conformal Skyrme–Faddeev models, consisting of linear combinations of the Nicole and AFZ models, are also investigated numerically. The transition of solutions for Hopf index four is mapped across these models. A topological change between linked and axial solutions occurs, with fewer models (or a limited range of parameter values) permitting axial solitons than linked solitons at Hopf index four
Stochastic stability and bifurcation in a macroeconomic model
International Nuclear Information System (INIS)
Li Wei; Xu Wei; Zhao Junfeng; Jin Yanfei
2007-01-01
On the basis of the work of Goodwin and Puu, a new business cycle model subject to a stochastically parametric excitation is derived in this paper. At first, we reduce the model to a one-dimensional diffusion process by applying the stochastic averaging method of quasi-nonintegrable Hamiltonian system. Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively to analyze the stochastic stability of the trivial solution of system. The numerical results obtained illustrate that the trivial solution of system must be globally stable if it is locally stable in the state space. Thirdly, we explore the stochastic Hopf bifurcation of the business cycle model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simply way on the potential applications of stochastic stability and bifurcation analysis
Energy Technology Data Exchange (ETDEWEB)
Verma, Dinkar, E-mail: dinkar@iitk.ac.in [Nuclear Engineering and Technology Program, Indian Institute of Technology Kanpur, Kanpur 208 016 (India); Kalra, Manjeet Singh, E-mail: drmanjeet.singh@dituniversity.edu.in [DIT University, Dehradun 248 009 (India); Wahi, Pankaj, E-mail: wahi@iitk.ac.in [Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016 (India)
2016-11-15
Highlights: • Simplified models with inclusion of the clad temperature are considered. • Boiling nonlinearity and core power removal have been modeled. • Method of multiple time scales has been used for nonlinear analysis to get the nature and amplitude of oscillations. • Incorporation of modeling complexities enhances the stability of system. • We find that reactors with higher nominal power are more desirable from the point of view of global stability. - Abstract: We study the effect of including boiling nonlinearity, clad temperature and void-dependent power removal from the primary loop in the mathematical modeling of a boiling water reactor (BWR) on its dynamic characteristics. The advanced heavy water reactor (AHWR) is taken as a case study. Towards this end, we have analyzed two different simplified models with different handling of the clad temperature. Each of these models has the necessary modifications pertaining to boiling nonlinearity and power removal from the primary loop. These simplified models incorporate the neutronics and thermal–hydraulic coupling. The effect of successive changes in the modeling assumptions on the linear stability of the reactor has been studied and we find that incorporation of each of these complexities in the model increases the stable operating region of the reactor. Further, the method of multiple time scales (MMTS) is exploited to carry out the nonlinear analysis with a view to predict the bifurcation characteristics of the reactor. Both subcritical and supercritical Hopf bifurcations are present in each model depending on the choice of operating parameters. These analytical observations from MMTS have been verified against numerical simulations. A parametric study on the effect of changing the nominal reactor power on the regions in the parametric space of void coefficient of reactivity and fuel temperature coefficient of reactivity with sub- and super-critical Hopf bifurcations has been performed for all
Bifurcation and chaos in neural excitable system
International Nuclear Information System (INIS)
Jing Zhujun; Yang Jianping; Feng Wei
2006-01-01
In this paper, we investigate the dynamical behaviors of neural excitable system without periodic external current (proposed by Chialvo [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] and with periodic external current as system's parameters vary. The existence and stability of three fixed points, bifurcation of fixed points, the conditions of existences of fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using bifurcation theory and center manifold theorem. The chaotic existence in the sense of Marotto's definition of chaos is proved. We then give the numerical simulated results (using bifurcation diagrams, computations of Maximum Lyapunov exponent and phase portraits), which not only show the consistence with the analytic results but also display new and interesting dynamical behaviors, including the complete period-doubling and inverse period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, simultaneous occurrence of two different routes (invariant cycle and period-doubling bifurcations) to chaos for a given bifurcation parameter, sudden disappearance of chaos at one critical point, a great abundance of period windows (period 2 to 10, 12, 19, 20 orbits, and so on) in transient chaotic regions with interior crises, strange chaotic attractors and strange non-chaotic attractor. In particular, the parameter k plays a important role in the system, which can leave the chaotic behavior or the quasi-periodic behavior to period-1 orbit as k varies, and it can be considered as an control strategy of chaos by adjusting the parameter k. Combining the existing results in [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] with the new results reported in this paper, a more complete description of the system is now obtained
Energy Technology Data Exchange (ETDEWEB)
Verma, Dinkar, E-mail: dinkar@iitk.ac.in [Nuclear Engineering and Technology Program, Indian Institute of Technology Kanpur, Kanpur 208 016 (India); Kalra, Manjeet Singh, E-mail: drmanjeet.singh@dituniversity.edu.in [DIT University, Dehradun 248 009 (India); Wahi, Pankaj, E-mail: wahi@iitk.ac.in [Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016 (India)
2017-04-15
Highlights: • A simplified model with nonlinear void reactivity feedback is studied. • Method of multiple scales for nonlinear analysis and oscillation characteristics. • Second order void reactivity dominates in determining system dynamics. • Opposing signs of linear and quadratic void reactivity enhances global safety. - Abstract: In the present work, the effect of nonlinear void reactivity on the dynamics of a simplified lumped-parameter model for a boiling water reactor (BWR) is investigated. A mathematical model of five differential equations comprising of neutronics and thermal-hydraulics encompassing the nonlinearities associated with both the reactivity feedbacks and the heat transfer process has been used. To this end, we have considered parameters relevant to RBMK for which the void reactivity is known to be nonlinear. A nonlinear analysis of the model exploiting the method of multiple time scales (MMTS) predicts the occurrence of the two types of Hopf bifurcation, namely subcritical and supercritical, leading to the evolution of limit cycles for a range of parameters. Numerical simulations have been performed to verify the analytical results obtained by MMTS. The study shows that the nonlinear reactivity has a significant influence on the system dynamics. A parametric study with varying nominal reactor power and operating conditions in coolant channel has also been performed which shows the effect of change in concerned parameter on the boundary between regions of sub- and super-critical Hopf bifurcations in the space constituted by the two coefficients of reactivities viz. the void and the Doppler coefficient of reactivities. In particular, we find that introduction of a negative quadratic term in the void reactivity feedback significantly increases the supercritical region and dominates in determining the system dynamics.
International Nuclear Information System (INIS)
Hajihosseini, Amirhossein; Maleki, Farzaneh; Rokni Lamooki, Gholam Reza
2011-01-01
Highlights: → We construct a recurrent neural network by generalizing a specific n-neuron network. → Several codimension 1 and 2 bifurcations take place in the newly constructed network. → The newly constructed network has higher capabilities to learn periodic signals. → The normal form theorem is applied to investigate dynamics of the network. → A series of bifurcation diagrams is given to support theoretical results. - Abstract: A class of recurrent neural networks is constructed by generalizing a specific class of n-neuron networks. It is shown that the newly constructed network experiences generic pitchfork and Hopf codimension one bifurcations. It is also proved that the emergence of generic Bogdanov-Takens, pitchfork-Hopf and Hopf-Hopf codimension two, and the degenerate Bogdanov-Takens bifurcation points in the parameter space is possible due to the intersections of codimension one bifurcation curves. The occurrence of bifurcations of higher codimensions significantly increases the capability of the newly constructed recurrent neural network to learn broader families of periodic signals.
Nonfamilial acrokeratosis verruciformis of Hopf
Directory of Open Access Journals (Sweden)
Nidhi Patel
2015-01-01
Full Text Available Acrokeratosis verruciformis (AKV of Hopf is an autosomal dominant genodermatosis with unknown etiology. It is characterized by multiple flat-topped keratotic papules resembling planar warts located mainly on the dorsum of hands and feet. Superficial ablation is the treatment of choice. A 41-year-old female presented with multiple hyperpigmented, hyperkeratotic papules and plaques over flexor aspect of both forearms, extensors of both legs and dorsum of the feet. Histopathology showed changes of AKV. Patient was treated with a combination of topical corticosteroids and cryotherapy with no visible improvement.
International Nuclear Information System (INIS)
Kanakoglou, K; Daskaloyannis, C
2008-01-01
Parabosonic algebra in finite or infinite degrees of freedom is considered as a Z 2 -graded associative algebra, and is shown to be a Z 2 -graded (or super) Hopf algebra. The super-Hopf algebraic structure of the parabosonic algebra is established directly without appealing to its relation to the osp(1/2n) Lie superalgebraic structure. The notion of super-Hopf algebra is equivalently described as a Hopf algebra in the braided monoidal category CZ 2 M. The bosonization technique for switching a Hopf algebra in the braided monoidal category H M (where H is a quasitriangular Hopf algebra) into an ordinary Hopf algebra is reviewed. In this paper, we prove that for the parabosonic algebra P B , beyond the application of the bosonization technique to the original super-Hopf algebra, a bosonization-like construction is also achieved using two operators, related to the parabosonic total number operator. Both techniques switch the same super-Hopf algebra P B to an ordinary Hopf algebra, thus producing two different variants of P B , with an ordinary Hopf structure
Bifurcation of cubic nonlinear parallel plate-type structure in axial flow
International Nuclear Information System (INIS)
Lu Li; Yang Yiren
2005-01-01
The Hopf bifurcation of plate-type beams with cubic nonlinear stiffness in axial flow was studied. By assuming that all the plates have the same deflections at any instant, the nonlinear model of plate-type beam in axial flow was established. The partial differential equation was turned into an ordinary differential equation by using Galerkin method. A new algebraic criterion of Hopf bifurcation was utilized to in our analysis. The results show that there's no Hopf bifurcation for simply supported plate-type beams while the cantilevered plate-type beams has. At last, the analytic expression of critical flow velocity of cantilevered plate-type beams in axial flow and the purely imaginary eigenvalues of the corresponding linear system were gotten. (authors)
Hopf Algebroids and Their Cyclic Theory
Kowalzig, N.
2009-01-01
The main objective of this thesis is to clarify concepts of generalised symmetries in noncommutative geometry (i.e., the noncommutative analogue of groupoids and Lie algebroids) and their associated (co)homologies. These ideas are incorporated by the notion of Hopf algebroids and Hopf-cyclic
1991-01-01
Dynamical Bifurcation Theory is concerned with the phenomena that occur in one parameter families of dynamical systems (usually ordinary differential equations), when the parameter is a slowly varying function of time. During the last decade these phenomena were observed and studied by many mathematicians, both pure and applied, from eastern and western countries, using classical and nonstandard analysis. It is the purpose of this book to give an account of these developments. The first paper, by C. Lobry, is an introduction: the reader will find here an explanation of the problems and some easy examples; this paper also explains the role of each of the other paper within the volume and their relationship to one another. CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage through Bifurcation and Limit Points. Asymptotic Theory and Applications.- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey.- V. Gautheron, E. Isambe...
Bifurcation diagram of a cubic three-parameter autonomous system
Directory of Open Access Journals (Sweden)
Lenka Barakova
2005-07-01
Full Text Available In this paper, we study the cubic three-parameter autonomous planar system $$displaylines{ dot x_1 = k_1 + k_2x_1 - x_1^3 - x_2,cr dot x_2 = k_3 x_1 - x_2, }$$ where $k_2, k_3$ are greater than 0. Our goal is to obtain a bifurcation diagram; i.e., to divide the parameter space into regions within which the system has topologically equivalent phase portraits and to describe how these portraits are transformed at the bifurcation boundaries. Results may be applied to the macroeconomical model IS-LM with Kaldor's assumptions. In this model existence of a stable limit cycles has already been studied (Andronov-Hopf bifurcation. We present the whole bifurcation diagram and among others, we prove existence of more difficult bifurcations and existence of unstable cycles.
Delayed feedback on the dynamical model of a financial system
International Nuclear Information System (INIS)
Son, Woo-Sik; Park, Young-Jai
2011-01-01
Research highlights: → Effect of delayed feedbacks on the financial model. → Proof on the occurrence of Hopf bifurcation by local stability analysis. → Numerical bifurcation analysis on delay differential equations. → Observation of supercritical and subcritical Hopf, fold limit cycle, Neimark-Sacker, double Hopf and generalized Hopf bifurcations. - Abstract: We investigate the effect of delayed feedbacks on the financial model, which describes the time variation of the interest rate, the investment demand, and the price index, for establishing the fiscal policy. By local stability analysis, we theoretically prove the occurrences of Hopf bifurcation. Through numerical bifurcation analysis, we obtain the supercritical and subcritical Hopf bifurcation curves which support the theoretical predictions. Moreover, the fold limit cycle and Neimark-Sacker bifurcation curves are detected. We also confirm that the double Hopf and generalized Hopf codimension-2 bifurcation points exist.
Directory of Open Access Journals (Sweden)
Jianguo Ren
2014-01-01
Full Text Available A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold value R0. By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique virus-free equilibrium is globally asymptotically stable if R01. Numerical examples are presented to illustrate possible behavioral scenarios of the mode.
Nonlinear stability control and λ-bifurcation
International Nuclear Information System (INIS)
Erneux, T.; Reiss, E.L.; Magnan, J.F.; Jayakumar, P.K.
1987-01-01
Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of λ-bifurcation and a generalization of it. λ-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch of divergence solutions which bifurcates subcritically from the basic solution. The shape of the bifurcation diagram then resembles the greek letter λ. When the system parameters are in the range where flutter occurs by λ-bifurcation, then as the flow velocity increase the flutter amplitude also increases, but the frequencies of the oscillations decrease to zero. This diminishes the damaging effects of structural fatigue by flutter, and permits the flow speed to exceed the critical flutter speed. If generalized λ-bifurcation occurs, then there is a jump transition from the flutter states to a divergence state with a substantially smaller amplitude, when the flow speed is sufficiently larger than the critical flutter speed
Hopf solitons in the Nicole model
International Nuclear Information System (INIS)
Gillard, Mike; Sutcliffe, Paul
2010-01-01
The Nicole model is a conformal field theory in a three-dimensional space. It has topological soliton solutions classified by the integer-valued Hopf charge, and all currently known solitons are axially symmetric. A volume-preserving flow is used to construct soliton solutions numerically for all Hopf charges from 1 to 8. It is found that the known axially symmetric solutions are unstable for Hopf charges greater than 2 and new lower energy solutions are obtained that include knots and links. A comparison with the Skyrme-Faddeev model suggests many universal features, though there are some differences in the link types obtained in the two theories.
Stability, bifurcation and a new chaos in the logistic differential equation with delay
International Nuclear Information System (INIS)
Jiang Minghui; Shen Yi; Jian Jigui; Liao Xiaoxin
2006-01-01
This Letter is concerned with bifurcation and chaos in the logistic delay differential equation with a parameter r. The linear stability of the logistic equation is investigated by analyzing the associated characteristic transcendental equation. Based on the normal form approach and the center manifold theory, the formula for determining the direction of Hopf bifurcation and the stability of bifurcation periodic solution in the first bifurcation values is obtained. By theoretical analysis and numerical simulation, we found a new chaos in the logistic delay differential equation
Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection.
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.
Hopf algebra structures in particle physics
International Nuclear Information System (INIS)
Weinzierl, Stefan
2004-01-01
In the recent years, Hopf algebras have been introduced to describe certain combinatorial properties of quantum field theories. I give a basic introduction to these algebras and review some occurrences in particle physics. (orig.)
Towards a classification of rational Hopf algebras
International Nuclear Information System (INIS)
Fuchs, J.; Ganchev, A.; Vecsernyes, P.
1994-02-01
Rational Hopf algebras, i.e. certain quasitriangular weak quasi-Hopf *-algebras, are expected to describe the quantum symmetry of rational field theories. In this paper methods are developed which allow for a classification of all rational Hopf algebras that are compatible with some prescribed set of fusion rules. The algebras are parametrized by the solutions of the square, pentagon and hexagon identities. As examples, we classify all solutions for fusion rules with not more than three sectors, as well as for the level three affine A 1 (1) fusion rules. We also establish several general properties of rational Hopf algebras and present a graphical description of the coassociator in terms of labelled tetrahedra. The latter construction allows to make contact with conformal field theory fusing matrices and with invariants of three-manifolds and topological lattice field theory. (orig.)
Polarization of light and Hopf fibration
International Nuclear Information System (INIS)
Jurco, B.
1987-01-01
A set of polarization states of quasi-monochromatic light is described geometrically in terms of the Hopf fibration. Several associated alternative polarization parametrizations are given explicitly, including the Stokes parameters. (author). 8 refs
Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses
Directory of Open Access Journals (Sweden)
Chuandong Li
2014-01-01
Full Text Available We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks.
Bifurcation in the Lengyel–Epstein system for the coupled reactors with diffusion
Directory of Open Access Journals (Sweden)
Shaban Aly
2016-01-01
Full Text Available The main goal of this paper is to continue the investigations of the important system of Fengqi et al. (2008. The occurrence of Turing and Hopf bifurcations in small homogeneous arrays of two coupled reactors via diffusion-linked mass transfer which described by a system of ordinary differential equations is considered. I study the conditions of the existence as well as stability properties of the equilibrium solutions and derive the precise conditions on the parameters to show that the Hopf bifurcation occurs. Analytically I show that a diffusion driven instability occurs at a certain critical value, when the system undergoes a Turing bifurcation, patterns emerge. The spatially homogeneous equilibrium loses its stability and two new spatially non-constant stable equilibria emerge which are asymptotically stable. Numerically, at a certain critical value of diffusion the periodic solution gets destabilized and two new spatially nonconstant periodic solutions arise by Turing bifurcation.
Stability and bifurcation in a simplified four-neuron BAM neural network with multiple delays
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We first study the distribution of the zeros of a fourth-degree exponential polynomial. Then we apply the obtained results to a simplified bidirectional associated memory (BAM neural network with four neurons and multiple time delays. By taking the sum of the delays as the bifurcation parameter, it is shown that under certain assumptions the steady state is absolutely stable. Under another set of conditions, there are some critical values of the delay, when the delay crosses these critical values, the Hopf bifurcation occurs. Furthermore, some explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form theory and center manifold reduction. Numerical simulations supporting the theoretical analysis are also included.
Bifurcation analysis of magnetization dynamics driven by spin transfer
International Nuclear Information System (INIS)
Bertotti, G.; Magni, A.; Bonin, R.; Mayergoyz, I.D.; Serpico, C.
2005-01-01
Nonlinear magnetization dynamics under spin-polarized currents is discussed by the methods of the theory of nonlinear dynamical systems. The fixed points of the dynamics are calculated. It is shown that there may exist 2, 4, or 6 fixed points depending on the values of the external field and of the spin-polarized current. The stability of the fixed points is analyzed and the conditions for the occurrence of saddle-node and Hopf bifurcations are determined
Bifurcation analysis of magnetization dynamics driven by spin transfer
Energy Technology Data Exchange (ETDEWEB)
Bertotti, G. [IEN Galileo Ferraris, Strada delle Cacce 91, 10135 Turin (Italy); Magni, A. [IEN Galileo Ferraris, Strada delle Cacce 91, 10135 Turin (Italy); Bonin, R. [Dipartimento di Fisica, Politecnico di Torino, Corso degli Abbruzzi, 10129 Turin (Italy)]. E-mail: bonin@ien.it; Mayergoyz, I.D. [Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742 (United States); Serpico, C. [Department of Electrical Engineering, University of Napoli Federico II, via Claudio 21, 80125 Naples (Italy)
2005-04-15
Nonlinear magnetization dynamics under spin-polarized currents is discussed by the methods of the theory of nonlinear dynamical systems. The fixed points of the dynamics are calculated. It is shown that there may exist 2, 4, or 6 fixed points depending on the values of the external field and of the spin-polarized current. The stability of the fixed points is analyzed and the conditions for the occurrence of saddle-node and Hopf bifurcations are determined.
Bifurcation in Z2-symmetry quadratic polynomial systems with delay
International Nuclear Information System (INIS)
Zhang Chunrui; Zheng Baodong
2009-01-01
Z 2 -symmetry systems are considered. Firstly the general forms of Z 2 -symmetry quadratic polynomial system are given, and then a three-dimensional Z 2 equivariant system is considered, which describes the relations of two predator species for a single prey species. Finally, the explicit formulas for determining the Fold and Hopf bifurcations are obtained by using the normal form theory and center manifold argument.
Bifurcation analysis on a delayed SIS epidemic model with stage structure
Directory of Open Access Journals (Sweden)
Kejun Zhuang
2007-05-01
Full Text Available In this paper, a delayed SIS (Susceptible Infectious Susceptible model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to guarantee the global existence of periodic solutions are established. Also some numerical simulations for supporting the theoretical are given.
Bifurcation analysis of nephron pressure and flow regulation
DEFF Research Database (Denmark)
Barfred, Mikael; Mosekilde, Erik; Holstein-Rathlou, N.-H.
1996-01-01
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...
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.
Subcriticality determination of nuclear reactor
International Nuclear Information System (INIS)
Borisenko, V.I.; Goranchuk, V.V.; Sidoruk, N.M.; Volokh, A.F.
2014-01-01
In this article the subcriticality determination of nuclear reactor is considered. Emphasized that, despite the requirements of regulatory documents on the subcriticality determination of WWER from the beginning of their operation, so far, this problem has not been solved. The results of subcriticality determination of Rossi-α method of the WWER-M is presented. The possibility of subcriticality determination of WWER is considered. The possibility of subcriticality determination of Rossi-α method with time resolution is of about 100 microseconds is also considered. The possible reasons for the error in subcriticality determination of the reactor are indicated
Bifurcation analysis of a product inhibition model of a continuous fermentation process
Energy Technology Data Exchange (ETDEWEB)
Lenbury, Y; Chiaranai, C
1987-03-01
A product inhibition model of a continuous fermentation process is considered. If the yield term is a variable function of ethanol concentration, oscillation in the cell and ethanol concentrations is shown to be a Hopf bifurcation in the underlying system of nonlinear, ordinary differential equations which comprises the model.
Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics
Directory of Open Access Journals (Sweden)
Robert Artebrant
2009-01-01
cells surrounded by collections of normal cells. Thus, the cell model features a discontinuous coefficient. Analytical techniques are applied to approximate the time-periodic solution that arises at the Hopf bifurcation point. Accurate numerical experiments are employed to complement our findings.
International Nuclear Information System (INIS)
Vega C, H. R.
2014-08-01
A Subcritical Nuclear Assembly is a device where the nuclear-fission chain reaction is initiated and maintained using an external neutron source. It is a valuable educational and research tool where in a safe way many reactor parameters can be measured. Here, we have used the Wigner-Seitz method in the six-factor formula to calculate the effective multiplication factor of a subcritical nuclear reactor Nuclear Chicago model 9000. This reactor has approximately 2500 kg of natural uranium heterogeneously distributed in slugs. The reactor uses a 239 PuBe neutron source that is located in the center of an hexagonal array. Using Monte Carlo methods, with the MCNP5 code, a three-dimensional model of the subcritical reactor was designed to estimate the effective multiplication factor, the neutron spectra, the total and thermal neutron fluences along the radial and axial axis. With the neutron spectra in two locations outside the reactor the ambient dose equivalent were estimated. (Author)
Generalized semilocal theories and higher Hopf maps
International Nuclear Information System (INIS)
Hindmarsh, M.; Holman, R.; Kephart, T.W.; Vachaspati, T.
1993-01-01
In semilocal theories, the vacuum manifold is fibered in a non-trivial way by the action of the gauge group. Here we generalize the original semilocal theory (which was based on the Hopf bundle S 3 → S1 S 2 ) to realize the next Hopf bundle S 7 →S 3 S 4 , and its extensions S 2n+1 → S3 HP n . The semilocal defects in this class of theories are classified by π 3 (S 3 ), and are interpreted as constrained instantons or generalized sphaleron configurations. We fail to find a field theoretic realization of the final Hopf bundle S 15 →S 7 S 8 , but are able to construct other semilocal spaces realizing Stiefel bundles over grassmannian spaces. (orig.)
BRAHMMA - accelerator driven subcritical facility
International Nuclear Information System (INIS)
Roy, Tushar; Shukla, Shefali; Shukla, M.; Ray, N.K.; Kashyap, Y.S.; Patel, T.; Gadkari, S.C.
2017-01-01
Accelerator Driven Subcritical systems are being studied worldwide for their potential in burning minor actinides and reducing long term radiotoxicity of spent nuclear fuels. In order to pursue the physics studies of Accelerator Driven Subcritical systems, a thermal subcritical assembly BRAHMMA (BeOReflectedAndHDPeModeratedMultiplying Assembly) has been developed at Purnima Labs, BARC. The facility consists of two major components: Subcritical core and Accelerator (DT/ DD Purnima Neutron Generator)
Poisson-Hopf limit of quantum algebras
International Nuclear Information System (INIS)
Ballesteros, A; Celeghini, E; Olmo, M A del
2009-01-01
The Poisson-Hopf analogue of an arbitrary quantum algebra U z (g) is constructed by introducing a one-parameter family of quantizations U z,ℎ (g) depending explicitly on ℎ and by taking the appropriate ℎ → 0 limit. The q-Poisson analogues of the su(2) algebra are discussed and the novel su q P (3) case is introduced. The q-Serre relations are also extended to the Poisson limit. This approach opens the perspective for possible applications of higher rank q-deformed Hopf algebras in semiclassical contexts
Bifurcación de hopf en un modelo sobre resistencia bacteriana
Directory of Open Access Journals (Sweden)
Saulo Mosquera-Lopez
2013-01-01
Full Text Available In 2011 Romero J. in his master’s thesis “Mathematical models for bacterial resistance to antibiotics” formulated and analyzed a nonlinear system of ordinary differential equations describing the acquisition of bacterial resistance through two mechanisms: action plasmids and treatment with antibiotics. Under certain conditions the system has three equilibrium points and one of them coexist both sensitive and resistant bacteria. Numerical simulations performed in this work suggest that around this equilibrium point exists a Hopf bifurcation. From these observations we have developed a project which aims to analyze the conditions to be satisfied by the parameters of the model, to ensure the existence of this bifurcation and classify their stability. The main objective of the conference is to present the progress made in the development of this project.
Bifurcation and Stability in a Delayed Predator-Prey Model with Mixed Functional Responses
Yafia, R.; Aziz-Alaoui, M. A.; Merdan, H.; Tewa, J. J.
2015-06-01
The model analyzed in this paper is based on the model set forth by Aziz Alaoui et al. [Aziz Alaoui & Daher Okiye, 2003; Nindjin et al., 2006] with time delay, which describes the competition between the predator and prey. This model incorporates a modified version of the Leslie-Gower functional response as well as that of Beddington-DeAngelis. In this paper, we consider the model with one delay consisting of a unique nontrivial equilibrium E* and three others which are trivial. Their dynamics are studied in terms of local and global stabilities and of the description of Hopf bifurcation at E*. At the third trivial equilibrium, the existence of the Hopf bifurcation is proven as the delay (taken as a parameter of bifurcation) that crosses some critical values.
Multiple-parameter bifurcation analysis in a Kuramoto model with time delay and distributed shear
Niu, Ben; Zhang, Jiaming; Wei, Junjie
2018-05-01
In this paper, time delay effect and distributed shear are considered in the Kuramoto model. On the Ott-Antonsen's manifold, through analyzing the associated characteristic equation of the reduced functional differential equation, the stability boundary of the incoherent state is derived in multiple-parameter space. Moreover, very rich dynamical behavior such as stability switches inducing synchronization switches can occur in this equation. With the loss of stability, Hopf bifurcating coherent states arise, and the criticality of Hopf bifurcations is determined by applying the normal form theory and the center manifold theorem. On one hand, theoretical analysis indicates that the width of shear distribution and time delay can both eliminate the synchronization then lead the Kuramoto model to incoherence. On the other, time delay can induce several coexisting coherent states. Finally, some numerical simulations are given to support the obtained results where several bifurcation diagrams are drawn, and the effect of time delay and shear is discussed.
International Nuclear Information System (INIS)
Song Yongli; Tadé, Moses O; Zhang Tonghua
2009-01-01
In this paper, a delayed neural network with unidirectional coupling is considered which consists of two two-dimensional nonlinear differential equation systems with exponential decay where one system receives a delayed input from the other system. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using the theory of functional differential equations. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the centre manifold theorem. We also investigate the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay-differential equations combined with representation theory of Lie groups. Then the global continuation of phase-locked periodic solutions is investigated. Numerical simulations are given to illustrate the results obtained
Quasi Hopf quantum symmetry in quantum theory
International Nuclear Information System (INIS)
Mack, G.; Schomerus, V.
1991-05-01
In quantum theory, internal symmetries more general than groups are possible. We show that quasitriangular quasi Hopf algebras G * as introduced by Drinfeld permit a consistent formulation of a transformation law of states in the physical Hilbert space H, of invariance of the ground state, and of a transformation law of field operators which is consistent with local braid relations of field operators as proposed by Froehlich. All this remains true when Drinfelds axioms are suitably weakened in order to build in truncated tensor products. Conversely, all the axioms of a weak quasitriangular quasi Hopf algebra are motivated from what physics demands of a symmetry. Unitarity requires in addition that G * admits a * -operation with certain properties. Invariance properties of Greens functions follow from invariance of the ground state and covariance of field operators as usual. Covariant adjoints and covariant products of field operators can be defined. The R-matrix elements in the local braid relations are in general operators in H. They are determined by the symmetry up to a phase factor. Quantum group algebras like U q (sl 2 ) with vertical strokeqvertical stroke=1 are examples of symmetries with special properties. We show that a weak quasitriangular quasi Hopf algebra G * is canonically associated with U q (sl 2 ) if q P =-1. We argue that these weak quasi Hopf algebras are the true symmetries of minimal conformal models. Their dual algebras G ('functions on the group') are neither commutative nor associative. (orig.)
Normal forms of Hopf-zero singularity
International Nuclear Information System (INIS)
Gazor, Majid; Mokhtari, Fahimeh
2015-01-01
The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative–nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov–Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov–Takens singularities. Despite this, the normal form computations of Bogdanov–Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative–nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto–Sivashinsky equations to demonstrate the applicability of our results. (paper)
Normal forms of Hopf-zero singularity
Gazor, Majid; Mokhtari, Fahimeh
2015-01-01
The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative-nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov-Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov-Takens singularities. Despite this, the normal form computations of Bogdanov-Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative-nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto-Sivashinsky equations to demonstrate the applicability of our results.
Feynman graphs and related Hopf algebras
International Nuclear Information System (INIS)
Duchamp, G H E; Blasiak, P; Horzela, A; Penson, K A; Solomon, A I
2006-01-01
In a recent series of communications we have shown that the reordering problem of bosons leads to certain combinatorial structures. These structures may be associated with a certain graphical description. In this paper, we show that there is a Hopf Algebra structure associated with this problem which is, in a certain sense, unique
Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback
Directory of Open Access Journals (Sweden)
Lei Li
2016-10-01
Full Text Available The parametric excitation system consisting of a flexible beam and shuttle mass widely exists in microelectromechanical systems (MEMS, which can exhibit rich nonlinear dynamic behaviors. This article aims to theoretically investigate the nonlinear jumping phenomena and bifurcation conditions of a class of electrostatically-driven MEMS actuators with a time-delay feedback controller. Considering the comb structure consisting of a flexible beam and shuttle mass, the partial differential governing equation is obtained with both the linear and cubic nonlinear parametric excitation. Then, the method of multiple scales is introduced to obtain a slow flow that is analyzed for stability and bifurcation. Results show that time-delay feedback can improve resonance frequency and stability of the system. What is more, through a detailed mathematical analysis, the discriminant of Hopf bifurcation is theoretically derived, and appropriate time-delay feedback force can make the branch from the Hopf bifurcation point stable under any driving voltage value. Meanwhile, through global bifurcation analysis and saddle node bifurcation analysis, theoretical expressions about the system parameter space and maximum amplitude of monostable vibration are deduced. It is found that the disappearance of the global bifurcation point means the emergence of monostable vibration. Finally, detailed numerical results confirm the analytical prediction.
Bifurcation analysis of a delayed mathematical model for tumor growth
International Nuclear Information System (INIS)
Khajanchi, Subhas
2015-01-01
In this study, we present a modified mathematical model of tumor growth by introducing discrete time delay in interaction terms. The model describes the interaction between tumor cells, healthy tissue cells (host cells) and immune effector cells. The goal of this study is to obtain a better compatibility with reality for which we introduced the discrete time delay in the interaction between tumor cells and host cells. We investigate the local stability of the non-negative equilibria and the existence of Hopf-bifurcation by considering the discrete time delay as a bifurcation parameter. We estimate the length of delay to preserve the stability of bifurcating periodic solutions, which gives an idea about the mode of action for controlling oscillations in the tumor growth. Numerical simulations of the model confirm the analytical findings
Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System
Directory of Open Access Journals (Sweden)
Wen-Qing Zhang
2013-01-01
Full Text Available Nonlinear properties of magnetic flux feedback control system have been investigated mainly in this paper. We analyzed the influence of magnetic flux feedback control system on control property by time delay and interfering signal of acceleration. First of all, we have established maglev nonlinear model based on magnetic flux feedback and then discussed hopf bifurcation’s condition caused by the acceleration’s time delay. The critical value of delayed time is obtained. It is proved that the period solution exists in maglev control system and the stable condition has been got. We obtained the characteristic values by employing center manifold reduction theory and normal form method, which represent separately the direction of hopf bifurcation, the stability of the period solution, and the period of the period motion. Subsequently, we discussed the influence maglev system on stability of by acceleration’s interfering signal and obtained the stable domain of interfering signal. Some experiments have been done on CMS04 maglev vehicle of National University of Defense Technology (NUDT in Tangshan city. The results of experiments demonstrate that viewpoints of this paper are correct and scientific. When time lag reaches the critical value, maglev system will produce a supercritical hopf bifurcation which may cause unstable period motion.
