Schikora, S.; Wünsche, H.-J.; Henneberger, F.
2011-02-01
A subcritical Hopf bifurcation is prepared in a multisection semiconductor laser. In the free-running state, hysteresis is absent due to noise-induced escape processes. The missing branches are recovered by stabilizing them against noise through application of phase-sensitive noninvasive delayed optical feedback control. The same type of control is successfully used to stabilize the unstable pulsations born in the Hopf bifurcation. This experimental finding represents an optical counterexample to the so-called odd-number limitation of delayed feedback control. However, as a leftover of the limitation, the domains of control are extremely small.
An explicit example of Hopf bifurcation in fluid mechanics
Kloeden, P.; Wells, R.
1983-01-01
It is observed that a complete and explicit example of Hopf bifurcation appears not to be known in fluid mechanics. Such an example is presented for the rotating Benard problem with free boundary conditions on the upper and lower faces, and horizontally periodic solutions. Normal modes are found for the linearization, and the Veronis computation of the wave numbers is modified to take into account the imposed horizontal periodicity. An invariant subspace of the phase space is found in which the hypotheses of the Joseph-Sattinger theorem are verified, thus demonstrating the Hopf bifurcation. The criticality calculations are carried through to demonstrate rigorously, that the bifurcation is subcritical for certain cases, and to demonstrate numerically that it is subcritical for all the cases in the paper.
On a quasi-periodic Hopf bifurcation
Braaksma, B.L.J.; Broer, H.W.
1987-01-01
In this paper we study quasi-periodic Hopf bifurcations for the model problem of a quasi-periodically forced oscillator, where the frequencies remain fixed. For this purpose we first consider Stoker's problem for small damping.
From Hopf Bifurcation to Limit Cycles Control in Underactuated Mechanical Systems
Khraief Haddad, Nahla; Belghith, Safya; Gritli, Hassène; Chemori, Ahmed
2017-06-01
This paper deals with the problem of obtaining stable and robust oscillations of underactuated mechanical systems. It is concerned with the Hopf bifurcation analysis of a Controlled Inertia Wheel Inverted Pendulum (C-IWIP). Firstly, the stabilization was achieved with a control law based on the Interconnection, Damping, Assignment Passive Based Control method (IDA-PBC). Interestingly, the considered closed-loop system exhibits both supercritical and subcritical Hopf bifurcation for certain gains of the control law. Secondly, we used the center manifold theorem and the normal form technique to study the stability and instability of limit cycles emerging from the Hopf bifurcation. Finally, numerical simulations were conducted to validate the analytical results in order to prove that with IDA-PBC we can control not only the unstable equilibrium but also some trajectories such as limit cycles.
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.
Dynamics at infinity and a Hopf bifurcation arising in a quadratic system with coexisting attractors
Wang, Zhen; Moroz, Irene; Wei, Zhouchao; Ren, Haipeng
2018-01-01
Dynamics at infinity and a Hopf bifurcation for a Sprott E system with a very small perturbation constant are studied in this paper. By using Poincaré compactification of polynomial vector fields in R^3, the dynamics near infinity of the singularities is obtained. Furthermore, in accordance with the centre manifold theorem, the subcritical Hopf bifurcation is analysed and obtained. Numerical simulations demonstrate the correctness of the dynamical and bifurcation analyses. Moreover, by choosing appropriate parameters, this perturbed system can exhibit chaotic, quasiperiodic and periodic dynamics, as well as some coexisting attractors, such as a chaotic attractor coexisting with a periodic attractor for a>0, and a chaotic attractor coexisting with a quasiperiodic attractor for a=0. Coexisting attractors are not associated with an unstable equilibrium and thus often go undiscovered because they may occur in a small region of parameter space, with a small basin of attraction in the space of initial conditions.
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.
Directory of Open Access Journals (Sweden)
Yan Zhang
2014-01-01
Full Text Available We revisit a homogeneous reaction-diffusion Turing model subject to the Neumann boundary conditions in the one-dimensional spatial domain. With the help of the Hopf bifurcation theory applicable to the reaction-diffusion equations, we are capable of proving the existence of Hopf bifurcations, which suggests the existence of spatially homogeneous and nonhomogeneous periodic solutions of this particular system. In particular, we also prove that the spatial homogeneous periodic solutions bifurcating from the smallest Hopf bifurcation point of the system are always unstable. This together with the instability results of the spatially nonhomogeneous periodic solutions by Yi et al., 2009, indicates that, in this model, all the oscillatory patterns from Hopf bifurcations are unstable.
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.
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.
Hopf and Generalized Hopf Bifurcations in a Recurrent Autoimmune Disease Model
Zhang, Wenjing; Yu, Pei
This paper is concerned with bifurcation and stability in an autoimmune model, which was established to study an important phenomenon — blips arising from such models. This model has two equilibrium solutions, disease-free equilibrium and disease equilibrium. The positivity of the solutions of the model and the global stability of the disease-free equilibrium have been proved. In this paper, we particularly focus on Hopf bifurcation which occurs from the disease equilibrium. We present a detailed study on the use of center manifold theory and normal form theory, and derive the normal form associated with Hopf bifurcation, from which the approximate amplitude of the bifurcating limit cycles and their stability conditions are obtained. Particular attention is also paid to the bifurcation of multiple limit cycles arising from generalized Hopf bifurcation, which may yield bistable phenomenon involving equilibrium and oscillating motion. This result may explain some complex dynamical behavior in real biological systems. Numerical simulations are compared with the analytical predictions to show a very good agreement.
Yang, Dong-Ping; Robinson, P. A.
2017-04-01
A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form quantitatively to underlying physiology that includes neural dynamics, axonal propagation, and time delays. Thus, a bridge is constructed that enables normal forms to be used to interpret quantitative data. The normal form of the Hopf bifurcations with delays is derived using Hale's theory, the center manifold theorem, and normal form analysis, and it is found to be explicitly expressed in terms of transfer functions and the sensitivity matrix of a reduced open-loop system. It can be applied to understand the effect of each physiological parameter on the critical dynamics and determine whether the Hopf bifurcation is supercritical or subcritical in instabilities that lead to absence and tonic-clonic seizures. Furthermore, the effects of thalamic and cortical nonlinearities on the bifurcation type are investigated, with implications for the roles of underlying physiology. The theoretical predictions about the bifurcation type and the onset dynamics are confirmed by numerical simulations and provide physiologically based criteria for determining bifurcation types from first principles. The results are consistent with experimental data from previous studies, imply that new regimes of seizure transitions may exist in clinical settings, and provide a simplified basis for control-systems interventions. Using the normal form, and the full equations from which it is derived, more complex dynamics, such as quasiperiodic cycles and saddle cycles, are discovered near the critical points of the subcritical Hopf bifurcations.
Yang, Dong-Ping; Robinson, P A
2017-04-01
A physiologically based corticothalamic model of large-scale brain activity is used to analyze critical dynamics of transitions from normal arousal states to epileptic seizures, which correspond to Hopf bifurcations. This relates an abstract normal form quantitatively to underlying physiology that includes neural dynamics, axonal propagation, and time delays. Thus, a bridge is constructed that enables normal forms to be used to interpret quantitative data. The normal form of the Hopf bifurcations with delays is derived using Hale's theory, the center manifold theorem, and normal form analysis, and it is found to be explicitly expressed in terms of transfer functions and the sensitivity matrix of a reduced open-loop system. It can be applied to understand the effect of each physiological parameter on the critical dynamics and determine whether the Hopf bifurcation is supercritical or subcritical in instabilities that lead to absence and tonic-clonic seizures. Furthermore, the effects of thalamic and cortical nonlinearities on the bifurcation type are investigated, with implications for the roles of underlying physiology. The theoretical predictions about the bifurcation type and the onset dynamics are confirmed by numerical simulations and provide physiologically based criteria for determining bifurcation types from first principles. The results are consistent with experimental data from previous studies, imply that new regimes of seizure transitions may exist in clinical settings, and provide a simplified basis for control-systems interventions. Using the normal form, and the full equations from which it is derived, more complex dynamics, such as quasiperiodic cycles and saddle cycles, are discovered near the critical points of the subcritical Hopf bifurcations.
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.
Two-parameters Hopf bifurcation in the Hodgkin-Huxley model
Energy Technology Data Exchange (ETDEWEB)
Wang Jiang [School of Electrical and Automation Engineering, Tianjin University, Tianjin 300072 (China)]. E-mail: jiangwang@tju.edu.cn; Geng Jianming [School of Electrical and Automation Engineering, Tianjin University, Tianjin 300072 (China); Fei Xiangyang [School of Electrical and Automation Engineering, Tianjin University, Tianjin 300072 (China)
2005-02-01
In this paper, the Hodgkin-Huxley model is studied with the leakage conductance and the sodium reversal potential selected as parameters for a two-parameter Hopf-bifurcation analysis. The influence of bifurcation on the HH model was also discussed and algebra criterion in high dimension equations was used to identify Hopf bifurcation. In addition, this paper also discuses the bifurcation approach to inherited disorders of ion channels in skeletal muscle excitable membranes.
Control by time delayed feedback near a Hopf bifurcation point
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Sjoerd Verduyn Lunel
2017-12-01
Full Text Available In this paper we study the stabilization of rotating waves using time delayed feedback control. It is our aim to put some recent results in a broader context by discussing two different methods to determine the stability of the target periodic orbit in the controlled system: 1 by directly studying the Floquet multipliers and 2 by use of the Hopf bifurcation theorem. We also propose an extension of the Pyragas control scheme for which the controlled system becomes a functional differential equation of neutral type. Using the observation that we are able to determine the direction of bifurcation by a relatively simple calculation of the root tendency, we find stability conditions for the periodic orbit as a solution of the neutral type equation.
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.
Stability and Hopf Bifurcation for a Delayed Computer Virus Model with Antidote in Vulnerable System
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Zizhen Zhang
2017-01-01
Full Text Available A delayed computer virus model with antidote in vulnerable system is investigated. Local stability of the endemic equilibrium and existence of Hopf bifurcation are discussed by analyzing the associated characteristic equation. Further, direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are presented to show consistency with the obtained results.
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.
Hopf bifurcation in love dynamical models with nonlinear couples and time delays
Energy Technology Data Exchange (ETDEWEB)
Liao Xiaofeng [School of Computer and Information, Chongqing Jiaotong University, Chonqing 400074 (China) and Department of Computer Science and Engineering, Chongqing University, Chongqing 400030 (China)]. E-mail: xflao@cqu.edu.cn; Ran Jiouhong [Hospital of Chongqing University, Chonqing University, Chongqing 400030 (China)
2007-02-15
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.
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...... by a small change in one of the variables, determines the features of the mixed-mode oscillations. Period-doubling and saddle-node bifurcations lead to closed families (called isolas) of periodic solutions in a bifurcation corresponding to a singular Hopf bifurcation....
Generic Hopf-Neimark-Sacker bifurcations in feed-forward systems
Broer, Henk W.; Vegter, Gert
We show that generic Hopf-Neimark-Sacker bifurcations occur in the dynamics of a large class of feed-forward coupled cell networks. To this end we present a framework for studying such bifurcations in parametrized families of perturbed forced oscillators near weak resonance points. Our approach is
Hopf Bifurcation Control in a FAST TCP and RED Model via Multiple Control Schemes
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Dawei Ding
2016-01-01
Full Text Available We focus on the Hopf bifurcation control problem of a FAST TCP model with RED gateway. The system gain parameter is chosen as the bifurcation parameter, and the stable region and stability condition of the congestion control model are given by use of the linear stability analysis. When the system gain passes through a critical value, the system loses the stability and Hopf bifurcation occurs. Considering the negative influence caused by Hopf bifurcation, we apply state feedback controller, hybrid controller, and time-delay feedback controller to postpone the onset of undesirable Hopf bifurcation. Numerical simulations show that the hybrid controller is the most sensitive method to delay the Hopf bifurcation with identical parameter conditions. However, nonlinear state feedback control and time-delay feedback control schemes have larger control parameter range in the Internet congestion control system with FAST TCP and RED gateway. Therefore, we can choose proper control method based on practical situation including unknown conditions or parameter requirements. This paper plays an important role in setting guiding system parameters for controlling the FAST TCP and RED model.
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.
Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System
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Xiaojun Liu
2014-01-01
Full Text Available The Hopf bifurcation of a fractional-order Van der Pol (VDP for short system with a random parameter is investigated. Firstly, the Chebyshev polynomial approximation is applied to study the stochastic fractional-order system. Based on the method, the stochastic system is reduced to the equivalent deterministic one, and then the responses of the stochastic system can be obtained by numerical methods. Then, according to the existence conditions of Hopf bifurcation, the critical parameter value of the bifurcation is obtained by theoretical analysis. Then, numerical simulations are carried out to verify the theoretical results.
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.
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.
Controlling the onset of Hopf bifurcation in the Hodgkin-Huxley model
Xie, Yong; Chen, Luonan; Kang, Yan Mei; Aihara, Kazuyuki
2008-06-01
It is a challenging problem to establish safe and simple therapeutic methods for various complicated diseases of the nervous system, particularly dynamical diseases such as epilepsy, Alzheimer’s disease, and Parkinson’s disease. From the viewpoint of nonlinear dynamical systems, a dynamical disease can be considered to be caused by a bifurcation induced by a change in the values of one or more regulating parameter. Therefore, the theory of bifurcation control may have potential applications in the diagnosis and therapy of dynamical diseases. In this study, we employ a washout filter-aided dynamic feedback controller to control the onset of Hopf bifurcation in the Hodgkin-Huxley (HH) model. Specifically, by the control scheme, we can move the Hopf bifurcation to a desired point irrespective of whether the corresponding steady state is stable or unstable. In other words, we are able to advance or delay the Hopf bifurcation, so as to prevent it from occurring in a certain range of the externally applied current. Moreover, we can control the criticality of the bifurcation and regulate the oscillation amplitude of the bifurcated limit cycle. In the controller, there are only two terms: the linear term and the nonlinear cubic term. We show that while the former determines the location of the Hopf bifurcation, the latter regulates the criticality of the Hopf bifurcation. According to the conditions of the occurrence of Hopf bifurcation and the bifurcation stability coefficient, we can analytically deduce the linear term and the nonlinear cubic term, respectively. In addition, we also show that mixed-mode oscillations (MMOs), featuring slow action potential generation, which are frequently observed in both experiments and models of chemical and biological systems, appear in the controlled HH model. It is well known that slow firing rates in single neuron models could be achieved only by type-I neurons. However, the controlled HH model is still classified as a type
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.
Dynamics at infinity and a Hopf bifurcation arising in a quadratic ...
Indian Academy of Sciences (India)
Dynamics at infinity and a Hopf bifurcation for a Sprott E system with a very small perturbation constant are studied in this paper. By using Poincaré compactification of polynomial vector fields in R 3 , the dynamics near infinity of the singularities is obtained. Furthermore, in accordance with the centre manifold theorem, the ...
Dynamics at infinity and a Hopf bifurcation arising in a quadratic ...
Indian Academy of Sciences (India)
Zhen Wang
2017-12-27
Dec 27, 2017 ... Dynamics at infinity and a Hopf bifurcation arising in a quadratic system with ... quadratic autonomous system, we raise the question: does there ..... 3200. + i. 41. 3200. , N22 = −. 23. 3200. − i. 41. 3200. ,. N12 = −. 41. 800 . The dynamics on the centre manifold is then governed by the equation. ˙w = 1. 2 iw +.
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 variable...
DEFF Research Database (Denmark)
Yang, Lihui; Xu, Zhao; Østergaard, Jacob
2009-01-01
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 variable...
Degenerate Hopf bifurcation in a self-exciting Faraday disc dynamo
Indian Academy of Sciences (India)
Weiquan Pan
2017-05-31
May 31, 2017 ... 2Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing,. Yulin Normal University .... of [21], but based on the analysis of [12,22,23], for the first Lyapunov coefficient l1, .... analysis of the first Lyapunov coefficient for the Hopf bifurcation of system (2.1) ...
Degenerate Hopf bifurcation in a self-exciting Faraday disc dynamo
Pan, Weiquan; Li, Lijie
2017-06-01
In order to further understand a self-exciting Faraday disc dynamo (Hide et al, in Proc. R. Soc. A 452, 1369 1996), showing chaotic attractors with very complicated topological structures, we present codimension one and two (degenerate) Hopf bifurcations and prove the existence of periodic solutions. In addition, numerical simulations are given for confirming the theoretical results.
Ding, Dawei; Qian, Xin; Hu, Wei; Wang, Nian; Liang, Dong
2017-11-01
In this paper, a time-delayed feedback controller is proposed in order to control chaos and Hopf bifurcation in a fractional-order memristor-based chaotic system with time delay. The associated characteristic equation is established by regarding the time delay as a bifurcation parameter. A set of conditions which ensure the existence of the Hopf bifurcation are gained by analyzing the corresponding characteristic equation. Then, we discuss the influence of feedback gain on the critical value of fractional order and time delay in the controlled system. Theoretical analysis shows that the controller is effective in delaying the Hopf bifurcation critical value via decreasing the feedback gain. Finally, some numerical simulations are presented to prove the validity of our theoretical analysis and confirm that the time-delayed feedback controller is valid in controlling chaos and Hopf bifurcation in the fractional-order memristor-based system.
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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.
Subcritical, nontypical and period-doubling bifurcations of a delta wing in a low speed wind tunnel
Korbahti, Banu; Kagambage, Emile; Andrianne, Thomas; Abdul Razak, Norizham; Dimitriadis, Grigorios
2011-04-01
Limit Cycle Oscillations (LCOs) involving Delta wings are an important area of research in modern aeroelasticity. Such phenomena can be the result of geometric or aerodynamic nonlinearity. In this paper, a flexible half-span Delta wing is tested in a low speed wind tunnel in order to investigate its dynamic response. The wing is designed to be more flexible than the models used in previous research on the subject in order to expand the airspeed range in which LCOs occur. The experiments reveal that this wing features a very rich bifurcation behavior. Three types of bifurcation are observed for the first time for such an aeroelastic system: subcritical bifurcations, period-doubling/period-halving and nontypical bifurcations. They give rise to a great variety of LCOs, even at very low angles of attack. The LCOs resulting from the nontypical bifurcation display Hopf-type behavior, i.e. having fundamental frequencies equal to one of the linear modal frequencies. All of the other LCOs have fundamental frequencies that are unrelated to the underlying linear system modes.
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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.
Cristiano, Rony; Carvalho, Tiago; Tonon, Durval J.; Pagano, Daniel J.
2017-05-01
In this paper, Hopf and homoclinic bifurcations that occur in the sliding vector field of switching systems in R3 are studied. In particular, a dc-dc boost converter with sliding mode control and washout filter is analyzed. This device is modeled as a three-dimensional Filippov system, characterized by the existence of sliding movement and restricted to the switching manifold. The operating point of the converter is a stable pseudo-equilibrium and it undergoes a subcritical Hopf bifurcation. Such a bifurcation occurs in the sliding vector field and creates, in this field, an unstable limit cycle. The limit cycle is connected to the switching manifold and disappears when it touches the visible-invisible two-fold point, resulting in a homoclinic loop which itself closes in this two-fold point. The study of these dynamic phenomena that can be found in different power electronic circuits controlled by sliding mode control strategies are relevant from the viewpoint of the global stability and robustness of the control design.
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)
Liming Zhao
2016-01-01
Full Text Available First of all, we establish a three-dimension open Kaldorian business cycle model under the condition of the fixed exchange rate. Secondly, with regard to the model, we discuss the existence of equilibrium point and the stability of the system near it with a time delay in currency supply as the bifurcating parameters of the system. Thirdly, we discuss the existence of Hopf bifurcation and investigate the stability of periodic solution generated by the Hopf bifurcation; then the direction of the Hopf bifurcation is given. Finally, a numerical simulation is given to confirm the theoretical results. This paper plays an important role in theoretical researching on the model of business cycle, and it is crucial for decision-maker to formulate the macroeconomic policies with the conclusions of this paper.
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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.
DEFF Research Database (Denmark)
Corradi, Olivier; Hjorth, Poul G.; Starke, Jens
2012-01-01
an onset of oscillations of the net pedestrian flux through the doorway, described by a Hopf bifurcation. An equation-free continuation of the Hopf point in the two parameters, door width and ratio of the pedestrian velocities of the two crowds, is performed. © 2012 Society for Industrial and Applied......Using an equation-free analysis approach we identify a Hopf bifurcation point and perform a twoparameter continuation of the Hopf point for the macroscopic dynamical behavior of an interacting particle model. Due to the nature of systems with a moderate number of particles and noise, the quality...... of the available numerical information requires the use of very robust numerical algorithms for each of the building blocks of the equation-free methodology. As an example, we consider a particle model of a crowd of pedestrians where particles interact through pairwise social forces. The pedestrians move along...
Hopf Bifurcation in an SEIDQV Worm Propagation Model with Quarantine Strategy
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Yu Yao
2012-01-01
Full Text Available Worms exploiting zero-day vulnerabilities have drawn significant attention owing to their enormous threats to the Internet. In general, users may immunize their computers with countermeasures in exposed and infectious state, which may take a period of time. Through theoretical analysis, time delay may lead to Hopf bifurcation phenomenon so that the worm propagation system will be unstable and uncontrollable. In view of the above factors, a quarantine strategy is thus proposed in the study. In real network, unknown worms and worm variants may lead to great risks, which misuse detection system fails to detect. However, anomaly detection is of help in detecting these kinds of worm. Consequently, our proposed quarantine strategy is built on the basis of anomaly intrusion detection system. Numerical experiments show that the quarantine strategy can diminish the infectious hosts sharply. In addition, the threshold τ0 is much larger after using our quarantine strategy, which implies that people have more time to remove worms so that the system is easier to be stable and controllable without Hopf bifurcation. Finally, simulation results match numerical ones well, which fully supports our analysis.
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.
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.
On the analysis of the double Hopf bifurcation in machining processes via centre manifold reduction.
Molnar, T G; Dombovari, Z; Insperger, T; Stepan, G
2017-11-01
The single-degree-of-freedom model of orthogonal cutting is investigated to study machine tool vibrations in the vicinity of a double Hopf bifurcation point. Centre manifold reduction and normal form calculations are performed to investigate the long-term dynamics of the cutting process. The normal form of the four-dimensional centre subsystem is derived analytically, and the possible topologies in the infinite-dimensional phase space of the system are revealed. It is shown that bistable parameter regions exist where unstable periodic and, in certain cases, unstable quasi-periodic motions coexist with the equilibrium. Taking into account the non-smoothness caused by loss of contact between the tool and the workpiece, the boundary of the bistable region is also derived analytically. The results are verified by numerical continuation. The possibility of (transient) chaotic motions in the global non-smooth dynamics is shown.
Dai, Yunxian; Lin, Yiping; Zhao, Huitao; Khalique, Chaudry Masood
2016-06-01
In this paper, a delayed computer virus propagation model with a saturation incidence rate and a time delay describing temporary immune period is proposed and its dynamical behaviors are studied. The threshold value ℜ0 is given to determine whether the virus dies out completely. By comparison arguments and iteration technique, sufficient conditions are obtained for the global asymptotic stabilities of the virus-free equilibrium and the virus equilibrium. Taking the delay as a parameter, local Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stabilities of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations (FDEs). Finally, numerical simulations are carried out to illustrate the main theoretical results.
Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics
Drogoul, Audric; Veltz, Romain
2017-02-01
In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived [De Masi et al., J. Stat. Phys. 158, 866-902 (2015) and Fournier and löcherbach, Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)] mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation. The second stems from the simulation of the full mean field. Finally, the last evidence comes from the simulation of the network for a large number of neurons. We provide a "recipe" to find such bifurcation which nicely complements the works in De Masi et al. [J. Stat. Phys. 158, 866-902 (2015)] and Fournier and löcherbach [Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)]. This suggests in return to revisit theoretically these mean field equations from a dynamical point of view. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronization in excitatory globally pulse-coupled networks.
Directory of Open Access Journals (Sweden)
Daogao Wei
2015-01-01
Full Text Available Multiaxle steering is widely used in commercial vehicles. However, the mechanism of the self-excited shimmy produced by the multiaxle steering system is not clear until now. This study takes a dual-front axle heavy truck as sample vehicle and considers the influences of mid-shift transmission and dry friction to develop a 9 DOF dynamics model based on Lagrange’s equation. Based on the Hopf bifurcation theorem and center manifold theory, the study shows that dual-front axle shimmy is a self-excited vibration produced from Hopf bifurcation. The numerical method is adopted to determine how the size of dry friction torque influences the Hopf bifurcation characteristics of the system and to analyze the speed range of limit cycles and numerical characteristics of the shimmy system. The consistency of results of the qualitative and numerical methods shows that qualitative methods can predict the bifurcation characteristics of shimmy systems. The influences of the main system parameters on the shimmy system are also discussed. Improving the steering transition rod stiffness and dry friction torque and selecting a smaller pneumatic trail and caster angle can reduce the self-excited shimmy, reduce tire wear, and improve the driving stability of vehicles.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Agliari, Anna [Dipartimento di Scienze Economiche e Sociali, Universita Cattolica del Sacro Cuore, Via Emilia Parmense, 84, 29100 Piacenza (Italy)]. E-mail: anna.agliari@unicatt.it
2006-08-15
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.
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.
Effects of internal noise in mesoscopic chemical systems near Hopf bifurcation
Energy Technology Data Exchange (ETDEWEB)
Xiao Tiejun [Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, 230026 (China); Ma Juan [Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, 230026 (China); Hou Zhonghuai [Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, 230026 (China); Xin Houwen [Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, 230026 (China)
2007-11-15
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.
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.
Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow
Riols, A.; Rincon, F.; Cossu, C.; Lesur, G.; Longaretti, P.-Y.; Ogilvie, G. I.; Herault, J.
2013-09-01
Magnetorotational dynamo action in Keplerian shear flow is a three-dimensional, nonlinear magnetohydrodynamic process whose study is relevant to the understanding of accretion and magnetic field generation in astrophysics. Transition to this form of dynamo is subcritical and shares many characteristics of transition to turbulence in non-rotating hydrodynamic shear flows. This suggests that these different fluid systems become active through similar generic bifurcation mechanisms, which in both cases have eluded detailed understanding so far. In this paper, we investigate numerically the bifurcation mechanisms at work in the incompressible Keplerian magnetorotational dynamo problem in the shearing box framework. Using numerical techniques imported from dynamical systems research, we show that the onset of chaotic dynamo action at magnetic Prandtl numbers larger than unity is primarily associated with global homoclinic and heteroclinic bifurcations of nonlinear magnetorotational dynamo cycles. These global bifurcations are supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. This suggests that nonlinear magnetorotational dynamo cycles provide the pathway to turbulent injection of both kinetic and magnetic energy in incompressible magnetohydrodynamic Keplerian shear flow in the absence of an externally imposed magnetic field. Studying the nonlinear physics and bifurcations of these cycles in different regimes and configurations may subsequently help to better understand the conditions of excitation of magnetohydrodynamic turbulence and instability-driven dynamos in various astrophysical systems and laboratory experiments. The detailed characterization of global bifurcations provided for this three-dimensional subcritical fluid dynamics problem may also prove useful for the problem of transition to turbulence in hydrodynamic shear flows.
Energy Technology Data Exchange (ETDEWEB)
Jiang Xiaowu [Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan (China); Zhou Xueyong [Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan (China)], E-mail: xueyongzhou@126.com; Shi Xiangyun [Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan (China); Song Xinyu [Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan (China)], E-mail: xysong88@163.com
2008-10-15
A delay differential mathematical model that described HIV infection of CD4{sup +} T-cells is analyzed. The stability of the non-negative equilibria and the existence of Hopf bifurcation are investigated. A stability switch in the system due to variation of delay parameter has been observed, so is the phenomena of Hopf bifurcation and stable limit cycle. The estimation of the length of delay to preserve stability has been calculated. Using the normal form theory and center manifold argument, the explicit formulaes which determine the stability, the direction and the periodic of bifurcating period solutions are derived. Numerical simulations are carried out to explain the mathematical conclusions.
Hopf bifurcation in a dynamic IS-LM model with time delay
Energy Technology Data Exchange (ETDEWEB)
Neamtu, Mihaela [Department of Economic Informatics, Mathematics and Statistics, Faculty of Economics, West University of Timisoara, str. Pestalozzi, nr. 16A, 300115 Timisoara (Romania)]. E-mail: mihaela.neamtu@fse.uvt.ro; Opris, Dumitru [Department of Applied Mathematics, Faculty of Mathematics, West University of Timisoara, Bd. V. Parvan, nr. 4, 300223 Timisoara (Romania)]. E-mail: opris@math.uvt.ro; Chilarescu, Constantin [Department of Economic Informatics, Mathematics and Statistics, Faculty of Economics, West University of Timisoara, str. Pestalozzi, nr. 16A, 300115 Timisoara (Romania)]. E-mail: cchilarescu@rectorat.uvt.ro
2007-10-15
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.
DROP TAIL AND RED QUEUE MANAGEMENT WITH SMALL BUFFERS:STABILITY AND HOPF BIFURCATION
Directory of Open Access Journals (Sweden)
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.
A bifurcation analysis of boiling water reactor on large domain of parametric spaces
Pandey, Vikas; Singh, Suneet
2016-09-01
The boiling water reactors (BWRs) are inherently nonlinear physical system, as any other physical system. The reactivity feedback, which is caused by both moderator density and temperature, allows several effects reflecting the nonlinear behavior of the system. Stability analyses of BWR is done with a simplified, reduced order model, which couples point reactor kinetics with thermal hydraulics of the reactor core. The linear stability analysis of the BWR for steady states shows that at a critical value of bifurcation parameter (i.e. feedback gain), Hopf bifurcation occurs. These stable and unstable domains of parametric spaces cannot be predicted by linear stability analysis because the stability of system does not include only stability of the steady states. The stability of other dynamics of the system such as limit cycles must be included in study of stability. The nonlinear stability analysis (i.e. bifurcation analysis) becomes an indispensable component of stability analysis in this scenario. Hopf bifurcation, which occur with one free parameter, is studied here and it formulates birth of limit cycles. The excitation of these limit cycles makes the system bistable in the case of subcritical bifurcation whereas stable limit cycles continues in an unstable region for supercritical bifurcation. The distinction between subcritical and supercritical Hopf is done by two parameter analysis (i.e. codimension-2 bifurcation). In this scenario, Generalized Hopf bifurcation (GH) takes place, which separates sub and supercritical Hopf bifurcation. The various types of bifurcation such as limit point bifurcation of limit cycle (LPC), period doubling bifurcation of limit cycles (PD) and Neimark-Sacker bifurcation of limit cycles (NS) have been identified with the Floquet multipliers. The LPC manifests itself as the region of bistability whereas chaotic region exist because of cascading of PD. This region of bistability and chaotic solutions are drawn on the various
Diekmann, O; Montijn, R
1982-01-01
We discuss a simple deterministic model for the spread, in a closed population, of an infectious disease which confers only temporary immunity. The model leads to a nonlinear Volterra integral equation of convolution type. We are interested in the bifurcation of periodic solutions from a constant solution (the endemic state) as a certain parameter (the population size) is varied. Thus we are led to study a characteristic equation. Our main result gives a fairly detailed description (in terms of Fourier coefficients of the kernel) of the traffic of roots across the imaginary axis. As a corollary we obtain the following: if the period of immunity is longer than the preceding period of incubation and infectivity, then the endemic state is unstable for large population sizes and at least one periodic solution will originate.
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...
Bifurcation and Hybrid Control for A Simple Hopfield Neural Networks with Delays
Directory of Open Access Journals (Sweden)
Zisen Mao
2013-01-01
Full Text Available A detailed analysis on the Hopf bifurcation of a delayed Hopfield neural network is given. Moreover, a new hybrid control strategy is proposed, in which time-delayed state feedback and parameter perturbation are used to control the Hopf bifurcation of the model. Numerical simulation results confirm that the new hybrid controller using time delay is efficient in controlling Hopf bifurcation.
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...the specific structure of the bifurcation near the homo- clinic orbit. Near the Hopf bifurcation, our results could also be obtained from known...on U which maps orbits of f onto orbits of g preserving the sense of time. An f E9 is structurally stable if there is a neighborhood U of f such that
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
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.
Iqbal, Amer
2012-01-01
We establish a relation between the refined Hopf link invariant and the S-matrix of the refined Chern-Simons theory. We show that the refined open string partition function corresponding to the Hopf link, calculated using the refined topological vertex, when expressed in the basis of Macdonald polynomials gives the S-matrix of the refined Chern-Simons theory.
Discretization analysis of bifurcation based nonlinear amplifiers
Directory of Open Access Journals (Sweden)
S. Feldkord
2017-09-01
Full Text Available 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.
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.
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.
Hypercrater Bifurcations, Attractor Coexistence, and Unfolding in a 5D Model of Economic Dynamics
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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.
Underwood, Robert G
2015-01-01
This text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras, and Hopf algebras. The last chapter (Chapter 4) discusses several applications of Hopf algebras, some of which are further developed in the author’s 2011 publication, An Introduction to Hopf Algebras. The book may be used as the main text or as a supplementary text for a graduate algebra course. Prerequisites for this text include standard material on groups, rings, modules, algebraic extension fields, finite fields, and linearly recursive sequences. The book consists of four chapters. Chapter 1 introduces algebras and coalgebras over a field K; Chapter 2 treats bialgebras; Chapter 3 discusses Hopf algebras and Chapter 4 consists of three applications of Hopf algebras. Each chapter begins with a short overview and ends with a collection of exercises which are designed to review and reinforce the material. Exercises range from straightforw...
Delayed Feedback Control and Bifurcation Analysis of an Autonomy System
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Zhen Wang
2013-01-01
Full Text Available An autonomy system with time-delayed feedback is studied by using the theory of functional differential equation and Hassard’s method; the conditions on which zero equilibrium exists and Hopf bifurcation occurs are given, the qualities of the Hopf bifurcation are also studied. Finally, several numerical simulations are given; which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable state or a stable periodic orbit.
Codimension-2 bifurcations of the Kaldor model of business cycle
Energy Technology Data Exchange (ETDEWEB)
Wu, Xiaoqin P., E-mail: xpaul_wu@yahoo.co [Department of Mathematics, Computer and Information Sciences, Mississippi Valley State University, Itta Bena, MS 38941 (United States)
2011-01-15
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 a spruce budworm model with diffusion and physiological structures
Xu, Xiaofeng; Wei, Junjie
2017-05-01
In this paper, the dynamics of a spruce budworm model with diffusion and physiological structures are investigated. The stability of steady state and the existence of Hopf bifurcation near positive steady state are investigated by analyzing the distribution of eigenvalues. The properties of Hopf bifurcation are determined by the normal form theory and center manifold reduction for partial functional differential equations. And global existence of periodic solutions is established by using the global Hopf bifurcation result of Wu. Finally, some numerical simulations are carried out to illustrate the analytical results.
Dynamics and geometry near resonant bifurcations
Broer, Hendrik; Holtman, Sijbo J.; Vegter, Gert; Vitolo, Renato
This paper provides an overview of the universal study of families of dynamical systems undergoing a Hopf-NeAmarck-Sacker bifurcation as developed in [1-4]. The focus is on the local resonance set, i.e., regions in parameter space for which periodic dynamics occurs. A classification of the
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
Energy Technology Data Exchange (ETDEWEB)
Zheng Baodong [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China)], E-mail: zbd@hit.edu.cn; Zheng Huifeng [Department of Electronics and Communication Engineering, Harbin Institute of Technology, Harbin 150001 (China)
2009-05-15
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.
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
Energy Technology Data Exchange (ETDEWEB)
Itovich, Griselda R. [Departamento de Matematica, FAEA, Universidad Nacional del Comahue, Neuquen Q8300BCX (Argentina)] e-mail: gitovich@arnet.com.ar; Moiola, Jorge L. [Departamento de Ingenieria Electrica y de Computadoras Universidad Nacional del Sur, Bahia Blanca B8000CPB (Argentina)] e-mail: jmoiola@criba.edu.ar
2006-02-01
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
National Research Council Canada - National Science Library
Caglar Uyulan; Metin Gokasan; Seta Bogosyan
2017-01-01
The main purpose of this paper is to analyze and compare the Hopf bifurcation behavior of a two-axle railway bogie and a dual wheelset in the presence of nonlinearities, which are yaw damping forces...
Bifurcation Behavior Analysis in a Predator-Prey Model
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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.
Hopf algebras and congruence subgroups
Sommerhauser, Yorck
2007-01-01
We prove that the kernel of the natural action of the modular group on the center of the Drinfel'd double of a semisimple Hopf algebra is a congruence subgroup. To do this, we introduce a class of generalized Frobenius-Schur indicators and endow it with an action of the modular group that is compatible with the original one.
Hopf Bifurcation in a Cobweb Model with Discrete Time Delays
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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.
Amplified Hopf bifurcations in feed-forward networks
Rink, B.W.; Sanders, J.A.
2013-01-01
In [B. Rink and J. Sanders, Trans. Amer. Math. Soc., to appear] the authors developed a method for computing normal forms of dynamical systems with a coupled cell network structure. We now apply this theory to one-parameter families of homogeneous feed-forward chains with 2-dimensional cells. Our
Integral Step Size Makes a Difference to Bifurcations of a Discrete-Time Hindmarsh-Rose Model
Yu, Yang; Cao, Hongjun
A three-dimensional discrete-time Hindmarsh-Rose model obtained by the forward Euler scheme is investigated in this paper. When the integral step size is chosen as a bifurcation parameter, conditions of existence for the fold bifurcation, the flip bifurcation, and the Hopf bifurcation are derived by using the center manifold theorem, bifurcation theory and a criterion of Hopf bifurcation. Numerical simulations including time series, bifurcation diagrams, Lyapunov exponents, phase portraits show the consistence with the analytical analysis. Our research results demonstrate that the integral step size makes a difference corresponding to local and global bifurcations of the three-dimensional discrete-time Hindmarsh-Rose model. These results can supply a solid analytical basis to the study of Hindmarsh-Rose model, and it is necessary to illustrate how much the integral step size is adopted in advance when numerical solutions or approximate solutions of the original continuous-time model is concerned.
Bifurcation analysis of a Kaldor-Kalecki model of business cycle with time delay
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Liancheng Wang
2009-10-01
Full Text Available In this paper, we investigate a Kaldor-Kalecki model of business cycle with delay in both the gross product and the capital stock. Stability analysis for the equilibrium point is carried out. We show that Hopf bifurcation occurs and periodic solutions emerge as the delay crosses some critical values. By deriving the normal forms for the system, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established. Examples are presented to confirm our results.
Energy Technology Data Exchange (ETDEWEB)
Peters, John W.; Miller, Anne-Frances; Jones, Anne K.; King, Paul W.; Adams, Michael W. W.
2016-04-01
Electron bifurcation is the recently recognized third mechanism of biological energy conservation. It simultaneously couples exergonic and endergonic oxidation-reduction reactions to circumvent thermodynamic barriers and minimize free energy loss. Little is known about the details of how electron bifurcating enzymes function, but specifics are beginning to emerge for several bifurcating enzymes. To date, those characterized contain a collection of redox cofactors including flavins and iron-sulfur clusters. Here we discuss the current understanding of bifurcating enzymes and the mechanistic features required to reversibly partition multiple electrons from a single redox site into exergonic and endergonic electron transfer paths.
