			Home About us Contact

Equilibrium Point (equilibrium + point)

Distribution by Scientific Domains

Engineering	50%
Mathematics and Statistics	15%
Business, Economics, Finance and Accounting	15%
Life Sciences	10%
Chemistry	10%

Kinds of Equilibrium Point

unstable equilibrium point

Selected Abstracts

A new method for transient stability analysis

ELECTRICAL ENGINEERING IN JAPAN, Issue 3 2007
Naoto Yorino
Abstract This paper proposes a brand-new method for transient stability analysis in power systems. The proposed method directly computes the critical trajectory for a given contingency to obtain the critical condition of the studied system. Although the method may be useful for general nonlinear dynamic systems, it is applied to the problem of obtaining a controlling UEP, unstable equilibrium point, which provides inevitable information for the energy function methods to assess transient stability. Namely, the proposed method effectively yields a critical trajectory on PEBS together with the controlling UEP, thus improving the conventional BCU method. The effectiveness of the proposed method is demonstrated in 3-machine 9-bus and 6-machine 30-bus systems. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 159(3): 26,33, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20245 [source]

A multi-agent-based negotiation support system for distributed transmission cost allocation

INTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE & MANAGEMENT, Issue 3 2001
Yonghe Yan
We have developed a multi-agent system (MAS), based on the network flow model and KQML, called MASCAN, to support negotiations in the cost allocation of network transmission. This is very important to industries that have different entities connected with lines or pipes, such as the Internet and telecommunications. Such an approach is especially useful to the utility industries, such as electricity and gas, and the transportation industry. In the system, each agent represents a node in a network, for example supplier or consumer. Agents do not receive any centralized controls or information from centralized sources to guarantee autonomy,a key requirement for the agent. In this all decisions are made locally based on the rules or knowledge that each agent has or captured to communicate or coordinate with other agents for the cheapest path under fair-play requirements. We also assume that each agent is rational, that is, one of the goals or objectives of agent decisions or movements is to minimize costs or increase profits. The solution to cost allocation is to search for the equilibrium point of a non-cooperative game subject to the given constraints, for example network capacity. We applied MASCAN to model and support the negotiation of cost allocation in power transmission, and the results and how this approach supported the process of negotiation are perceived to be closer to the real-world negotiation and the outcomes were accepted more easily by the participants. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Global stability analysis of bidirectional associative memory neural networks with time delay

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 2 2001
Jiye Zhang
Abstract In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, we present new conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of bidirectional associative memory neural networks with fixed time delays or distributed time delays. The results are applicable to both symmetric and non-symmetric interconnection matrices, and all continuous non-monotonic neuron activation functions. Copyright © 2001 John Wiley & Sons, Ltd. [source]

The mathematical modelling of the osmotic dehydration of shark fillets at different brine temperatures

INTERNATIONAL JOURNAL OF FOOD SCIENCE & TECHNOLOGY, Issue 4 2006
Saheeda Mujaffar
Summary The effect of brine temperature (20, 30, 40 and 50 °C) on the osmotic drying behaviour of shark slabs (10 × 5 × 1 cm) in saturated (100°) brine was investigated. The parameters investigated were weight reduction, water loss, salt gain and water activity. Salt uptake and moisture data were analysed using various mathematical solutions based on Fick's Law of Diffusion and the effective diffusion coefficients were predicted after considering the process variables. The expressions presented by Azuara et al. (1992), based on the model presented by Crank (1975), were successfully used to predict the equilibrium point and to calculate diffusion coefficients at not only the initial stages of dehydration, but also at different times during the osmotic process. [source]

The rotation-vibration spectrum for Scarf II potential

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 13 2010
Wen-Chao Qiang
Abstract The arbitrary l -state solutions of the Schrödinger equation with Scarf II potential are presented by taking a new approximate scheme to the centrifugal term. This is realized by expanding the variable around the minimum equilibrium point of the potential. The wave functions can be expressed by hypergeometric functions. It is shown that the calculated energy levels are in good agreement with accurate numerical ones. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source]