Energy Technology Data Exchange (ETDEWEB)
Emelianova, Yu.P., E-mail: yuliaem@gmail.com [Department of Electronics and Instrumentation, Saratov State Technical University, Polytechnicheskaya 77, Saratov 410054 (Russian Federation); Kuznetsov, A.P., E-mail: apkuz@rambler.ru [Kotel' nikov' s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelyenaya 38, Saratov 410019 (Russian Federation); Turukina, L.V., E-mail: lvtur@rambler.ru [Kotel' nikov' s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelyenaya 38, Saratov 410019 (Russian Federation); Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam (Germany)
2014-01-10
The dynamics of the four dissipatively coupled van der Pol oscillators is considered. Lyapunov chart is presented in the parameter plane. Its arrangement is discussed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators. Here are quasi-periodic saddle-node, Hopf and Neimark–Sacker bifurcations. The effect of increase of the threshold for the “amplitude death” regime and the possibilities of complete and partial broadband synchronization are revealed.
Energy Technology Data Exchange (ETDEWEB)
Vega C, H. R., E-mail: fermineutron@yahoo.com [Universidad Autonoma de Zacatecas, Unidad Academica de Estudios Nucleares, Cipres No. 10, Fracc. La Penuela, 98068 Zacatecas (Mexico)
2014-08-15
A Subcritical Nuclear Assembly is a device where the nuclear-fission chain reaction is initiated and maintained using an external neutron source. It is a valuable educational and research tool where in a safe way many reactor parameters can be measured. Here, we have used the Wigner-Seitz method in the six-factor formula to calculate the effective multiplication factor of a subcritical nuclear reactor Nuclear Chicago model 9000. This reactor has approximately 2500 kg of natural uranium heterogeneously distributed in slugs. The reactor uses a {sup 239}PuBe neutron source that is located in the center of an hexagonal array. Using Monte Carlo methods, with the MCNP5 code, a three-dimensional model of the subcritical reactor was designed to estimate the effective multiplication factor, the neutron spectra, the total and thermal neutron fluences along the radial and axial axis. With the neutron spectra in two locations outside the reactor the ambient dose equivalent were estimated. (Author)
Bursting oscillations, bifurcation and synchronization in neuronal systems
Energy Technology Data Exchange (ETDEWEB)
Wang Haixia [School of Science, Nanjing University of Science and Technology, Nanjing 210094 (China); Wang Qingyun, E-mail: drwangqy@gmail.com [Department of Dynamics and Control, Beihang University, Beijing 100191 (China); Lu Qishao [Department of Dynamics and Control, Beihang University, Beijing 100191 (China)
2011-08-15
Highlights: > We investigate bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. > Two types of fast-slow bursters are analyzed in detail. > We show the properties of some crucial bifurcation points. > Synchronization transition and the neural excitability are explored in the coupled bursters. - Abstract: This paper investigates bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. It is shown that for some appropriate parameters, the modified Morris-Lecar neuron can exhibit two types of fast-slow bursters, that is 'circle/fold cycle' bursting and 'subHopf/homoclinic' bursting with class 1 and class 2 neural excitability, which have different neuro-computational properties. By means of the analysis of fast-slow dynamics and phase plane, we explore bifurcation mechanisms associated with the two types of bursters. Furthermore, the properties of some crucial bifurcation points, which can determine the type of the burster, are studied by the stability and bifurcation theory. In addition, we investigate the influence of the coupling strength on synchronization transition and the neural excitability in two electrically coupled bursters with the same bursting type. More interestingly, the multi-time-scale synchronization transition phenomenon is found as the coupling strength varies.
The geometric Hopf invariant and surgery theory
Crabb, Michael
2017-01-01
Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .
On the analysis of local bifurcation and topological horseshoe of a new 4D hyper-chaotic system
International Nuclear Information System (INIS)
Zhou, Leilei; Chen, Zengqiang; Wang, Zhonglin; Wang, Jiezhi
2016-01-01
Highlights: • A new 4D smooth quadratic autonomous system with complex hyper-chaotic dynamics is presented. • The stability of equilibria is observed near the bifurcation points. • The Hopf bifurcation and pitchfork bifurcation are analyzed by using the center manifold theorem and bifurcation theory. • A horseshoe with two-directional expansions in the 4D hyper-chaotic system has been found, which rigorously proves the existence of hyper-chaos in theory. - Abstract: In this paper, a new four-dimensional (4D) smooth quadratic autonomous system with complex hyper-chaotic dynamics is presented and analyzed. The Lyapunov exponent (LE) spectrum, bifurcation diagram and various phase portraits of the system are provided. The stability, Hopf bifurcation and pitchfork bifurcation of equilibrium point are discussed by using the center manifold theorem and bifurcation theory. Numerical simulation results are consistent with the theoretical analysis. Besides, by combining the topological horseshoe theory with a computer-assisted method of Poincaré maps and utilizing the algorithm for finding horseshoes in 3D hyper-chaotic maps, a horseshoe with two-directional expansions in the 4D hyper-chaotic system is successfully found, which rigorously proves the existence of hyper-chaos in theory.
Gaudreault, Mathieu; Drolet, François; Viñals, Jorge
2010-11-01
Analytical expressions for pitchfork and Hopf bifurcation thresholds are given for a nonlinear stochastic differential delay equation with feedback. Our results assume that the delay time τ is small compared to other characteristic time scales, not a significant limitation close to the bifurcation line. A pitchfork bifurcation line is found, the location of which depends on the conditional average , where x(t) is the dynamical variable. This conditional probability incorporates the combined effect of fluctuation correlations and delayed feedback. We also find a Hopf bifurcation line which is obtained by a multiple scale expansion around the oscillatory solution near threshold. We solve the Fokker-Planck equation associated with the slowly varying amplitudes and use it to determine the threshold location. In both cases, the predicted bifurcation lines are in excellent agreement with a direct numerical integration of the governing equations. Contrary to the known case involving no delayed feedback, we show that the stochastic bifurcation lines are shifted relative to the deterministic limit and hence that the interaction between fluctuation correlations and delay affect the stability of the solutions of the model equation studied.
Multistability and gluing bifurcation to butterflies in coupled networks with non-monotonic feedback
International Nuclear Information System (INIS)
Ma Jianfu; Wu Jianhong
2009-01-01
Neural networks with a non-monotonic activation function have been proposed to increase their capacity for memory storage and retrieval, but there is still a lack of rigorous mathematical analysis and detailed discussions of the impact of time lag. Here we consider a two-neuron recurrent network. We first show how supercritical pitchfork bifurcations and a saddle-node bifurcation lead to the coexistence of multiple stable equilibria (multistability) in the instantaneous updating network. We then study the effect of time delay on the local stability of these equilibria and show that four equilibria lose their stability at a certain critical value of time delay, and Hopf bifurcations of these equilibria occur simultaneously, leading to multiple coexisting periodic orbits. We apply centre manifold theory and normal form theory to determine the direction of these Hopf bifurcations and the stability of bifurcated periodic orbits. Numerical simulations show very interesting global patterns of periodic solutions as the time delay is varied. In particular, we observe that these four periodic solutions are glued together along the stable and unstable manifolds of saddle points to develop a butterfly structure through a complicated process of gluing bifurcations of periodic solutions
Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
Lukierski, Jerzy; Meljanac, Daniel; Meljanac, Stjepan; Pikutić, Danijel; Woronowicz, Mariusz
2018-02-01
We consider new Abelian twists of Poincare algebra describing nonsymmetric generalization of the ones given in [1], which lead to the class of Lie-deformed quantum Minkowski spaces. We apply corresponding twist quantization in two ways: as generating quantum Poincare-Hopf algebra providing quantum Poincare symmetries, and by considering the quantization which provides Hopf algebroid describing class of quantum relativistic phase spaces with built-in quantum Poincare covariance. If we assume that Lorentz generators are orbital i.e. do not describe spin degrees of freedom, one can embed the considered generalized phase spaces into the ones describing the quantum-deformed Heisenberg algebras.
Differential geometry on Hopf algebras and quantum groups
International Nuclear Information System (INIS)
Watts, P.
1994-01-01
The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash product, and used to define and discuss quantum Lie algebras and their properties. The Cartan calculus of the exterior derivative, Lie derivative, and inner derivation is found for both the universal and general differential calculi of an arbitrary Hopf algebra, and, by restricting to the quasitriangular case and using the numerical R-matrix formalism, the aforementioned structures for quantum groups are determined
Bifurcation and Fractal of the Coupled Logistic Map
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.
Stochastic Bifurcation Analysis of an Elastically Mounted Flapping Airfoil
Directory of Open Access Journals (Sweden)
Bose Chandan
2018-01-01
Full Text Available The present paper investigates the effects of noisy flow fluctuations on the fluid-structure interaction (FSI behaviour of a span-wise flexible wing modelled as a two degree-of-freedom elastically mounted flapping airfoil. In the sterile flow conditions, the system undergoes a Hopf bifurcation as the free-stream velocity exceeds a critical limit resulting in a stable limit-cycle oscillation (LCO from a fixed point response. On the other hand, the qualitative dynamics changes from a stochastic fixed point to a random LCO through an intermittent state in the presence of irregular flow fluctuations. The probability density function depicts the most probable system state in the phase space. A phenomenological bifurcation (P-bifurcation analysis based on the transition in the topology associated with the structure of the joint probability density function (pdf of the response variables has been carried out. The joint pdf corresponding to the stochastic fixed point possesses a Dirac delta function like structure with a sharp single peak around zero. As the mean flow speed crosses the critical value, the joint pdf bifurcates to a crater-like structure indicating the occurrence of a P-bifurcation. The intermittent state is characterized by the co-existence of the unimodal as well as the crater like structure.
Stability and Bifurcation of a Fishery Model with Crowley-Martin Functional Response
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.
From racks to pointed Hopf algebras
Andruskiewitsch, Nicolás; Graña, Matı́as
2003-01-01
A fundamental step in the classification of finite-dimensional complex pointed Hopf algebras is the determination of all finite-dimensional Nichols algebras of braided vector spaces arising from groups. The most important class of braided vector spaces arising from groups is the class of braided vector spaces (CX, c^q), where C is the field of complex numbers, X is a rack and q is a 2-cocycle on X with values in C^*. Racks and cohomology of racks appeared also in the work of topologists. This...
Macular variant of acrokeratosis verruciformis of Hopf
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Rita Vipul Vora
2017-01-01
Full Text Available Acrokeratosis verruciformis (AKV of Hopf is an autosomal dominant condition characterized by multiple flesh-colored or lightly pigmented flat or convex warty papules over dorsa of hands, feet, knees, elbows, and forearms. It affects both sexes and is usually present at birth or appears in early childhood. Two forms of the disease have been described, namely, classical AKV and sporadic AKV. Histological examination differentiates it from other similar conditions. Superficial ablation is the treatment of choice. We represent a case of a young female with extensive lesions over contralateral limbs, of classical AKV interspersed with multiple hypopigmented macular lesions of AKV.
The Leibniz-Hopf algebra and Lyndon words
M. Hazewinkel (Michiel)
1996-01-01
textabstractLet ${cal Z$ denote the free associative algebra ${ol Z langle Z_1 , Z_2 , ldots rangle$ over the integers. This algebra carries a Hopf algebra structure for which the comultiplication is $Z_n mapsto Sigma_{i+j=n Z_i otimes Z_j$. This the noncommutative Leibniz-Hopf algebra. It carries a
International Nuclear Information System (INIS)
Jiang Yu; Lozada-Cassou, M.; Vinet, A.
2003-01-01
The spatiotemporal dynamics of networks based on a ring of coupled oscillators with regular shortcuts beyond the nearest-neighbor couplings is studied by using master stability equations and numerical simulations. The generic criterion for dynamic synchronization has been extended to arbitrary network topologies with zero row-sum. The symmetry-breaking oscillation patterns that resulted from the Hopf bifurcation from synchronous states are analyzed by the symmetry group theory
Unfolding the Riddling Bifurcation
DEFF Research Database (Denmark)
Maistrenko, Yu.; Popovych, O.; Mosekilde, Erik
1999-01-01
We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation.......We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation....
Bifurcation analysis of Rössler system with multiple delayed feedback
Directory of Open Access Journals (Sweden)
Meihong Xu
2010-10-01
Full Text Available In this paper, regarding the delay as parameter, we investigate the effect of delay on the dynamics of a Rössler system with multiple delayed feedback proposed by Ghosh and Chowdhury. At first we consider the stability of equilibrium and the existence of Hopf bifurcations. Then an explicit algorithm for determining the direction and the stability of the bifurcating periodic solutions is derived by using the normal form theory and center manifold argument. Finally, we give a numerical simulation example which indicates that chaotic oscillation is converted into a stable steady state or a stable periodic orbit when the delay passes through certain critical values.
Turing instability and bifurcation analysis in a diffusive bimolecular system with delayed feedback
Wei, Xin; Wei, Junjie
2017-09-01
A diffusive autocatalytic bimolecular model with delayed feedback subject to Neumann boundary conditions is considered. We mainly study the stability of the unique positive equilibrium and the existence of periodic solutions. Our study shows that diffusion can give rise to Turing instability, and the time delay can affect the stability of the positive equilibrium and result in the occurrence of Hopf bifurcations. By applying the normal form theory and center manifold reduction for partial functional differential equations, we investigate the stability and direction of the bifurcations. Finally, we give some simulations to illustrate our theoretical results.
International Nuclear Information System (INIS)
Li, Jinhui; Teng, Zhidong; Wang, Guangqing; Zhang, Long; Hu, Cheng
2017-01-01
In this paper, we introduce the saturated treatment and logistic growth rate into an SIR epidemic model with bilinear incidence. The treatment function is assumed to be a continuously differential function which describes the effect of delayed treatment when the medical condition is limited and the number of infected individuals is large enough. Sufficient conditions for the existence and local stability of the disease-free and positive equilibria are established. And the existence of the stable limit cycles also is obtained. Moreover, by using the theory of bifurcations, it is shown that the model exhibits backward bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcations. Finally, the numerical examples are given to illustrate the theoretical results and obtain some additional interesting phenomena, involving double stable periodic solutions and stable limit cycles.
Stability and dynamics of a controlled van der Pol-Duffing oscillator
International Nuclear Information System (INIS)
Ji, J.C.; Hansen, C.H.
2006-01-01
The trivial equilibrium of a van der Pol-Duffing oscillator under a linear-plus-nonlinear feedback control may change its stability either via a single or via a double Hopf bifurcation if the time delay involved in the feedback reaches certain values. It is found that the trivial equilibrium may lose its stability via a subcritical or supercritical Hopf bifurcation and regain its stability via a reverse subcritical or supercritical Hopf bifurcation as the time delay increases. A stable limit cycle appears after a supercritical Hopf bifurcation occurs and disappears through a reverse supercritical Hopf bifurcation. The interaction of the weakly periodic excitation and the stable bifurcating solution is investigated for the forced system under primary resonance conditions. It is shown that the forced periodic response may lose its stability via a Neimark-Sacker bifurcation. Analytical results are validated by a comparison with those of direct numerical integration
Subcriticality monitoring method for reactor
International Nuclear Information System (INIS)
Ueda, Makoto.
1991-01-01
The present invention accurately monitors the reactor subcriticality and ensures the critical safety, irrespective of the presence or absence of artificial neutron sources. That is, when the subcriticality is monitored upon reactivity changing operation which causes reactivity change to the reactor during shutdown, neutron monitors are disposed at a plurality of monitoring positions. Then, neutron counting ratio before and after conducting the reactivity changing operation is determined. The subcriticality of the reactor is monitored by the ratio and the state of scattering of the ratio of neutron counting rate between each of the neutron monitors. With such procedures, signals of the neutron monitors are used, the characteristic that the change of the signals depend on the change of the neutron multiplication of the reactor core can be utilized whether artificial neutron sources (external neutron sources) are disposed or not. Accordingly, the subcriticality can be monitored more reliably. (I.S.)
Wigner oscillators, twisted Hopf algebras and second quantization
Energy Technology Data Exchange (ETDEWEB)
Castro, P.G.; Toppan, F. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mails: pgcastro@cbpf.br; toppan@cbpf.br; Chakraborty, B. [S. N. Bose National Center for Basic Sciences, Kolkata (India)]. E-mail: biswajit@bose.res.in
2008-07-01
By correctly identifying the role of central extension in the centrally extended Heisenberg algebra h, we show that it is indeed possible to construct a Hopf algebraic structure on the corresponding enveloping algebra U(h) and eventually deform it through Drinfeld twist. This Hopf algebraic structure and its deformed version U{sup F}(h) is shown to be induced from a more 'fundamental' Hopf algebra obtained from the Schroedinger field/oscillator algebra and its deformed version, provided that the fields/oscillators are regarded as odd-elements of a given superalgebra. We also discuss the possible implications in the context of quantum statistics. (author)
Accelerator driven sub-critical core
McIntyre, Peter M; Sattarov, Akhdiyor
2015-03-17
Systems and methods for operating an accelerator driven sub-critical core. In one embodiment, a fission power generator includes a sub-critical core and a plurality of proton beam generators. Each of the proton beam generators is configured to concurrently provide a proton beam into a different area of the sub-critical core. Each proton beam scatters neutrons within the sub-critical core. The plurality of proton beam generators provides aggregate power to the sub-critical core, via the proton beams, to scatter neutrons sufficient to initiate fission in the sub-critical core.
Transport Bifurcation in a Rotating Tokamak Plasma
International Nuclear Information System (INIS)
Highcock, E. G.; Barnes, M.; Schekochihin, A. A.; Parra, F. I.; Roach, C. M.; Cowley, S. C.
2010-01-01
The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all nonzero flow shear values, but that subcritical turbulence can be sustained nonlinearly at a wide range of temperature gradients. Flow shear increases the nonlinear temperature gradient threshold for turbulence but also increases the sensitivity of the heat flux to changes in the temperature gradient, except over a small range near the threshold where the sensitivity is decreased. A bifurcation in the equilibrium gradients is found: for a given input of heat, it is possible, by varying the applied torque, to trigger a transition to significantly higher temperature and flow gradients.
Accelerator driven subcritical reactors
International Nuclear Information System (INIS)
Salvatores, M.
2001-01-01
ADS concepts have been proposed in the last decade for a variety of applications. However, there is a convergence of interest of several countries and laboratories on the application of ADS to transmutation. This applies to plutonium, and/or minor actinides (MA) and long-lived fission products (LLFP). As far as the so-called partitioning and transmutation (PIT) strategies, it was indicated that they can be clarified according to the option taken with respect to Pu and MA, i.e., a) keep Pu and MA together, b) separate Pu from MA. At present several programs are going on ADS: in Japan, USA Europe, where activities in 9 countries are coordinated by a European Technical Working Group (ETWG), and in Russia. As far as the implications for the definition of nuclear data needs, dedicated subcritical cores should have new type of fuels (Pu+MA in different proportions). Proposals are being worked out. For example, composite (such as ceramic-metallic or ceramic-ceramic) fuels are presently under study. The actinide oxide is dispersed in a metallic matrix (Zr, or W or Mo) or in an oxide matrix (e.g., MgO). In these cases, reliable data are required for the matrix materials. As far as coolants, Pb/Bi, Pb, and gas are considered, besides Na. Hard (or very hard) fast neutron spectrum is required. As far as LLFP, transmutation strategies in ADS are proposed. Candidates are 129 I, 99 Tc, 135 Cs, but also 79 Se, 107 Pd, 93 Zr etc. At present, there is no clear option for their transmutation (one needs a high level of thermalized neutrons, support matrixes for target irradiation, isotopic separations, reprocessing techniques, etc.). Finally, ADS transmutation will give rise to fuel cycles, where very active materials will be present. Cm and higher mass isotopes (up to 252 Cf) will be contributors to dose and neutron source strength. This area will deserve attention in future, in order to define the relevant data needs. It is recommended to coordinate work on MA data as a priority
Relative Lyapunov Center Bifurcations
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2014-01-01
Relative equilibria (REs) and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and rigid body motion. REs are equilibria, and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov...... center bifurcations are bifurcations of RPOs from REs corresponding to Lyapunov center bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov center theorem by combining recent results on the persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov...... center theorem of Montaldi, Roberts, and Stewart. We then develop numerical methods for the detection of relative Lyapunov center bifurcations along branches of RPOs and for their computation. We apply our methods to Lagrangian REs of the N-body problem....
Bifurcation analysis of a delay reaction-diffusion malware propagation model with feedback control
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.
On the analysis of spatial chaos and Hopf bifurcation in an optical open flow
International Nuclear Information System (INIS)
Saha, Papri; Rakshit, B.; Chowdhury, A. Roy
2005-01-01
Spatial chaos in a system of copropagating nonlinear beam, interacting mutually, is explored. The case of four beams belonging to two weakly degenerate mode in a multimode fibre is analysed. The modulation of the waves due to mutual energy exchange is shown to give rise to chaos. We characterize the chaos with the help of Lyapunov exponent and phase space analysis. The case of centre manifold with imaginary eigenvalue is separated with the help of normal form analysis, when the system is reduced to a two component one. The reduced problem is then analysed with the help of a tangent field diagram
Induction of Hopf bifurcation and oscillation death by delays in coupled networks
International Nuclear Information System (INIS)
Cheng, C.-Y.
2009-01-01
This work explores a system of two coupled networks that each has four nodes. Delayed effects of short-cuts in each network and the coupling between the two groups are considered. When the short-cut delay is fixed, the arising and death of oscillations are caused by the variational coupling delay.
Qualitative properties and hopf bifurcation in haematopoietic disease model with chemotherapy
Directory of Open Access Journals (Sweden)
Yafia R.
2014-01-01
Full Text Available In this paper, we consider a model describing the dynamics of Hematopoietic Stem Cells (HSC disease with chemotherapy. The model is given by a system of three ordinary differential equations with discrete delay. Its dynamics are studied in term of local stability of the possible steady states for the case without drug intervention term. We prove the existence of periodic oscillations for each case when the delay passes trough a critical values. In the end, we illustrate our results by some numerical simulations.
Hopf Bifurcation and Delay-Induced Turing Instability in a Diffusive lac Operon Model
Cao, Xin; Song, Yongli; Zhang, Tonghua
In this paper, we investigate the dynamics of a lac operon model with delayed feedback and diffusion effect. If the system is without delay or the delay is small, the positive equilibrium is stable so that there are no spatial patterns formed; while the time delay is large enough the equilibrium becomes unstable so that rich spatiotemporal dynamics may occur. We have found that time delay can not only incur temporal oscillations but also induce imbalance in space. With different initial values, the system may have different spatial patterns, for instance, spirals with one head, four heads, nine heads, and even microspirals.
Dynamics at infinity and a Hopf bifurcation arising in a quadratic ...
Indian Academy of Sciences (India)
Zhen Wang
2017-12-27
Dec 27, 2017 ... the mathematical, physical and chemical sciences etc., searching for new chaotic ... especially in high-dimensional systems, most people will use numerical ..... a relative narrow range of the parameter a. 6. Conclusion.
Stability, convergence and Hopf bifurcation analyses of the classical car-following model
Kamath, Gopal Krishna; Jagannathan, Krishna; Raina, Gaurav
2016-01-01
Reaction delays play an important role in determining the qualitative dynamical properties of a platoon of vehicles traversing a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of the Classical Car-Following Model (CCFM). Specifically, we analyze the CCFM in no delay, small delay and arbitrary delay regimes. First, we derive a sufficient condition for local stability of the CCFM in no-delay and small-delay regimes using. Next, we derive the necessar...
Subcritical assemblies, use and their feasibility assessment
International Nuclear Information System (INIS)
Haroon, M.R.
1982-03-01
In developing countries, subcritical assemblies can be a useful tool for training and research in the field of nuclear technology with minimum cost. The historical development of subcritical assemblies and the reactor physics experiments which can be carried out using this facility are outlined. The different types of subcritical assemblies have been described and material requirements for each assembly have been pointed out. (author)
Directory of Open Access Journals (Sweden)
Randhir Singh Baghel
2012-02-01
Full Text Available In this article, we propose a three dimensional mathematical model of phytoplankton dynamics with the help of reaction-diffusion equations that studies the bifurcation and pattern formation mechanism. We provide an analytical explanation for understanding phytoplankton dynamics with three population classes: susceptible, incubated, and infected. This model has a Holling type II response function for the population transformation from susceptible to incubated class in an aquatic ecosystem. Our main goal is to provide a qualitative analysis of Hopf bifurcation mechanisms, taking death rate of infected phytoplankton as bifurcation parameter, and to study further spatial patterns formation due to spatial diffusion. Here analytical findings are supported by the results of numerical experiments. It is observed that the coexistence of all classes of population depends on the rate of diffusion. Also we obtained the time evaluation pattern formation of the spatial system.
Ideal relaxation of the Hopf fibration
Smiet, Christopher Berg; Candelaresi, Simon; Bouwmeester, Dirk
2017-07-01
Ideal magnetohydrodynamics relaxation is the topology-conserving reconfiguration of a magnetic field into a lower energy state where the net force is zero. This is achieved by modeling the plasma as perfectly conducting viscous fluid. It is an important tool for investigating plasma equilibria and is often used to study the magnetic configurations in fusion devices and astrophysical plasmas. We study the equilibrium reached by a localized magnetic field through the topology conserving relaxation of a magnetic field based on the Hopf fibration in which magnetic field lines are closed circles that are all linked with one another. Magnetic fields with this topology have recently been shown to occur in non-ideal numerical simulations. Our results show that any localized field can only attain equilibrium if there is a finite external pressure, and that for such a field a Taylor state is unattainable. We find an equilibrium plasma configuration that is characterized by a lowered pressure in a toroidal region, with field lines lying on surfaces of constant pressure. Therefore, the field is in a Grad-Shafranov equilibrium. Localized helical magnetic fields are found when plasma is ejected from astrophysical bodies and subsequently relaxes against the background plasma, as well as on earth in plasmoids generated by, e.g., a Marshall gun. This work shows under which conditions an equilibrium can be reached and identifies a toroidal depression as the characteristic feature of such a configuration.
Simplest bifurcation diagrams for monotone families of vector fields on a torus
Baesens, C.; MacKay, R. S.
2018-06-01
In part 1, we prove that the bifurcation diagram for a monotone two-parameter family of vector fields on a torus has to be at least as complicated as the conjectured simplest one proposed in Baesens et al (1991 Physica D 49 387–475). To achieve this, we define ‘simplest’ by sequentially minimising the numbers of equilibria, Bogdanov–Takens points, closed curves of centre and of neutral saddle, intersections of curves of centre and neutral saddle, Reeb components, other invariant annuli, arcs of rotational homoclinic bifurcation of horizontal homotopy type, necklace points, contractible periodic orbits, points of neutral horizontal homoclinic bifurcation and half-plane fan points. We obtain two types of simplest case, including that initially proposed. In part 2, we analyse the bifurcation diagram for an explicit monotone family of vector fields on a torus and prove that it has at most two equilibria, precisely four Bogdanov–Takens points, no closed curves of centre nor closed curves of neutral saddle, at most two Reeb components, precisely four arcs of rotational homoclinic connection of ‘horizontal’ homotopy type, eight horizontal saddle-node loop points, two necklace points, four points of neutral horizontal homoclinic connection, and two half-plane fan points, and there is no simultaneous existence of centre and neutral saddle, nor contractible homoclinic connection to a neutral saddle. Furthermore, we prove that all saddle-nodes, Bogdanov–Takens points, non-neutral and neutral horizontal homoclinic bifurcations are non-degenerate and the Hopf condition is satisfied for all centres. We also find it has four points of degenerate Hopf bifurcation. It thus provides an example of a family satisfying all the assumptions of part 1 except the one of at most one contractible periodic orbit.
Modelling, singular perturbation and bifurcation analyses of bitrophic food chains.
Kooi, B W; Poggiale, J C
2018-04-20
Two predator-prey model formulations are studied: for the classical Rosenzweig-MacArthur (RM) model and the Mass Balance (MB) chemostat model. When the growth and loss rate of the predator is much smaller than that of the prey these models are slow-fast systems leading mathematically to singular perturbation problem. In contradiction to the RM-model, the resource for the prey are modelled explicitly in the MB-model but this comes with additional parameters. These parameter values are chosen such that the two models become easy to compare. In both models a transcritical bifurcation, a threshold above which invasion of predator into prey-only system occurs, and the Hopf bifurcation where the interior equilibrium becomes unstable leading to a stable limit cycle. The fast-slow limit cycles are called relaxation oscillations which for increasing differences in time scales leads to the well known degenerated trajectories being concatenations of slow parts of the trajectory and fast parts of the trajectory. In the fast-slow version of the RM-model a canard explosion of the stable limit cycles occurs in the oscillatory region of the parameter space. To our knowledge this type of dynamics has not been observed for the RM-model and not even for more complex ecosystem models. When a bifurcation parameter crosses the Hopf bifurcation point the amplitude of the emerging stable limit cycles increases. However, depending of the perturbation parameter the shape of this limit cycle changes abruptly from one consisting of two concatenated slow and fast episodes with small amplitude of the limit cycle, to a shape with large amplitude of which the shape is similar to the relaxation oscillation, the well known degenerated phase trajectories consisting of four episodes (concatenation of two slow and two fast). The canard explosion point is accurately predicted by using an extended asymptotic expansion technique in the perturbation and bifurcation parameter simultaneously where the small
Bifurcation and category learning in network models of oscillating cortex
Baird, Bill
1990-06-01
A genetic model of oscillating cortex, which assumes “minimal” coupling justified by known anatomy, is shown to function as an associative memory, using previously developed theory. The network has explicit excitatory neurons with local inhibitory interneuron feedback that forms a set of nonlinear oscillators coupled only by long-range excitatory connections. Using a local Hebb-like learning rule for primary and higher-order synapses at the ends of the long-range connections, the system learns to store the kinds of oscillation amplitude patterns observed in olfactory and visual cortex. In olfaction, these patterns “emerge” during respiration by a pattern forming phase transition which we characterize in the model as a multiple Hopf bifurcation. We argue that these bifurcations play an important role in the operation of real digital computers and neural networks, and we use bifurcation theory to derive learning rules which analytically guarantee CAM storage of continuous periodic sequences-capacity: N/2 Fourier components for an N-node network-no “spurious” attractors.
Bifurcations of transition states: Morse bifurcations
International Nuclear Information System (INIS)
MacKay, R S; Strub, D C
2014-01-01
A transition state for a Hamiltonian system is a closed, invariant, oriented, codimension-2 submanifold of an energy level that can be spanned by two compact codimension-1 surfaces of unidirectional flux whose union, called a dividing surface, locally separates the energy level into two components and has no local recrossings. For this to happen robustly to all smooth perturbations, the transition state must be normally hyperbolic. The dividing surface then has locally minimal geometric flux through it, giving an upper bound on the rate of transport in either direction. Transition states diffeomorphic to S 2m−3 are known to exist for energies just above any index-1 critical point of a Hamiltonian of m degrees of freedom, with dividing surfaces S 2m−2 . The question addressed here is what qualitative changes in the transition state, and consequently the dividing surface, may occur as the energy or other parameters are varied? We find that there is a class of systems for which the transition state becomes singular and then regains normal hyperbolicity with a change in diffeomorphism class. These are Morse bifurcations. Various examples are considered. Firstly, some simple examples in which transition states connect or disconnect, and the dividing surface may become a torus or other. Then, we show how sequences of Morse bifurcations producing various interesting forms of transition state and dividing surface are present in reacting systems, by considering a hypothetical class of bimolecular reactions in gas phase. (paper)
International Nuclear Information System (INIS)
Olmstead, W.E.; Davis, S.H.; Rosenblat, S.; Kath, W.L.
