Compensation for loads during arm movements using equilibrium-point control.

PubMed

Gribble, P L; Ostry, D J

2000-12-01

A significant problem in motor control is how information about movement error is used to modify control signals to achieve desired performance. A potential source of movement error and one that is readily controllable experimentally relates to limb dynamics and associated movement-dependent loads. In this paper, we have used a position control model to examine changes to control signals for arm movements in the context of movement-dependent loads. In the model, based on the equilibrium-point hypothesis, equilibrium shifts are adjusted directly in proportion to the positional error between desired and actual movements. The model is used to simulate multi-joint movements in the presence of both "internal" loads due to joint interaction torques, and externally applied loads resulting from velocity-dependent force fields. In both cases it is shown that the model can achieve close correspondence to empirical data using a simple linear adaptation procedure. An important feature of the model is that it achieves compensation for loads during movement without the need for either coordinate transformations between positional error and associated corrective forces, or inverse dynamics calculations.

The equilibrium-point hypothesis--past, present and future.

PubMed

Feldman, Anatol G; Levin, Mindy F

2009-01-01

This chapter is a brief account of fundamentals of the equilibrium-point hypothesis or more adequately called the threshold control theory (TCT). It also compares the TCT with other approaches to motor control. The basic notions of the TCT are reviewed with a major focus on solutions to the problems of multi-muscle and multi-degrees of freedom redundancy. The TCT incorporates cognitive aspects by explaining how neurons recognize that internal (neural) and external (environmental) events match each other. These aspects as well as how motor learning occurs are subjects of further development of the TCT hypothesis.

Evolution of Motor Control: From Reflexes and Motor Programs to the Equilibrium-Point Hypothesis.

PubMed

Latash, Mark L

2008-01-01

This brief review analyzes the evolution of motor control theories along two lines that emphasize active (motor programs) and reactive (reflexes) features of voluntary movements. It suggests that the only contemporary hypothesis that integrates both approaches in a fruitful way is the equilibrium-point hypothesis. Physical, physiological, and behavioral foundations of the EP-hypothesis are considered as well as relations between the EP-hypothesis and the recent developments of the notion of motor synergies. The paper ends with a brief review of the criticisms of the EP-hypothesis and challenges that the hypothesis faces at this time.

Floquet stability analysis of the longitudinal dynamics of two hovering model insects

PubMed Central

Wu, Jiang Hao; Sun, Mao

2012-01-01

Because of the periodically varying aerodynamic and inertial forces of the flapping wings, a hovering or constant-speed flying insect is a cyclically forcing system, and, generally, the flight is not in a fixed-point equilibrium, but in a cyclic-motion equilibrium. Current stability theory of insect flight is based on the averaged model and treats the flight as a fixed-point equilibrium. In the present study, we treated the flight as a cyclic-motion equilibrium and used the Floquet theory to analyse the longitudinal stability of insect flight. Two hovering model insects were considered—a dronefly and a hawkmoth. The former had relatively high wingbeat frequency and small wing-mass to body-mass ratio, and hence very small amplitude of body oscillation; while the latter had relatively low wingbeat frequency and large wing-mass to body-mass ratio, and hence relatively large amplitude of body oscillation. For comparison, analysis using the averaged-model theory (fixed-point stability analysis) was also made. Results of both the cyclic-motion stability analysis and the fixed-point stability analysis were tested by numerical simulation using complete equations of motion coupled with the Navier–Stokes equations. The Floquet theory (cyclic-motion stability analysis) agreed well with the simulation for both the model dronefly and the model hawkmoth; but the averaged-model theory gave good results only for the dronefly. Thus, for an insect with relatively large body oscillation at wingbeat frequency, cyclic-motion stability analysis is required, and for their control analysis, the existing well-developed control theories for systems of fixed-point equilibrium are no longer applicable and new methods that take the cyclic variation of the flight dynamics into account are needed. PMID:22491980

Synergies in the space of control variables within the equilibrium-point hypothesis

PubMed Central

Ambike, Satyajit; Mattos, Daniela; Zatsiorsky, Vladimir M.; Latash, Mark L.

2015-01-01

We use an approach rooted in the recent theory of synergies to analyze possible co-variation between two hypothetical control variables involved in finger force production based in the equilibrium-point hypothesis. These control variables are the referent coordinate (R) and apparent stiffness (C) of the finger. We tested a hypothesis that inter-trial co-variation in the {R; C} space during repeated, accurate force production trials stabilizes the fingertip force. This was expected to correspond to a relatively low amount of inter-trial variability affecting force and a high amount of variability keeping the force unchanged. We used the “inverse piano” apparatus to apply small and smooth positional perturbations to fingers during force production tasks. Across trials, R and C showed strong co-variation with the data points lying close to a hyperbolic curve. Hyperbolic regressions accounted for over 99% of the variance in the {R; C} space. Another analysis was conducted by randomizing the original {R; C} data sets and creating surrogate data sets that were then used to compute predicted force values. The surrogate sets always showed much higher force variance compared to the actual data, thus reinforcing the conclusion that finger force control was organized in the {R; C} space, as predicted by the equilibrium-point hypothesis, and involved co-variation in that space stabilizing total force. PMID:26701299

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

Rasouli, C.; Abbasi Davani, F.; Rokrok, B.

Plasma confinement using external magnetic field is one of the successful ways leading to the controlled nuclear fusion. Development and validation of the solution process for plasma equilibrium in the experimental toroidal fusion devices is the main subject of this work. Solution of the nonlinear 2D stationary problem as posed by the Grad-Shafranov equation gives quantitative information about plasma equilibrium inside the vacuum chamber of hot fusion devices. This study suggests solving plasma equilibrium equation which is essential in toroidal nuclear fusion devices, using a mesh-free method in a condition that the plasma boundary is unknown. The Grad-Shafranov equation hasmore » been solved numerically by the point interpolation collocation mesh-free method. Important features of this approach include truly mesh free, simple mathematical relationships between points and acceptable precision in comparison with the parametric results. The calculation process has been done by using the regular and irregular nodal distribution and support domains with different points. The relative error between numerical and analytical solution is discussed for several test examples such as small size Damavand tokamak, ITER-like equilibrium, NSTX-like equilibrium, and typical Spheromak.« less

Evolution of Motor Control: From Reflexes and Motor Programs to the Equilibrium-Point Hypothesis

PubMed Central

Latash, Mark L.

2009-01-01

This brief review analyzes the evolution of motor control theories along two lines that emphasize active (motor programs) and reactive (reflexes) features of voluntary movements. It suggests that the only contemporary hypothesis that integrates both approaches in a fruitful way is the equilibrium-point hypothesis. Physical, physiological, and behavioral foundations of the EP-hypothesis are considered as well as relations between the EP-hypothesis and the recent developments of the notion of motor synergies. The paper ends with a brief review of the criticisms of the EP-hypothesis and challenges that the hypothesis faces at this time. PMID:19823595

A new two-scroll chaotic attractor with three quadratic nonlinearities, its adaptive control and circuit design

NASA Astrophysics Data System (ADS)

Lien, C.-H.; Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D new two-scroll chaotic attractor with three quadratic nonlinearities is investigated in this paper. First, the qualitative and dynamical properties of the new two-scroll chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new two-scroll dissipative chaotic system has three unstable equilibrium points. As an engineering application, global chaos control of the new two-scroll chaotic system with unknown system parameters is designed via adaptive feedback control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic two-scroll attractor model.

Mathematical Analysis of an Epidemic System in the Presence of Optimal Control and Population Dispersal

NASA Astrophysics Data System (ADS)

Nandi, Swapan Kumar; Jana, Soovoojeet; Mandal, Manotosh; Kar, T. K.

In this paper, we proposed and analyzed a susceptible-infected-recovered (SIR) type epidemic model to investigate the effect of transport-related infectious diseases namely tuberculosis, measles, rubella, influenza, sexually transmitted diseases, etc. The existence and stability criteria of both the diseases include free equilibrium point and endemic equilibrium point which are established and the threshold parametric condition for which the system passes through a transcritical bifurcation is also obtained. Optimal control strategy for control parameters is formulated and solved both theoretically and numerically. Lastly, we not only illustrate our theoretical results through graphical illustrations but also computer simulation is used to show that our model would be a good model to study the SARS epidemic in 2003.

Should the Equilibrium Point Hypothesis (EPH) be Considered a Scientific Theory?

PubMed Central

Sainburg, Robert L.

2017-01-01

The purpose of this commentary is to discuss factors that limit consideration of the equilibrium point hypothesis as a scientific theory. The EPH describes control of motor neuron threshold through the variable lambda, which corresponds to a unique referent configuration for a muscle, joint, or combination of joints. One of the most compelling features of the equilibrium point hypothesis is the integration of posture and movement control into a single mechanism. While the essential core of the hypothesis is based upon spinal circuitry interacting with peripheral mechanics, the proponents have extended the theory to include the higher-level processes that generate lambda, and in doing so, imposed an injunction against the supraspinal nervous system modeling, computing, or predicting dynamics. This limitation contradicts evidence that humans take account of body and environmental dynamics in motor selection, motor control, and motor adaptation processes. A number of unresolved limitations to the EPH have been debated in the literature for many years, including whether muscle resistance to displacement, measured during movement, is adequate to support this form of control, violations in equifinality predictions, spinal circuits that alter the proposed invariant characteristic for muscles, and limitations in the description of how the complexity of spinal circuitry might be integrated to yield a unique and stable equilibrium position for a given motor neuron threshold. In addition, an important empirical limitation of EPH is the measurement of the invariant characteristic, which needs to be done under a constant central state. While there is no question that the EPH is an elegant and generative hypothesis for motor control research, the claim that this hypothesis has reached the status of a scientific theory is premature. PMID:25386681

Should the Equilibrium Point Hypothesis (EPH) be Considered a Scientific Theory?