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...
Bifurcation and Firing Patterns of the Pancreatic β-Cell
Wang, Jing; Liu, Shenquan; Liu, Xuanliang; Zeng, Yanjun
Using a model of individual isolated pancreatic β-cells, we investigated bifurcation diagrams of interspike intervals (ISIs) and largest Lyapunov exponents (LLE), which clearly demonstrated a wide range of transitions between different firing patterns. The numerical simulation results revealed the effect of different time constants and ion channels on the neuronal discharge rhythm. Furthermore, an individual cell exhibited tonic spiking, square-wave bursting, and tapered bursting. Additionally, several bifurcation phenomena can be observed in this paper, such as period-doubling, period-adding, inverse period-doubling and inverse period-adding scenarios. In addition, we researched the mechanisms underlying two kinds of bursting (tapered and square-wave bursting) by use of fast-slow dynamics analysis. Finally, we analyzed the codimension-two bifurcation of the fast subsystem and studied cusp bifurcation, generalized Hopf (or Bautin) bifurcation and Bogdanov-Takens bifurcation.
Global Bifurcation of a Novel Computer Virus Propagation Model
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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.
The Wiener-Hopf method in electromagnetics
Zich, Rodolfo; Daniele, Vito
2014-01-01
A function-theoretic method, The Wiener-Hopf technique has found applications in a variety of fields, most notably in analytical studies of diffraction and scattering of waves. The Wiener‐Hopf Method in Electromagnetics is an advanced academic book which provides a rare comprehensive treatment of the Wiener-Hopf method. Using a high level mathematical approach to complex electromagnetics problems and applications, this new book illustrates the wide range of the latest applications, including ...
Control of bifurcation-delay of slow passage effect by delayed self-feedback
Premraj, D.; Suresh, K.; Banerjee, Tanmoy; Thamilmaran, K.
2017-01-01
The slow passage effect in a dynamical system generally induces a delay in bifurcation that imposes an uncertainty in the prediction of the dynamical behaviors around the bifurcation point. In this paper, we investigate the influence of linear time-delayed self-feedback on the slow passage through the delayed Hopf and pitchfork bifurcations in a parametrically driven nonlinear oscillator. We perform linear stability analysis to derive the Hopf bifurcation point and its stability as a function of self-feedback time delay. Interestingly, the bifurcation-delay associated with Hopf bifurcation behaves differently in two different edges. In the leading edge of the modulating signal, it decreases with increasing self-feedback delay, whereas in the trailing edge, it behaves in an opposite manner. We also show that the linear time-delayed self-feedback can reduce bifurcation-delay in pitchfork bifurcation. These results are illustrated numerically and corroborated experimentally. We also propose a mechanistic explanation of the observed behaviors. In addition, we show that our observations are robust in the presence of noise. We believe that this study of interplay of two time delays of different origins will shed light on the control of bifurcation-delay and improve our knowledge of time-delayed systems.
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.
Yu, Jinchen; Peng, Mingshu
2016-10-01
In this paper, a Kaldor-Kalecki model of business cycle with both discrete and distributed delays is considered. With the corresponding characteristic equation analyzed, the local stability of the positive equilibrium is investigated. It is found that there exist Hopf bifurcations when the discrete time delay passes a sequence of critical values. By applying the method of multiple scales, the explicit formulae which determine the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, numerical simulations are carried out to illustrate our main results.
Stability and bifurcation analysis in hematopoietic stem cell dynamics with multiple delays
Qu, Ying; Wei, Junjie; Ruan, Shigui
2010-10-01
This paper is devoted to the analysis of a maturity structured system of hematopoietic stem cell (HSC) populations in the bone marrow. The model is a system of differential equations with several time delays. We discuss the stability of equilibria and perform the analysis of Hopf bifurcation. More precisely, we first obtain a set of improved sufficient conditions ensuring the global asymptotical stability of the zero solution using the Lyapunov method and the embedding technique of asymptotically autonomous semiflows. Then we prove that there exists at least one positive periodic solution for the n-dimensional system as a time delay varies in some region. This result is established by combining Hopf bifurcation theory, the global Hopf bifurcation theorem due to Wu [J. Wu, Symmetric functional differential equations and neural networks with memory, Trans. Amer. Math. Soc. 350 (1998) 4799-4838], and a continuation theorem of coincidence degree theory. Some numerical simulations are also presented to illustrate the analytic results.
The dynamo bifurcation in rotating spherical shells
Morin, Vincent; 10.1142/S021797920906378X
2010-01-01
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. We show that the nature of the bifurcation, which can be either supercritical or subcritical or even take the form of isola (or detached lobes) strongly depends on the parameters. This dependence is described in a range of parameters numerically accessible (which unfortunately remains remote from geophysical application), and we show how the magnetic Prandtl number and the Ekman number control these transitions.
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 analysis for a delayed food chain system with two functional responses
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2013-09-01
Full Text Available A delayed three-species food chain system with two types of functional response, Holling type and Beddington-DeAngelis type, is investigated. By analyzing the distribution of the roots of the associated characteristic equation, we get the sufficient conditions for the stability of the positive equilibrium and the existence of Hopf bifurcation. In particular, using the normal form theory and center manifold theorem, the properties of Hopf bifurcation such as direction and stability are determined. Finally, numerical simulations are given to substantiate the theoretical results.
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.
Bifurcation analysis of the transition of dune shapes under a unidirectional wind.
Niiya, Hirofumi; Awazu, Akinori; Nishimori, Hiraku
2012-04-13
A bifurcation analysis of dune shape transition is made. By use of a reduced model of dune morphodynamics, the Dune Skeleton model, we elucidate the transition mechanism between different shapes of dunes under unidirectional wind. It was found that the decrease in the total amount of sand in the system and/or the lateral sand flow shifts the stable state from a straight transverse dune to a wavy transverse dune through a pitchfork bifurcation. A further decrease causes wavy transverse dunes to shift into barchans through a Hopf bifurcation. These bifurcation structures reveal the transition mechanism of dune shapes under unidirectional wind.
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
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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.
Bifurcation analysis on a delayed SIS epidemic model with stage structure
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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.
Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation
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Reit Marco
2016-06-01
Full Text Available Since the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on the normal form of the Andronov-Hopf bifurcation is a peculiar exception of nonlinear amplifiers. This feature allows an exact mathematical formulation of the input-output characteristic and thus deeper insights of the nonlinear behavior. Aside from the Hopf-type amplifier we investigate an extension of the Hopf system with focus on ambiguities, especially the separation of solution sets, and double hysteresis behavior in the input-output characteristic. Our results are validated by a DSP implementation.
Energy Technology Data Exchange (ETDEWEB)
Erjaee, G H [Mathematics and Physics Department, Qatar University, Doha (Qatar)], E-mail: erjaee@qu.edu.qa
2008-02-15
In this article saddle and Hopf bifurcation points of predator-prey fractional differential equations system with a constant rate harvesting are investigated. The numerical results based on Grunwald-Letnikov discretization for fractional differential equations together with the Mickens' non-standard discretization method agree with those found by the corresponding ordinary differential equation system.
Erjaee, G. H.
2008-02-01
In this article saddle and Hopf bifurcation points of predator-prey fractional differential equations system with a constant rate harvesting are investigated. The numerical results based on Grunwald-Letnikov discretization for fractional differential equations together with the Mickens' non-standard discretization method agree with those found by the corresponding ordinary differential equation system.
Subcritical multiplication determination studies
Energy Technology Data Exchange (ETDEWEB)
Estes, G.P.; Goulding, C.A.
1995-07-01
A series of measurements and improvements to computational techniques are in progress at Los Alamos National Laboratory that are aimed at better understanding the determination of the reactivity of subcritical systems from measurements of the apparent multiplication of the system. Such studies are being performed in order to improve the special nuclear material (SNM) assays of unknown systems such as those encountered in SNM safeguards, arms-control verification, imports of foreign-generated SNM, etc. Improved techniques and understanding are needed since measured multiplication is not always an invariant characteristic of a subcritical system, especially if one has a system with no significant intrinsic internal neutron source that is illuminated nonuniformly with an external source (i.e., a non-normal mode system).
Uesugi, T.; Morikawa, M.; Shiromizu, T.
1996-08-01
We quantize subcritical bubbles which are formed in the weakly first order phase transition. We find that the typical size of the thermal fluctuation reduces in quantum-statistical physics. We estimate the typical size and the amplitude of thermal fluctuations near the critical temperature in the electroweak phase transition using a quantum statistical average. Furthermore, based on our study, we discuss implications for the dynamics of phase transitions.
A generalization of Connes-Kreimer Hopf algebra
Byun, Jungyoon
2005-07-01
"Bonsai" Hopf algebras, introduced here, are generalizations of Connes-Kreimer Hopf algebras, which are motivated by Feynman diagrams and renormalization. We show that we can find operad structure on the set of bonsais. We introduce a new differential on these bonsai Hopf algebras, which is inspired by the tree differential. The cohomologies of these are computed here, and the relationship of this differential with the appending operation * of Connes-Kreimer Hopf algebras is investigated.
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)
Homfly Polynomials of Generalized Hopf Links
Morton, Hugh R.; Hadji, Richard J.
2001-01-01
Following the recent work by T.-H. Chan in [HOMFLY polynomial of some generalized Hopf links, J. Knot Theory Ramif. 9 (2000) 865--883] on reverse string parallels of the Hopf link we give an alternative approach to finding the Homfly polynomials of these links, based on the Homfly skein of the annulus. We establish that two natural skein maps have distinct eigenvalues, answering a question raised by Chan, and use this result to calculate the Homfly polynomial of some more general reverse stri...
Coset for Hopf fibration and squashing
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Machiko; Tomizawa, Shinya, E-mail: mhatsuda@post.kek.j, E-mail: tomizawa@post.kek.j [Theory Division, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801 (Japan)
2009-11-21
We provide a simple derivation of metrics for fundamental geometrical deformations such as Hopf fibration, squashing and the Z{sub k} quotient which play essential roles in recent studies on the AdS{sub 4}/CFT{sub 3}. A general metric formula of Hopf fibrations for complex and quaternion cosets is presented. Squashing is given by a similarity transformation which changes the metric preserving the isometric symmetry of the projective space. On the other hand, the Z{sub k} quotient is given as a lens space which changes the topology preserving the 'local' metric.
Modeling and Bifurcation Research of a Worm Propagation Dynamical System with Time Delay
Directory of Open Access Journals (Sweden)
Yu Yao
2014-01-01
Full Text Available Both vaccination and quarantine strategy are adopted to control the Internet worm propagation. By considering the interaction infection between computers and external removable devices, a worm propagation dynamical system with time delay under quarantine strategy is constructed based on anomaly intrusion detection system (IDS. By regarding the time delay caused by time window of anomaly IDS as the bifurcation parameter, local asymptotic stability at the positive equilibrium and local Hopf bifurcation are discussed. Through theoretical analysis, a threshold τ0 is derived. When time delay is less than τ0, the worm propagation is stable and easy to predict; otherwise, Hopf bifurcation occurs so that the system is out of control and the containment strategy does not work effectively. Numerical analysis and discrete-time simulation experiments are given to illustrate the correctness of theoretical analysis.
Bifurcations of relative periodic orbits in NLS/GP with a triple-well potential
Goodman, Roy H.
2017-11-01
The nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation is considered in the presence of three equally-spaced potentials. The problem is reduced to a finite-dimensional Hamiltonian system by a Galerkin truncation. Families of oscillatory orbits are sought in the neighborhoods of the system's nine branches of standing wave solutions. Normal forms are computed in the neighborhood of these branches' various Hamiltonian Hopf and saddle-node bifurcations, showing how the oscillatory orbits change as a parameter is increased. Numerical experiments show agreement between normal form theory and numerical solutions to the reduced system and NLS/GP near the Hamiltonian Hopf bifurcations and some subtle disagreements near the saddle-node bifurcations due to exponentially small terms in the asymptotics.
Bifurcation Analysis of a Class of (n + 1)-Dimension Internet Congestion Control Systems
Xu, Wenying; Cao, Jinde; Xiao, Min
This paper investigates the stability and Hopf bifurcation induced by the time delay in a class of (n + 1)-dimension Internet congestion control systems. Although there are several previous works on simplified models of Internet congestion systems with only one or two sources and such works can reflect partly dynamical behaviors of real Internet systems, some complicated problems may inevitably be overlooked. Hence, it is meaningful to study high-dimensional models which stand closer to general realistic large-scale Internet congestion networks. By analyzing the distribution of the associated characteristic roots, we can obtain conditions for keeping systems stable. When the delay increases and exceeds a critical value, the system will undergo a Hopf bifurcation. Furthermore, the explicit formulas to determine the stability and the direction of the bifurcating periodic solution are derived by applying the normal form theory and the center manifold reduction. Finally, two numerical examples are given to verify our theoretical analysis.
Feynman graphs and related Hopf algebras
Energy Technology Data Exchange (ETDEWEB)
Duchamp, G H E [Institut Galilee, LIPN, CNRS UMR 7030 99 Av. J.-B. Clement, F-93430 Villetaneuse (France); Blasiak, P [H. Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences ul. Eliasza-Radzikowskiego 152, PL 31342 Cracow (Poland); Horzela, A [H. Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences ul. Eliasza-Radzikowskiego 152, PL 31342 Cracow (Poland); Penson, K A [Laboratoire de Physique Theorique de la Matiere Condensee Universite Pierre et Marie Curie, CNRS UMR 7600 Tour 24 - 2ieme et., 4 pl. Jussieu, F 75252 Paris Cedex 05 (France); Solomon, A I [Laboratoire de Physique Theorique de la Matiere Condensee Universite Pierre et Marie Curie, CNRS UMR 7600 Tour 24 - 2ieme et., 4 pl. Jussieu, F 75252 Paris Cedex 05 (France); Open University, Physics and Astronomy Department Milton Keynes MK7 6AA (United Kingdom)
2006-02-28
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.
Numerical bifurcation analysis of a class of nonlinear renewal equations
Directory of Open Access Journals (Sweden)
Dimitri Breda
2016-09-01
Full Text Available 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 transcritical, Hopf and period doubling bifurcations. The reliability is demonstrated by comparing the results to those obtained by a reduction to a Hamiltonian Kaplan-Yorke system and to those obtained by direct application of collocation methods (the latter also yield estimates for positive Lyapunov exponents in the chaotic regime. We conclude that the methodology described here works well for a class of delay equations for which currently no tailor-made tools exist (and for which it is doubtful that these will ever be constructed.
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.
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. .
Differential geometry on Hopf algebras and quantum groups
Energy Technology Data Exchange (ETDEWEB)
Watts, Paul [Univ. of California, Berkeley, CA (United States)
1994-12-15
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.
About Bifurcational Parametric Simplification
Gol'dshtein, V; Yablonsky, G
2015-01-01
A concept of "critical" simplification was proposed by Yablonsky and Lazman in 1996 for the oxidation of carbon monoxide over a platinum catalyst using a Langmuir-Hinshelwood mechanism. The main observation was a simplification of the mechanism at ignition and extinction points. The critical simplification is an example of a much more general phenomenon that we call \\emph{a bifurcational parametric simplification}. Ignition and extinction points are points of equilibrium multiplicity bifurcations, i.e., they are points of a corresponding bifurcation set for parameters. Any bifurcation produces a dependence between system parameters. This is a mathematical explanation and/or justification of the "parametric simplification". It leads us to a conjecture that "maximal bifurcational parametric simplification" corresponds to the "maximal bifurcation complexity." This conjecture can have practical applications for experimental study, because at points of "maximal bifurcation complexity" the number of independent sys...
Dangerous Bifurcations Revisited
Avrutin, Viktor; Zhusubaliyev, Zhanybai T.; Saha, Arindam; Banerjee, Soumitro; Sushko, Irina; Gardini, Laura
2016-12-01
A dangerous border collision bifurcation has been defined as the dynamical instability that occurs when the basins of attraction of stable fixed points shrink to a set of zero measure as the parameter approaches the bifurcation value from either side. This results in almost all trajectories diverging off to infinity at the bifurcation point, despite the eigenvalues of the fixed points before and after the bifurcation being within the unit circle. In this paper, we show that similar bifurcation phenomena also occur when the stable orbit in question is of a higher periodicity or is chaotic. Accordingly, we propose a generalized definition of dangerous bifurcation suitable for any kind of attracting sets. We report two types of dangerous border collision bifurcations and show that, in addition to the originally reported mechanism typically involving singleton saddle cycles, there exists one more situation where the basin boundary is formed by a repelling closed invariant curve.
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.
Generalized Cole–Hopf transformations for generalized Burgers ...
Indian Academy of Sciences (India)
2015-10-15
Oct 15, 2015 ... A detailed review of the invention of Cole–Hopf transformations for the Burgers equation and all the subsequent works which include generalizations of the Burgers equation and the corresponding developments in Cole–Hopf transformations are documented.
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
Generalized Poincare algebras, Hopf algebras and {kappa}-Minkowski spacetime
Energy Technology Data Exchange (ETDEWEB)
Kovacevic, D., E-mail: domagoj.kovacevic@fer.hr [Faculty of Electrical Engineering and Computing, Unska 3, HR-10000 Zagreb (Croatia); Meljanac, S., E-mail: meljanac@irb.hr [Rudjer Boskovic Institute, Bijenicka c. 54, HR-10002 Zagreb (Croatia); Pachol, A., E-mail: pachol@raunvis.hi.is [Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavik (Iceland); Strajn, R., E-mail: rina.strajn@gmail.com [Rudjer Boskovic Institute, Bijenicka c. 54, HR-10002 Zagreb (Croatia)
2012-05-01
We propose a generalized description for the {kappa}-Poincare-Hopf algebra as a symmetry quantum group of underlying {kappa}-Minkowski spacetime. We investigate all the possible implementations of (deformed) Lorentz algebras which are compatible with the given choice of {kappa}-Minkowski algebra realization. For the given realization of {kappa}-Minkowski spacetime there is a unique {kappa}-Poincare-Hopf algebra with undeformed Lorentz algebra. We have constructed a three-parameter family of deformed Lorentz generators with {kappa}-Poincare algebras which are related to {kappa}-Poincare-Hopf algebra with undeformed Lorentz algebra. Known bases of {kappa}-Poincare-Hopf algebra are obtained as special cases. Also deformation of igl(4) Hopf algebra compatible with the {kappa}-Minkowski spacetime is presented. Some physical applications are briefly discussed.
Modeling and Bifurcation Research of a Worm Propagation Dynamical System with Time Delay
Yao, Yu; Zhang, Zhao; Xiang, Wenlong; Yang, Wei; Gao, Fuxiang
2014-01-01
Both vaccination and quarantine strategy are adopted to control the Internet worm propagation. By considering the interaction infection between computers and external removable devices, a worm propagation dynamical system with time delay under quarantine strategy is constructed based on anomaly intrusion detection system (IDS). By regarding the time delay caused by time window of anomaly IDS as the bifurcation parameter, local asymptotic stability at the positive equilibrium and local Hopf bi...
Stability and bifurcation for an SEIS epidemic model with the impact of media
Huo, Hai-Feng; Yang, Peng; Xiang, Hong
2018-01-01
A novel SEIS epidemic model with the impact of media is introduced. By analyzing the characteristic equation of equilibrium, the basic reproduction number is obtained and the stability of the steady states is proved. The occurrence of a forward, backward and Hopf bifurcation is derived. Numerical simulations and sensitivity analysis are performed. Our results manifest that media can regard as a good indicator in controlling the emergence and spread of the epidemic disease.
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.
Ferruzzo Correa, Diego Paolo; Wulff, Claudia; Piqueira, José Roberto Castilho
2015-05-01
In recent years there has been an increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry patterns can emerge in these networks, as a consequence a part of the system might repeat itself, and properties of this subsystem are representative of the dynamics on the whole phase space. In this paper an analysis of the second order N-node time-delay fully connected network is presented which is based on previous work: synchronous states in time-delay coupled periodic oscillators: a stability criterion. Correa and Piqueira (2013), for a 2-node network. This study is carried out using symmetry groups. We show the existence of multiple eigenvalues forced by symmetry, as well as the existence of Hopf bifurcations. Three different models are used to analyze the network dynamics, namely, the full-phase, the phase, and the phase-difference model. We determine a finite set of frequencies ω , that might correspond to Hopf bifurcations in each case for critical values of the delay. The Sn map is used to actually find Hopf bifurcations along with numerical calculations using the Lambert W function. Numerical simulations are used in order to confirm the analytical results. Although we restrict attention to second order nodes, the results could be extended to higher order networks provided the time-delay in the connections between nodes remains equal.
Bifurcation without parameters
Liebscher, Stefan
2015-01-01
Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points.
A versatile class of prototype dynamical systems for complex bifurcation cascades of limit cycles
Sándor, Bulcsú; Gros, Claudius
2015-07-01
A general class of prototype dynamical systems is introduced, which allows to study the generation of complex bifurcation cascades of limit cycles, including bifurcations breaking spontaneously a symmetry of the system, period doubling and homoclinic bifurcations, and transitions to chaos induced by sequences of limit cycle bifurcations. The prototype systems are adaptive, with friction forces f(V(x)) being functionally dependent exclusively on the mechanical potential V(x), characterized in turn by a finite number of local minima. We discuss several low-dimensional systems, with friction forces f(V) which are linear, quadratic or cubic polynomials in the potential V. We point out that the zeros of f(V) regulate both the relative importance of energy uptake and dissipation respectively, serving at the same time as bifurcation parameters, hence allowing for an intuitive interpretation of the overall dynamical behavior. Starting from simple Hopf- and homoclinic bifurcations, complex sequences of limit cycle bifurcations are observed when the energy uptake gains progressively in importance.
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.
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...
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.
Degenerate Hopf bifurcation in a self-exciting Faraday disc dynamo
Indian Academy of Sciences (India)
School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, People's Republic of China; Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, People's Republic of China ...
Effect of pollution on the total factor productivity and the Hopf bifurcation
David Desmarchelier
2013-01-01
In a recent contribution, Empora and Mamuneas (2011) find a positive relation between pollution emissions and the total factor productivity (TFP). In the present paper, we show that this positive effect reduces the effect of pollution on the marginal utility of consumption for which a limit cycle occurs.
Numerical Bifurcation Analysis
Meijer, Hil Gaétan Ellart; Dercole, Fabio; Oldeman, Bart; Myers, R.A.
The theory of dynamical systems studies the behavior of solutions of systems, like nonlinear ordinary differential equations (ODEs), depending upon parameters. Using qualitative methods of bifurcation theory, the behavior of the system is characterized for various parameter combinations. In
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.
Turing Bifurcation and Pattern Formation of Stochastic Reaction-Diffusion System
Directory of Open Access Journals (Sweden)
Qianiqian Zheng
2017-01-01
Full Text Available Noise is ubiquitous in a system and can induce some spontaneous pattern formations on a spatially homogeneous domain. In comparison to the Reaction-Diffusion System (RDS, Stochastic Reaction-Diffusion System (SRDS is more complex and it is very difficult to deal with the noise function. In this paper, we have presented a method to solve it and obtained the conditions of how the Turing bifurcation and Hopf bifurcation arise through linear stability analysis of local equilibrium. In addition, we have developed the amplitude equation with a pair of wave vector by using Taylor series expansion, multiscaling, and further expansion in powers of small parameter. Our analysis facilitates finding regions of bifurcations and understanding the pattern formation mechanism of SRDS. Finally, the simulation shows that the analytical results agree with numerical simulation.
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.
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).
Izhikevich, Eugene M.
1998-04-01
The cusp bifurcation provides one of the simplest routes leading to bistability and hysteresis in neuron dynamics. We show that weakly connected networks of neurons near cusp bifurcations that satisfy a certain adaptation condition have quite interesting and complicated dynamics. First, we prove that any such network can be transformed into a canonical model by an appropriate continuous change of variables. Then we show that the canonical model can operate as a multiple attractor neural network or as a globally asymptotically stable neural network depending on the choice of parameters.
Bifurcation analysis to the Lugiato-Lefever equation in one space dimension
Miyaji, T.; Ohnishi, I.; Tsutsumi, Y.
2010-11-01
We study the stability and bifurcation of steady states for a certain kind of damped driven nonlinear Schrödinger equation with cubic nonlinearity and a detuning term in one space dimension, mathematically in a rigorous sense. It is known by numerical simulations that the system shows lots of coexisting spatially localized structures as a result of subcritical bifurcation. Since the equation does not have a variational structure, unlike the conservative case, we cannot apply a variational method for capturing the ground state. Hence, we analyze the equation from a viewpoint of bifurcation theory. In the case of a finite interval, we prove the fold bifurcation of nontrivial stationary solutions around the codimension two bifurcation point of the trivial equilibrium by exact computation of a fifth-order expansion on a center manifold reduction. In addition, we analyze the steady-state mode interaction and prove the bifurcation of mixed-mode solutions, which will be a germ of localized structures on a finite interval. Finally, we study the corresponding problem on the entire real line by use of spatial dynamics. We obtain a small dissipative soliton bifurcated adequately from the trivial equilibrium.
Bifurcation of Hyperbolic Planforms
Chossat, Pascal; Faye, Grégory; Faugeras, Olivier
2011-02-01
Motivated by a model for the perception of textures by the visual cortex in primates, we analyze the bifurcation of periodic patterns for nonlinear equations describing the state of a system defined on the space of structure tensors, when these equations are further invariant with respect to the isometries of this space. We show that the problem reduces to a bifurcation problem in the hyperbolic plane {D} (Poincaré disc). We make use of the concept of a periodic lattice in {D} to further reduce the problem to one on a compact Riemann surface {D}/\\varGamma, where Γ is a cocompact, torsion-free Fuchsian group. The knowledge of the symmetry group of this surface allows us to use the machinery of equivariant bifurcation theory. Solutions which generically bifurcate are called "H-planforms", by analogy with the "planforms" introduced for pattern formation in Euclidean space. This concept is applied to the case of an octagonal periodic pattern, where we are able to classify all possible H-planforms satisfying the hypotheses of the Equivariant Branching Lemma. These patterns are, however, not straightforward to compute, even numerically, and in the last section we describe a method for computation illustrated with a selection of images of octagonal H-planforms.
Universal Baxterization for Z-graded Hopf algebras
Energy Technology Data Exchange (ETDEWEB)
Dancer, K A; Finch, P E; Isaac, P S [Centre for Mathematical Physics, School of Physical Sciences, University of Queensland, Brisbane 4072 (Australia)
2007-12-14
We present a method for Baxterizing solutions of the constant Yang-Baxter equation associated with Z-graded Hopf algebras. To demonstrate the approach, we provide examples for the Taft algebras and the quantum group U{sub q}[sl(2)]. (fast track communication)
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.
Euler potentials for the MHD Kamchatnov-Hopf soliton solution
Semenov, VS; Korovinski, DB; Biernat, HK
2002-01-01
In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf
Generalized Cole–Hopf transformations for generalized Burgers ...
Indian Academy of Sciences (India)
2015-10-15
Oct 15, 2015 ... Generalized Cole–Hopf transformations for generalized. Burgers equations. B MAYIL VAGANAN∗ and E EMILY PRIYA. Department of Applied Mathematics and Statistics, School of Mathematics,. Madurai Kamaraj University, Madurai 625 021, India. ∗Corresponding author. E-mail: vkbmv66@gmail.com.
The planar algebra of a semisimple and cosemisimple Hopf algebra
Indian Academy of Sciences (India)
To a semisimple and cosemisimple Hopf algebra over an algebraically closed field, we associate a planar algebra defined by generators and relations and show that it is a connected, irreducible, spherical, non-degenerate planar algebra with non-zero modulus and of depth two. This association is shown to yield a bijection ...
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...
Subcritical flutter in the acoustics of friction
National Research Council Canada - National Science Library
O.N Kirillov
2008-01-01
...-simple eigenfrequencies at the nodes. At contact with friction pads, the rotating continua, such as the singing wine glass or the squealing disc brake, start to vibrate owing to the subcritical flutter instability...
Response and bifurcation of rotor with squeeze film damper on elastic support
Energy Technology Data Exchange (ETDEWEB)
Qin Weiyang; Zhang Jinfu; Ren Xingmin [Department of Engineering Mechanics, Northwestern Polytechnical University, Xi' an 710072 (China)
2009-01-15
This paper investigates the nonlinear response and bifurcation of rotor with Squeezed Film Damper (SFD) supported on elastic foundation. The motion equations are derived. To analyze the bifurcation of nonlinear response of SFD rotor, the Floquet Multipliers is obtained by solving the perturbation equations with numerical method. For computing Floquet Multipliers, a novel method is presented in this paper, which can begin integration at the stable solution. Simulation results are given in two figures. One figure, which consists of eight subfigures, gives the effect of rotating speed on the response of SFD damper supported on elastic foundation: with increasing rotating speed, the nonlinear response evolves from quasi-period to period, then jumps between different periods, and finally returns to quasi-period; the corresponding bifurcations are saddle-node bifurcation and secondary Hopf bifurcation. The second figure, which consists of six subfigures, shows that: the support stiffness has large influence on the response of bearings and film force in SFD; large support stiffness can lead to oil whirl in SFD.
Bifurcations and chaos of time delay Lorenz system with dimension 2n+1
Mahmoud, Gamal M.; Arafa, Ayman A.; Mahmoud, Emad E.
2017-11-01
The aim of this paper is to introduce a generalized form of the Lorenz system with time delay. Instead of considering each state variable of the Lorenz system belonging to R, the paper considers two of them belonging to Rn. Hence the Lorenz system has (2 n+1) dimension. This system appears in several applied sciences such as engineering, physics and networks. The stability of the trivial and nontrivial fixed points and the existence of Hopf bifurcations are studied analytically. Using the normal form theory and center manifold argument, the direction and the stability of the bifurcating periodic solutions are determined. Finally, numerical simulations are calculated to confirm our theoretical results. The paper concludes that the dynamics of this system are rich. Additionally, the values of the delay parameter at which chaotic and hyperchaotic solutions exist for different values of n using Lyapunov exponents and Kolmogorov-Sinai entropy are calculated numerically.
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
Directory of Open Access Journals (Sweden)
Kazuki Hasebe
2010-09-01
Full Text Available This paper is a review of monopoles, lowest Landau level, fuzzy spheres, and their mutual relations. The Hopf maps of division algebras provide a prototype relation between monopoles and fuzzy spheres. Generalization of complex numbers to Clifford algebra is exactly analogous to generalization of fuzzy two-spheres to higher dimensional fuzzy spheres. Higher dimensional fuzzy spheres have an interesting hierarchical structure made of ''compounds'' of lower dimensional spheres. We give a physical interpretation for such particular structure of fuzzy spheres by utilizing Landau models in generic even dimensions. With Grassmann algebra, we also introduce a graded version of the Hopf map, and discuss its relation to fuzzy supersphere in context of supersymmetric Landau model.
A generic Hopf algebra for quantum statistical mechanics
Energy Technology Data Exchange (ETDEWEB)
Solomon, A I [Physics and Astronomy Department, The 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.u, E-mail: gduchamp2@free.f, E-mail: pawel.blasiak@ifj.edu.p, E-mail: andrzej.horzela@ifj.edu.p, E-mail: penson@lptl.jussieu.f [Lab. de Phys. Theor. de la Matiere Condensee, University of Paris VI (France)
2010-09-15
In this paper, we present a Hopf algebra description of a bosonic quantum model, using the elementary combinatorial elements of Bell and Stirling numbers. Our objective in doing this is as follows. Recent studies have revealed that perturbative quantum field theory (pQFT) displays an astonishing interplay between analysis (Riemann zeta functions), topology (Knot theory), combinatorial graph theory (Feynman diagrams) and algebra (Hopf structure). Since pQFT is an inherently complicated study, so far not exactly solvable and replete with divergences, the essential simplicity of the relationships between these areas can be somewhat obscured. The intention here is to display some of the above-mentioned structures in the context of a simple bosonic quantum theory, i.e. a quantum theory of non-commuting operators that do not depend on space-time. The combinatorial properties of these boson creation and annihilation operators, which is our chosen example, may be described by graphs, analogous to the Feynman diagrams of pQFT, which we show possess a Hopf algebra structure. Our approach is based on the quantum canonical partition function for a boson gas.
Asymmetric bifurcated halogen bonds.
Novák, Martin; Foroutan-Nejad, Cina; Marek, Radek
2015-03-07
Halogen bonding (XB) is being extensively explored for its potential use in advanced materials and drug design. Despite significant progress in describing this interaction by theoretical and experimental methods, the chemical nature remains somewhat elusive, and it seems to vary with the selected system. In this work we present a detailed DFT analysis of three-center asymmetric halogen bond (XB) formed between dihalogen molecules and variously 4-substituted 1,2-dimethoxybenzene. The energy decomposition, orbital, and electron density analyses suggest that the contribution of electrostatic stabilization is comparable with that of non-electrostatic factors. Both terms increase parallel with increasing negative charge of the electron donor molecule in our model systems. Depending on the orientation of the dihalogen molecules, this bifurcated interaction may be classified as 'σ-hole - lone pair' or 'σ-hole - π' halogen bonds. Arrangement of the XB investigated here deviates significantly from a recent IUPAC definition of XB and, in analogy to the hydrogen bonding, the term bifurcated halogen bond (BXB) seems to be appropriate for this type of interaction.
The physics of accelerator driven sub-critical reactors
Indian Academy of Sciences (India)
Keywords. Accelerator driven systems; nuclear waste transmutation; computer codes; reactor physics; reactor noise; kinetics; burnup; transport theory; Monte Carlo; thorium utilization; neutron multiplication; sub-criticality; sub-critical facilities.
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.
Mechanisms of Subcritical Cracking in Calcite
Royne, A.; Dysthe, D. K.; Bisschop, J.
2008-12-01
Brittle materials are characterized by a critical stress intensity factor above which they will fail catastrophically by dynamic cracking. However, it has been observed that materials can also fail at much lower stresses, through slow crack growth, often referred to as subcritical cracking. This phenomenon can take place even in vacuum, but is greatly enhanced by water and other reactive species in the environment. For a given material and environmental condition there is a systematic relationship between the crack tip velocity and the stress intensity factor. The presence of a lower stress limit to subcritical cracking has been predicted from thermodynamics but has not been firmly demonstrated experimentally. This parameter would control the long- term strength of geological materials. Subcritical cracking must necessarily be important in controlling the rock strength in near-surface processes where water and other active species are present and the displacements and stresses are low. Weathering is one example of such a process. Modelling has shown that fracture networks generated by a high degree of subcritical cracking will percolate at much lower fracture densities than purely stochastical fracture networks. This has important implications for how water can move through the crust. Understanding the mechanisms for subcritical crack growth in geological materials is also important in assessing the stability and long term performance of sequestration reservoirs for CO2 or nuclear waste. The mechanism for stress corrosion is well known for glasses and quartz. For carbonate minerals, the mechanism for subcritical crack growth has not been identified, and the only experimental studies on calcitic materials have been on polycrystalline rocks such as marble. Suggested mechanisms include stress corrosion (weakening reactions at the crack tip), preferential dissolution at the crack tip with rapid removal of dissolved species, and environmentally controlled
On the bifurcations of a rigid rotor response in squeeze-film dampers
Inayat-Hussain, J. I.; Kanki, H.; Mureithi, N. W.
2003-03-01
The effectiveness of squeeze-film dampers in controlling vibrations in rotating machinery may be limited by the nonlinear interactions between large rotor imbalance forces with fluid-film forces induced by dampers operating in cavitated conditions. From a practical point of view, the occurrence of nonsynchronous and chaotic motion in rotating machinery is undesirable and should be avoided as they introduce cyclic stresses in the rotor, which in turn may rapidly induce fatigue failure. The bifurcations in the response of a rigid rotor supported by cavitated squeeze-film dampers resulting from such interactions are presented in this paper. The effects of design and operating parameters, namely the bearing parameter (/B), gravity parameter (/W), spring parameter (/S) and unbalance parameter (/U), on the bifurcations of the rotor response are investigated. Spring parameter (/S) values between 0 and 1 are considered. A spring parameter value of /S=0 represents the special case of dampers without centering springs. With the exception of the case /S=1, jump phenomena appeared to be a common bifurcation that occurred at certain combinations of /B, /W and /U irrespective of the value of /S. Period-doubling and secondary Hopf bifurcations which occurred for low values of /S (=0.5. For very low stiffness values (/Sfilm forces in cavitated dampers, occurring in industrial rotating machinery, cannot be de-emphasized.
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...
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.; 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).
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
Bifurcations in two-dimensional reversible maps
Post, T.; Capel, H.W.; Quispel, G.R.W.; van der Weele, J.P.
1990-01-01
We give a treatment of the non-resonant bifurcations involving asymmetric fixed points with Jacobian J≠1 in reversible mappings of the plane. These bifurcations include the saddle-node bifurcation not in the neighbourhood of a fixed point with J≠1, as well as the so-called transcritical bifurcations
Bifurcation Adds Flavor to Basketball
Min, Byeong June
2016-01-01
We report an emergence of bifurcation in basketball, a single-particle system governed by Newtonian mechanics. When shooting the basketball, the obvious control parameters are the launch speed and the launch angle. We propose to use the three-dimensional velocity phase-space volume associated with the given launch parameters to quantify the difficulty of the shooting. The optimal launch angle that maximizes the associated phase-space volume undergoes a bifurcation as the launch speed is increased, if the shooter is farther than a critical distance away from the hoop. Thus, the bifurcation makes it very important to control the launch speed accurately. If the air resistance is removed, the bifurcation disappears and the phase-space volume distribution becomes dispersionless and shrinks in magnitude.
Hopf-algebra description of noncommutative-spacetime symmetries
Agostini, A; D'Andrea, F; Andrea, Francesco D'
2003-01-01
In the study of certain noncommutative versions of Minkowski spacetime there is still a large ambiguity concerning the characterization of their symmetries. Adopting as our case study the kappaMinkowski noncommutative space-time, on which a large literature is already available, we propose a line of analysis of noncommutative-spacetime symmetries that relies on the introduction of a Weyl map (connecting a given function in the noncommutative Minkowski with a corresponding function in commutative Minkowski) and of a compatible notion of integration in the noncommutative spacetime. We confirm (and we establish more robustly) previous suggestions that the commutative-spacetime notion of Lie-algebra symmetries must be replaced, in the noncommutative-spacetime context, by the one of Hopf-algebra symmetries. We prove that in kappaMinkowski it is possible to construct an action which is invariant under a Poincare-like Hopf algebra of symmetries with 10 generators, in which the noncommutativity length scale has the r...
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.)
Collet, Carlos; Onuma, Yoshinobu; Cavalcante, Rafael; Grundeken, Maik; Généreux, Philippe; Popma, Jeffrey; Costa, Ricardo; Stankovic, Goran; Tu, Shengxian; Reiber, Johan H. C.; Aben, Jean-Paul; Lassen, Jens Flensted; Louvard, Yves; Lansky, Alexandra; Serruys, Patrick W.