1986-01-01
A model equation containing a memory integral is posed. The extent of the memory, the relaxation time lambda, controls the bifurcation behavior as the control parameter R is increased. Small (large) lambda gives steady (periodic) bifurcation. There is a double eigenvalue at lambda = lambda 1 , separating purely steady (lambda 1 ) from combined steady/T-periodic (lambda > lambda 1 ) states with T → infinity as lambda → lambda + 1 . Analysis leads to the co-existence of stable steady/periodic states and as R is increased, the periodic states give way to the steady states. Numerical solutions show that this behavior persists away from lambda = lambda 1
Dynamics and Physiological Roles of Stochastic Firing Patterns Near Bifurcation Points
Jia, Bing; Gu, Huaguang
2017-06-01
Different stochastic neural firing patterns or rhythms that appeared near polarization or depolarization resting states were observed in biological experiments on three nervous systems, and closely matched those simulated near bifurcation points between stable equilibrium point and limit cycle in a theoretical model with noise. The distinct dynamics of spike trains and interspike interval histogram (ISIH) of these stochastic rhythms were identified and found to build a relationship to the coexisting behaviors or fixed firing frequency of four different types of bifurcations. Furthermore, noise evokes coherence resonances near bifurcation points and plays important roles in enhancing information. The stochastic rhythms corresponding to Hopf bifurcation points with fixed firing frequency exhibited stronger coherence degree and a sharper peak in the power spectrum of the spike trains than those corresponding to saddle-node bifurcation points without fixed firing frequency. Moreover, the stochastic firing patterns changed to a depolarization resting state as the extracellular potassium concentration increased for the injured nerve fiber related to pathological pain or static blood pressure level increased for aortic depressor nerve fiber, and firing frequency decreased, which were different from the physiological viewpoint that firing frequency increased with increasing pressure level or potassium concentration. This shows that rhythms or firing patterns can reflect pressure or ion concentration information related to pathological pain information. Our results present the dynamics of stochastic firing patterns near bifurcation points, which are helpful for the identification of both dynamics and physiological roles of complex neural firing patterns or rhythms, and the roles of noise.
Emergence of the bifurcation structure of a Langmuir–Blodgett transfer model
Köpf, Michael H
2014-10-07
© 2014 IOP Publishing Ltd & London Mathematical Society. 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.
Experimental Investigation of Bifurcations in a Thermoacoustic Engine
Directory of Open Access Journals (Sweden)
Vishnu R. Unni
2015-06-01
Full Text Available In this study, variation in the characteristics of the pressure oscillations in a thermoacoustic engine is explored as the input heat flux is varied. A bifurcation diagram is plotted to study the variation in the qualitative behavior of the acoustic oscillations as the input heat flux changes. At a critical input heat flux (60 Watt, the engine begins to produce acoustic oscillations in its fundamental longitudinal mode. As the input heat flux is increased, incommensurate frequencies appear in the power spectrum. The simultaneous presence of incommensurate frequencies results in quasiperiodic oscillations. On further increase of heat flux, the fundamental mode disappears and second mode oscillations are observed. These bifurcations in the characteristics of the pressure oscillations are the result of nonlinear interaction between multiple modes present in the thermoacoustic engine. Hysteresis in the bifurcation diagram suggests that the bifurcation is subcritical. Further, the qualitative analysis of different dynamic regimes is performed using nonlinear time series analysis. The physical reason for the observed nonlinear behavior is discussed. Suggestions to avert the variations in qualitative behavior of the pressure oscillations in thermoacoustic engines are also provided.
q-deformed conformal superalgebra and its Hopf subalgebras
International Nuclear Information System (INIS)
Dobrev, V.K.; Lukierski, J.; Sobczyk, J.; Tolstoy, V.N.
1992-07-01
We present in detail a Hopf superalgebra U q (su(2,2/2)) which is a q-deformation of the conformal superalgebra su(2,2/1). The superalgebra U q (su(2,2/1)) contains as a subalgebra a q-deformed super-Poincare algebra and as Hopf subalgebras two conjugate 16-generator q-deformed super-Weyl algebras, which are q-deformation of parabolic subalgebras of su(2,2/1). We use several (anti-) involutions, including the standard Cartan involution and a *-antiinvolution under which the super-Weyl algebras are *-subalgebras of U q (su(2,2/1)). The q-deformed Lorentz algebra is Hopf subalgebra of both Weyl algebras and is preserved by all (anti-) involutions considered. (author). 26 refs
Energetics and monsoon bifurcations
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.
Macdonald operators and homological invariants of the colored Hopf link
International Nuclear Information System (INIS)
Awata, Hidetoshi; Kanno, Hiroaki
2011-01-01
Using a power sum (boson) realization for the Macdonald operators, we investigate the Gukov, Iqbal, Kozcaz and Vafa (GIKV) proposal for the homological invariants of the colored Hopf link, which include Khovanov-Rozansky homology as a special case. We prove the polynomiality of the invariants obtained by GIKV's proposal for arbitrary representations. We derive a closed formula of the invariants of the colored Hopf link for antisymmetric representations. We argue that a little amendment of GIKV's proposal is required to make all the coefficients of the polynomial non-negative integers. (paper)
Quantum walks, deformed relativity and Hopf algebra symmetries.
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2016-05-28
We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras-the usual Poincaré and theκ-Poincaré algebras. © 2016 The Author(s).
Directory of Open Access Journals (Sweden)
Ajith Ananthakrishna Pillai
2012-03-01
Full Text Available 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.
Twisted Acceleration-Enlarged Newton-Hooke Hopf Algebras
International Nuclear Information System (INIS)
Daszkiewicz, M.
2010-01-01
Ten Abelian twist deformations of acceleration-enlarged Newton-Hooke Hopf algebra are considered. The corresponding quantum space-times are derived as well. It is demonstrated that their contraction limit τ → ∞ leads to the new twisted acceleration-enlarged Galilei spaces. (author)
Generating loop graphs via Hopf algebra in quantum field theory
International Nuclear Information System (INIS)
Mestre, Angela; Oeckl, Robert
2006-01-01
We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation of the graphs is such that they can be evaluated directly as contributions to the connected n-point functions. The recursion proceeds by loop order and vertex number
Cup products in Hopf cyclic cohomology with coefficients in contramodules
Rangipour, Bahram
2010-01-01
We use stable anti Yetter-Drinfeld contramodules to improve the cup products in Hopf cyclic cohomology. The improvement fixes the lack of functoriality of the cup products previously defined and show that the cup products are sensitive to the coefficients.
Hopf structure and Green ansatz of deformed parastatistics algebras
Energy Technology Data Exchange (ETDEWEB)
Aneva, Boyka [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, bld. Tsarigradsko chaussee 72, BG-1784 Sofia (Bulgaria); Popov, Todor [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, bld. Tsarigradsko chaussee 72, BG-1784 Sofia (Bulgaria)
2005-07-22
Deformed parabose and parafermi algebras are revised and endowed with Hopf structure in a natural way. The noncocommutative coproduct allows for construction of parastatistics Fock-like representations, built out of the simplest deformed Bose and Fermi representations. The construction gives rise to quadratic algebras of deformed anomalous commutation relations which define the generalized Green ansatz.
Generalized Cole–Hopf transformations for generalized Burgers ...
Indian Academy of Sciences (India)
2015-10-15
Oct 15, 2015 ... Cole–Hopf transformations; Burgers equation; invariance analysis. ... was to generate nonlinear parabolic equations from a linear parabolic equation via a ..... BMV acknowledges the financial support to attend the NMI Workshop ... [16] P J Olver, Applications of Lie Groups to differential equations, Graduate ...
Probe Knots and Hopf Insulators with Ultracold Atoms
Deng, Dong-Ling; Wang, Sheng-Tao; Sun, Kai; Duan, L.-M.
2018-01-01
Knots and links are fascinating and intricate topological objects. Their influence spans from DNA and molecular chemistry to vortices in superfluid helium, defects in liquid crystals and cosmic strings in the early universe. Here we find that knotted structures also exist in a peculiar class of three-dimensional topological insulators—the Hopf insulators. In particular, we demonstrate that the momentum-space spin textures of Hopf insulators are twisted in a nontrivial way, which implies the presence of various knot and link structures. We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-flight images in cold atoms as preimage contours of spin orientations in stereographic coordinates. The extracted Hopf invariants, knots, and links are validated to be robust to typical experimental imperfections. Our work establishes the existence of knotted structures in Hopf insulators, which may have potential applications in spintronics and quantum information processing. D.L.D., S.T.W. and L.M.D. are supported by the ARL, the IARPA LogiQ program, and the AFOSR MURI program, and supported by Tsinghua University for their visits. K.S. acknowledges the support from NSF under Grant No. PHY1402971. D.L.D. is also supported by JQI-NSF-PFC and LPS-MPO-CMTC at the final stage of this paper.
Bifurcation and Nonlinear Oscillations.
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
Numerical analysis of bifurcations
International Nuclear Information System (INIS)
Guckenheimer, J.
1996-01-01
This paper is a brief survey of numerical methods for computing bifurcations of generic families of dynamical systems. Emphasis is placed upon algorithms that reflect the structure of the underlying mathematical theory while retaining numerical efficiency. Significant improvements in the computational analysis of dynamical systems are to be expected from more reliance of geometric insight coming from dynamical systems theory. copyright 1996 American Institute of Physics
Regularizations of two-fold bifurcations in planar piecewise smooth systems using blowup
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Hogan, S. J.
2015-01-01
type of limit cycle that does not appear to be present in the original PWS system. For both types of limit cycle, we show that the criticality of the Hopf bifurcation that gives rise to periodic orbits is strongly dependent on the precise form of the regularization. Finally, we analyse the limit cycles...... as locally unique families of periodic orbits of the regularization and connect them, when possible, to limit cycles of the PWS system. We illustrate our analysis with numerical simulations and show how the regularized system can undergo a canard explosion phenomenon...
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.
Workshop on Subcritical Neutron Production
International Nuclear Information System (INIS)
Walter Sadowski; Roald Sagdeev
2006-01-01
Executive Summary of the Workshop on Subcritical Neutron Production A workshop on Subcritical Neutron Production was sponsored by the East-West Center of the University of Maryland on October 11-13, 2004. The subject of the workshop was the application of subcritical neutrons to transmutation of actinides. The workshop was attended by members of the fission, accelerator and fusion communities. Papers on the state of development of neutron production by accelerators, fusion devices, and fission reactors were presented. Discussions were held on the potential of these technologies to solve the problems of spent nuclear waste storage and nuclear non-proliferation presented by current and future nuclear power reactors. A list of participants including their affiliation and their E-Mail addresses is attached. The workshop concluded that the technologies, presently available or under development, hold out the exciting possibility of improving the environmental quality and long term energy resources of nuclear power while strengthening proliferation resistance. The workshop participants agreed on the following statements. The workshop considered a number of technologies to deal with spent nuclear fuels and current actinide inventories. The conclusion was reached that substantial increase in nuclear power production will require that the issue of spent nuclear fuel be resolved. The Workshop concluded that 14 MeV fusion neutrons can be used to destroy nuclear reactor by-products, some of which would otherwise have to be stored for geologic periods of time. The production of 14 MeV neutrons is based on existing fusion technologies at different research institutions in several countries around the world. At the present time this technology is used to produce 14 MeV neutrons in JET. More development work will be required, however, to bring fusion technology to the level where it can be used for actinide burning on an industrial scale. The workshop concluded that the potential
Benchmarking criticality safety calculations with subcritical experiments
International Nuclear Information System (INIS)
Mihalczo, J.T.
1984-06-01
Calculation of the neutron multiplication factor at delayed criticality may be necessary for benchmarking calculations but it may not be sufficient. The use of subcritical experiments to benchmark criticality safety calculations could result in substantial savings in fuel material costs for experiments. In some cases subcritical configurations could be used to benchmark calculations where sufficient fuel to achieve delayed criticality is not available. By performing a variety of measurements with subcritical configurations, much detailed information can be obtained which can be compared directly with calculations. This paper discusses several measurements that can be performed with subcritical assemblies and presents examples that include comparisons between calculation and experiment where possible. Where not, examples from critical experiments have been used but the measurement methods could also be used for subcritical experiments
Bifurcation analysis in the diffusive Lotka-Volterra system: An application to market economy
International Nuclear Information System (INIS)
Wijeratne, A.W.; Yi Fengqi; Wei Junjie
2009-01-01
A diffusive Lotka-Volterra system is formulated in this paper that represents the dynamics of market share at duopoly. A case in Sri Lankan mobile telecom market was considered that conceptualized the model in interest. Detailed Hopf bifurcation, transcritical and pitchfork bifurcation analysis were performed. The distribution of roots of the characteristic equation suggests that a stable coexistence equilibrium can be achieved by increasing the innovation while minimizing competition by each competitor while regulating existing policies and introducing new ones for product differentiation and value addition. The avenue is open for future research that may use real time information in order to formulate mathematically sound tools for decision making in competitive business environments.
Bifurcation analysis in the diffusive Lotka-Volterra system: An application to market economy
Energy Technology Data Exchange (ETDEWEB)
Wijeratne, A.W. [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China); Department of Agri-Business Management, Sabaragamuwa University of Sri Lanka, Belihuloya 70140 (Sri Lanka); Yi Fengqi [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China); Wei Junjie [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China)], E-mail: weijj@hit.edu.cn
2009-04-30
A diffusive Lotka-Volterra system is formulated in this paper that represents the dynamics of market share at duopoly. A case in Sri Lankan mobile telecom market was considered that conceptualized the model in interest. Detailed Hopf bifurcation, transcritical and pitchfork bifurcation analysis were performed. The distribution of roots of the characteristic equation suggests that a stable coexistence equilibrium can be achieved by increasing the innovation while minimizing competition by each competitor while regulating existing policies and introducing new ones for product differentiation and value addition. The avenue is open for future research that may use real time information in order to formulate mathematically sound tools for decision making in competitive business environments.
Bubble transport in bifurcations
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.
Measurement of subcriticality by a pulsing α-method
International Nuclear Information System (INIS)
Jitarev, V.E.; Kachanov, V.M.; Kuzmin, A.N.
1999-01-01
The report presents results of a pulsing α-method [1] for determination of the WWER system subcriticality. The pulsing α-method permits to conduct measurements of system subcriticality in conditions of subcritical state and large neutron background. Therefore this method can be used for the control of a subcriticality of storehouses of a burn up nuclear fuel and stopped reactor. (Authors)
International Nuclear Information System (INIS)
Hao, Lijie; Yang, Zhuoqin; Lei, Jinzhi
2015-01-01
Highlights: • A delay differentiation equation model for CREB regulation is developed. • Increasing the time delay can generate various bifurcations. • Increasing the time delay can induce chaos by two routes. - Abstract: The ability to form long-term memories is an important function for the nervous system, and the formation process is dynamically regulated through various transcription factors, including CREB proteins. In this paper, we investigate the dynamics of a delay differential equation model for CREB protein activities, which involves two positive and two negative feedbacks in the regulatory network. We discuss the dynamical mechanisms underlying the induction of long-term memory, in which bistability is essential for the formation of long-term memory, while long time delay can destabilize the high level steady state to inhibit the long-term memory formation. The model displays rich dynamical response to stimuli, including monostability, bistability, and oscillations, and can transit between different states by varying the negative feedback strength. Introduction of a time delay to the model can generate various bifurcations such as Hopf bifurcation, fold limit cycle bifurcation, Neimark–Sacker bifurcation of cycles, and period-doubling bifurcation, etc. Increasing the time delay can induce chaos by two routes: quasi-periodic route and period-doubling cascade.
Second Hopf map and supersymmetric mechanics with Yang monopole
International Nuclear Information System (INIS)
Gonzales, M.; Toppan, F.; Kuznetsova, Z.; Nersessian, F.; Yeghikyan, V.
2009-01-01
We propose to use the second Hopf map for the reduction (via SU(2) group action) of the eight-dimensional supersymmetric mechanics to five-dimensional supersymmetric systems specified by the presence of an SU(2) Yang monopole. For our purpose we develop the relevant Lagrangian reduction procedure. The reduced system is characterized by its invariance under the N = 5 or N = 4 supersymmetry generators (with or without an additional conserved BRST charge operator) which commute with the su(2) generators. (author)
Compact quantum group C*-algebras as Hopf algebras with approximate unit
International Nuclear Information System (INIS)
Do Ngoc Diep; Phung Ho Hai; Kuku, A.O.
1999-04-01
In this paper, we construct and study the representation theory of a Hopf C*-algebra with approximate unit, which constitutes quantum analogue of a compact group C*-algebra. The construction is done by first introducing a convolution-product on an arbitrary Hopf algebra H with integral, and then constructing the L 2 and C*-envelopes of H (with the new convolution-product) when H is a compact Hopf *-algebra. (author)
International Nuclear Information System (INIS)
Kalkofen, W.
1985-01-01
The assumptions of Ayres' model of the upper solar atmosphere are examined. It is found that the bistable character of his model is postulated - through the assumptions concerning the opacity sources and the effect of mechanical waves, which are allowed to destroy the CO molecules but not to heat the gas. The neglect of cooling by metal lines is based on their reduced local cooling rate, but it ignores the increased depth over which this cooling occurs. Thus, the bifurcated model of the upper solar atmosphere consists of two models, one cold at the temperature minimum, with a kinetic temperature of 2900 K, and the other hot, with a temperature of 4900 K. 8 references
ENHANCED ELECTROCHEMICAL PROCESSES IN SUBCRITICAL WATER
Energy Technology Data Exchange (ETDEWEB)
Steven B. Hawthorne
2000-07-01
This project involved designing and performing preliminary electrochemical experiments in subcritical water. An electrochemical cell with substantially better performance characteristics than presently available was designed, built, and tested successfully. The electrochemical conductivity of subcritical water increased substantially with temperature, e.g., conductivities increased by a factor of 120 when the temperature was increased from 25 to 250 C. Cyclic voltammograms obtained with platinum and nickel demonstrated that the voltage required to produce hydrogen and oxygen from water can be dropped by a factor of three in subcritical water compared to the voltages required at ambient temperatures. However, no enhancement in the degradation of 1,2-dichlorobenzene and the polychlorinated biphenyl 3,3',4,4'-tetrachlorobiphenyl was observed with applied potential in subcritical water.
Bifurcations sights, sounds, and mathematics
Matsumoto, Takashi; Kokubu, Hiroshi; Tokunaga, Ryuji
1993-01-01
Bifurcation originally meant "splitting into two parts. " Namely, a system under goes a bifurcation when there is a qualitative change in the behavior of the sys tem. Bifurcation in the context of dynamical systems, where the time evolution of systems are involved, has been the subject of research for many scientists and engineers for the past hundred years simply because bifurcations are interesting. A very good way of understanding bifurcations would be to see them first and study theories second. Another way would be to first comprehend the basic concepts and theories and then see what they look like. In any event, it is best to both observe experiments and understand the theories of bifurcations. This book attempts to provide a general audience with both avenues toward understanding bifurcations. Specifically, (1) A variety of concrete experimental results obtained from electronic circuits are given in Chapter 1. All the circuits are very simple, which is crucial in any experiment. The circuits, howev...
Subcritical thermal convection of liquid metals in a rapidly rotating sphere
Cardin, P.; Schaeffer, N.; Guervilly, C.; Kaplan, E.
2017-12-01
Planetary cores consist of liquid metals (low Prandtl number Pr) that convect as the core cools. Here we study nonlinear convection in a rotating (low Ekman number Ek) planetary core using a fully 3D direct (down to Ek=10-7) and a quasi geostrophic (down to Ek=10-10) numerical simulations. Near the critical thermal forcing (Rayleigh number Ra), convection onsets as thermal Rossby waves, but as Ra increases, this state is superceded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are continuously connected. As the planetary core rotates faster, the continuous transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at Ekforcing decreases well below the linear onset of convection (Ra 0.4Racrit in this study for Ek=10-10 and Pr=0.01). We highlight the importance of the Reynolds stress, which is required for convection to persist below the linear onset. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective subcritical state. Our study suggests that, in the asymptotic regime of rapid rotation relevant for planetary interiors, thermal convection of liquid metals in a sphere onsets and shuts down through a subcritical bifurcation. This scenario may be relevant to explain the lunar and martian dynamo extinctions.
International Nuclear Information System (INIS)
Gritli, Hassène; Belghith, Safya
2017-01-01
Highlights: • We study the passive walking dynamics of the compass-gait model under OGY-based state-feedback control. • We analyze local bifurcations via a hybrid Poincaré map. • We show exhibition of the super(sub)-critical flip bifurcation, the saddle-node(saddle) bifurcation and a saddle-flip bifurcation. • An analysis via a two-parameter bifurcation diagram is presented. • Some new hidden attractors in the controlled passive walking dynamics are displayed. - Abstract: In our previous work, we have analyzed the passive dynamic walking of the compass-gait biped model under the OGY-based state-feedback control using the impulsive hybrid nonlinear dynamics. Such study was carried out through bifurcation diagrams. It was shown that the controlled bipedal gait exhibits attractive nonlinear phenomena such as the cyclic-fold (saddle-node) bifurcation, the period-doubling (flip) bifurcation and chaos. Moreover, we revealed that, using the controlled continuous-time dynamics, we encountered a problem in finding, identifying and hence following branches of (un)stable solutions in order to characterize local bifurcations. The present paper solves such problem and then provides a further investigation of the controlled bipedal walking dynamics using the developed analytical expression of the controlled hybrid Poincaré map. Thus, we show that analysis via such Poincaré map allows to follow branches of both stable and unstable fixed points in bifurcation diagrams and hence to explore the complete dynamics of the controlled compass-gait biped model. We demonstrate the generation, other than the conventional local bifurcations in bipedal walking, i.e. the flip bifurcation and the saddle-node bifurcation, of a saddle-saddle bifurcation, a subcritical flip bifurcation and a new type of a local bifurcation, the saddle-flip bifurcation. In addition, to further understand the occurrence of the local bifurcations, we present an analysis with a two-parameter bifurcation
Neimark-Sacker bifurcations and evidence of chaos in a discrete dynamical model of walkers
International Nuclear Information System (INIS)
Rahman, Aminur; Blackmore, Denis
2016-01-01
Bouncing droplets on a vibrating fluid bath can exhibit wave-particle behavior, such as being propelled by interacting with its own wave field. These droplets seem to walk across the bath, and thus are dubbed walkers. Experiments have shown that walkers can exhibit exotic dynamical behavior indicative of chaos. While the integro-differential models developed for these systems agree well with the experiments, they are difficult to analyze mathematically. In recent years, simpler discrete dynamical models have been derived and studied numerically. The numerical simulations of these models show evidence of exotic dynamics such as period doubling bifurcations, Neimark–Sacker (N–S) bifurcations, and even chaos. For example, in [1], based on simulations Gilet conjectured the existence of a supercritical N-S bifurcation as the damping factor in his one- dimensional path model. We prove Gilet’s conjecture and more; in fact, both supercritical and subcritical (N-S) bifurcations are produced by separately varying the damping factor and wave-particle coupling for all eigenmode shapes. Then we compare our theoretical results with some previous and new numerical simulations, and find complete qualitative agreement. Furthermore, evidence of chaos is shown by numerically studying a global bifurcation.
Riddling bifurcation and interstellar journeys
International Nuclear Information System (INIS)
Kapitaniak, Tomasz
2005-01-01
We show that riddling bifurcation which is characteristic for low-dimensional attractors embedded in higher-dimensional phase space can give physical mechanism explaining interstellar journeys described in science-fiction literature
Dynamic bifurcations on financial markets
International Nuclear Information System (INIS)
Kozłowska, M.; Denys, M.; Wiliński, M.; Link, G.; Gubiec, T.; Werner, T.R.; Kutner, R.; Struzik, Z.R.
2016-01-01
We provide evidence that catastrophic bifurcation breakdowns or transitions, preceded by early warning signs such as flickering phenomena, are present on notoriously unpredictable financial markets. For this we construct robust indicators of catastrophic dynamical slowing down and apply these to identify hallmarks of dynamical catastrophic bifurcation transitions. This is done using daily closing index records for the representative examples of financial markets of small and mid to large capitalisations experiencing a speculative bubble induced by the worldwide financial crisis of 2007-08.
International Workshop "Groups, Rings, Lie and Hopf Algebras"
2003-01-01
The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.
Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra
van den Hijligenberg, N.W.; van den Hijligenberg, N.W.; Martini, Ruud
1995-01-01
We discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra structure of
Differential Hopf algebra structures on the universal enveloping algebra ofa Lie algebra
N.W. van den Hijligenberg; R. Martini
1995-01-01
textabstractWe discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra
Differential Hopf algebra structures on the Universal Enveloping Algebra of a Lie Algebra
van den Hijligenberg, N.W.; van den Hijligenberg, N.; Martini, Ruud
1995-01-01
We discuss a method to construct a De Rham complex (differential algebra) of Poincaré–Birkhoff–Witt type on the universal enveloping algebra of a Lie algebra g. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebrastructure of U(g).
Nonlinear analysis of a closed-loop tractor-semitrailer vehicle system with time delay
Liu, Zhaoheng; Hu, Kun; Chung, Kwok-wai
2016-08-01
In this paper, a nonlinear analysis is performed on a closed-loop system of articulated heavy vehicles with driver steering control. The nonlinearity arises from the nonlinear cubic tire force model. An integration method is employed to derive an analytical periodic solution of the system in the neighbourhood of the critical speed. The results show that excellent accuracy can be achieved for the calculation of periodic solutions arising from Hopf bifurcation of the vehicle motion. A criterion is obtained for detecting the Bautin bifurcation which separates branches of supercritical and subcritical Hopf bifurcations. The integration method is compared to the incremental harmonic balance method in both supercritical and subcritical scenarios.
Cygnus Performance in Subcritical Experiments
International Nuclear Information System (INIS)
G Corrow; M Hansen; D Henderson; S Lutz; C Mitton
2008-01-01
The Cygnus Dual Beam Radiographic Facility consists of two identical radiographic sources with the following specifications: 4-rad dose at 1 m, 1-mm spot size, 50-ns pulse length, 2.25-MeV endpoint energy. The facility is located in an underground tunnel complex at the Nevada Test Site. Here SubCritical Experiments (SCEs) are performed to study the dynamic properties of plutonium. The Cygnus sources were developed as a primary diagnostic for these tests. Since SCEs are single-shot, high-value events - reliability and reproducibility are key issues. Enhanced reliability involves minimization of failure modes through design, inspection, and testing. Many unique hardware and operational features were incorporated into Cygnus to insure reliability. Enhanced reproducibility involves normalization of shot-to-shot output also through design, inspection, and testing. The first SCE to utilize Cygnus, Armando, was executed on May 25, 2004. A year later, April - May 2005, calibrations using a plutonium step wedge were performed. The results from this series were used for more precise interpretation of the Armando data. In the period February - May 2007 Cygnus was fielded on Thermos, which is a series of small-sample plutonium shots using a one-dimensional geometry. Pulsed power research generally dictates frequent change in hardware configuration. Conversely, SCE applications have typically required constant machine settings. Therefore, while operating during the past four years we have accumulated a large database for evaluation of machine performance under highly consistent operating conditions. Through analysis of this database Cygnus reliability and reproducibility on Armando, Step Wedge, and Thermos is presented
Cygnus Performance in Subcritical Experiments
Energy Technology Data Exchange (ETDEWEB)
G. Corrow, M. Hansen, D. Henderson, S. Lutz, C. Mitton, et al.
2008-02-01
The Cygnus Dual Beam Radiographic Facility consists of two identical radiographic sources with the following specifications: 4-rad dose at 1 m, 1-mm spot size, 50-ns pulse length, 2.25-MeV endpoint energy. The facility is located in an underground tunnel complex at the Nevada Test Site. Here SubCritical Experiments (SCEs) are performed to study the dynamic properties of plutonium. The Cygnus sources were developed as a primary diagnostic for these tests. Since SCEs are single-shot, high-value events - reliability and reproducibility are key issues. Enhanced reliability involves minimization of failure modes through design, inspection, and testing. Many unique hardware and operational features were incorporated into Cygnus to insure reliability. Enhanced reproducibility involves normalization of shot-to-shot output also through design, inspection, and testing. The first SCE to utilize Cygnus, Armando, was executed on May 25, 2004. A year later, April - May 2005, calibrations using a plutonium step wedge were performed. The results from this series were used for more precise interpretation of the Armando data. In the period February - May 2007 Cygnus was fielded on Thermos, which is a series of small-sample plutonium shots using a one-dimensional geometry. Pulsed power research generally dictates frequent change in hardware configuration. Conversely, SCE applications have typically required constant machine settings. Therefore, while operating during the past four years we have accumulated a large database for evaluation of machine performance under highly consistent operating conditions. Through analysis of this database Cygnus reliability and reproducibility on Armando, Step Wedge, and Thermos is presented.
Large subcriticality measurement by pulsed neutron method
International Nuclear Information System (INIS)
Yamane, Y.; Yoshida, A.; Nishina, K.; Kobayashi, K.; Kanda, K.
1985-01-01
To establish the method determining large subcriticalities in the field of nuclear criticality safety, the authors performed pulsed neutron experiments using the Kyoto University Critical Assembly (KUCA) at Research Reactor Institute, Kyoto University and the Cockcroft-Walton type accelerator attached to the assembly. The area-ratio method proposed by Sjoestrand was employed to evaluate subcriticalities from neutron decay curves measured. This method has the shortcomings that the neutron component due to a decay of delayed neutrons remarkably decreases as the subcriticality of an objective increases. To overcome the shortcoming, the authors increased the frequency of pulsed neutron generation. The integral-version of the area-ratio method proposed by Kosaly and Fisher was employed in addition in order to remove a contamination of spatial higher modes from the decay curve. The latter becomes significant as subcriticality increases. The largest subcriticality determined in the present experiments was 125.4 dollars, which was equal to 0.5111 in a multiplication factor. The calculational values evaluated by the computer code KENO-IV with 137 energy groups based on the Monte Carlo method agreed well with those experimental values
Relative Hom-Hopf modules and total integrals
Energy Technology Data Exchange (ETDEWEB)
Guo, Shuangjian [School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025 (China); Zhang, Xiaohui [Department of Mathematics, Southeast University, Nanjing 210096 (China); Wang, Shengxiang, E-mail: wangsx-math@163.com [School of Mathematics and Finance, Chuzhou University, Chuzhou 239000 (China); Department of Mathematics, Nanjing University, Nanjing 210093 (China)
2015-02-15
Let (H, α) be a monoidal Hom-Hopf algebra and (A, β) a right (H, α)-Hom-comodule algebra. We first investigate the criterion for the existence of a total integral of (A, β) in the setting of monoidal Hom-Hopf algebras. Also, we prove that there exists a total integral ϕ : (H, α) → (A, β) if and only if any representation of the pair (H, A) is injective in a functorial way, as a corepresentation of (H, α), which generalizes Doi’s result. Finally, we define a total quantum integral γ : H → Hom(H, A) and prove the following affineness criterion: if there exists a total quantum integral γ and the canonical map ψ : A⊗{sub B}A → A ⊗ H, a⊗{sub B}b ↦ β{sup −1}(a) b{sub [0]} ⊗ α(b{sub [1]}) is surjective, then the induction functor A⊗{sub B}−:ℋ{sup ~}(ℳ{sub k}){sub B}→ℋ{sup ~}(ℳ{sub k}){sub A}{sup H} is an equivalence of categories.
Rota-Baxter algebras and the Hopf algebra of renormalization
Energy Technology Data Exchange (ETDEWEB)
Ebrahimi-Fard, K.
2006-06-15
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)
CP1 model with Hopf interaction: the quantum theory
International Nuclear Information System (INIS)
Chakraborty, B.; Ghosh, Subir; Malik, R.P.
2001-01-01
The CP 1 model with Hopf interaction is quantised following the Batalin-Tyutin (BT) prescription. In this scheme, extra BT fields are introduced which allow for the existence of only commuting first-class constraints. Explicit expression for the quantum correction to the expectation value of the energy density and angular momentum in the physical sector of this model is derived. The result shows, in the particular operator ordering prescription we have chosen to work with, that the quantum effect has the usual divergent contribution of O(ℎ 2 ) in the energy expectation value. But, interestingly the Hopf term, though topological in nature, can have a finite O(ℎ) contribution to energy density in the homotopically nontrivial topological sector. The angular momentum operator, however, is found to have no quantum correction at O(ℎ), indicating the absence of any fractional spin even at this quantum level. Finally, the extended Lagrangian incorporating the BT auxiliary fields is computed in the conventional framework of BRST formalism exploiting Faddeev-Popov technique of path integral method
Rota-Baxter algebras and the Hopf algebra of renormalization
International Nuclear Information System (INIS)
Ebrahimi-Fard, K.
2006-06-01
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)
Relative Hom-Hopf modules and total integrals
International Nuclear Information System (INIS)
Guo, Shuangjian; Zhang, Xiaohui; Wang, Shengxiang
2015-01-01
Let (H, α) be a monoidal Hom-Hopf algebra and (A, β) a right (H, α)-Hom-comodule algebra. We first investigate the criterion for the existence of a total integral of (A, β) in the setting of monoidal Hom-Hopf algebras. Also, we prove that there exists a total integral ϕ : (H, α) → (A, β) if and only if any representation of the pair (H, A) is injective in a functorial way, as a corepresentation of (H, α), which generalizes Doi’s result. Finally, we define a total quantum integral γ : H → Hom(H, A) and prove the following affineness criterion: if there exists a total quantum integral γ and the canonical map ψ : A⊗ B A → A ⊗ H, a⊗ B b ↦ β −1 (a) b [0] ⊗ α(b [1] ) is surjective, then the induction functor A⊗ B −:ℋ ~ (ℳ k ) B →ℋ ~ (ℳ k ) A H is an equivalence of categories
Ensuring the validity of calculated subcritical limits
International Nuclear Information System (INIS)
Clark, H.K.