PubMed

Sainburg, Robert L

2015-04-01

The purpose of this commentary is to discuss factors that limit consideration of the equilibrium point hypothesis as a scientific theory. The EPH describes control of motor neuron threshold through the variable lambda, which corresponds to a unique referent configuration for a muscle, joint, or combination of joints. One of the most compelling features of the equilibrium point hypothesis is the integration of posture and movement control into a single mechanism. While the essential core of the hypothesis is based upon spinal circuitry interacting with peripheral mechanics, the proponents have extended the theory to include the higher-level processes that generate lambda, and in doing so, imposed an injunction against the supraspinal nervous system modeling, computing, or predicting dynamics. This limitation contradicts evidence that humans take account of body and environmental dynamics in motor selection, motor control, and motor adaptation processes. A number of unresolved limitations to the EPH have been debated in the literature for many years, including whether muscle resistance to displacement, measured during movement, is adequate to support this form of control, violations in equifinality predictions, spinal circuits that alter the proposed invariant characteristic for muscles, and limitations in the description of how the complexity of spinal circuitry might be integrated to yield a unique and stable equilibrium position for a given motor neuron threshold. In addition, an important empirical limitation of EPH is the measurement of the invariant characteristic, which needs to be done under a constant central state. While there is no question that the EPH is an elegant and generative hypothesis for motor control research, the claim that this hypothesis has reached the status of a scientific theory is premature.

Raoult's law revisited: accurately predicting equilibrium relative humidity points for humidity control experiments.

PubMed

Bowler, Michael G; Bowler, David R; Bowler, Matthew W

2017-04-01

The humidity surrounding a sample is an important variable in scientific experiments. Biological samples in particular require not just a humid atmosphere but often a relative humidity (RH) that is in equilibrium with a stabilizing solution required to maintain the sample in the same state during measurements. The controlled dehydration of macromolecular crystals can lead to significant increases in crystal order, leading to higher diffraction quality. Devices that can accurately control the humidity surrounding crystals while monitoring diffraction have led to this technique being increasingly adopted, as the experiments become easier and more reproducible. Matching the RH to the mother liquor is the first step in allowing the stable mounting of a crystal. In previous work [Wheeler, Russi, Bowler & Bowler (2012). Acta Cryst. F 68 , 111-114], the equilibrium RHs were measured for a range of concentrations of the most commonly used precipitants in macromolecular crystallography and it was shown how these related to Raoult's law for the equilibrium vapour pressure of water above a solution. However, a discrepancy between the measured values and those predicted by theory could not be explained. Here, a more precise humidity control device has been used to determine equilibrium RH points. The new results are in agreement with Raoult's law. A simple argument in statistical mechanics is also presented, demonstrating that the equilibrium vapour pressure of a solvent is proportional to its mole fraction in an ideal solution: Raoult's law. The same argument can be extended to the case where the solvent and solute molecules are of different sizes, as is the case with polymers. The results provide a framework for the correct maintenance of the RH surrounding a sample.

An algorithm for engineering regime shifts in one-dimensional dynamical systems

NASA Astrophysics Data System (ADS)

Tan, James P. L.

2018-01-01

Regime shifts are discontinuous transitions between stable attractors hosting a system. They can occur as a result of a loss of stability in an attractor as a bifurcation is approached. In this work, we consider one-dimensional dynamical systems where attractors are stable equilibrium points. Relying on critical slowing down signals related to the stability of an equilibrium point, we present an algorithm for engineering regime shifts such that a system may escape an undesirable attractor into a desirable one. We test the algorithm on synthetic data from a one-dimensional dynamical system with a multitude of stable equilibrium points and also on a model of the population dynamics of spruce budworms in a forest. The algorithm and other ideas discussed here contribute to an important part of the literature on exercising greater control over the sometimes unpredictable nature of nonlinear systems.

Congestion schemes and Nash equilibrium in complex networks

NASA Astrophysics Data System (ADS)

Almendral, Juan A.; López, Luis; Cholvi, Vicent; Sanjuán, Miguel A. F.

2005-09-01

Whenever a common resource is scarce, a set of rules are needed to share it in a fairly way. However, most control schemes assume that users will behave in a cooperative way, without taking care of guaranteeing that they will not act in a selfish manner. Then, a fundamental issue is to evaluate the impact of cheating. From the point of view of game theory, a Nash equilibrium implies that nobody can take advantage by unilaterally deviating from this stable state, even in the presence of selfish users. In this paper we prove that any efficient Nash equilibrium strongly depends on the number of users, if the control scheme policy does not record their previous behavior. Since this is a common pattern in real situations, this implies that the system would be always out of equilibrium. Consequently, this result proves that, in practice, oblivious control schemes must be improved to cope with selfish users.

Maxwell's conjecture on three point charges with equal magnitudes

NASA Astrophysics Data System (ADS)

Tsai, Ya-Lun

2015-08-01

Maxwell's conjecture on three point charges states that the number of non-degenerate equilibrium points of the electrostatic field generated by them in R3 is at most four. We prove the conjecture in the cases when three point charges have equal magnitudes and show the number of isolated equilibrium points can only be zero, two, three, or four. Specifically, fixing positions of two positive charges in R3, we know exactly where to place the third positive charge to have two, three, or four equilibrium points. All equilibrium points are isolated and there are no other possibilities for the number of isolated equilibrium points. On the other hand, if both two of the fixed charges have negative charge values, there are always two equilibrium points except when the third positive charge lies in the line segment connecting the two negative charges. The exception cases are when the field contains only a curve of equilibrium points. In this paper, computations assisted by computer involve symbolic and exact integer computations. Therefore, all the results are proved rigorously.

Motor control theories and their applications.

PubMed

Latash, Mark L; Levin, Mindy F; Scholz, John P; Schöner, Gregor

2010-01-01

We describe several influential hypotheses in the field of motor control including the equilibrium-point (referent configuration) hypothesis, the uncontrolled manifold hypothesis, and the idea of synergies based on the principle of motor abundance. The equilibrium-point hypothesis is based on the idea of control with thresholds for activation of neuronal pools; it provides a framework for analysis of both voluntary and involuntary movements. In particular, control of a single muscle can be adequately described with changes in the threshold of motor unit recruitment during slow muscle stretch (threshold of the tonic stretch reflex). Unlike the ideas of internal models, the equilibrium-point hypothesis does not assume neural computations of mechanical variables. The uncontrolled manifold hypothesis is based on the dynamic system approach to movements; it offers a toolbox to analyze synergic changes within redundant sets of elements related to stabilization of potentially important performance variables. The referent configuration hypothesis and the principle of abundance can be naturally combined into a single coherent scheme of control of multi-element systems. A body of experimental data on healthy persons and patients with movement disorders are reviewed in support of the mentioned hypotheses. In particular, movement disorders associated with spasticity are considered as consequences of an impaired ability to shift threshold of the tonic stretch reflex within the whole normal range. Technical details and applications of the mentioned hypo-theses to studies of motor learning are described. We view the mentioned hypotheses as the most promising ones in the field of motor control, based on a solid physical and neurophysiological foundation.

Two-craft Coulomb formation study about circular orbits and libration points

NASA Astrophysics Data System (ADS)

Inampudi, Ravi Kishore

This dissertation investigates the dynamics and control of a two-craft Coulomb formation in circular orbits and at libration points; it addresses relative equilibria, stability and optimal reconfigurations of such formations. The relative equilibria of a two-craft tether formation connected by line-of-sight elastic forces moving in circular orbits and at libration points are investigated. In circular Earth orbits and Earth-Moon libration points, the radial, along-track, and orbit normal great circle equilibria conditions are found. An example of modeling the tether force using Coulomb force is discussed. Furthermore, the non-great-circle equilibria conditions for a two-spacecraft tether structure in circular Earth orbit and at collinear libration points are developed. Then the linearized dynamics and stability analysis of a 2-craft Coulomb formation at Earth-Moon libration points are studied. For orbit-radial equilibrium, Coulomb forces control the relative distance between the two satellites. The gravity gradient torques on the formation due to the two planets help stabilize the formation. Similar analysis is performed for along-track and orbit-normal relative equilibrium configurations. Where necessary, the craft use a hybrid thrusting-electrostatic actuation system. The two-craft dynamics at the libration points provide a general framework with circular Earth orbit dynamics forming a special case. In the presence of differential solar drag perturbations, a Lyapunov feedback controller is designed to stabilize a radial equilibrium, two-craft Coulomb formation at collinear libration points. The second part of the thesis investigates optimal reconfigurations of two-craft Coulomb formations in circular Earth orbits by applying nonlinear optimal control techniques. The objective of these reconfigurations is to maneuver the two-craft formation between two charged equilibria configurations. The reconfiguration of spacecraft is posed as an optimization problem using the calculus of variations approach. The optimality criteria are minimum time, minimum acceleration of the separation distance, minimum Coulomb and electric propulsion fuel usage, and minimum electrical power consumption. The continuous time problem is discretized using a pseudospectral method, and the resulting finite dimensional problem is solved using a sequential quadratic programming algorithm. The software package, DIDO, implements this approach. This second part illustrates how pseudospectral methods significantly simplify the solution-finding process.

Intrinsic dynamics and total energy-shaping control of the ballbot system

NASA Astrophysics Data System (ADS)

Satici, A. C.; Donaire, A.; Siciliano, B.

2017-12-01

Research on bipedal locomotion has shown that a dynamic walking gait is energetically more efficient than a statically stable one. Analogously, even though statically stable multi-wheeled robots are easier to control, they are energetically less efficient and have low accelerations to avoid tipping over. In contrast, the ballbot is an underactuated, nonholonomically constrained mobile robot, whose upward equilibrium point has to be stabilised by active control. In this work, we derive coordinate-invariant, reduced, Euler-Poincaré equations of motion for the ballbot. By means of partial feedback linearisation, we obtain two independent passive outputs with corresponding storage functions and utilise these to come up with energy-shaping control laws which move the system along the trajectories of a new Lagrangian system whose desired equilibrium point is asymptotically stable by construction. The basin of attraction of this controller is shown to be almost global under certain conditions on the design of the mechanism which are reflected directly in the mass matrix of the unforced equations of motion.

Analysis of kinematically redundant reaching movements using the equilibrium-point hypothesis.