Quadratic form of stable sub-manifold for power systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9-10 2004
Daizhan Cheng
Abstract The stable sub-manifold of type-1 unstable equilibrium point is fundamental in determining the region of attraction of a stable working point for power systems, because such sub-manifolds form the boundary of the region (IEEE Trans. Automat. Control 1998; 33(1):16,27; IEEE Trans. Circuit Syst. 1988; 35(6):712,728). The quadratic approximation has been investigated in some recent literatures (Automatica 1997; 33(10):1877,1883; IEEE Trans. Power Syst. 1997; 12(2):797,802). First, the paper reports our recent result: a precise formula is obtained, which provides the unique quadratic approximation with the error of 0(,,x,,3). Then the result is applied to differential,algebraic systems. The real form of practical large scale power systems are of this type. A detailed algorithm is obtained for the quadratic approximation of the stable sub-manifold of type-1 unstable equilibrium points of such systems. Some examples are presented to illustrate the algorithm and the application of the approximation to stability analysis of power systems. Copyright © 2004 John Wiley & Sons, Ltd. [source]

STABILITY ANALYSIS OF A TRITROPHIC FOOD CHAIN MODEL WITH AN ADAPTIVE PARAMETER FOR THE PREDATOR

NATURAL RESOURCE MODELING, Issue 2 2009
JEAN M. TCHUENCHE
Abstract The study of three-species communities have become the focus of considerable attention, and because the studies of ecological communities start with their food web, we consider a tritrophic food chain model comprised of the prey, the predator, and the super-predator. The classical assumption of the domino effect is supplemented with an adaptive parameter for the predator (in the absence of prey). Thus, the model exhibits an equilibrium with the predator-top-predator steady state, which is a saddle point. Dynamical behaviors such as boundedness, existence of periodic orbits, persistence, as well as stability are analyzed. The long-term coexistence of the three interacting species is addressed, and the stability analysis of the model shows that the biologically most relevant equilibrium point is globally asymptotically stable whenever it satisfies a certain criterion. Practical implications are explored and related to real populations. [source]

Stabilization of the Furuta Pendulum with backlash using H, -LMI technique: experimental validation,

ASIAN JOURNAL OF CONTROL, Issue 4 2010
Gisela Pujol
Abstract The rotary inverted pendulum, also named Furuta Pendulum, has been studied extensively for control performance evaluation in under-actuated mechanisms. The H, control invoking linear matrix inequality (H, -LMI) has been also widely employed for linear control design. This paper deals with the feasibility of the H, -LMI technique to stabilize the rotary inverted pendulum around its unstable equilibrium point when there exists a backlash nonlinearity in the actuator. So, the H, -LMI faces the nonlinear effect in the actuator and the non-linear pendulum model. Experimental realization of the designed H, -LMI control also shows evidence of the good performance of the controller subject to external perturbation. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

Stabilization of the inverted spherical pendulum via Lyapunov approach,

ASIAN JOURNAL OF CONTROL, Issue 6 2009
O. Octavio Gutiérrez F.
Abstract In this paper a nonlinear controller is presented for the stabilization of the spherical inverted pendulum system. The control strategy is based on the Lyapunov approach in conjunction with LaSalle's invariance principle. The proposed controller is able to bring the pendulum to the unstable upright equilibrium point with the position of the movable base at the origin. The obtained closed-loop system has a very large domain of attraction, that can be as large as desired, for any initial position of the pendulum which lies above the horizontal plane. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