1977-01-01
The care taken at the Savannah River Laboratory and Plant to ensure the validity of calculated subcritical limits is described. Close attention is given to ANSI N16.1-1975, ''Validation of Calculational Methods for Nuclear Criticality Safety.'' The computer codes used for criticality safety computations, which are listed and are briefly described, have been placed in the SRL JOSHUA system to facilitate calculation and to reduce input errors. A driver module, KOKO, simplifies and standardizes input and links the codes together in various ways. For any criticality safety evaluation, correlations of the calculational methods are made with experiment to establish bias. Occasionally subcritical experiments are performed expressly to provide benchmarks. Calculated subcritical limits contain an adequate but not excessive margin to allow for uncertainty in the bias. The final step in any criticality safety evaluation is the writing of a report describing the calculations and justifying the margin
Steyn-Ross, Moira L.; Steyn-Ross, D. A.; Sleigh, J. W.
2013-04-01
Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the
Directory of Open Access Journals (Sweden)
Moira L. Steyn-Ross
2013-05-01
Full Text Available Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1 Hz similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial symmetry-breaking bifurcation that is modulated by a Hopf (temporal instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural
Dynamical Regimes and the Dynamo Bifurcation in Geodynamo Simulations
Petitdemange, L.
2017-12-01
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core : in a rotating spherical shell with thermally driven motions with no-slip boundaries. Unlike previous studies on dynamo bifurcations, the control parameters have been varied significantly in order to deduce general tendencies. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing dipole-dominated dynamos and the reversing non-dipole-dominated multipolar solutions. We show that, by considering weak initial fields, the above transition is replaced by a region of bistability for which dipolar and multipolar dynamos coexist. Such a result was also observed in models with free-slip boundaries in which the strong shear of geostrophic zonal flows can develop and gives rise to non-dipolar fields. We show that a similar process develops in no-slip models when viscous effects are reduced sufficiently.Close to the onset of convection (Rac), the axial dipole grows exponentially in the kinematic phase and saturation occurs by marginally changing the flow structure close to the dynamo threshold Rmc. The resulting bifurcation is then supercritical.In the range 3RacIf (Ra/Ra_c>10), important zonal flows develop in non-magnetic models with low viscosity. The field topology depends on the initial magnetic field. The dipolar branch has a subcritical behaviour whereas the multipolar branch is supercritical. By approaching more realistic parameters, the extension of this bistable regime increases (lower Rossby numbers). An hysteretic behaviour questions the common interpretation for geomagnetic reversals. Far above Rm_c$, the Lorentz force becomes dominant, as it is expected in planetary cores.
Modeling of Parameters of Subcritical Assembly SAD
Petrochenkov, S; Puzynin, I
2005-01-01
The accepted conceptual design of the experimental Subcritical Assembly in Dubna (SAD) is based on the MOX core with a nominal unit capacity of 25 kW (thermal). This corresponds to the multiplication coefficient $k_{\\rm eff} =0.95$ and accelerator beam power 1 kW. A subcritical assembly driven with the existing 660 MeV proton accelerator at the Joint Institute for Nuclear Research has been modelled in order to make choice of the optimal parameters for the future experiments. The Monte Carlo method was used to simulate neutron spectra, energy deposition and doses calculations. Some of the calculation results are presented in the paper.
Continuous reactivity calculation for subcritical system
International Nuclear Information System (INIS)
Silva, Cristiano; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. da
2011-01-01
With the rise of a new generation of nuclear reactors as for existence the ADS (Accelerator-Driven System), it is important to have a fast and accurate prediction of the variation in reactivity during a possible variation in the intensity of external sources. This paper presents a formulation for the calculation of reactivity in subcritical systems using the inverse method related only to nuclear power derivatives. One of the applications of the proposed method is the possibility of developing reactimeters that allow the continuous monitoring of subcritical systems. (author)
Continuous reactivity calculation for subcritical system
Energy Technology Data Exchange (ETDEWEB)
Silva, Cristiano; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. da, E-mail: cristiano@herzeleid.net, E-mail: aquilino@lmp.ufrj.br, E-mail: fernando@con.ufrj.br [Coordenacao dos Programas de Pos-Graduacao em Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear; Palma, Daniel A.P., E-mail: dapalma@cnen.gov.br [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil)
2011-07-01
With the rise of a new generation of nuclear reactors as for existence the ADS (Accelerator-Driven System), it is important to have a fast and accurate prediction of the variation in reactivity during a possible variation in the intensity of external sources. This paper presents a formulation for the calculation of reactivity in subcritical systems using the inverse method related only to nuclear power derivatives. One of the applications of the proposed method is the possibility of developing reactimeters that allow the continuous monitoring of subcritical systems. (author)
Subcritical calculation of the nuclear material warehouse
International Nuclear Information System (INIS)
Garcia M, T.; Mazon R, R.
2009-01-01
In this work the subcritical calculation of the nuclear material warehouse of the Reactor TRIGA Mark III labyrinth in the Mexico Nuclear Center is presented. During the adaptation of the nuclear warehouse (vault I), the fuel was temporarily changed to the warehouse (vault II) and it was also carried out the subcritical calculation for this temporary arrangement. The code used for the calculation of the effective multiplication factor, it was the Monte Carlo N-Particle Extended code known as MCNPX, developed by the National Laboratory of Los Alamos, for the particles transport. (Author)
Neutron chain length distributions in subcritical systems
International Nuclear Information System (INIS)
Nolen, S.D.; Spriggs, G.
1999-01-01
In this paper, the authors present the results of the chain-length distribution as a function of k in subcritical systems. These results were obtained from a point Monte Carlo code and a three-dimensional Monte Carlo code, MC++. Based on these results, they then attempt to explain why several of the common neutron noise techniques, such as the Rossi-α and Feynman's variance-to-mean techniques, are difficult to perform in highly subcritical systems using low-efficiency detectors
Quantitative angiography methods for bifurcation lesions
DEFF Research Database (Denmark)
Collet, Carlos; Onuma, Yoshinobu; Cavalcante, Rafael
2017-01-01
Bifurcation lesions represent one of the most challenging lesion subsets in interventional cardiology. The European Bifurcation Club (EBC) is an academic consortium whose goal has been to assess and recommend the appropriate strategies to manage bifurcation lesions. The quantitative coronary...... angiography (QCA) methods for the evaluation of bifurcation lesions have been subject to extensive research. Single-vessel QCA has been shown to be inaccurate for the assessment of bifurcation lesion dimensions. For this reason, dedicated bifurcation software has been developed and validated. These software...
International Nuclear Information System (INIS)
Zhu, Zhi-Wen; Zhang, Qing-Xin; Xu, Jia
2014-01-01
A kind of shape memory alloy (SMA) hysteretic nonlinear model was developed, and the nonlinear dynamics and bifurcation characteristics of the SMA thin film subjected to in-plane stochastic excitation were investigated. Van der Pol difference item was introduced to describe the hysteretic phenomena of the SMA strain–stress curves, and the nonlinear dynamic model of the SMA thin film subjected to in-plane stochastic excitation was developed. The conditions of global stochastic stability of the system were determined in singular boundary theory, and the probability density function of the system response was obtained. Finally, the conditions of stochastic Hopf bifurcation were analyzed. The results of theoretical analysis and numerical simulation indicate that self-excited vibration is induced by the hysteretic nonlinear characteristics of SMA, and stochastic Hopf bifurcation appears when the bifurcation parameter was changed; there are two limit cycles in the stationary probability density of the dynamic response of the system in some cases, which means that there are two vibration amplitudes whose probabilities are both very high, and jumping phenomena between the two vibration amplitudes appear with the change in conditions. The results obtained in this current paper are helpful for the application of the SMA thin film in stochastic vibration fields. - Highlights: • Hysteretic nonlinear model of shape memory alloy was developed. • Van der Pol item was introduced to interpret hysteretic strain–stress curves. • Nonlinear dynamic characteristics of the shape memory alloy film were analyzed. • Jumping phenomena were observed in the change of the parameters
Pierce instability and bifurcating equilibria
International Nuclear Information System (INIS)
Godfrey, B.B.
1981-01-01
The report investigates the connection between equilibrium bifurcations and occurrence of the Pierce instability. Electrons flowing from one ground plane to a second through an ion background possess a countable infinity of static equilibria, of which only one is uniform and force-free. Degeneracy of the uniform and simplest non-uniform equilibria at a certain ground plan separation marks the onset of the Pierce instability, based on a newly derived dispersion relation appropriate to all the equilibria. For large ground plane separations the uniform equilibrium is unstable and the non-uniform equilibrium is stable, the reverse of their stability properties at small separations. Onset of the Pierce instability at the first bifurcation of equilibria persists in more complicated geometries, providing a general criterion for marginal stability. It seems probable that bifurcation analysis can be a useful tool in the overall study of stable beam generation in diodes and transport in finite cavities
Budzinskiy, S. S.; Razgulin, A. V.
2017-08-01
In this paper we study one-dimensional rotating and standing waves in a model of an O(2)-symmetric nonlinear optical system with diffraction and delay in the feedback loop whose dynamics is governed by a system of coupled delayed parabolic equation and linear Schrodinger-type equation. We elaborate a two-step approach: transition to a rotating coordinate system to obtain the profiles of the waves as small parameter expansions and the normal form technique to study their qualitative dynamic behavior and stability. Theoretical results stand in a good agreement with direct computer simulations presented.
Shalashov, A. G.; Gospodchikov, E. D.; Izotov, I. V.; Mansfeld, D. A.; Skalyga, V. A.; Tarvainen, O.
2018-04-01
We report the first experimental evidence of a controlled transition from the generation of periodic bursts of electromagnetic radiation into the continuous-wave regime of a cyclotron maser formed in magnetically confined nonequilibrium plasma. The kinetic cyclotron instability of the extraordinary wave of weakly inhomogeneous magnetized plasma is driven by the anisotropic electron population resulting from electron cyclotron plasma heating in a MHD-stable minimum-B open magnetic trap.
Bifurcation of Lane Change and Control on Highway for Tractor-Semitrailer under Rainy Weather
Directory of Open Access Journals (Sweden)
Tao Peng
2017-01-01
Full Text Available A new method is proposed for analyzing the nonlinear dynamics and stability in lane changes on highways for tractor-semitrailer under rainy weather. Unlike most of the literature associated with a simulated linear dynamic model for tractor-semitrailers steady steering on dry road, a verified 5DOF mechanical model with nonlinear tire based on vehicle test was used in the lane change simulation on low adhesion coefficient road. According to Jacobian matrix eigenvalues of the vehicle model, bifurcations of steady steering and sinusoidal steering on highways under rainy weather were investigated using a numerical method. Furthermore, based on feedback linearization theory, taking the tractor yaw rate and joint angle as control objects, a feedback linearization controller combined with AFS and DYC was established. The numerical simulation results reveal that Hopf bifurcations are identified in steady and sinusoidal steering conditions, which translate into an oscillatory behavior leading to instability. And simulations of urgent step and single-lane change in high velocity show that the designed controller has good effects on eliminating bifurcations and improving lateral stability of tractor-semitrailer, during lane changing on highway under rainy weather. It is a valuable reference for safety design of tractor-semitrailers to improve the traffic safety with driver-vehicle-road closed-loop system.
A Geometric Problem and the Hopf Lemma. Ⅱ
Institute of Scientific and Technical Information of China (English)
YanYan LI; Louis NIRENBERG
2006-01-01
A classical result of A. D. Alexandrov states that a connected compact smooth n-dimensional manifold without boundary, embedded in Rn+1, and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of M in a hyperplane Xn+1 =constant in case M satisfies: for any two points (X′, Xn+1), (X′, ^Xn+1)on M, with Xn+1 ＞ ^Hn+1, the mean curvature at the first is not greater than that at the second. Symmetry need not always hold, but in this paper, we establish it under some additional conditions. Some variations of the Hopf Lemma are also presented. Several open problems are described. Part Ⅰ dealt with corresponding one dimensional problems.
From Quantum Mechanics to Quantum Field Theory: The Hopf route
Energy Technology Data Exchange (ETDEWEB)
Solomon, A I [Physics and Astronomy Department, Open University, Milton Keynes MK7 6AA (United Kingdom); Duchamp, G H E [Institut Galilee, LIPN, CNRS UMR 7030 99 Av. J.-B. Clement, F-93430 Villetaneuse (France); Blasiak, P; Horzela, A [H. Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Division of Theoretical Physics, ul. Eliasza-Radzikowskiego 152, PL 31-342 Krakow (Poland); Penson, K A, E-mail: a.i.solomon@open.ac.uk, E-mail: gduchamp2@free.fr, E-mail: pawel.blasiak@ifj.edu.pl, E-mail: andrzej.horzela@ifj.edu.pl, E-mail: penson@lptl.jussieu.fr [Lab.de Phys.Theor. de la Matiere Condensee, University of Paris VI (France)
2011-03-01
We show that the combinatorial numbers known as Bell numbers are generic in quantum physics. This is because they arise in the procedure known as Normal ordering of bosons, a procedure which is involved in the evaluation of quantum functions such as the canonical partition function of quantum statistical physics, inter alia. In fact, we shall show that an evaluation of the non-interacting partition function for a single boson system is identical to integrating the exponential generating function of the Bell numbers, which is a device for encapsulating a combinatorial sequence in a single function. We then introduce a remarkable equality, the Dobinski relation, and use it to indicate why renormalisation is necessary in even the simplest of perturbation expansions for a partition function. Finally we introduce a global algebraic description of this simple model, giving a Hopf algebra, which provides a starting point for extensions to more complex physical systems.
Homoclinic bifurcation in Chua's circuit
Indian Academy of Sciences (India)
spiking and bursting behaviors of neurons. Recent experiments ... a limit cycle increases in a wiggle with alternate sequences of stable and unstable orbits via ... further changes in parameter, the system shows period-adding bifurcation when .... [21–23] transition from limit cycle to single scroll chaos via PD and then to alter-.
Bifurcation of steady tearing states
International Nuclear Information System (INIS)
Saramito, B.; Maschke, E.K.
1985-10-01
We apply the bifurcation theory for compact operators to the problem of the nonlinear solutions of the 3-dimensional incompressible visco-resistive MHD equations. For the plane plasma slab model we compute branches of nonlinear tearing modes, which are stationary for the range of parameters investigated up to now
International Nuclear Information System (INIS)
Zhu, Zhiwen; Zhang, Qingxin; Xu, Jia
2014-01-01
Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film–shape memory alloy (GMF–SMA) composite cantilever plate subjected to in-plane harmonic and stochastic excitation were studied. Van der Pol items were improved to interpret the hysteretic phenomena of both GMF and SMA, and the nonlinear dynamic model of a GMF–SMA composite cantilever plate subjected to in-plane harmonic and stochastic excitation was developed. The probability density function of the dynamic response of the system was obtained, and the conditions of stochastic Hopf bifurcation were analyzed. The conditions of noise-induced chaotic response were obtained in the stochastic Melnikov integral method, and the fractal boundary of the safe basin of the system was provided. Finally, the chaos control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that stochastic Hopf bifurcation and chaos appear in the parameter variation process. The boundary of the safe basin of the system has fractal characteristics, and its area decreases when the noise intensifies. The system reliability was improved through stochastic optimal control, and the safe basin area of the system increased
Bifurcation in a buoyant horizontal laminar jet
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.
Wiener-Hopf operators on spaces of functions on R+ with values in a Hilbert space
Petkova, Violeta
2006-01-01
A Wiener-Hopf operator on a Banach space of functions on R+ is a bounded operator T such that P^+S_{-a}TS_a=T, for every positive a, where S_a is the operator of translation by a. We obtain a representation theorem for the Wiener-Hopf operators on a large class of functions on R+ with values in a separable Hilbert space.
The Hopf algebra structure of the character rings of classical groups
International Nuclear Information System (INIS)
Fauser, Bertfried; Jarvis, Peter D; King, Ronald C
2013-01-01
The character ring Char-GL of covariant irreducible tensor representations of the general linear group admits a Hopf algebra structure isomorphic to the Hopf algebra Symm-Λ of symmetric functions. Here we study the character rings Char-O and Char-Sp of the orthogonal and symplectic subgroups of the general linear group within the same framework of symmetric functions. We show that Char-O and Char-Sp also admit natural Hopf algebra structures that are isomorphic to that of Char-GL, and hence to Symm-Λ. The isomorphisms are determined explicitly, along with the specification of standard bases for Char-O and Char-Sp analogous to those used for Symm-Λ. A major structural change arising from the adoption of these bases is the introduction of new orthogonal and symplectic Schur–Hall scalar products. Significantly, the adjoint with respect to multiplication no longer coincides, as it does in the Char-GL case, with a Foulkes derivative or skew operation. The adjoint and Foulkes derivative now require separate definitions, and their properties are explored here in the orthogonal and symplectic cases. Moreover, the Hopf algebras Char-O and Char-Sp are not self-dual. The dual Hopf algebras Char-O * and Char-Sp are identified. Finally, the Hopf algebra of the universal rational character ring Char-GLrat of mixed irreducible tensor representations of the general linear group is introduced and its structure maps identified. (paper)
Subcritical thermal convection of liquid metals in a rotating sphere using a quasi-geostrophic model
Cardin, P.; Guervilly, C.
2016-12-01
We study non-linear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals (10-2-1). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than 10-6, which is continuous at the onset (supercritical bifurcation) and consists of the interaction of thermal Rossby waves, and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of 10-8. On the strong branch, the Reynolds number of the flow is greater than 1000, and a strong zonal flow with multiple jets develops, even close to the non-linear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis (E = 10-6, Pr =10-2). Non-linear oscillations are observed near the onset of convection for E = 10-7 and Pr = 10-1.
Subcritical convection of liquid metals in a rotating sphere using a quasi-geostrophic model
Guervilly, Céline; Cardin, Philippe
2016-12-01
We study nonlinear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals ($Pr\\in[10^{-2},10^{-1}]$). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than $10^{-6}$, which is continuous at the onset (supercritical bifurcation) and consists of thermal Rossby waves, and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of $10^{-8}$. On the strong branch, the Reynolds number of the flow is greater than $10^3$, and a strong zonal flow with multiple jets develops, even close to the nonlinear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis ($Ek=10^{-6}$, $Pr=10^{-2}$). Nonlinear oscillations are observed near the onset of convection for $Ek=10^{-7}$ and $Pr=10^{-1}$.
Subcritical limits for special fissile actinides
International Nuclear Information System (INIS)
Clark, H.K.
1980-01-01
Critical masses and subcritical mass limits in oxide-water mixtures were calculated for actinide nuclides other than /sup 233/U, /sup 235/U, and /sup 239/Pu that have an odd number of neutrons in the nucleus; S/sub n/ transport theory was used together with cross sections, drawn from the GLASS multigroup library, developed to provide accurate forecasts of actinide production at Savannah River
Bifurcations of Fibonacci generating functions
Energy Technology Data Exchange (ETDEWEB)
Ozer, Mehmet [Istanbul Kultur University, E5 Karayolu Uzeri Sirinevler, 34191 Istanbul (Turkey) and Semiconductor Physics Institute, LT-01108 and Vilnius Gediminas Technical University, Sauletekio 11, LT-10223 (Lithuania)]. E-mail: m.ozer@iku.edu.tr; Cenys, Antanas [Semiconductor Physics Institute, LT-01108 and Vilnius Gediminas Technical University, Sauletekio 11, LT-10223 (Lithuania); Polatoglu, Yasar [Istanbul Kultur University, E5 Karayolu Uzeri Sirinevler, 34191 Istanbul (Turkey); Hacibekiroglu, Guersel [Istanbul Kultur University, E5 Karayolu Uzeri Sirinevler, 34191 Istanbul (Turkey); Akat, Ercument [Yeditepe University, 26 Agustos Campus Kayisdagi Street, Kayisdagi 81120, Istanbul (Turkey); Valaristos, A. [Aristotle University of Thessaloniki, GR-54124, Thessaloniki (Greece); Anagnostopoulos, A.N. [Aristotle University of Thessaloniki, GR-54124, Thessaloniki (Greece)
2007-08-15
In this work the dynamic behaviour of the one-dimensional family of maps F{sub p,q}(x) = 1/(1 - px - qx {sup 2}) is examined, for specific values of the control parameters p and q. Lyapunov exponents and bifurcation diagrams are numerically calculated. Consequently, a transition from periodic to chaotic regions is observed at values of p and q, where the related maps correspond to Fibonacci generating functions associated with the golden-, the silver- and the bronze mean.
Bifurcations of Fibonacci generating functions
International Nuclear Information System (INIS)
Ozer, Mehmet; Cenys, Antanas; Polatoglu, Yasar; Hacibekiroglu, Guersel; Akat, Ercument; Valaristos, A.; Anagnostopoulos, A.N.
2007-01-01
In this work the dynamic behaviour of the one-dimensional family of maps F p,q (x) = 1/(1 - px - qx 2 ) is examined, for specific values of the control parameters p and q. Lyapunov exponents and bifurcation diagrams are numerically calculated. Consequently, a transition from periodic to chaotic regions is observed at values of p and q, where the related maps correspond to Fibonacci generating functions associated with the golden-, the silver- and the bronze mean
Deep subcritical levels measurements dependents upon kinetic distortion factors
International Nuclear Information System (INIS)
Pan Shibiao; Li Xiang; Fu Guo'en; Huang Liyuan; Mu Keliang
2013-01-01
The measurement of deep subcritical levels, with the increase of subcriticality, showed that the results impact on the kinetic distortion effect, along with neutron flux strongly deteriorated. Using the diffusion theory, calculations have been carried out to quantify the kinetic distortion correction factors in subcritical systems, and these indicate that epithermal neutron distributions are strongly affected by kinetic distortion. Subcriticality measurements in four different rod-state combination at the zero power device was carried out. The test data analysis shows that, with increasing subcriticality, kinetic distortion effect correction factor gradually increases from 1.052 to 1.065, corresponding reactive correction amount of 0.78β eff ∼ 3.01β eff . Thus, it is necessary to consider the kinetic distortion effect in the deep subcritical reactivity measurements. (authors)
Volume-preserving normal forms of Hopf-zero singularity
International Nuclear Information System (INIS)
Gazor, Majid; Mokhtari, Fahimeh
2013-01-01
A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a nonzero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any nondegenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified Rössler and generalized Kuramoto–Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple. (paper)
Volume-preserving normal forms of Hopf-zero singularity
Gazor, Majid; Mokhtari, Fahimeh
2013-10-01
A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a nonzero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any nondegenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified Rössler and generalized Kuramoto-Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple.
Design project of fast subcritical system 'Mala Lasta'
International Nuclear Information System (INIS)
Milosevic, M.; Stefanovic, D.; Popovic, D.; Pesic, M.; Zavaljevski, N.; Nikolic, D.; Arsenovic, M.
1988-10-01
This report contains two parts. Part one covers the objective and fundamental elements for the choice of fast subcritical system 'Mala Lasta', review of the existing fast subcritical assemblies, and a description of the available domestic computer codes applied for calculating neutron reactor parameters. Comparison of results obtained by these codes for a number of existing subcritical assemblies was used for the choice of the design project described in part two of this report. It contains detailed description of the operating parameters of the chosen subcritical system based on the obtained calculated parameters
Bifurcations in the response of a flexible rotor in squeeze-film dampers with retainer springs
International Nuclear Information System (INIS)
Inayat-Hussain, Jawaid I.
2009-01-01
Squeeze-film dampers are commonly used in conjunction with rolling-element or hydrodynamic bearings in rotating machinery. Although these dampers serve to provide additional damping to the rotor-bearing system, there have however been some cases of rotors mounted in these dampers exhibiting non-linear behaviour. In this paper a numerical study is undertaken to determine the effects of design parameters, i.e., gravity parameter, W, mass ratio, α, and stiffness ratio, K, on the bifurcations in the response of a flexible rotor mounted in squeeze-film dampers with retainer springs. The numerical simulations were undertaken for a range of speed parameter, Ω, between 0.1 and 5.0. Numerical results showed that increasing K causes the onset speed of bifurcation to increase, whilst an increase of α reduces the onset speed of bifurcation. For a specific combination of K and α values, the onset speed of bifurcation appeared to be independent of W. The instability of the rotor response at this onset speed was due to a saddle-node bifurcation for all the parameter values investigated in this work with the exception of the combination of α = 0.1 and K = 0.5, where a secondary Hopf bifurcation was observed. The speed range of non-synchronous response was seen to decrease with the increase of α; in fact non-synchronous rotor response was totally absent for α=0.4. With the exception of the case α = 0.1, the speed range of non-synchronous response was also seen to decrease with the increase of K. Multiple responses of the rotor were observed at certain values of Ω for various combinations of parameters W, α and K, where, depending on the values of the initial conditions the rotor response could be either synchronous or quasi-periodic. The numerical results presented in this work were obtained for an unbalance parameter, U, value of 0.1, which is considered as the upper end of the normal unbalance range of most practical rotor systems. These results provide some insights
Resonant Homoclinic Flips Bifurcation in Principal Eigendirections
Directory of Open Access Journals (Sweden)
Tiansi Zhang
2013-01-01
Full Text Available A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the Poincaré return map and the bifurcation equation. A detailed investigation produces the number and the existence of 1-homoclinic orbit, 1-periodic orbit, and double 1-periodic orbits. We also locate their bifurcation surfaces in certain regions.
Baird, Bill
1986-08-01
A neural network model describing pattern recognition in the rabbit olfactory bulb is analysed to explain the changes in neural activity observed experimentally during classical Pavlovian conditioning. EEG activity recorded from an 8×8 arry of 64 electrodes directly on the surface on the bulb shows distinct spatial patterns of oscillation that correspond to the animal's recognition of different conditioned odors and change with conditioning to new odors. The model may be considered a variant of Hopfield's model of continuous analog neural dynamics. Excitatory and inhibitory cell types in the bulb and the anatomical architecture of their connection requires a nonsymmetric coupling matrix. As the mean input level rises during each breath of the animal, the system bifurcates from homogenous equilibrium to a spatially patterned oscillation. The theory of multiple Hopf bifurcations is employed to find coupled equations for the amplitudes of these unstable oscillatory modes independent of frequency. This allows a view of stored periodic attractors as fixed points of a gradient vector field and thereby recovers the more familiar dynamical systems picture of associative memory.
Superfluid helium at subcritical active core
International Nuclear Information System (INIS)
Vasil'ev, V.V.; Lopatkin, A.V.; Muratov, V.G.; Rakhno, I.L.
2002-01-01
Power range and neutron flux wherein super thermal source was realized at high volume of superfluid helium were investigated. MCU, BRAND, MCNP codes were used for the calculation of reactors. It is shown that the availability of full-size diameter for cryogenic source of ultracold neutrons, as the source with superfluid helium is considered, is possible in the reflector of subcritical assembly. Results obtained from the MCNP-4B code application demonstrated that the density of thermal neutron flux in helium must be not higher than 2.3 x 10 11 s -1 cm -2 [ru
Hydrolysis of corn oil using subcritical water
Directory of Open Access Journals (Sweden)
Pinto Jair Sebastião S.
2006-01-01
Full Text Available This work presents the results of a study on the use of subcritical water as both solvent and reactant for the hydrolysis of corn oil without the use of acids or alkalis at temperatures of 150-280 degreesC. Corn oil hydrolysis leads to the formation of its respective fatty acids with the same efficiency of conventional methods. Fatty acids form an important group of products, which are used in a range of applications. The confirmation and identification of the hydrolysis products was done by HT-HRGC-FID and HRGC/MS.
Some neutronics of innovative subcritical assembly with fast neutron spectrum
International Nuclear Information System (INIS)
Kiyavitskaya, H.; Fokov, Yu.; Rutkovskaya, Ch.; Sadovich, S.; Kasuk, D.; Gohar, Y.; Bolshinsky, I.
2013-01-01
Conclusion: • New assembly can be used to: • develop the experimental techniques and adapt the existing ones for monitoring the sub-criticality level, neutron spectra measurements, etc; • study the spatial kinetics of sub-critical and critical systems with fast neutron spectra; • measure the transmutation reaction rates of minor-actinides etc
Choosing the optimal parameters of subcritical reactors driven by accelerators
International Nuclear Information System (INIS)
Khudaverdyan, A.G.; Zhamkochyan, V.M.
1998-03-01
Physical aspects of a subcritical Nuclear Power Plants (NPP) driven by proton accelerators are considered. Estimated theoretical calculations are made for subcritical regimes of various types of reactors. It was shown that the creation of the quite effective explosion-safe NPP is real at an existing level of the accelerator technique by using available reactor units (including the serial ones). (author)
International Nuclear Information System (INIS)
Ji, J.C.; Zhang, N.
2009-01-01
Non-resonant bifurcations of codimension two may appear in the controlled van der Pol-Duffing oscillator when two critical time delays corresponding to a double Hopf bifurcation have the same value. With the aid of centre manifold theorem and the method of multiple scales, the non-resonant response and two types of primary resonances of the forced van der Pol-Duffing oscillator at non-resonant bifurcations of codimension two are investigated by studying the possible solutions and their stability of the four-dimensional ordinary differential equations on the centre manifold. It is shown that the non-resonant response of the forced oscillator may exhibit quasi-periodic motions on a two- or three-dimensional (2D or 3D) torus. The primary resonant responses admit single and mixed solutions and may exhibit periodic motions or quasi-periodic motions on a 2D torus. Illustrative examples are presented to interpret the dynamics of the controlled system in terms of two dummy unfolding parameters and exemplify the periodic and quasi-periodic motions. The analytical predictions are found to be in good agreement with the results of numerical integration of the original delay differential equation.
Integrable N dimensional systems on the Hopf algebra and q deformations
International Nuclear Information System (INIS)
Lisitsyn, Ya.V.; Shapovalov, A.V.
2000-01-01
The class of integrable classic and quantum systems on the Hopf algebra, describing the n of interacting particles, is plotted. The general structure of the integrable Hamiltonian system for the Hopf algebra A(g) of the Lee simple algebra g is obtained, wherefrom it follows, that motion integrals depend on the linear combinations k of the phase space coordinates. The q-deformation standard procedure is carried out and the corresponding integrable system is obtained. The general scheme is illustrated by the examples of the sl(2), sl(3) and o(3, 1) algebras. The exact solution is achieved for the N-dimensional Hamiltonian system quantum analog on the Hopf algebra A (sl(2)) through the method of noncommutative integration of linear differential equations [ru
Steady squares and hexagons on a subcritical ramp
International Nuclear Information System (INIS)
Hoyle, R.B.
1995-01-01
Steady squares and hexagons on a subcritical ramp are studied, both analytically and numerically, within the framework of the lowest-order amplitude equations. On the subcritical ramp, the external stress or control parameter varies continuously in space from subcritical to supercritical values. At the subcritical end of the ramp, pattern formation is suppressed, and patterns fade away into the conduction solution. It is shown that three-dimensional patterns may change shape on a subcritical ramp. A square pattern becomes a pattern of rolls as it fades, with the roll axes aligned in the direction orthogonal to that in which the control parameter varies. Hexagons in systems with horizontal midplane symmetry become a pattern of rectangles before reaching the conduction solution. There is a suggestion that hexagons in systems which lack this symmetry might fade away through a roll pattern. Numerical simulations are used to illustrate these phenomena
La factorización de una transformada de Fourier en el método de Wiener-Hopf
Directory of Open Access Journals (Sweden)
José Rosales-Ortega
2009-02-01
Full Text Available Using the Wiener-Hopf method, we factorize the Fourier Transform of the kernel of a singular integral equation as the product of two functions: one holomorphic in the upper semiplan and the other holomophic in the lower semiplan. Keywords: function product, Fourier transform, Wiener-Hopf method.
La factorización de una transformada de Fourier en el método de Wiener-Hopf
José Rosales-Ortega; Carlos Márquez Rivera
2009-01-01
Using the Wiener-Hopf method, we factorize the Fourier Transform of the kernel of a singular integral equation as the product of two functions: one holomorphic in the upper semiplan and the other holomophic in the lower semiplan. Keywords: function product, Fourier transform, Wiener-Hopf method.
Subcritical limits for special fissile actinides
International Nuclear Information System (INIS)
Clark, H.K.