PubMed

Cesari, P; Shiratori, T; Olivato, P; Duarte, M

2001-03-01

Six subjects performed a planar reaching arm movement to a target while unpredictable perturbations were applied to the endpoint; the perturbations consisted of pulling springs having different stiffness. Two conditions were applied; in the first, subjects had to reach for the target despite the perturbation, in the second condition, the subjects were asked to not correct the motion as a perturbation was applied. We analyzed the kinematics profiles of the three arm segments and, by means of inverse dynamics, calculated the joint torques. The framework of the equilibrium-point (EP) hypothesis, the lambda model, allowed the reconstruction of the control variables, the "equilibrium trajectories", in the "do not correct" condition for the wrist and the elbow joints as well as for the end point final position, while for the other condition, the reconstruction was less reliable. The findings support and extend to a multiple-joint planar movement, the paradigm of the EP hypothesis along with the "do not correct" instruction.

Dynamical behaviours and control measures of rumour-spreading model with consideration of network topology

NASA Astrophysics Data System (ADS)

Zhu, Linhe; Zhao, Hongyong

2017-07-01

A series of online rumours have seriously influenced the normal production and living of people. This paper aims to study the combined impact of psychological factor, propagation delay, network topology and control strategy on rumour diffusion over the online social networks. Based on an online social network, which is seen as a scale-free network, we model the spread of rumours by using a delayed SIS (Susceptible and Infected) epidemic-like model with consideration of psychological factor and network topology. First, through theoretical analysis, we illustrate the boundedness of the density of rumour-susceptible individuals and rumour-infected individuals. Second, we obtain the basic reproduction number R0 and prove the stability of the non-rumour equilibrium point and the rumour-spreading equilibrium point. Third, control strategies, such as uniform immunisation control, proportional immunisation control, targeted immunisation control and optimum control, are put forward to restrain rumour diffusion. Meanwhile, we have compared the differences of these control strategies. Finally, some representative numerical simulations are performed to verify the theoretical analysis results.

The case for an internal dynamics model versus equilibrium point control in human movement.

PubMed

Hinder, Mark R; Milner, Theodore E

2003-06-15

The equilibrium point hypothesis (EPH) was conceived as a means whereby the central nervous system could control limb movements by a relatively simple shift in equilibrium position without the need to explicitly compensate for task dynamics. Many recent studies have questioned this view with results that suggest the formation of an internal dynamics model of the specific task. However, supporters of the EPH have argued that these results are not incompatible with the EPH and that there is no reason to abandon it. In this study, we have tested one of the fundamental predictions of the EPH, namely, equifinality. Subjects learned to perform goal-directed wrist flexion movements while a motor provided assistance in proportion to the instantaneous velocity. It was found that the subjects stopped short of the target on the trials where the magnitude of the assistance was randomly decreased, compared to the preceding control trials (P = 0.003), i.e. equifinality was not achieved. This is contrary to the EPH, which predicts that final position should not be affected by external loads that depend purely on velocity. However, such effects are entirely consistent with predictions based on the formation of an internal dynamics model.

Adaptive Chemical Networks under Non-Equilibrium Conditions: The Evaporating Droplet.

PubMed

Armao, Joseph J; Lehn, Jean-Marie

2016-10-17

Non-volatile solutes in an evaporating drop experience an out-of-equilibrium state due to non-linear concentration effects and complex flow patterns. Here, we demonstrate a small molecule chemical reaction network that undergoes a rapid adaptation response to the out-of-equilibrium conditions inside the droplet leading to control over the molecular constitution and spatial arrangement of the deposition pattern. Adaptation results in a pronounced coffee stain effect and coupling to chemical concentration gradients within the drop is demonstrated. Amplification and suppression of network species are readily identifiable with confocal fluorescence microscopy. We anticipate that these observations will contribute to the design and exploration of out-of-equilibrium chemical systems, as well as be useful towards the development of point-of-care medical diagnostics and controlled deposition of small molecules through inkjet printing. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Experimental testing of olivine-melt equilibrium models at high temperatures

NASA Astrophysics Data System (ADS)

Krasheninnikov, S. P.; Sobolev, A. V.; Batanova, V. G.; Kargaltsev, A. A.; Borisov, A. A.

2017-08-01

Data are presented on the equilibrium compositions of olivine and melts in the products of 101 experiments performed at 1300-1600°C, atmospheric pressure, and controlled oxygen fugacity by means of new equipment at the Vernadsky Institute. It was shown that the available models of the olivine-melt equilibrium describe with insufficient adequacy the natural systems at temperatures over 1400°C. The most adequate is the model by Ford et al. (1983). However, this model overestimates systematically the equilibrium temperature with underestimating by 20-40°C at 1450-1600°C. These data point to the need for developing a new, improved quantitative model of the olivine-melt equilibrium for high-temperature magnesian melts, as well as to the possibility of these studies on the basis of the equipment presented.

Orbital stability close to asteroid 624 Hektor using the polyhedral model

NASA Astrophysics Data System (ADS)

Jiang, Yu; Baoyin, Hexi; Li, Hengnian

2018-03-01

We investigate the orbital stability close to the unique L4-point Jupiter binary Trojan asteroid 624 Hektor. The gravitational potential of 624 Hektor is calculated using the polyhedron model with observational data of 2038 faces and 1021 vertexes. Previous studies have presented three different density values for 624 Hektor. The equilibrium points in the gravitational potential of 624 Hektor with different density values have been studied in detail. There are five equilibrium points in the gravitational potential of 624 Hektor no matter the density value. The positions, Jacobian, eigenvalues, topological cases, stability, as well as the Hessian matrix of the equilibrium points are investigated. For the three different density values the number, topological cases, and the stability of the equilibrium points with different density values are the same. However, the positions of the equilibrium points vary with the density value of the asteroid 624 Hektor. The outer equilibrium points move away from the asteroid's mass center when the density increases, and the inner equilibrium point moves close to the asteroid's mass center when the density increases. There exist unstable periodic orbits near the surface of 624 Hektor. We calculated an orbit near the primary's equatorial plane of this binary Trojan asteroid; the results indicate that the orbit remains stable after 28.8375 d.

A new chaotic attractor with two quadratic nonlinearities, its synchronization and circuit implementation

NASA Astrophysics Data System (ADS)

Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Gundara, G.; Mada Sanjaya, W. S.; Subiyanto

2018-03-01

A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model.

Artificial equilibrium points for a generalized sail in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Aliasi, Generoso; Mengali, Giovanni; Quarta, Alessandro A.

2012-10-01

Different types of propulsion systems with continuous and purely radial thrust, whose modulus depends on the distance from a massive body, may be conveniently described within a single mathematical model by means of the concept of generalized sail. This paper discusses the existence and stability of artificial equilibrium points maintained by a generalized sail within an elliptic restricted three-body problem. Similar to the classical case in the absence of thrust, a generalized sail guarantees the existence of equilibrium points belonging only to the orbital plane of the two primaries. The geometrical loci of existing artificial equilibrium points are shown to coincide with those obtained for the circular three body problem when a non-uniformly rotating and pulsating coordinate system is chosen to describe the spacecraft motion. However, the generalized sail has to provide a periodically variable acceleration to maintain a given artificial equilibrium point. A linear stability analysis of the artificial equilibrium points is provided by means of the Floquet theory.

Dynamical analysis of a fractional SIR model with birth and death on heterogeneous complex networks

NASA Astrophysics Data System (ADS)

Huo, Jingjing; Zhao, Hongyong

2016-04-01

In this paper, a fractional SIR model with birth and death rates on heterogeneous complex networks is proposed. Firstly, we obtain a threshold value R0 based on the existence of endemic equilibrium point E∗, which completely determines the dynamics of the model. Secondly, by using Lyapunov function and Kirchhoff's matrix tree theorem, the globally asymptotical stability of the disease-free equilibrium point E0 and the endemic equilibrium point E∗ of the model are investigated. That is, when R0 < 1, the disease-free equilibrium point E0 is globally asymptotically stable and the disease always dies out; when R0 > 1, the disease-free equilibrium point E0 becomes unstable and in the meantime there exists a unique endemic equilibrium point E∗, which is globally asymptotically stable and the disease is uniformly persistent. Finally, the effects of various immunization schemes are studied and compared. Numerical simulations are given to demonstrate the main results.

Comment on "Out-of-plane equilibrium points in the restricted three-body problem with oblateness (Research Note)"

NASA Astrophysics Data System (ADS)

Wu, Nan; Wang, Xuefeng; Zhou, Li-Yong

2018-06-01

Douskos & Markellos (2006, A&A, 446, 357) first reported the existence of the out-of-plane equilibrium points in restricted three-body problem with oblateness. This result deviates significantly from the intuitive physical point of view that there is no other force that can balance the combined gravitation in Z direction. In fact, the out-of-plane equilibrium in that model is illusory and we prove here that such equilibrium points arise from the improper application of the potential function.

Assessing the effect of extrinsic incubation period (EIP) prolongation in controlling dengue transmission with wolbachia-infected mosquito intervention

NASA Astrophysics Data System (ADS)

Putri, Y. E.; Rozi, S.; Tasman, H.; Aldila, D.

2017-03-01

A mathematical model of dengue disease transmission with involving Extrinsic Incubation Period (EIP) effect as a consequence of wolbachia introduction into mossquito population will be discussed in this article. Mathematical model analysis to find equilibrium points, basic reproductive ratio (ℛ0), and criteria of endemic occurrence which depend on some parameters were performed. From analytical result, we find that ℛ0 hold an important role to determine the existence and local stability of equilibrium points. From sensitivity analysis of ℛ0 and numerical simulation, we conclude that prolongation of EIP with wolbachia intervention succeed to reduce number of infected human and mosquito significantly.

Motor Synergies and the Equilibrium-Point Hypothesis

PubMed Central

Latash, Mark L.

2010-01-01

The article offers a way to unite three recent developments in the field of motor control and coordination: (1) The notion of synergies is introduced based on the principle of motor abundance; (2) The uncontrolled manifold hypothesis is described as offering a computational framework to identify and quantify synergies; and (3) The equilibrium-point hypothesis is described for a single muscle, single joint, and multi-joint systems. Merging these concepts into a single coherent scheme requires focusing on control variables rather than performance variables. The principle of minimal final action is formulated as the guiding principle within the referent configuration hypothesis. Motor actions are associated with setting two types of variables by a controller, those that ultimately define average performance patterns and those that define associated synergies. Predictions of the suggested scheme are reviewed, such as the phenomenon of anticipatory synergy adjustments, quick actions without changes in synergies, atypical synergies, and changes in synergies with practice. A few models are briefly reviewed. PMID:20702893

Motor synergies and the equilibrium-point hypothesis.