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
MCNP multiplication analysis of subcritical HEU experiments
Energy Technology Data Exchange (ETDEWEB)
Estes, G.P. [Los Alamos National Lab., NM (United States); Brockhoff, R.C. [Kansas State Univ., Manhattan, KS (United States)
1998-12-31
A series of measurements and improvements to computational techniques was described in Ref. 1 that were aimed at better understanding the determination of the reactivity of subcritical systems from measurements of the multiplying characteristics of the system. This methodology has been applied to a number of the bare highly enriched uranium (HEU) measurements (simulating 0.5- to 21.5-kg balls with nesting shells) of Ref. 2, demonstrating that the experimental multiplication results can be reproduced computationally with good accuracy. This capability promises to improve special nuclear material (SNM) assays of unknown systems such as those encountered in SNM safeguards, arms-control verification, imports of foreign-generated SNM, smuggling of SNM, etc. Improved techniques and understanding are needed since traditionally measured or calculated multiplications are not always an invariant characteristic of a subcritical system, especially if one has an SNM system with no significant intrinsic internal neutron source that is illuminated nonuniformly with an external source (i.e., a nonnormal mode system). The measurement techniques used in Refs. 1 and 2 to determine multiplication are based on the Feynman variance-to-mean method, which has been previously documented in Refs. 3 and 4 and applied successfully to normal mode systems such as plutonium and uranium spheres. These techniques have been applied to nonnormal mode problems with less success, and both Refs. 1 and 2 as well as the current paper are attempts to better understand the subcritical multiplication of such systems.
Subcritical neutron production using multiple accelerators
Energy Technology Data Exchange (ETDEWEB)
Yoon, W.Y.; Jones, J.L. [Idaho National Engineering Lab., Idaho Falls, ID (United States); Harmon, J.F. [Idaho State Univ., Pocatello, ID (United States)
1994-12-31
A subcritical neutron production technique using multiple accelerators is being developed to provide a selective alternative (for small volumes) to nuclear reactor neutron production. The concept combines the capabilities of multiple commercially-available linear accelerators and a compact subcritical assembly design to generate reactor-like thermal neutron fluxes (i.e., 10{sup 13}-10{sup 14} n/cm{sup 2}/s) in small irradiation volumes of up to 500 cm{sup 3}. In addition, fast and epithermal neutron fluxes will also be available. The neutron source utilizes radially-oriented, pulsed, electron accelerators. The subcritical neutron production assembly is in the form of a compact right-cylinder (approximately 20-cm dia.). This assembly uses an outer ring of graphite (i.e., reflector) with re-entrant holes to enable penetration of the electron beam to the internal structure which comprises of uranium as an electron convertor/neutron multiplier followed by H{sub 2}O beryllium, H{sub 2}O aluminum, and D{sub 2}O in succession toward the center. The inner-most region filled with D{sub 2}O is the central irradiation volume. The material configuration and overall design is to maximize thermal neutron fluxes in the central irradiation volume based on photoneutron/photofission and neutron multiplication processes as well as neutron transport. This assembly will be designed not to reach a nuclear critical state under any normal and/or accidental condition.
Subcritical convection in a rapidly rotating sphere at low Prandtl number
Guervilly, Celine
2016-01-01
We study non-linear convection in a low Prandtl number fluid ($Pr = 0.01-0.1$) in a rapidly rotating sphere with internal heating. 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 a superposition 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 non-linear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl nu...
Subcritical Thermal Convection of Liquid Metals in a Rapidly Rotating Sphere
Kaplan, E. J.; Schaeffer, N.; Vidal, J.; Cardin, P.
2017-09-01
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 numerical simulation. Near the critical thermal forcing (Rayleigh number Ra), convection onsets as thermal Rossby waves, but as Ra increases, this state is superseded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the planetary core rotates faster, the smooth transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at Ek <10-6. Here, the strong branch persists even as the thermal forcing drops well below the linear onset of convection (Ra =0.7 Racrit in this study). We highlight the importance of the Reynolds stress, which is required for convection to subsist below the linear onset. In addition, the Péclet number is consistently above 10 in the strong branch. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective 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 through a subcritical bifurcation.
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.
Inverse Problem In Optical Tomography Using Diffusion Approximation and Its Hopf-Cole Transformation
Directory of Open Access Journals (Sweden)
Taufiquar R. Khan
2003-12-01
Full Text Available In this paper, we derive the Hopf-Cole transformation to the diffusion approximation. We find the analytic solution to the one dimensional diffusion approximation and its Hopf-Cole transformation for a homogenous constant background medium. We demonstrate that for a homogenous constant background medium in one dimension, the Hopf-Cole transformation improves the stability of the inverse problem. We also derive a Green's function scaling of the higher dimensional diffusion approximation for an inhomogeneous background medium and discuss a two step reconstruction algorithm.
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...
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.
Fredholm theory for Wiener-Hopf plus Hankel operators
Bogveradze, Giorgi
2008-01-01
Na presente tese consideramos combinações algébricas de operadores de Wiener-Hopf e de Hankel com diferentes classes de símbolos de Fourier. Nomeadamente, foram considerados símbolos matriciais na classe de elementos quase periódicos, semi-quase periódicos, quase periódicos por troços e certas funções matriciais sectoriais. Adicionalmente, foi dedicada atenção também aos operadores de Toeplitz mais Hankel com símbolos quase periódicos por troços e com símbolos escalares poss...
Quasi-Hopf twistors for elliptic quantum groups
Jimbo, M; Odake, S; Shiraishi, J
1997-01-01
The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda et al., Felder). Fronsdal made a penetrating observation that both of them are quasi-Hopf algebras, obtained by twisting the standard quantum affine algebra U_q(g). In this paper we present an explicit formula for the twistors in the form of an infinite product of the universal R matrix of U_q(g). We also prove the shifted cocycle condition for the twistors, thereby completing Fronsdal's findings. This construction entails that, for generic values of the deformation parameters, representation theory for U_q(g) carries over to the elliptic algebras, including such objects as evaluation modules, highest weight modules and vertex operators. In particular, we confirm the conjectures of Foda et al. concerning the elliptic algebra A_{q,p}(^sl_2).
Monte Carlo simulation of a perturbed subcritical core
Energy Technology Data Exchange (ETDEWEB)
Jaradat, Mustafa K.; Park, Chang Je [KAERI, Daejeon (Korea, Republic of)
2012-10-15
Jordan Subcritical Assembly (JSA) is designed for the purpose of education, training, and experiment research. Jordan subcritical assembly is considered Jordan's First Nuclear Facility Moving Jordan into the nuclear age. It is a teaching and training experimental facility that is designed to stay in a subcriticality A subcritical assembly is a multiplying system of nuclear fuel and moderator whose effective multiplication factor is less than unity. An extraneous source of neutron is required for the operation in order to compensate for the difference between the production rate of fission neutrons in the fuel and the rate of loss caused by absorption and leakage.
Two-Tone Suppression and Combination Tone Generation as Computations Performed by the Hopf Cochlea
Stoop, R.; Kern, A.
2004-12-01
Recent evidence suggests that the compressive nonlinearity responsible for the extreme dynamic range of the mammalian cochlea is implemented in the form of Hopf amplifiers. Whereas Helmholtz's original concept of the cochlea was that of a frequency analyzer, Hopf amplifiers can be stimulated not only by one, but also by neighboring frequencies. To reduce the resulting computational overhead, the mammalian cochlea is aided by two-tone suppression. We show that the laws governing two-tone suppression and the generation of combination tones naturally emerge from the Hopf-cochlea concept. Thus the Hopf concept of the cochlea reproduces not only local properties like the correct frequency response, but additionally accounts for more complex hearing phenomena that may be related to auditory signal computation.
Asset Price Dynamics in a Chartist-Fundamentalist Model with Time Delays: A Bifurcation Analysis
Directory of Open Access Journals (Sweden)
Loretti I. Dobrescu
2016-01-01
Full Text Available This paper studies the dynamic behavior of asset prices using a chartist-fundamentalist model with two speculative markets. To this effect, we employ a differential system with delays à la Dibeh (2007 to describe the price dynamics and we assume that the two markets are coupled via diffusive coupling terms. We study two different time delay cases, namely, when both markets experience the same time delay and when the time delay is different across markets. First, we theoretically determine that the equilibrium exists and investigate its stability. Second, we establish the general conditions for the existence of local Hopf bifurcations and analyze their direction and stability. The common conclusion from both the delay scenarios we consider is that coupled speculative markets with heterogeneous agents in each, but with different price dynamics, can be synchronized through diffusive coupling. Finally, we provide some numerical illustrations to confirm our theoretical findings.
Subcritical water extraction of lipids from wet algal biomass
Deng, Shuguang; Reddy, Harvind K.; Schaub, Tanner; Holguin, Francisco Omar
2016-05-03
Methods of lipid extraction from biomass, in particular wet algae, through conventionally heated subcritical water, and microwave-assisted subcritical water. In one embodiment, fatty acid methyl esters from solids in a polar phase are further extracted to increase biofuel production.
Production of value added materials by subcritical water hydrolysis ...
African Journals Online (AJOL)
The aim of this study was the determination of the best experimental conditions for the production of useful materials such as amino acids by subcritical water hydrolysis from supercritical carbon dioxide extracted krill residues and to compare the results with raw krill. Subcritical water hydrolysis efficiency from raw and ...
The physics of accelerator driven sub-critical reactors
Indian Academy of Sciences (India)
utilization; neutron multiplication; sub-criticality; sub-critical facilities. PACS Nos 89.30.Gg; 28.41.-I; 28.50.-k. 1. Introduction. Accelerator driven systems (ADS) are attracting worldwide attention increasingly due to their superior safety characteristics and their potential for burning actinide and fission product-waste and energy ...
Subcritical water extraction of bioactive compounds from dry loquat ...
African Journals Online (AJOL)
ERASTO
concentrated in a rotary evaporator at 60°C until dry. The total extraction yield was obtained by the mean value of the total extracts divided by the mass of dry loquat leaves used. Subcritical water extraction. Subcritical water extraction was carried using an extractor. (Hangzhou Huali Co. Ltd, Hangzhou, China). The extractor ...
Bifurcations analysis of turbulent energy cascade
Energy Technology Data Exchange (ETDEWEB)
Divitiis, Nicola de, E-mail: n.dedivitiis@gmail.com
2015-03-15
This note studies the mechanism of turbulent energy cascade through an opportune bifurcations analysis of the Navier–Stokes equations, and furnishes explanations on the more significant characteristics of the turbulence. A statistical bifurcations property of the Navier–Stokes equations in fully developed turbulence is proposed, and a spatial representation of the bifurcations is presented, which is based on a proper definition of the fixed points of the velocity field. The analysis first shows that the local deformation can be much more rapid than the fluid state variables, then explains the mechanism of energy cascade through the aforementioned property of the bifurcations, and gives reasonable argumentation of the fact that the bifurcations cascade can be expressed in terms of length scales. Furthermore, the study analyzes the characteristic length scales at the transition through global properties of the bifurcations, and estimates the order of magnitude of the critical Taylor-scale Reynolds number and the number of bifurcations at the onset of turbulence.
[Intracranial carotid artery bifurcation aneurysms].
Vega-Basulto, S D; Montejo-Montejo, J
Intracranial carotid artery bifurcation aneurysms are infrequent but its clinical behavior, high risk of bleeding and complex anatomic relationships of the sac permit to consider these lesions as a challenge cases. 497 patients harboring intracranial aneurysms were operated on at Manuel Ascunce Domenech Hospital, Camagüey, Cuba between January 1982 to august 2001. We utilized microsurgical procedures, optical magnification, specialized neuroanesthesia and Intensive Care Unit postoperatory following. All patients were evaluated clinically with World Federation Neurological Surgeon Scale and Glasgow Outcome Scale. There were 16 patients with intracranial carotid artery bifurcation aneurysms (3.2 %). 12 patients were under 40 years and 50% were between 16 and 30 years old. All patients present intracranial bleeding. There was 87.5% of total or partial recuperation. There was one death only. Postoperative deficit were observed at 44% but 31% disappeared three month later. Intracranial carotid artery bifurcation aneurysms are complex anatomoclinical lesions. Clinically, we observed high tendency to bleed and multiplicity. Anatomically, these sacs have complex arterial relationship that difficult dissection and clipping. They have frequent postoperative morbidity. Multiple or bilateral aneurysmal sacs will be clipped by one surgical procedure.
Dynamics of Subcritical Bubbles in First Order Phase Transition
Shiromizu, T.; Morikawa, M.; Yokoyama, J.
1995-11-01
We derivate the Langevin and the Fokker-Planck equations for the radius of O(3)-symmetric subcritical bubbles as a phenomenological model to treat thermal fluctuation. The effect of thermal noise on subcritical bubbles is examined. We find that the fluctuation-dissipation relation holds and that in the high temperature phase the system settles down rapidly to the thermal equilibrium state even if it was in a nonequilibrium state initially. We then estimate the typical size of subcritical bubbles as well as the amplitude of fluctuations on that scale. We also discuss their implication to the electroweak phase transition.
Design, Development and Installation of Jordan Subcritical Assembly
Ned Xoubi
2013-01-01
Following its announcement in 2007 to pursue a nuclear power program and in the absence of any nuclear facility essential for the education, training, and research, Jordan decided to build a subcritical reactor as its first nuclear facility. Jordan Subcritical Assembly (JSA) is uranium fueled light water moderated and reflected subcritical reactor driven by a plutonium-beryllium source, and the core consists of 313 LEU fuel rods, loaded into a water-filled vessel in a square lattice of 19.11 ...
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.
Bifurcation characteristics and safe basin of MSMA microgripper subjected to stochastic excitation
Directory of Open Access Journals (Sweden)
Z. W. Zhu
2015-02-01
Full Text Available A kind of magnetic shape memory alloy (MSMA microgripper is proposed in this paper, and its nonlinear dynamic characteristics are studied when the stochastic perturbation is considered. Nonlinear differential items are introduced to explain the hysteretic phenomena of MSMA, and the constructive relationships among strain, stress, and magnetic field intensity are obtained by the partial least-square regression method. The nonlinear dynamic model of a MSMA microgripper subjected to in-plane stochastic excitation is developed. The stationary probability density function of the system’s response is obtained, the transition sets of the system are determined, and the conditions of stochastic bifurcation are obtained. The homoclinic and heteroclinic orbits of the system are given, and the boundary of the system’s safe basin is obtained by stochastic Melnikov integral method. The numerical and experimental results show that the system’s motion depends on its parameters, and stochastic Hopf bifurcation appears in the variation of the parameters; the area of the safe basin decreases with the increase of the stochastic excitation, and the boundary of the safe basin becomes fractal. The results of this paper are helpful for the application of MSMA microgripper in engineering fields.
Bifurcations in the regularized Ericksen bar model
Grinfeld, M.; Lord, G. J. (Gabriel J.)
2007-01-01
We consider the regularized Ericksen model of an elastic bar on an elastic foundation on an interval with Dirichlet boundary conditions as a two-parameter bifurcation problem. We explore, using local bifurcation analysis and continuation methods, the structure of bifurcations from double zero eigenvalues. Our results provide evidence in support of M\\"uller's conjecture \\cite{Muller} concerning the symmetry of local minimizers of the associated energy functional and describe in detail the stru...
Astrobionibbler: In Situ Microfluidic Subcritical Water Extraction of Amino Acids
Noell, A. C.; Fisher, A. M.; Takano, N.; Fors-Francis, K.; Sherrit, S.; Grunthaner, F.
2016-10-01
A fluidic-chip based instrument for subcritical water extraction (SCWE) of amino acids and other organics from powder samples has been developed. A variety of soil analog extractions have been performed to better understand SCWE capabilities.
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.
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)
On Respiratory Rate of Cherry Tomatoes under Subcritical Heights
Directory of Open Access Journals (Sweden)
Fang Duan
2013-01-01
Full Text Available The influence of subcritical drop heights on respiratory rate was studied for cherry tomatoes. The cherry tomatoes were dropped, and the mean value of O2 concentration was measured, and then the respiration rate was calculated. The results showed that the respiration rate of the cherry tomatoes increases remarkably with the dropping height. Finally, the relationship between the subcritical dropping heights and respiration rate was modeled and validated, showing good agreement.
On Respiratory Rate of Cherry Tomatoes under Subcritical Heights
Fang Duan; Yu-fen Chen; Zhong-zheng Sun; Ming-qing Chen; Hui Zhang; Jing Zhang
2013-01-01
The influence of subcritical drop heights on respiratory rate was studied for cherry tomatoes. The cherry tomatoes were dropped, and the mean value of O2 concentration was measured, and then the respiration rate was calculated. The results showed that the respiration rate of the cherry tomatoes increases remarkably with the dropping height. Finally, the relationship between the subcritical dropping heights and respiration rate was modeled and validated, showing good agreement.
Wiener-Hopf Design of the Two-Degree-of-Freedom Controller for the Standard Model
Energy Technology Data Exchange (ETDEWEB)
Cho, Yong Seok [Konyang University (Korea); Choi, Goon Ho [Han Mi Technique research institute (Korea); Park, Ki Heon [Sungkyunkwan University (Korea)
2000-03-01
In this paper, Wiener-Hopf design of the two-degree-of-freedom(2DOF) controller configuration is treated for the standard plant model. It is shown that the 2DOF structure makes it possible to treat the design of feedback properties and reference tracking problem separately. Wiener-Hopf factorization technique is used to obtain the optimal controller which minimizes a given quadratic cost index. The class of all stabilizing controllers that yield finite cost index is also characterized An illustrative example is given for the step reference tracking problem which can not be treated by the conventional H{sub 2} controller formula. (author). 10 refs., 3 figs.
Bifurcations in dissipative fermionic dynamics
Napolitani, Paolo; Colonna, Maria; Di Prima, Mariangela
2014-05-01
The Boltzmann-Langevin One-Body model (BLOB), is a novel one-body transport approach, based on the solution of the Boltzmann-Langevin equation in three dimensions; it is used to handle large-amplitude phase-space fluctuations and has a broad applicability for dissipative fermionic dynamics. We study the occurrence of bifurcations in the dynamical trajectories describing heavy-ion collisions at Fermi energies. The model, applied to dilute systems formed in such collisions, reveals to be closer to the observation than previous attempts to include a Langevin term in Boltzmann theories. The onset of bifurcations and bimodal behaviour in dynamical trajectories, determines the fragment-formation mechanism. In particular, in the proximity of a threshold, fluctuations between two energetically favourable mechanisms stand out, so that when evolving from the same entrance channel, a variety of exit channels is accessible. This description gives quantitative indications about two threshold situations which characterise heavy-ion collisions at Fermi energies. First, the fusion-to-multifragmentation threshold in central collisions, where the system either reverts to a compact shape, or splits into several pieces of similar sizes. Second, the transition from binary mechanisms to neck fragmentation (in general, ternary channels), in peripheral collisions.
Neutrino Physics with Accelerator Driven Subcritical Reactors
Ciuffoli, Emilio
2017-09-01
Accelerator Driven Subcritical System (ADS) reactors are being developed around the world, to produce energy and, at the same time, to provide an efficient way to dispose of and to recycle nuclear waste. Used nuclear fuel, by itself, cannot sustain a chain reaction; however in ADS reactors the additional neutrons which are required will be supplied by a high-intensity accelerator. This accelerator will produce, as a by-product, a large quantity of {\\bar{ν }}μ via muon Decay At Rest (µDAR). Using liquid scintillators, it will be possible to to measure the CP-violating phase δCP and to look for experimental signs of the presence of sterile neutrinos in the appearance channel, testing the LSND and MiniBooNE anomalies. Even in the first stage of the project, when the beam energy will be lower, it will be possible to produce {\\bar{ν }}e via Isotope Decay At Rest (IsoDAR), which can be used to provide competitive bounds on sterile neutrinos in the disappearance channel. I will consider several experimental setups in which the antineutrinos are created using accelerators that will be constructed as part of the China-ADS program.
Crisis bifurcations in plane Poiseuille flow.
Zammert, Stefan; Eckhardt, Bruno
2015-04-01
Many shear flows follow a route to turbulence that has striking similarities to bifurcation scenarios in low-dimensional dynamical systems. Among the bifurcations that appear, crisis bifurcations are important because they cause global transitions between open and closed attractors, or indicate drastic increases in the range of the state space that is covered by the dynamics. We here study exterior and interior crisis bifurcations in direct numerical simulations of transitional plane Poiseuille flow in a mirror-symmetric subspace. We trace the state space dynamics from the appearance of the first three-dimensional exact coherent structures to the transition from an attractor to a chaotic saddle in an exterior crisis. For intermediate Reynolds numbers, the attractor undergoes several interior crises, in which new states appear and intermittent behavior can be observed. The bifurcations contribute to increasing the complexity of the dynamics and to a more dense coverage of state space.
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.
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.
Deformations of constant mean curvature surfaces preserving symmetries and the Hopf differential
DEFF Research Database (Denmark)
Brander, David; Dorfmeister, Josef
2015-01-01
We define certain deformations between minimal and non-minimal constant mean curvature (CMC) surfaces in Euclidean space E3 which preserve the Hopf differential. We prove that, given a CMC H surface f, either minimal or not, and a fixed basepoint z0 on this surface, there is a naturally defined...
The Hopf algebra of (q)multiple polylogarithms with non-positive arguments
Ebrahimi-Fard, Kurusch; Manchon, Dominique; Singer, Johannes
2015-01-01
We consider multiple polylogarithms in a single variable at non-positive integers. Defining a connected graded Hopf algebra, we apply Connes' and Kreimer's algebraic Birkhoff decomposition to renormalize multiple polylogarithms at non-positive integer arguments, which satisfy the shuffle relation. The q-analogue of this result is as well presented, and compared to the classical case.
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.
Subcritical water as reaction environment: fundamentals of hydrothermal biomass transformation.
Möller, Maria; Nilges, Peter; Harnisch, Falk; Schröder, Uwe
2011-05-23
Subcritical water, that is, water above the boiling and below critical point, is a unique and sustainable reaction medium. Based on its solvent properties, in combination with the often considerable intrinsic water content of natural biomass, it is often considered as a potential solvent for biomass processing. Current knowledge on biomass transformation in subcritical water is, however, still rather scattered without providing a consistent picture. Concentrating on fundamental physical and chemical aspects, this review summarizes the current state of knowledge of hydrothermal biomass conversion in subcritical water. After briefly introducing subcritical water as a reaction medium, its advantages for biomass processing compared to other thermal processes are highlighted. Subsequently, the physical-chemical properties of subcritical water are discussed in the light of their impact on the occurring chemical reactions. The influence of major operational parameters, including temperature, pressure, and reactant concentration on hydrothermal biomass transformation processes are illustrated for selected carbohydrates. Major emphasis is put on the nature of the carbohydrate monomers, since the conversion of the respective polymers is analogous with the additional prior step of hydrolytic depolymerization. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Semiclassical catastrophe theory of simple bifurcations
Magner, A. G.; Arita, K.
2017-10-01
The Fedoriuk-Maslov catastrophe theory of caustics and turning points is extended to solve the bifurcation problems by the improved stationary phase method (ISPM). The trace formulas for the radial power-law (RPL) potentials are presented by the ISPM based on the second- and third-order expansion of the classical action near the stationary point. A considerable enhancement of contributions of the two orbits (pair consisting of the parent and newborn orbits) at their bifurcation is shown. The ISPM trace formula is proposed for a simple bifurcation scenario of Hamiltonian systems with continuous symmetries, where the contributions of the bifurcating parent orbits vanish upon approaching the bifurcation point due to the reduction of the end-point manifold. This occurs since the contribution of the parent orbits is included in the term corresponding to the family of the newborn daughter orbits. Taking this feature into account, the ISPM level densities calculated for the RPL potential model are shown to be in good agreement with the quantum results at the bifurcations and asymptotically far from the bifurcation points.
Attractivity and bifurcation for nonautonomous dynamical systems
Rasmussen, Martin
2007-01-01
Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions, which are useful to describe the global asymptotic behavior of systems on compact phase spaces. Furthermore, methods from the qualitative theory for linear and nonlinear systems are derived, and nonautonomous counterparts of the classical one-dimensional autonomous bifurcation patterns are developed.
Modeling of the CTEx subcritical unit using MCNPX code
Energy Technology Data Exchange (ETDEWEB)
Santos, Avelino [Divisao de Defesa Quimica, Biologica e Nuclear. Centro Tecnologico do Exercito - CTEx, Guaratiba, Rio de Janeiro, RJ (Brazil); Silva, Ademir X. da, E-mail: ademir@con.ufrj.br [Programa de Engenharia Nuclear. Universidade Federal do Rio de Janeiro - UFRJ Centro de Tecnologia, Rio de Janeiro, RJ (Brazil); Rebello, Wilson F. [Secao de Engenharia Nuclear - SE/7 Instituto Militar de Engenharia - IME Rio de Janeiro, RJ (Brazil); Cunha, Victor L. Lassance [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil)
2011-07-01
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{sub eff}, a higher concentration of U235 can be proposed, provided it safely remains below one. (author)
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...
Bifurcating optical pattern recognition in photorefractive crystals
Liu, Hua-Kuang
1993-01-01
A concept of bifurcating optical pattern rocognizer (BIOPAR) is described and demonstrated experimentally, using barium titanate crystal. When an input is applied to BIOPAR, the output may be directed to two ports.
Uniform semiclassical approximations for umbilic bifurcation catastrophes
Main, J
1998-01-01
Gutzwiller's trace formula for the semiclassical density of states diverges at the bifurcation points of periodic orbits and has to be replaced with uniform semiclassical approximations. We present a method to derive these expressions from the standard representations of the elementary catastrophes and to directly relate the uniform solutions to classical periodic orbit parameters. The method is simple even for ungeneric bifurcations with corank 2 such as the umbilic catastrophes. We demonstrate the technique on a hyperbolic umbilic in the diamagnetic Kepler problem.
Nonlinear Characteristics of Randomly Excited Transonic Flutter
DEFF Research Database (Denmark)
Christiansen, Lasse Engbo; Lehn-Schiøler, Tue; Mosekilde, Erik
2002-01-01
shown that the self-sustained oscillations arise in a subcritical Hopf bifurcation. However, analysis of the experimental data also reveals that this bifurcation is modified in various ways. We present an outline of the construction of a 6 DOF model of the aeroelastic behavior of the wing structure...... reproduce several of the experimentally observed modifications of the flutter transition. In particular, the models display the characteristic phenomena of coherence resonance....
Optimal response to non-equilibrium disturbances under truncated Burgers-Hopf dynamics
Thalabard, Simon; Turkington, Bruce
2017-04-01
We model and compute the average response of truncated Burgers-Hopf dynamics to finite perturbations away from the Gibbs equipartition energy spectrum using a dynamical optimization framework recently conceptualized in a series of papers. Non-equilibrium averages are there approximated in terms of geodesic paths in probability space that ‘best-fit’ the Liouvillean dynamics over a family of quasi-equilibrium trial densities. By recasting the geodesic principle as an optimal control problem, we solve numerically for the non-equilibrium responses using an augmented Lagrangian, non-linear conjugate gradient descent method. For moderate perturbations, we find an excellent agreement between the optimal predictions and the direct numerical simulations of the truncated Burgers-Hopf dynamics. In this near-equilibrium regime, we argue that the optimal response theory provides an approximate yet predictive counterpart to fluctuation-dissipation identities.
A note on sub-Riemannian structures associated with complex Hopf fibrations
Li, Chengbo; Zhan, Huaying
2013-03-01
Sub-Riemannian structures on odd-dimensional spheres respecting the Hopf fibration naturally appear in quantum mechanics. We study the curvature maps for such a sub-Riemannian structure and express them using the Riemannian curvature tensor of the Fubini-Study metric of the complex projective space and the curvature form of the Hopf fibration. We also estimate the number of conjugate points of a sub-Riemannian extremal in terms of the bounds of the sectional curvature and the curvature form. It presents a typical example for the study of curvature maps and comparison theorems for a general corank 1 sub-Riemannian structure with symmetries done by C. Li and I. Zelenko (2011) in [2].
Microwave ion source for accelerator driven sub-critical system
Cui Bao Qun; Jiang Wei; LiLiQiang; WangRongWen
2002-01-01
A microwave ion source is under developing for a demonstration prototype of a accelerator driven sub-critical system at CIAE (China Institute of Atomic Energy), 100 mA hydrogen beam has been extracted from the source through a 7.3 mm aperture in diameter, proton ratio is more than 85%, reliability has been tested for 100 h without any failures
Experimental Study of Subcritical Water Liquefaction of Biomass
DEFF Research Database (Denmark)
Zhu, Zhe; Toor, Saqib; Rosendahl, Lasse
2014-01-01
In this work, hydrothermal liquefaction (HTL) of wood industry residues (wood, bark, sawdust) and macroalgae for producing biofuels has been investigated under subcritical water conditions (at temperature of 300 C), with and without the presence of catalyst. The effects of catalyst and biomass type...
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 ...
Monte Carlo Alpha Iteration Algorithm for a Subcritical System Analysis
Directory of Open Access Journals (Sweden)
Hyung Jin Shim
2015-01-01
Full Text Available The α-k iteration method which searches the fundamental mode alpha-eigenvalue via iterative updates of the fission source distribution has been successfully used for the Monte Carlo (MC alpha-static calculations of supercritical systems. However, the α-k iteration method for the deep subcritical system analysis suffers from a gigantic number of neutron generations or a huge neutron weight, which leads to an abnormal termination of the MC calculations. In order to stably estimate the prompt neutron decay constant (α of prompt subcritical systems regardless of subcriticality, we propose a new MC alpha-static calculation method named as the α iteration algorithm. The new method is derived by directly applying the power method for the α-mode eigenvalue equation and its calculation stability is achieved by controlling the number of time source neutrons which are generated in proportion to α divided by neutron speed in MC neutron transport simulations. The effectiveness of the α iteration algorithm is demonstrated for two-group homogeneous problems with varying the subcriticality by comparisons with analytic solutions. The applicability of the proposed method is evaluated for an experimental benchmark of the thorium-loaded accelerator-driven system.
Local energy losses at positive and negative steps in subcritical ...
African Journals Online (AJOL)
2010-04-22
7) 554-568. MORRIS HM and WIGGERT JM (1972) Applied Hydraulics in. Engineering. John Wiley & Sons, New York. ÖRSEL SI (2002) Local Losses at a Step in a Sub-critical Open. Channel Flow. M.Sc. Thesis, Department ...
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.
Re-Entrant Hexagons and Locked Turing-Hopf Fronts in the CIMA Reaction
DEFF Research Database (Denmark)
Mosekilde, Erik; Larsen, F.; Dewel, G.
1998-01-01
Aspects of the mode-interaction and pattern-selection processes in far-from-equilibrium chemical reaction-diffusion systems are studied through numerical simulation of the Lengyel-Epstein Model. The competition between Hopf oscillations and Turing stripes is investigated by following the propagat...... the propagation of a front connecting the two modes. In certain parameter regimes, mode-locking is found to occur....
A nonlinear deformed su(2) algebra with a two-colour quasitriangular Hopf structure
Bonatsos, Dennis; Kolokotronis, P; Ludu, A; Quesne, C
1996-01-01
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 ${\\cal A}^+_q(1)$. This algebra is shown to possess two series of (N+1)-dimensional unitary irreducible representations, where N=0, 1, 2, .... 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 ${\\cal A}^+_q(1)$, 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 car...
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...
The imprint of the Hawking effect in subcritical flows
Coutant, Antonin
2016-01-01
We study the propagation of low frequency shallow water waves on a one dimensional flow of varying depth. When taking into account dispersive effects, the linear propagation of long wavelength modes on uneven bottoms excites new solutions of the dispersion relation which possess a much shorter wavelength. The peculiarity is that one of these new solutions has a negative energy. When the flow becomes supercritical, this mode has been shown to be responsible for the (classical) analog of the Hawking effect. For subcritical flows, the production of this mode has been observed numerically and experimentally, but the precise physics governing the scattering remained unclear. In this work, we provide an analytic treatment of this effect in subcritical flows. We analyze the scattering of low frequency waves using a new perturbative series, derived from a generalization of the Bremmer series. We show that the production of short wavelength modes is governed by a complex value of the position: a complex turning point....
Analysis of reactivity determination methods in the subcritical experiment Yalina
Persson, Carl-Magnus; Seltborg, Per; Åhlander, Alexandra; Gudowski, Waclaw; Stummer, Thomas; Kiyavitskaya, Hanna; Bournos, Victor; Fokov, Yurij; Serafimovich, Ivan; Chigrinov, Sergey
2005-12-01
Different reactivity determination methods have been investigated, based on experiments performed at the subcritical assembly Yalina in Minsk, Belarus. The development of techniques for on-line monitoring of the reactivity level in a future accelerator-driven system (ADS) is of major importance for safe operation. Since an ADS is operating in a subcritical mode, the safety margin to criticality must be sufficiently large. The investigated methods are the Slope Fit Method, the Sjöstrand Method and the Source Jerk Method. The results are compared with Monte Carlo simulations performed with different nuclear data libraries. The results of the Slope Fit Method are in good agreement with the Monte Carlo simulation results, whereas the Sjöstrand Method appears to underestimate the criticality somewhat. The Source Jerk Method is subject to inadequate statistical accuracy.
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.
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
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.
Secondary bifurcation for a nonlocal Allen-Cahn equation
Kuto, Kousuke; Mori, Tatsuki; Tsujikawa, Tohru; Yotsutani, Shoji
2017-09-01
This paper studies the Neumann problem of a nonlocal Allen-Cahn equation in an interval. A main result finds a symmetry breaking (secondary) bifurcation point on the bifurcation curve of solutions with odd-symmetry. Our proof is based on a level set analysis for the associated integral map. A method using the complete elliptic integrals proves the uniqueness of secondary bifurcation point. We also show some numerical simulations concerning the global bifurcation structure.
Design, Development and Installation of Jordan Subcritical Assembly
Directory of Open Access Journals (Sweden)
Ned Xoubi
2013-01-01
Full Text Available Following its announcement in 2007 to pursue a nuclear power program and in the absence of any nuclear facility essential for the education, training, and research, Jordan decided to build a subcritical reactor as its first nuclear facility. Jordan Subcritical Assembly (JSA is uranium fueled light water moderated and reflected subcritical reactor driven by a plutonium-beryllium source, and the core consists of 313 LEU fuel rods, loaded into a water-filled vessel in a square lattice of 19.11 mm pitch. The fuel rods are based on PWR fuel structural pattern type, made of uranium oxide (UO2 with 3.4 wt% 235U enrichment in zirconium alloy (Zr-4 cladding. Design, optimization, and verification were performed using MCNP5 nuclear code; the computed effective multiplication factor is 0.95923. The JSA is designed to fulfill the training needs of students and is equipped to perform all of the fundamental experiments required for a typical nuclear engineering university program. This paper presents the design, development, modeling, core analysis, and utilization of Jordan’s first nuclear facility and why this simplified low cost reactor presents an attractive choice to fulfill the preliminary experimental needs of nuclear engineering education in developing countries.
Helical waves and non-linear dynamics of fluid/structure interactions in a tube row
Energy Technology Data Exchange (ETDEWEB)
Moon, F.C.; Thothadri, M. [Cornell Univ., Ithaca, NY (United States)
1997-12-31
The goal of this study has been to investigate low-dimensional models for fluid-structure dynamics of flow across a row of cylindrical tubes. Four principle results of this experimental-theoretical study are discussed. (i) Experimental evidence has shown that the dynamic instability of the tube row is a subcritical Hopf bifurcation. (ii) The critical flow velocity decreases as the number of flexible cylinders increases. (iii) The linear model exhibits coupled helical wave solutions in the tube dynamics. (iv) A nonlinear model of the tube motions shows a complex subcritical Hopf bifurcation with a secondary bifurcation to a torus or quasi-periodic oscillation. In this analysis the tools of center manifolds, normal forms and numerical simulation are used.
Symmetric/asymmetric bifurcation behaviours of a bogie system
DEFF Research Database (Denmark)
Xue-jun, Gao; Ying-hui, Li; Yuan, Yue
2013-01-01
Based on the bifurcation and stability theory of dynamical systems, the symmetric/asymmetric bifurcation behaviours and chaotic motions of a railway bogie system under a complex nonlinear wheel–rail contact relation are investigated in detail by the ‘resultant bifurcation diagram’ method with slo...
Codimension 2 Bifurcations of Iterated Maps
Meijer, H.G.E.
2006-01-01
This thesis investigates some properties of discrete-time dynamical systems, generated by iterated maps. In particular we study local bifurcations where two parameters are essential to describe the dynamical properties of the system near a fixed point or a cycle. There are 11 such cases. Knowledge
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.
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
Solvability of an Integral Equation of Volterra-Wiener-Hopf Type
Directory of Open Access Journals (Sweden)
Nurgali K. Ashirbayev
2014-01-01
Full Text Available The paper presents results concerning the solvability of a nonlinear integral equation of Volterra-Stieltjes type. We show that under some assumptions that equation has a continuous and bounded solution defined on the interval 0,∞ and having a finite limit at infinity. As a special case of the mentioned integral equation we obtain an integral equation of Volterra-Wiener-Hopf type. That fact enables us to formulate convenient and handy conditions ensuring the solvability of the equation in question in the class of functions defined and continuous on the interval 0,∞ and having finite limits at infinity.
Exponentially Small Heteroclinic Breakdown in the Generic Hopf-Zero Singularity
Baldomá Barraca, Inmaculada; Castejón i Company, Oriol; Martínez-Seara Alonso, M. Teresa
2013-01-01
In this paper we prove the breakdown of a heteroclinic connection in the analytic versal unfoldings of the generic Hopf-zero singularity in an open set of the parameter space. This heteroclinic orbit appears at any order if one performs the normal form around the origin, therefore it is a phenomenon “beyond all orders”. In this paper we provide a formula for the distance between the corresponding stable and unstable one-dimensional manifolds which is given by an exponentially s...
Red'kov, V. M.
2011-01-01
In the work some relations between three techniques, Hopf's bundle, Kustaanheimo-Stiefel's bundle, 3-space with spinor structure have been examined. The spinor space is viewed as a real space that is minimally (twice as much) extended in comparison with an ordinary vector 3-space: at this instead of 2\\pi-rotation now only 4\\pi-rotation is taken to be the identity transformation in the geometrical space. With respect to a given P-orientation of an initial unextended manyfold, vector or pseudov...
Cole-Hopf-like transformation for Schroedinger equations containing complex nonlinearities
Energy Technology Data Exchange (ETDEWEB)
Kaniadakis, G.; Scarfone, A.M. [Dipartimento di Fisica, Politecnico di Torino, Torino (Italy) and Istituto Nazionale di Fisica della Materia, Unita del Politecnico di Torino, Torino (Italy)]. E-mails: kaniadakis@polito.it; scarfone@polito.it
2002-03-01
We consider systems which conserve the particle number and are described by Schroedinger equations containing complex nonlinearities. In the case of canonical systems, we study their main symmetries and conservation laws. We introduce a Cole-Hopf-like transformation both for canonical and noncanonical systems, which changes the evolution equation into another one containing purely real nonlinearities, and reduces the continuity equation to the standard form of the linear theory. This approach allows us to treat, in a unifying scheme, a wide variety of canonical and noncanonical nonlinear systems, some of them already known in the literature. (author)
Climate bifurcation during the last deglaciation
Lenton, T. M.; Livina, V. N.; Dakos, V.; Scheffer, M.