1980-01-01
Critical masses and subcritical mass limits in oxide-water mixtures were calculated for actinide nuclides other than 233 U, 235 U, and 239 Pu that have an odd number of neutrons in the nucleus: S/sub n/ transport theory was used together with cross sections, drawn from the GLASS multigroup library, developed to provide accurate forecasts of actinide production at Savannah River. The subcritical limits are 201 g for 241 Pu, 13 g for 242 /sup m/Am, 90 g for 243 Cm, 30 g for 245 Cm, 900 g for 247 Cm, 10 g for 249 Cf, and 5 g for 251 Cf. Association of 241 Pu with an equal mass of 240 Pu increases the 241 Pu limit to a value greater than that for pure 239 Pu. Association of 242 /sup m/Am with 241 Am increases the limit for the mixture to that for dry, theoretical density AmO 2 at isotopic concentrations of 242 /sup m/Am less than approx. 6%. Association of 245 Cm with 244 Cm increases the limit according to the formula 30 + 0.3 244 Cm/ 245 Cm up to the limit for dry CmO 2 . A limiting mass of 8.15 kg for plutonium containing at least 67% 238 Pu as oxide was calculated that applies (provided 240 Pu exceeds 241 Pu) with no limit on moderation. 1 figure, 5 tables
Criticality Analysis of SAMOP Subcritical Assembly
International Nuclear Information System (INIS)
Tegas-Sutondo; Syarip; Triwulan-Tjiptono
2005-01-01
A critically analysis has been performed for homogenous system of uranyl nitrate solution, as part of a preliminary design assessment on neutronic aspect of SAMOP sub-critical assembly. The analysis is intended to determine some critical parameters such as the minimum of critical dimension and critical mass for the desired concentration. As the basis of this analysis, it has been defined a fuel system with an enrichment of 20% for cylindrical geometry of both bare and graphite reflected of 30 cm thickness. The MCNP code has been utilized for this purpose, for variation of concentrations ranging from 150 g/l to 500 g/l. It is found that the best concentration giving the minimum geometrical dimension is around 400 g/l, for both the bare and reflected systems. Whilst the best one, of minimum critical mass is corresponding to the concentration of around 200 g/l with critical mass around 14.1 kg and 4.2 kg for the bare and reflected systems respectively. Based on the result of calculations, it is concluded that by taking into consideration of the critical limit, the SAMOP subcritical assembly is neutronically can be made. (author)
Bifurcations of optimal vector fields: an overview
Kiseleva, T.; Wagener, F.; Rodellar, J.; Reithmeier, E.
2009-01-01
We develop a bifurcation theory for the solution structure of infinite horizon optimal control problems with one state variable. It turns out that qualitative changes of this structure are connected to local and global bifurcations in the state-costate system. We apply the theory to investigate an
A nonlinear deformed su(2) algebra with a two-color quasitriangular Hopf structure
International Nuclear Information System (INIS)
Bonatsos, D.; Daskaloyannis, C.; Kolokotronis, P.; Ludu, A.; Quesne, C.
1997-01-01
Nonlinear deformations of the enveloping algebra of su(2), involving two arbitrary functions of J 0 and generalizing the Witten algebra, were introduced some time ago by Delbecq and Quesne. In the present paper, the problem of endowing some of them with a Hopf algebraic structure is addressed by studying in detail a specific example, referred to as scr(A) q + (1). This algebra is shown to possess two series of (N+1)-dimensional unitary irreducible representations, where N=0,1,2,hor-ellipsis. To allow the coupling of any two such representations, a generalization of the standard Hopf axioms is proposed by proceeding in two steps. In the first one, a variant and extension of the deforming functional technique is introduced: variant because a map between two deformed algebras, su q (2) and scr(A) q + (1), is considered instead of a map between a Lie algebra and a deformed one, and extension because use is made of a two-valued functional, whose inverse is singular. As a result, the Hopf structure of su q (2) is carried over to scr(A) q + (1), thereby endowing the latter with a double Hopf structure. In the second step, the definition of the coproduct, counit, antipode, and scr(R)-matrix is extended so that the double Hopf algebra is enlarged into a new algebraic structure. The latter is referred to as a two-color quasitriangular Hopf algebra because the corresponding scr(R)-matrix is a solution of the colored Yang endash Baxter equation, where the open-quotes colorclose quotes parameters take two discrete values associated with the two series of finite-dimensional representations. copyright 1997 American Institute of Physics
Voltage stability, bifurcation parameters and continuation methods
Energy Technology Data Exchange (ETDEWEB)
Alvarado, F L [Wisconsin Univ., Madison, WI (United States)
1994-12-31
This paper considers the importance of the choice of bifurcation parameter in the determination of the voltage stability limit and the maximum power load ability of a system. When the bifurcation parameter is power demand, the two limits are equivalent. However, when other types of load models and bifurcation parameters are considered, the two concepts differ. The continuation method is considered as a method for determination of voltage stability margins. Three variants of the continuation method are described: the continuation parameter is the bifurcation parameter the continuation parameter is initially the bifurcation parameter, but is free to change, and the continuation parameter is a new `arc length` parameter. Implementations of voltage stability software using continuation methods are described. (author) 23 refs., 9 figs.
On left Hopf algebras within the framework of inhomogeneous quantum groups for particle algebras
Energy Technology Data Exchange (ETDEWEB)
Rodriguez-Romo, Suemi [Facultad de Estudios Superiores Cuautitlan, Universidad Nacional Autonoma de Mexico (Mexico)
2012-10-15
We deal with some matters needed to construct concrete left Hopf algebras for inhomogeneous quantum groups produced as noncommutative symmetries of fermionic and bosonic creation/annihilation operators. We find a map for the bidimensional fermionic case, produced as in Manin's [Quantum Groups and Non-commutative Hopf Geometry (CRM Univ. de Montreal, 1988)] seminal work, named preantipode that fulfills all the necessary requirements to be left but not right on the generators of the algebra. Due to the complexity and importance of the full task, we consider our result as an important step that will be extended in the near future.
Recent perspective on coronary artery bifurcation interventions.
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.
Non linear stability analysis of parallel channels with natural circulation
Energy Technology Data Exchange (ETDEWEB)
Mishra, Ashish Mani; Singh, Suneet, E-mail: suneet.singh@iitb.ac.in
2016-12-01
Highlights: • Nonlinear instabilities in natural circulation loop are studied. • Generalized Hopf points, Sub and Supercritical Hopf bifurcations are identified. • Bogdanov–Taken Point (BT Point) is observed by nonlinear stability analysis. • Effect of parameters on stability of system is studied. - Abstract: Linear stability analysis of two-phase flow in natural circulation loop is quite extensively studied by many researchers in past few years. It can be noted that linear stability analysis is limited to the small perturbations only. It is pointed out that such systems typically undergo Hopf bifurcation. If the Hopf bifurcation is subcritical, then for relatively large perturbation, the system has unstable limit cycles in the (linearly) stable region in the parameter space. Hence, linear stability analysis capturing only infinitesimally small perturbations is not sufficient. In this paper, bifurcation analysis is carried out to capture the non-linear instability of the dynamical system and both subcritical and supercritical bifurcations are observed. The regions in the parameter space for which subcritical and supercritical bifurcations exist are identified. These regions are verified by numerical simulation of the time-dependent, nonlinear ODEs for the selected points in the operating parameter space using MATLAB ODE solver.
Massive subcritical compact arrays of plutonium metal
Energy Technology Data Exchange (ETDEWEB)
Rothe, R.E.
1998-04-01
Two experimental critical-approach programs are reported. Both were performed at the Rocky Flats Plant near Denver, Colorado; and both date back to the late 1960s. Both involve very large arrays of massive plutonium ingots. These ingots had been cast in the foundry at the Rocky Flats Plant as part of their routine production operations; they were not specially prepared for either study. Consequently, considerable variation in ingot mass is encountered. This mass varied between approximately 7 kg and a little more than 10 kg. One program, performed in the spring of 1969, involved stacked arrays of ingots contained within cylindrical, disk-shaped, thin, steel cans. This program studied four arrays defined by the pattern of steel cans in a single layer. The four were: 1 x N, 3 x N, 2 x 2 x N, and 3 x 3 x N. The second was a tightly-packed, triangular-pitched patterns; the last two were square-pitched patterns. The other program, performed about a year earlier, involved similar ingots also contained in similar steel cans, but these canned plutonium ingots were placed in commercial steel drums. This study pertained to one-, two-, and three-layered horizontal arrays of drums. All cases proved to be well subcritical. Most would have remained subcritical had the parameters of the array under study been continued infinitely beyond the reciprocal multiplication safety limit. In one case for the drum arrays, an uncertain extrapolation of the data of the earlier program suggests that criticality might have eventually been attained had several thousand additional kilograms of plutonium been available for use.
Nonlinear dead water resistance at subcritical speed
Grue, John
2015-08-01
The dead water resistance F 1 = /1 2 C d w ρ S U 2 (ρ fluid density, U ship speed, S wetted body surface, Cdw resistance coefficient) on a ship moving at subcritical speed along the upper layer of a two-layer fluid is calculated by a strongly nonlinear method assuming potential flow in each layer. The ship dimensions correspond to those of the Polar ship Fram. The ship draught, b0, is varied in the range 0.25h0-0.9h0 (h0 the upper layer depth). The calculations show that Cdw/(b0/h0)2 depends on the Froude number only, in the range close to critical speed, Fr = U/c0 ˜ 0.875-1.125 (c0 the linear internal long wave speed), irrespective of the ship draught. The function Cdw/(b0/h0)2 attains a maximum at subcritical Froude number depending on the draught. Maximum Cdw/(b0/h0)2 becomes 0.15 for Fr = 0.76, b0/h0 = 0.9, and 0.16 for Fr = 0.74, b0/h0 = 1, where the latter extrapolated value of the dead water resistance coefficient is about 60 times higher than the frictional drag coefficient and relevant for the historical dead water observations. The nonlinear Cdw significantly exceeds linear theory (Fr < 0.85). The ship generated waves have a wave height comparable to the upper layer depth. Calculations of three-dimensional wave patterns at critical speed compare well to available laboratory experiments. Upstream solitary waves are generated in a wave tank of finite width, when the layer depths differ, causing an oscillation of the force. In a wide ocean, a very wide wave system develops at critical speed. The force approaches a constant value for increasing time.
Massive subcritical compact arrays of plutonium metal
International Nuclear Information System (INIS)
Rothe, R.E.
1998-01-01
Two experimental critical-approach programs are reported. Both were performed at the Rocky Flats Plant near Denver, Colorado; and both date back to the late 1960s. Both involve very large arrays of massive plutonium ingots. These ingots had been cast in the foundry at the Rocky Flats Plant as part of their routine production operations; they were not specially prepared for either study. Consequently, considerable variation in ingot mass is encountered. This mass varied between approximately 7 kg and a little more than 10 kg. One program, performed in the spring of 1969, involved stacked arrays of ingots contained within cylindrical, disk-shaped, thin, steel cans. This program studied four arrays defined by the pattern of steel cans in a single layer. The four were: 1 x N, 3 x N, 2 x 2 x N, and 3 x 3 x N. The second was a tightly-packed, triangular-pitched patterns; the last two were square-pitched patterns. The other program, performed about a year earlier, involved similar ingots also contained in similar steel cans, but these canned plutonium ingots were placed in commercial steel drums. This study pertained to one-, two-, and three-layered horizontal arrays of drums. All cases proved to be well subcritical. Most would have remained subcritical had the parameters of the array under study been continued infinitely beyond the reciprocal multiplication safety limit. In one case for the drum arrays, an uncertain extrapolation of the data of the earlier program suggests that criticality might have eventually been attained had several thousand additional kilograms of plutonium been available for use
Modeling of the CTEx subcritical unit using MCNPX code
International Nuclear Information System (INIS)
Santos, Avelino; Silva, Ademir X. da; Rebello, Wilson F.; Cunha, Victor L. Lassance
2011-01-01
The present work aims at simulating the subcritical unit of Army Technology Center (CTEx) namely ARGUS pile (subcritical uranium-graphite arrangement) by using the computational code MCNPX. Once such modeling is finished, it could be used in k-effective calculations for systems using natural uranium as fuel, for instance. ARGUS is a subcritical assembly which uses reactor-grade graphite as moderator of fission neutrons and metallic uranium fuel rods with aluminum cladding. The pile is driven by an Am-Be spontaneous neutron source. In order to achieve a higher value for k eff , a higher concentration of U235 can be proposed, provided it safely remains below one. (author)
Uniform in Time Description for Weak Solutions of the Hopf Equation with Nonconvex Nonlinearity
Directory of Open Access Journals (Sweden)
Antonio Olivas Martinez
2009-01-01
Full Text Available We consider the Riemann problem for the Hopf equation with concave-convex flux functions. Applying the weak asymptotics method we construct a uniform in time description for the Cauchy data evolution and show that the use of this method implies automatically the appearance of the Oleinik E-condition.
Twisting products in Hopf algebras and the construction of the quantum double
International Nuclear Information System (INIS)
Ferrer Santos, W.R.
1992-04-01
Let H be a finite dimensional Hopf algebra and B an (H, H*)-comodule algebra. The purpose of this note is to present a construction in which the product of B is twisted by the given actions. The constructions of the smash product and of the Quantum Double appear as special cases. (author). 7 refs
The Hopf fibration over S8 admits no S1-subfibration
International Nuclear Information System (INIS)
Loo, B.; Verjovsky, A.
1990-10-01
It is shown that there does not exist a PL-bundle over S 8 with fibre and total space PL-manifolds homotopy equivalent to CP 3 and CP 7 respectively. Consequently, the Hopf fibration over S 8 admits no subfibration by PL-circles. (author). 27 refs
The Hopf fibration over S8 admits no S1-subfibration
International Nuclear Information System (INIS)
Loo, B.; Verjovsky, A.
1990-05-01
It is shown that there does not exist a PL-bundle over S 8 with fibre and total space PL-manifolds homotopy equivalent to CP 3 and CP 7 respectively. Consequently, the Hopf fibration over S 8 admits no subfibration by PL-circles. (author). 27 refs
WIENER-HOPF SOLVER WITH SMOOTH PROBABILITY DISTRIBUTIONS OF ITS COMPONENTS
Directory of Open Access Journals (Sweden)
Mr. Vladimir A. Smagin
2016-12-01
Full Text Available The Wiener – Hopf solver with smooth probability distributions of its component is presented. The method is based on hyper delta approximations of initial distributions. The use of Fourier series transformation and characteristic function allows working with the random variable method concentrated in transversal axis of absc.
Quantum entanglement and fixed-point bifurcations
International Nuclear Information System (INIS)
Hines, Andrew P.; McKenzie, Ross H.; Milburn, G.J.
2005-01-01
How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state--the ground state--achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation
A case study in bifurcation theory
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.
Bifurcations of non-smooth systems
Angulo, Fabiola; Olivar, Gerard; Osorio, Gustavo A.; Escobar, Carlos M.; Ferreira, Jocirei D.; Redondo, Johan M.
2012-12-01
Non-smooth systems (namely piecewise-smooth systems) have received much attention in the last decade. Many contributions in this area show that theory and applications (to electronic circuits, mechanical systems, …) are relevant to problems in science and engineering. Specially, new bifurcations have been reported in the literature, and this was the topic of this minisymposium. Thus both bifurcation theory and its applications were included. Several contributions from different fields show that non-smooth bifurcations are a hot topic in research. Thus in this paper the reader can find contributions from electronics, energy markets and population dynamics. Also, a carefully-written specific algebraic software tool is presented.
Bifurcation Control of Chaotic Dynamical Systems
National Research Council Canada - National Science Library
Wang, Hua O; Abed, Eyad H
1992-01-01
A nonlinear system which exhibits bifurcations, transient chaos, and fully developed chaos is considered, with the goal of illustrating the role of two ideas in the control of chaotic dynamical systems...
Bifurcation and instability problems in vortex wakes
DEFF Research Database (Denmark)
Aref, Hassan; Brøns, Morten; Stremler, Mark A.
2007-01-01
A number of instability and bifurcation problems related to the dynamics of vortex wake flows are addressed using various analytical tools and approaches. We discuss the bifurcations of the streamline pattern behind a bluff body as a vortex wake is produced, a theory of the universal Strouhal......-Reynolds number relation for vortex wakes, the bifurcation diagram for "exotic" wake patterns behind an oscillating cylinder first determined experimentally by Williamson & Roshko, and the bifurcations in topology of the streamlines pattern in point vortex streets. The Hamiltonian dynamics of point vortices...... in a periodic strip is considered. The classical results of von Kármán concerning the structure of the vortex street follow from the two-vortices-in-a-strip problem, while the stability results follow largely from a four-vortices-in-a-strip analysis. The three-vortices-in-a-strip problem is argued...
Bifurcation structure of successive torus doubling
International Nuclear Information System (INIS)
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
Nuclear data requirements for accelerator driven sub-critical systems
Indian Academy of Sciences (India)
The development of accelerator driven sub-critical systems (ADSS) require significant amount of new nuclear data in extended energy regions as well as for a variety of new materials. This paper reviews these perspectives in the Indian context.
Sub-criticality monitoring for ADTR trademark control
International Nuclear Information System (INIS)
Ashworth, Roger
2014-01-01
Following the debut of the Accelerator Driven Thorium Reactor (ADTR trademark) Power Station at ENC 2010 in Barcelona, thorium as a reactor fuel has gained increasing support. The ADTR trademark concept reactor introduced the combination of an accelerator driven system (ADS) with traditional control rod technology, to provide a very high gain novel sub-critical ADS reactor design. The high gain of the system, while significantly reducing the demands on the accelerator design, pushes up operational sub-criticality (k eff ) closer to unity. In this paper we review this design and the progress made since ENC 2010. We compare 2 different methods of measuring the sub-critical neutron multiplication factor as the fuel cycle develops. The paper discusses the most recent work on k eff measurement and the interesting relationship between neutron flux, accelerator current and fuel temperature when using beam pulse methods to determine operational sub-criticality, of which a European patent is being granted. (orig.)
Systematic parameter study of dynamo bifurcations in geodynamo simulations
Petitdemange, Ludovic
2018-04-01
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core, i.e. in a rotating spherical shell with thermally driven motions with no-slip boundaries. Unlike in previous studies on dynamo bifurcations, the control parameters have been varied significantly in order to deduce general tendencies. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing dipole-dominated dynamos and the reversing non-dipole-dominated multipolar solutions. We show that, by considering weak initial fields, the above transition disappears and is replaced by a region of bistability for which dipolar and multipolar dynamos coexist. Such a result was also observed in models with free-slip boundaries in which the geostrophic zonal flow can develop and participate to the dynamo mechanism for non-dipolar fields. We show that a similar process develops in no-slip models when viscous effects are reduced sufficiently. The following three regimes are distinguished: (i) Close to the onset of convection (Rac) with only the most critical convective mode (wave number) being present, dynamos set in supercritically in the Ekman number regime explored here and are dipole-dominated. Larger critical magnetic Reynolds numbers indicate that they are particularly inefficient. (ii) in the range 3 10) , the relative importance of zonal flows increases with Ra in non-magnetic models. The field topology depends on the magnitude of the initial magnetic field. The dipolar branch has a subcritical behavior whereas the multipolar branch has a supercritical behavior. By approaching more realistic parameters, the extension of this bistable regime increases. A hysteretic behavior questions the common interpretation for geomagnetic reversals. Far above the dynamo threshold (by increasing the magnetic Prandtl number), Lorentz forces contribute to the first order force balance, as predicted for planetary dynamos. When
Physics of subcritical multiplying regions and experimental validation
International Nuclear Information System (INIS)
Salvatores, M.
1996-01-01
The coupling of a particle accelerator with a spallation target and with a subcritical multiplying region has been proposed in the fifties and is called here a hybrid system. This article gives some ideas about the energetic balance of such a system. The possibilities of experimental validation of some properties of a subcritical multiplying region by using MASURCA facility at CEA-Cadarache are examined. The results of a preliminary experiment called MUSE are presented. (A.C.)
Pulsed neutron source based on accelerator-subcritical-assembly
Energy Technology Data Exchange (ETDEWEB)
Inoue, Makoto; Noda, Akira; Iwashita, Yoshihisa; Okamoto, Hiromi; Shirai, Toshiyuki [Kyoto Univ., Uji (Japan). Inst. for Chemical Research
1997-03-01
A new pulsed neutron source which consists of a 300MeV proton linac and a nuclear fuel subcritical assembly is proposed. The proton linac produces pulsed spallation neutrons, which are multipied by the subcritical assembly. A prototype proton linac that accelerates protons up to 7MeV has been developed and a high energy section of a DAW structure is studied with a power model. Halo formations in high intensity beam are also being studied. (author)
International Nuclear Information System (INIS)
Suarez Antola, R.
2011-01-01
is obtained. Analytical formulae are derived for the frequency of oscillation and the parameters that determine the stability of the steady states, including sub- and supercritical oincar?-Andronov- Hopf (AH) bifurcations. A Bautin's bifurcation scenario seems possible on the power-flow plane: near the boundary of stability, a region where stable steady states are surrounded by unstable limit cycles surrounded at their turn by stable limit cycles. The qualitative analytical results are compared with recent digital simulations and applications of semi-analytical bifurcation theory done with reduced order models of BWR.
Geometrically Induced Interactions and Bifurcations
Binder, Bernd
2010-01-01
In order to evaluate the proper boundary conditions in spin dynamics eventually leading to the emergence of natural and artificial solitons providing for strong interactions and potentials with monopole charges, the paper outlines a new concept referring to a curvature-invariant formalism, where superintegrability is given by a special isometric condition. Instead of referring to the spin operators and Casimir/Euler invariants as the generator of rotations, a curvature-invariant description is introduced utilizing a double Gudermann mapping function (generator of sine Gordon solitons and Mercator projection) cross-relating two angular variables, where geometric phases and rotations arise between surfaces of different curvature. Applying this stereographic projection to a superintegrable Hamiltonian can directly map linear oscillators to Kepler/Coulomb potentials and/or monopoles with Pöschl-Teller potentials and vice versa. In this sense a large scale Kepler/Coulomb (gravitational, electro-magnetic) wave dynamics with a hyperbolic metric could be mapped as a geodesic vertex flow to a local oscillator singularity (Dirac monopole) with spherical metrics and vice versa. Attracting fixed points and dynamic constraints are given by special isometries with magic precession angles. The nonlinear angular encoding directly provides for a Shannon mutual information entropy measure of the geodesic phase space flow. The emerging monopole patterns show relations to spiral Fresnel holography and Berry/Aharonov-Bohm geometric phases subject to bifurcation instabilities and singularities from phase ambiguities due to a local (entropy) overload. Neutral solitons and virtual patterns emerging and mediating in the overlap region between charged or twisted holographic patterns are visualized and directly assigned to the Berry geometric phase revealing the role of photons, neutrons, and neutrinos binding repulsive charges in Coulomb, strong and weak interaction.
Grand unification and subcritical hybrid inflation
International Nuclear Information System (INIS)
Buchmueller, Wilfried; Ishiwata, Koji
2014-12-01
We consider hybrid inflation for small couplings of the inflaton to matter such that the critical value of the inflaton field exceeds the Planck mass. It has recently been shown that inflation then continues at subcritical inflaton field values where quantum fluctuations generate an effective inflaton mass. The effective inflaton potential interpolates between a quadratic potential at small field values and a plateau at large field values. An analysis of the allowed parameter space leads to predictions for the scalar spectral index n s and the tensor-to-scalar ratio r similar to those of natural inflation. Using the range for n s and r favoured by the Planck data, we find that the energy scale of the plateau is constrained to the interval (1.6-2.4) x 10 16 GeV which includes the energy scale of gauge coupling unification in the supersymmetric standard model. The tensor-to-scalar ratio is predicted to have the lower bound r>0.049 for 60 e-folds before the end of inflation.
Safety features of subcritical fluid fueled systems
International Nuclear Information System (INIS)
Bell, C.R.
1995-01-01
Accelerator-driven transmutation technology has been under study at Los Alamos for several years for application to nuclear waste treatment, tritium production, energy generation, and recently, to the disposition of excess weapons plutonium. Studies and evaluations performed to date at Los Alamos have led to a current focus on a fluid-fuel, fission system operating in a neutron source-supported subcritical mode, using molten salt reactor technology and accelerator-driven proton-neutron spallation. In this paper, the safety features and characteristics of such systems are explored from the perspective of the fundamental nuclear safety objectives that any reactor-type system should address. This exploration is qualitative in nature and uses current vintage solid-fueled reactors as a baseline for comparison. Based on the safety perspectives presented, such systems should be capable of meeting the fundamental nuclear safety objectives. In addition, they should be able to provide the safety robustness desired for advanced reactors. However, the manner in which safety objectives and robustness are achieved is very different from that associated with conventional reactors. Also, there are a number of safety design and operational challenges that will have to be addressed for the safety potential of such systems to be credible
Safety features of subcritical fluid fueled systems
International Nuclear Information System (INIS)
Bell, C.R.
1994-01-01
Accelerator-driven transmutation technology has been under study at Los Alamos for several years for application to nuclear waste treatment, tritium production, energy generation, and recently, to the disposition of excess weapons plutonium. Studies and evaluations performed to date at Los Alamos have led to a current focus on a fluid-fuel, fission system operating in a neutron source-supported subcritical mode, using molten salt reactor technology and accelerator-driven proton-neutron spallation. In this paper, the safety features and characteristics of such systems are explored from the perspective of the fundamental nuclear safety objectives that any reactor-type system should address. This exploration is qualitative in nature and uses current vintage solid-fueled reactors as a baseline for comparison. Based on the safety perspectives presented, such systems should be capable of meeting the fundamental nuclear safety objectives. In addition, they should be able to provide the safety robustness desired for advanced reactors. However, the manner in which safety objectives and robustness are achieved in very different from that associated with conventional reactors. Also, there are a number of safety design and operational challenges that will have to be addressed for the safety potential of such systems to be credible
Safety features of subcritical fluid fueled systems
Energy Technology Data Exchange (ETDEWEB)
Bell, C.R. [Los Alamos National Laboratory, NM (United States)
1995-10-01
Accelerator-driven transmutation technology has been under study at Los Alamos for several years for application to nuclear waste treatment, tritium production, energy generation, and recently, to the disposition of excess weapons plutonium. Studies and evaluations performed to date at Los Alamos have led to a current focus on a fluid-fuel, fission system operating in a neutron source-supported subcritical mode, using molten salt reactor technology and accelerator-driven proton-neutron spallation. In this paper, the safety features and characteristics of such systems are explored from the perspective of the fundamental nuclear safety objectives that any reactor-type system should address. This exploration is qualitative in nature and uses current vintage solid-fueled reactors as a baseline for comparison. Based on the safety perspectives presented, such systems should be capable of meeting the fundamental nuclear safety objectives. In addition, they should be able to provide the safety robustness desired for advanced reactors. However, the manner in which safety objectives and robustness are achieved is very different from that associated with conventional reactors. Also, there are a number of safety design and operational challenges that will have to be addressed for the safety potential of such systems to be credible.
Bifurcation and phase diagram of turbulence constituted from three different scale-length modes
Energy Technology Data Exchange (ETDEWEB)
Itoh, S.-I.; Kitazawa, A.; Yagi, M. [Kyushu Univ., Research Inst. for Applied Mechanics, Kasuga, Fukuoka (Japan); Itoh, K. [National Inst. for Fusion Science, Toki, Gifu (Japan)
2002-04-01
Cases where three kinds of fluctuations having the different typical scale-lengths coexist are analyzed, and the statistical theory of strong turbulence in inhomogeneous plasmas is developed. Statistical nonlinear interactions between fluctuations are kept in the analysis as the renormalized drag, statistical noise and the averaged drive. The nonlinear interplay through them induces a quenching or suppressing effect, even if all the modes are unstable when they are analyzed independently. Variety in mode appearance takes place: one mode quenches the other two modes, or one mode is quenched by the other two modes, etc. The bifurcation of turbulence is analyzed and a phase diagram is drawn. Phase diagrams with cusp type catastrophe and butterfly type catastrophe are obtained. The subcritical bifurcation is possible to occur through the nonlinear interplay, even though each one is supercritical turbulence when analyzed independently. Analysis reveals that the nonlinear stability boundary (marginal point) and the amplitude of each mode may substantially shift from the conventional results of independent analyses. (author)
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels Ramsing; Curzen, Nicholas P
2011-01-01
Background— Controversy persists regarding the correct strategy for bifurcation lesions. Therefore, we combined the patient-level data from 2 large trials with similar methodology: the NORDIC Bifurcation Study (NORDIC I) and the British Bifurcation Coronary Study (BBC ONE). Methods and Results— B...
International Nuclear Information System (INIS)
Bondarenko, Vladimir E.; Cymbalyuk, Gennady S.; Patel, Girish; DeWeerth, Stephen P.; Calabrese, Ronald L.
2004-01-01
Oscillatory activity in the central nervous system is associated with various functions, like motor control, memory formation, binding, and attention. Quasiperiodic oscillations are rarely discussed in the neurophysiological literature yet they may play a role in the nervous system both during normal function and disease. Here we use a physical system and a model to explore scenarios for how quasiperiodic oscillations might arise in neuronal networks. An oscillatory system of two mutually inhibitory neuronal units is a ubiquitous network module found in nervous systems and is called a half-center oscillator. Previously we created a half-center oscillator of two identical oscillatory silicon (analog Very Large Scale Integration) neurons and developed a mathematical model describing its dynamics. In the mathematical model, we have shown that an in-phase limit cycle becomes unstable through a subcritical torus bifurcation. However, the existence of this torus bifurcation in experimental silicon two-neuron system was not rigorously demonstrated or investigated. Here we demonstrate the torus predicted by the model for the silicon implementation of a half-center oscillator using complex time series analysis, including bifurcation diagrams, mapping techniques, correlation functions, amplitude spectra, and correlation dimensions, and we investigate how the properties of the quasiperiodic oscillations depend on the strengths of coupling between the silicon neurons. The potential advantages and disadvantages of quasiperiodic oscillations (torus) for biological neural systems and artificial neural networks are discussed
A generalization of the deformed algebra of quantum group SU(2)q for Hopf algebra
International Nuclear Information System (INIS)
Ludu, A.; Gupta, R.K.
1992-12-01
A generalization of the deformation of Lie algebra of SU(2) group is established for the Hopf algebra, by modifying the J 3 component in all of its defining commutators. The modification is carried out in terms of a polynomial f, of J 3 and the q-deformation parameter, which contains the known q-deformation functionals as its particular cases. (author). 20 refs
Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
International Nuclear Information System (INIS)
Sasai, Yuya; Sasakura, Naoki
2008-01-01
Domain wall solitons are the simplest topological objects in field theories. The conventional translational symmetry in a field theory is the generator of a one-parameter family of domain wall solutions, and induces a massless moduli field which propagates along a domain wall. We study similar issues in braided noncommutative field theories possessing Hopf algebraic translational symmetries. As a concrete example, we discuss a domain wall soliton in the scalar φ 4 braided noncommutative field theory in Lie-algebraic noncommutative space-time, [x i ,x j ]=2iκε ijk x k (i,j,k=1,2,3), which has a Hopf algebraic translational symmetry. We first discuss the existence of a domain wall soliton in view of Derrick's theorem, and construct explicitly a one-parameter family of solutions in perturbation of the noncommutativity parameter κ. We then find the massless moduli field which propagates on the domain wall soliton. We further extend our analysis to the general Hopf algebraic translational symmetry
Reaction kinetics of cellulose hydrolysis in subcritical and supercritical water
Olanrewaju, Kazeem Bode
The uncertainties in the continuous supply of fossil fuels from the crisis-ridden oil-rich region of the world is fast shifting focus on the need to utilize cellulosic biomass and develop more efficient technologies for its conversion to fuels and chemicals. One such technology is the rapid degradation of cellulose in supercritical water without the need for an enzyme or inorganic catalyst such as acid. This project focused on the study of reaction kinetics of cellulose hydrolysis in subcritical and supercritical water. Cellulose reactions at hydrothermal conditions can proceed via the homogeneous route involving dissolution and hydrolysis or the heterogeneous path of surface hydrolysis. The work is divided into three main parts. First, the detailed kinetic analysis of cellulose reactions in micro- and tubular reactors was conducted. Reaction kinetics models were applied, and kinetics parameters at both subcritical and supercritical conditions were evaluated. The second major task was the evaluation of yields of water soluble hydrolysates obtained from the hydrolysis of cellulose and starch in hydrothermal reactors. Lastly, changes in molecular weight distribution due to hydrothermolytic degradation of cellulose were investigated. These changes were also simulated based on different modes of scission, and the pattern generated from simulation was compared with the distribution pattern from experiments. For a better understanding of the reaction kinetics of cellulose in subcritical and supercritical water, a series of reactions was conducted in the microreactor. Hydrolysis of cellulose was performed at subcritical temperatures ranging from 270 to 340 °C (tau = 0.40--0.88 s). For the dissolution of cellulose, the reaction was conducted at supercritical temperatures ranging from 375 to 395 °C (tau = 0.27--0.44 s). The operating pressure for the reactions at both subcritical and supercritical conditions was 5000 psig. The results show that the rate-limiting step in
Analysis of the MUSE-3 subcritical experiment
Energy Technology Data Exchange (ETDEWEB)
Aliberti, G; Rimpault, G; Jacqmin, R; Lebrat, J F; Chauvin, J P; Granget, G [CEA Cadarache, Dept. d' Etudes des Reacteurs 13 - Saint Paul lez Durance (France); Salvatores, M [CEA Saclay, Dir. de l' Energie Nucleaire, 91 - Gif sur Yvette (France)
2001-07-01
The purpose of the MUSE (MUltiplication avec Source Externe) experimental programme is to investigate the neutronic properties of fast sub-critical cores coupled with known external sources of neutrons. Measurements of the MUSE-3 experiments (third phase of the MUSE program) included reactivity, U-235 fission rates across various traverses, absolute fission rates and dynamic measurements. Special care was taken in assessing the various sources of errors and uncertainties affecting the results when modelling and analysing MUSE-3 experiments with the ERANOS neutronic code system. Measured and calculated values agree well with each other (discrepancies within the uncertainty bars) except absolute fission rates which are affected by the large uncertainties associated with the inherent source (30 %) and with the strength of the fusion source (25%). However, such uncertainties do not contribute to the uncertainty in the importance of the source, {phi}{sup *}, which is linked to the ratio of the measured reaction rate with and without the fusion source (the generator being switched off and on). The analysis yielded therefore valuable results, in particular on the relative importance of the source from one configuration to another. The uncertainty in the calculated {phi}{sup *}, is of 1-2% (JEF2 and ERALIB1) for configurations without diffuser and 6% for the configuration with a Pb diffuser. There is therefore no bias in this important ADS characteristic as calculations lie within the measured error bars. From this analysis, it can be concluded that MUSE-3-type experiments are suitable for the assessment of tools used for designing ADS. (author)
The spatial kinetic analysis of accelerator-driven subcritical reactor
International Nuclear Information System (INIS)
Takahashi, H.; An, Y.; Chen, X.