On the dynamics of a spherical scaffold in rotating bioreactors

BIOTECHNOLOGY & BIOENGINEERING, Issue 3 2003
L. E. S. Ramirez
Abstract We analyze the dynamics of a spherical scaffold in rotating bioreactors (or clinostats). The idealized clinostat environment consists of a purely rotational flow that is perpendicular to a gravitational field. We confirm through a detailed analytical study that lift effects considerably alter the position of the equilibrium point reached by the scaffolds in the (vertical) direction collinear to the gravitational field. This result holds for small particle and shear Reynolds numbers. Our analysis shows that the inertial lift effect is negligible in the horizontal direction. We show that for all rotations of practical interest, and for the range of particle Reynolds number smaller than unity, the vertical coordinate of the equilibrium point is strongly affected by consideration of lift effects. For light (heavy) particles, inclusion of lift in the formation forces the equilibrium position to be below (above) the horizontal plane that contains the axis of rotation. The equilibrium point for light particles is stable and therefore is observable experimentally. The equilibrium point for heavy particles is unstable. We also estimate the stress level applied to the scaffold and derive an algebraic expression that indicates that the stress level acting on the scaffold decreases with increasing shear Reynolds number. © 2003 Wiley Periodicals, Inc. Biotechnol Bioeng 84: 382,389, 2003. [source]

Periodic Orbits near equilibria

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 9 2010
Luis Barreira
Lyapunov, Weinstein, and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory, we establish a similar result for a differential system without assuming the existence of a first integral. Our result can also be interpreted as a kind of special Hopf bifurcation. © 2010 Wiley Periodicals, Inc. [source]

Optimal Design of the Online Auction Channel: Analytical, Empirical, and Computational Insights,

DECISION SCIENCES, Issue 4 2002
Ravi Bapna
ABSTRACT The focus of this study is on business-to-consumer (B2C) online auctions made possible by the advent of electronic commerce over an open-source, ubiquitous Internet Protocol (IP) computer network. This work presents an analytical model that characterizes the revenue generation process for a popular B2C online auction, namely, Yankee auctions. Such auctions sell multiple identical units of a good to multiple buyers using an ascending and open auction mechanism. The methodologies used to validate the analytical model range from empirical analysis to simulation. A key contribution of this study is the design of a partitioning scheme of the discrete valuation space of the bidders such that equilibrium points with higher revenue structures become identifiable and feasible. Our analysis indicates that the auctioneers are, most of the time, far away from the optimal choice of key control factors such as the bid increment, resulting in substantial losses in a market with already tight margins. With this in mind, we put forward a portfolio of tools, varying in their level of abstraction and information intensity requirements, which help auctioneers maximize their revenues. [source]

A time-stepping method for stiff multibody dynamics with contact and friction,

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2002
Mihai Anitescu
Abstract We define a time-stepping procedure to integrate the equations of motion of stiff multibody dynamics with contact and friction. The friction and non-interpenetration constraints are modelled by complementarity equations. Stiffness is accommodated by a technique motivated by a linearly implicit Euler method. We show that the main subproblem, a linear complementarity problem, is consistent for a sufficiently small time step h. In addition, we prove that for the most common type of stiff forces encountered in rigid body dynamics, where a damping or elastic force is applied between two points of the system, the method is well defined for any time step h. We show that the method is stable in the stiff limit, unconditionally with respect to the damping parameters, near the equilibrium points of the springs. The integration step approaches, in the stiff limit, the integration step for a system where the stiff forces have been replaced by corresponding joint constraints. Simulations for one- and two-dimensional examples demonstrate the stable behaviour of the method. Published in 2002 by John Wiley & Sons, Ltd. [source]

A nonlinear adaptive speed tracking control for sensorless permanent magnet step motors with unknown load torque

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 3 2008
P. Tomei
Abstract Assuming that only stator currents and voltages are available for feedback, a nonlinear adaptive speed tracking control algorithm is proposed for a permanent magnet step motor with unknown constant load torque. It relies on three new theoretical results: the ,s-alignment' and ,c-alignment' procedures, in which the motor is forced to reach certain known equilibrium points, and an output feedback controller which guarantees asymptotic speed tracking for every initial condition belonging to an explicitly computed domain of attraction (global exponential convergence is achieved in the case of known constant load torque). Numerical simulation results illustrate the effectiveness of the proposed solution. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Cellular neural networks based on resonant tunnelling diodes