2012-01-01
The last deglaciation was characterised by two abrupt warming events, at the start of the Bølling-Allerød and at the end of the Younger Dryas, but their underlying causes 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. However, the abrupt Dansgaard-Oeschger (DO) events during the last ice age were probably triggered by stochastic fluctuations without bifurcation or early warning, and whether the onset of the Bølling-Allerød (DO event 1) was preceded by slowing down or not is debated. Here we show that the interval from the Last Glacial Maximum to the end of the Younger Dryas, as recorded in three Greenland ice cores with two different climate proxies, was accompanied by a robust slowing down in climate dynamics and an increase in climate variability, consistent with approaching bifurcation. 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 Bølling warming marked a distinct destabilisation of the climate system, which excited an internal mode of variability in Atlantic meridional overturning circulation strength, causing multi-centennial climate fluctuations. There is some evidence for slowing down in the transition to and during the Younger Dryas. We infer that a bifurcation point was finally 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. The lack of a large triggering perturbation at the end of the Younger Dryas, and the fact that subsequent meltwater perturbations did not cause sustained cooling, support the
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.
Topological Hopf and Chain Link Semimetal States and Their Application to Co2 Mn Ga
Chang, Guoqing; Xu, Su-Yang; Zhou, Xiaoting; Huang, Shin-Ming; Singh, Bahadur; Wang, Baokai; Belopolski, Ilya; Yin, Jiaxin; Zhang, Songtian; Bansil, Arun; Lin, Hsin; Hasan, M. Zahid
2017-10-01
Topological semimetals can be classified by the connectivity and dimensionality of the band crossings in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimetal are zero-dimensional (0D) points, whereas the band crossings of a nodal-line semimetal are one-dimensional (1D) closed loops. Here we propose that the presence of perpendicular crystalline mirror planes can protect three-dimensional (3D) band crossings characterized by nontrivial links such as a Hopf link or a coupled chain, giving rise to a variety of new types of topological semimetals. We show that the nontrivial winding number protects topological surface states distinct from those in previously known topological semimetals with a vanishing spin-orbit interaction. We also show that these nontrivial links can be engineered by tuning the mirror eigenvalues associated with the perpendicular mirror planes. Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co2 MnGa as a candidate. Both Hopf link and chainlike bulk band crossings and unconventional topological surface states are identified.
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.
Bifurcations at the dawn of Modern Science
Coullet, Pierre
2012-11-01
In this article we review two classical bifurcation problems: the instability of an axisymmetric floating body studied by Archimedes, 2300 years ago and the multiplicity of images observed in curved mirrors, a problem which has been solved by Alhazen in the 11th century. We will first introduce these problems in trying to keep some of the flavor of the original analysis and then, we will show how they can be reduced to a question of extremal distances studied by Apollonius.
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....
Energy Technology Data Exchange (ETDEWEB)
Takahashi, Hiroshi
1994-04-01
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.
Stenting of bifurcation lesions: a rational approach.
Lefèvre, T; Louvard, Y; Morice, M C; Loubeyre, C; Piéchaud, J F; Dumas, P
2001-12-01
The occurrence of stenosis in or next to coronary bifurcations is relatively frequent and generally underestimated. In our experience, such lesions account for 15%-18% of all percutaneous coronary intervention > (PCI). The main reasons for this are (1) the coronary arteries are like the branches of a tree with many ramifications and (2) because of axial plaque redistribution, especially after stent implantation, PCI of lesions located next to a coronary bifurcation almost inevitably cause plaque shifting in the side branches. PCI treatment of coronary bifurcation lesions remains challenging. Balloon dilatation treatment used to be associated with less than satisfactory immediate results, a high complication rate, and an unacceptable restenosis rate. The kissing balloon technique resulted in improved, though suboptimal, outcomes. Several approaches were then suggested, like rotative or directional atherectomy, but these techniques did not translate into significantly enhanced results. With the advent of second generation stents, in 1996, the authors decided to set up an observational study on coronary bifurcation stenting combined with a bench test of the various stents available. Over the last 5 years, techniques, strategies, and stent design have improved. As a result, the authors have been able to define a rational approach to coronary bifurcation stenting. This bench study analyzed the behavior of stents and allowed stents to be discarded that are not compatible with the treatment of coronary bifurcations. Most importantly, this study revealed that stent deformation due to the opening of a strut is a constant phenomenon that must be corrected by kissing balloon inflation. Moreover, it was observed that the opening of a stent strut into a side branch could permit the stenting, at least partly, of the side branch ostium. This resulted in the provocative concept of "stenting both branches with a single stent." Therefore, a simple approach is currently implemented
Subcritical and supercritical water oxidation of CELSS model wastes
Takahashi, Y.; Wydeven, T.; Koo, C.
1989-01-01
A mixture of ammonium hydroxide with acetic acid and a slurry of human feces, urine, and wipes were used as CELSS model wastes to be wet-oxidized at temperatures from 250 to 500 C, i.e. below and above the critical point of water (374 C and 218 kg/sq cm or 21.4 MPa). The effects of oxidation temperature ( 250-500 C) and residence time (0-120 mn) on carbon and nitrogen and on metal corrosion from the reactor material were studied. Almost all of the organic matter in the model wastes was oxidized in the temperature range from 400 to 500 C, above the critical conditions for water. In contrast, only a small portion of the organic matter was oxidized at subcritical conditions. A substantial amount of nitrogen remained in solution in the form of ammonia at temperatures ranging from 350 to 450 C suggesting that, around 400 C, organic carbon is completely oxidized and most of the nitrogen is retained in solution. The Hastelloy C-276 alloy reactor corroded during subcritical and supercritical water oxidation.
Hydrolysis of sweet blue lupin hull using subcritical water technology.
Ciftci, Deniz; Saldaña, Marleny D A
2015-10-01
Hydrolysis of sweet blue lupin hulls was conducted in this study using subcritical water technology. Effects of process parameters, such as pressure (50-200 bar), temperature (160-220°C), flow rate (2-10 mL/min), and pH (2-12), were studied to optimize maximum hemicellulose sugars recovery in the extracts. Extracts were analyzed for total hemicellulose sugars, phenolics and organic carbon contents and solid residues left after treatments were also characterized. Temperature, flow rate, and pH had a significant effect on hemicellulose sugar removal; however, the effect of pressure was not significant. The highest yield of hemicellulose sugars in the extracts (85.5%) was found at 180°C, 50 bar, 5 mL/min and pH 6.2. The thermal stability of the solid residue obtained at optimum conditions improved after treatment and the crystallinity index increased from 11.5% to 58.6%. The results suggest that subcritical water treatment is a promising technology for hemicellulose sugars removal from biomass. Copyright © 2015 Elsevier Ltd. All rights reserved.
Subcritical water extractor for Mars analog soil analysis.
Amashukeli, Xenia; Grunthaner, Frank J; Patrick, Steven B; Yung, Pun To
2008-06-01
Abstract Technologies that enable rapid and efficient extraction of biomarker compounds from various solid matrices are a critical requirement for the successful implementation of in situ chemical analysis of the martian regolith. Here, we describe a portable subcritical water extractor that mimics multiple organic solvent polarities by tuning the dielectric constant of liquid water through adjustment of temperature and pressure. Soil samples, collected from the Yungay region of the Atacama Desert (martian regolith analogue) in the summer of 2005, were used to test the instrument's performance. The total organic carbon was extracted from the samples at concentrations of 0.2-55.4 parts per million. The extraction data were compared to the total organic carbon content in the bulk soil, which was determined via a standard analytical procedure. The instrument's performance was examined over the temperature range of 25-250 degrees C at a fixed pressure of 20.7 MPa. Under these conditions, water remains in a subcritical fluid state with a dielectric constant varying between approximately 80 (at 25 degrees C) and approximately 30 (at 250 degrees C).
Understanding a Period-Doubling Bifurcation in Cardiac Cells
Berger, Carolyn; Zhao, Xiaopeng; Schaeffer, David; Idriss, Salim; Gauthier, Daniel
2008-03-01
Bifurcations in the electrical response of cardiac tissue can destabilize spatio-temporal waves of electrochemical activity in the heart, leading to tachycardia or even fibrillation. Therefore, it is important to classify these bifurcations so that we can understand the mechanisms that cause instabilities in cardiac tissue. We have determined that the period-doubling bifurcation in paced myocardium is of the unfolded border-collision type. To understand how this new type of bifurcation manifest itself in cardiac tissue, we have also studied the role of calcium in inducing the bifurcation. We will discuss the nature of the unfolded border-collision bifurcation and present our results of dual voltage and calcium measurements in a frog ventricle preparation.
Stability and Symmetry-Breaking Bifurcation for the Ground States of a NLS with a δ' Interaction
Adami, Riccardo; Noja, Diego
2013-02-01
We determine and study the ground states of a focusing Schrödinger equation in dimension one with a power nonlinearity | ψ|2 μ ψ and a strong inhomogeneity represented by a singular point perturbation, the so-called (attractive) δ' interaction, located at the origin. The time-dependent problem turns out to be globally well posed in the subcritical regime, and locally well posed in the supercritical and critical regime in the appropriate energy space. The set of the (nonlinear) ground states is completely determined. For any value of the nonlinearity power, it exhibits a symmetry breaking bifurcation structure as a function of the frequency (i.e., the nonlinear eigenvalue) ω. More precisely, there exists a critical value ω* of the nonlinear eigenvalue ω, such that: if ω0 ground state and it is an odd function; if ω > ω* then there exist two non-symmetric ground states. We prove that before bifurcation (i.e., for ω ground state is orbitally stable. After bifurcation (ω = ω* + 0), ground states are stable if μ does not exceed a value {μ^star} that lies between 2 and 2.5, and become unstable for μ > μ*. Finally, for μ > 2 and {ω ≫ ω^*}, all ground states are unstable. The branch of odd ground states for ω ω*, obtaining a family of orbitally unstable stationary states. Existence of ground states is proved by variational techniques, and the stability properties of stationary states are investigated by means of the Grillakis-Shatah-Strauss framework, where some non-standard techniques have to be used to establish the needed properties of linearization operators.
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
Roy, D.; Balanarayan, P.; Gadre, Shridhar R.
2008-11-01
The Poincaré-Hopf relation is studied for molecular electrostatic potentials (MESPs) of a few test systems such as cyclopropane, cyclobutane, pyridine, and benzene. Appropriate spheres centered at various points, including the center of mass of the system under study, are constructed and the MESP gradient is evaluated on the corresponding spherical grid. The change in directional nature of MESP gradient on the surface of these spheres gives indication of the critical points of the function. This is used for developing a method for locating the critical points of MESP. The strategy also enables a general definition of the Euler characteristic (EC) of the molecule, independent of any region or space. Further, the effect of basis set and level of theory on the EC is discussed.
Venturi, Daniele
2016-11-01
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics, quantum field theory and statistical physics. For example, in the context of fluid dynamics, the Hopf characteristic functional equation was deemed by Monin and Yaglom to be "the most compact formulation of the turbulence problem", which is the problem of determining the statistical properties of the velocity and pressure fields of Navier-Stokes equations given statistical information on the initial state. However, no effective numerical method has yet been developed to compute the solution to functional differential equations. In this talk I will provide a new perspective on this general problem, and discuss recent progresses in approximation theory for nonlinear functionals and functional equations. The proposed methods will be demonstrated through various examples.
Wiener-Hopf optimal control of a hydraulic canal prototype with fractional order dynamics.
Feliu-Batlle, Vicente; Feliu-Talegón, Daniel; San-Millan, Andres; Rivas-Pérez, Raúl
2017-06-26
This article addresses the control of a laboratory hydraulic canal prototype that has fractional order dynamics and a time delay. Controlling this prototype is relevant since its dynamics closely resembles the dynamics of real main irrigation canals. Moreover, the dynamics of hydraulic canals vary largely when the operation regime changes since they are strongly nonlinear systems. All this makes difficult to design adequate controllers. The controller proposed in this article looks for a good time response to step commands. The design criterium for this controller is minimizing the integral performance index ISE. Then a new methodology to control fractional order processes with a time delay, based on the Wiener-Hopf control and the Padé approximation of the time delay, is developed. Moreover, in order to improve the robustness of the control system, a gain scheduling fractional order controller is proposed. Experiments show the adequate performance of the proposed controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Bifurcation and stability for a nonlinear parabolic partial differential equation
Chafee, N.
1973-01-01
Theorems are developed to support bifurcation and stability of nonlinear parabolic partial differential equations in the solution of the asymptotic behavior of functions with certain specified properties.
Sequences of gluing bifurcations in an analog electronic circuit
Energy Technology Data Exchange (ETDEWEB)
Akhtanov, Sayat N.; Zhanabaev, Zeinulla Zh. [Physico-Technical Department, Al Farabi Kazakh National University, Al Farabi Av. 71, Almaty, 050038 Kazakhstan (Kazakhstan); Zaks, Michael A., E-mail: zaks@math.hu-berlin.de [Institute of Mathematics, Humboldt University, Rudower Chaussee 25, D-12489 Berlin (Germany)
2013-10-01
We report on the experimental investigation of gluing bifurcations in the analog electronic circuit which models a dynamical system of the third order: Lorenz equations with an additional quadratic nonlinearity. Variation of one of the resistances in the circuit changes the coefficient at this nonlinearity and replaces the Lorenz route to chaos by a different scenario which leads, through the sequence of homoclinic bifurcations, from periodic oscillations of the voltage to the irregular ones. Every single bifurcation “glues” in the phase space two stable periodic orbits and creates a new one, with the doubled length: a sequence of such bifurcations results in the birth of the chaotic attractor.
Bifurcations in two coupled Rössler systems
DEFF Research Database (Denmark)
Rasmussen, J; Mosekilde, Erik; Reick, C.
1996-01-01
The paper presents a detailed bifurcation analysis of two symmetrically coupled Rössler systems. The symmetry in the coupling does not allow any one direction to become preferred, and the coupled system is therefore an example of a dissipative system that cannot be considered as effectively one......-dimensional. The results are presented in terms of one- and two-parmeter bifurcation diagrams. A particularly interesting finding is the replacement of some of the period-doubling bifurcations by torus bifurcations. By virtue of this replacement, instead of a Feigenbaum transition to chaos a transition via torus...
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.
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
Periodic orbits near a bifurcating slow manifold
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall
2015-01-01
(\\epsilon^{1/3})$-distance from the union of the normally elliptic slow manifolds that occur as a result of the bifurcation. Here $\\epsilon\\ll 1$ measures the time scale separation. These periodic orbits are predominantly unstable. The proof is based on averaging of two blowup systems, allowing one to estimate...... the effect of the singularity, combined with results on asymptotics of the second Painleve equation. The stable orbits of smallest amplitude that are {persistently} obtained by these methods remain slightly further away from the slow manifold being distant by an order $\\mathcal O(\\epsilon^{1/3}\\ln^{1/2}\\ln...
Thorium as a Fuel for Accelerator Driven Subcritical Electronuclear Systems
Barashenkov, V S; Singh, V
2000-01-01
Neutron yield and energy production in a very large, practically infinite, uranium and thorium target-blocks irradiated by protons with energies in the range 0.1-2 GeV are studied by Monte Carlo method. Though the comparison of uranium and thorium targets shows that the neutron yield in the latter is 30-40 % less and the energy gain is approximatelly two times smaller, accelerator Driven subcritical Systems (ADS) with thorium fuel are very perspective at the bombarding energies higher than several hundreds MeV. An admixture of fissile elements U^{233}, U^{235}, Pu^{239} in the set-up gives larger neutron multiplication which in turn shows better energy amplification. It is argued that due to the practically complete burning of the fuel in such set-up there is no need of technology of conversion of the exhaust fuel.
Gravity-driven soap film dynamics in subcritical regimes
Auliel, M. I.; Castro, F.; Sosa, R.; Artana, G.
2015-10-01
We undertake the analysis of soap-film dynamics with the classical approach of asymptotic expansions. We focus our analysis in vertical soap film tunnels operating in subcritical regimes with elastic Mach numbers Me=O(10-1) . Considering the associated set of nondimensional numbers that characterize this flow, we show that the flow behaves as a two-dimensional (2D) divergence free flow with variable mass density. When the soap film dynamics agrees with that of a 2D and almost constant mass density flow, the regions where the second invariant of the velocity gradient is non-null correspond to regions where the rate of change of film thickness is non-negligible.
Subcritical-Water Extraction of Organics from Solid Matrices
Amashukeli, Xenia; Grunthaner, Frank; Patrick, Steven; Kirby, James; Bickler, Donald; Willis, Peter; Pelletier, Christine; Bryson, Charles
2009-01-01
An apparatus for extracting organic compounds from soils, sands, and other solid matrix materials utilizes water at subcritical temperature and pressure as a solvent. The apparatus, called subcritical water extractor (SCWE), is a prototype of subsystems of future instrumentation systems to be used in searching for organic compounds as signs of past or present life on Mars. An aqueous solution generated by an apparatus like this one can be analyzed by any of a variety of established chromatographic or spectroscopic means to detect the dissolved organic compound( s). The apparatus can be used on Earth: indeed, in proof-of-concept experiments, SCWE was used to extract amino acids from soils of the Atacama Desert (Chile), which was chosen because the dryness and other relevant soil conditions there approximate those on Mars. The design of the apparatus is based partly on the fact that the relative permittivity (also known as the dielectric constant) of liquid water varies with temperature and pressure. At a temperature of 30 C and a pressure of 0.1 MPa, the relative permittivity of water is 79.6, due to the strong dipole-dipole electrostatic interactions between individual molecular dipoles. As the temperature increases, increasing thermal energy causes increasing disorientation of molecular dipoles, with a consequent decrease in relative permittivity. For example, water at a temperature of 325 C and pressure of 20 MPa has a relative permittivity of 17.5, which is similar to the relative permittivities of such nonpolar organic solvents as 1-butanol (17.8). In the operation of this apparatus, the temperature and pressure of water are adjusted so that the water can be used in place of commonly used organic solvents to extract compounds that have dissimilar physical and chemical properties.
Droplet Breakup Dynamics in Bi-Layer Bifurcating Microchannel
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Yong Ren
2018-01-01
Full Text Available Breakup of droplets at bi-layer bifurcating junction in polydimethylsiloxane (PDMS microchannel has been investigated by experiments and numerical simulation. The pressure drop in bi-layer bifurcating channel was investigated and compared with single-layer bifurcating channel. Daughter droplet size variation generated in bi-layer bifurcating microchannel was analyzed. The correlation was proposed to predict the transition between breakup and non-breakup conditions of droplets in bi-layer bifurcating channel using a phase diagram. In the non-breakup regime, droplets exiting port can be switched via tuning flow resistance by controlling radius of curvature, and or channel height ratio. Compared with single-layer bifurcating junction, 3-D cutting in diagonal direction from bi-layer bifurcating junction induces asymmetric fission to form daughter droplets with distinct sizes while each size has good monodispersity. Lower pressure drop is required in the new microsystem. The understanding of the droplet fission in the novel microstructure will enable more versatile control over the emulsion formation, fission and sorting. The model system can be developed to investigate the encapsulation and release kinetics of emulsion templated particles such as drug encapsulated microcapsules as they flow through complex porous media structures, such as blood capillaries or the porous tissue structures, which feature with bifurcating junctions.
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...
Emergence and bifurcations of Lyapunov manifolds in nonlinear wave equations
Bakri, Taoufik; Meijer, Hil Gaétan Ellart; Verhulst, Ferdinand
2009-01-01
Persistence and bifurcations of Lyapunov manifolds can be studied by a combination of averaging-normalization and numerical bifurcation methods. This can be extended to infinite-dimensional cases when using suitable averaging theorems. The theory is applied to the case of a parametrically excited
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
Quantum Localization near Bifurcations in Classically Chaotic Systems
Varga, I; Eckhardt, B
1999-01-01
We show that strongly localized wave functions occur around classical bifurcations. Near a saddle node bifurcation the scaling of the inverse participation ratio on Planck's constant and the dependence on the parameter is governed by an Airy function. Analytical estimates are supported by numerical calculations for the quantum kicked rotor.
Analysis of Vehicle Steering and Driving Bifurcation Characteristics
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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.
Seasonal Variation of the North/South Equatorial Current Bifurcation
Chen, Z.
2016-02-01
The seasonal variation of the North/South Equatorial Current (NEC/SEC) bifurcation off the Philippine/Madagascar/Australian coast is investigated. It is shown that the seasonal cycles of the NEC/SEC bifurcation are generally analogous to each other, all of which shift synchronously back and forth seasonally and arrive at their southernmost positions in boreal late spring and early summer. It is demonstrated that the linear, reduced gravity, long Rossby model, which works well for the NEC bifurcation, is insufficient to reproduce the seasonal cycles of the SEC bifurcation off the Madagascar/Australian coast particularly in their south-north migrations. This can be attributed to the existence of the isolated island in the Madagascar case and the seasonally-varying wind forcing around the Australian coast, while they are almost absent in the NEC bifurcation case. Without considering the existence of an island and the alongshore winds, we propose a simple bifurcation model under the framework of linear Rossby wave dynamics. It is found that the seasonal bifurcation latitude is predominantly determined by the spatial pattern of the wind and baroclinic Rossby wave propagation. This model explains the roles of local/remote wind forcing and baroclinic adjustment in the south-north migration and peak seasons of the bifurcation latitude.
Critical bifurcation surfaces of 3D discrete dynamics
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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.
On a Five-Dimensional Chaotic System Arising from Double-Diffusive Convection in a Fluid Layer
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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.
Climate bifurcation during the last deglaciation?
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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
Climate bifurcation during the last deglaciation?
Lenton, T. M.; Livina, V. N.; Dakos, V.; Scheffer, M.
2012-07-01
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 spliced record of the
Coupled Subcritical Water and Solid Phase Extraction for In-Situ Chemical Analysis Project
National Aeronautics and Space Administration — Leiden Measurement Technology (LMT) will design and develop a low volume analyte separation, concentration, and transfer system (ConTech), that couples a Subcritical...
Peng Hu; Gao-Wei Zhang; Long-Xiang Chen; Ming-Hou Liu
2017-01-01
Electrothermal energy storage (ETES) provides bulk electricity storage based on heat pump and heat engine technologies. A subcritical ETES is described in this paper. Based on the extremum principle of entransy dissipation, a geometry model is developed for heat transfer optimization for subcritical ETES. The exergy during the heat transfer process is deduced in terms of entropy production. The geometry model is validated by the extremum principle of entropy production. The theoretical analys...
Bifurcated intraarticular long head of biceps tendon
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Vivek Pandey
2014-01-01
Full Text Available Though rare, many anomalous origins of long head of the biceps tendon (LHBT have been reported in the literature. Anatomic variations commonly explained are a third humeral head, anomalous insertion, congenital absence and adherence to the rotator cuff. We report a rare case who underwent shoulder arthroscopy with impingement symptoms where in LHBT was found to be bifurcated with a part attached to superior labrum and the other part to the posterior capsule of joint. Furthermore, intraarticular portion of LHBT was adherent to the undersurface of the supraspinatus tendon. Awareness of such an anatomical aberration during the shoulder arthroscopy is of great importance as it can potentially avoid unnecessary confusion and surgery.
Bifurcated SEN with Fluid Flow Conditioners
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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
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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.
Clausius entropy for arbitrary bifurcate null surfaces
Baccetti, Valentina; Visser, Matt
2014-02-01
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 {\\rm{d}}S = \\unicode{x111} Q/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.
Subcritical Noise Analysis Measurements with Fresh and Spent Research Reactor Fuels Elements
Energy Technology Data Exchange (ETDEWEB)
Valentine, T.E.; Mihalczo, J.T.; Kryter, R.C.; Miller, V.C.
1999-02-01
The verification of the subcriticality is of utmost importance for the safe transportation and storage of nuclear reactor fuels. Transportation containers and storage facilities are designed such that nuclear fuels remain in a subcritical state. Such designs often involve excess conservatism because of the lack of relevant experimental data to verify the accuracy of Monte Carlo codes used in nuclear criticality safety analyses. A joint experimental research program between Oak Ridge National Laboratory, Westinghouse Safety Management Solutions, Inc., and the University of Missouri was initiated to obtain measured quantities that could be directly related to the subcriticality of simple arrays of Missouri University Research Reactor (MURR) fuel elements. A series of measurement were performed to assess the reactivity of materials such as BORAL, stainless steel, aluminum, and lead that are typically used in the construction of shipping casks. These materials were positioned between the fuel elements. In addition, a limited number of measurements were performed with configurations of fresh and spent (irradiated) fuel elements to ascertain the reactivity of the spent fuel elements. In these experiments, fresh fuel elements were replaced by spent fuel elements such that the subcritical reactivity change could be measured. The results of these measurements were used by Westinghouse Safety Management Solutions to determine the subcriticality of MURR fuel elements isolated by absorbing materials. The measurements were interpreted using the MCNP-DSP Monte Carlo code to obtain the subcritical neutron multiplication factor k(sub eff), and the bias in K(sub eff) that are used in criticality safety analyses.
Numerical simulations of subcritical reactor kinetics in thermal hydraulic transient phases
Energy Technology Data Exchange (ETDEWEB)
Yoo, J.; Park, W. S. [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1998-12-31
A subcritical reactor driven by a linear proton accelerator has been considered as a nuclear waste incinerator at Korea Atomic Energy Research Institute (KAERI). Since the multiplication factor of a subcritical reactor is less than unity, to compensate exponentially decreasing fission neutrons, external neutrons form spallation reactions are essentially required for operating the reactor in its steady state. Furthermore, the profile of accelerator beam currents is very important in controlling a subcritical reactor, because the reactor power varies in accordance to the profile of external neutrons. We have developed a code system to find numerical solutions of reactor kinetics equations, which are the simplest dynamic model for controlling reactors. In a due course of our previous numerical study of point kinetics equations for critical reactors, however, we learned that the same code system can be used in studying dynamic behavior of the subcritical reactor. Our major motivation of this paper is to investigate responses of subcritical reactors for small changes in thermal hydraulic parameters. Building a thermal hydraulic model for the subcritical reactor dynamics, we performed numerical simulations for dynamic responses of the reactor based on point kinetics equations with a source term. Linearizing a set of coupled differential equations for reactor responses, we focus our research interest on dynamic responses of the reactor to variations of the thermal hydraulic parameters in transient phases. 5 refs., 8 figs. (Author)
Subcritical Water Hydrolysis of Peptides: Amino Acid Side-Chain Modifications
Powell, Thomas; Bowra, Steve; Cooper, Helen J.
2017-09-01
Previously we have shown that subcritical water may be used as an alternative to enzymatic digestion in the proteolysis of proteins for bottom-up proteomics. Subcritical water hydrolysis of proteins was shown to result in protein sequence coverages greater than or equal to that obtained following digestion with trypsin; however, the percentage of peptide spectral matches for the samples treated with trypsin were consistently greater than for those treated with subcritical water. This observation suggests that in addition to cleavage of the peptide bond, subcritical water treatment results in other hydrolysis products, possibly due to modifications of amino acid side chains. Here, a model peptide comprising all common amino acid residues (VQSIKCADFLHYMENPTWGR) and two further model peptides (VCFQYMDRGDR and VQSIKADFLHYENPTWGR) were treated with subcritical water with the aim of probing any induced amino acid side-chain modifications. The hydrolysis products were analyzed by direct infusion electrospray tandem mass spectrometry, either collision-induced dissociation or electron transfer dissociation, and liquid chromatography collision-induced dissociation tandem mass spectrometry. The results show preferential oxidation of cysteine to sulfinic and sulfonic acid, and oxidation of methionine. In the absence of cysteine and methionine, oxidation of tryptophan was observed. In addition, water loss from aspartic acid and C-terminal amidation were observed in harsher subcritical water conditions. [Figure not available: see fulltext.
Experimental subcritical facility driven by D-D/D-T neutron generator at BARC, India
Sinha, Amar; Roy, Tushar; Kashyap, Yogesh; Ray, Nirmal; Shukla, Mayank; Patel, Tarun; Bajpai, Shefali; Sarkar, P. S.; Bishnoi, Saroj
2015-05-01
The paper presents design of an experimental subcritical assembly driven by D-D/D-T neutron and preliminary experimental measurements. The system has been developed for investigating the static and dynamic neutronic properties of accelerator driven sub-critical systems. This system is modular in design and it is first in the series of subcritical assemblies being designed. The subcritical core consists of natural uranium fuel with high density polyethylene as moderator and beryllium oxide as reflector. The fuel is embedded in high density polyethylene moderator matrix. Estimated keff of the system is ∼0.89. One of the unique features of subcritical core is the use of Beryllium oxide (BeO) as reflector and HDPE as moderator making the assembly a compact modular system. The subcritical core is coupled to Purnima Neutron Generator which works in D-D and D-T mode with both DC and pulsed operation. It has facility for online source strength monitoring using neutron tagging and programmable source modulation. Preliminary experiments have been carried out for spatial flux measurement and reactivity estimation using pulsed neutron source (PNS) techniques with D-D neutrons. Further experiments are being planned to measure the reactivity and other kinetic parameters using noise methods. This facility would also be used for carrying out studies on effect of source importance and measurement of source multiplication factor ks and external neutron source efficiency φ∗ in great details. Experiments with D-T neutrons are also underway.
The Lefschetz-Hopf theorem and axioms for the Lefschetz number
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Brown Robert F
2004-01-01
Full Text Available The reduced Lefschetz number, that is, where denotes the Lefschetz number, is proved to be the unique integer-valued function on self-maps of compact polyhedra which is constant on homotopy classes such that (1 for and ; (2 if is a map of a cofiber sequence into itself, then ; (3 , where is a self-map of a wedge of circles, is the inclusion of a circle into the th summand, and is the projection onto the th summand. If is a self-map of a polyhedron and is the fixed point index of on all of , then we show that satisfies the above axioms. This gives a new proof of the normalization theorem: if is a self-map of a polyhedron, then equals the Lefschetz number of . This result is equivalent to the Lefschetz-Hopf theorem: if is a self-map of a finite simplicial complex with a finite number of fixed points, each lying in a maximal simplex, then the Lefschetz number of is the sum of the indices of all the fixed points of .
Turing-Hopf instability in biochemical reaction networks arising from pairs of subnetworks.
Mincheva, Maya; Roussel, Marc R
2012-11-01
Network conditions for Turing instability in biochemical systems with two biochemical species are well known and involve autocatalysis or self-activation. On the other hand general network conditions for potential Turing instabilities in large biochemical reaction networks are not well developed. A biochemical reaction network with any number of species where only one species moves is represented by a simple digraph and is modeled by a reaction-diffusion system with non-mass action kinetics. A graph-theoretic condition for potential Turing-Hopf instability that arises when a spatially homogeneous equilibrium loses its stability via a single pair of complex eigenvalues is obtained. This novel graph-theoretic condition is closely related to the negative cycle condition for oscillations in ordinary differential equation models and its generalizations, and requires the existence of a pair of subnetworks, each containing an even number of positive cycles. The technique is illustrated with a double-cycle Goodwin type model. Copyright © 2012 Elsevier Inc. All rights reserved.
FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions
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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.
Optimization Design and Application of Underground Reinforced Concrete Bifurcation Pipe
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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.
Pulsatile flow in coronary bifurcations for different stenting techniques
García García, Javier; Manuel Martín, Fernando Jaime; Doce Carrasco, Y.; Castro Ruiz, F.; Crespo Martínez, Antonio; Goicolea Marin, P.; Fernandez Diaz, J.A.
2012-01-01
The objective of this work is to analyze the local hem odynamic changes caused in a coronary bifurcation by three different stenting techniques: simple stenting of the main vessel, simple stenting of the main vessel with kissing balloon in the side branch and culotte. To carry out this study an idealized geometry of a coronary bifurcation is used, and two bifurcation angles, 45º and 90º, are chosen as representative of the wide variety of re al configurations. In order to quantify th...
The Persistence of a Slow Manifold with Bifurcation
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Palmer, P.; Robert, M.
2012-01-01
his paper considers the persistence of a slow manifold with bifurcation in a slow-fast two degree of freedom Hamiltonian system. In particular, we consider a system with a supercritical pitchfork bifurcation in the fast space which is unfolded by the slow coordinate. The model system is motivated...... by tethered satellites. It is shown that an almost full measure subset of a neighborhood of the slow manifold's normally elliptic branches persists in an adiabatic sense. We prove this using averaging and a blow-up near the bifurcation....
Bifurcation control in the Burgers-KdV equation
Energy Technology Data Exchange (ETDEWEB)
Maccari, Attilio [Technical Institute ' G. Cardano' , Piazza della Resistenza 1, 00015 Monterotondo (Rome) (Italy)], E-mail: solitone@yahoo.it
2008-03-15
We consider the bifurcation control for the forced Burgers-KdV equation by means of delay feedback linear terms. We use a perturbation method in order to find amplitude and phase modulation equations as well as external force-response and frequency-response curves. We observe in the resonance response a saddle-node bifurcation that leads to jump and hysteresis phenomena. We compare the uncontrolled and controlled systems and demonstrate that control terms can delay or remove the occurrence of the saddle-node bifurcation and reduce the amplitude peak of the resonant response.
Yamada, S
2002-01-01
In this trust fund, we reviewed subcriticality measuring methods and neutron or gamma ray measuring and date transmission systems appropriate for realizing inexpensive on-line criticality surveillance systems, which is required for ensuring the safety of nuclear fuel reprocessing plants. Since the neutron flux level in subcritical systems is fairly low without external neutron sources, it is desirable to use pulse type neutron detectors for subcritical measurement systems. This logically implies that subcriticality measurement methods based on the temporal domain should be used for developing an on-line criticality surveillance system. In the deep subcriticality conditions, a strong external neutron source is needed for eactivity measurement and a D-T tube can be used in order to improve the accuracy of the measurement. A D-T tube is convenient since it is free from Tritium problem since Tritium is sealed in an airtight container and also can be controlled by power supply. Hence, under deep subcritical condit...
Subcritical hydrothermal conversion of organic wastes and biomass. Reaction pathways
Directory of Open Access Journals (Sweden)
Alejandro Amadeus Castro Vega
2010-04-01
Full Text Available Hydrothermal conversion is a procedure which emulates organic matter’s natural conversion into bio-crude having physical and chemical properties analogous to petroleum. The artificial transformation of biomass requi- res previous knowledge of the main reaction routes and product availability. The main component of biomass (depolymerisation by hydrolysis is presented in hydrothermal cellulose conversion, producing oligosaccharides which exhibit dehydration and retro-aldol condensation reactions for transforming into furfurals and carboxylic acids. Other biomass components (such as lignin, proteins, and fat esters present both hydrolysis and pyrolysis reaction routes. As long as biomass mainly contains carbohydrates, subcritical hydrothermal conversion products and their wastes will be fundamentally analogous to those displaying cellulose. These substances have added- value by far surpassing raw material’s acquisition cost. When the main hydrothermal conversion products’ O/C, H/C molar ratios as reported in literature are plotted, an evolutionary tralectory for conversion products appears to be closely or even overlapped with fossil fuels’ geological evolution.
Effect of fluid salinity on subcritical crack propagation in calcite
Rostom, Fatma; Røyne, Anja; Dysthe, Dag Kristian; Renard, François
2013-01-01
The slow propagation of cracks, also called subcritical crack growth, is a mechanism of fracturing responsible for a ductile deformation of rocks under crustal conditions. In the present study, the double-torsion technique was used to measure the effect of fluid chemistry on the slow propagation of cracks in calcite single crystals at room temperature. Time-lapse images and measurements of force and load-point displacement allowed accurate characterization of crack velocities in a range of 10- 8 to 10- 4 m/s. Velocity curves as a function of energy-release rates were obtained for different fluid compositions, varying NH4Cl and NaCl concentrations. Our results show the presence of a threshold in fluid composition, separating two regimes: weakening conditions where the crack propagation is favored, and strengthening conditions where crack propagation slows down. We suggest that electrostatic surface forces that modify the repulsion forces between the two surfaces of the crack may be responsible for this behavior.
Effective Subcritical Butane Extraction of Bifenthrin Residue in Black Tea.
Zhang, Yating; Gu, Lingbiao; Wang, Fei; Kong, Lingjun; Qin, Guangyong
2017-03-30
As a natural and healthy beverage, tea is widely enjoyed; however, the pesticide residues in tea leaves affect the quality and food safety. To develop a highly selective and efficient method for the facile removal of pesticide residues, the subcritical butane extraction (SBE) technique was employed, and three variables involving temperature, time and extraction cycles were studied. The optimum SBE conditions were found to be as follows: extraction temperature 45 °C, extraction time 30 min, number of extraction cycles 1, and in such a condition that the extraction efficiency reached as high as 92%. Further, the catechins, theanine, caffeine and aroma components, which determine the quality of the tea, fluctuated after SBE treatment. Compared with the uncrushed leaves, pesticide residues can more easily be removed from crushed leaves, and the practical extraction efficiency was 97%. These results indicate that SBE is a useful method to efficiently remove the bifenthrin, and as appearance is not relevant in the production process, tea leaves should first be crushed and then extracted in order that residual pesticides are thoroughly removed.
The Chain-Length Distribution in Subcritical Systems
Energy Technology Data Exchange (ETDEWEB)
Nolen, Steven Douglas [Texas A & M Univ., College Station, TX (United States)
2000-06-01
The individual fission chains that appear in any neutron multiplying system provide a means, via neutron noise analysis, to unlock a wealth of information regarding the nature of the system. This work begins by determining the probability density distributions for fission chain lengths in zero-dimensional systems over a range of prompt neutron multiplication constant (K) values. This section is followed by showing how the integral representation of the chain-length distribution can be used to obtain an estimate of the system's subcritical prompt multiplication (MP). The lifetime of the chains is then used to provide a basis for determining whether a neutron noise analysis will be successful in assessing the neutron multiplication constant, k, of the system in the presence of a strong intrinsic source. A Monte Carlo transport code, MC++, is used to model the evolution of the individual fission chains and to determine how they are influenced by spatial effects. The dissertation concludes by demonstrating how experimental validation of certain global system parameters by neutron noise analysis may be precluded in situations in which the system K is relatively low and in which realistic detector efficiencies are simulated.
Catalytic upgrading of duckweed biocrude in subcritical water.
Zhang, Caicai; Duan, Peigao; Xu, Yuping; Wang, Bing; Wang, Feng; Zhang, Lei
2014-08-01
Herein, a duckweed biocrude produced from the hydrothermal liquefaction of Lemna minor was treated in subcritical water with added H₂. Effects of several different commercially available materials such as Ru/C, Pd/C, Pt/C, Pt/γ-Al₂O₃, Pt/C-sulfide, Rh/γ-Al₂O₃, activated carbon, MoS₂, Mo₂C, Co-Mo/γ-Al₂O₃, and zeolite on the yields of product fractions and the deoxygenation, denitrogenation, and desulfurization of biocrude at 350°C were examined, respectively. All the materials showed catalytic activity for deoxygenation and desulfurization of the biocrude and only Ru/C showed activity for denitrogenation. Of those catalysts examined, Pt/C showed the best performance for deoxygenation. Among all the upgraded oils, the oil produced with Ru/C shows the lowest sulfur, the highest hydrocarbon content (25.6%), the highest energy recovery (85.5%), and the highest higher heating value (42.6 MJ/kg). The gaseous products were mainly unreacted H₂, CH₄, CO₂, and C₂H6. Copyright © 2014 Elsevier Ltd. All rights reserved.