PubMed

Latash, Mark L

2010-07-01

The article offers a way to unite three recent developments in the field of motor control and coordination: (1) The notion of synergies is introduced based on the principle of motor abundance; (2) The uncontrolled manifold hypothesis is described as offering a computational framework to identify and quantify synergies; and (3) The equilibrium-point hypothesis is described for a single muscle, single joint, and multijoint systems. Merging these concepts into a single coherent scheme requires focusing on control variables rather than performance variables. The principle of minimal final action is formulated as the guiding principle within the referent configuration hypothesis. Motor actions are associated with setting two types of variables by a controller, those that ultimately define average performance patterns and those that define associated synergies. Predictions of the suggested scheme are reviewed, such as the phenomenon of anticipatory synergy adjustments, quick actions without changes in synergies, atypical synergies, and changes in synergies with practice. A few models are briefly reviewed.

Plasma boundary shape control and real-time equilibrium reconstruction on NSTX-U

DOE PAGES

Boyer, M. D.; Battaglia, D. J.; Mueller, D.; ...

2018-01-25

Here, the upgrade to the National Spherical Torus eXperiment (NSTX-U) included two main improvements: a larger center-stack, enabling higher toroidal field and longer pulse duration, and the addition of three new tangentially aimed neutral beam sources, which increase available heating and current drive, and allow for flexibility in shaping power, torque, current, and particle deposition profiles. To best use these new capabilities and meet the high-performance operational goals of NSTX-U, major upgrades to the NSTX-U control system (NCS) hardware and software have been made. Several control algorithms, including those used for real-time equilibrium reconstruction and shape control, have been upgradedmore » to improve and extend plasma control capabilities. As part of the commissioning phase of first plasma operations, the shape control system was tuned to control the boundary in both inner-wall limited and diverted discharges. It has been used to accurately track the requested evolution of the boundary (including the size of the inner gap between the plasma and central solenoid, which is a challenge for the ST configuration), X-point locations, and strike point locations, enabling repeatable discharge evolutions for scenario development and diagnostic commissioning.« less

Plasma boundary shape control and real-time equilibrium reconstruction on NSTX-U

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

Boyer, M. D.; Battaglia, D. J.; Mueller, D.

Here, the upgrade to the National Spherical Torus eXperiment (NSTX-U) included two main improvements: a larger center-stack, enabling higher toroidal field and longer pulse duration, and the addition of three new tangentially aimed neutral beam sources, which increase available heating and current drive, and allow for flexibility in shaping power, torque, current, and particle deposition profiles. To best use these new capabilities and meet the high-performance operational goals of NSTX-U, major upgrades to the NSTX-U control system (NCS) hardware and software have been made. Several control algorithms, including those used for real-time equilibrium reconstruction and shape control, have been upgradedmore » to improve and extend plasma control capabilities. As part of the commissioning phase of first plasma operations, the shape control system was tuned to control the boundary in both inner-wall limited and diverted discharges. It has been used to accurately track the requested evolution of the boundary (including the size of the inner gap between the plasma and central solenoid, which is a challenge for the ST configuration), X-point locations, and strike point locations, enabling repeatable discharge evolutions for scenario development and diagnostic commissioning.« less

Plasma boundary shape control and real-time equilibrium reconstruction on NSTX-U

NASA Astrophysics Data System (ADS)

Boyer, M. D.; Battaglia, D. J.; Mueller, D.; Eidietis, N.; Erickson, K.; Ferron, J.; Gates, D. A.; Gerhardt, S.; Johnson, R.; Kolemen, E.; Menard, J.; Myers, C. E.; Sabbagh, S. A.; Scotti, F.; Vail, P.

2018-03-01

The upgrade to the National Spherical Torus eXperiment (NSTX-U) included two main improvements: a larger center-stack, enabling higher toroidal field and longer pulse duration, and the addition of three new tangentially aimed neutral beam sources, which increase available heating and current drive, and allow for flexibility in shaping power, torque, current, and particle deposition profiles. To best use these new capabilities and meet the high-performance operational goals of NSTX-U, major upgrades to the NSTX-U control system (NCS) hardware and software have been made. Several control algorithms, including those used for real-time equilibrium reconstruction and shape control, have been upgraded to improve and extend plasma control capabilities. As part of the commissioning phase of first plasma operations, the shape control system was tuned to control the boundary in both inner-wall limited and diverted discharges. It has been used to accurately track the requested evolution of the boundary (including the size of the inner gap between the plasma and central solenoid, which is a challenge for the ST configuration), X-point locations, and strike point locations, enabling repeatable discharge evolutions for scenario development and diagnostic commissioning.

A real time study of the human equilibrium using an instrumented insole with 3 pressure sensors.

PubMed

Abou Ghaida, Hussein; Mottet, Serge; Goujon, Jean-Marc

2014-01-01

The present work deals with the study of the human equilibrium using an ambulatory e-health system. One of the point on which we focus is the fall risk, when losing equilibrium control. A specific postural learning model is presented, and an ambulatory instrumented insole is developed using 3 pressures sensors per foot, in order to determine the real-time displacement and the velocity of the centre of pressure (CoP). The increase of these parameters signals a loss of physiological sensation, usually of vision or of the inner ear. The results are compared to those obtained from classical more complex systems.

Terminal Sliding Modes In Nonlinear Control Systems

NASA Technical Reports Server (NTRS)

Venkataraman, Subramanian T.; Gulati, Sandeep

1993-01-01

Control systems of proposed type called "terminal controllers" offers increased precision and stability of robotic operations in presence of unknown and/or changing parameters. Systems include special computer hardware and software implementing novel control laws involving terminal sliding modes of motion: closed-loop combination of robot and terminal controller converge, in finite time, to point of stable equilibrium in abstract space of velocity and/or position coordinates applicable to particular control problem.

Model of two infectious diseases in nettle caterpillar population

NASA Astrophysics Data System (ADS)

Firdausi, F. Z.; Nuraini, N.

2016-04-01

Palm oil is a vital commodity to the economy of Indonesia. The area of oil palm plantations in Indonesia has increased from year to year. However, the effectiveness of palm oil production is reduced by pest infestation. One of the pest which often infests oil palm plantations is nettle caterpillar. The pest control used in this study is biological control, viz. biological agents given to oil palm trees. This paper describes a mathematical model of two infectious diseases in nettle caterpillar population. The two infectious diseases arise due to two biological agents, namely Bacillus thuringiensis bacterium and parasite which usually attack nettle caterpillars. The derivation of the model constructed in this paper is obtained from ordinary differential equations without time delay. The equilibrium points are analyzed. Two of three equilibrium points are stable if the Routh-Hurwitz criteria are fulfilled. In addition, this paper also presents the numerical simulation of the model which has been constructed.

Pneumatic Variable Series Elastic Actuator.

PubMed

Zheng, Hao; Wu, Molei; Shen, Xiangrong

2016-08-01

Inspired by human motor control theory, stiffness control is highly effective in manipulation and human-interactive tasks. The implementation of stiffness control in robotic systems, however, has largely been limited to closed-loop control, and suffers from multiple issues such as limited frequency range, potential instability, and lack of contribution to energy efficiency. Variable-stiffness actuator represents a better solution, but the current designs are complex, heavy, and bulky. The approach in this paper seeks to address these issues by using pneumatic actuator as a variable series elastic actuator (VSEA), leveraging the compressibility of the working fluid. In this work, a pneumatic actuator is modeled as an elastic element with controllable stiffness and equilibrium point, both of which are functions of air masses in the two chambers. As such, for the implementation of stiffness control in a robotic system, the desired stiffness/equilibrium point can be converted to the desired chamber air masses, and a predictive pressure control approach is developed to control the timing of valve switching to obtain the desired air mass while minimizing control action. Experimental results showed that the new approach in this paper requires less expensive hardware (on-off valve instead of proportional valve), causes less control action in implementation, and provides good control performance by leveraging the inherent dynamics of the actuator.

Pneumatic Variable Series Elastic Actuator

PubMed Central

Zheng, Hao; Wu, Molei; Shen, Xiangrong

2016-01-01

Inspired by human motor control theory, stiffness control is highly effective in manipulation and human-interactive tasks. The implementation of stiffness control in robotic systems, however, has largely been limited to closed-loop control, and suffers from multiple issues such as limited frequency range, potential instability, and lack of contribution to energy efficiency. Variable-stiffness actuator represents a better solution, but the current designs are complex, heavy, and bulky. The approach in this paper seeks to address these issues by using pneumatic actuator as a variable series elastic actuator (VSEA), leveraging the compressibility of the working fluid. In this work, a pneumatic actuator is modeled as an elastic element with controllable stiffness and equilibrium point, both of which are functions of air masses in the two chambers. As such, for the implementation of stiffness control in a robotic system, the desired stiffness/equilibrium point can be converted to the desired chamber air masses, and a predictive pressure control approach is developed to control the timing of valve switching to obtain the desired air mass while minimizing control action. Experimental results showed that the new approach in this paper requires less expensive hardware (on–off valve instead of proportional valve), causes less control action in implementation, and provides good control performance by leveraging the inherent dynamics of the actuator. PMID:27354755

Human arm stiffness and equilibrium-point trajectory during multi-joint movement.