1998-02-01
The operation of the accelerator driven reactor with subcritical condition provides a more flexible choice of the reactor materials and of design parameters. A deep subcriticality is chosen sometime from the analysis of point kinetics. When a large reactor is operated in deep subcritical condition by using a localized spallation source, the power distribution has strong spatial dependence, and point kinetics does not provide proper analysis for reactor safety. In order to analyze the spatial and energy dependent kinetic behavior in the subcritical reactor, the authors developed a computation code which is composed of two parts, the first one is for creating the group cross section and the second part solves the multi-group kinetic diffusion equations. The reactor parameters such as the cross section of fission, scattering, and energy transfer among the several energy groups and regions are calculated by using a code modified from the Monte Carlo codes MCNPA and LAHET instead of the usual analytical method of ANISN, TWOTRAN codes. Thus the complicated geometry of the accelerator driven reactor core can be precisely taken into account. The authors analyzed the subcritical minor actinide transmutor studied by Japan Atomic Energy Research Institute (JAERI) using the code
A novel concept for CRIEC-driven subcritical research reactors
International Nuclear Information System (INIS)
Nieto, M.; Miley, G.H.
2001-01-01
A novel scheme is proposed to drive a low-power subcritical fuel assembly by means of a long Cylindrical Radially-convergent Inertial Electrostatic Confinement (CRIEC) used as a neutron source. The concept is inherently safe in the sense that the fuel assembly remains subcritical at all times. Previous work has been done for the possible implementation of CRIEC as a subcritical assembly driver for power reactors. However, it has been found that the present technology and stage of development of IEC-based neutron sources can not meet the neutron flux requirements to drive a system as big as a power reactor. Nevertheless, smaller systems, such as research and training reactors, could be successfully driven with levels of neutron flux that seem more reasonable to be achieved in the near future by IEC devices. The need for custom-made expensive nuclear fission fuel, as in the case of the TRIGA reactors, is eliminated, and the CRIEC presents substantial advantages with respect to the accelerator-driven subcritical reactors in terms of simplicity and cost. In the present paper, a conceptual design for a research/training CRIEC-driven subcritical assembly is presented, emphasizing the description, principle of operation and performance of the CRIEC neutron source, highlighting its advantages and discussing some key issues that require study for the implementation of this concept. (author)
Measurements relevant to simulating subcriticality in ADS facilities with blanket
International Nuclear Information System (INIS)
Titarenko, Yu. E.; Batyaev, V.F.; Borovlev, S.P.; Gladkikh, N.G.; Igumnov, M.M.; Legostaev, V.O.; Karpikhin, E.I.; Konev, V.N.; Kushnerev, Yu.T.; Popkov, V.N.; Ryazhsky, V.I.; Spiridonov, V.G.; Chernyavsky, E.V.; Shvedov, O.V.
2009-10-01
The work presents the results of determining the blanket subcriticality for a zero-power heavy water reactor MAKET at the Institute for Theoretical and Experimental Physics, Moscow. The blanket is hexagonal lattice made of 36 90%-enriched 235U fuel rods spaced 173mm apart. The subcriticality was varied from ∼0.3% to 5% by adjusting the heavy water level. The subcriticality values were calibrated using the dependence of reactivity on heavy water level. The pulsed neutron source technique was used to measure the temporal dependence of neutron field at different blanket points for the calibrated subcriticality values. The subciticality values obtained in terms of the 'inverse clock' formulae using the decay constants of the measured dependences proved to differ from the calibrated subcriticalities by not more than 7% at the average. The MCNP code-aided simulations of the experiment made has given the calibrated keff values at prescribed heavy water levels and led to the neutron field decay constants at given points, which differ on the average from their experimental values by not more than 7% too. (author)
Subcriticality determination of nuclear fuel assembly by Mihalczo method
International Nuclear Information System (INIS)
Yamane, Yoshihiro; Watanabe, Shoji; Nishina, Kojiro; Miyoshi, Yoshinori; Suzaki, Takenori; Kobayashi, Iwao.
1986-01-01
To establish a technique of on-site subcriticality determination suitable for the criticality safety management of nuclear fuel assembly, the applicability of the method proposed by Mihalczo was examined with the Tank-type Critical Assembly (TCA) of the Japan Atomic Energy Research Institute. In the Mihalczo method, cross power spectral densities and auto power spectral densities are evaluated from the output currents of an ionization chamber containing 252 Cf neutron source and two neutron detectors. The principle of this method is that the spectral ratio formed by the power spectral densities mentioned can be related to the subcriticality by the help of a stochastic theory. Throughout our data processing, an improved formula taking account of the neutron extinction at a detection process was used. Up to the subcriticality of 15 dollars, the Mihalczo method agreed with the water-level worth method, which has been a standard method of reactivity determination at the TCA facility. The systems treated in the present report hold symmetry concerning the nuclear fuel configuration and the 252 Cf chamber position. It was clarified that, contrary to Mihalczo's assertion, the factor converting the spectral ratio to a subcriticality depends on subcriticality itself. (author)
Attractors near grazing–sliding bifurcations
International Nuclear Information System (INIS)
Glendinning, P; Kowalczyk, P; Nordmark, A B
2012-01-01
In this paper we prove, for the first time, that multistability can occur in three-dimensional Fillipov type flows due to grazing–sliding bifurcations. We do this by reducing the study of the dynamics of Filippov type flows around a grazing–sliding bifurcation to the study of appropriately defined one-dimensional maps. In particular, we prove the presence of three qualitatively different types of multiple attractors born in grazing–sliding bifurcations. Namely, a period-two orbit with a sliding segment may coexist with a chaotic attractor, two stable, period-two and period-three orbits with a segment of sliding each may coexist, or a non-sliding and period-three orbit with two sliding segments may coexist
International Nuclear Information System (INIS)
Sushko, Iryna; Agliari, Anna; Gardini, Laura
2006-01-01
We study the structure of the 2D bifurcation diagram for a two-parameter family of piecewise smooth unimodal maps f with one break point. Analysing the parameters of the normal form for the border-collision bifurcation of an attracting n-cycle of the map f, we describe the possible kinds of dynamics associated with such a bifurcation. Emergence and role of border-collision bifurcation curves in the 2D bifurcation plane are studied. Particular attention is paid also to the curves of homoclinic bifurcations giving rise to the band merging of pieces of cyclic chaotic intervals
Bifurcation of Jovian magnetotail current sheet
Directory of Open Access Journals (Sweden)
P. L. Israelevich
2006-07-01
Full Text Available Multiple crossings of the magnetotail current sheet by a single spacecraft give the possibility to distinguish between two types of electric current density distribution: single-peaked (Harris type current layer and double-peaked (bifurcated current sheet. Magnetic field measurements in the Jovian magnetic tail by Voyager-2 reveal bifurcation of the tail current sheet. The electric current density possesses a minimum at the point of the Bx-component reversal and two maxima at the distance where the magnetic field strength reaches 50% of its value in the tail lobe.
Bifurcation of Jovian magnetotail current sheet
Directory of Open Access Journals (Sweden)
P. L. Israelevich
2006-07-01
Full Text Available Multiple crossings of the magnetotail current sheet by a single spacecraft give the possibility to distinguish between two types of electric current density distribution: single-peaked (Harris type current layer and double-peaked (bifurcated current sheet. Magnetic field measurements in the Jovian magnetic tail by Voyager-2 reveal bifurcation of the tail current sheet. The electric current density possesses a minimum at the point of the B_{x}-component reversal and two maxima at the distance where the magnetic field strength reaches 50% of its value in the tail lobe.
Subcritical reactivity measurement at Angra 1 nuclear power plant
International Nuclear Information System (INIS)
Kuramoto, Renato Yoichi Ribeiro; Miranda, Anselmo Ferreira
2011-01-01
In order to speed up the Angra 1 NPP physics tests, this work intends to develop a digital reactivity meter combined with a methodology of the modified Neutron Source Multiplication (NSM) method with correction factors for subcriticality measurements at Angra 1 NPP. In the first part of this work, we have applied the Modified Neutron Source Multiplication (MNSM) Method with fundamental mode extraction, in order to improve the monitoring of the subcriticality at Angra 1 NPP during the criticality approach. In the second part, we developed a preliminary subcritical reactivity meter algorithm based on the point-reactor inverse kinetic model with six delayed neutron groups and external neutron source. The source strength was obtained through the Least Squares Inverse Kinetics Method (LSIKM). (author)
Reactor Dynamics Experiments with a Sub-Critical Assembly
International Nuclear Information System (INIS)
Miley, G.H.; Yang, Y.; Wu, L.; Momota, H.
2004-01-01
A resurgence in use of nuclear power is now underway worldwide. However due to the shutdown of many university research reactors , student laboratories must rely more heavily on use of sub-critical assemblies. Here a driven sub-critical is described that uses a cylindrical Inertial Electrostatic Confinement (IEC) device to provide a fusion neutron source. The small IEC neutron source would be inserted in a fuel element position, with its power input controlled externally at a control panel. This feature opens the way to use of the critical assembly for a number of transient experiments such as sub-critical pulsing and neutron wave propagation. That in turn adds important new insights and excitement for the student teaching laboratory
Evaluating Subcriticality during the Ebola Epidemic in West Africa.
Directory of Open Access Journals (Sweden)
Wayne T A Enanoria
Full Text Available The 2014-2015 Ebola outbreak is the largest and most widespread to date. In order to estimate ongoing transmission in the affected countries, we estimated the weekly average number of secondary cases caused by one individual infected with Ebola throughout the infectious period for each affected West African country using a stochastic hidden Markov model fitted to case data from the World Health Organization. If the average number of infections caused by one Ebola infection is less than 1.0, the epidemic is subcritical and cannot sustain itself. The epidemics in Liberia and Sierra Leone have approached subcriticality at some point during the epidemic; the epidemic in Guinea is ongoing with no evidence that it is subcritical. Response efforts to control the epidemic should continue in order to eliminate Ebola cases in West Africa.
Development of High Flux Isotope Reactor (HFIR) subcriticality monitoring methods
International Nuclear Information System (INIS)
Rothrock, R.B.
1991-01-01
Use of subcritical source multiplication measurements during refueling has been investigated as a possible replacement for out-of-reactor subcriticality measurements formerly made on fresh HFIR fuel elements at the ORNL Critical Experiment Facility. These measurements have been used in the past for preparation of estimated critical rod positions, and as a partial verification, prior to reactor startup, that the requirements for operational shutdown margin would be met. Results of subcritical count rate data collection during recent HFIR refuelings and supporting calculations are described illustrating the intended measurement method and its expected uncertainty. These results are compared to historical uses of the out-of-reactor core measurements and their accuracy requirements, and a planned in-reactor test is described which will establish the sensitivity of the method and calibrate it for future routine use during HFIR refueling. 2 refs., 1 fig., 2 tabs
Discretizing the transcritical and pitchfork bifurcations – conjugacy results
Ló czi, Lajos
2015-01-01
© 2015 Taylor & Francis. We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions
Estimation of subcriticality with the computed values. 2
Energy Technology Data Exchange (ETDEWEB)
Sakurai, Kiyoshi; Arakawa, Takuya; Naito, Yoshitaka [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1996-02-01
For measurements of reactivities and neutron count rate space distributions, seven subcritical cores including non-square array cores were constructed using critical assembly TCA. MCNP-4A was used for the experimental analysis. The calculational results of the neutron count rate space distributions agreed with the measured ones within the each error range. It means that for calculation error indirect estimation method, the calculated neutron multiplication factors are equal to ones of experimental reactivities. It is shown that from these experiments and calculations estimation method of subcriticality with the computed values based on the calculation error indirect estimation method is also applicable to six non-square array cores. (author).
ITEP Subcritical Neutron Generator driven by charged particle accelerator
Energy Technology Data Exchange (ETDEWEB)
Shvedov, O.V.; Chuvilo, I.V.; Vasiliev, V.V. [Institute of Theoretical and Experimental Physics, Moscow (Russian Federation)] [and others
1995-10-01
A research facility prototype including a combination of a linear accelerator, a neutron generating target, a nuclear safety ensuring and means of its attainment for Subcritical Neutron Generator are considered. The scheme of the multiplying is shown. The assembly will be mounted in the body of the partly dismantled ITEP HWR. Requirements for subcritical assembly are worked out and their feasibility within the framework of the heavy-water blanket is shown. The facility`s application as a full-scale model of more powerful installations of this kind and for fundamental experimental research has been investigated.
Subcritical crack growth along polymer interfaces
Gurumurthy, Charavana Kumara
2000-10-01
The adhesion characteristics have been investigated for a polyimide (PI)/model epoxy (ME) interface that is important for microelectronic applications. The fracture toughness (G*c) of this interface has been measured using an asymmetric double cantilever beam (ADCB) technique. The G*c is low, 10-25 J/m 2, and is sensitive to the mechanical phase angle psi. A modified ADCB setup has been used to measure the subcritical crack growth velocity v due to the stress-assisted water attack (SAWA) at various relative humidities (RH) and temperatures (T) as a function of its driving force (the strain energy release rate) G*. The threshold G* decreases remarkably. Above the threshold log v rises linearly with √ G* (a hydrolysis controlled regime) but then enters a regime where the crack velocity is almost independent of √G*, i.e., v = v* (a transport controlled regime). A model for SAWA has been developed based on thermally-activated kinetics for hydrolysis of the ester covalent bonds that bridge from one side to the other of the interface. A new technique has been developed for the determination of the fatigue crack growth under thermal (T) and hydro-thermal (HT) conditions as a function of the range in the strain energy release rate (DeltaG). Under T-fatigue, the fatigue crack growth per unit temperature cycle (da/dN) increases as a power of DeltaG, i.e., a Paris law relationship holds. The HT da/dN measured is higher than da/dN under T-fatigue conditions and has been successfully modeled as a summation of two components: (a) the da/dN due to T-fatigue and (b) the da/dN due to the SAWA along the interface for a given T-cycle. A surface modification procedure that converts a thin interpenetrated by a solvent cast ME is used to strengthen ME/PI interface. The G* c increases with the interpenetration distance w. Increasing w also improves the resistance of the PI/ME interface to SAWA with the threshold G* increasing and the water transport controlled velocity (v
Designing a mini subcritical nuclear reactor
International Nuclear Information System (INIS)
Escobedo G, C. R.; Vega C, H. R.; Davila H, V. M.
2015-10-01
In this work the design of a mini subcritical nuclear reactor formed by means of light water moderator, uranium as fuel, and isotopic neutron source of 239 PuBe was carried out. The design was done by Monte Carlo methods with the code MCNP5 in which uranium was modeled in an array of concentric holes cylinders of 8.5, 14.5, 20.5, 26.5, 32.5 cm of internal radius and 3 cm of thickness, 36 cm of height. Different models were made from a single fuel cylinder (natural uranium) to five. The neutron source of 239 PuBe was situated in the center of the mini reactor; in each arrangement was used water as moderator. Cross sections libraries Endf/Vi were used and the number of stories was large enough to ensure less uncertainty than 3%. For each case the effective multiplication factor k e -f f , the amplification factor and the power was calculated. Outside the mini reactor the ambient dose equivalent H (10) was calculated for different cases. The value of k eff , the amplification factor and power are directly related to the number of cylinders of uranium as fuel. Although the average energy of the neutrons 239 PuBe is between 4.5 and 5 MeV in the case of the mini reactor for a cylinder, in the neutron spectrum the presence of thermal neutrons does not exist, so that produced fissions are generated with fast neutrons, and in designs of two and three rings the neutron spectra shows the presence of thermal neutrons, however the fissions are being generated with fast neutrons. Finally in the four and five cases the amount of moderator is enough to thermalized the neutrons and thereby produce the fission. The maximum value for k eff was 0.82; this value is very close to the assembly of Universidad Autonoma de Zacatecas generating a k eff of 0.86. According to the safety and radiation protection standards for the design of mini reactor of one, two and three cylinders they comply with the established safety, while designs of four and five cylinders not met. (Author)
Comments on the Bifurcation Structure of 1D Maps
DEFF Research Database (Denmark)
Belykh, V.N.; Mosekilde, Erik
1997-01-01
-within-a-box structure of the total bifurcation set. This presents a picture in which the homoclinic orbit bifurcations act as a skeleton for the bifurcational set. At the same time, experimental results on continued subharmonic generation for piezoelectrically amplified sound waves, predating the Feigenbaum theory......, are called into attention....
Bifurcation of elastic solids with sliding interfaces
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.
Climate bifurcation during the last deglaciation?
Lenton, T.M.; Livina, V.N.; Dakos, V.; Scheffer, M.
2012-01-01
There were two abrupt warming events during the last deglaciation, at the start of the Bolling-Allerod and at the end of the Younger Dryas, but their underlying dynamics are unclear. Some abrupt climate changes may involve gradual forcing past a bifurcation point, in which a prevailing climate state
Bifurcation structure of an optical ring cavity
DEFF Research Database (Denmark)
Kubstrup, C.; Mosekilde, Erik
1996-01-01
One- and two-dimensional continuation techniques are applied to determine the basic bifurcation structure for an optical ring cavity with a nonlinear absorbing element (the Ikeda Map). By virtue of the periodic structure of the map, families of similar solutions develop in parameter space. Within...
Resource competition: a bifurcation theory approach.
Kooi, B.W.; Dutta, P.S.; Feudel, U.
2013-01-01
We develop a framework for analysing the outcome of resource competition based on bifurcation theory. We elaborate our methodology by readdressing the problem of competition of two species for two resources in a chemostat environment. In the case of perfect-essential resources it has been
Digital subtraction angiography of carotid bifurcation
International Nuclear Information System (INIS)
Vries, A.R. de.
1984-01-01
This study demonstrates the reliability of digital subtraction angiography (DSA) by means of intra- and interobserver investigations as well as indicating the possibility of substituting catheterangiography by DSA in the diagnosis of carotid bifurcation. Whenever insufficient information is obtained from the combination of non-invasive investigation and DSA, a catheterangiogram will be necessary. (Auth.)
Percutaneous coronary intervention for coronary bifurcation disease
DEFF Research Database (Denmark)
Lassen, Jens Flensted; Holm, Niels Ramsing; Banning, Adrian
2016-01-01
of combining the opinions of interventional cardiologists with the opinions of a large variety of other scientists on bifurcation management. The present 11th EBC consensus document represents the summary of the up-to-date EBC consensus and recommendations. It points to the fact that there is a multitude...
Bifurcation of self-folded polygonal bilayers
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.
Modified jailed balloon technique for bifurcation lesions.
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.
Local energy losses at positive and negative steps in subcritical ...
African Journals Online (AJOL)
Local energy losses occur when there is a transition in open channel flow. Even though local losses in subcritical open channel flow due to changes in channel width have been studied, to date no studies have been reported for losses due to changes in bed elevations. Steps are commonly used in engineering applications ...
Improving subcritical crack growth resistance for alumina glass dental composite
Zhu, Q.; With, de G.
2005-01-01
The improvement of subcritical crack growth (SCG) resistance for alumina glass dental composites was explored in this study. The addition of nitrogen to the glass phases in the composite was found to increase the SCG resistance, where the SCG exponent n increases from 22 for the oxide glass
Extraction of antioxidants from Chlorella sp. using subcritical water treatment
Zakaria, S. M.; Mustapa Kamal, S. M.; Harun, M. R.; Omar, R.; Siajam, S. I.
2017-06-01
Chlorella sp. microalgae is one of the main source of natural bioactive compounds used in the food and pharmaceutical industries. Subcritical water extraction is the technique that offers an efficient, non-toxic, and environmental-friendly method to obtain natural ingredients. In this work, the extracts of Chlorella sp. microalgae was evaluated in terms of: chemical composition, extraction (polysaccharides) yield and antioxidant activity, using subcritical water extraction. Extractions were performed at temperatures ranging from 100°C to 300°C. The results show that by using subcritical water, the highest yield of polysaccharides is 23.6 that obtained at 150°C. Analysis on the polysaccharides yield show that the contents were highly influenced by the extraction temperature. The individual antioxidant activity were evaluated by in vitro assay using a free radical method. In general, the antioxidant activity of the extracts obtained at different water temperatures was high, with values of 31.08-54.29 . The results indicated that extraction by subcritical water was effective and Chlorella sp. can be a useful source of natural antioxidants.
Introduction of fusion driven subcritical system plasma design
International Nuclear Information System (INIS)
Bin Wu
2003-01-01
Fusion driven subcritical nuclear system (FDS) is a multifunctional hybrid reactor, which could breed nuclear fuel, transmute long-lived wastes, producing tritium and so on. This paper presents an introduction of FDS plasma design. Several different advance equilibrium configurations have been proposed and a 1.5-D discharge simulation of FDS was also present
Comparative analysis of sub-critical transmutation reactor concepts
International Nuclear Information System (INIS)
Chang, S. H.
1997-01-01
The long-lived nuclear wastes have been substantially generated from the light water reactor for a few decades. The toxicity of these spent fuels will be higher than that of the uranium ore, even if those will be stored in the repository more than ten thousands. Hence the means of transmuting the key long-lived nuclear wastes, primarily the minor actinides, using a hybrid proton accelerator and subcritical transmutation reactor, are proposed. Until now, the representative concepts for a subcritical transmutation reactor are the Energy Amplifier, the OMEGA project, the ATW and the MSBR. The detailed concepts and the specifications are illustrated in Table 1. The design requirements for the subcritical transmutation reactor are the high transmutation rate of long-lived nuclear wastes, safety and economics. And to propose the subcritical transmutation reactor concepts, the coolant, the target material and fuel type are carefully considered. In these aspects, the representative concepts for a subcritical transmutation reactor in Table 1 have been surveyed. The requirements for a target and a coolant are the reliable, low maintenance operation and safe operation to minimize the wastes. The reliable, low maintenance operation and safe operation to minimize the wastes. The reliable coolant must have the low melting point, high heat capacity and excellent physical properties. And the target material must have high neutron yield for a given proton condition and easy heat removal capability. Therefore in respect with the above requirements, Pb-Bi is proposed as the coolant and the target material for the subcritical reactor. Because the neutron yield for a given proton energy increases linearly with mass number up to bismuth but in heavier elements spallation events sharply increase both the neutron and heat outputs, Pb-Bi meets not only such the requirements as the above for the coolant but also those for the coolant and target, the simplification of system can be achieved
Stochastic bifurcation in a model of love with colored noise
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.
Hopf-algebraic renormalization of QED in the linear covariant gauge
Energy Technology Data Exchange (ETDEWEB)
Kißler, Henry, E-mail: kissler@physik.hu-berlin.de
2016-09-15
In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.
Influence of surrounding environment on subcritical crack growth in marble
Nara, Yoshitaka; Kashiwaya, Koki; Nishida, Yuki; , Toshinori, Ii
2017-06-01
Understanding subcritical crack growth in rock is essential for determining appropriate measures to ensure the long-term integrity of rock masses surrounding structures and for construction from rock material. In this study, subcritical crack growth in marble was investigated experimentally, focusing on the influence of the surrounding environment on the relationship between the crack velocity and stress intensity factor. The crack velocity increased with increasing temperature and/or relative humidity. In all cases, the crack velocity increased with increasing stress intensity factor. However, for Carrara marble (CM) in air, we observed a region in which the crack velocity still increased with temperature, but the increase in the crack velocity with increasing stress intensity factor was not significant. This is similar to Region II of subcritical crack growth observed in glass in air. Region II in glass is controlled by mass transport to the crack tip. In the case of rock, the transport of water to the crack tip is important. In general, Region II is not observed for subcritical crack growth in rock materials, because rocks contain water. Because the porosity of CM is very low, the amount of water contained in the marble is also very small. Therefore, our results imply that we observed Region II in CM. Because the crack velocity increased in both water and air with increasing temperature and humidity, we concluded that dry conditions at low temperature are desirable for the long-term integrity of a carbonate rock mass. Additionally, mass transport to the crack tip is an important process for subcritical crack growth in rock with low porosity.
Subcriticality determination in ADS: Valina-Booster experiments
International Nuclear Information System (INIS)
Persson, C. M.; Gudowski, W.; Fokau, A.; Bournos, V.; Fokov, Y.; Routkovskaia, C.; Serafimovich, I.; Kiyavitskaya, H.
2007-01-01
A major problem in operating a full-scale subcritical accelerator-driven system (ADS) is to ensure sufficient margin to criticality. Therefore, reliable techniques for subcriticality monitoring are required. In order to develop such techniques, a full understanding of existing reactivity determination methods is essential. In this work, reactivity determination methods, such as pulsed neutron source methods and noise methods, are studied experimentally in the subcritical facility YALINA-Booster. YALINA-Booster: The subcritical assembly YALINA-Booster: recently constructed at the Joint Institute for Power and Nuclear Research - Sosny, consists of a subcritical core driven by an external neutron source. The neutron source is a powerful neutron generator consisting of a deuteron accelerator and a target of deuterium or tritium embedded in titanium. Through (d, d) - or (d, t)-reactions neutrons are created with energy around 2.5 MeV and 14.1 MeV respectively. Neutrons are born in the centre of the core and multiply through a lead matrix fuelled with highly enriched uranium (90% and 36%). This zone is referred to as the booster zone and is surrounded by a thermal zone, moderated by polyethylene. In order to reach sufficient high effective multiplication factor, the thermal zone is fuelled by approximately one thousand rods of 10% enriched uranium dioxide in cylindrical geometry. To prevent thermal neutrons from diffusing into the fast booster zone, an interface, consisting of boron carbide and natural uranium rods, is located between the zones. YALINA-Booster has a radial graphite reflector of thickness 24 cm. Experiments: Experiments using the neutron source in pulsed mode will be presented, relying on methods such as the area method and the method of prompt neutron decay rate determination. Moreover, results from noise analysis using for instance the Feynman-α method will be presented
Symmetry breaking bifurcations of a current sheet
International Nuclear Information System (INIS)
Parker, R.D.; Dewar, R.L.; Johnson, J.L.
1990-01-01
Using a time evolution code with periodic boundary conditions, the viscoresistive hydromagnetic equations describing an initially static, planar current sheet with large Lundquist number have been evolved for times long enough to reach a steady state. A cosh 2 x resistivity model was used. For long periodicity lengths L p , the resistivity gradient drives flows that cause forced reconnection at X point current sheets. Using L p as a bifurcation parameter, two new symmetry breaking bifurcations were found: a transition to an asymmetric island chain with nonzero, positive, or negative phase velocity, and a transition to a static state with alternating large and small islands. These states are reached after a complex transient behavior, which involves a competition between secondary current sheet instability and coalescence
Symmetry breaking bifurcations of a current sheet
International Nuclear Information System (INIS)
Parker, R.D.; Dewar, R.L.; Johnson, J.L.
1988-08-01
Using a time evolution code with periodic boundary conditions, the viscoresistive hydromagnetic equations describing an initially static, planar current sheet with large Lundquist number have been evolved for times long enough to reach a steady state. A cosh 2 x resistivity model was used. For long periodicity lengths, L p , the resistivity gradient drives flows which cause forced reconnection at X point current sheets. Using L p as a bifurcation parameter, two new symmetry breaking bifurcations were found - a transition to an asymmetric island chain with nonzero, positive or negative phase velocity, and a transition to a static state with alternating large and small islands. These states are reached after a complex transient behavior which involves a competition between secondary current sheet instability and coalescence. 31 refs., 6 figs
Experimental Study of Flow in a Bifurcation
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.
Generalized Ginzburg-Landau equation for self-pulsing instability in a two-photon laser
Energy Technology Data Exchange (ETDEWEB)
Cunzheng, Ning; Haken, H [Inst. fuer Theoretische Physik und Synergetik, Univ. Stuttgart (Germany)
1989-10-01
A nonlinear analysis is made for a degenerate two-photon ring laser near its critical point corresponding to a self-pulsing instability by using the slaving principle and normal form theory. It turns out that the system undergoes two kinds of transitions, a usual Hopf bifurcation to a stable or unstable limit cycle and a co-dimension two Hopf bifurcation where the limit cycles disappear. An analytical criterion is given to distinguish the super - form the sub-critical bifurcation. We have also solved the equations numerically to confirm and to supplement our analytical results. In the case of super-critical bifurcation, a period-doubling bifurcation sequence to chaos is also observed with the decrease in pumping. (orig.).
Bifurcations and chaos of DNA solitonic dynamics
International Nuclear Information System (INIS)
Gonzalez, J.A.; Martin-Landrove, M.; Carbo, J.R.; Chacon, M.
1994-09-01
We investigated the nonlinear DNA torsional equations proposed by Yakushevich in the presence of damping and external torques. Analytical expressions for some solutions are obtained in the case of the isolated chain. Special attention is paid to the stability of the solutions and the range of soliton interaction in the general case. The bifurcation analysis is performed and prediction of chaos is obtained for some set of parameters. Some biological implications are suggested. (author). 11 refs, 13 figs
Torus bifurcations in multilevel converter systems
DEFF Research Database (Denmark)
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Yanochkina, Olga O.
2011-01-01
embedded one into the other and with their basins of attraction delineated by intervening repelling tori. The paper illustrates the coexistence of three stable tori with different resonance behaviors and shows how reconstruction of these tori takes place across the borders of different dynamical regimes....... The paper also demonstrates how pairs of attracting and repelling tori emerge through border-collision torus-birth and border-collision torus-fold bifurcations. © 2011 World Scientific Publishing Company....
Perturbed period-doubling bifurcation. I. Theory
DEFF Research Database (Denmark)
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1990-01-01
-defined way that is a function of the amplitude and the frequency of the signal. New scaling laws between the amplitude of the signal and the detuning δ are found; these scaling laws apply to a variety of quantities, e.g., to the shift of the bifurcation point. It is also found that the stability...... of a microwave-driven Josephson junction confirm the theory. Results should be of interest in parametric-amplification studies....
Sex differences in intracranial arterial bifurcations
DEFF Research Database (Denmark)
Lindekleiv, Haakon M; Valen-Sendstad, Kristian; Morgan, Michael K
2010-01-01
Subarachnoid hemorrhage (SAH) is a serious condition, occurring more frequently in females than in males. SAH is mainly caused by rupture of an intracranial aneurysm, which is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation. T....... The female preponderance is usually explained by systemic factors (hormonal influences and intrinsic wall weakness); however, the uneven sex distribution of intracranial aneurysms suggests a possible physiologic factor-a local sex difference in the intracranial arteries....
Drift bifurcation detection for dissipative solitons
International Nuclear Information System (INIS)
Liehr, A W; Boedeker, H U; Roettger, M C; Frank, T D; Friedrich, R; Purwins, H-G
2003-01-01
We report on the experimental detection of a drift bifurcation for dissipative solitons, which we observe in the form of current filaments in a planar semiconductor-gas-discharge system. By introducing a new stochastic data analysis technique we find that due to a change of system parameters the dissipative solitons undergo a transition from purely noise-driven objects with Brownian motion to particles with a dynamically stabilized finite velocity
Twist deformations leading to κ-Poincaré Hopf algebra and their application to physics
International Nuclear Information System (INIS)
Jurić, Tajron; Meljanac, Stjepan; Samsarov, Andjelo
2016-01-01
We consider two twist operators that lead to kappa-Poincaré Hopf algebra, the first being an Abelian one and the second corresponding to a light-like kappa-deformation of Poincaré algebra. The adventage of the second one is that it is expressed solely in terms of Poincaré generators. In contrast to this, the Abelian twist goes out of the boundaries of Poincaré algebra and runs into envelope of the general linear algebra. Some of the physical applications of these two different twist operators are considered. In particular, we use the Abelian twist to construct the statistics flip operator compatible with the action of deformed symmetry group. Furthermore, we use the light-like twist operator to define a star product and subsequently to formulate a free scalar field theory compatible with kappa-Poincaré Hopf algebra and appropriate for considering the interacting ϕ 4 scalar field model on kappa-deformed space. (paper)
Energized Oxygen : Speiser Current Sheet Bifurcation
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
International Nuclear Information System (INIS)
Sriram, K.