Reynolds number effect on VIV: from subcritical to supercritical flow
Energy Technology Data Exchange (ETDEWEB)
Triantafyllou, M.S.; Hover, F.S.; Techet, A.H. [Massachusetts Inst. of Tech., Dept. of Ocean Engineering, Cambridge, MA (United States)
2004-07-01
Vortex Induced Vibrations in flexibly supported rigid cylinders and long, flexible slender structures, such as cables and risers, are caused by the formation of large-scale vortices, whose dynamics are controlled to a large extend by inviscid mechanisms. Reynolds number remains a very important parameter, however, because it influences the formation and shedding mechanisms of the vortical patterns. For low Reynolds numbers, below a few thousand, a nearly complete understanding has been obtained in recent years, at least for flexibly mounted rigid cylinders. This is not the case, though, for VIV above Re=10,000 and - especially - above the critical Reynolds number of about Re=250,000 for smooth cylinders. The talk provides observed WV trends of flexibly mounted cylinders, obtained in recent experiments as function of the Reynolds number, from Re about 1,000 up to 1,000,000. In particular, similarities and differences between subcritical and supercritical force and motion data will be discussed, and conclusions on the governing principal mechanisms will be drawn, including transitions in the arrangement of vortical patterns and effects of correlation length. (authors)
Effective Subcritical Butane Extraction of Bifenthrin Residue in Black Tea
Directory of Open Access Journals (Sweden)
Yating Zhang
2017-03-01
Full Text Available As a natural and healthy beverage, tea is widely enjoyed; however, the pesticide residues in tea leaves affect the quality and food safety. To develop a highly selective and efficient method for the facile removal of pesticide residues, the subcritical butane extraction (SBE technique was employed, and three variables involving temperature, time and extraction cycles were studied. The optimum SBE conditions were found to be as follows: extraction temperature 45 °C, extraction time 30 min, number of extraction cycles 1, and in such a condition that the extraction efficiency reached as high as 92%. Further, the catechins, theanine, caffeine and aroma components, which determine the quality of the tea, fluctuated after SBE treatment. Compared with the uncrushed leaves, pesticide residues can more easily be removed from crushed leaves, and the practical extraction efficiency was 97%. These results indicate that SBE is a useful method to efficiently remove the bifenthrin, and as appearance is not relevant in the production process, tea leaves should first be crushed and then extracted in order that residual pesticides are thoroughly removed.
Enhanced Capabilities for Subcritical Experiments (ECSE) Risk Management Plan
Energy Technology Data Exchange (ETDEWEB)
Urban, Mary Elizabeth [Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Process Modeling and Analysis Group
2016-05-02
Risk is a factor, element, constraint, or course of action that introduces an uncertainty of outcome that could impact project objectives. Risk is an inherent part of all activities, whether the activity is simple and small, or large and complex. Risk management is a process that identifies, evaluates, handles, and monitors risks that have the potential to affect project success. The risk management process spans the entire project, from its initiation to its successful completion and closeout, including both technical and programmatic (non-technical) risks. This Risk Management Plan (RMP) defines the process to be used for identifying, evaluating, handling, and monitoring risks as part of the overall management of the Enhanced Capabilities for Subcritical Experiments (ECSE) ‘Project’. Given the changing nature of the project environment, risk management is essentially an ongoing and iterative process, which applies the best efforts of a knowledgeable project staff to a suite of focused and prioritized concerns. The risk management process itself must be continually applied throughout the project life cycle. This document was prepared in accordance with DOE O 413.3B, Program and Project Management for the Acquisition of Capital Assets, its associated guide for risk management DOE G 413.3-7, Risk Management Guide, and LANL ADPM AP-350-204, Risk and Opportunity Management.
Experimental subcritical facility driven by D-D/D-T neutron generator at BARC, India
Energy Technology Data Exchange (ETDEWEB)
Sinha, Amar, E-mail: image@barc.gov.in; Roy, Tushar; Kashyap, Yogesh; Ray, Nirmal; Shukla, Mayank; Patel, Tarun; Bajpai, Shefali; Sarkar, P.S.; Bishnoi, Saroj
2015-05-01
Highlights: •Experimental subcritical facility BRAHMMA coupled to D-D/D-T neutron generator. •Preliminary results of PNS experiments reported. •Feynman-alpha noise measurements explored with continuous source. -- Abstract: The paper presents design of an experimental subcritical assembly driven by D-D/D-T neutron and preliminary experimental measurements. The system has been developed for investigating the static and dynamic neutronic properties of accelerator driven sub-critical systems. This system is modular in design and it is first in the series of subcritical assemblies being designed. The subcritical core consists of natural uranium fuel with high density polyethylene as moderator and beryllium oxide as reflector. The fuel is embedded in high density polyethylene moderator matrix. Estimated k{sub eff} of the system is ∼0.89. One of the unique features of subcritical core is the use of Beryllium oxide (BeO) as reflector and HDPE as moderator making the assembly a compact modular system. The subcritical core is coupled to Purnima Neutron Generator which works in D-D and D-T mode with both DC and pulsed operation. It has facility for online source strength monitoring using neutron tagging and programmable source modulation. Preliminary experiments have been carried out for spatial flux measurement and reactivity estimation using pulsed neutron source (PNS) techniques with D-D neutrons. Further experiments are being planned to measure the reactivity and other kinetic parameters using noise methods. This facility would also be used for carrying out studies on effect of source importance and measurement of source multiplication factor k{sub s} and external neutron source efficiency φ{sup ∗} in great details. Experiments with D-T neutrons are also underway.
Bifurcation dynamics of the tempered fractional Langevin equation.
Zeng, Caibin; Yang, Qigui; Chen, YangQuan
2016-08-01
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.
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.
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...
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
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)
HIGH BIFURCATION OF THE BRACHIAL ARTERY - A COMMON VARIANT
Directory of Open Access Journals (Sweden)
Sesi
2015-10-01
Full Text Available 28 cadavers were dissected for variations in the bifurcation of brachial artery bilaterally {n=56} at the department of anatomy, Rangaraya Medical College, Kakinada, A.P. from 2010 to 2015 . Found variations during routine dissections for first year MBBS students. The findings have thrown light on the common as well as rare variants in the anatomy of brachial artery bifurcation and the course of radial and ulnar arteries in current study
Grundeken, Maik J; Collet, Carlos; Ishibashi, Yuki; Généreux, Philippe; Muramatsu, Takashi; LaSalle, Laura; Kaplan, Aaron V; Wykrzykowska, Joanna J; Morel, Marie-Angèle; Tijssen, Jan G; de Winter, Robbert J; Onuma, Yoshinobu; Leon, Martin B; Serruys, Patrick W
2017-08-24
To compare visual estimation with different quantitative coronary angiography (QCA) methods (single-vessel versus bifurcation software) to assess coronary bifurcation lesions. QCA has been developed to overcome the limitations of visual estimation. Conventional QCA however, developed in "straight vessels," has proved to be inaccurate in bifurcation lesions. Therefore, bifurcation QCA was developed. However, the impact of these different modalities on bifurcation lesion severity classification is yet unknown METHODS: From a randomized controlled trial investigating a novel bifurcation stent (Clinicaltrials.gov NCT01258972), patients with baseline assessment of lesion severity by means of visual estimation, single-vessel QCA, 2D bifurcation QCA and 3D bifurcation QCA were included. We included 113 bifurcations lesions in which all 5 modalities were assessed. The primary end-point was to evaluate how the different modalities affected the classification of bifurcation lesion severity and extent of disease. On visual estimation, 100% of lesions had side-branch diameter stenosis (%DS) >50%, whereas in 83% with single-vessel QCA, 27% with 2D bifurcation QCA and 26% with 3D bifurcation QCA a side-branch %DS >50% was found (P < 0.0001). With regard to the percentage of "true" bifurcation lesions, there was a significant difference between visual estimate (100%), single-vessel QCA (75%) and bifurcation QCA (17% with 2D bifurcation software and 13% with 3D bifurcation software, P < 0.0001). Our study showed that bifurcation lesion complexity was significantly affected when more advanced bifurcation QCA software were used. "True" bifurcation lesion rate was 100% on visual estimation, but as low as 13% when analyzed with dedicated bifurcation QCA software. © 2017 Wiley Periodicals, Inc.
Bifurcation magnetic resonance in films magnetized along hard magnetization axis
Energy Technology Data Exchange (ETDEWEB)
Vasilevskaya, Tatiana M., E-mail: t_vasilevs@mail.ru [Ulyanovsk State University, Leo Tolstoy 42, 432017 Ulyanovsk (Russian Federation); Sementsov, Dmitriy I.; Shutyi, Anatoliy M. [Ulyanovsk State University, Leo Tolstoy 42, 432017 Ulyanovsk (Russian Federation)
2012-09-15
We study low-frequency ferromagnetic resonance in a thin film magnetized along the hard magnetization axis performing an analysis of magnetization precession dynamics equations and numerical simulation. Two types of films are considered: polycrystalline uniaxial films and single-crystal films with cubic magnetic anisotropy. An additional (bifurcation) resonance initiated by the bistability, i.e. appearance of two closely spaced equilibrium magnetization states is registered. The modification of dynamic modes provoked by variation of the frequency, amplitude, and magnetic bias value of the ac field is studied. Both steady and chaotic magnetization precession modes are registered in the bifurcation resonance range. - Highlights: Black-Right-Pointing-Pointer An additional bifurcation resonance arises in a case of a thin film magnetized along HMA. Black-Right-Pointing-Pointer Bifurcation resonance occurs due to the presence of two closely spaced equilibrium magnetization states. Black-Right-Pointing-Pointer Both regular and chaotic precession modes are realized within bifurcation resonance range. Black-Right-Pointing-Pointer Appearance of dynamic bistability is typical for bifurcation resonance.
Editorial: at the bifurcation of the last frontiers.
Nguyen, Thach; Chen, Shao Liang; Xu, Bo; Kwan, Tak; Nguyen, Katrina; Nanjundappa, Aravinda; Van Ho, Bao; Gao, Run-Lin
2010-08-01
The concept of coronary angioplasty percutaneous coronary intervention (PCI) was pioneered by Andreas Gruntzig. Since then, several modifications, innovative devices, techniques, and advances have revolutionized the practice of interventional cardiology. Coronary bifurcation and chronic total occlusion are the last two frontiers that continue to challenge the skills of the interventional cardiologists. Proceedings of the second Bifurcation Summit held from November 26 to 28, 2009 in Nanjing, China are published in this symposium. In a general review, the state of the art in management of bifurcation lesion is summarized in the statement of the "Bifurcation Club in KOKURA." A new-presented concept was the "extension distance" between the main vessel and the sidebranch ostia and its association with restenosis. The results of two studies on shear stress (SS) after PCI showed that contradictory lower SS after stenting was associated with lower in-stent restenosis. There was better fractional flow reserve after double kissing crush technique than provisional one-stent technique. There was also lower rate of stent thrombosis after bifurcation stenting with excellent final angiographic results. In a negative note, the SYNTAX score had no predictive values on trifurcated left main stenting. In summary, different aspects of percutaneous management for bifurcated lesion are described seen from different perspectives and evidenced by novel techniques and strategies.
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...
High power ring methods and accelerator driven subcritical reactor application
Energy Technology Data Exchange (ETDEWEB)
Tahar, Malek Haj [Univ. of Grenoble (France)
2016-08-07
High power proton accelerators allow providing, by spallation reaction, the neutron fluxes necessary in the synthesis of fissile material, starting from Uranium 238 or Thorium 232. This is the basis of the concept of sub-critical operation of a reactor, for energy production or nuclear waste transmutation, with the objective of achieving cleaner, safer and more efficient process than today’s technologies allow. Designing, building and operating a proton accelerator in the 500-1000 MeV energy range, CW regime, MW power class still remains a challenge nowadays. There is a limited number of installations at present achieving beam characteristics in that class, e.g., PSI in Villigen, 590 MeV CW beam from a cyclotron, SNS in Oakland, 1 GeV pulsed beam from a linear accelerator, in addition to projects as the ESS in Europe, a 5 MW beam from a linear accelerator. Furthermore, coupling an accelerator to a sub-critical nuclear reactor is a challenging proposition: some of the key issues/requirements are the design of a spallation target to withstand high power densities as well as ensure the safety of the installation. These two domains are the grounds of the PhD work: the focus is on the high power ring methods in the frame of the KURRI FFAG collaboration in Japan: upgrade of the installation towards high intensity is crucial to demonstrate the high beam power capability of FFAG. Thus, modeling of the beam dynamics and benchmarking of different codes was undertaken to validate the simulation results. Experimental results revealed some major losses that need to be understood and eventually overcome. By developing analytical models that account for the field defects, one identified major sources of imperfection in the design of scaling FFAG that explain the important tune variations resulting in the crossing of several betatron resonances. A new formula is derived to compute the tunes and properties established that characterize the effect of the field imperfections on the
Solubility of Benzo[a]pyrene and Organic Matter of Soil in Subcritical Water
Directory of Open Access Journals (Sweden)
Svetlana Sushkova
2015-12-01
Full Text Available A dynamic subcritical water extraction method of benzo[a]pyrene from soils is under consideration. The optimum conditions for benzo[a]pyrene extraction from soil are described including the soil treatment by subcritical water at 250 °C and 100 atm for 30 min. The effectiveness of developed method was determined using the matrix spiking recovery technique. A comparative analysis was made to evaluate the results of benzo[a]pyrene extraction from soils using the subcritical water and organic solvents. The advantages of the subcritical water extraction involve the use of ecologically friendly solvent, a shorter time for the analysis and a higher amount of benzo[a]pyrene extracted from soil (96 %. The influence of subcritical water extraction on soil properties was measured the investigation of the processes occurring within soil under the influence the high temperature and pressure. Under appropriate conditions of the experiment there is the destruction of the soil organic matter while the composition of the soil mineral fraction remains practically unchanged.
Khuwijitjaru, Pramote; Sayputikasikorn, Nucha; Samuhasaneetoo, Suched; Penroj, Parinda; Siriwongwilaichat, Prasong; Adachi, Shuji
2012-01-01
Cinnamon bark (Cinnamomum zeylanicum) powder was treated with subcritical water at 150 and 200°C in a semi-continuous system at a constant flow rate (3 mL/min) and pressure (6 MPa). Major flavoring compounds, i.e., cinnamaldehyde, cinnamic acid, cinnamyl alcohol and coumarin, were extracted at lower recoveries than the extraction using methanol, suggesting that degradation of these components might occur during the subcritical water treatment. Caffeic, ferulic, p-coumaric, protocatechuic and vanillic acids were identified from the subcritical water treatment. Extraction using subcritical water was more effective to obtain these acids than methanol (50% v/v) in both number of components and recovery, especially at 200°C. Subcritical water treatment at 200°C also resulted in a higher total phenolic content and DPPH radical scavenging activity than the methanol extraction. The DPPH radical scavenging activity and total phenolic content linearly correlated but the results suggested that the extraction at 200°C might result in other products that possessed a free radical scavenging activity other than the phenolic compounds.
Effect of water on critical and subcritical fracture properties of Woodford shale
Chen, Xiaofeng; Eichhubl, Peter; Olson, Jon E.
2017-04-01
Subcritical fracture behavior of shales under aqueous conditions is poorly characterized despite increased relevance to oil and gas resource development and seal integrity in waste disposal and subsurface carbon sequestration. We measured subcritical fracture properties of Woodford shale in ambient air, dry CO2 gas, and deionized water by using the double-torsion method. Compared to tests in ambient air, the presence of water reduces fracture toughness by 50%, subcritical index by 77%, and shear modulus by 27% and increases inelastic deformation. Comparison between test specimens coated with a hydrophobic agent and uncoated specimens demonstrates that the interaction of water with the bulk rock results in the reduction of fracture toughness and enhanced plastic effects, while water-rock interaction limited to the vicinity of the propagating fracture tip by a hydrophobic specimen coating lowers subcritical index and increases fracture velocity. The observed deviation of a rate-dependent subcritical index from the power law K-V relations for coated specimens tested in water is attributed to a time-dependent weakening process resulting from the interaction between water and clays in the vicinity of the fracture tip.
Directory of Open Access Journals (Sweden)
Javier Benezet
2016-01-01
Full Text Available We present a complex bifurcation lesion treated with a new two-stent strategy combining a dedicated sirolimus eluting bifurcation stent, BiOSS Lim, with a bioresorbable vascular scaffold (BVS. The advantages of this strategy compared with the conventional two-stent approach are as follows: the dedicated stent protects the carina from being damaged, the large cell at the middle zone of the BiOSS Lim gives possibility to enter easily into the side branch (SB with any standard size conventional device, and, finally, the additional use of BVS in the SB could have a long-term benefit in terms of restenosis.
Concept of turbines for ultrasupercritical, supercritical, and subcritical steam conditions
Mikhailov, V. E.; Khomenok, L. A.; Pichugin, I. I.; Kovalev, I. A.; Bozhko, V. V.; Vladimirskii, O. A.; Zaitsev, I. V.; Kachuriner, Yu. Ya.; Nosovitskii, I. A.; Orlik, V. G.
2017-11-01
The article describes the design features of condensing turbines for ultrasupercritical initial steam conditions (USSC) and large-capacity cogeneration turbines for super- and subcritical steam conditions having increased steam extractions for district heating purposes. For improving the efficiency and reliability indicators of USSC turbines, it is proposed to use forced cooling of the head high-temperature thermally stressed parts of the high- and intermediate-pressure rotors, reaction-type blades of the high-pressure cylinder (HPC) and at least the first stages of the intermediate-pressure cylinder (IPC), the double-wall HPC casing with narrow flanges of its horizontal joints, a rigid HPC rotor, an extended system of regenerative steam extractions without using extractions from the HPC flow path, and the low-pressure cylinder's inner casing moving in accordance with the IPC thermal expansions. For cogeneration turbines, it is proposed to shift the upper district heating extraction (or its significant part) to the feedwater pump turbine, which will make it possible to improve the turbine plant efficiency and arrange both district heating extractions in the IPC. In addition, in the case of using a disengaging coupling or precision conical bolts in the coupling, this solution will make it possible to disconnect the LPC in shifting the turbine to operate in the cogeneration mode. The article points out the need to intensify turbine development efforts with the use of modern methods for improving their efficiency and reliability involving, in particular, the use of relatively short 3D blades, last stages fitted with longer rotor blades, evaporation techniques for removing moisture in the last-stage diaphragm, and LPC rotor blades with radial grooves on their leading edges.
Characterization of the Subcritical Water Extraction of Fluoxetine-Hydrochloride.
Murakami, Jillian N; Thurbide, Kevin B; Lambertus, Gordon; Jensen, Eric
2012-08-10
The characteristics of using Subcritical Water Extraction (SWE) to recover Fluoxetine-Hydrochloride from both standard solutions and the contents of commercial capsule formulations were investigated. Analysis of solutions and extracts was done by HPLC with UV detection at 254 nm. Standard solutions of Fluoxetine-Hydrochloride were exposed to a variety of SWE operating conditions, including temperatures from 125 to 275°C and periods ranging from 5 to 30 min. Fluoxetine-Hydrochloride could be quantitatively recovered from standard solutions (1.0mg/mL) that were heated up to 175°C for 30 min, up to 200°C for 15 min, or up to 225°C for 10 min. At higher temperatures and/or times, Fluoxetine-Hydrochloride recoveries were generally incomplete and often produced decomposition by-products during the process. By comparison, the concentration of Fluoxetine-Hydrochloride in the standard solution had relatively little effect on recovery. Considering these parameters, an SWE method was developed to extract Fluoxetine-Hydrochloride from the contents of Prozac(®) capsules. It was found that Fluoxetine-Hydrochloride could be quantitatively extracted from the capsule contents in 8 min at a temperature of 200°C using 3.5 mL of water as the extraction solvent. Gelatinization of the starch excipient in the capsule contents was also observed to occur temporarily during the capsule extractions, before ultimately disappearing again. The period of this phenomenon was dependent on both temperature and sample size. The results indicate that SWE can be a very useful method for Fluoxetine-Hydrochloride extraction and suggest that it may be interesting to explore other pharmaceuticals using this method as well. Copyright © 2012 Elsevier B.V. All rights reserved.
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Huaguang eGu
2015-08-01
Full Text Available In rabbit depressor nerve fibers, an on-off firing pattern, period-1 firing, and integer multiple firing with quiescent state were observed as the static pressure level was increased. A bursting pattern with bursts at the systolic phase of blood pressure, continuous firing, and bursting with burst at diastolic phase and quiescent state at systolic phase were observed as the mean level of the dynamic blood pressure was increased. For both static and dynamic pressures, the firing frequency of the first two firing patterns increased and of the last firing pattern decreased due to the quiescent state. If the quiescent state is disregarded, the spike frequency becomes an increasing trend. The instantaneous spike frequency of the systolic phase bursting, continuous firing, and diastolic phase bursting can reflect the temporal process of the systolic phase, whole procedure, and diastolic phase of the dynamic blood pressure signal, respectively. With increasing the static current corresponding to pressure level, the deterministic Hodgkin-Huxley (HH model manifests a process from a resting state first to period-1 firing via a subcritical Hopf bifurcation and then to a resting state via a supercritical Hopf bifurcation, and the firing frequency increases. The on-off firing and integer multiple firing were here identified as noise-induced firing patterns near the subcritical and supercritical Hopf bifurcation points, respectively, using the stochastic HH model. The systolic phase bursting and diastolic phase bursting were identified as pressure-induced firings near the subcritical and supercritical Hopf bifurcation points, respectively, using an HH model with a dynamic signal. The firing, spike frequency, and instantaneous spike frequency observed in the experiment were simulated and explained using HH models. The results illustrate the dynamics of different firing patterns and the frequency and temporal coding mechanisms of aortic baroreceptor.
Mammalian evolution may not be strictly bifurcating.
Hallström, Björn M; Janke, Axel
2010-12-01
The massive amount of genomic sequence data that is now available for analyzing evolutionary relationships among 31 placental mammals reduces the stochastic error in phylogenetic analyses to virtually zero. One would expect that this would make it possible to finally resolve controversial branches in the placental mammalian tree. We analyzed a 2,863,797 nucleotide-long alignment (3,364 genes) from 31 placental mammals for reconstructing their evolution. Most placental mammalian relationships were resolved, and a consensus of their evolution is emerging. However, certain branches remain difficult or virtually impossible to resolve. These branches are characterized by short divergence times in the order of 1-4 million years. Computer simulations based on parameters from the real data show that as little as about 12,500 amino acid sites could be sufficient to confidently resolve short branches as old as about 90 million years ago (Ma). Thus, the amount of sequence data should no longer be a limiting factor in resolving the relationships among placental mammals. The timing of the early radiation of placental mammals coincides with a period of climate warming some 100-80 Ma and with continental fragmentation. These global processes may have triggered the rapid diversification of placental mammals. However, the rapid radiations of certain mammalian groups complicate phylogenetic analyses, possibly due to incomplete lineage sorting and introgression. These speciation-related processes led to a mosaic genome and conflicting phylogenetic signals. Split network methods are ideal for visualizing these problematic branches and can therefore depict data conflict and possibly the true evolutionary history better than strictly bifurcating trees. Given the timing of tectonics, of placental mammalian divergences, and the fossil record, a Laurasian rather than Gondwanan origin of placental mammals seems the most parsimonious explanation.
Subcritical measurements of the WINCO slab tank experiment using the source-jerk technique
Energy Technology Data Exchange (ETDEWEB)
Spriggs, G.D.; Hansen, G.E.; Martin, E.R.; Plassmann, E.A.; Pederson, R.A.; Schlesser, J.A.; Krawczyk, T.L.; Tanner, J.E.; Smolen, G.R. (Los Alamos National Lab., NM (USA); Martin Marietta Energy Systems, Inc., Oak Ridge, TN (USA); Westinghouse Idaho Nuclear Co., Inc., Idaho Falls, ID (USA); Martin Marietta Energy Systems, Inc., Oak Ridge, TN (USA))
1989-01-01
Subcritical measurements of the WINCO slab tank using the source-jerk technique are presented. This technique determines subcriticality by analyzing the transient response produced by the sudden removal of an extraneous neutron source (i.e., a source jerk). We have found that the technique can provide an accurate means of measuring k in configurations that are close to critical (i.e., 0.90 < k < 1.0). As the system becomes more subcritical (i.e., k < 0.90), spatial effects introduce significant biases depending on the source and detector positions. A comparison between the measurements and Monte Carlo code calculations is also presented. 15 refs., 6 figs., 2 tabs.
Bistability in Coupled Oscillators Exhibiting Synchronized Dynamics
Olusola, O. I.; Vincent, U. E.; Njah, A. N.; Olowofela, J. A.
2010-05-01
We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators (DDOs). Some sufficient algebraic criteria for global chaos synchronization of the drive and response DDOs via linear state error feedback control are obtained by means of Lyapunov stability theory. The synchronization is achieved through a bistable state in which a periodic attractor co-exists with a chaotic attractor. Using the linear perturbation analysis, the prevalence of attractors in parameter space and the associated bifurcations are examined. Subcritical and supercritical Hopf bifurcations and abundance of Arnold tongues — a signature of mode locking phenomenon are found.
Energy Technology Data Exchange (ETDEWEB)
Garcia M, T.; Mazon R, R., E-mail: teodoro.garcia@inin.gob.m [ININ, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico)
2009-07-01
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)
The Lefschetz-Hopf theorem and axioms for the Lefschetz number
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Robert F. Brown
2004-03-01
Full Text Available The reduced Lefschetz number, that is, L(Ã¢Â‹Â…Ã¢ÂˆÂ’1 where L(Ã¢Â‹Â… denotes the Lefschetz number, is proved to be the unique integer-valued function ÃŽÂ» on self-maps of compact polyhedra which is constant on homotopy classes such that (1 ÃŽÂ»(fg=ÃŽÂ»(gf for f:XÃ¢Â†Â’Y and g:YÃ¢Â†Â’X; (2 if (f1,f2,f3 is a map of a cofiber sequence into itself, then ÃŽÂ»(f1=ÃŽÂ»(f1+ÃŽÂ»(f3; (3 ÃŽÂ»(f=Ã¢ÂˆÂ’(deg(p1fe1+Ã¢Â‹Â¯+deg(pkfek, where f is a self-map of a wedge of k circles, er is the inclusion of a circle into the rth summand, and pr is the projection onto the rth summand. If f:XÃ¢Â†Â’X is a self-map of a polyhedron and I(f is the fixed point index of f on all of X, then we show that I(Ã¢Â‹Â…Ã¢ÂˆÂ’1 satisfies the above axioms. This gives a new proof of the normalization theorem: if f:XÃ¢Â†Â’X is a self-map of a polyhedron, then I(f equals the Lefschetz number L(f of f. This result is equivalent to the Lefschetz-Hopf theorem: if f:XÃ¢Â†Â’X is a self-map of a finite simplicial complex with a finite number of fixed points, each lying in a maximal simplex, then the Lefschetz number of f is the sum of the indices of all the fixed points of f.
Subcritical water extraction of amino acids from Mars analog soils.
Noell, Aaron C; Fisher, Anita M; Fors-Francis, Kisa; Sherrit, Stewart
2018-01-18
For decades, the Martian regolith has stymied robotic mission efforts to catalog the organic molecules present. Perchlorate salts, found widely throughout Mars, are the main culprit as they breakdown and react with organics liberated from the regolith during pyrolysis, the primary extraction technique attempted to date on Mars. This work further develops subcritical water extraction (SCWE) as a technique for extraction of amino acids on future missions. The effect of SCWE temperature (185, 200, and 215°C) and duration of extraction (10-120 min) on the total amount and distribution of amino acids recovered was explored for three Mars analog soils (JSC Mars-1A simulant, an Atacama desert soil, and an Antarctic Dry Valleys soil) and bovine serum albumin (as a control solution of known amino acid content). Total amounts of amino acids extracted increased with both time and temperature; however, the distribution shifted notably due to the destruction of the amino acids with charged or polar side chains at the higher temperatures. The pure bovine serum albumin solution and JSC Mars 1A also showed lower yields than the Atacama and Antarctic extractions suggesting that SCWE may be less effective at hydrolyzing large or aggregated proteins. Changing solvent from water to a dilute (10 mM) HCl solution allowed total extraction efficiencies comparable to the higher temperature/time combinations while using the lowest temperature/time (185°C/20 min). The dilute HCl extractions also did not lead to the shift in amino acid distribution observed at the higher temperatures. Additionally, adding sodium perchlorate salt to the extraction did not interfere with recoveries. Native magnetite in the JSC Mars-1A may have been responsible for destruction of glycine, as evidenced by its uncharacteristic decrease as the temperature/time of extraction increased. This work shows that SCWE can extract high yields of native amino acids out of Mars analog soils with minimal disruption of the
Anatomical Considerations on Surgical Anatomy of the Carotid Bifurcation
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Adamantios Michalinos
2016-01-01
Full Text Available Surgical anatomy of carotid bifurcation is of unique importance for numerous medical specialties. Despite extensive research, many aspects such as precise height of carotid bifurcation, micrometric values of carotid arteries and their branches as their diameter, length, and degree of tortuosity, and variations of proximal external carotid artery branches are undetermined. Furthermore carotid bifurcation is involved in many pathologic processes, atheromatous disease being the commonest. Carotid atheromatous disease is a major predisposing factor for disabling and possibly fatal strokes with geometry of carotid bifurcation playing an important role in its natural history. Consequently detailed knowledge of various anatomic parameters is of paramount importance not only for understanding of the disease but also for design of surgical treatment, especially selection between carotid endarterectomy and carotid stenting. Carotid bifurcation paragangliomas constitute unique tumors with diagnostic accuracy, treatment design, and success of operative intervention dependent on precise knowledge of anatomy. Considering those, it becomes clear that selection and application of proper surgical therapy should consider anatomical details. Further research might ameliorate available treatment options or even lead to innovative ones.
Bifurcation of an Orbit Homoclinic to a Hyperbolic Saddle of a Vector Field in R4
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Tiansi Zhang
2015-01-01
Full Text Available We perform a bifurcation analysis of an orbit homoclinic to a hyperbolic saddle of a vector field in R4. We give an expression of the gap between returning points in a transverse section by renormalizing system, through which we find the existence of homoclinic-doubling bifurcation in the case 1+α>β>ν. Meanwhile, after reparametrizing the parameter, a periodic-doubling bifurcation appears and may be close to a saddle-node bifurcation, if the parameter is varied. These scenarios correspond to the occurrence of chaos. Based on our analysis, bifurcation diagrams of these bifurcations are depicted.
Directory of Open Access Journals (Sweden)
Omid Arjmandi-Tash
2012-12-01
Full Text Available Introduction: Atherosclerosis is a focal disease that susceptibly forms near bifurcations, anastomotic joints, side branches, and curved vessels along the arterial tree. In this study, pulsatile blood flow in a bifurcation model with a non-planar branch is investigated. Methods: Wall shear stress (WSS distributions along generating lines on vessels for different bifurcation angles are calculated during the pulse cycle. Results: The WSS at the outer side of the bifurcation plane vanishes especially for higher bifurcation angles but by increasing the bifurcation angle low WSS region squeezes. At the systolic phase there is a high possibility of formation of a separation region at the outer side of bifurcation plane for all the cases. WSS peaks exist on the inner side of bifurcation plane near the entry section of daughter vessels and these peaks drop as bifurcation angle is increased. Conclusion: It was found that non-planarity of the daughter vessel lowers the minimum WSS at the outer side of the bifurcation and increases the maximum WSS at the inner side. So it seems that the formation of atherosclerotic plaques at bifurcation region in direction of non-planar daughter vessel is more risky.
Shin, Susanna Hewon; Starnes, Benjamin Ware
2017-11-01
Up to 40% of abdominal aortic aneurysms (AAAs) have coexistent iliac artery aneurysms (IAAs). In the past, successful endovascular repair required internal iliac artery (IIA) embolization, which can lead to pelvic or buttock ischemia. This study describes a technique that uses a readily available solution with a minimally altered off-the-shelf bifurcated graft in the IAA to maintain IIA perfusion. From August 2009 to May 2015, 14 patients with AAAs and coexisting IAAs underwent repair with a bifurcated-bifurcated approach. A 22-mm or 24-mm bifurcated main body device was used in the IAA with extension of the "contralateral" limb into the IIA. Intraoperative details including operative time, fluoroscopy time, and contrast agent use were recorded. Outcome measures assessed were operative technical success and a composite outcome measure of IIA patency, freedom from reintervention, and clinically significant endoleak at 1 year. Fourteen patients underwent bifurcated-bifurcated repair during the study period. Technical success was achieved in 93% of patients, with successful treatment of the AAA and IAA and preservation of flow to at least one IIA. The procedure was performed with a completely percutaneous bilateral femoral approach in 92% of patients. Three patients had a type II endoleak on initial follow-up imaging, but none were clinically significant. There were no cases of bowel ischemia or erectile dysfunction. One patient had buttock claudication ipsilateral to IIA coil embolization (contralateral to bifurcated iliac repair and preserved IIA) that resolved by 6-month follow-up. Two patients required reinterventions. One patient presented to his first follow-up visit on postoperative day 25 with thrombosis of the right external iliac limb ipsilateral to the bifurcated iliac repair, which was successfully treated with thrombectomy and stenting of the limb. This same patient presented at 83 months with growth of the preserved IIA to 3.9 cm and underwent coil
Noisy zigzag transition, fluctuations, and thermal bifurcation threshold
Delfau, Jean-Baptiste; Coste, Christophe; Saint Jean, Michel
2013-06-01
We study the zigzag transition in a system of particles with screened electrostatic interaction, submitted to a thermal noise. At finite temperature, this configurational phase transition is an example of noisy supercritical pitchfork bifurcation. The measurements of transverse fluctuations allow a complete description of the bifurcation region, which takes place between the deterministic threshold and a thermal threshold beyond which thermal fluctuations do not allow the system to flip between the symmetric zigzag configurations. We show that a divergence of the saturation time for the transverse fluctuations allows a precise and unambiguous definition of this thermal threshold. Its evolution with the temperature is shown to be in good agreement with theoretical predictions from noisy bifurcation theory.
Local bifurcation of electrohydrodynamic waves on a conducting fluid
Lin, Zhi; Zhu, Yi; Wang, Zhan
2017-03-01
We are concerned with progressive waves propagating on a two-dimensional conducting fluid when a uniform electric field is applied in the direction perpendicular to the undisturbed free surface. The competing effects of gravity, surface tension, and electrically induced forces are investigated using both analytical and numerical techniques for an inviscid and incompressible fluid flowing irrotationally. We simplify the full Euler equations by expanding and truncating the Dirichlet-Neumann operators in the Hamiltonian formulation of the problem. The numerical results show that when the electric parameter is in a certain range, the bifurcation structure near the minimum of the phase speed is rich with Stokes, solitary, generalized solitary, and dark solitary waves. In addition to symmetric solutions, asymmetric solitary waves featuring a multi-packet structure are found to occur along a branch of asymmetric generalized solitary waves that itself bifurcates from Stokes waves of finite amplitude. The detailed bifurcation diagrams, together with typical wave profiles, are presented.
Spike-train bifurcation scaling in two coupled chaotic neurons
Energy Technology Data Exchange (ETDEWEB)
Huerta, R.; Rabinovich, M.I. [Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402 (United States); Abarbanel, H.D. [Department of Physics and Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California 92093-0402 (United States); Bazhenov, M. [Howard Hughes Medical Institute, The Salk Institute, Computational Neurobiology Laboratory, La Jolla, California 92037 (United States)
1997-03-01
We investigate the variation of the out-of-phase periodic rhythm produced by two chaotic neurons {bold (}Hindmarsh-Rose neurons [J. L. Hindmarsh and R. M. Rose, Proc. R. Soc. London B {bold 221}, 87 (1984)]{bold )} coupled by electrical and reciprocally synaptic connections. The exploration of a two-parametric bifurcation diagram, as a function of the strength of the electrical and inhibitory coupling, reveals that the periodic rhythms associated to the limit cycles bounded by saddle-node bifurcations, undergo a strong variation as a function of small changes of electrical coupling. We found that there is a scaling law for the bifurcations of the limit cycles as a function of the strength of both couplings. From the functional point of view of this mixed typed of coupling, the small variation of electrical coupling provides a high sensitivity for period regulation inside the regime of out-of-phase synchronization. {copyright} {ital 1997} {ital The American Physical Society}
High-resolution mapping of bifurcations in nonlinear biochemical circuits
Genot, A. J.; Baccouche, A.; Sieskind, R.; Aubert-Kato, N.; Bredeche, N.; Bartolo, J. F.; Taly, V.; Fujii, T.; Rondelez, Y.
2016-08-01
Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.
Dynamical systems V bifurcation theory and catastrophe theory
1994-01-01
Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, the first printing of w...
Bifurcations in the optimal elastic foundation for a buckling column
Energy Technology Data Exchange (ETDEWEB)
Rayneau-Kirkhope, Daniel, E-mail: ppxdr@nottingham.ac.u [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom); Farr, Robert [Unilever R and D, Olivier van Noortlaan 120, AT3133, Vlaardingen (Netherlands); London Institute for Mathematical Sciences, 22 South Audley Street, Mayfair, London (United Kingdom); Ding, K. [Department of Physics, Fudan University, Shanghai, 200433 (China); Mao, Yong [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom)
2010-12-01
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
Bifurcation-free design method of pulse energy converter controllers
Energy Technology Data Exchange (ETDEWEB)
Kolokolov, Yury [Institute of Applied Mathematics, Informatics and Control, Yugra State University, 16 Chekhova str., Khanty-Mansiysk 628012 (Russian Federation); Ustinov, Pavel [Department of Design and Technology of Electronic and Computer Systems, Orel State Technical University, 29 Naugorskoye Shosse, Orel 302020 (Russian Federation); CReSTIC, Universite de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, Reims Cedex 2, 51687 (France)], E-mail: pavel-ustinov@yandex.ru; Essounbouli, Najib; Hamzaoui, Abdelaziz [CReSTIC, Universite de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, Reims Cedex 2, 51687 (France)
2009-12-15
In this paper, a design method of pulse energy converter (PEC) controllers is proposed. This method develops a classical frequency domain design, based on the small signal modeling, by means of an addition of a nonlinear dynamics analysis stage. The main idea of the proposed method consists in fact that the PEC controller, designed with an application of the small signal modeling, is tuned after with taking into the consideration an essentially nonlinear nature of the PEC that makes it possible to avoid bifurcation phenomena in the PEC dynamics at the design stage (bifurcation-free design). Also application of the proposed method allows an improvement of the designed controller performance. The application of this bifurcation-free design method is demonstrated on an example of the controller design of direct current-direct current (DC-DC) buck converter with an input electromagnetic interference filter.