PubMed

Gomi, H; Kawato, M

1997-03-01

By using a newly designed high-performance manipulandum and a new estimation algorithm, we measured human multi-joint arm stiffness parameters during multi-joint point-to-point movements on a horizontal plane. This manipulandum allows us to apply a sufficient perturbation to subject's arm within a brief period during movement. Arm stiffness parameters were reliably estimated using a new algorithm, in which all unknown structural parameters could be estimated independent of arm posture (i.e., constant values under any arm posture). Arm stiffness during transverse movement was considerably greater than that during corresponding posture, but not during a longitudinal movement. Although the ratios of elbow, shoulder, and double-joint stiffness were varied in time, the orientation of stiffness ellipses during the movement did not change much. Equilibrium-point trajectories that were predicted from measured stiffness parameters and actual trajectories were slightly sinusoidally curved in Cartesian space and their velocity profiles were quite different from the velocity profiles of actual hand trajectories. This result contradicts the hypothesis that the brain does not take the dynamics into account in movement control depending on the neuromuscular servo mechanism; rather, it implies that the brain needs to acquire some internal models of controlled objects.

Whole body pointing movements in transient microgravity: preliminary results.

PubMed

Tagliabue, Michele; Pedrocchi, Alessandra; Gower, Valerio; Ferrigno, Giancarlo; Pozzo, Thierry

2004-07-01

The aim of the present study is a better comprehension of strategies of motor coordination during complex movements. In this field of research microgravity represent a unique experimental condition for the investigation of the role of equilibrium control in movement planning. Namely, here we focus on two important issues: the centre of mass control and the endpoint trajectory. Preliminary results of the center of mass position and the finger path curvature during pointing movements performed under normal and transient microgravity conditions are presented.

EAST kinetic equilibrium reconstruction combining with Polarimeter-Interferometer internal measurement constraints

NASA Astrophysics Data System (ADS)

Lian, H.; Liu, H. Q.; Li, K.; Zou, Z. Y.; Qian, J. P.; Wu, M. Q.; Li, G. Q.; Zeng, L.; Zang, Q.; Lv, B.; Jie, Y. X.; EAST Team

2017-12-01

Plasma equilibrium reconstruction plays an important role in the tokamak plasma research. With a high temporal and spatial resolution, the POlarimeter-INTerferometer (POINT) system on EAST has provided effective measurements for 102s H-mode operation. Based on internal Faraday rotation measurements provided by the POINT system, the equilibrium reconstruction with a more accurate core current profile constraint has been demonstrated successfully on EAST. Combining other experimental diagnostics and external magnetic fields measurement, the kinetic equilibrium has also been reconstructed on EAST. Take the pressure and edge current information from kinetic EFIT into the equilibrium reconstruction with Faraday rotation constraint, the new equilibrium reconstruction not only provides a more accurate internal current profile but also contains edge current and pressure information. One time slice result using new kinetic equilibrium reconstruction with POINT data constraints is demonstrated in this paper and the result shows there is a reversed shear of q profile and the pressure profile is also contained. The new improved equilibrium reconstruction is greatly helpful to the future theoretical analysis.

Measurement of the equilibrium relative humidity for common precipitant concentrations: facilitating controlled dehydration experiments.

PubMed

Wheeler, Matthew J; Russi, Silvia; Bowler, Michael G; Bowler, Matthew W

2012-01-01

The dehydration of crystals of macromolecules has long been known to have the potential to increase their diffraction quality. A number of methods exist to change the relative humidity that surrounds crystals, but for reproducible results, with complete characterization of the changes induced, a precise humidity-control device coupled with an X-ray source is required. The first step in these experiments is to define the relative humidity in equilibrium with the mother liquor of the system under study; this can often be quite time-consuming. In order to reduce the time spent on this stage of the experiment, the equilibrium relative humidity for a range of concentrations of the most commonly used precipitants has been measured. The relationship between the precipitant solution and equilibrium relative humidity is explained by Raoult's law for the equilibrium vapour pressure of water above a solution. The results also have implications for the choice of cryoprotectant and solutions used to dehydrate crystals. For the most commonly used precipitants (10-30% PEG 2000-8000), the starting point will be a relative humidity of 99.5%. © 2012 International Union of Crystallography. All rights reserved.

Recent tests of the equilibrium-point hypothesis (lambda model).

PubMed

Feldman, A G; Ostry, D J; Levin, M F; Gribble, P L; Mitnitski, A B

1998-07-01

The lambda model of the equilibrium-point hypothesis (Feldman & Levin, 1995) is an approach to motor control which, like physics, is based on a logical system coordinating empirical data. The model has gone through an interesting period. On one hand, several nontrivial predictions of the model have been successfully verified in recent studies. In addition, the explanatory and predictive capacity of the model has been enhanced by its extension to multimuscle and multijoint systems. On the other hand, claims have recently appeared suggesting that the model should be abandoned. The present paper focuses on these claims and concludes that they are unfounded. Much of the experimental data that have been used to reject the model are actually consistent with it.

[Hypothesis on the equilibrium point and variability of amplitude, speed and time of single-joint movement].

PubMed

Latash, M; Gottleib, G

1990-01-01

Problems of single-joint movement variability are analysed in the framework of the equilibrium-point hypothesis (the lambda-model). Control of the movements is described with three parameters related to movement amplitude speed, and time. Three strategies emerge from this description. Only one of them is likely to lead to a Fitts' type speed-accuracy trade-off. Experiments were performed to test one of the predictions of the model. Subjects performed identical sets of single-joint fast movements with open or closed eyes and some-what different instructions. Movements performed with closed eyes were characterized with higher peak speeds and unchanged variability in seeming violation of the Fitt's law and in a good correspondence to the model.

Pointing control using a moving base of support.

PubMed

Hondzinski, Jan M; Kwon, Taegyong

2009-07-01

The purposes of this study were to determine whether gaze direction provides a control signal for movement direction for a pointing task requiring a step and to gain insight into why discrepancies previously identified in the literature for endpoint accuracy with gaze directed eccentrically exist. Straight arm pointing movements were performed to real and remembered target locations, either toward or 30 degrees eccentric to gaze direction. Pointing occurred in normal room lighting or darkness while subjects sat, stood still or side-stepped left or right. Trunk rotation contributed 22-65% to gaze orientations when it was not constrained. Error differences for different target locations explained discrepancies among previous experiments. Variable pointing errors were influenced by gaze direction, while mean systematic pointing errors and trunk orientations were influenced by step direction. These data support the use of a control strategy that relies on gaze direction and equilibrium inputs for whole-body goal-directed movements.

New phenomena in non-equilibrium quantum physics

NASA Astrophysics Data System (ADS)

Kitagawa, Takuya

From its beginning in the early 20th century, quantum theory has become progressively more important especially due to its contributions to the development of technologies. Quantum mechanics is crucial for current technology such as semiconductors, and also holds promise for future technologies such as superconductors and quantum computing. Despite of the success of quantum theory, its applications have been mostly limited to equilibrium or static systems due to 1. lack of experimental controllability of non-equilibrium quantum systems 2. lack of theoretical frameworks to understand non-equilibrium dynamics. Consequently, physicists have not yet discovered too many interesting phenomena in non-equilibrium quantum systems from both theoretical and experimental point of view and thus, non-equilibrium quantum physics did not attract too much attentions. The situation has recently changed due to the rapid development of experimental techniques in condensed matter as well as cold atom systems, which now enables a better control of non-equilibrium quantum systems. Motivated by this experimental progress, we constructed theoretical frameworks to study three different non-equilibrium regimes of transient dynamics, steady states and periodically drives. These frameworks provide new perspectives for dynamical quantum process, and help to discover new phenomena in these systems. In this thesis, we describe these frameworks through explicit examples and demonstrate their versatility. Some of these theoretical proposals have been realized in experiments, confirming the applicability of the theories to realistic experimental situations. These studies have led to not only the improved fundamental understanding of non-equilibrium processes in quantum systems, but also suggested entirely different venues for developing quantum technologies.

Critical fluid thermal equilibration experiment (19-IML-1)

NASA Technical Reports Server (NTRS)

Wilkinson, R. Allen

1992-01-01

Gravity sometimes blocks all experimental techniques of making a desired measurement. Any pure fluid possesses a liquid-vapor critical point. It is defined by a temperature, pressure, and density state in thermodynamics. The critical issue that this experiment attempts to understand is the time it takes for a sample to reach temperature and density equilibrium as the critical point is approached; is it infinity due to mass and thermal diffusion, or do pressure waves speed up energy transport while mass is still under diffusion control. The objectives are to observe: (1) large phase domain homogenization without and with stirring; (2) time evolution of heat and mass after temperature step is applied to a one phase equilibrium sample; (3) phase evolution and configuration upon going two phase from a one phase equilibrium state; (4) effects of stirring on a low g two phase configuration; (5) two phase to one phase healing dynamics starting from a two phase low g configuration; and (6) effects of shuttle acceleration events on spatially and temporally varying compressible critical fluid dynamics.

Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models

NASA Astrophysics Data System (ADS)

Ahmed, E.; El-Sayed, A. M. A.; El-Saka, H. A. A.

2007-01-01

In this paper we are concerned with the fractional-order predator-prey model and the fractional-order rabies model. Existence and uniqueness of solutions are proved. The stability of equilibrium points are studied. Numerical solutions of these models are given. An example is given where the equilibrium point is a centre for the integer order system but locally asymptotically stable for its fractional-order counterpart.

A Consideration of HALO Type Orbit Designation and Maintaining for KUAFU-A and WSO/UV Missions

NASA Astrophysics Data System (ADS)

Nianchuan, J.; Xian, S.; Jianguo, Y.; Guangli, W.; Jingsong, P.

In the new era of deep space exploration more and more explorations at special places or points in solar system are carried out and planned There are five equilibrium points in the Sun-Earth system and the orbits around these points have good dynamic attribute Due to this reason The areas vicinity equilibrium points have many advantages for space exploration In recent 20 years the NASA and ESA have successfully launched several spacecrafts orbiting the Sun-Earth collinear equilibrium points Following the developing steps of space and deep space exploration in China Chinese scientists and engineers are considering and suggesting two equilibrium points explorations One is named KUAFU-A mission whose craft will orbit L1 point and the scientific target is studying the evolution of space weather of solar-terrestrial area The other is WSO UV mission whose craft will orbit L2 point and the scientific target is studying the structure and evolution of galaxies This report is mainly about HALO type orbit designation and maintaining for these two missions Following points are included 1 Briefly reviewing the explorations at the equilibrium points launched by NASA and ESA 2 Simply introducing the exploration KUAFU-A and WSO UV 3 Discussing the designation and maintaining of HALO type orbits in some detail for KUAFU-A and WSO UV

Testing hypotheses and the advancement of science: recent attempts to falsify the equilibrium point hypothesis.