2006-01-01
This paper describes both the experimental and numerical investigations on the effect of positive electrical feedback in the oscillating Belovsou-Zhabotinsky (BZ) reaction under batch conditions. Positive electrical feedback causes an increase in the amplitude and period of the oscillations with the corresponding increase of the feedback strength. Oregonator model with a positive feedback term suitably incorporated in one of the dynamical variables is used to account for these experimental observations. Further, the effect of positive feedback on the Hopf points are investigated numerically by constructing the bifurcation diagrams. In the absence of feedback, for a particular stoichiometric parameter, the model exhibits both supercritical and subcritical Hopf bifurcations with canard existing near the former Hopf point. In the presence of positive feedback it is observed that (i) both the Hopf points advances, (ii) the distance between the two Hopf points decreases linearly, while the period increases exponentially with the increase of feedback strength near the Hopf points, (iii) only supercritical Hopf point without canard survives for a very strong positive feedback strength and (iv) moderate feedback strength takes the system away from limit cycle to the canard regime. These observations are explained in terms of Field-Koeroes-Noyes mechanism of the Belousov-Zhabotinsky reaction. This may be the first instance where the advancement of Hopf points due to positive feedback is clearly shown
Solubility and degradation of paracetamol in subcritical water
Directory of Open Access Journals (Sweden)
Emire Zuhal
2017-01-01
Full Text Available In this study, solubility and degradation of paracetamol were examined using subcritical water. Effect of temperature and static time was investigated during solubility process in subcritical water at constant pressure (50 bar. Experimental results show that temperature and static time have crucial effect on the degradation and solubility rates. Maximum mole fraction for solubility of paracetamol was obtained at 403 K as (14.68 ± 0.74×103. Approximation model for solubility of paracetamol was proposed. O2 and H2O2 were used in degradation process of paracetamol. Maximum degradation rate was found as 68.66 ± 1.05 and 100 ± 0.00 % using O2 and H2O2, respectively.
Subcriticality calculation in nuclear reactors with external neutron sources
Energy Technology Data Exchange (ETDEWEB)
Silva, Adilson Costa da; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE). Programa de Engenharia Nuclear]. E-mails: asilva@con.ufrj.br; aquilino@lmp.ufrj.br; fernando@con.ufrj.br
2007-07-01
The main objective of this paper consists on the development of a methodology to monitor subcriticality. We used the inverse point kinetic equation with 6 precursor groups and external neutron sources for the calculation of reactivity. The input data for the inverse point kinetic equation was adjusted, in order to use the neutron counting rates obtained from the subcritical multiplication (1/M) in a nuclear reactor. In this paper, we assumed that the external neutron sources strength is constant and we define it in terms of a known initial condition. The results obtained from inverse point kinetic equation with external neutron sources were compared with the results obtained with a benchmark calculation, and showed good accuracy (author)
Subcriticality calculation in nuclear reactors with external neutron sources
International Nuclear Information System (INIS)
Silva, Adilson Costa da; Martinez, Aquilino Senra; Silva, Fernando Carvalho da
2007-01-01
The main objective of this paper consists on the development of a methodology to monitor subcriticality. We used the inverse point kinetic equation with 6 precursor groups and external neutron sources for the calculation of reactivity. The input data for the inverse point kinetic equation was adjusted, in order to use the neutron counting rates obtained from the subcritical multiplication (1/M) in a nuclear reactor. In this paper, we assumed that the external neutron sources strength is constant and we define it in terms of a known initial condition. The results obtained from inverse point kinetic equation with external neutron sources were compared with the results obtained with a benchmark calculation, and showed good accuracy (author)
A microfluidic sub-critical water extraction instrument
Sherrit, Stewart; Noell, Aaron C.; Fisher, Anita; Lee, Mike C.; Takano, Nobuyuki; Bao, Xiaoqi; Kutzer, Thomas C.; Grunthaner, Frank
2017-11-01
This article discusses a microfluidic subcritical water extraction (SCWE) chip for autonomous extraction of amino acids from astrobiologically interesting samples. The microfluidic instrument is composed of three major components. These include a mixing chamber where the soil sample is mixed and agitated with the solvent (water), a subcritical water extraction chamber where the sample is sealed with a freeze valve at the chip inlet after a vapor bubble is injected into the inlet channels to ensure the pressure in the chip is in equilibrium with the vapor pressure and the slurry is then heated to ≤200 °C in the SCWE chamber, and a filter or settling chamber where the slurry is pumped to after extraction. The extraction yield of the microfluidic SCWE chip process ranged from 50% compared to acid hydrolysis and 80%-100% compared to a benchtop microwave SCWE for low biomass samples.
Evaluation of subcritical hybrid systems loaded with reprocessed fuel
International Nuclear Information System (INIS)
Velasquez, Carlos E.; Barros, Graiciany de P.; Pereira, Claubia; Veloso, Maria Auxiliadora F.; Costa, Antonella L.
2015-01-01
Highlights: • Accelerator driven systems (ADS) and fusion–fission systems are investigated for transmutation and fuel regeneration. • The calculations were performed using Monteburns code. • The results indicate the most suitable system for achieve transmutation. - Abstract: Two subcritical hybrid systems containing spent fuel reprocessed by Ganex technique and spiked with thorium were submitted to neutron irradiation of two different sources: ADS (Accelerator-driven subcritical) and Fusion. The aim is to investigate the nuclear fuel evolution using reprocessed fuel and the neutronic parameters under neutron irradiation. The source multiplication factor and fuel depletion for both systems were analysed during 10 years. The simulations were performed using MONTEBURNS code (MCNP/ORIGEN). The results indicate the main differences when irradiating the fuel with different neutron sources as well as the most suitable system for achieving transmutation
Subcritical to supercritical flow transition in a horizontal stratified flow
International Nuclear Information System (INIS)
Asaka, H.; Kukita, Y.
1995-01-01
The conditions for a transition from hydraulically subcritical to supercritical flow in the hot legs of a pressurized water reactor (PWR) were studied using data obtained from a two-phase natural circulation experiment conducted at the ROSA-IV Large Scale Test Facility (LSTF). The LSTF is a 1/48 volumetrically-scaled simulator of a Westinghouse-type PWR. The conditions for the transition were compared with the theory of Gardner. While the model explains the trend in the experimental data, the quantitative agreement was not satisfactory. It was found that the conditions for the transition from the subcritical to supercritical flow were predicted well by introducing energy loss term into the theory. (author)
Simulation an Accelerator driven Subcritical Reactor core with thorium fuel
International Nuclear Information System (INIS)
Shirmohammadi, L.; Pazirandeh, A.
2011-01-01
The main purpose of this work is simulation An Accelerator driven Subcritical core with Thorium as a new generation nuclear fuel. In this design core , A subcritical core coupled to an accelerator with proton beam (E p =1 GeV) is simulated by MCNPX code .Although the main purpose of ADS systems are transmutation and use MA (Minor Actinides) as a nuclear fuel but another use of these systems are use thorium fuel. This simulated core has two fuel assembly type : (Th-U) and (U-Pu) . Consequence , Neutronic parameters related to ADS core are calculated. It has shown that Thorium fuel is use able in this core and less nuclear waste ,Although Iran has not Thorium reserves but study on Thorium fuel cycle can open a new horizontal in use nuclear energy as a clean energy and without nuclear waste
Breaking rocks made easy: subcritical processes and tectonic predesign
Voigtlaender, Anne; Krautblatter, Michael
2017-04-01
In geomorphic studies, to change in landforms, e.g. by rock slope failure, fluvial or glacial erosion, a threshold is commonly assumed, which is crossed either by an increase in external driving or a decrease of internal resisting forces, respectively. If the threshold is crossed, bedrock breaks and slope fails, rivers incise and glaciers plug and sew their bed. Here we put forward a focus on the decrease of the resisting forces, as an increase in the driving forces, to match the strength of bedrock, is not that likely. We suggest that the degradation of resisting forces of bedrock can be better explained by subcritical processes like creep, fatigue and stress corrosion interplaying with tectonic predesign. Both concepts, subcritical processes and tectonic predesign have been issued in the last century, but have not been widely accepted nor have their assumptions been explicitly stressed in recent case studies. Moreover both concepts profit especially on scale issues if merged. Subcritical crack growth, includes different mechanisms promoting fractures well below the ultimate strength. Single infinitesimal but irreversible damage and deformations are induced in the material over time. They interact with inherent microstructural flaws and low applied stresses, limiting local strength and macroscopic behavior of bedrock. This reissues the concept of tectonic predesigned, as proposed by A.E. Scheidegger, which not only encompasses structural features that determine the routing of drainage patterns and shear planes, e.g. joints, faults and foliations, but also the (neo)tectonic stress-field and the (in-situ) strain state of bedrocks and mountains. Combining subcritical processes and tectonic predesign we can better explain, why and where we see a dissected, eroded and geomorphic divers' landscape. In this conceptual framework actual magnitudes of the driving forces are accounted for and so is the nature of the bedrock material, to better understand the trajectories of
A simple proof of exponential decay of subcritical contact processes
Czech Academy of Sciences Publication Activity Database
Swart, Jan M.
2018-01-01
Roč. 170, 1-2 (2018), s. 1-9 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA16-15238S Institutional support: RVO:67985556 Keywords : subcritical contact process * sharpness of the phase transition * eigenmeasure Subject RIV: BA - General Mathematics Impact factor: 1.895, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/swart-0462694.pdf
Inverse kinetics for subcritical systems with external neutron source
International Nuclear Information System (INIS)
Carvalho Gonçalves, Wemerson de; Martinez, Aquilino Senra; Carvalho da Silva, Fernando
2017-01-01
Highlights: • It was developed formalism for reactivity calculation. • The importance function is related to the system subcriticality. • The importance function is also related with the value of the external source. • The equations were analyzed for seven different levels of sub criticality. • The results are physically consistent with others formalism discussed in the paper. - Abstract: Nuclear reactor reactivity is one of the most important properties since it is directly related to the reactor control during the power operation. This reactivity is influenced by the neutron behavior in the reactor core. The time-dependent neutrons behavior in response to any change in material composition is important for the reactor operation safety. Transient changes may occur during the reactor startup or shutdown and due to accidental disturbances of the reactor operation. Therefore, it is very important to predict the time-dependent neutron behavior population induced by changes in neutron multiplication. Reactivity determination in subcritical systems driven by an external neutron source can be obtained through the solution of the inverse kinetics equation for subcritical nuclear reactors. The main purpose of this paper is to find the solution of the inverse kinetics equation the main purpose of this paper is to device the inverse kinetics equations for subcritical systems based in a previous paper published by the authors (Gonçalves et al., 2015) and by (Gandini and Salvatores, 2002; Dulla et al., 2006). The solutions of those equations were also obtained. Formulations presented in this paper were tested for seven different values of k eff with external neutrons source constant in time and for a powers ratio varying exponentially over time.
Development and Investigation of Reactivity Measurement Methods in Subcritical Cores
Energy Technology Data Exchange (ETDEWEB)
Wright, Johanna
2005-05-01
Subcriticality measurements during core loading and in future accelerator driven systems have a clear safety relevance. In this thesis two subcriticality methods are treated: the Feynman-alpha and the source modulation method. The Feynman-alpha method is a technique to determine the reactivity from the relative variance of the detector counts during a measurement period. The period length is varied to get the full time dependence of the variance-to-mean. The corresponding theoretical formula was known only with stationary sources. In this thesis, due to its relevance for novel reactivity measurement methods, the Feynman-alpha formulae for pulsed sources for both the stochastic and the deterministic cases are treated. Formulae neglecting as well as including the delayed neutrons are derived. The formulae neglecting delayed neutrons are experimentally verified with quite good agreement. The second reactivity measurement technique investigated in this thesis is the so-called source modulation technique. The theory of the method was elaborated on the assumption of point kinetics, but in practice the method will be applied by using the signal from a single local neutron detector. Applicability of the method therefore assumes point kinetic behaviour of the core. Hence, first the conditions of the point kinetic behaviour of subcritical cores was investigated. After that the performance of the source modulation technique in the general case as well as and in the limit of exact point kinetic behaviour was examined. We obtained the unexpected result that the method has a finite, non-negligible error even in the limit of point kinetic behaviour, and a substantial error in the operation range of future accelerator driven subcritical reactors (ADS). In practice therefore the method needs to be calibrated by some other method for on-line applications.
Development and Investigation of Reactivity Measurement Methods in Subcritical Cores
International Nuclear Information System (INIS)
Wright, Johanna
2005-05-01
Subcriticality measurements during core loading and in future accelerator driven systems have a clear safety relevance. In this thesis two subcriticality methods are treated: the Feynman-alpha and the source modulation method. The Feynman-alpha method is a technique to determine the reactivity from the relative variance of the detector counts during a measurement period. The period length is varied to get the full time dependence of the variance-to-mean. The corresponding theoretical formula was known only with stationary sources. In this thesis, due to its relevance for novel reactivity measurement methods, the Feynman-alpha formulae for pulsed sources for both the stochastic and the deterministic cases are treated. Formulae neglecting as well as including the delayed neutrons are derived. The formulae neglecting delayed neutrons are experimentally verified with quite good agreement. The second reactivity measurement technique investigated in this thesis is the so-called source modulation technique. The theory of the method was elaborated on the assumption of point kinetics, but in practice the method will be applied by using the signal from a single local neutron detector. Applicability of the method therefore assumes point kinetic behaviour of the core. Hence, first the conditions of the point kinetic behaviour of subcritical cores was investigated. After that the performance of the source modulation technique in the general case as well as and in the limit of exact point kinetic behaviour was examined. We obtained the unexpected result that the method has a finite, non-negligible error even in the limit of point kinetic behaviour, and a substantial error in the operation range of future accelerator driven subcritical reactors (ADS). In practice therefore the method needs to be calibrated by some other method for on-line applications
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Bifurcation of rupture path by linear and cubic damping force
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.
Measurement of kinetic parameters in the fast subcritical core MASURCA
International Nuclear Information System (INIS)
Baeten, Peter; Abderrahim, Hamid Aiet
2004-01-01
In the MUSE shared cost action of the European Fifth Framework Program measurements have been performed to investigate the neutronic behavior of the fast subcritical core MASURCA coupled with the GENEPI accelerator. The aim is to examine the applicability of different measurement techniques for the determination of the main kinetic parameters. The measurement of Rossi-alpha distributions, recorded with the accelerator turned off, showed that the analysis of the obtained distributions is feasible for deep subcritical levels, but with strongly deteriorated statistics. From Rossi-alpha distributions, recorded with the pulsed neutron source in operation, the alpha decay constant was easily derived due to good statistics on the correlated signal resulting from the strong intensity of the neutron pulse. When applying the pulsed neutron source analysis, the reactivity (in dollars) together with the ratio of the mean neutron lifetime l and the effective delayed neutron fraction β eff is immediately derived. Although these first results are very promising, further measurements are needed to qualify the method at larger subcritical levels which are representative for future ADS
Calculated characteristics of subcritical assembly with anisotropic transport of neutrons
International Nuclear Information System (INIS)
Gorin, N.V.; Lipilina, E.N.; Lyutov, V.D.; Saukov, A.I.
2003-01-01
There was considered possibility of creating enough sub-critical system that multiply neutron fluence from a primary source by many orders. For assemblies with high neutron tie between parts, it is impossible. That is why there was developed a construction consisting of many units (cascades) having weak feedback with preceding cascades. The feedback attenuation was obtained placing layers of slow neutron absorber and moderators between the cascades of fission material. Anisotropy of fast neutron transport through the layers was used. The system consisted of many identical cascades aligning one by another. Each cascade consists of layers of moderator, fissile material and absorber of slow neutrons. The calculations were carried out using the code MCNP.4a with nuclear data library ENDF/B5. In this construction neutrons spread predominantly in one direction multiplying in each next fissile layer, and they attenuate considerably in the opposite direction. In a calculated construction, multiplication factor of one cascade is about 1.5 and multiplication factor of whole construction composed of n cascades is 1.5 n . Calculated keff value is 0.9 for one cascade and does not exceed 0.98 for a system containing any number of cascades. Therefore the assembly is always sub-critical and therefore it is safe in respect of criticality. There was considered using such a sub-critical assembly to create a powerful neutron fluence for neutron boron-capturing therapy. The system merits and demerits were discussed. (authors)
Accelerator-driven subcritical facility:Conceptual design development
Gohar, Yousry; Bolshinsky, Igor; Naberezhnev, Dmitry; Duo, Jose; Belch, Henry; Bailey, James
2006-06-01
A conceptual design development of an accelerator-driven subcritical facility has been carried out in the preparation of a joint activity with Kharkov Institute of Physics and Technology of Ukraine. The main functions of the facility are the medical isotope production and the support of the Ukraine nuclear industry. An electron accelerator is considered to drive the subcritical assembly. The neutron source intensity and spectrum have been studied. The energy deposition, spatial neutron generation, neutron utilization fraction, and target dimensions have been quantified to define the main target performance parameters, and to select the target material and beam parameters. Different target conceptual designs have been developed based the engineering requirements including heat transfer, thermal hydraulics, structure, and material issues. The subcritical assembly is designed to obtain the highest possible neutron flux level with a Keff of 0.98. Different fuel materials, uranium enrichments, and reflector materials are considered in the design process. The possibility of using low enrichment uranium without penalizing the facility performance is carefully evaluated. The mechanical design of the facility has been developed to maximize its utility and minimize the time for replacing the target and the fuel assemblies. Safety, reliability, and environmental considerations are included in the facility conceptual design. The facility is configured to accommodate future design improvements, upgrades, and new missions. In addition, it has large design margins to accommodate different operating conditions and parameters. In this paper, the conceptual design and the design analyses of the facility will be presented.
Plant pathogenic bacteria inject a cocktail of effector proteins into host plant cells to modulate the host immune response, thereby promoting pathogenicity. How or whether these effectors work cooperatively is largely unknown. The Pseudomonas syringae DC3000 effector HopF2 suppresses the host plan...
Predicting bifurcation angle effect on blood flow in the microvasculature.
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 theory for toroidal MHD instabilities
International Nuclear Information System (INIS)
Maschke, E.K.; Morros Tosas, J.; Urquijo, G.
1992-01-01
Using a general representation of magneto-hydrodynamics in terms of stream functions and potentials, proposed earlier, a set of reduced MHD equations for the case of toroidal geometry had been derived by an appropriate ordering with respect to the inverse aspect ratio. When all dissipative terms are neglected in this reduced system, it has the same linear stability limits as the full ideal MHD equations, to the order considered. When including resistivity, thermal conductivity and viscosity, we can apply bifurcation theory to investigate nonlinear stationary solution branches related to various instabilities. In particular, we show that a stationary solution of the internal kink type can be found
Spijkerboer, T.P.
2017-01-01
The externalization of European migration policy has resulted in a bifurcation of global human mobility, which is divided along a North/South axis. In two judgments, the EU Court of Justice was confronted with cases challenging the exclusion of Syrian refugees from Europe. These cases concern core
Wiener-Hopf factorization of piecewise meromorphic matrix-valued functions
International Nuclear Information System (INIS)
Adukov, Victor M
2009-01-01
Let D + be a multiply connected domain bounded by a contour Γ, let D - be the complement of D + union Γ in C-bar=C union {∞}, and a(t) be a continuous invertible matrix-valued function on Γ which can be meromorphically extended into the open disconnected set D - (as a piecewise meromorphic matrix-valued function). An explicit solution of the Wiener-Hopf factorization problem for a(t) is obtained and the partial factorization indices of a(t) are calculated. Here an explicit solution of a factorization problem is meant in the sense of reducing it to the investigation of finitely many systems of linear algebraic equations with matrices expressed in closed form, that is, in quadratures. Bibliography: 15 titles.
International Nuclear Information System (INIS)
Kanakoglou, K.; Daskaloyannis, C.; Herrera-Aguilar, A.
2010-01-01
The mathematical structure of a mixed paraparticle system (combining both parabosonic and parafermionic degrees of freedom) commonly known as the Relative Parabose Set, will be investigated and a braided group structure will be described for it. A new family of realizations of an arbitrary Lie superalgebra will be presented and it will be shown that these realizations possess the valuable representation-theoretic property of transferring invariably the super-Hopf structure. Finally two classes of virtual applications will be outlined: The first is of interest for both mathematics and mathematical physics and deals with the representation theory of infinite dimensional Lie superalgebras, while the second is of interest in theoretical physics and has to do with attempts to determine specific classes of solutions of the Skyrme model.
Energy Technology Data Exchange (ETDEWEB)
Milosevic, M; Stefanovic, D; Popovic, D; Pesic, M; Zavaljevski, N; Nikolic, D; Arsenovic, M [Boris Kidric Institute of nuclear sciences Vinca, Belgrade (Yugoslavia)
1988-10-15
This report contains two parts. Part one covers the objective and fundamental elements for the choice of fast subcritical system 'Mala Lasta', review of the existing fast subcritical assemblies, and a description of the available domestic computer codes applied for calculating neutron reactor parameters. Comparison of results obtained by these codes for a number of existing subcritical assemblies was used for the choice of the design project described in part two of this report. It contains detailed description of the operating parameters of the chosen subcritical system based on the obtained calculated parameters.
Subcritical tests - nuclear weapon testing under the Comprehensive Test Ban Treaty
International Nuclear Information System (INIS)
Hoeibraaten, S.
1998-10-01
The report discusses possible nuclear weapons related experiments and whether these are permitted under the 1996 Comprehensive Test Ban Treaty (CTBT). The term ''subcritical experiments'' as used in the United States includes experiments in which one studies fissile materials (so far only plutonium) under extreme conditions generated by conventional high explosives, and in which a self-sustained chain reaction never develops in the fissile material. The known facts about the American subcritical experiments are presented. There is very little reason to doubt that these experiments were indeed subcritical and therefore permitted under the CTBT. Little is known about the Russian efforts that are being made on subcritical experiments
Bifurcation into functional niches in adaptation.
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.
Bifurcation theory of ac electric arcing
International Nuclear Information System (INIS)
Christen, Thomas; Peinke, Emanuel
2012-01-01
The performance of alternating current (ac) electric arcing devices is related to arc extinction or its re-ignition at zero crossings of the current (so-called ‘current zero’, CZ). Theoretical investigations thus usually focus on the transient behaviour of arcs near CZ, e.g. by solving the modelling differential equations in the vicinity of CZ. This paper proposes as an alternative approach to investigate global mathematical properties of the underlying periodically driven dynamic system describing the electric circuit containing the arcing device. For instance, the uniqueness of the trivial solution associated with the insulating state indicates the extinction of any arc. The existence of non-trivial attractors (typically a time-periodic state) points to a re-ignition of certain arcs. The performance regions of arcing devices, such as circuit breakers and arc torches, can thus be identified with the regions of absence and existence, respectively, of non-trivial attractors. Most important for applications, the boundary of a performance region in the model parameter space is then associated with the bifurcation of the non-trivial attractors. The concept is illustrated for simple black-box arc models, such as the Mayr and the Cassie model, by calculating for various cases the performance boundaries associated with the bifurcation of ac arcs. (paper)
Hou, Saing Paul; Haddad, Wassim M; Meskin, Nader; Bailey, James M
2015-12-01
With the advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in understanding the molecular properties of anesthetic agents. However, there has been little focus on how the molecular properties of anesthetic agents lead to the observed macroscopic property that defines the anesthetic state, that is, lack of responsiveness to noxious stimuli. In this paper, we use dynamical system theory to develop a mechanistic mean field model for neural activity to study the abrupt transition from consciousness to unconsciousness as the concentration of the anesthetic agent increases. The proposed synaptic drive firing-rate model predicts the conscious-unconscious transition as the applied anesthetic concentration increases, where excitatory neural activity is characterized by a Poincaré-Andronov-Hopf bifurcation with the awake state transitioning to a stable limit cycle and then subsequently to an asymptotically stable unconscious equilibrium state. Furthermore, we address the more general question of synchronization and partial state equipartitioning of neural activity without mean field assumptions. This is done by focusing on a postulated subset of inhibitory neurons that are not themselves connected to other inhibitory neurons. Finally, several numerical experiments are presented to illustrate the different aspects of the proposed theory.
Identification of dynamic basins in boiling fluxes
International Nuclear Information System (INIS)
Juanico, L.E.
1997-01-01
A theoretical and experimental study of the dynamic behavior of a boiling channel is presented. In particular, the existence of different basins of attraction during instabilities was established. A fully analytical treatment of boiling channel dynamics were performed using a algebraic delay model. Subcritical and supercritical Hopf bifurcations could be identified and analyzed using perturbation methods. The derivation of a fully analytical criterion for Hopf bifurcation transcription was applied to determine the amplitude of the limit cycles and the maximum allowed perturbations necessary to break the system stability. A lumped parameters model which allows the representation of flow reversal is presented. The dynamic of very large amplitude oscillations, out of the Hopf bifurcation domain, was studied. The analysis revealed the existence of new dynamical basins of attraction, where the system may evolve to and return from with hysteresis. Finally, an experimental study was conducted, in a water loop at atmospheric pressure, designed to reproduce the operating conditions analyzed in the theory. Different dynamic phase previously predicted in the theory were found and their nonlinear characteristics were studied. In particular, subcritical and supercritical Hopf bifurcations and very large amplitude oscillations with flow reversal were identified. (author). 53 refs., figs
Analysis of Vehicle Steering and Driving Bifurcation Characteristics
Directory of Open Access Journals (Sweden)
Xianbin Wang
2015-01-01
Full Text Available The typical method of vehicle steering bifurcation analysis is based on the nonlinear autonomous vehicle model deriving from the classic two degrees of freedom (2DOF linear vehicle model. This method usually neglects the driving effect on steering bifurcation characteristics. However, in the steering and driving combined conditions, the tyre under different driving conditions can provide different lateral force. The steering bifurcation mechanism without the driving effect is not able to fully reveal the vehicle steering and driving bifurcation characteristics. Aiming at the aforementioned problem, this paper analyzed the vehicle steering and driving bifurcation characteristics with the consideration of driving effect. Based on the 5DOF vehicle system dynamics model with the consideration of driving effect, the 7DOF autonomous system model was established. The vehicle steering and driving bifurcation dynamic characteristics were analyzed with different driving mode and driving torque. Taking the front-wheel-drive system as an example, the dynamic evolution process of steering and driving bifurcation was analyzed by phase space, system state variables, power spectral density, and Lyapunov index. The numerical recognition results of chaos were also provided. The research results show that the driving mode and driving torque have the obvious effect on steering and driving bifurcation characteristics.
Sediment discharge division at two tidally influenced river bifurcations
Sassi, M.G.; Hoitink, A.J.F.; Vermeulen, B.; Hidayat, H.
2013-01-01
[1] We characterize and quantify the sediment discharge division at two tidally influenced river bifurcations in response to mean flow and secondary circulation by employing a boat-mounted acoustic Doppler current profiler (ADCP), to survey transects at bifurcating branches during a semidiurnal
Bifurcations of heterodimensional cycles with two saddle points
Energy Technology Data Exchange (ETDEWEB)
Geng Fengjie [School of Information Technology, China University of Geosciences (Beijing), Beijing 100083 (China)], E-mail: gengfengjie_hbu@163.com; Zhu Deming [Department of Mathematics, East China Normal University, Shanghai 200062 (China)], E-mail: dmzhu@math.ecnu.edu.cn; Xu Yancong [Department of Mathematics, East China Normal University, Shanghai 200062 (China)], E-mail: yancongx@163.com
2009-03-15
The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed.
Numerical bifurcation analysis of a class of nonlinear renewal equations
Breda, Dimitri; Diekmann, Odo; Liessi, Davide; Scarabel, Francesca
2016-01-01
We show, by way of an example, that numerical bifurcation tools for ODE yield reliable bifurcation diagrams when applied to the pseudospectral approximation of a one-parameter family of nonlinear renewal equations. The example resembles logistic-and Ricker-type population equations and exhibits
Bifurcations of heterodimensional cycles with two saddle points
International Nuclear Information System (INIS)
Geng Fengjie; Zhu Deming; Xu Yancong
2009-01-01
The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed.
Critical bifurcation surfaces of 3D discrete dynamics
Directory of Open Access Journals (Sweden)
Michael Sonis
2000-01-01
Full Text Available This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.
Bifurcation of transition paths induced by coupled bistable systems.
Tian, Chengzhe; Mitarai, Namiko
2016-06-07
We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example and show that its transition paths are bifurcating. We then derive a criterion to predict the bifurcation of transition paths in a generalized coupled bistable system. We confirm the validity of the theory for the example system by numerical simulation. We also demonstrate in the example system that, if the steady states of individual gene circuits are not changed by the coupling, the bifurcation pattern is not dependent on the number of gene circuits. We further show that the transition rate exponentially decreases with the number of gene circuits when the transition path does not bifurcate, while a bifurcation facilitates the transition by lowering the quasi-potential energy barrier.
Bifurcation of solutions to Hamiltonian boundary value problems
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.
Convection in a nematic liquid crystal with homeotropic alignment and heated from below
Energy Technology Data Exchange (ETDEWEB)
Ahlers, G. [Univ. of California, Santa Barbara, CA (United States)
1995-12-31
Experimental results for convection in a thin horizontal layer of a homeotropically aligned nematic liquid crystal heated from below and in a vertical magnetic field are presented. A subcritical Hopf bifurcation leads to the convecting state. There is quantitative agreement between the measured and the predicted bifurcation line as a function of magnetic field. The nonlinear state near the bifurcation is one of spatio-temporal chaos which seems to be the result of a zig-zag instability of the straight-roll state.
Energy Technology Data Exchange (ETDEWEB)
Shimizu, Kuniyasu, E-mail: kuniyasu.shimizu@it-chiba.ac.jp [Department of Electrical, Electronics and Computer Engineering, Chiba Institute of Technology, Narashino 275-0016 (Japan); Sekikawa, Munehisa [Department of Mechanical and Intelligent Engineering, Utsunomiya University, Utsunomiya 321-8585 (Japan); Inaba, Naohiko [Organization for the Strategic Coordination of Research and Intellectual Property, Meiji University, Kawasaki 214-8571 (Japan)
2015-02-15
Bifurcations of complex mixed-mode oscillations denoted as mixed-mode oscillation-incrementing bifurcations (MMOIBs) have frequently been observed in chemical experiments. In a previous study [K. Shimizu et al., Physica D 241, 1518 (2012)], we discovered an extremely simple dynamical circuit that exhibits MMOIBs. Our model was represented by a slow/fast Bonhoeffer-van der Pol circuit under weak periodic perturbation near a subcritical Andronov-Hopf bifurcation point. In this study, we experimentally and numerically verify that our dynamical circuit captures the essence of the underlying mechanism causing MMOIBs, and we observe MMOIBs and chaos with distinctive waveforms in real circuit experiments.
Climate bifurcation during the last deglaciation?
Directory of Open Access Journals (Sweden)
T. M. Lenton
2012-07-01
Full Text Available There were two abrupt warming events during the last deglaciation, at the start of the Bølling-Allerød and at the end of the Younger Dryas, but their underlying dynamics are unclear. Some abrupt climate changes may involve gradual forcing past a bifurcation point, in which a prevailing climate state loses its stability and the climate tips into an alternative state, providing an early warning signal in the form of slowing responses to perturbations, which may be accompanied by increasing variability. Alternatively, short-term stochastic variability in the climate system can trigger abrupt climate changes, without early warning. Previous work has found signals consistent with slowing down during the last deglaciation as a whole, and during the Younger Dryas, but with conflicting results in the run-up to the Bølling-Allerød. Based on this, we hypothesise that a bifurcation point was approached at the end of the Younger Dryas, in which the cold climate state, with weak Atlantic overturning circulation, lost its stability, and the climate tipped irreversibly into a warm interglacial state. To test the bifurcation hypothesis, we analysed two different climate proxies in three Greenland ice cores, from the Last Glacial Maximum to the end of the Younger Dryas. Prior to the Bølling warming, there was a robust increase in climate variability but no consistent slowing down signal, suggesting this abrupt change was probably triggered by a stochastic fluctuation. The transition to the warm Bølling-Allerød state was accompanied by a slowing down in climate dynamics and an increase in climate variability. We suggest that the Bølling warming excited an internal mode of variability in Atlantic meridional overturning circulation strength, causing multi-centennial climate fluctuations. However, the return to the Younger Dryas cold state increased climate stability. We find no consistent evidence for slowing down during the Younger Dryas, or in a longer
Subcritical enhanced safety molten-salt reactor concept
International Nuclear Information System (INIS)
Alekseev, P.N.; Ignatiev, V.V.; Men'shikov, L.I.; Prusakov, V.N.; Ponomarev-Stepnoy, N.N.; Subbotin, S.A.; Krasnykh, A.K.; Rudenko, V.T.; Somov, L.N.
1995-01-01
The nuclear power and its fuel cycle safety requirements can be met in the main by providing nuclear power with subcritical molten salt reactors (SMSR) - 'burner' with an external neutron source. The utilized molten salt fuel is the decisive advantage of the SMSR over other burners. Fissile and fertile nuclides in the burner are solved in a liquid salt in the form of fluorides. This composition acts simultaneously as: a) fuel, b) coolant, c) medium for chemical partitioning and reprocessing. The effective way of reducing the external source power consists in the cascade neutron multiplication in the system of coupled reactors with suppressed feedback between them. (author)
Spatial and spectral effects in subcritical system pulsed experiments
International Nuclear Information System (INIS)
Dulla, S.; Nervo, M.; Ravetto, P.; Carta, M.