Global bifurcations in a piecewise-smooth Cournot duopoly game
Energy Technology Data Exchange (ETDEWEB)
Tramontana, Fabio, E-mail: f.tramontana@univpm.i [Universita degli Studi di Urbino, Department of Economics and Quantitative Methods, Via Saffi 42, 61029 Urbino (Italy); Gardini, Laura, E-mail: laura.gardini@uniurb.i [Universita degli Studi di Urbino, Department of Economics and Quantitative Methods, Via Saffi 42, 61029 Urbino (Italy); Puu, Toenu [CERUM, Umea University, SE-90187 Umea (Sweden)
2010-12-15
The object of the work is to perform the global analysis of the Cournot duopoly model with isoelastic demand function and unit costs, presented in Puu . The bifurcation of the unique Cournot fixed point is established, which is a resonant case of the Neimark-Sacker bifurcation. New properties associated with the introduction of horizontal branches are evidenced. These properties differ significantly when the constant value is zero or positive and small. The good behavior of the case with positive constant is proved, leading always to positive trajectories. Also when the Cournot fixed point is unstable, stable cycles of any period may exist.
Global Bifurcation of a Novel Computer Virus Propagation Model
Ren, Jianguo; Xu, Yonghong; Liu, Jiming
2014-01-01
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 bif...
Discretizing the transcritical and pitchfork bifurcations – conjugacy results
Lóczi, Lajos
2015-01-07
© 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 on the one-step discretization method of order (Formula presented.) , we show that the time- (Formula presented.) exact and the step-size- (Formula presented.) discretized dynamics are topologically equivalent by constructing a two-parameter family of conjugacies in each case. As a main result, we prove that the constructed conjugacy maps are (Formula presented.) -close to the identity and these estimates are optimal.
Bifurcation in tidal streams of Sagittarius Dwarf Galaxy: Numerical Simulations
Camargo Camargo, Y.; Casas-Miranda, R.
2018-01-01
We performed N-body simulations between Sagittarius dwarf galaxy and the Milky Way. The Sagittarius galaxy is modeled with two components: dark matter halo and stellar disc. The Milky Way is modeled with three components: dark matter halo, stellar disc and bulge. The goal of this work is to reproduce the bifurcations in the tidal tails and the physical properties of the Sagittarius dwarf galaxy. For it, we simulated the interaction of the progenitor of this galaxy with the Milky Way. Although bifurcations could be reproduced, the position and physical properties of Sagittarius remnant could not be obtained simultaneously.
Wall shear stress evolution in carotid artery bifurcation
Bernad, S. I.; Bosioc, A. I.; Totorean, A. F.; Petre, I.; Bernad, E. S.
2017-07-01
The steady flow in an anatomically realistic human carotid bifurcation was simulated numerically. Main parameters such as wall shear stress (WSS), velocity profiles and pressure distributions are investigated in the carotid artery, namely in bifurcation and sinusoidal enlargement regions. Flow in the carotid sinus is dominated by a single secondary vortex motion accompanied by a strong helical flow. This type of flow is induced primarily by the curvature and asymmetry of the in vivo geometry. Low wall shear stress concentration occurs at both the anterior and posterior aspects of the proximal internal bulb.
Nonlinear dynamics aspects of subcritical transitions and singular flows in viscoelastic fluids
Becherer, Paul
2008-01-01
Recently, there has been a renewed interest in theoretical aspects of flows of viscoelastic fluids (such as dilute polymer solutions). This thesis addresses two distinct issues related to such flows. Motivated by the possible occurrence of subcritical (finite-amplitude) instabilities in parallel
Subcritical water - a perspective reaction media for biomass processing to chemicals
Pavlovič, Irena; Škerget, Mojca; Knez, Željko
2015-01-01
Biomass and water are recognized as a key renewable feedstock in sustainable production of chemicals, fuels and energy. Subcritical water (SubCW), or commonly referred as hot compressed water (HCW), is the water above boiling and below critical point (CP
Energy Technology Data Exchange (ETDEWEB)
Zhou, Shengcheng; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi, E-mail: yqzheng@mail.xjtu.edu.cn; Huang, Kai; He, Mingtao; Li, Xunzhao
2014-10-15
Highlights: • A new code system for design studies of accelerator driven subcritical reactors (ADSRs) is developed. • S{sub N} transport solver in triangular-z meshes, fine deletion analysis and multi-channel thermal-hydraulics analysis are coupled in the code. • Numerical results indicate that the code is reliable and efficient for design studies of ADSRs. - Abstract: Accelerator driven subcritical reactors (ADSRs) have been proposed and widely investigated for the transmutation of transuranics (TRUs). ADSRs have several special characteristics, such as the subcritical core driven by spallation neutrons, anisotropic neutron flux distribution and complex geometry etc. These bring up requirements for development or extension of analysis codes to perform design studies. A code system named LAVENDER has been developed in this paper. It couples the modules for spallation target simulation and subcritical core analysis. The neutron transport-depletion calculation scheme is used based on the homogenized cross section from assembly calculations. A three-dimensional S{sub N} nodal transport code based on triangular-z meshes is employed and a multi-channel thermal-hydraulics analysis model is integrated. In the depletion calculation, the evolution of isotopic composition in the core is evaluated using the transmutation trajectory analysis algorithm (TTA) and fine depletion chains. The new code is verified by several benchmarks and code-to-code comparisons. Numerical results indicate that LAVENDER is reliable and efficient to be applied for the steady-state analysis and reactor core design of ADSRs.
Gao, Da-Ming; Kobayashi, Takashi; Adachi, Shuji
2015-01-01
The influence of water-miscible alcohols (methanol, 1-propanol, 2-propanol, and t-butyl alcohol) on the isomerization of glucose to fructose and mannose was investigated under subcritical aqueous conditions (180-200 °C). Primary and secondary alcohols promoted the conversion and isomerization of glucose to afford fructose and mannose with high and low selectivity, respectively. On the other hand, the decomposition (side-reaction) of glucose was suppressed in the presence of the primary and secondary alcohols compared with that in subcritical water. The yield of fructose increased with increasing concentration of the primary and secondary alcohols, and the species of the primary and secondary alcohols tested had little effect on the isomerization behavior of glucose. In contrast, the isomerization of glucose was suppressed in subcritical aqueous t-butyl alcohol. Both the conversion of glucose and the yield of fructose decreased with increasing concentration of t-butyl alcohol. In addition, mannose was not detected in reactions using subcritical aqueous t-butyl alcohol.
DEFF Research Database (Denmark)
Bang, O.; Juul Rasmussen, J.; Christiansen, P.L.
1994-01-01
Discretizing the continuous nonlinear Schrodinger equation with arbitrary power nonlinearity influences the time evolution of its ground state solitary solution. In the subcritical case, for grid resolutions above a certain transition value, depending on the degree of nonlinearity, the solution w...
Subcritical crack growth behavior of AI2O3-Glass dental composites
Zhu, Q.; With, G. de; Dortmans, L.J.M.G.; Feenstra, F.
2003-01-01
The purpose of this study is to investigate the subcritical crack growth (SCG) behavior of alumina-glass dental composites. Alumina-glass composites were fabricated by infiltrating molten glass to porous alumina preforms. Rectangular bars of the composite were subject to dynamic loading in air, with
Plutonium Critical Mass Curve Comparison to Mass at Upper Subcritical Limit (USL) Using Whisper
Energy Technology Data Exchange (ETDEWEB)
Alwin, Jennifer Louise [Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Monte Carlo Codes; Zhang, Ning [Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Nuclear Criticality Safety Division
2016-09-27
Whisper is computational software designed to assist the nuclear criticality safety analyst with validation studies with the MCNP^{®} Monte Carlo radiation transport package. Standard approaches to validation rely on the selection of benchmarks based upon expert judgment. Whisper uses sensitivity/uncertainty (S/U) methods to select relevant benchmarks to a particular application or set of applications being analyzed. Using these benchmarks, Whisper computes a calculational margin. Whisper attempts to quantify the margin of subcriticality (MOS) from errors in software and uncertainties in nuclear data. The combination of the Whisper-derived calculational margin and MOS comprise the baseline upper subcritical limit (USL), to which an additional margin may be applied by the nuclear criticality safety analyst as appropriate to ensure subcriticality. A series of critical mass curves for plutonium, similar to those found in Figure 31 of LA-10860-MS, have been generated using MCNP6.1.1 and the iterative parameter study software, WORM_Solver. The baseline USL for each of the data points of the curves was then computed using Whisper 1.1. The USL was then used to determine the equivalent mass for plutonium metal-water system. ANSI/ANS-8.1 states that it is acceptable to use handbook data, such as the data directly from the LA-10860-MS, as it is already considered validated (Section 4.3 _{4)} “Use of subcritical limit data provided in ANSI/ANS standards or accepted reference publications does not require further validation.”). This paper attempts to take a novel approach to visualize traditional critical mass curves and allows comparison with the amount of mass for which the k_{eff} is equal to the USL (calculational margin + margin of subcriticality). However, the intent is to plot the critical mass data along with USL, not to suggest that already accepted handbook data should have new and more rigorous requirements for validation.
Dynamical Analysis of the Hindmarsh-Rose Neuron With Time Delays.
Lakshmanan, S; Lim, C P; Nahavandi, S; Prakash, M; Balasubramaniam, P
2017-08-01
This brief is mainly concerned with a series of dynamical analyses of the Hindmarsh-Rose (HR) neuron with state-dependent time delays. The dynamical analyses focus on stability, Hopf bifurcation, as well as chaos and chaos control. Through the stability and bifurcation analysis, we determine that increasing the external current causes the excitable HR neuron to exhibit periodic or chaotic bursting/spiking behaviors and emit subcritical Hopf bifurcation. Furthermore, by choosing a fixed external current and varying the time delay, the stability of the HR neuron is affected. We analyze the chaotic behaviors of the HR neuron under a fixed external current through time series, bifurcation diagram, Lyapunov exponents, and Lyapunov dimension. We also analyze the synchronization of the chaotic time-delayed HR neuron through nonlinear control. Based on an appropriate Lyapunov-Krasovskii functional with triple integral terms, a nonlinear feedback control scheme is designed to achieve synchronization between the uncontrolled and controlled models. The proposed synchronization criteria are derived in terms of linear matrix inequalities to achieve the global asymptotical stability of the considered error model under the designed control scheme. Finally, numerical simulations pertaining to stability, Hopf bifurcation, periodic, chaotic, and synchronized models are provided to demonstrate the effectiveness of the derived theoretical results.
Control of Fold Bifurcation Application on Chemostat around Critical Dilution Rate
DEFF Research Database (Denmark)
Pedersen, Kurt; Jørgensen, Sten Bay
1999-01-01
Based on a bifurcation analysis of a process it is possible to point out where there might be operational problems due to change of stability of the process. One such change is investigated, Fold bifurcations. This type of bifurcation is associated with hysteresis/multiple steady states, which co...
A gravel-sand bifurcation : a simple model and the stability of the equilibrium states
Schielen, Ralph M.J.; Blom, Astrid
2017-01-01
A river bifurcation, can be found in, for instance, a river delta, in braided or anabranching reaches, and in manmade side channels in restored river reaches. Depending on the partitioning of water and sediment over the bifurcating branches, the bifurcation develops toward (a) a stable state with
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...
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...
Bifurcation analysis can unify ecological and evolutionary aspects of ecosystems.
Troost, T.A.; Kooi, B.W.; Kooijman, S.A.L.M.
2007-01-01
Bifurcation theory is commonly used to study the dynamical behaviour of ecosystems. It involves the analysis of points in the parameter space where the stability of the system changes qualitatively. Generally, such changes are related only to changes in environmental parameters, while the organism's
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 pr...
Bifurcation diagrams in relation to synchronization in chaotic systems
Indian Academy of Sciences (India)
We numerically study some of the three-dimensional dynamical systems which exhibit complete synchronization as well as generalized synchronization to show that these systems can be conveniently partitioned into equivalent classes facilitating the study of bifurcation diagrams within each class. We demonstrate how ...
Improved homoclinic predictor for Bogdanov-Takens bifurcation
Kuznetsov, Yuri; Meijer, Hil; Al Hdaibat, Bashir; Govaerts, Willy
2014-01-01
An improved homoclinic predictor at a generic codim 2 Bogdanov-Takens (BT) bifucation is derived. We use the classical ‘blow-up’ technique to reduce the canonical smooth normal form near a generic BT bifurcation to a perturbed Hamiltonian system. With a simple perturbation method, we derive explicit
Bifurcation analysis and the travelling wave solutions of the Klein ...
Indian Academy of Sciences (India)
Math. Comput. 189, 271 (2007); Li et al, Appl. Math. Comput. 175, 61 (2006)). Keywords. Klein–Gordon–Zakharov equations; travelling wave solutions; bifurcation analysis. PACS Nos 05.45.Yv; 2.30.Jr; 04.20.Jb .... level h, it is shown that the exact periodic solutions evolute into solitary wave solution. In ref. [27], by using the ...
Bifurcation analysis and the travelling wave solutions of the Klein ...
Indian Academy of Sciences (India)
In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by ...
Coronary bifurcation lesions treated with simple or complex stenting
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels R; de Belder, Adam J
2016-01-01
AIMS: Randomized trials of coronary bifurcation stenting have shown better outcomes from a simple (provisional) strategy rather than a complex (planned two-stent) strategy in terms of short-term efficacy and safety. Here, we report the 5-year all-cause mortality based on pooled patient-level data...
A simple SIS epidemic model with a backward bifurcation.
van den Driessche, P; Watmough, J
2000-06-01
It is shown that an SIS epidemic model with a non-constant contact rate may have multiple stable equilibria, a backward bifurcation and hysteresis. The consequences for disease control are discussed. The model is based on a Volterra integral equation and allows for a distributed infective period. The analysis includes both local and global stability of equilibria.
Bifurcation Analysis and Chaos Control in a Discrete Epidemic System
Directory of Open Access Journals (Sweden)
Wei Tan
2015-01-01
Full Text Available The dynamics of discrete SI epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail. By using the center manifold theorem and bifurcation theorem in the interior R+2, the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived. Numerical simulation not only presents our theoretical analysis but also exhibits rich and complex dynamical behavior existing in the case of the windows of period-1, period-3, period-5, period-6, period-7, period-9, period-11, period-15, period-19, period-23, period-34, period-42, and period-53 orbits. Meanwhile, there appears the cascade of period-doubling 2, 4, 8 bifurcation and chaos sets from the fixed point. These results show the discrete model has more richer dynamics compared with the continuous model. The computations of the largest Lyapunov exponents more than 0 confirm the chaotic behaviors of the system x→x+δ[rN(1-N/K-βxy/N-(μ+mx], y→y+δ[βxy/N-(μ+dy]. Specifically, the chaotic orbits at an unstable fixed point are stabilized by using the feedback control method.
Experimental bifurcation analysis of an impact oscillator – Determining stability
DEFF Research Database (Denmark)
Bureau, Emil; Schilder, Frank; Elmegård, Michael
2014-01-01
We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior. A...
Bifurcations of phase portraits of pendulum with vibrating suspension point
Neishtadt, A. I.; Sheng, K.
2017-06-01
We consider a simple pendulum whose suspension point undergoes fast vibrations in the plane of motion of the pendulum. The averaged over the fast vibrations system is a Hamiltonian system with one degree of freedom depending on two parameters. We give a complete description of bifurcations of phase portraits of this averaged system.
AEROSOL TRANSPORT AND DEPOSITION IN SEQUENTIALLY BIFURCATING AIRWAYS
Deposition patterns and efficiencies of a dilute suspension of inhaled particles in three-dimensional double bifurcating airway models for both in-plane and 90 deg out-of-plane configurations have been numerically simulated assuming steady, laminar, constant-property air flow wit...
Bifurcations of phase portraits of pendulum with vibrating suspension point
Neishtadt, Anatoly; Sheng, Kaicheng
2016-01-01
We consider a simple pendulum whose suspension point undergoes fast vibrations in the plane of motion of the pendulum. The averaged over the fast vibrations system is a Hamiltonian system with one degree of freedom depending on two parameters. We give complete description of bifurcations of phase portraits of this averaged system.
Race-ethnic variation in carotid bifurcation geometry.
Koch, Sebastian; Nelson, Donoffa; Rundek, Tatjana; Mandrekar, Jay; Rabinstein, Alejandro
2009-01-01
Disturbances in local blood flow influenced by arterial geometry contribute to atherogenesis. Carotid bifurcation hemodynamics depend on the relative sizes of the common carotid artery (CCA), internal carotid artery (ICA), and external carotid artery (ECA), which vary considerably among individuals. The prevalence of carotid bifurcation atherosclerosis differs among race-ethnic groups and is generally lower in African Americans despite a more adverse vascular risk factor profile. We here examine whether there are race-ethnic differences in carotid bifurcation anatomy. The diameters of the CCA, carotid bulb, ICA, and ECA were measured from consecutive cerebral angiograms of African American, white, and Caribbean Hispanic patients. The bulb/CCA, ICA/CCA, ECA/CCA, ECA/ICA, and total cross-sectional outflow/inflow ratio ([ICA(2) + ECA(2)]/CCA(2)) were calculated. The final analysis included 272 bifurcations of which 103 were among white, 87 Hispanic, and 82 African American patients. The mean age of the population was 59.8 +/- 15.8 years and 148 (54.4%) were men. African Americans had a lower ICA/CCA ratio (P ECA ratio (P ECA/CCA ratio (P groups. We found significant differences in the relative sizes of the ICA, ECA, and CCA among race-ethnic groups. African Americans had a proportionally smaller ICA and larger ECA in comparison with whites and Caribbean Hispanics.
Percutaneous transluminal angioplasty and stenting for carotid bifurcation stenosis
Vos, J.A.
2009-01-01
Carotid Endartectomy (CEA) has been proven to benefit patients with carotid bifurcation stenosis. For patients unfit for this therapy an alternative has been developed, namely Carotid Angioplasty and Stenting (CAS). No anesthesia or neck dissection is necessary in this procedure. In this thesis
Low-crosstalk bifurcation detectors for coupled flux qubits
De Groot, P.C.; Van Loo, A.F.; Lisenfeld, J.; Schouten, R.N.; Lupa?cu, A.; Harmans, C.J.P.M.; Mooij, J.E.
2010-01-01
We present experimental results on the crosstalk between two ac-operated dispersive bifurcation detectors, implemented in a circuit for high-fidelity readout of two strongly coupled flux qubits. Both phase-dependent and phase-independent contributions to the crosstalk are analyzed. For proper tuning
Numerical computation of bifurcations in large equilibrium systems in MATLAB.
Bindel, David; Friedman, Mark; Govaerts, Willy; Hughes, Jeremy; Kuznetsov, Yuri
2014-01-01
The Continuation of Invariant Subspaces (CIS) algorithm produces a smoothly-varying basis for an invariant subspace R(s) of a parameter-dependent matrix A(s). We have incorporated the CIS algorithm into Cl_matcont, a Matlab package for the study of dynamical systems and their bifurcations. Using
Perturbed period-doubling bifurcation. II. Experiments on Josephson junctions
DEFF Research Database (Denmark)
Eriksen, Gert Friis; Hansen, Jørn Bindslev
1990-01-01
We present experimental results on the effect of periodic perturbations on a driven, dynamic system that is close to a period-doubling bifurcation. In the preceding article a scaling law for the change of stability of such a system was derived for the case where the perturbation frequency ω...
The symplectic fermion ribbon quasi-Hopf algebra and the SL(2,Z)-action on its centre
Energy Technology Data Exchange (ETDEWEB)
Farsad, Vanda
2017-06-14
This thesis is concerned with ''N pairs of symplectic fermions'' which are examples of logarithmic conformal field theories in two dimensions. The mathematical language of two-dimensional conformal field theories (on Riemannian surfaces of genus zero) are vertex operator algebras. The representation category of the even part of the symplectic fermion vertex operator super-algebra Rep V{sub ev} is conjecturally a factorisable finite ribbon tensor category. This determines an isomorphism of projective representations between two SL(2,Z)-actions associated to V{sub ev}. The first action is obtained by modular transformations on the space of so-called pseudo-trace functions of a vertex operator algebra. For V{sub ev} this was developed by A.M.Gaberdiel and I. Runkel. For the action one uses that Rep V{sub ev} is conjecturally a factorisable finite ribbon tensor category and thus carries a projective SL(2,Z)-action on a certain Hom-space [Ly1,Ly2,KL]. To do so we calculate the SL(2,Z)-action on the representation category of a general factorisable quasi-Hopf algebras. Then we show that Rep V{sub ev} is conjecturally ribbon equivalent to Rep Q, for Q a factorisable quasi-Hopf algebra, and calculate the SL(2,Z)-action explicitly on Rep Q. The result is that the two SL(2,Z)-action indeed agree. This poses the first example of such comparison for logarithmic conformal field theories.
Control of Limit Cycle Oscillations of a Two-Dimensional Aeroelastic System
Directory of Open Access Journals (Sweden)
M. Ghommem
2010-01-01
Full Text Available Linear and nonlinear static feedback controls are implemented on a nonlinear aeroelastic system that consists of a rigid airfoil supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. The normal form is used to investigate the Hopf bifurcation that occurs as the freestream velocity is increased and to analytically predict the amplitude and frequency of the ensuing limit cycle oscillations (LCO. It is shown that linear control can be used to delay the flutter onset and reduce the LCO amplitude. Yet, its required gains remain a function of the speed. On the other hand, nonlinear control can be effciently implemented to convert any subcritical Hopf bifurcation into a supercritical one and to significantly reduce the LCO amplitude.
DEFF Research Database (Denmark)
Beier, Søren Prip; Jonsson, Gunnar Eigil
2007-01-01
A vibrating membrane bioreactor, in which the fouling problems are reduced by vibrating a hollow fiber membrane module, has been tested in constant flux microfiltration above (supra-critical) and below (sub-critical) an experimentally determined critical flux. Suspensions of bakers yeast cells were....... Filtration just below the critical flux (sub-critical) seems to be a good compromise between acceptable flux level and acceptable increase of fouling resistance and trans-membrane pressure (TMP) in a given time period. EPS from the yeast cells causes the membrane module to foul and part of the fouling...... is continually washed out during supra-critical flux operation whereas the washing out at sub-critical flux operation is not observed. This might be due to locally different hydrodynamic conditions at the membrane surface and pore entrances at supra- and sub-critical flux respectively....
Energy Technology Data Exchange (ETDEWEB)
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.
Subcritical water (hot water under enough pressure to maintain the liquid state) was used to remove polycyclic aromatic hydrocarbons (PAHs) and pesticides from highly contaminated soils. Laboratory-scale (8 g of soil) experiments were used to determine conditions f...
Research Programme for the 660 Mev Proton Accelerator Driven MOX-Plutonium Subcritical Assembly
Barashenkov, V S; Buttseva, G L; Dudarev, S Yu; Polanski, A; Puzynin, I V; Sissakian, A N
2000-01-01
The paper presents a research programme of the Experimental Acclerator Driven System (ADS), which employs a subcritical assembly and a 660 MeV proton acceletator operating at the Laboratory of Nuclear Problems of the JINR, Dubna. MOX fuel (25% PuO_2 + 75% UO_2) designed for the BN-600 reactor use will be adopted for the core of the assembly. The present conceptual design of the experimental subcritical assembly is based on a core of a nominal unit capacity of 15 kW (thermal). This corresponds to the multiplication coefficient k_eff = 0.945, energetic gain G = 30 and the accelerator beam power 0.5 kW.
Dzubiella, J; Chakrabarti, J; Löwen, H
2009-07-28
The distance-resolved effective interaction between two colloidal particles in a subcritical solvent is explored both by an explicit and implicit modeling. An implicit solvent approach based on a simple thermodynamic interface model is tested against grand-canonical Monte Carlo computer simulations using explicit Lennard-Jones solvent molecules. Close to liquid-gas coexistence, a joint gas bubble surrounding the colloidal particle pair yields an effective attraction between the colloidal particles, the strength of which can be vastly tuned by the solvophobicity of the colloids. The implicit model is in good agreement with our explicit computer simulations, thus enabling an efficient modeling and evaluation of colloidal interactions and self-assembly in subcritical solvent environments.
A fusion-driven subcritical system concept based on viable technologies
Wu, Y.; Jiang, J.; Wang, M.; Jin, M.; FDS Team
2011-10-01
A fusion-driven hybrid subcritical system (FDS) concept has been designed and proposed as spent fuel burner based on viable technologies. The plasma fusion driver can be designed based on relatively easily achieved plasma parameters extrapolated from the successful operation of existing fusion experimental devices such as the EAST tokamak in China and other tokamaks in the world, and the subcritical fission blanket can be designed based on the well-developed technologies of fission power plants. The simulation calculations and performance analyses of plasma physics, neutronics, thermal-hydraulics, thermomechanics and safety have shown that the proposed concept can meet the requirements of tritium self-sufficiency and sufficient energy gain as well as effective burning of nuclear waste from fission power plants and efficient breeding of nuclear fuel to feed fission power plants.
Directory of Open Access Journals (Sweden)
Peng Hu
2017-02-01
Full Text Available Electrothermal energy storage (ETES provides bulk electricity storage based on heat pump and heat engine technologies. A subcritical ETES is described in this paper. Based on the extremum principle of entransy dissipation, a geometry model is developed for heat transfer optimization for subcritical ETES. The exergy during the heat transfer process is deduced in terms of entropy production. The geometry model is validated by the extremum principle of entropy production. The theoretical analysis results show that the extremum principle of entransy dissipation is an effective criterion for the optimization, and the optimum heat transfer for different cases with the same mass flux or pressure has been discussed. The optimum heat transfer can be achieved by adjusting the mass flux and pressure of the working fluid. It also reveals that with the increase of mass flux, there is a minimum exergy in the range under consideration, and the exergy decreases with the increase of the pressure.
Determination of subcriticality and effective source strength by source drop and jerk experiments
Energy Technology Data Exchange (ETDEWEB)
Taninaka, Hiroshi [Interdisciplinary Graduate School of Science and Technology, Kinki University, 3-4-1, Kowakae, Higashi-Osaka, 577-8502 (Japan); Hashimoto, Kengo [Atomic Energy Research Institute, Kinki University, 3-4-1, Kowakae, Higashi-Osaka, 577-8502 (Japan)
2008-07-01
This paper presents applicability of least squares inverse kinetics method (LSIKM) to source drop and source jerk experiments. The LSIKM can estimate both reactivity and source strength by applying least square approximation to a correlation between time-sequence count data and inverse kinetics analysis data. The experiments were performed in the UTR-KINKI reactor to demonstrate the applicability of the LSIKM. To source jerk data, for comparison, conventional integral method is also applied. In the subcriticality and source strength obtained by the LSIKM, spatial dependence is slightly observed. However, the integral method leads to significant spatial dependence. The sub-criticalities inferred from source drop data are consistent with the results from source jerk data. (authors)
Influence of moderator to fuel ratio (MFR) on burning thorium in a subcritical assembly
Energy Technology Data Exchange (ETDEWEB)
Wojciechowski, Andrzej, E-mail: andrzej.wojciechowski@ncbj.gov.pl [National Center for Nuclear Research, Otwock-Swierk (Poland); Joint Institute for Nuclear Research, Dubna (Russian Federation)
2014-10-15
The conversion ratio (CR) of Th-232 to U-233 calculation results for a subcritical reactor assembly is presented as a function of MFR, burnup, power density (PD) and fissile concentration. The calculated model is based on subcritical assembly which makes configuration of fuel rods and volumes of moderator and coolant changes possible. This comfortable assembly enables investigation of CR in a thorium cycle for different value of MFR. Additionally, the calculation results of U-233 saturation concentration are explained by mathematical model. The value of MFR main influences the saturation concentration of U-233 and fissile and the fissile concentration dependence of CR. The saturation value of CR is included in the range CR ∈ (0.911, 0.966) and is a slowly increasing function of MFR. The calculations were done with a MCNPX 2.7 code.
Wang, Yongqiang; Gao, Yujie; Ding, Hui; Liu, Shejiang; Han, Xu; Gui, Jianzhou; Liu, Dan
2017-03-01
A large-scale process to extract flavonoids from Moringa oleifera leaf by subcritical ethanol was developed and HPLC-MS analysis was conducted to qualitatively identify the compounds in the extracts. To optimize the effects of process parameters on the yield of flavonoids, a Box-Behnken design combined with response surface methodology was conducted in the present work. The results indicated that the highest extraction yield of flavonoids by subcritical ethanol extraction could reach 2.60% using 70% ethanol at 126.6°C for 2.05h extraction. Under the optimized conditions, flavonoids yield was substantially improved by 26.7% compared with the traditional ethanol reflux method while the extraction time was only 2h, and obvious energy saving was observed. FRAP and DPPH assays showed that the extracts had strong antioxidant and free radical scavenging activities. Copyright © 2016 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Zafar Faisal
2017-09-01
Full Text Available The presence of naphthenic acids (NAs in crude oil is the major cause of corrosion in the refineries and its processing equipment. The goal of this study is to reduce the total acid number (TAN of NAs by treating them with subcritical methanol in the presence of acidic ionic liquid (AIL catalysts. Experiments were carried out in an autoclave batch reactor and the effect of different reaction parameters was investigated. It was observed that TAN reduction was positively dependent on the temperature and concentration of the AIL whereas excess of methanol has a negative effect. Approximately 90% TAN reduction was achieved under the optimized reaction conditions using [BMIM]HSO4 as catalyst. It was also perceived from the experimental results that the AILs with longer alkyl chain exhibited higher catalytic activity. The activity and stability of AIL showed that they can be promising catalyst to esterify NAs under subcritical methanol.
Zhang, Hongdan; Wu, Shubin
2014-04-01
Most biomass pretreatment processes for sugar production are run at low-solid concentration (carbon dioxide (CO2) could provide a more sustainable pretreatment medium while using relative high-solid contents (15 wt.%). The effects of subcritical CO2 pretreatment of sugarcane bagasse to the solid and glucan recoveries at different pretreatment conditions were investigated. Subsequently, enzymatic hydrolysis at different hydrolysis time was applied to obtain maximal glucose yield, which can be used for ethanol fermentation. The maximum glucose yield in enzyme hydrolyzate reached 38.5 g based on 100g raw material after 72 h of enzymatic hydrolysis, representing 93.0% glucose in sugarcane bagasse. The enhanced digestibilities of subcritical CO2 pretreated sugarcane bagasse were due to the removal of hemicellulose, which were confirmed by XRD, FTIR, SEM, and TGA analyses. Copyright © 2014 Elsevier Ltd. All rights reserved.
Equilibria of ternary system acetic acid-water-CO2 under subcritical conditions
DEFF Research Database (Denmark)
Gutierrez, Jose M. Jimenez; Mussatto, Solange I.; Tsou, Joana
in a very wide range of applications. However, those conditions, especially the levels of high pressure required at larger scale, involve certain equipment limitations. An alternative to overcome those restrictions is to use subcritical carbon dioxide. In order to understand the different systems......) of the ternary system HAc—H2O—CO2 at different subcritical conditions. A proposed computer model could be validated with experimental data, leading to a certain degree of adjustment due to specific factors, such as the binary interaction parameter kij, used in the model based on the Peng-Robinson EoS coupled...... it will be returned to the atmosphere (as part of the carbon cycle), CO2 is an inexpensive and clean source with numerous industrial applications in diverse fields: from chemical processes to biotechnological purposes [1]. Many of these studies have been focused on supercritical CO2, due to its broad potential uses...
Sub-Critical Closed String Field Theory in D Less Than 26
Kaku, Michio
1993-01-01
We construct the second quantized action for sub-critical closed string field theory with zero cosmological constant in dimensions $ 2 \\leq D < 26$, generalizing the non-polynomial closed string field theory action proposed by the author and the Kyoto and MIT groups for $D = 26$. The proof of gauge invariance is considerably complicated by the presence of the Liouville field $\\phi$ and the non-polynomial nature of the action. However, we explicitly show that the polyhedral vertex functions ob...
Ebrahimkhani, Marziye; Hassanzadeh, Mostafa; Feghhi, Sayed Amier Hossian; Masti, Darush
2016-01-01
Calculation of the core neutronic parameters is one of the key components in all nuclear reactors. In this research, the energy spectrum and spatial distribution of the neutron flux in a uranium target have been calculated. In addition, sensitivity of the core neutronic parameters in accelerator-driven subcritical advanced liquid metal reactors, such as electron beam energy (Ee) and source multiplication coefficient (ks), has been investigated. A Monte Carlo code (MCNPX_2.6) has been used to ...
Dhale, A D; Mahajani, V V
2001-06-01
Subcritical mineralization of sodium salt of dodecyl benzene sulfonate via hybrid process-sonication followed by wet oxidation (SONIWO) has been investigated. Sonication of the compound enhanced the rates and % COD reduction during wet oxidation. In this process, homogenous CuSO4 catalyst was found to be effective. In wet oxidation studies, phenol, hydroquinone, maleic acid, oxalic acid, propionic acid, and acetic acid were identified as intermediates. The global rate equations for wet oxidation in terms of COD reduction were developed.
Observation of subcritical geodesic acoustic mode excitation in the large helical device
Ido, T.; Itoh, K.; Lesur, M.; Osakabe, M.; Shimizu, A.; Ogawa, K.; Nishiura, M.; Yamada, I.; Yasuhara, R.; Kosuga, Y.; Sasaki, M.; Ida, K.; Inagaki, S.; Itoh, S.-I.; the LHD Experiment Group
2017-07-01
The abrupt and strong excitation of the geodesic acoustic mode (GAM) has been found in the large helical device (LHD), when the frequency of a chirping energetic particle-driven GAM (EGAM) approaches twice that of the GAM frequency. The temporal evolution of the phase relation between the abrupt GAM and the chirping EGAM is common in all events. The result indicates a coupling between the GAM and the EGAM. In addition, the nonlinear evolution of the growth rate of the GAM is observed, and there is a threshold in the amplitude of the GAM for the appearance of nonlinear behavior. A threshold in the amplitude of the EGAM for the abrupt excitation of the GAM is also observed. According to one theory (Lesur et al 2016 Phys. Rev. Lett. 116 015003, Itoh et al 2016 Plasma Phys. Rep. 42 418) the observed abrupt phenomenon can be interpreted as the excitation of the subcritical instability of the GAM. The excitation of a subcritical instability requires a trigger and a seed with sufficient amplitude. The observed threshold in the amplitude of the GAM seems to correspond with the threshold in the seed, and the threshold in the amplitude of the EGAM seems to correspond with the threshold in the magnitude of the trigger. Thus, the observed threshold supports the interpretation that the abrupt phenomenon is the excitation of a subcritical instability of the GAM.
Efficient decomposition of perchlorate to chloride ions in subcritical water by use of steel slag.
Hori, Hisao; Kamijo, Ayae; Inoue, Miki; Chino, Asako; Wu, Qian; Kannan, Kurunthachalam
2016-08-03
Decomposition of perchlorate (ClO4(-)) in subcritical water in the presence of steel slag, a by-product of the steel industry, was investigated. Reactivity of ClO4(-) was low in pure subcritical water state up to 300 °C, whereas adding steel slag efficiently accelerated the decomposition of ClO4(-) to Cl(-), with no leaching of heavy metals such as chromium and other environmentally undesirable elements (boron and fluorine). When the reaction was performed in subcritical water at a relatively low temperature (250 °C) for 6 h, virtually all ClO4(-) ions were removed from the reaction solution. The concentration of Cl(-) after the reaction was well accounted for by the sum of the amount of Cl(-) ascribed to the decomposition of ClO4(-) and the amount of Cl(-) leached from the slag. This method was successfully applied to decompose ClO4(-) in water samples collected from a man-made reflection pond following a fireworks display, even though these samples contained much higher concentrations of Cl(-) and SO4(2-) than ClO4(-).
Energy Technology Data Exchange (ETDEWEB)
Talamo, Alberto [Argonne National Lab. (ANL), Argonne, IL (United States). Nuclear Engineering Division; Gohar, Yousry [Argonne National Lab. (ANL), Argonne, IL (United States). Nuclear Engineering Division
2016-06-01
This report describes different methodologies to calculate the effective neutron multiplication factor of subcritical assemblies by processing the neutron detector signals using MATLAB scripts. The subcritical assembly can be driven either by a spontaneous fission neutron source (e.g. californium) or by a neutron source generated from the interactions of accelerated particles with target materials. In the latter case, when the particle accelerator operates in a pulsed mode, the signals are typically stored into two files. One file contains the time when neutron reactions occur and the other contains the times when the neutron pulses start. In both files, the time is given by an integer representing the number of time bins since the start of the counting. These signal files are used to construct the neutron count distribution from a single neutron pulse. The built-in functions of MATLAB are used to calculate the effective neutron multiplication factor through the application of the prompt decay fitting or the area method to the neutron count distribution. If the subcritical assembly is driven by a spontaneous fission neutron source, then the effective multiplication factor can be evaluated either using the prompt neutron decay constant obtained from Rossi or Feynman distributions or the Modified Source Multiplication (MSM) method.
Th and U fuel photofission study by NTD for AD-MSR subcritical assembly
Energy Technology Data Exchange (ETDEWEB)
Sajo-Bohus, Laszlo; Greaves, Eduardo D.; Barros, Haydn; Pino, Felix; Barrera, Maria T.; Farina, Fulvio [Universidad Simón Bolívar, Nuclear Physics Laboratory, Apdo 89000, Caracas 1080A (Venezuela, Bolivarian Republic of); Davila, Jesus [Física Médica C. A. and Universidad Central de Venezuela, Caracas (Venezuela, Bolivarian Republic of)
2015-07-23
During the last decade a considerable effort has been devoted for developing energy generating systems based on advanced nuclear technology within the design concepts of GEN-IV. Thorium base fuel systems such as accelerator driven nuclear reactors are one of the often mentioned attractive and affordable options. Several radiotherapy linear accelerators are on the market and due to their reliability, they could be employed as drivers for subcritical liquid fuel assemblies. Bremsstrahlung photons with energies above 5.5MeV, induce (γ,n) and (e,e’n) reactions in the W-target. Resulting gamma radiation and photo or fission neutrons may be absorbed in target materials such as thorium and uranium isotopes to induce sustained fission or nuclear transmutation in waste radioactive materials. Relevant photo driven and photo-fission reaction cross sections are important for actinides {sup 232}Th, {sup 238}U and {sup 237}Np in the radiotherapy machines energy range of 10-20 MV. In this study we employ passive nuclear track detectors (NTD) to determine fission rates and neutron production rates with the aim to establish the feasibility for gamma and photo-neutron driven subcritical assemblies. To cope with these objectives a 20 MV radiotherapy machine has been employed with a mixed fuel target. Results will support further development for a subcritical assembly employing a thorium containing liquid fuel. It is expected that acquired technological knowledge will contribute to the Venezuelan nuclear energy program.
Bifurcation study of blood flow control in the kidney
Ford Versypt, Ashlee N.; Makrides, Elizabeth; Arciero, Julia C.; Ellwein, Laura; Layton, Anita T.