PubMed

Feldman, Anatol G; Latash, Mark L

2005-02-01

Criticisms of the equilibrium point (EP) hypothesis have recently appeared that are based on misunderstandings of some of its central notions. Starting from such interpretations of the hypothesis, incorrect predictions are made and tested. When the incorrect predictions prove false, the hypothesis is claimed to be falsified. In particular, the hypothesis has been rejected based on the wrong assumptions that it conflicts with empirically defined joint stiffness values or that it is incompatible with violations of equifinality under certain velocity-dependent perturbations. Typically, such attempts use notions describing the control of movements of artificial systems in place of physiologically relevant ones. While appreciating constructive criticisms of the EP hypothesis, we feel that incorrect interpretations have to be clarified by reiterating what the EP hypothesis does and does not predict. We conclude that the recent claims of falsifying the EP hypothesis and the calls for its replacement by EMG-force control hypothesis are unsubstantiated. The EP hypothesis goes far beyond the EMG-force control view. In particular, the former offers a resolution for the famous posture-movement paradox while the latter fails to resolve it.

An Analytical Design Method for a Regenerative Braking Control System for DC-electrified Railway Systems under Light Load Conditions

NASA Astrophysics Data System (ADS)

Saito, Tatsuhito; Kondo, Keiichiro; Koseki, Takafumi

A DC-electrified railway system that is fed by diode rectifiers at a substation is unable to return the electric power to an AC grid. Accordingly, the braking cars have to restrict regenerative braking power when the power consumption of the powering cars is not sufficient. However, the characteristics of a DC-electrified railway system, including the powering cars, is not known, and a mathematical model for designing a controller has not been established yet. Hence, the object of this study is to obtain the mathematical model for an analytical design method of the regenerative braking control system. In the first part of this paper, the static characteristics of this system are presented to show the position of the equilibrium point. The linearization of this system at the equilibrium point is then performed to describe the dynamic characteristics of the system. An analytical design method is then proposed on the basis of these characteristics. The proposed design method is verified by experimental tests with a 1kW class miniature model, and numerical simulations.

Mathematical analysis of tuberculosis transmission model with delay

NASA Astrophysics Data System (ADS)

Lapaan, R. D.; Collera, J. A.; Addawe, J. M.

2016-11-01

In this paper, a delayed Tuberculosis infection model is formulated and investigated. We showed the existence of disease free equilibrium and endemic equilibrium points. We used La Salle-Lyapunov Invariance Principle to show that if the reproductive number R0 < 1, the disease-free equilibrium of the model is globally asymptotically stable. Numerical simulations are then performed to illustrate the existence of the disease free equilibrium and the endemic equilibrium point for a given value of R0. Thus, when R0 < 1, the disease dies out in the population.

Synergies in the space of control variables within the equilibrium-point hypothesis.

PubMed

Ambike, S; Mattos, D; Zatsiorsky, V M; Latash, M L

2016-02-19

We use an approach rooted in the recent theory of synergies to analyze possible co-variation between two hypothetical control variables involved in finger force production based on the equilibrium-point (EP) hypothesis. These control variables are the referent coordinate (R) and apparent stiffness (C) of the finger. We tested a hypothesis that inter-trial co-variation in the {R; C} space during repeated, accurate force production trials stabilizes the fingertip force. This was expected to correspond to a relatively low amount of inter-trial variability affecting force and a high amount of variability keeping the force unchanged. We used the "inverse piano" apparatus to apply small and smooth positional perturbations to fingers during force production tasks. Across trials, R and C showed strong co-variation with the data points lying close to a hyperbolic curve. Hyperbolic regressions accounted for over 99% of the variance in the {R; C} space. Another analysis was conducted by randomizing the original {R; C} data sets and creating surrogate data sets that were then used to compute predicted force values. The surrogate sets always showed much higher force variance compared to the actual data, thus reinforcing the conclusion that finger force control was organized in the {R; C} space, as predicted by the EP hypothesis, and involved co-variation in that space stabilizing total force. Copyright © 2015 IBRO. Published by Elsevier Ltd. All rights reserved.

Ab Initio Infrared and Raman Spectra.

DTIC Science & Technology

1982-08-01

equilibrium and non -equilibrium systems. It b pointed out that a similar ab !ni- te QFC molecular dynamic approach could be used to compute other types of...applied to -2- equilibrium and non -equilibrium system. It is pointed out that a similar oh im- ib QFCT molecular dynamic approach could be used to...desire to be able to experimentally identify and understand transient species or states (such as those existing during the course of chemical

Point defect reduction in MOCVD (Al)GaN by chemical potential control and a comprehensive model of C incorporation in GaN

NASA Astrophysics Data System (ADS)

Reddy, Pramod; Washiyama, Shun; Kaess, Felix; Kirste, Ronny; Mita, Seiji; Collazo, Ramon; Sitar, Zlatko

2017-12-01

A theoretical framework that provides a quantitative relationship between point defect formation energies and growth process parameters is presented. It enables systematic point defect reduction by chemical potential control in metalorganic chemical vapor deposition (MOCVD) of III-nitrides. Experimental corroboration is provided by a case study of C incorporation in GaN. The theoretical model is shown to be successful in providing quantitative predictions of CN defect incorporation in GaN as a function of growth parameters and provides valuable insights into boundary phases and other impurity chemical reactions. The metal supersaturation is found to be the primary factor in determining the chemical potential of III/N and consequently incorporation or formation of point defects which involves exchange of III or N atoms with the reservoir. The framework is general and may be extended to other defect systems in (Al)GaN. The utility of equilibrium formalism typically employed in density functional theory in predicting defect incorporation in non-equilibrium and high temperature MOCVD growth is confirmed. Furthermore, the proposed theoretical framework may be used to determine optimal growth conditions to achieve minimum compensation within any given constraints such as growth rate, crystal quality, and other practical system limitations.

Stable Spheromaks with Profile Control

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

Fowler, T K; Jayakumar, R

A spheromak equilibrium with zero edge current is shown to be stable to both ideal MHD and tearing modes that normally produce Taylor relaxation in gun-injected spheromaks. This stable equilibrium differs from the stable Taylor state in that the current density j falls to zero at the wall. Estimates indicate that this current profile could be sustained by non-inductive current drive at acceptable power levels. Stability is determined using the NIMROD code for linear stability analysis. Non-linear NIMROD calculations with non-inductive current drive could point the way to improved fusion reactors.

An equilibrium-point model of electromyographic patterns during single-joint movements based on experimentally reconstructed control signals.

PubMed

Latash, M L; Goodman, S R

1994-01-01

The purpose of this work has been to develop a model of electromyographic (EMG) patterns during single-joint movements based on a version of the equilibrium-point hypothesis, a method for experimental reconstruction of the joint compliant characteristics, the dual-strategy hypothesis, and a kinematic model of movement trajectory. EMG patterns are considered emergent properties of hypothetical control patterns that are equally affected by the control signals and peripheral feedback reflecting actual movement trajectory. A computer model generated the EMG patterns based on simulated movement kinematics and hypothetical control signals derived from the reconstructed joint compliant characteristics. The model predictions have been compared to published recordings of movement kinematics and EMG patterns in a variety of movement conditions, including movements over different distances, at different speeds, against different-known inertial loads, and in conditions of possible unexpected decrease in the inertial load. Changes in task parameters within the model led to simulated EMG patterns qualitatively similar to the experimentally recorded EMG patterns. The model's predictive power compares it favourably to the existing models of the EMG patterns. Copyright © 1994. Published by Elsevier Ltd.

Bifurcation analysis in SIR epidemic model with treatment

NASA Astrophysics Data System (ADS)

Balamuralitharan, S.; Radha, M.

2018-04-01

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

Multibody Parachute Flight Simulations for Planetary Entry Trajectories Using "Equilibrium Points"

NASA Technical Reports Server (NTRS)

Raiszadeh, Ben

2003-01-01

A method has been developed to reduce numerical stiffness and computer CPU requirements of high fidelity multibody flight simulations involving parachutes for planetary entry trajectories. Typical parachute entry configurations consist of entry bodies suspended from a parachute, connected by flexible lines. To accurately calculate line forces and moments, the simulations need to keep track of the point where the flexible lines meet (confluence point). In previous multibody parachute flight simulations, the confluence point has been modeled as a point mass. Using a point mass for the confluence point tends to make the simulation numerically stiff, because its mass is typically much less that than the main rigid body masses. One solution for stiff differential equations is to use a very small integration time step. However, this results in large computer CPU requirements. In the method described in the paper, the need for using a mass as the confluence point has been eliminated. Instead, the confluence point is modeled using an "equilibrium point". This point is calculated at every integration step as the point at which sum of all line forces is zero (static equilibrium). The use of this "equilibrium point" has the advantage of both reducing the numerical stiffness of the simulations, and eliminating the dynamical equations associated with vibration of a lumped mass on a high-tension string.

Criticality in a non-equilibrium, driven system: charged colloidal rods (fd-viruses) in electric fields.

PubMed

Kang, K; Dhont, J K G

2009-11-01

Experiments on suspensions of charged colloidal rods (fd-virus particles) in external electric fields are performed, which show that a non-equilibrium critical point can be identified. Several transition lines of field-induced phases and states meet at this point and it is shown that there is a length- and time-scale which diverge at the non-equilibrium critical point. The off-critical and critical behavior is characterized, with both power law and logarithmic divergencies. These experiments show that analogous features of the classical, critical divergence of correlation lengths and relaxation times in equilibrium systems are also exhibited by driven systems that are far out of equilibrium, related to phases/states that do not exist in the absence of the external field.