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 5 2001
Martin Hänggi
Resonant tunnelling diodes (RTDs) have intriguing properties which make them a primary nanoelectronic device for both analogue and digital applications. We propose two different types of RTD-based cells for the cellular neural network (CNN) which exhibit superior performance in terms of complexity, functionality, or processing speed compared to standard cells. In the first cell model, the resistor of the standard cell is replaced by an RTD, which results in a more compact and versatile cell which requires neither self-feedback nor a non-linear output function, and allows three stable equilibrium points. If a resonant tunnelling transistor (RTT) is used instead of the RTD, the dynamics can be controlled through its gate voltage as an additional network parameter. In a majority of CNN applications, bistable cells are sufficient. Utilizing RTD-based bistable logic elements to store the state of the cell, switching occurs almost instantaneously as virtually no charge transfer is necessary, and it is possible to implement non-linear connections in a straightforward manner. Hence, it turns out that RTD-based CNNs are tailor-made for the implementation of extremely fast bipolar operations and non-linear templates. The ideas presented in this paper may also be beneficially applied to other types of circuits and systems such as A/D converters or sigma-delta modulators. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Stochastic models for chemically reacting systems using polynomial stochastic hybrid systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2005
João Pedro Hespanha
Abstract A stochastic model for chemical reactions is presented, which represents the population of various species involved in a chemical reaction as the continuous state of a polynomial stochastic hybrid system (pSHS). pSHSs correspond to stochastic hybrid systems with polynomial continuous vector fields, reset maps, and transition intensities. We show that for pSHSs, the dynamics of the statistical moments of its continuous states, evolves according to infinite-dimensional linear ordinary differential equations (ODEs), which can be approximated by finite-dimensional nonlinear ODEs with arbitrary precision. Based on this result, a procedure to build this types of approximation is provided. This procedure is used to construct approximate stochastic models for a variety of chemical reactions that have appeared in literature. These reactions include a simple bimolecular reaction, for which one can solve the Master equation; a decaying,dimerizing reaction set which exhibits two distinct time scales; a reaction for which the chemical rate equations have a continuum of equilibrium points; and the bistable Schögl reaction. The accuracy of the approximate models is investigated by comparing with Monte Carlo simulations or the solution to the Master equation, when available. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Quadratic form of stable sub-manifold for power systems

ENDOGENOUS GROWTH, PRICE STABILITY AND MARKET DISEQUILIBRIA

METROECONOMICA, Issue 1 2010
Orlando Gomes
ABSTRACT Resorting to an endogenous growth framework, the paper studies the implications of taking market clearing as a long-term possibility rather than an every period implicit assumption, as in conventional growth analysis. The underlying main assumption respects to an adjustment mechanism in which: (1) transitional dynamics are characterized by the persistence of an accumulated market imbalance, and (2) monetary authorities are able to guarantee price stability. The implications of this modeling structure are the following: (1) a market-clearing equilibrium may co-exist with other equilibrium points, (2) several types of stability outcomes are obtainable, and (3) monetary policy becomes relevant for growth. [source]

Nonparametric Inference for Local Extrema with Application to Oligonucleotide Microarray Data in Yeast Genome

BIOMETRICS, Issue 2 2006
Peter X.-K.
Summary Identifying local extrema of expression profiles is one primary objective in some cDNA microarray experiments. To study the replication dynamics of the yeast genome, for example, local peaks of hybridization intensity profiles correspond to putative replication origins. We propose a nonparametric kernel smoothing (NKS) technique to detect local hybridization intensity extrema across chromosomes. The novelty of our approach is that we base our inference procedures on equilibrium points, namely those locations at which the first derivative of the intensity curve is zero. The proposed smoothing technique provides both point and interval estimation for the location of local extrema. Also, this technique can be used to test for the hypothesis of either one or multiple suspected locations being the true equilibrium points. We illustrate the proposed method on a microarray data set from an experiment designed to study the replication origins in the yeast genome, in that the locations of autonomous replication sequence (ARS) elements are identified through the equilibrium points of the smoothed intensity profile curve. Our method found a few ARS elements that were not detected by the current smoothing methods such as the Fourier convolution smoothing. [source]