2016-01-01
Renal blood flow is maintained within a narrow window by a set of intrinsic autoregulatory mechanisms. Here, a mathematical model of renal hemodynamics control in the rat kidney is used to understand the interactions between two major renal autoregulatory mechanisms: the myogenic response and tubuloglomerular feedback. A bifurcation analysis of the model equations is performed to assess the effects of the delay and sensitivity of the feedback system and the time constants governing the response of vessel diameter and smooth muscle tone. The results of the bifurcation analysis are verified using numerical simulations of the full nonlinear model. Both the analytical and numerical results predict the generation of limit cycle oscillations under certain physiologically relevant conditions, as observed in vivo. PMID:25747903
Bifurcations and Crises in a Shape Memory Oscillator
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Luciano G. Machado
2004-01-01
Full Text Available The remarkable properties of shape memory alloys have been motivating the interest in applications in different areas varying from biomedical to aerospace hardware. The dynamical response of systems composed by shape memory actuators presents nonlinear characteristics and a very rich behavior, showing periodic, quasi-periodic and chaotic responses. This contribution analyses some aspects related to bifurcation phenomenon in a shape memory oscillator where the restitution force is described by a polynomial constitutive model. The term bifurcation is used to describe qualitative changes that occur in the orbit structure of a system, as a consequence of parameter changes, being related to chaos. Numerical simulations show that the response of the shape memory oscillator presents period doubling cascades, direct and reverse, and crises.
Local bifurcations in differential equations with state-dependent delay.
Sieber, Jan
2017-11-01
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.
Power-dependent internal loss in Josephson bifurcation amplifiers
Watanabe, Michio; Inomata, Kunihiro; Yamamoto, Tsuyoshi; Tsai, Jaw-Shen
2009-11-01
We have studied nonlinear superconducting resonators: λ/2 coplanar-waveguide (CPW) resonators with Josephson junctions (JJs) placed in the middle and λ/4 CPW resonators terminated by JJs, which can be used for the qubit readout as “bifurcation amplifiers.” The nonlinearity of the resonators arises from the Josephson junctions, and because of the nonlinearity, the resonators with appropriate parameters are expected to show a hysteretic response to the frequency sweep, or “bifurcation,” when they are driven with a sufficiently large power. We designed and fabricated resonators whose resonant frequencies were around 10 GHz. We characterized the resonators at low temperatures, Tresonators with increasing drive power in the relevant power range. As a possible origin of the power-dependent loss, the quasiparticle channel of conductance of the JJs is discussed.
A bifurcation analysis for the Lugiato-Lefever equation
Godey, Cyril
2017-05-01
The Lugiato-Lefever equation is a cubic nonlinear Schrödinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a four-dimensional reversible dynamical system in which the evolutionary variable is the space variable. Relying upon tools from bifurcation theory and normal forms theory, we discuss the codimension 1 bifurcations. We prove the existence of various types of steady solutions, including spatially localized, periodic, or quasi-periodic solutions. Contribution to the Topical Issue: "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.
Local bifurcations in differential equations with state-dependent delay
Sieber, Jan
2017-11-01
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.
Bifurcation analysis of the regulation of nociceptive neuronal activity
Dik, O. E.
2017-11-01
A model of the membrane of a nociceptive neuron from a rat dorsal ganglion has been used to address the problem of analyzing the regulation of nociceptive signals by 5-hydroxy-γ-pyrone-2-carboxylic acid, which is the active pharmaceutic ingredient of the analgesic Anoceptin. The study has applied bifurcation analysis to report the relationship between the values of model parameters and the type of problem solution before and after the parameters change in response to analgesic modulation.
Application of the bifurcation method to the modified Boussinesq equation
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Shaoyong Li
2014-08-01
Firstly, we give a property of the solutions of the equation, that is, if $1+u(x, t$ is a solution, so is $1-u(x, t$. Secondly, by using the bifurcation method of dynamical systems we obtain some explicit expressions of solutions for the equation, which include kink-shaped solutions, blow-up solutions, periodic blow-up solutions and solitary wave solutions. Some previous results are extended.
Bifurcation for non linear ordinary differential equations with singular perturbation
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Safia Acher Spitalier
2016-10-01
Full Text Available We study a family of singularly perturbed ODEs with one parameter and compare their solutions to the ones of the corresponding reduced equations. The interesting characteristic here is that the reduced equations have more than one solution for a given set of initial conditions. Then we consider how those solutions are organized for different values of the parameter. The bifurcation associated to this situation is studied using a minimal set of tools from non standard analysis.
An alternative bifurcation analysis of the Rose-Hindmarsh model
Energy Technology Data Exchange (ETDEWEB)
Nikolov, Svetoslav [Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia (Bulgaria)]. E-mail: s.nikolov@imbm.bas.bg
2005-03-01
The paper presents an alternative study of the bifurcation behavior of the Rose-Hindmarsh model using Lyapunov-Andronov's theory. This is done on the basis of the obtained analytical formula expressing the first Lyapunov's value (this is not Lyapunov exponent) at the boundary of stability. From the obtained results the following new conclusions are made: Transition to chaos and the occurrence of chaotic oscillations in the Rose-Hindmarsh system take place under hard stability loss.
Time-Periodic Einstein-Klein-Gordon Bifurcations of Kerr
Chodosh, Otis; Shlapentokh-Rothman, Yakov
2017-12-01
We construct one-parameter families of solutions to the Einstein-Klein-Gordon equations bifurcating off the Kerr solution such that the underlying family of spacetimes are each an asymptotically flat, stationary, axisymmetric, black hole spacetime, and such that the corresponding scalar fields are non-zero and time-periodic. An immediate corollary is that for these Klein-Gordon masses, the Kerr family is not asymptotically stable as a solution to the Einstein-Klein-Gordon equations.
Bifurcation of solutions of nonlinear Sturm–Liouville problems
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Gulgowski Jacek
2001-01-01
Full Text Available A global bifurcation theorem for the following nonlinear Sturm–Liouville problem is given Moreover we give various versions of existence theorems for boundary value problems The main idea of these proofs is studying properties of an unbounded connected subset of the set of all nontrivial solutions of the nonlinear spectral problem , associated with the boundary value problem , in such a way that .
Bifurcation kinetics of drug uptake by Gram-negative bacteria.
Westfall, David A; Krishnamoorthy, Ganesh; Wolloscheck, David; Sarkar, Rupa; Zgurskaya, Helen I; Rybenkov, Valentin V
2017-01-01
Cell envelopes of many bacteria consist of two membranes studded with efflux transporters. Such organization protects bacteria from the environment and gives rise to multidrug resistance. We report a kinetic model that accurately describes the permeation properties of this system. The model predicts complex non-linear patterns of drug uptake complete with a bifurcation, which recapitulate the known experimental anomalies. We introduce two kinetic parameters, the efflux and barrier constants, which replace those of Michaelis and Menten for trans-envelope transport. Both compound permeation and efflux display transitions, which delineate regimes of efficient and inefficient efflux. The first transition is related to saturation of the transporter by the compound and the second one behaves as a bifurcation and involves saturation of the outer membrane barrier. The bifurcation was experimentally observed in live bacteria. We further found that active efflux of a drug can be orders of magnitude faster than its diffusion into a cell and that the efficacy of a drug depends both on its transport properties and therapeutic potency. This analysis reveals novel physical principles in the behavior of the cellular envelope, creates a framework for quantification of small molecule permeation into bacteria, and should invigorate structure-activity studies of novel antibiotics.
Stability and bifurcation for Marchuk's model of an immune system
Marzuki, Ira Syazwani Mohamad; Roslan, Ummu'Atiqah Mohd
2017-08-01
The investigation of an immune system has long been and will continue to be one of dominant themes in both ecology and biology due to its importance. In this paper, we consider Marchuk's model of an immune system where this model is governed by a system of three differential equations with time. This model has two equilibrium states which are healthy state and chronic state. It is healthy state when the antigen reproduction is small while chronic state is when antigen reproduction rate is large. The objectives of this paper are to analyse the stability of this model, to summarize this stability using bifurcation diagram and to discuss interaction between the healthy and chronic states at stationary solution. The methods involved are stability theory and bifurcation theory. Our results show that healthy states are saddle and only one chronic state is asymptotically stable for a region of parameter considered. For the bifurcation's case, as we increase the value of a parameter in this model, the chronic state shows that there are increment in the number of antigen, plasma cell and the antibody production.
Bifurcation in autonomous and nonautonomous differential equations with discontinuities
Akhmet, Marat
2017-01-01
This book is devoted to bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types. That is, those with jumps present either in the right-hand-side or in trajectories or in the arguments of solutions of equations. The results obtained in this book can be applied to various fields such as neural networks, brain dynamics, mechanical systems, weather phenomena, population dynamics, etc. Without any doubt, bifurcation theory should be further developed to different types of differential equations. In this sense, the present book will be a leading one in this field. The reader will benefit from the recent results of the theory and will learn in the very concrete way how to apply this theory to differential equations with various types of discontinuity. Moreover, the reader will learn new ways to analyze nonautonomous bifurcation scenarios in these equations. The book will be of a big interest both for beginners and experts in the field. For the former group o...
Intermittency and bifurcation in SEPICs under voltage-mode control
Liu, Fang
2010-08-01
A stroboscopic map for voltage-controlled single ended primary inductor converter (SEPIC) with pulse width modulation (PWM) is presented, where low-frequency oscillating phenomena such as quasi-periodic and intermittent quasi-periodic bifurcations occurring in the system are captured by numerical and experimental methods. According to bifurcation diagrams and nonlinear dynamical theory, the characteristics of the low-frequency oscillation and the mechanism for the appearance of the low-frequency oscillation are investigated. It is shown that as the controller parameter varies, the change in the conduction mode takes place from the continuous conduction mode (CCM) under the originally stable period one and high periodic orbits to the intermittent changes between CCM and discontinuous conduction mode (DCM), which may be related to the losing stability of the system and brought the system to exhibiting low-frequency oscillating behaviour in the time domain. Moreover, the occurrence of the intermittent quasi-periodic oscillation reflects that the system undergoes a Neimark-Sacker bifurcation.
Reverse bifurcation and fractal of the compound logistic map
Wang, Xingyuan; Liang, Qingyong
2008-07-01
The nature of the fixed points of the compound logistic map is researched and the boundary equation of the first bifurcation of the map in the parameter space is given out. Using the quantitative criterion and rule of chaotic system, the paper reveal the general features of the compound logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the map may emerge out of double-periodic bifurcation and (2) the chaotic crisis phenomena and the reverse bifurcation are found. At the same time, we analyze the orbit of critical point of the compound logistic map and put forward the definition of Mandelbrot-Julia set of compound logistic map. We generalize the Welstead and Cromer's periodic scanning technology and using this technology construct a series of Mandelbrot-Julia sets of compound logistic map. We investigate the symmetry of Mandelbrot-Julia set and study the topological inflexibility of distributing of period region in the Mandelbrot set, and finds that Mandelbrot set contain abundant information of structure of Julia sets by founding the whole portray of Julia sets based on Mandelbrot set qualitatively.
Estimating the stochastic bifurcation structure of cellular networks.
Directory of Open Access Journals (Sweden)
Carl Song
2010-03-01
Full Text Available High throughput measurement of gene expression at single-cell resolution, combined with systematic perturbation of environmental or cellular variables, provides information that can be used to generate novel insight into the properties of gene regulatory networks by linking cellular responses to external parameters. In dynamical systems theory, this information is the subject of bifurcation analysis, which establishes how system-level behaviour changes as a function of parameter values within a given deterministic mathematical model. Since cellular networks are inherently noisy, we generalize the traditional bifurcation diagram of deterministic systems theory to stochastic dynamical systems. We demonstrate how statistical methods for density estimation, in particular, mixture density and conditional mixture density estimators, can be employed to establish empirical bifurcation diagrams describing the bistable genetic switch network controlling galactose utilization in yeast Saccharomyces cerevisiae. These approaches allow us to make novel qualitative and quantitative observations about the switching behavior of the galactose network, and provide a framework that might be useful to extract information needed for the development of quantitative network models.
Bifurcation control for the Zakharov-Kusnetsov equation
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Maccari, Attilio, E-mail: solitone@yahoo.i [Via Alfredo Casella 3, 00013 Mentana (Rome) (Italy)
2010-05-01
We consider the bifurcation control for the forced Zakharov-Kusnetsov (ZK) equation by means of delay feedback linear control terms. Using a perturbation method, we obtain two slow flow equations on the amplitude and phase of the response as well as external force-response and frequency-response curves for the fundamental resonance. We observe in the resonance response for the uncontrolled system a saddle-center bifurcation, jumps and hysteresis phenomena and, using energy considerations, we show the existence of closed orbits of the slow flow equations. A limit cycle corresponds to a two-period quasi-periodic modulated motion for the ZK equation and we demonstrate that, in certain cases, a second low frequency appears in addition to the forcing frequency and then stable two-period quasi-periodic motions are present with amplitudes depending on the initial conditions. The value of the low frequency depends on the amplitude of the external excitation. Subsequently, we compare the uncontrolled and controlled systems and, to reduce the amplitude peak of the fundamental resonance and to remove saddle-center bifurcations and two-period quasi-periodic motions, we find appropriate choices of the feedback gains and time delay.
Bifurcation of solutions of separable parameterized equations into lines
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Yun-Qiu Shen
2010-09-01
Full Text Available Many applications give rise to separable parameterized equations of the form $A(y, muz+b(y, mu=0$, where $y in mathbb{R}^n$, $z in mathbb{R}^N$ and the parameter $mu in mathbb{R}$; here $A(y, mu$ is an $(N+n imes N$ matrix and $b(y, mu in mathbb{R}^{N+n}$. Under the assumption that $A(y,mu$ has full rank we showed in [21] that bifurcation points can be located by solving a reduced equation of the form $f(y, mu=0$. In this paper we extend that method to the case that $A(y,mu$ has rank deficiency one at the bifurcation point. At such a point the solution curve $(y,mu,z$ branches into infinitely many additional solutions, which form a straight line. A numerical method for reducing the problem to a smaller space and locating such a bifurcation point is given. Applications to equilibrium solutions of nonlinear ordinary equations and solutions of discretized partial differential equations are provided.
Electromagnetic two-body problem: recurrent dynamics in the presence of state-dependent delay
Energy Technology Data Exchange (ETDEWEB)
De Luca, Jayme [Departamento de Fisica, Universidade Federal de Sao Carlos, Caixa Postal 676, Sao Carlos, Sao Paulo 13565-905 (Brazil); Guglielmi, Nicola [Dipartimento di Matematica Pura ed Applicata, Universita degli Studi di L' Aquila, I-67010, L' Aquila (Italy); Humphries, Tony [Department of Mathematics and Statistics, McGill University, Montreal, Quebec H3A 2K6 (Canada); Politi, Antonio, E-mail: deluca@df.ufscar.b [Istituto dei Sistemi Complessi, CNR Via Madonna del Piano 10-Sesto, Fiorentino I-50019 (Italy)
2010-05-21
We study the electromagnetic two-body problem of classical electrodynamics as a prototype dynamical system with state-dependent delays. The equations of motion are analysed with reference to motion along a straight line in the presence of an electrostatic field. We consider the general electromagnetic equations of motion for point charges with advanced and retarded interactions and study two limits, (a) retarded-only interactions (Dirac electrodynamics) and (b) half-retarded plus half-advanced interactions (Wheeler-Feynman electrodynamics). A fixed point is created where the electrostatic field balances the Coulombian attraction, and we use local analysis near this fixed point to derive necessary conditions for a Hopf bifurcation. In case (a), we study a Hopf bifurcation about an unphysical fixed point and find that it is subcritical. In case (b), there is a Hopf bifurcation about a physical fixed point and we study several families of periodic orbits near this point. The bifurcating periodic orbits are illustrated and simulated numerically, by introducing a surrogate dynamical system into the numerical analysis which transforms future data into past data by exploiting the periodicity, thus obtaining systems with only delays.
Codimension-Two Bifurcation Analysis in DC Microgrids Under Droop Control
Lenz, Eduardo; Pagano, Daniel J.; Tahim, André P. N.
This paper addresses local and global bifurcations that may appear in electrical power systems, such as DC microgrids, which recently has attracted interest from the electrical engineering society. Most sources in these networks are voltage-type and operate in parallel. In such configuration, the basic technique for stabilizing the bus voltage is the so-called droop control. The main contribution of this work is a codimension-two bifurcation analysis of a small DC microgrid considering the droop control gain and the power processed by the load as bifurcation parameters. The codimension-two bifurcation set leads to practical rules for achieving a robust droop control design. Moreover, the bifurcation analysis also offers a better understanding of the dynamics involved in the problem and how to avoid possible instabilities. Simulation results are presented in order to illustrate the bifurcation analysis.
Dynamical Analysis and Big Bang Bifurcations of 1D and 2D Gompertz's Growth Functions
Rocha, J. Leonel; Taha, Abdel-Kaddous; Fournier-Prunaret, D.
In this paper, we study the dynamics and bifurcation properties of a three-parameter family of 1D Gompertz's growth functions, which are defined by the population size functions of the Gompertz logistic growth equation. The dynamical behavior is complex leading to a diversified bifurcation structure, leading to the big bang bifurcations of the so-called “box-within-a-box” fractal type. We provide and discuss sufficient conditions for the existence of these bifurcation cascades for 1D Gompertz's growth functions. Moreover, this work concerns the description of some bifurcation properties of a Hénon's map type embedding: a “continuous” embedding of 1D Gompertz's growth functions into a 2D diffeomorphism. More particularly, properties that characterize the big bang bifurcations are considered in relation with this coupling of two population size functions, varying the embedding parameter. The existence of communication areas of crossroad area type or swallowtails are identified for this 2D diffeomorphism.
Schomerus, H
1997-01-01
We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems with one degree of freedom is presented. We derive uniform approximations to be used in semiclassical trace formulas and determine also certain global bifurcations in conjunction with Stokes transitions that become important in the ensuing diffraction catastrophe integrals.
Critical Points and Bifurcations of the Three-Dimensional Onsager Model for Liquid Crystals
Vollmer, Michaela A. C.
2017-11-01
We study the bifurcation diagram of the Onsager free-energy functional for liquid crystals with orientation parameter on the sphere. In particular, we concentrate on the bifurcations from the isotropic solution for a general class of two-body interaction potentials including the Onsager kernel. Reformulating the problem as a non-linear eigenvalue problem for the kernel operator, we prove that spherical harmonics are the corresponding eigenfunctions and we present a direct relationship between the coefficients of the Taylor expansion of this class of interaction potentials and their eigenvalues. We find explicit expressions for all bifurcation points corresponding to bifurcations from the isotropic state of the Onsager free-energy functional equipped with the Onsager interaction potential. A substantial amount of our analysis is based on the use of spherical harmonics and a special algorithm for computing expansions of products of spherical harmonics in terms of spherical harmonics is presented. Using a Lyapunov-Schmidt reduction, we derive a bifurcation equation depending on five state variables. The dimension of this state space is further reduced to two dimensions by using the rotational symmetry of the problem and the invariant theory of groups. On the basis of these results, we show that the first bifurcation from the isotropic state of the Onsager interaction potential is a transcritical bifurcation and that the corresponding solution is uniaxial. In addition, we prove some global properties of the bifurcation diagram such as the fact that the trivial solution is the unique local minimiser if the bifurcation parameter is high, that it is not a local minimiser if the bifurcation parameter is small, the boundedness of all equilibria of the functional and that the bifurcation branches are either unbounded or that they meet another bifurcation branch.
National Research Council Canada - National Science Library
Luo, Kang; Yi, Hong-Liang; Tan, He-Ping
2014-01-01
Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct...
Evaluation of reactivity monitoring techniques at the Yalina - Booster sub-critical facility
Energy Technology Data Exchange (ETDEWEB)
Becares Palacios, V.
2014-07-01
The management of long-lived radioactive wastes produced by nuclear reactors constitutes one of the main challenges of nuclear technology nowadays. A possible option for its management consists in the transmutation of long lived nuclides into shorter lived ones. Accelerator Driven Subcritical Systems (ADS) are one of the technologies in development to achieve this goal. An ADS consists in a subcritical nuclear reactor maintained in a steady state by an external neutron source driven by a particle accelerator. The interest of these systems lays on its capacity to be loaded with fuels having larger contents of minor actinides than conventional critical reactors, and in this way, increasing the transmutation rates of these elements, that are the main responsible of the long-term radiotoxicity of nuclear waste. One of the key points that have been identified for the operation of an industrial-scale ADS is the need of continuously monitoring the reactivity of the subcritical system during operation. For this reason, since the 1990s a number of experiments have been conducted in zero-power subcritical assemblies (MUSE, RACE, KUCA, Yalina, GUINEVERE/FREYA) in order to experimentally validate these techniques. In this context, the present thesis is concerned with the validation of reactivity monitoring techniques at the Yalina-Booster subcritical assembly. This assembly belongs to the Joint Institute for Power and Nuclear Research (JIPNR-Sosny) of the National Academy of Sciences of Belarus. Experiments concerning reactivity monitoring have been performed in this facility under the EUROTRANS project of the 6th EU Framework Program in year 2008 under the direction of CIEMAT. Two types of experiments have been carried out: experiments with a pulsed neutron source (PNS) and experiments with a continuous source with short interruptions (beam trips). For the case of the first ones, PNS experiments, two fundamental techniques exist to measure the reactivity, known as the prompt
Energy Technology Data Exchange (ETDEWEB)
Rodriguez, David; Merwin, Augustus; Karmiol, Zachary; Chidambaram, Dev, E-mail: dcc@unr.edu
2017-05-15
Highlights: • Mixtures of oxides containing Ni, Fe, Cr and Nb formed on the surface. • Short term exposure tests observed breakdown of native film. • Formation of a Fe rich oxide layer on Inconel 718 prevents mass loss. - Abstract: Corrosion behavior of Inconel 625 and 718 in subcritical, supercritical and ultrasupercritical water was studied as a function of temperature and time. The change in the chemistry of the as-received surface film on Inconel 625 and 718 after exposure to subcritical water at 325 °C and supercritical water at 425 °C and 527.5 °C for 2 h was studied. After exposure to 325 °C subcritical water, the CrO{sub 4}{sup 2−} based film formed; however minor quantities of NiFe{sub x}Cr{sub 2-x}O{sub 4} spinel compounds were observed. The oxide film formed on both alloys when exposed to supercritical water at 425 °C consisted of NiFe{sub x}Cr{sub 2-x}O{sub 4} spinel. The surface films on both alloys were identified as NiFe{sub 2}O{sub 4} when exposed to supercritical water at 527.5 °C. To characterize the fully developed oxide layer, studies were conducted at test solution temperatures of 527.5 and 600 °C. Samples were exposed to these temperatures for 24, 96, and 200 h. Surface chemistry was analyzed using X-ray diffraction, as well as Raman and X-ray photoelectron spectroscopies. Inconel 718 exhibited greater mass gain than Inconel 625 for all temperatures and exposure times. The differences in corrosion behavior of the two alloys are attributed to the lower content of chromium and increased iron content of Inconel 718 as compared to Inconel 625.
Rodriguez, David; Merwin, Augustus; Karmiol, Zachary; Chidambaram, Dev
2017-05-01
Corrosion behavior of Inconel 625 and 718 in subcritical, supercritical and ultrasupercritical water was studied as a function of temperature and time. The change in the chemistry of the as-received surface film on Inconel 625 and 718 after exposure to subcritical water at 325 °C and supercritical water at 425 °C and 527.5 °C for 2 h was studied. After exposure to 325 °C subcritical water, the CrO42- based film formed; however minor quantities of NiFexCr2-xO4 spinel compounds were observed. The oxide film formed on both alloys when exposed to supercritical water at 425 °C consisted of NiFexCr2-xO4 spinel. The surface films on both alloys were identified as NiFe2O4 when exposed to supercritical water at 527.5 °C. To characterize the fully developed oxide layer, studies were conducted at test solution temperatures of 527.5 and 600 °C. Samples were exposed to these temperatures for 24, 96, and 200 h. Surface chemistry was analyzed using X-ray diffraction, as well as Raman and X-ray photoelectron spectroscopies. Inconel 718 exhibited greater mass gain than Inconel 625 for all temperatures and exposure times. The differences in corrosion behavior of the two alloys are attributed to the lower content of chromium and increased iron content of Inconel 718 as compared to Inconel 625.
Stochastic Calculus: Application to Dynamic Bifurcations and Threshold Crossings
Jansons, Kalvis M.; Lythe, G. D.
1998-01-01
For the dynamic pitchfork bifurcation in the presence of white noise, the statistics of the last time at zero are calculated as a function of the noise level ∈ and the rate of change of the parameter μ. The threshold crossing problem used, for example, to model the firing of a single cortical neuron is considered, concentrating on quantities that may be experimentally measurable but have so far received little attention. Expressions for the statistics of pre-threshold excursions, occupation density, and last crossing time of zero are compared with results from numerical generation of paths.
Bifurcation analysis of dengue transmission model in Baguio City, Philippines
Libatique, Criselda P.; Pajimola, Aprimelle Kris J.; Addawe, Joel M.
2017-11-01
In this study, we formulate a deterministic model for the transmission dynamics of dengue fever in Baguio City, Philippines. We analyzed the existence of the equilibria of the dengue model. We computed and obtained conditions for the existence of the equilibrium states. Stability analysis for the system is carried out for disease free equilibrium. We showed that the system becomes stable under certain conditions of the parameters. A particular parameter is taken and with the use of the Theory of Centre Manifold, the proposed model demonstrates a bifurcation phenomenon. We performed numerical simulation to verify the analytical results.
One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Mosekilde, Erik
1996-01-01
The paper presents a qualitative analysis of coupled map lattices (CMLs) for the case of arbitrary nonlinearity of the local map and with space-shift as well as diffusion coupling. The effect of synchronization where, independently of the initial conditions, all elements of a CML acquire uniform...... dynamics is investigated and stable chaotic time behaviors, steady structures, and traveling waves are described. Finally, the bifurcations occurring under the transition from spatiotemporal chaos to chaotic synchronization and the peculiarities of CMLs with specific symmetries are discussed....
Plastic bottle oscillator: Rhythmicity and mode bifurcation of fluid flow
Kohira, Masahiro I.; Magome, Nobuyuki; Kitahata, Hiroyuki; Yoshikawa, Kenichi
2007-01-01
The oscillatory flow of water draining from an upside-down plastic bottle with a thin pipe attached to its head is studied as an example of a dissipative structure generated under far-from-equilibrium conditions. Mode bifurcation was observed in the water/air flow: no flow, oscillatory flow, and counter flow were found when the inner diameter of the thin pipe was changed. The modes are stable against perturbations. A coupled two-bottle system exhibits either in-phase or anti-phase self-synchr...
Bifurcation in the chemotactic behavior of Physarum plasmodium
Shirakawa, Tomohiro; Gunji, Yukio-Pegio; Sato, Hiroshi; Tsubakino, Hiroto
2017-07-01
The plasmodium of true slime mold Physarum polycephalum is a unicellular and multinuclear giant amoeba. Since the cellular organism has some computational abilities, it is attracting much attention in the field of information science. However, previous studies have mainly focused on the optimization behavior of the plasmodium for a single-modality stimulus, and there are few studies on how the organism adapts to multi-modal stimuli. We stimulated the plasmodium with mixture of attractant and repellent stimuli, and we observed bifurcation in the chemotactic behavior of the plasmodium.
Chen Hai Yan
2002-01-01
Numerical simulations of flow field were performed by using the PHOENICS 3.2 code for the proposed spallation target of accelerator-driven subcritical reactor system (ADS). The fluid motion in the target is axisymmetric and is treated as a 2-D steady-state problem. A body-fitted coordinate system (BFC) is then chosen and a two-dimensional mesh of the flow channel is generated. Results are presented for the ADS target under both upward and downward flow, and for the target with diffuser plate installed below the window under downward flow
Yu Qi; Xu Tao Guang
2002-01-01
As a prior option of the next generation of energy source, the accelerator driven subcritical nuclear power system (ADS) can use efficiently the uranium and thorium resource, transmute the high-level long-lived radioactive wastes and raise nuclear safety. The ADS accelerator should provide the proton beam with tens megawatts. The superconducting linac (SCL) is a good selection of ADS accelerator because of its high efficiency and low beam loss rate. It is constitute by a series of the superconducting accelerating cavities. The cavity geometry is determined by means of the electromagnetic field computation. The SCL main parameters are determined by the particle dynamics computation
Subcritical experiments at the FREYA experiment; Experimentos subcriticos en el proyecto FREYA
Energy Technology Data Exchange (ETDEWEB)
Becares Palacios, V.; Villamarin fernandez, D.
2013-07-01
The FREYA Project of the 7th Framework Program is aimed to the study of the kinetics of subcritical reactors coupled to an external neutron source, and, more specifically, to the validation of reactivity monitoring techniques. CIEMAT activities within the frame of this project have consisted in analyzing the possible ways of correcting the spatial and energy effects on these reactivity monitoring techniques, as well as analyzing the effects that may have on them the presence of different materials in the reflector and the position of the neutron source.
Ion acoustic wave generation by a standing electromagnetic field in a subcritical plasma
P. Fischer; Gauthereau, C.; Godiot, J.; G. Matthieussent
1987-01-01
An electromagnetic wave ( f = 9 GHz, Pi = 150 kW, τ = 1.5 μs) is launched into a subcritical argon plasma (n e ≃1011 cm-3, P0 ≃ 5 × 10-4 Torr), resulting in a standing wave. The associated ponderomotive force generates an ion acoustic wave with a wave vector equal to twice the electromagnetic one and with a frequency satisfying the usual dispersion relation (fA ≃ 150 kHz). The main features of the ion acoustic wave, as measured in this 3D experiment, agree with a simple theory. However, varyi...
PRACTICAL APPLICATION OF THE SINGLE-PARAMETER SUBCRITICAL MASS LIMIT FOR PLUTONIUM METAL
Energy Technology Data Exchange (ETDEWEB)
MITCHELL, MARK VON [Los Alamos National Laboratory
2007-01-10
According to ANS-8.1, operations with fissile materials can be performed safely by complying with any of the listed single-parameter subcritical limits. For metallic units, when interspersed moderators are present, the mass limits apply to a single piece having no concave surfaces. On a practical level, when has any operation with fissile metal involved a single piece and absolutely no moderating material, e.g., water, oil, plastic, etc.? This would be rare. This paper explores the application of the single-parameter plutonium metal mass limit for realistic operational environments.
DEFF Research Database (Denmark)
Toor, Saqib; Reddy, H.; Deng, S.
2013-01-01
Six hydrothermal liquefaction experiments on Nannochloropsis salina and Spirulina platensis at subcritical and supercritical water conditions (220-375 °C, 20-255 bar) were carried out to explore the feasibility of extracting lipids from wet algae, preserving nutrients in lipid-extracted algae solid...... on Nannochloropsis salina at 350 °C and 175 bar. For Spirulina platensis algae sample, the optimal hydrothermal liquefaction condition appears to be at 310 °C and 115 bar, while the optimal condition for Nannochloropsis salina is at 350 °C and 175 bar. Preliminary data also indicate that a lipid-extracted algae...
Semiclassical Limit of the Non-linear Schroedinger-Poisson Equation With Subcritical Initial Data
2002-12-01
lim ∇xargψ. As noted earlier, this argument is self - consistent as long as the solution of the Euler- Poisson system (1.5)-(1.6) remains classical...00-2003 to 00-00-2003 4. TITLE AND SUBTITLE Semiclassical Limit of the Non-linear Schrodinger - Poisson Equation with Subcritical Initial Data 5a...classical limit of a self - consistent quantum-Vlasov equation in 3-D, Math. Models Methods Appl. Sci., 3 (1993), pp. 109–124. [SMM] C. Sparber, P. Markowich
Criticality Safety Evaluation of the LLNL Inherently Safe Subcritical Assembly (ISSA)
Energy Technology Data Exchange (ETDEWEB)
Percher, Catherine [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2012-06-19
The LLNL Nuclear Criticality Safety Division has developed a training center to illustrate criticality safety and reactor physics concepts through hands-on experimental training. The experimental assembly, the Inherently Safe Subcritical Assembly (ISSA), uses surplus highly enriched research reactor fuel configured in a water tank. The training activities will be conducted by LLNL following the requirements of an Integration Work Sheet (IWS) and associated Safety Plan. Students will be allowed to handle the fissile material under the supervision of LLNL instructors. This report provides the technical criticality safety basis for instructional operations with the ISSA experimental assembly.
Dauchot, Olivier; Bertin, Eric
2014-04-01
The starting point of the present work is the observation of possible analogies, both at the phenomenological and at the methodological level, between the subcritical transition to turbulence and the glass transition. Having recalled the phenomenology of the subcritical transition to turbulence, we review the theories of the glass transition at a very basic level, focusing on the history of their development as well as on the concepts they have elaborated. Doing so, we aim at attracting the attention on the above-mentioned analogies, which we believe could inspire new developments in the theory of the subcritical transition to turbulence. We then briefly describe a model inspired by one of the simplest and most inspiring models of the glass transition, the so-called Random Energy Model, as a first step in that direction.
Directory of Open Access Journals (Sweden)
D. Lachos-Perez
2017-06-01
Full Text Available This review summarizes the recent essential aspects of subcritical and supercritical water technology applied tothe extraction, hydrolysis, carbonization, and gasification processes. These are clean and fast technologies which do not need pretreatment, require less reaction time, generate less corrosion and residues, do not usetoxic solvents, and reduce the synthesis of degradation byproducts. The equipment design, process parameters, and types of biomass used for subcritical and supercritical water process are presented. The benefits of catalysis to improve process efficiency are addressed. Bioactive compounds, reducing sugars, hydrogen, biodiesel, and hydrothermal char are the final products of subcritical and supercritical water processes. The present review also revisits advances of the research trends in the development of subcriticaland supercritical water process technologies.
Consequences of entropy bifurcation in non-Maxwellian astrophysical environments
Leubner, M. P.
2008-07-01
Non-extensive systems, accounting for long-range interactions and correlations, are fundamentally related to non-Maxwellian distributions where a duality of equilibria appears in two families, the non-extensive thermodynamic equilibria and the kinetic equilibria. Both states emerge out of particular entropy generalization leading to a class of probability distributions, where bifurcation into two stationary states is naturally introduced by finite positive or negative values of the involved entropic index kappa. The limiting Boltzmann-Gibbs-Shannon state (BGS), neglecting any kind of interactions within the system, is subject to infinite entropic index and thus characterized by self-duality. Fundamental consequences of non-extensive entropy bifurcation, manifest in different astrophysical environments, as particular core-halo patterns of solar wind velocity distributions, the probability distributions of the differences of the fluctuations in plasma turbulence as well as the structure of density distributions in stellar gravitational equilibrium are discussed. In all cases a lower entropy core is accompanied by a higher entropy halo state as compared to the standard BGS solution. Data analysis and comparison with high resolution observations significantly support the theoretical requirement of non-extensive entropy generalization when dealing with systems subject to long-range interactions and correlations.
Bifurcation analysis of the fully symmetric language dynamical equation.
Mitchener, W Garrett
2003-03-01
In this paper, I study a continuous dynamical system that describes language acquisition and communication in a group of individuals. Children inherit from their parents a mechanism to learn their language. This mechanism is constrained by a universal grammar which specifies a restricted set of candidate languages. Language acquisition is not error-free. Children may or may not succeed in acquiring exactly the language of their parents. Individuals talk to each other, and successful communication contributes to biological (or cultural) fitness. I provide a full bifurcation analysis of the case where the parameters are chosen to yield a highly symmetric dynamical system. Populations approach either an incoherent steady state, where many different candidate languages are represented in the population, or a coherent steady state, where the majority of the population speaks a single language. The main result of the paper is a description of how learning reliability affects the stability of these two kinds of equilibria. I rigorously find all fixed points, determine their stabilities, and prove that all populations tend to some fixed point. I also demonstrate that the fixed point representing an incoherent steady state becomes unstable in an S (n)-symmetric transcritical bifurcation as learning becomes more reliable.
Modal bifurcation in a high-Tc superconducting levitation system
Taguchi, D.; Fujiwara, S.; Sugiura, T.
2011-05-01
This paper deals with modal bifurcation of a multi-degree-of-freedom high-Tc superconducting levitation system. As modeling of large-scale high-Tc superconducting levitation applications, where plural superconducting bulks are often used, it can be helpful to consider a system constituting of multiple oscillators magnetically coupled with each other. This paper investigates nonlinear dynamics of two permanent magnets levitated above high-Tc superconducting bulks and placed between two fixed permanent magnets without contact. First, the nonlinear equations of motion of the levitated magnets were derived. Then the method of averaging was applied to them. It can be found from the obtained solutions that this nonlinear two degree-of-freedom system can have two asymmetric modes, in addition to a symmetric mode and an antisymmetric mode both of which also exist in the linearized system. One of the backbone curves in the frequency response shows a modal bifurcation where the two stable asymmetric modes mentioned above appear with destabilization of the antisymmetric mode, thus leading to modal localization. These analytical predictions have been confirmed in our numerical analysis and experiments of free vibration and forced vibration. These results, never predicted by linear analysis, can be important for application of high-Tc superconducting levitation systems.
Partitioning of red blood cell aggregates in bifurcating microscale flows
Kaliviotis, E.; Sherwood, J. M.; Balabani, S.
2017-03-01
Microvascular flows are often considered to be free of red blood cell aggregates, however, recent studies have demonstrated that aggregates are present throughout the microvasculature, affecting cell distribution and blood perfusion. This work reports on the spatial distribution of red blood cell aggregates in a T-shaped bifurcation on the scale of a large microvessel. Non-aggregating and aggregating human red blood cell suspensions were studied for a range of flow splits in the daughter branches of the bifurcation. Aggregate sizes were determined using image processing. The mean aggregate size was marginally increased in the daughter branches for a range of flow rates, mainly due to the lower shear conditions and the close cell and aggregate proximity therein. A counterintuitive decrease in the mean aggregate size was apparent in the lower flow rate branches. This was attributed to the existence of regions depleted by aggregates of certain sizes in the parent branch, and to the change in the exact flow split location in the T-junction with flow ratio. The findings of the present investigation may have significant implications for microvascular flows and may help explain why the effects of physiological RBC aggregation are not deleterious in terms of in vivo vascular resistance.
Dynamics of Surfactant Liquid Plugs at Bifurcating Lung Airway Models
Tavana, Hossein
2013-11-01
A surfactant liquid plug forms in the trachea during surfactant replacement therapy (SRT) of premature babies. Under air pressure, the plug propagates downstream and continuously divides into smaller daughter plugs at continuously branching lung airways. Propagating plugs deposit a thin film on airway walls to reduce surface tension and facilitate breathing. The effectiveness of SRT greatly depends on the final distribution of instilled surfactant within airways. To understand this process, we investigate dynamics of splitting of surfactant plugs in engineered bifurcating airway models. A liquid plug is instilled in the parent tube to propagate and split at the bifurcation. A split ratio, R, is defined as the ratio of daughter plug lengths in the top and bottom daughter airway tubes and studied as a function of the 3D orientation of airways and different flow conditions. For a given Capillary number (Ca), orienting airways farther away from a horizontal position reduced R due to the flow of a larger volume into the gravitationally favored daughter airway. At each orientation, R increased with 0.0005 < Ca < 0.05. This effect diminished by decrease in airways diameter. This approach will help elucidate surfactant distribution in airways and develop effective SRT strategies.