Spread of Ebola disease with susceptible exposed infected isolated recovered (SEIIhR) model

NASA Astrophysics Data System (ADS)

Azizah, Afina; Widyaningsih, Purnami; Retno Sari Saputro, Dewi

2017-06-01

Ebola is a deadly infectious disease and has caused an epidemic on several countries in West Africa. Mathematical modeling to study the spread of Ebola disease has been developed, including through models susceptible infected removed (SIR) and susceptible exposed infected removed (SEIR). Furthermore, susceptible exposed infected isolated recovered (SEIIhR) model has been derived. The aims of this research are to derive SEIIhR model for Ebola disease, to determine the patterns of its spread, to determine the equilibrium point and stability of the equilibrium point using phase plane analysis, and also to apply the SEIIhR model on Ebola epidemic in Sierra Leone in 2014. The SEIIhR model is a differential equation system. Pattern of ebola disease spread with SEIIhR model is solution of the differential equation system. The equilibrium point of SEIIhR model is unique and it is a disease-free equilibrium point that stable. Application of the model is based on the data Ebola epidemic in Sierra Leone. The free-disease equilibrium point (Se; Ee; Ie; Ihe; Re )=(5743865, 0, 0, 0, 0) is stable.

Modeling a distribution of point defects as misfitting inclusions in stressed solids

NASA Astrophysics Data System (ADS)

Cai, W.; Sills, R. B.; Barnett, D. M.; Nix, W. D.

2014-05-01

The chemical equilibrium distribution of point defects modeled as non-overlapping, spherical inclusions with purely positive dilatational eigenstrain in an isotropically elastic solid is derived. The compressive self-stress inside existing inclusions must be excluded from the stress dependence of the equilibrium concentration of the point defects, because it does no work when a new inclusion is introduced. On the other hand, a tensile image stress field must be included to satisfy the boundary conditions in a finite solid. Through the image stress, existing inclusions promote the introduction of additional inclusions. This is contrary to the prevailing approach in the literature in which the equilibrium point defect concentration depends on a homogenized stress field that includes the compressive self-stress. The shear stress field generated by the equilibrium distribution of such inclusions is proved to be proportional to the pre-existing stress field in the solid, provided that the magnitude of the latter is small, so that a solid containing an equilibrium concentration of point defects can be described by a set of effective elastic constants in the small-stress limit.

Malaria and global change: Insights, uncertainties and possible surprises

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

Martin, P.H.; Steel, A.

Malaria may change with global change. Indeed, global change may affect malaria risk and malaria epidemiology. Malaria risk may change in response to a greenhouse warming; malaria epidemiology, in response to the social, economic, and political developments which a greenhouse warming may trigger. To date, malaria receptivity and epidemiology futures have been explored within the context of equilibrium studies. Equilibrium studies of climate change postulate an equilibrium present climate (the starting point) and a doubled-carbon dioxide climate (the end point), simulate conditions in both instances, and compare the two. What happens while climate changes, i.e., between the starting point andmore » the end point, is ignored. The present paper focuses on malaria receptivity and addresses what equilibrium studies miss, namely transient malaria dynamics.« less

Mathematical model for HIV spreads control program with ART treatment

NASA Astrophysics Data System (ADS)

Maimunah; Aldila, Dipo

2018-03-01

In this article, using a deterministic approach in a seven-dimensional nonlinear ordinary differential equation, we establish a mathematical model for the spread of HIV with an ART treatment intervention. In a simplified model, when no ART treatment is implemented, disease-free and the endemic equilibrium points were established analytically along with the basic reproduction number. The local stability criteria of disease-free equilibrium and the existing criteria of endemic equilibrium were analyzed. We find that endemic equilibrium exists when the basic reproduction number is larger than one. From the sensitivity analysis of the basic reproduction number of the complete model (with ART treatment), we find that the increased number of infected humans who follow the ART treatment program will reduce the basic reproduction number. We simulate this result also in the numerical experiment of the autonomous system to show how treatment intervention impacts the reduction of the infected population during the intervention time period.

Gaussian random bridges and a geometric model for information equilibrium

NASA Astrophysics Data System (ADS)

Mengütürk, Levent Ali

2018-03-01

The paper introduces a class of conditioned stochastic processes that we call Gaussian random bridges (GRBs) and proves some of their properties. Due to the anticipative representation of any GRB as the sum of a random variable and a Gaussian (T , 0) -bridge, GRBs can model noisy information processes in partially observed systems. In this spirit, we propose an asset pricing model with respect to what we call information equilibrium in a market with multiple sources of information. The idea is to work on a topological manifold endowed with a metric that enables us to systematically determine an equilibrium point of a stochastic system that can be represented by multiple points on that manifold at each fixed time. In doing so, we formulate GRB-based information diversity over a Riemannian manifold and show that it is pinned to zero over the boundary determined by Dirac measures. We then define an influence factor that controls the dominance of an information source in determining the best estimate of a signal in the L2-sense. When there are two sources, this allows us to construct information equilibrium as a functional of a geodesic-valued stochastic process, which is driven by an equilibrium convergence rate representing the signal-to-noise ratio. This leads us to derive price dynamics under what can be considered as an equilibrium probability measure. We also provide a semimartingale representation of Markovian GRBs associated with Gaussian martingales and a non-anticipative representation of fractional Brownian random bridges that can incorporate degrees of information coupling in a given system via the Hurst exponent.

Guidance of a Solar Sail Spacecraft to the Sun - L(2) Point.

NASA Astrophysics Data System (ADS)

Hur, Sun Hae

The guidance of a solar sail spacecraft along a minimum-time path from an Earth orbit to a region near the Sun-Earth L_2 libration point is investigated. Possible missions to this point include a spacecraft "listening" for possible extra-terrestrial electromagnetic signals and a science payload to study the geomagnetic tail. A key advantage of the solar sail is that it requires no fuel. The control variables are the sail angles relative to the Sun-Earth line. The thrust is very small, on the order of 1 mm/s^2, and its magnitude and direction are highly coupled. Despite this limited controllability, the "free" thrust can be used for a wide variety of terminal conditions including halo orbits. If the Moon's mass is lumped with the Earth, there are quasi-equilibrium points near L_2. However, they are unstable so that some form of station keeping is required, and the sail can provide this without any fuel usage. In the two-dimensional case, regulating about a nominal orbit is shown to require less control and result in smaller amplitude error response than regulating about a quasi-equilibrium point. In the three-dimensional halo orbit case, station keeping using periodically varying gains is demonstrated. To compute the minimum-time path, the trajectory is divided into two segments: the spiral segment and the transition segment. The spiral segment is computed using a control law that maximizes the rate of energy increase at each time. The transition segment is computed as the solution of the time-optimal control problem from the endpoint of the spiral to the terminal point. It is shown that the path resulting from this approximate strategy is very close to the exact optimal path. For the guidance problem, the approximate strategy in the spiral segment already gives a nonlinear full-state feedback law. However, for large perturbations, follower guidance using an auxiliary propulsion is used for part of the spiral. In the transition segment, neighboring extremal feedback guidance using the solar sail, with feedforward control only near the terminal point, is used to correct perturbations in the initial conditions.

Equilibrium point control of a monkey arm simulator by a fast learning tree structured artificial neural network.

PubMed

Dornay, M; Sanger, T D

1993-01-01

A planar 17 muscle model of the monkey's arm based on realistic biomechanical measurements was simulated on a Symbolics Lisp Machine. The simulator implements the equilibrium point hypothesis for the control of arm movements. Given initial and final desired positions, it generates a minimum-jerk desired trajectory of the hand and uses the backdriving algorithm to determine an appropriate sequence of motor commands to the muscles (Flash 1987; Mussa-Ivaldi et al. 1991; Dornay 1991b). These motor commands specify a temporal sequence of stable (attractive) equilibrium positions which lead to the desired hand movement. A strong disadvantage of the simulator is that it has no memory of previous computations. Determining the desired trajectory using the minimum-jerk model is instantaneous, but the laborious backdriving algorithm is slow, and can take up to one hour for some trajectories. The complexity of the required computations makes it a poor model for biological motor control. We propose a computationally simpler and more biologically plausible method for control which achieves the benefits of the backdriving algorithm. A fast learning, tree-structured network (Sanger 1991c) was trained to remember the knowledge obtained by the backdriving algorithm. The neural network learned the nonlinear mapping from a 2-dimensional cartesian planar hand position (x,y) to a 17-dimensional motor command space (u1, . . ., u17). Learning 20 training trajectories, each composed of 26 sample points [[x,y], [u1, . . ., u17] took only 20 min on a Sun-4 Sparc workstation. After the learning stage, new, untrained test trajectories as well as the original trajectories of the hand were given to the neural network as input. The network calculated the required motor commands for these movements. The resulting movements were close to the desired ones for both the training and test cases.

The motion near L{sub 4} equilibrium point under non-point mass primaries

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

Huda, I. N., E-mail: ibnu.nurul@students.itb.ac.id; Utama, J. A.; Madley, D.

2015-09-30

The Circular Restricted Three-Body Problem (CRTBP) possesses five equilibrium points, that comprise three collinear (L{sub 1}, L{sub 2}, and L{sub 3}) and two triangular points (L{sub 4} and L{sub 5}). The classical study (with the primaries are point mass) suggests that the equilibrium points may cause the velocity of infinitesimal object relatively becomes zero and reveals the zero velocity curve. We study the motion of infinitesimal object near triangular equilibrium point (L{sub 4}) and determine its zero velocity curve. We extend the study by taking into account the effects of radiation of the bigger primary (q{sub 1} ≠ 1, q{submore » 2} = 1) and oblateness of the smaller primary (A{sub 1} = 0, A{sub 2} ≠ 0). The location of L{sub 4} is analytically derived then the stability of L{sub 4} and its zero velocity curves are studied numerically. Our study suggests that the oblateness and the radiation of primaries may affect the stability and zero velocity curve around L{sub 4}.« less

The timing of control signals underlying fast point-to-point arm movements.