2013-01-01
Accurate neutronic models are needed for the interpretation of pulsed experiments in subcritical systems. In this work, the extent of spatial and spectral effects in the pulse propagation phenomena is investigated and the analysis is applied to the GUINEVERE experiment. The multigroup cross section data is generated by the Monte Carlo SERPENT code and the neutronic evolution following the source pulse is simulated by a kinetic diffusion code. The results presented show that important spatial and spectral aspects need to be properly accounted for and that a detailed energy approach may be needed to adequately capture the physical features of the system to the pulse injection. (authors)
Treatment of fluctuations of startup rates for core subcriticality monitoring
International Nuclear Information System (INIS)
Mol, Antonio Carlos de Abreu; Martinez, Aquilino Senra
1996-01-01
In this paper it is presented a method to eliminate the variations in the source and intermediate range count rate, which are used for the on-line and real time monitoring of the critical safety function Subcriticality. The method may be applied to a safety parameters display system, because it is very simple and precise, which it will not affect the real time requirements of such systems. Variations in the count range could cause a temporary positive startup rate, that could lead to incorrect addressing of function restoration guideline. (author)
Orbital storage and supply of subcritical liquid nitrogen
Aydelott, John C.
1990-01-01
Subcritical cryogenic fluid management has long been recognized as an enabling technology for key propulsion applications, such as space transfer vehicles (STV) and the on-orbit cryogenic fuel depots which will provide STV servicing capability. The LeRC Cryogenic Fluids Technology Office (CFTO), under the sponsorship of OAST, has the responsibility of developing the required technology via a balanced program involving analytical modeling, ground based testing, and in-space experimentation. Topics covered in viewgraph form include: cryogenic management technologies; nitrogen storage and supply; cryogenic nitrogen cooling capability; and LN2 system demonstration technical objectives.
Measurement of subcritical multiplication by the interval distribution method
International Nuclear Information System (INIS)
Nelson, G.W.
1985-01-01
The prompt decay constant or the subcritical neutron multiplication may be determined by measuring the distribution of the time intervals between successive neutron counts. The distribution data is analyzed by least-squares fitting to a theoretical distribution function derived from a point reactor probability model. Published results of measurements with one- and two-detector systems are discussed. Data collection times are shorter, and statistical errors are smaller the nearer the system is to delayed critical. Several of the measurements indicate that a shorter data collection time and higher accuracy are possible with the interval distribution method than with the Feynman variance method
Bifurcations and Patterns in Nonlinear Dissipative Systems
Energy Technology Data Exchange (ETDEWEB)
Guenter Ahlers
2005-05-27
This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.
The bifurcations of nearly flat origami
Santangelo, Christian
Self-folding origami structures provide one means of fabricating complex, three-dimensional structures from a flat, two-dimensional sheet. Self-folding origami structures have been fabricated on scales ranging from macroscopic to microscopic and can have quite complicated structures with hundreds of folds arranged in complex patterns. I will describe our efforts to understand the mechanics and energetics of self-folding origami structures. Though the dimension of the configuration space of an origami structure scales with the size of the boundary and not with the number of vertices in the interior of the structure, a typical origami structure is also floppy in the sense that there are many possible ways to assign fold angles consistently. I will discuss our theoretical progress in understanding the geometry of the configuration space of origami. For random origami, the number of possible bifurcations grows surprisingly quickly even when the dimension of the configuration space is small. EFRI ODISSEI-1240441, DMR-0846582.
Bifurcated SEN with Fluid Flow Conditioners
Directory of Open Access Journals (Sweden)
F. Rivera-Perez
2014-01-01
Full Text Available This work evaluates the performance of a novel design for a bifurcated submerged entry nozzle (SEN used for the continuous casting of steel slabs. The proposed design incorporates fluid flow conditioners attached on SEN external wall. The fluid flow conditioners impose a pseudosymmetric pattern in the upper zone of the mold by inhibiting the fluid exchange between the zones created by conditioners. The performance of the SEN with fluid flow conditioners is analyzed through numerical simulations using the CFD technique. Numerical results were validated by means of physical simulations conducted on a scaled cold water model. Numerical and physical simulations confirmed that the performance of the proposed SEN is superior to a traditional one. Fluid flow conditioners reduce the liquid free surface fluctuations and minimize the occurrence of vortexes at the free surface.
Oscillatory bifurcation for semilinear ordinary differential equations
Directory of Open Access Journals (Sweden)
Tetsutaro Shibata
2016-06-01
\\] where $f(u = u + (1/2\\sin^k u$ ($k \\ge 2$ and $\\lambda > 0$ is a bifurcation parameter. It is known that $\\lambda$ is parameterized by the maximum norm $\\alpha = \\Vert u_\\lambda\\Vert_\\infty$ of the solution $u_\\lambda$ associated with $\\lambda$ and is written as $\\lambda = \\lambda(k,\\alpha$. When we focus on the asymptotic behavior of $\\lambda(k,\\alpha$ as $\\alpha \\to \\infty$, it is natural to expect that $\\lambda(k, \\alpha \\to \\pi^2/4$, and its convergence rate is common to $k$. Contrary to this expectation, we show that $\\lambda(2n_1+1,\\alpha$ tends to $\\pi^2/4$ faster than $\\lambda(2n_2,\\alpha$ as $\\alpha \\to \\infty$, where $n_1\\ge 1,\\ n_2 \\ge 1$ are arbitrary given integers.
Equilibrium-torus bifurcation in nonsmooth systems
DEFF Research Database (Denmark)
Zhusubahyev, Z.T.; Mosekilde, Erik
2008-01-01
Considering a set of two coupled nonautonomous differential equations with discontinuous right-hand sides describing the behavior of a DC/DC power converter, we discuss a border-collision bifurcation that can lead to the birth of a two-dimensional invariant torus from a stable node equilibrium...... point. We obtain the chart of dynamic modes and show that there is a region of parameter space in which the system has a single stable node equilibrium point. Under variation of the parameters, this equilibrium may disappear as it collides with a discontinuity boundary between two smooth regions...... in the phase space. The disappearance of the equilibrium point is accompanied by the soft appearance of an unstable focus period-1 orbit surrounded by a resonant or ergodic torus. Detailed numerical calculations are supported by a theoretical investigation of the normal form map that represents the piecewise...
International Nuclear Information System (INIS)
2004-03-01
Under the Research Committee on Reactor Physics, the Working Party on Reactor Physics of Subcritical System (ADS-WP) was set in July 2001 to research reactor physics of subcritical system such as Accelerator-Driven System (ADS). The WP, at the first meeting, discussed a guideline of its activity for two years and decided to perform theoretical research for the following subjects: (1) study of reactor physics for a subcritical core, (2) benchmark problems for a subcritical core and their calculations, (3) study of physical parameters affecting to set subcriticality of ADS, and (4) study of measurement and surveillance methods of subcriticality of a subcritical core. The activity of ADS-WP continued up to March 2003. In this duration, the members of the WP met together eight times, including four meetings jointly held with the Workshop on Accelerator-Driven Subcritical Reactor at Kyoto University Research Reactor Institute. This report summarizes the result obtained by the above WP activity and research. (author)
Clausius entropy for arbitrary bifurcate null surfaces
International Nuclear Information System (INIS)
Baccetti, Valentina; Visser, Matt
2014-01-01
Jacobson’s thermodynamic derivation of the Einstein equations was originally applied only to local Rindler horizons. But at least some parts of that construction can usefully be extended to give meaningful results for arbitrary bifurcate null surfaces. As presaged in Jacobson’s original article, this more general construction sharply brings into focus the questions: is entropy objectively ‘real’? Or is entropy in some sense subjective and observer-dependent? These innocent questions open a Pandora’s box of often inconclusive debate. A consensus opinion, though certainly not universally held, seems to be that Clausius entropy (thermodynamic entropy, defined via a Clausius relation dS=đQ/T) should be objectively real, but that the ontological status of statistical entropy (Shannon or von Neumann entropy) is much more ambiguous, and much more likely to be observer-dependent. This question is particularly pressing when it comes to understanding Bekenstein entropy (black hole entropy). To perhaps further add to the confusion, we shall argue that even the Clausius entropy can often be observer-dependent. In the current article we shall conclusively demonstrate that one can meaningfully assign a notion of Clausius entropy to arbitrary bifurcate null surfaces—effectively defining a ‘virtual Clausius entropy’ for arbitrary ‘virtual (local) causal horizons’. As an application, we see that we can implement a version of the generalized second law (GSL) for this virtual Clausius entropy. This version of GSL can be related to certain (nonstandard) integral variants of the null energy condition. Because the concepts involved are rather subtle, we take some effort in being careful and explicit in developing our framework. In future work we will apply this construction to generalize Jacobson’s derivation of the Einstein equations. (paper)
International Nuclear Information System (INIS)
Jesus Barbosa, S. de.
1987-01-01
The effective multiplication factor and the nuclear parameters associated with the variation of (RESUCO- Subcritical Experimental Reactor of Uranium with Oxygen) Subcritical Assembly Configuration, using pulsed neutron technique are analysed. BF3 detectors were used to detect the variation of thermal neutrons in the system, positioned parallelly to fuel elements, and a proton recoil detector was used for monitoring the neutron generation. (M.C.K.) [pt
International Nuclear Information System (INIS)
Takahashi, Hiroshi
1994-01-01
I suggest that an accelerator can be used to increase the safety and neutron economy of a power reactor and a transmutor of long-lived radioactive wastes, such as minor actinides and fission products, by providing neutrons for its subcritical operation. Instead of the large subcriticality k=0.9-0.95 which we originally proposed for such transmutor, we propose to use a slightly subcritical reactor, such as k=0.99, which will avoid many of the technical difficulties that are associated with large subcriticality, such as localized power peaking, radiation damage due to injection of medium-energy protons, the high current accelerator, and the requirement for a long beam-expansion section. We analyze the power drop that occurred in Phenix reactor, and show that the operating this reactor in subcritical conditions improves safety. (author). 13 refs., 5 figs
International Nuclear Information System (INIS)
Takahashi, Hiroshi.
1994-01-01
This report describes methods in which an accelerator can be used to increase the safety and neutron economy of a power reactor and transmutor of long-lived radioactive wastes, such as minor actinides and fission products, by providing neutrons for its subcritical operation. Instead of the rather large subcriticality of k=0.9--0.95 which we originally proposed for such a transmutor, we propose to use a slightly subcritical reactor, such as k=0.99, which will avoid many of the technical difficulties that are associated with large subcriticality, such as localized power peaking, radiation damage due to the injection of medium-energy protons, the high current accelerator, and the requirement for a long beam-expansion section. We analyzed the power drop that occurred in Phoenix reactor, and show that the operating this reactor in subcritical condition improves its safety
Carmona, J. M.; Cortés, J. L.; Relancio, J. J.
2018-03-01
A new proposal for the notion of spacetime in a relativistic generalization of special relativity based on a modification of the composition law of momenta is presented. Locality of interactions is the principle which defines the spacetime structure for a system of particles. The formulation based on κ -Poincaré Hopf algebra is shown to be contained in this framework as a particular example.
Yalina booster subcritical assembly performance with low enriched uranium fuel
International Nuclear Information System (INIS)
Talamo, Alberto; Gohar, Yousry
2011-01-01
The YALINA Booster facility is a subcritical assembly located in Minsk, Belarus. The facility has special features that result in fast and thermal neutron spectra in different zones. The fast zone of the assembly uses a lead matrix and uranium fuels with different enrichments: 90% and 36%, 36%, or 21%. The thermal zone of the assembly contains 10% enriched uranium fuel in a polyethylene matrix. This study discusses the performance of the three YALINA Booster configurations with the different fuel enrichments. In order to maintain the same subcriticality level in the three configurations, the number of fuel rods in the thermal zone is increased as the uranium fuel enrichment in the fast zone is decreased. The maximum number of fuel rods that can be loaded in the thermal zone is about 1185. Consequently, the neutron multiplication of the configuration with 21% enriched uranium fuel in the fast zone is enhanced by changing the position of the boron carbide and the natural uranium absorber rods, located between the fast and the thermal zones, to form an annular rather than a square arrangement. (author)
Yalina booster subcritical assembly performance with low enriched uranium fuel
Energy Technology Data Exchange (ETDEWEB)
Talamo, Alberto; Gohar, Yousry, E-mail: alby@anl.gov [Argonne National Laboratory, Lemont, IL (United States)
2011-07-01
The YALINA Booster facility is a subcritical assembly located in Minsk, Belarus. The facility has special features that result in fast and thermal neutron spectra in different zones. The fast zone of the assembly uses a lead matrix and uranium fuels with different enrichments: 90% and 36%, 36%, or 21%. The thermal zone of the assembly contains 10% enriched uranium fuel in a polyethylene matrix. This study discusses the performance of the three YALINA Booster configurations with the different fuel enrichments. In order to maintain the same subcriticality level in the three configurations, the number of fuel rods in the thermal zone is increased as the uranium fuel enrichment in the fast zone is decreased. The maximum number of fuel rods that can be loaded in the thermal zone is about 1185. Consequently, the neutron multiplication of the configuration with 21% enriched uranium fuel in the fast zone is enhanced by changing the position of the boron carbide and the natural uranium absorber rods, located between the fast and the thermal zones, to form an annular rather than a square arrangement. (author)
Estimation of subcriticality by neutron source multiplication method
International Nuclear Information System (INIS)
Sakurai, Kiyoshi; Suzaki, Takenori; Arakawa, Takuya; Naito, Yoshitaka
1995-03-01
Subcritical cores were constructed in a core tank of the TCA by arraying 2.6% enriched UO 2 fuel rods into nxn square lattices of 1.956 cm pitch. Vertical distributions of the neutron count rates for the fifteen subcritical cores (n=17, 16, 14, 11, 8) with different water levels were measured at 5 cm interval with 235 U micro-fission counters at the in-core and out-core positions arranging a 252 C f neutron source at near core center. The continuous energy Monte Carlo code MCNP-4A was used for the calculation of neutron multiplication factors and neutron count rates. In this study, important conclusions are as follows: (1) Differences of neutron multiplication factors resulted from exponential experiment and MCNP-4A are below 1% in most cases. (2) Standard deviations of neutron count rates calculated from MCNP-4A with 500000 histories are 5-8%. The calculated neutron count rates are consistent with the measured one. (author)
Candidate molten salt investigation for an accelerator driven subcritical core
Energy Technology Data Exchange (ETDEWEB)
Sooby, E., E-mail: soobyes@tamu.edu [Texas A and M University, Accelerator Research Laboratory, 3380 University Dr. East, College Station, TX 77845 (United States); Baty, A. [Texas A and M University, Accelerator Research Laboratory, 3380 University Dr. East, College Station, TX 77845 (United States); Beneš, O. [European Commission, DG Joint Research Centre, Institute for Transuranium Elements, P.O. Box 2340, 76125 Karlsruhe (Germany); McIntyre, P.; Pogue, N. [Texas A and M University, Accelerator Research Laboratory, 3380 University Dr. East, College Station, TX 77845 (United States); Salanne, M. [Université Pierre et Marie Curie, CNRS, Laboratoire PECSA, F-75005 Paris (France); Sattarov, A. [Texas A and M University, Accelerator Research Laboratory, 3380 University Dr. East, College Station, TX 77845 (United States)
2013-09-15
Highlights: • Developing accelerator driven subcritical fission to destroy transuranics in SNF. • The core is a vessel containing a molten mixture of NaCl and transuranic chlorides. • Molecular dynamics used to calculate the thermophysical properties of the salt. • Density and molecular structure for actinide salts reported here. • The neutronics of ADS fission in molten salt are presented. -- Abstract: We report a design for accelerator-driven subcritical fission in a molten salt core (ADSMS) that utilizes a fuel salt composed of NaCl and transuranic (TRU) chlorides. The ADSMS core is designed for fast neutronics (28% of neutrons >1 MeV) to optimize TRU destruction. The choice of a NaCl-based salt offers benefits for corrosion, operating temperature, and actinide solubility as compared with LiF-based fuel salts. A molecular dynamics (MD) code has been used to estimate properties of the molten salt system which are important for ADSMS design but have never been measured experimentally. Results from the MD studies are reported. Experimental measurements of fuel salt properties and studies of corrosion and radiation damage on candidate metals for the core vessel are anticipated.
Candidate molten salt investigation for an accelerator driven subcritical core
International Nuclear Information System (INIS)
Sooby, E.; Baty, A.; Beneš, O.; McIntyre, P.; Pogue, N.; Salanne, M.; Sattarov, A.
2013-01-01
Highlights: • Developing accelerator driven subcritical fission to destroy transuranics in SNF. • The core is a vessel containing a molten mixture of NaCl and transuranic chlorides. • Molecular dynamics used to calculate the thermophysical properties of the salt. • Density and molecular structure for actinide salts reported here. • The neutronics of ADS fission in molten salt are presented. -- Abstract: We report a design for accelerator-driven subcritical fission in a molten salt core (ADSMS) that utilizes a fuel salt composed of NaCl and transuranic (TRU) chlorides. The ADSMS core is designed for fast neutronics (28% of neutrons >1 MeV) to optimize TRU destruction. The choice of a NaCl-based salt offers benefits for corrosion, operating temperature, and actinide solubility as compared with LiF-based fuel salts. A molecular dynamics (MD) code has been used to estimate properties of the molten salt system which are important for ADSMS design but have never been measured experimentally. Results from the MD studies are reported. Experimental measurements of fuel salt properties and studies of corrosion and radiation damage on candidate metals for the core vessel are anticipated
Neutronic calculations for a subcritical system with external source
International Nuclear Information System (INIS)
Cintas, A; Lopasso, E.M; Marquez Damian, J. I
2006-01-01
We present a neutronic study on an A D S, systems capable of transmute minor actinides and fission products in order to reduce their radiotoxicity and mean-life.We compare neutronic parameters obtained with Scale/Tort and M C N P modelling a sub-critical system with source from a N E A Benchmark.Due to lack of nuclear data at the temperature of the system, we perform calculations at available temperature of libraries (300 K); to compensate the reactivity insertion due to the temperature change we reduce the size of the fuel zone in order to get a sub-critical system that allow u s to evaluate neutronic parameters of the system with source.We have found that the numerical results (neutron spectrum, neutron flux distributions and other neutronic parameters) are in agreement with the M C N P and with those of the benchmark participants even though the geometric models used are not exactly the same. We conclude that with the real temperature cross sections, the calculation scheme developed (Scale/Tort and M C N P) will give reliable results in A D S evaluations [es
Neutron noise measurements at the Delphi subcritical assembly
International Nuclear Information System (INIS)
Szieberth, M.; Klujber, G.; Kloosterman, J. L.; De Haas, D.
2012-01-01
The paper presents the results and evaluations of a comprehensive set of neutron noise measurements on the Delphi subcritical assembly of the Delft Univ. of Technology. The measurements investigated the effect of different source distributions (inherent spontaneous fission and 252 Cf) and the position of the detectors applied (both radially and vertically). The evaluation of the measured data has been performed by the variance-to-mean ratio (VTMR, Feynman-α), the autocorrelation (ACF, Rossi-α) and the cross-correlation (CCF) methods. The values obtained for the prompt decay constant show a strong bias, which depends both on the detector position and on the source distribution. This is due to the presence of higher modes in the system. It has been observed that the α value fitted is higher when the detector is close to the boundary of the core or to the 252 Cf point-source. The higher alpha-modes have also been observed by fitting functions describing two alpha-modes. The successful set of measurement also provides a good basis for further theoretical investigations including the Monte Carlo simulation of the noise measurements and the calculation of the alpha-modes in the Delphi subcritical assembly. (authors)
Fractional noise destroys or induces a stochastic bifurcation
Energy Technology Data Exchange (ETDEWEB)
Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Sciences, South China University of Technology, Guangzhou 510640 (China); Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn [School of Sciences, South China University of Technology, Guangzhou 510640 (China); School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640 (China); Wang, Cong, E-mail: wangcong@scut.edu.cn [School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640 (China)
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.
Optimization Design and Application of Underground Reinforced Concrete Bifurcation Pipe
Directory of Open Access Journals (Sweden)
Chao Su
2015-01-01
Full Text Available Underground reinforced concrete bifurcation pipe is an important part of conveyance structure. During construction, the workload of excavation and concrete pouring can be significantly decreased according to optimized pipe structure, and the engineering quality can be improved. This paper presents an optimization mathematical model of underground reinforced concrete bifurcation pipe structure according to real working status of several common pipe structures from real cases. Then, an optimization design system was developed based on Particle Swarm Optimization algorithm. Furthermore, take the bifurcation pipe of one hydropower station as an example: optimization analysis was conducted, and accuracy and stability of the optimization design system were verified successfully.
Arctic melt ponds and bifurcations in the climate system
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.
FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions
Directory of Open Access Journals (Sweden)
L. Borkowski
2015-01-01
Full Text Available The dynamics of a ring of seven unidirectionally coupled nonlinear Duffing oscillators is studied. We show that the FFT analysis presented in form of a bifurcation graph, that is, frequency distribution versus a control parameter, can provide a valuable and helpful complement to the corresponding typical bifurcation diagram and the course of Lyapunov exponents, especially in context of detailed identification of the observed attractors. As an example, bifurcation analysis of routes to chaos via 2-frequency and 3-frequency quasiperiodicity is demonstrated.
Bifurcation of learning and structure formation in neuronal maps
DEFF Research Database (Denmark)
Marschler, Christian; Faust-Ellsässer, Carmen; Starke, Jens
2014-01-01
to map formation in the laminar nucleus of the barn owl's auditory system. Using equation-free methods, we perform a bifurcation analysis of spatio-temporal structure formation in the associated synaptic-weight matrix. This enables us to analyze learning as a bifurcation process and follow the unstable...... states as well. A simple time translation of the learning window function shifts the bifurcation point of structure formation and goes along with traveling waves in the map, without changing the animal's sound localization performance....
Noether analysis of the twisted Hopf symmetries of canonical noncommutative spacetimes
International Nuclear Information System (INIS)
Amelino-Camelia, Giovanni; Gubitosi, Giulia; Marciano, Antonino; Martinetti, Pierre; Mercati, Flavio; Briscese, Fabio
2008-01-01
We study the twisted Hopf-algebra symmetries of observer-independent canonical spacetime noncommutativity, for which the commutators of the spacetime coordinates take the form [x^ μ ,x^ ν ]=iθ μν with observer-independent (and coordinate-independent) θ μν . We find that it is necessary to introduce nontrivial commutators between transformation parameters and spacetime coordinates, and that the form of these commutators implies that all symmetry transformations must include a translation component. We show that with our noncommutative transformation parameters the Noether analysis of the symmetries is straightforward, and we compare our canonical-noncommutativity results with the structure of the conserved charges and the ''no-pure-boost'' requirement derived in a previous study of κ-Minkowski noncommutativity. We also verify that, while at intermediate stages of the analysis we do find terms that depend on the ordering convention adopted in setting up the Weyl map, the final result for the conserved charges is reassuringly independent of the choice of Weyl map and (the corresponding choice of) star product.
The Epstein-Glaser approach to perturbative quantum field theory: graphs and Hopf algebras
International Nuclear Information System (INIS)
Lange, Alexander
2005-01-01
The paper aims at investigating perturbative quantum field theory in the approach of Epstein and Glaser (EG) and, in particular, its formulation in the language of graphs and Hopf algebras (HAs). Various HAs are encountered, each one associated with a special combination of physical concepts such as normalization, localization, pseudounitarity, causal regularization, and renormalization. The algebraic structures, representing the perturbative expansion of the S-matrix, are imposed on operator-valued distributions equipped with appropriate graph indices. Translation invariance ensures the algebras to be analytically well defined and graded total symmetry allows to formulate bialgebras. The algebraic results are given embedded in the corresponding physical framework, covering the two EG versions by Fredenhagen and Scharf that differ with respect to the concrete recursive implementation of causality. Besides, the ultraviolet divergences occurring in Feynman's representation are mathematically reasoned. As a final result, the change of the renormalization scheme in the context of EG is modeled via a HA and interpreted as the EG analog of Kreimer's HA
A simple delay model for two-phase flow dynamics
Energy Technology Data Exchange (ETDEWEB)
Clausse, A.; Delmastro, D.F.; Juanico`, L.E. [Centro Atomico Bariloche (Argentina)
1995-09-01
A model based in delay equations for density-wave oscillations is presented. High Froude numbers and moderate ones were considered. The equations were numerically analyzed and compared with more sophisticated models. The influence of the gravity term was studied. Different kinds of behavior were found, particularly sub-critical and super-critical Hopf bifurcations. Moreover the present approach can be used to better understand the complicated dynamics of boiling flows systems.
On a Five-Dimensional Chaotic System Arising from Double-Diffusive Convection in a Fluid Layer
Directory of Open Access Journals (Sweden)
R. Idris
2013-01-01
Full Text Available A chaotic system arising from double-diffusive convection in a fluid layer is investigated in this paper based on the theory of dynamical systems. A five-dimensional model of chaotic system is obtained using the Galerkin truncated approximation. The results showed that the transition from steady convection to chaos via a Hopf bifurcation produced a limit cycle which may be associated with a homoclinic explosion at a slightly subcritical value of the Rayleigh number.
CISM Session on Bifurcation and Stability of Dissipative Systems
1993-01-01
The first theme concerns the plastic buckling of structures in the spirit of Hill’s classical approach. Non-bifurcation and stability criteria are introduced and post-bifurcation analysis performed by asymptotic development method in relation with Hutchinson’s work. Some recent results on the generalized standard model are given and their connection to Hill’s general formulation is presented. Instability phenomena of inelastic flow processes such as strain localization and necking are discussed. The second theme concerns stability and bifurcation problems in internally damaged or cracked colids. In brittle fracture or brittle damage, the evolution law of crack lengths or damage parameters is time-independent like in plasticity and leads to a similar mathematical description of the quasi-static evolution. Stability and non-bifurcation criteria in the sense of Hill can be again obtained from the discussion of the rate response.
Bifurcation dynamics of the tempered fractional Langevin equation
Energy Technology Data Exchange (ETDEWEB)
Zeng, Caibin, E-mail: macbzeng@scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China); Chen, YangQuan, E-mail: ychen53@ucmerced.edu [MESA LAB, School of Engineering, University of California, Merced, 5200 N. Lake Road, Merced, California 95343 (United States)
2016-08-15
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
Deformable 4DCT lung registration with vessel bifurcations
International Nuclear Information System (INIS)
Hilsmann, A.; Vik, T.; Kaus, M.; Franks, K.; Bissonette, J.P.; Purdie, T.; Beziak, A.; Aach, T.
2007-01-01
In radiotherapy planning of lung cancer, breathing motion causes uncertainty in the determination of the target volume. Image registration makes it possible to get information about the deformation of the lung and the tumor movement in the respiratory cycle from a few images. A dedicated, automatic, landmark-based technique was developed that finds corresponding vessel bifurcations. Hereby, we developed criteria to characterize pronounced bifurcations for which correspondence finding was more stable and accurate. The bifurcations were extracted from automatically segmented vessel trees in maximum inhale and maximum exhale CT thorax data sets. To find corresponding bifurcations in both data sets we used the shape context approach of Belongie et al. Finally, a volumetric lung deformation was obtained using thin-plate spline interpolation and affine registration. The method is evaluated on 10 4D-CT data sets of patients with lung cancer. (orig.)
Multiple bifurcations and periodic 'bubbling' in a delay population model
International Nuclear Information System (INIS)
Peng Mingshu
2005-01-01
In this paper, the flip bifurcation and periodic doubling bifurcations of a discrete population model without delay influence is firstly studied and the phenomenon of Feigenbaum's cascade of periodic doublings is also observed. Secondly, we explored the Neimark-Sacker bifurcation in the delay population model (two-dimension discrete dynamical systems) and the unique stable closed invariant curve which bifurcates from the nontrivial fixed point. Finally, a computer-assisted study for the delay population model is also delved into. Our computer simulation shows that the introduction of delay effect in a nonlinear difference equation derived from the logistic map leads to much richer dynamic behavior, such as stable node → stable focus → an lower-dimensional closed invariant curve (quasi-periodic solution, limit cycle) or/and stable periodic solutions → chaotic attractor by cascading bubbles (the combination of potential period doubling and reverse period-doubling) and the sudden change between two different attractors, etc
Bifurcation theory for hexagonal agglomeration in economic geography
Ikeda, Kiyohiro
2014-01-01
This book contributes to an understanding of how bifurcation theory adapts to the analysis of economic geography. It is easily accessible not only to mathematicians and economists, but also to upper-level undergraduate and graduate students who are interested in nonlinear mathematics. The self-organization of hexagonal agglomeration patterns of industrial regions was first predicted by the central place theory in economic geography based on investigations of southern Germany. The emergence of hexagonal agglomeration in economic geography models was envisaged by Krugman. In this book, after a brief introduction of central place theory and new economic geography, the missing link between them is discovered by elucidating the mechanism of the evolution of bifurcating hexagonal patterns. Pattern formation by such bifurcation is a well-studied topic in nonlinear mathematics, and group-theoretic bifurcation analysis is a well-developed theoretical tool. A finite hexagonal lattice is used to express uniformly distri...
Periodic solutions and bifurcations of delay-differential equations
International Nuclear Information System (INIS)
He Jihuan
2005-01-01
In this Letter a simple but effective iteration method is proposed to search for limit cycles or bifurcation curves of delay-differential equations. An example is given to illustrate its convenience and effectiveness
Defining Electron Bifurcation in the Electron-Transferring Flavoprotein Family.
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
International Nuclear Information System (INIS)
Chen Sen; Wu Yican; Jin Ming; Chen Zhibin; Bai Yunqing; Zhao Zhumin
2014-01-01
Accelerator Driven Sub-critical System (ADS) has particular neutronics behaviors compared with the critical system. Prompt jump approximation point reactor kinetics equations taken external source into account have been deduced using an approach of prompt jump approximation. And the relationship between injection reactivity and power ampliation has been achieved. In addition, based on the RELAP5 code the prolong development of point reactor kinetics code used into assessing sub-critical system have been promoted. Different sub-criticality (k eff = 0.90, 0.95, 0.97, 0.98 and 0.99) have been assessed in preliminary design of a type of natural circulation cooling sub-critical reactor under conditions of reactivity injection +1 β in one second. It shows that the external source prompt transient approximation method has an accurate solution after injecting reactivity around short time and has a capacity to solve the dynamic equation, and the sub-critical system has an inner stability while the deeper sub-criticality the less impact on the sub-critical system. (authors)
Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models
Giona, M.; Brasiello, A.; Crescitelli, S.
2015-11-01
One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.
Bunch lengthening with bifurcation in electron storage rings
Energy Technology Data Exchange (ETDEWEB)
Kim, Eun-San; Hirata, Kohji [National Lab. for High Energy Physics, Tsukuba, Ibaraki (Japan)
1996-08-01
The mapping which shows equilibrium particle distribution in synchrotron phase space for electron storage rings is discussed with respect to some localized constant wake function based on the Gaussian approximation. This mapping shows multi-periodic states as well as double bifurcation in dynamical states of the equilibrium bunch length. When moving around parameter space, the system shows a transition/bifurcation which is not always reversible. These results derived by mapping are confirmed by multiparticle tracking. (author)
Iterative Controller Tuning for Process with Fold Bifurcations
DEFF Research Database (Denmark)
Huusom, Jakob Kjøbsted; Poulsen, Niels Kjølstad; Jørgensen, Sten Bay
2007-01-01
Processes involving fold bifurcation are notoriously difficult to control in the vicinity of the fold where most often optimal productivity is achieved . In cases with limited process insight a model based control synthesis is not possible. This paper uses a data driven approach with an improved...... version of iterative feedback tuning to optimizing a closed loop performance criterion, as a systematic tool for tuning process with fold bifurcations....
Bifurcated states of the error-field-induced magnetic islands
International Nuclear Information System (INIS)
Zheng, L.-J.; Li, B.; Hazeltine, R.D.
2008-01-01
We find that the formation of the magnetic islands due to error fields shows bifurcation when neoclassical effects are included. The bifurcation, which follows from including bootstrap current terms in a description of island growth in the presence of error fields, provides a path to avoid the island-width pole in the classical description. The theory offers possible theoretical explanations for the recent DIII-D and JT-60 experimental observations concerning confinement deterioration with increasing error field
Attractors, bifurcations, & chaos nonlinear phenomena in economics
Puu, Tönu
2003-01-01
The present book relies on various editions of my earlier book "Nonlinear Economic Dynamics", first published in 1989 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and republished in three more, successively revised and expanded editions, as a Springer monograph, in 1991, 1993, and 1997, and in a Russian translation as "Nelineynaia Economicheskaia Dinamica". The first three editions were focused on applications. The last was differ ent, as it also included some chapters with mathematical background mate rial -ordinary differential equations and iterated maps -so as to make the book self-contained and suitable as a textbook for economics students of dynamical systems. To the same pedagogical purpose, the number of illus trations were expanded. The book published in 2000, with the title "A ttractors, Bifurcations, and Chaos -Nonlinear Phenomena in Economics", was so much changed, that the author felt it reasonable to give it a new title. There were two new math ematics ch...