Bifurcation to forward flapping flight at intermediate Reynolds number.
Vandenberghe, Nicolas; Zhang, Jun; Childress, Stephen
2003-11-01
The locomotion of most fish and birds is realized by flapping wings or fins transverse to the direction of travel. According to early theoretical studies, a flapping wing translating at finite speed in an inviscid fluid experiences a propulsive force. In steady forward flight this thrust is balanced by drag. Such "lift-based mechanisms" of thrust production are characteristic of the Eulerian realm, where discrete vortical structures are shed. But, when the Reynolds number is small, viscous forces dominate and reciprocal flapping motions are ineffective. A flapping wing experiences a net drag and cannot be used to propel an organism. We have devised an experiment to bridge the two regimes, and to examine the transition to forward flight at intermediate Reynolds numbers. We study the dynamics of an horizontal wing that is flapped up and down and is free to move either forwards or backwards. This very simple kinematics emphasizes the demarcation between low and high Reynolds number because it is effective in the Eulerian realm but has no effect in the Stokesian realm. We show that flapping flight occurs abruptly as a symmetry breaking bifurcation at a critical flapping frequency. Beyond the bifurcation the forward speed increases linearly with the flapping frequency. The experiment establishes a clear demarcation between the different strategies of locomotion at large and small Reynolds number.
Prediction of fibre architecture and adaptation in diseased carotid bifurcations.
LENUS (Irish Health Repository)
Creane, Arthur
2011-12-01
Many studies have used patient-specific finite element models to estimate the stress environment in atherosclerotic plaques, attempting to correlate the magnitude of stress to plaque vulnerability. In complex geometries, few studies have incorporated the anisotropic material response of arterial tissue. This paper presents a fibre remodelling algorithm to predict the fibre architecture, and thus anisotropic material response in four patient-specific models of the carotid bifurcation. The change in fibre architecture during disease progression and its affect on the stress environment in the plaque were predicted. The mean fibre directions were assumed to lie at an angle between the two positive principal strain directions. The angle and the degree of dispersion were assumed to depend on the ratio of principal strain values. Results were compared with experimental observations and other numerical studies. In non-branching regions of each model, the typical double helix arterial fibre pattern was predicted while at the bifurcation and in regions of plaque burden, more complex fibre architectures were found. The predicted change in fibre architecture in the arterial tissue during plaque progression was found to alter the stress environment in the plaque. This suggests that the specimen-specific anisotropic response of the tissue should be taken into account to accurately predict stresses in the plaque. Since determination of the fibre architecture in vivo is a difficult task, the system presented here provides a useful method of estimating the fibre architecture in complex arterial geometries.
Bifurcations in two-image photometric stereo for orthogonal illuminations
Kozera, R.; Prokopenya, A.; Noakes, L.; Śluzek, A.
2017-07-01
This paper discusses the ambiguous shape recovery in two-image photometric stereo for a Lambertian surface. The current uniqueness analysis refers to linearly independent light-source directions p = (0, 0, -1) and q arbitrary. For this case necessary and sufficient condition determining ambiguous reconstruction is governed by a second-order linear partial differential equation with constant coefficients. In contrast, a general position of both non-colinear illumination directions p and q leads to a highly non-linear PDE which raises a number of technical difficulties. As recently shown, the latter can also be handled for another family of orthogonal illuminations parallel to the OXZ-plane. For the special case of p = (0, 0, -1) a potential ambiguity stems also from the possible bifurcations of sub-local solutions glued together along a curve defined by an algebraic equation in terms of the data. This paper discusses the occurrence of similar bifurcations for such configurations of orthogonal light-source directions. The discussion to follow is supplemented with examples based on continuous reflectance map model and generated synthetic images.
Energy Technology Data Exchange (ETDEWEB)
Reinhold H. Dauskardt
2005-08-30
Final technical report detailing unique experimental and multi-scale computational modeling capabilities developed to study fracture and subcritical cracking in thin-film structures. Our program to date at Stanford has studied the mechanisms of fracture and fatigue crack-growth in structural ceramics at high temperature, bulk and thin-film glasses in selected moist environments where we demonstrated the presence of a true mechanical fatigue effect in some glass compositions. We also reported on the effects of complex environments and fatigue loading on subcritical cracking that effects the reliability of MEMS and other micro-devices using novel micro-machined silicon specimens and nanomaterial layers.
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
Directory of Open Access Journals (Sweden)
Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
Detecting the onset of bifurcations and their precursors from noisy data
Energy Technology Data Exchange (ETDEWEB)
Omberg, Larsson [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Royal Institute of Technology (KTH), Stockholm, (Sweden); Dolan, Kevin [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Neiman, Alexander [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Moss, Frank [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States)
2000-05-01
We study the problem of the detection of noise-induced precursors of periodic motion instabilities in stochastic dynamical systems. In particular, we concentrate on the period-doubling bifurcation. We have developed a statistical method to detect the onset of bifurcations and their precursors based on the previously established topological recurrence technique. (c) 2000 The American Physical Society.
Generic Hopf–Neĭmark–Sacker bifurcations in feed-forward systems
Broer, Henk W.; Vegter, Gert
2008-01-01
We show that generic Hopf–Neĭmark–Sacker bifurcations occur in the dynamics of a large class of feed-forward coupled cell networks. To this end we present a framework for studying such bifurcations in parametrized families of perturbed forced oscillators near weak resonance points. Our approach is
$\\Delta I=4$ and $\\Delta I=8$ bifurcations in rotational bands of diatomic molecules
Bonatsos, Dennis; Lalazissis, G A; Drenska, S B; Minkov, N; Raychev, P P; Roussev, R P; Bonatsos, Dennis
1996-01-01
It is shown that the recently observed $\\Delta I=4$ bifurcation seen in superdeformed nuclear bands is also occurring in rotational bands of diatomic molecules. In addition, signs of a $\\Delta I=8$ bifurcation, of the same order of magnitude as the $\\Delta I=4$ one, are observed both in superdeformed nuclear bands and rotational bands of diatomic molecules.
Qualitatively different bifurcation scenarios observed in the firing of identical nerve fibers
Energy Technology Data Exchange (ETDEWEB)
Zheng Qiaohua; Liu Zhiqiang; Yang Minghao; Wu Xiaobo [College of Life Science, Shaanxi Normal University, Xi' an 710062 (China); Gu Huaguang [College of Life Science, Shaanxi Normal University, Xi' an 710062 (China)], E-mail: guhuaguang@263.net; Ren Wei [College of Life Science, Shaanxi Normal University, Xi' an 710062 (China)], E-mail: renwei1964@vip.sina.com
2009-01-26
This Letter reports various bifurcation scenarios, including period-adding bifurcations with chaos and those with stochastic firing patterns, generated by identical neural pacemakers. The scenarios are studied by properly adjusting two physiological parameters, one is 4-aminopyridine sensitive potassium conductance and the other is extracellular calcium concentration, in both experimentation and simulation.
The anatomy of the bifurcated neural spine and its occurrence within Tetrapoda.
Woodruff, D Cary
2014-09-01
Vertebral neural spine bifurcation has been historically treated as largely restrictive to sauropodomorph dinosaurs; wherein it is inferred to be an adaptation in response to the increasing weight from the horizontally extended cervical column. Because no extant terrestrial vertebrates have massive, horizontally extended necks, extant forms with large cranial masses were examined for the presence of neural spine bifurcation. Here, I report for the first time on the soft tissue surrounding neural spine bifurcation in a terrestrial quadruped through the dissection of three Ankole-Watusi cattle. With horns weighing up to a combined 90 kg, the Ankole-Watusi is unlike any other breed of cattle in terms of cranial weight and presence of neural spine bifurcation. Using the Ankole-Watusi as a model, it appears that neural spine bifurcation plays a critical role in supporting a large mobile weight adjacent to the girdles. In addition to neural spine bifurcation being recognized within nonavian dinosaurs, this vertebral feature is also documented within many members of temnospondyls, captorhinids, seymouriamorphs, diadectomorphs, Aves, marsupials, artiodactyls, perissodactyls, and Primates, amongst others. This phylogenetic distribution indicates that spine bifurcation is more common than previously thought, and that this vertebral adaptation has contributed throughout the evolutionary history of tetrapods. Neural spine bifurcation should now be recognized as an anatomical component adapted by some vertebrates to deal with massive, horizontal, mobile weights adjacent the girdles. © 2014 Wiley Periodicals, Inc.
Cascades of alternating pitchfork and flip bifurcations in H-bridge inverters
DEFF Research Database (Denmark)
Avrutin, Viktor; Zhusubaliyev, Zhanybai T.; Mosekilde, Erik
2017-01-01
-phase inverter, the present paper discusses a number of unusual phenomena that can occur in piecewise smooth maps with a very large number of switching manifolds. We show in particular how smooth (pitchfork and flip) bifurcations may form a macroscopic pattern that stretches across the overall bifurcation...
Qualitative changes in phase-response curve and synchronization at the saddle-node-loop bifurcation
Hesse, Janina; Schleimer, Jan-Hendrik; Schreiber, Susanne
2017-05-01
Prominent changes in neuronal dynamics have previously been attributed to a specific switch in onset bifurcation, the Bogdanov-Takens (BT) point. This study unveils another, relevant and so far underestimated transition point: the saddle-node-loop bifurcation, which can be reached by several parameters, including capacitance, leak conductance, and temperature. This bifurcation turns out to induce even more drastic changes in synchronization than the BT transition. This result arises from a direct effect of the saddle-node-loop bifurcation on the limit cycle and hence spike dynamics. In contrast, the BT bifurcation exerts its immediate influence upon the subthreshold dynamics and hence only indirectly relates to spiking. We specifically demonstrate that the saddle-node-loop bifurcation (i) ubiquitously occurs in planar neuron models with a saddle node on invariant cycle onset bifurcation, and (ii) results in a symmetry breaking of the system's phase-response curve. The latter entails an increase in synchronization range in pulse-coupled oscillators, such as neurons. The derived bifurcation structure is of interest in any system for which a relaxation limit is admissible, such as Josephson junctions and chemical oscillators.
Symmons, M F; Martin, S R; Bayley, P M
1996-11-01
Microtubule assembly kinetics have been studied quantitatively under solution conditions supporting microtubule dynamic instability. Purified GTP-tubulin (Tu-GTP) and covalently cross-linked short microtubule seeds (EGS-seeds; Koshland et al. (1988) Nature 331, 499) were used with and without biotinylation. Under sub-critical concentration conditions ([Tu-GTP] assembly, that was found to abolish the GDP release. The variation of the GDP release with tubulin concentration (Jh(c) plot) was determined below the critical concentration (Cc). The GDP production observed was consistent with the elongation of the observed seeded microtubules with an apparent rate constant of 1.5 x 10(6) M-1 second-1 above a threshold of approximately 1 microM tubulin. The form of this Jh(c) plot for elongation below Cc is reproduced by the Lateral Cap model for microtubule dynamic instability adapted for seeded assembly. The behaviour of the system is contrasted with that previously studied in the absence of detectable microtubule elongation (Caplow and Shanks (1990) J. Biol. Chem. 265, 8935-8941). The approach provides a means of monitoring microtubule dynamics at concentrations inaccessible to optical microscopy, and shows that essentially the same dynamic mechanisms apply at all concentrations. Numerical simulation of the subcritical concentration regime shows dynamic growth features applicable to the initiation of microtubule growth in vivo.
Marin, Timothy W; Janik, Ireneusz; Bartels, David M; Chipman, Daniel M
2017-05-17
The nature and extent of hydrogen bonding in water has been scrutinized for decades, including how it manifests in optical properties. Here we report vacuum ultraviolet absorption spectra for the lowest-lying electronic state of subcritical and supercritical water. For subcritical water, the spectrum redshifts considerably with increasing temperature, demonstrating the gradual breakdown of the hydrogen-bond network. Tuning the density at 381 °C gives insight into the extent of hydrogen bonding in supercritical water. The known gas-phase spectrum, including its vibronic structure, is duplicated in the low-density limit. With increasing density, the spectrum blueshifts and the vibronic structure is quenched as the water monomer becomes electronically perturbed. Fits to the supercritical water spectra demonstrate consistency with dimer/trimer fractions calculated from the water virial equation of state and equilibrium constants. Using the known water dimer interaction potential, we estimate the critical distance between molecules (ca. 4.5 Å) needed to explain the vibronic structure quenching.
Total acid number reduction kinetics of naphthenic acids using non-catalytic subcritical methanol
Zafar, Faisal; Mandal, Pradip Chandra; Shaari, Ku Zilati bt Ku; Nadeem, Saad
2017-10-01
Naphthenic acids (NAs) are weak organic acids present in the heavy crude oil and Oil Sand Bitumens. Whereas, the NAs are the major cause of corrosion in different processing, handling and storage equipment's of the refinery. Esterification of these acids can be an interesting method to reduce the NAs content in the crude oil besides its esters are valuable commodity and can be used as added lubricant in the oils. In this study, NAs reduction kinetics were investigated in a batch type reactor with subcritical methanol, the experiments were performed at temperatures of 150-210°C and fixed methanol partial pressure of 2 MPa. Findings of this study demonstrate that the 59% of total acid number (TAN) reduction was achieved at the temperature of 210°C, methanol partial pressure of 2 MPa and reaction time of 150 min. The TAN reduction followed second order kinetics with activation energy and frequency factor of 54.15 KJ/mol and 7.6×103, respectively. These results suggest that subcritical methanol can be an effective to reduce the TAN non-catalytically.
Directory of Open Access Journals (Sweden)
Mandal Pradip C.
2016-09-01
Full Text Available Cyclopentane carboxylic acid (CPCA is a model compound of Naphthenic acids (NAs. This objective of this paper is to discover total acid number (TAN reduction kinetics and pathways of the reaction between CAPA and subcritical methanol (SubC-MeOH. The experiments were carried out in an autoclave reactor at temperatures of 180-220°C, a methanol partial pressure (MPP of 3 MPa, reaction times of 0-30 min and CPCA initial gas phase concentrations of 0.016-0.04 g/mL. TAN content of the samples were analyzed using ASTM D 974 techniques. The reaction products were identified and quantified with the help of GC/MS and GC-FID respectively. Experimental results reveal that TAN removal kinetics followed first order kinetics with an activation energy of 13.97 kcal/mol and a pre-exponential factor of 174.21 s-1. Subcritical methanol is able to reduce TAN of CPCA decomposing CPCA into new compounds such as cyclopentane, formaldehyde, methyl acetate and 3-pentanol.
Subcritical saturation of the magnetorotational instability through mean magnetic field generation
Xie, Jin-Han; Julien, Keith; Knobloch, Edgar
2018-03-01
The magnetorotational instability is widely believed to be responsible for outward angular momentum transport in astrophysical accretion discs. The efficiency of this transport depends on the amplitude of this instability in the saturated state. We employ an asymptotic expansion based on an explicit, astrophysically motivated time-scale separation between the orbital period, Alfvén crossing time and viscous or resistive dissipation time-scales, originally proposed by Knobloch and Julien, to formulate a semi-analytical description of the saturated state in an incompressible disc. In our approach a Keplerian shear flow is maintained by the central mass but the instability saturates via the generation of a mean vertical magnetic field. The theory assumes that the time-averaged angular momentum flux and the radial magnetic flux are constant and determines both self-consistently. The results predict that, depending on parameters, steady saturation may be supercritical or subcritical, and in the latter case that the upper (lower) solution branch is always stable (unstable). The angular momentum flux is always outward, consistent with the presence of accretion, and for fixed wavenumber peaks in the subcritical regime. The limit of infinite Reynolds number at large but finite magnetic Reynolds number is also discussed.
Ultrasound-Enhanced Subcritical CO2 Extraction of Lutein from Chlorella pyrenoidosa.
Fan, Xiao-Dan; Hou, Yan; Huang, Xing-Xin; Qiu, Tai-Qiu; Jiang, Jian-Guo
2015-05-13
Lutein is an important pigment of Chlorella pyrenoidosa with many beneficial functions in human health. The main purpose of this study was to extract lutein from C. pyrenoidosa using ultrasound-enhanced subcritical CO2 extraction (USCCE). Effects of operating conditions on the extraction, including extraction pretreatment, temperature, pressure, time, CO2 flow rate, and ultrasonic power, were investigated, and an orthogonal experiment was designed to study the effects of extraction pressure, temperature, cosolvent amount, and time on the extraction yields. The USCCE method was compared with other extraction methods in terms of the yields of lutein and the microstructure of C. pyrenoidosa powder by scanning electron microscopy. A maximal extraction yield of 124.01 mg lutein/100 g crude material was achieved under optimal conditions of extraction temperature at 27 °C, extraction pressure at 21 MPa, cosolvent amount at 1.5 mL/g ethanol, and ultrasound power at 1000 W. Compared to other methods, USCCE could significantly increase the lutein extraction yield at lower extraction temperature and pressure. Furthermore, the kinetic models of USCCE and subcritical CO2 extraction (SCCE) of lutein from C. pyrenoidosa were set as E = 130.64 × (1 - e(-0.6599t)) and E = 101.82 × (1 - e(-0.5683t)), respectively. The differences of parameters in the kinetic models indicate that ultrasound was able to enhance the extraction process of SCCE.
Directory of Open Access Journals (Sweden)
Yajie Tian
2017-03-01
Full Text Available The subcritical water extraction (SWE is a high-efficiency and environment-friendly extraction method. The extraction of resveratrol (RES of grape seeds obtained from the wine production process was proposed using subcritical water extraction (SWE. The effects of different extraction process parameters on RES yield were investigated by single factors. Extraction optimization was conducted using response surface methodology (RSM. Extraction temperature was proven to be the most significant factor influencing RES yield. The optimal conditions was as follows: extraction pressure of 1.02 MPa, temperature of 152.32 °C, time of 24.89 min, and a solid/solvent ratio of 1:15 g/mL. Under these optimal conditions, the predicted extraction RES yield was 6.90 μg/g and the recoveries was up to 91.98%. Compared to other previous studies, this method required less pollution and less treatment time to extract RES from grape seeds. From these results, added economic value to this agroindustrial residue is proposed using environmentally friendly extraction techniques.
Release of phenolic acids from defatted rice bran by subcritical water treatment.
Fabian, Cynthia; Tran-Thi, Ngoc Yen; Kasim, Novy S; Ju, Yi-Hsu
2010-12-01
Oil production from rice bran, an undervalued by-product of rice milling, produces defatted rice bran (DRB) as a waste material. Although it is considered a less valuable product, DRB still contains useful substances such as phenolic compounds with antioxidant, UV-B-protecting and anti-tumour activities. In this study the phenolic acids in DRB were extracted with subcritical water at temperatures of 125, 150, 175 and 200 °C. Analysis of total phenolics using Folin-Ciocalteu reagent showed about 2-20 g gallic acid equivalent kg(-1) bran in the extracts. High-performance liquid chromatography analysis showed low contents of phenolic acids (about 0.4-2 g kg(-1) bran). Ferulic, p-coumaric, gallic and caffeic acids were the major phenolic acids identified in the extracts. Thermal analysis of the phenolic acids was also done. The thermogravimetric curves showed that p-coumaric, caffeic and ferulic acids started to decompose at about 170 °C, while gallic acid did not start to decompose until about 200 °C. Subcritical water can be used to hydrolyse rice bran and release phenolic compounds, but the high temperatures used in the extraction can also cause the decomposition of phenolic acids. Copyright © 2010 Society of Chemical Industry.
Pilot-scale subcritical solvent extraction of curcuminoids from Curcuma long L.
Kwon, Hye-Lim; Chung, Myong-Soo
2015-10-15
Curcuminoids consisted curcumin, demethoxycurcumin and bisdemethoxycurcumin, were extracted from turmeric using subcritical solvent by varying conditions of temperature (110-150 °C), time (1-10 min), pressure (5-100 atm), solid-to-solvent ratio, and mixing ratio of solvent. Preliminary lab-scale experiments were conducted to determine the optimum extraction temperature and mixing ratio of water and ethanol for the pilot-scale extraction. The maximum yield of curcuminoids in the pilot-scale system was 13.58% (curcumin 4.94%, demethoxycurcumin 4.73%, and bisdemethoxycurcumin 3.91% in dried extracts) at 135 °C/5 min with water/ethanol mixture (50:50, v/v) as a solvent. On the other hand, the extraction yields of curcuminoids were obtained as 10.49%, 13.71% and 13.96% using the 50%, 95% and 100% ethanol, respectively, at the atmospheric condition (60 °C/120 min). Overall results showed that the subcritical solvent extraction is much faster and efficient extraction method considering extracted curcuminoids contents and has a potential to develop a commercial process for the extraction of curcuminoids. Copyright © 2015 Elsevier Ltd. All rights reserved.
van Wyk, F.; Highcock, E. G.; Field, A. R.; Roach, C. M.; Schekochihin, A. A.; Parra, F. I.; Dorland, W.
2017-11-01
We investigate the effect of varying the ion temperature gradient (ITG) and toroidal equilibrium scale sheared flow on ion-scale turbulence in the outer core of MAST by means of local gyrokinetic simulations. We show that nonlinear simulations reproduce the experimental ion heat flux and that the experimentally measured values of the ITG and the flow shear lie close to the turbulence threshold. We demonstrate that the system is subcritical in the presence of flow shear, i.e., the system is formally stable to small perturbations, but transitions to a turbulent state given a large enough initial perturbation. We propose that the transition to subcritical turbulence occurs via an intermediate state dominated by low number of coherent long-lived structures, close to threshold, which increase in number as the system is taken away from the threshold into the more strongly turbulent regime, until they fill the domain and a more conventional turbulence emerges. We show that the properties of turbulence are effectively functions of the distance to threshold, as quantified by the ion heat flux. We make quantitative comparisons of correlation lengths, times, and amplitudes between our simulations and experimental measurements using the MAST BES diagnostic. We find reasonable agreement of the correlation properties, most notably of the correlation time, for which significant discrepancies were found in previous numerical studies of MAST turbulence.
Production of valued materials from squid viscera by subcritical water hydrolysis.
Uddin, M Salim; Ahn, Hyang-Min; Kishimura, Hideki; Chun, Byung-Soo
2010-09-01
Subcritical water hydrolysis was carried out to produce valued materials from squid viscera, the waste product of fish processing industries. The reaction temperatures for hydrolysis of rawand deoiled squid viscera were maintained from 180 to 280 degrees C for5 min. The ratio of material to water forhydrolysis was 1:50. Most of the proteins from deoiled squid viscera were recovered at high temperature. The protein yield in raw squid viscera hydrolyzate decreased with the rise of temperature. The reducing sugar yield was higher at high temperature in subcritical water hydrolysis of both raw and deoiled squid viscera. The highest yield of amino acids in raw and deoiled squid viscera hydrolyzates were 233.25 +/- 3.25 and 533.78 +/- 4.13 mg g(-1) at 180 and 280 degrees C, respectively. Most amino acids attained highest yield at the reaction temperature range of 180-220 degrees C and 260-280 degrees C for raw and deoiled samples, respectively. The recovery of amino acids from deoiled squid viscera was about 1.5 times higher than that of raw squid viscera.
Beam transient analyses of Accelerator Driven Subcritical Reactors based on neutron transport method
Energy Technology Data Exchange (ETDEWEB)
He, Mingtao; Wu, Hongchun [School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, Shaanxi (China); Zheng, Youqi, E-mail: yqzheng@mail.xjtu.edu.cn [School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, Shaanxi (China); Wang, Kunpeng [Nuclear and Radiation Safety Center, PO Box 8088, Beijing 100082 (China); Li, Xunzhao; Zhou, Shengcheng [School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, Shaanxi (China)
2015-12-15
Highlights: • A transport-based kinetics code for Accelerator Driven Subcritical Reactors is developed. • The performance of different kinetics methods adapted to the ADSR is investigated. • The impacts of neutronic parameters deteriorating with fuel depletion are investigated. - Abstract: The Accelerator Driven Subcritical Reactor (ADSR) is almost external source dominated since there is no additional reactivity control mechanism in most designs. This paper focuses on beam-induced transients with an in-house developed dynamic analysis code. The performance of different kinetics methods adapted to the ADSR is investigated, including the point kinetics approximation and space–time kinetics methods. Then, the transient responds of beam trip and beam overpower are calculated and analyzed for an ADSR design dedicated for minor actinides transmutation. The impacts of some safety-related neutronics parameters deteriorating with fuel depletion are also investigated. The results show that the power distribution varying with burnup leads to large differences in temperature responds during transients, while the impacts of kinetic parameters and feedback coefficients are not very obvious. Classification: Core physic.
Directory of Open Access Journals (Sweden)
A.R. Vatankhah
2017-01-01
Full Text Available Introduction: A free overfall offers a simple device for flow discharge measuring by a single measurement of depth at the end of the channel yb which is known as the end depth or brink depth. When the bottom of a channel drops suddenly, the flow separates from sharp edge of the brink and the pressure distribution is not hydrostatic because of the curvature of the flow. In channels with subcritical flow regime, control section occurs at the upstream with a critical depth (yc. Although pressure distribution at the critical depth is hydrostatic, the location of the critical depth can vary with respect to the discharge value. So, the end depth at brink is offered to estimate the discharge. A unique relationship between the brink depth (yb and critical depth (yc, known as end-depth ratio (EDR = yb/yc, exist. Since a relationship between the discharge and critical depth exists, the discharge can ultimately be related to yb. However, when the approaching flow is supercritical, critical section does not exist. Therefore, the discharge will be a function of end depth and channel longitudinal slope. In current study, an analytical model is presented for a circular free overfall with different flat base height in subcritical and supercritical flow regimes. The flow over a drop in a free overfall is simulated by applying the energy to calculate the EDR and end depth-discharge (EDD relationship. End-depth-discharge relationship: The flow of a free overfall in a channel can be assumed that is similar to the flow over a sharp-crested weir by taking weir height equal to zero. It is assumed that pressure at the end section is atmospheric, and also streamlines at the end section are parallel. To account for the curvature of streamlines, the deflection of jet due to gravity, the coefficient of contraction, Cc, is considered. At a short distance upstream the end section, the pressure is hydrostatic. By applying the energy equation between end section and control
Sushkova, Svetlana; Minkina, Tatiana; Kizilkaya, Ridvan; Mandzhieva, Saglara; Batukaev, Abdulmalik; Bauer, Tatiana; Gulser, Coskun
2016-04-01
The purpose of research is the assessment of main marker of polycyclic aromatic hydrocarbons contamination, benzo[a]pyrene (BaP) content in soils of emission zone of the power complex plant in soils with use of ecologically clean and effective subcritical water extraction method. Studies were conducted on the soils of monitoring plots subjected to Novocherkassk Power Plant emissions from burning coal. In 2000, monitoring plots were established at different distances from the NPS (1.0-20.0 km). Soil samples for the determination of soil properties and the contents of BaP were taken from a depth of 0-20 cm. The soil cover in the region under study consisted of ordinary chernozems, meadow-chernozemic soils, and alluvial meadow soils. This soil revealed the following physical and chemical properties: Corg-3.1-5.0%, pH-7.3-7.6, ECE-31.2-47.6 mmol(+)/100g; CaCO3-0.2-1.0%, the content of physical clay - 51-67% and clay - 3-37%. BaP extraction from soils was carried out by a subcritical water extraction method. Subcritical water extraction of BaP from soil samples was conducted in a specially developed extraction cartridge made of stainless steel and equipped with screw-on caps at both ends. It was also equipped with a manometer that included a valve for pressure release to maintain an internal pressure of 100 atm. The extraction cartridge containing a sample and water was placed into an oven connected to a temperature regulator under temperature 250oC and pressure 60 atm. The BaP concentration in the acetonitrile extract was determined by HPLC. The efficiency of BaP extraction from soil was determined using a matrix spike. The main accumulation of pollutant in 20 cm layer of soils is noted directly in affected zone on the plots situated at 1.2, 1.6, 5.0, 8.0 km from emission source in the direction of prevailing winds. The maximum quantity of a pollutant was founded in the soil of the plot located mostly close to a source of pollution in the direction of prevailing winds
Dynamics of a linear magnetic “microswimmer molecule”
Babel, S.; Löwen, H.; Menzel, A. M.
2016-03-01
In analogy to nanoscopic molecules that are composed of individual atoms, we consider an active “microswimmer molecule”. It is made of three individual magnetic colloidal microswimmers that are connected by harmonic springs and interact hydrodynamically. In the ground state, they form a linear straight molecule. We analyze the relaxation dynamics for perturbations of this straight configuration. As a central result, with increasing self-propulsion, we observe an oscillatory instability in accord with a subcritical Hopf bifurcation scenario. It is accompanied by a corkscrew-like swimming trajectory of increasing radius. Our results can be tested experimentally, using, for instance, magnetic self-propelled Janus particles, supposably linked by DNA molecules.
Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow
Energy Technology Data Exchange (ETDEWEB)
Smith, L. D., E-mail: lachlan.smith@monash.edu [Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria 3800 (Australia); CSIRO Mineral Resources, Clayton, Victoria 3800 (Australia); Rudman, M. [Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria 3800 (Australia); Lester, D. R. [School of Civil, Environmental and Chemical Engineering, RMIT University, Melbourne, Victoria 3000 (Australia); Metcalfe, G. [CSIRO Manufacturing, Highett, Victoria 3190 (Australia); Department of Mechanical and Product Design Engineering, Swinburne University of Technology, Hawthorn, Victoria 3122 (Australia); School of Mathematical Sciences, Monash University, Clayton, Victoria 3800 (Australia)
2016-05-15
Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversal in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.
Asada, Toichiro; Douskos, Christos; Markellos, Panagiotis
2011-01-01
The stability of equilibrium and the possibility of generation of business cycles in a discrete interregional Kaldorian macrodynamic model with fixed exchange rates are explored using numerical methods. One of the aims is to illustrate the feasibility and effectiveness of the numerical approach for dynamical systems of moderately high dimensionality and several parameters. The model considered is five-dimensional with four parameters, the speeds of adjustment of the goods markets and the degrees of economic interactions between the regions through trade and capital movement. Using a grid search method for the determination of the region of stability of equilibrium in two-dimensional parameter subspaces, and coefficient criteria for the flip bifurcation - and Hopf bifurcation - curve, we determine the stability region in several parameter ranges and identify Hopf bifurcation curves when they exist. It is found that interregional cycles emerge only for sufficient interregional trade. The relevant threshold is predicted by the model at 14 - 16 % of trade transactions. By contrast, no minimum level of capital mobility exists in a global sense as a requirement for the emergence of interregional cycles; the main conclusion being, therefore, that cycles may occur for very low levels of capital mobility if trade is sufficient. Examples of bifurcation and Lyapunov exponent diagrams illustrating the occurrence of cycles or period doubling, and examples of the development of the occurring cycles, are given. Both supercritical and subcritical bifurcations are found to occur, the latter type indicating coexistence of a point and a cyclical attractor.
Targeted particle tracking in computational models of human carotid bifurcations.
Marshall, Ian
2011-12-01
A significant and largely unsolved problem of computational fluid dynamics (CFD) simulation of flow in anatomically relevant geometries is that very few calculated pathlines pass through regions of complex flow. This in turn limits the ability of CFD-based simulations of imaging techniques (such as MRI) to correctly predict in vivo performance. In this work, I present two methods designed to overcome this filling problem, firstly, by releasing additional particles from areas of the flow inlet that lead directly to the complex flow region ("preferential seeding") and, secondly, by tracking particles both "downstream" and "upstream" from seed points within the complex flow region itself. I use the human carotid bifurcation as an example of complex blood flow that is of great clinical interest. Both idealized and healthy volunteer geometries are investigated. With uniform seeding in the inlet plane (in the common carotid artery (CCA)) of an idealized bifurcation geometry, approximately half the particles passed through the internal carotid artery (ICA) and half through the external carotid artery. However, of those particles entering the ICA, only 16% passed directly through the carotid bulb region. Preferential seeding from selected regions of the CCA was able to increase this figure to 47%. In the second method, seeding of particles within the carotid bulb region itself led to a very high proportion (97%) of pathlines running from CCA to ICA. Seeding of particles in the bulb plane of three healthy volunteer carotid bifurcation geometries led to much better filling of the bulb regions than by particles seeded at the inlet alone. In all cases, visualization of the origin and behavior of recirculating particles led to useful insights into the complex flow patterns. Both seeding methods produced significant improvements in filling the carotid bulb region with particle tracks compared with uniform seeding at the inlet and led to an improved understanding of the complex
DEFF Research Database (Denmark)
Zhu, Zhe; Toor, Saqib; Rosendahl, Lasse
2014-01-01
In this study, hydrothermal liquefaction of barley straw in subcritical and supercritical water with potassium carbonate catalyst was performed in the temperatures range of 280-400°C. The influence of final reaction temperature on products yield was investigated and some physicochemical properties...
Gnayfeed, M H; Daood, H G; Illés, V; Biacs, P A
2001-06-01
Ground paprika (Capsicum annuum L.) was extracted with supercritical carbon dioxide (SC-CO(2)) and subcritical propane at different conditions of pressure and temperature to estimate the yield and variation in carotenoid, tocopherol, and capsaicinoid contents and composition. The yield of paprika extract was found to be affected by the extraction conditions with SC-CO(2) but fairly constant at different conditions with subcritical propane. The maximum yields of oleoresin were 7.9 and 8.1% of ground paprika by SC-CO(2) and subcritical propane, respectively. The quantitative distribution of carotenoids, tocopherols, and capsaicinoids between paprika extract and powder was influenced by extraction conditions. SC-CO(2) was inefficient in the extraction of diesters of xanthophylls even at 400 bar and 55 degrees C, whereas tocopherols and capsaicinoids were easy to extract at these conditions. Under mild conditions subcritical propane was superior to SC-CO(2) in the extraction of carotenoids and tocopherols but less efficient in the extraction of capsaicinoids.
Pan, Z.; Chou, I.-Ming; Burruss, R.C.
2009-01-01
The advantages of using fused silica capillary reactor (FSCR) instead of conventional autoclave for studying chemical reactions at elevated pressure and temperature conditions were demonstrated in this study, including the allowance for visual observation under a microscope and in situ Raman spectroscopic characterization of polycarbonate and coexisting phases during hydrolysis in subcritical water. ?? 2009 The Royal Society of Chemistry.
Sheathless electrokinetic particle separation in a bifurcating microchannel
Li, Di; Lu, Xinyu; Song, Yongxin; Wang, Junsheng; Li, Dongqing
2016-01-01
Particle separation has found practical applications in many areas from industry to academia. Current electrokinetic particle separation techniques primarily rely on dielectrophoresis, where the electric field gradients are generated by either active microelectrodes or inert micro-insulators. We develop herein a new type of electrokinetic method to continuously separate particles in a bifurcating microchannel. This sheath-free separation makes use of the inherent wall-induced electrical lift to focus particles towards the centerline of the main-branch and then deflect them to size-dependent flow paths in each side-branch. A theoretical model is also developed to understand such a size-based separation, which simulates the experimental observations with a good agreement. This electric field-driven sheathless separation can potentially be operated in a parallel or cascade mode to increase the particle throughput or resolution. PMID:27703590
Analysis of Spatiotemporal Dynamic and Bifurcation in a Wetland Ecosystem
Directory of Open Access Journals (Sweden)
Yi Wang
2015-01-01
Full Text Available A wetland ecosystem is studied theoretically and numerically to reveal the rules of dynamics which can be quite accurate to better describe the observed spatial regularity of tussock vegetation. Mathematical theoretical works mainly investigate the stability of constant steady states, the existence of nonconstant steady states, and bifurcation, which can deduce a standard parameter control relation and in return can provide a theoretical basis for the numerical simulation. Numerical analysis indicates that the theoretical works are correct and the wetland ecosystem can show rich dynamical behaviors not only regular spatial patterns. Our results further deepen and expand the study of dynamics in the wetland ecosystem. In addition, it is successful to display tussock formation in the wetland ecosystem may have important consequences for aquatic community structure, especially for species interactions and biodiversity. All these results are expected to be useful in the study of the dynamic complexity of wetland ecosystems.
10th International Workshop on Bifurcation and Degradation in Geomaterials
Zhao, Jidong
2015-01-01
This book contains contributions to the 10th International Workshop on Bifurcation and Degradation in Geomaterials held in Hong Kong, May 28-30, 2014. This event marks the silver Jubilee anniversary of an international conference series dedicated to the research on localization, instability, degradation and failure of geomaterials since 1988 when its first workshop was organized in Germany. This volume of book collects the latest progresses and state-of-the-art research from top researchers around the world, and covers topics including multiscale modeling, experimental characterization and theoretical analysis of various instability and degradation phenomena in geomaterials as well as their relevance to contemporary issues in engineering practice. This book can be used as a useful reference for research students, academics and practicing engineers who are interested in the instability and degradation problems in geomechanics and geotechnical engineering.
Plastic bottle oscillator: Rhythmicity and mode bifurcation of fluid flow
Kohira, Masahiro I.; Magome, Nobuyuki; Kitahata, Hiroyuki; Yoshikawa, Kenichi
2007-10-01
The oscillatory flow of water draining from an upside-down plastic bottle with a thin pipe attached to its head is studied as an example of a dissipative structure generated under far-from-equilibrium conditions. Mode bifurcation was observed in the water/air flow: no flow, oscillatory flow, and counter flow were found when the inner diameter of the thin pipe was changed. The modes are stable against perturbations. A coupled two-bottle system exhibits either in-phase or anti-phase self-synchronization. These characteristic behaviors imply that the essential features of the oscillatory flow in a single bottle system can be described as a limit-cycle oscillation.
Wake-sleep transition as a noisy bifurcation
Yang, Dong-Ping; McKenzie-Sell, Lauren; Karanjai, Angela; Robinson, P. A.
2016-08-01
A recent physiologically based model of the ascending arousal system is used to analyze the dynamics near the transition from wake to sleep, which corresponds to a saddle-node bifurcation at a critical point. A normal form is derived by approximating the dynamics by those of a particle in a parabolic potential well with dissipation. This mechanical analog is used to calculate the power spectrum of fluctuations in response to a white noise drive, and the scalings of fluctuation variance and spectral width are derived versus distance from the critical point. The predicted scalings are quantitatively confirmed by numerical simulations, which show that the variance increases and the spectrum undergoes critical slowing, both in accord with theory. These signals can thus serve as potential precursors to indicate imminent wake-sleep transition, with potential application to safety-critical occupations in transport, air-traffic control, medicine, and heavy industry.
Phase dynamics of edge transport bifurcation induced by external biasing
Li, B.; Wang, X. Y.; Xie, Z. J.; Li, P. F.; Gentle, K. W.
2018-02-01
Edge transport bifurcation induced by external biasing is explored with self-consistent turbulence simulations in a flux-driven system with both closed and open magnetic field lines. Without bias, the nonlinear evolution of interchange turbulence produces large-scale turbulent eddies, leading to the high levels of radial transport in the edge region. With sufficiently strong biasing, a strong suppression of turbulence is found. The plasma potential structures are strongly modified with the generation of sheared mean flows at the plasma edge. Consequently, the turbulence-driven flux is decreased to a much lower level, indicating a transition to a state of reduced transport. The simulations show that the dynamics of the phase and amplitude of fluctuations play a crucial role in the mechanism of transport suppression driven by biasing.