PubMed

Ghafouri, M; Feldman, A G

2001-04-01

It is known that proprioceptive feedback induces muscle activation when the facilitation of appropriate motoneurons exceeds their threshold. In the suprathreshold range, the muscle-reflex system produces torques depending on the position and velocity of the joint segment(s) that the muscle spans. The static component of the torque-position relationship is referred to as the invariant characteristic (IC). According to the equilibrium-point (EP) hypothesis, control systems produce movements by changing the activation thresholds and thus shifting the IC of the appropriate muscles in joint space. This control process upsets the balance between muscle and external torques at the initial limb configuration and, to regain the balance, the limb is forced to establish a new configuration or, if the movement is prevented, a new level of static torques. Taken together, the joint angles and the muscle torques generated at an equilibrium configuration define a single variable called the EP. Thus by shifting the IC, control systems reset the EP. Muscle activation and movement emerge following the EP resetting because of the natural physical tendency of the system to reach equilibrium. Empirical and simulation studies support the notion that the control IC shifts and the resulting EP shifts underlying fast point-to-point arm movements are gradual rather than step-like. However, controversies exist about the duration of these shifts. Some studies suggest that the IC shifts cease with the movement offset. Other studies propose that the IC shifts end early in comparison to the movement duration (approximately, at peak velocity). The purpose of this study was to evaluate the duration of the IC shifts underlying fast point-to-point arm movements. Subjects made fast (hand peak velocity about 1.3 m/s) planar arm movements toward different targets while grasping a handle. Hand forces applied to the handle and shoulder/elbow torques were, respectively, measured from a force sensor placed on the handle, or computed with equations of motion. In some trials, an electromagnetic brake prevented movements. In such movements, the hand force and joint torques reached a steady state after a time that was much smaller than the movement duration in unobstructed movements and was approximately equal to the time to peak velocity (mean difference < 80 ms). In an additional experiment, subjects were instructed to rapidly initiate corrections of the pushing force in response to movement arrest. They were able to initiate such corrections only when the joint torques and the pushing force had practically reached a steady state. The latency of correction onset was, however, smaller than the duration of unobstructed movements. We concluded that during the time at which the steady state torques were reached, the control pattern of IC shifts remained the same despite the movement block. Thereby the duration of these shifts did not exceed the time of reaching the steady state torques. Our findings are consistent with the hypothesis that, in unobstructed movements, the IC shifts and resulting shifts in the EP end approximately at peak velocity. In other words, during the latter part of the movement, the control signals responsible for the equilibrium shift remained constant, and the movement was driven by the arm inertial, viscous and elastic forces produced by the muscle-reflex system. Fast movements may thus be completed without continuous control guidance. As a consequence, central corrections and sequential commands may be issued rapidly, without waiting for the end of kinematic responses to each command, which may be important for many motor behaviours including typing, piano playing and speech. Our study also illustrates that the timing of the control signals may be substantially different from that of the resulting motor output and that the same control pattern may produce different motor outputs depending on external conditions.

Rambling and trembling in response to body loading.

PubMed

Tahayor, Behdad; Riley, Zachary A; Mahmoudian, Armaghan; Koceja, David M; Hong, Siang Lee

2012-04-01

Various studies have suggested that postural sway is controlled by at least two subsystems. Rambling-Trembling analysis is a widely accepted methodology to dissociate the signals generated by these two hypothetical subsystems. The core assumption of this method is based on the equilibrium point hypothesis which suggests that the central nervous system preserves upright standing by transiently shifting the center of pressure (COP) from one equilibrium point to another. The trajectory generated by this shifting is referred to as rambling and its difference from the original COP signal is referred to as trembling. In this study we showed that these two components of COP are differentially affected when standing with external loads. Using Detrended Fluctuation analysis, we compared the pattern of these two signals in different configurations of body loading. Our findings suggest that by applying an external load, the dynamics of the trembling component is altered independently of the area of postural sway and also independently of the rambling component. The dynamics of rambling changed only during the backloading condition in which the postural sway area also substantially increased. It can be suggested that during loaded standing, the trembling mechanism (which is suggested to be activated by peripheral mechanisms and reflexes) is altered without affecting the central influence on the shifts of the equilibrium point.

Nonlinear analysis and control of an aircraft in the neighbourhood of deep stall

NASA Astrophysics Data System (ADS)

Kolb, Sébastien; Hétru, Laurent; Faure, Thierry M.; Montagnier, Olivier

2017-01-01

When an aircraft is locked in a stable equilibrium at high angle-of-attack, we have to do with the so-called deep stall which is a very dangerous situation. Airplanes with T-tail are mainly concerned with this phenomenon since the wake of the main wing flows over the horizontal tail and renders it ineffective but other aircrafts such as fighters can also be affected. First the phase portrait and bifurcation diagram are determined and characterized (with three equilibria in a deep stall prone configuration). It allows to diagnose the configurations of aircrafts susceptible to deep stall and also to point out the different types of time evolutions. Several techniques are used in order to determine the basin of attraction of the stable equilibrium at high angle-of-attack. They are based on the calculation of the stable manifold of the saddle-point equilibrium at medium angle-of-attack. Then several ways are explored in order to try to recover from deep stall. They exploits static features (such as curves of pitching moment versus angle-of-attack for full pitch down and full pitch up elevators) or dynamic aspects (excitation of the eigenmodes and improvement of the aerodynamic efficiency of the tail). Finally, some properties of a deep stall prone aircraft are pointed out and some control tools are also implemented. We try also to apply this mathematical results in a concrete situation by taking into account the captors specificities or by estimating the relevant variables thanks to other available information.

Modeling the intracellular pathogen-immune interaction with cure rate

NASA Astrophysics Data System (ADS)

Dubey, Balram; Dubey, Preeti; Dubey, Uma S.

2016-09-01

Many common and emergent infectious diseases like Influenza, SARS, Hepatitis, Ebola etc. are caused by viral pathogens. These infections can be controlled or prevented by understanding the dynamics of pathogen-immune interaction in vivo. In this paper, interaction of pathogens with uninfected and infected cells in presence or absence of immune response are considered in four different cases. In the first case, the model considers the saturated nonlinear infection rate and linear cure rate without absorption of pathogens into uninfected cells and without immune response. The next model considers the effect of absorption of pathogens into uninfected cells while all other terms are same as in the first case. The third model incorporates innate immune response, humoral immune response and Cytotoxic T lymphocytes (CTL) mediated immune response with cure rate and without absorption of pathogens into uninfected cells. The last model is an extension of the third model in which the effect of absorption of pathogens into uninfected cells has been considered. Positivity and boundedness of solutions are established to ensure the well-posedness of the problem. It has been found that all the four models have two equilibria, namely, pathogen-free equilibrium point and pathogen-present equilibrium point. In each case, stability analysis of each equilibrium point is investigated. Pathogen-free equilibrium is globally asymptotically stable when basic reproduction number is less or equal to unity. This implies that control or prevention of infection is independent of initial concentration of uninfected cells, infected cells, pathogens and immune responses in the body. The proposed models show that introduction of immune response and cure rate strongly affects the stability behavior of the system. Further, on computing basic reproduction number, it has been found to be minimum for the fourth model vis-a-vis other models. The analytical findings of each model have been exemplified by numerical simulations.

Non-equilibrium phase transitions in a driven-dissipative system of interacting bosons

NASA Astrophysics Data System (ADS)

Young, Jeremy T.; Foss-Feig, Michael; Gorshkov, Alexey V.; Maghrebi, Mohammad F.

2017-04-01

Atomic, molecular, and optical systems provide unique opportunities to study simple models of driven-dissipative many-body quantum systems. Typically, one is interested in the resultant steady state, but the non-equilibrium nature of the physics involved presents several problems in understanding its behavior theoretically. Recently, it has been shown that in many of these models, it is possible to map the steady-state phase transitions onto classical equilibrium phase transitions. In the language of Keldysh field theory, this relation typically only becomes apparent after integrating out massive fields near the critical point, leaving behind a single massless field undergoing near-equilibrium dynamics. In this talk, we study a driven-dissipative XXZ bosonic model and discover critical points at which two fields become gapless. Each critical point separates three different possible phases: a uniform phase, an anti-ferromagnetic phase, and a limit cycle phase. Furthermore, a description in terms of an equilibrium phase transition does not seem possible, so the associated phase transitions appear to be inherently non-equilibrium.

The Dynamics of HPV Infection and Cervical Cancer Cells.

PubMed

Asih, Tri Sri Noor; Lenhart, Suzanne; Wise, Steven; Aryati, Lina; Adi-Kusumo, F; Hardianti, Mardiah S; Forde, Jonathan

2016-01-01

The development of cervical cells from normal cells infected by human papillomavirus into invasive cancer cells can be modeled using population dynamics of the cells and free virus. The cell populations are separated into four compartments: susceptible cells, infected cells, precancerous cells and cancer cells. The model system of differential equations also has a free virus compartment in the system, which infect normal cells. We analyze the local stability of the equilibrium points of the model and investigate the parameters, which play an important role in the progression toward invasive cancer. By simulation, we investigate the boundary between initial conditions of solutions, which tend to stable equilibrium point, representing controlled infection, and those which tend to unbounded growth of the cancer cell population. Parameters affected by drug treatment are varied, and their effect on the risk of cancer progression is explored.

Multistability of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays.

PubMed

Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde

2015-11-01

The problem of coexistence and dynamical behaviors of multiple equilibrium points is addressed for a class of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays. By virtue of the fixed point theorem, nonsmooth analysis theory and other analytical tools, some sufficient conditions are established to guarantee that such n-dimensional memristive Cohen-Grossberg neural networks can have 5(n) equilibrium points, among which 3(n) equilibrium points are locally exponentially stable. It is shown that greater storage capacity can be achieved by neural networks with the non-monotonic activation functions introduced herein than the ones with Mexican-hat-type activation function. In addition, unlike most existing multistability results of neural networks with monotonic activation functions, those obtained 3(n) locally stable equilibrium points are located both in saturated regions and unsaturated regions. The theoretical findings are verified by an illustrative example with computer simulations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Points of Equilibrium in Electrostatic Fields.

ERIC Educational Resources Information Center

Rogers, Peter J.

1979-01-01

Discusses the electric field line pattern for four equal charges of the same sign placed at the corners of a square. The electric field intensity and the point of equilibrium are interpreted, taking into account three dimensions. (HM)

Retaining the equilibrium point hypothesis as an abstract description of the neuromuscular system.

PubMed

Tresilian, J R

1999-01-01

The lambda version of the equilibrium point (EP) hypothesis for motor control is examined in light of recent criticisms of its various instantiations. Four important assumptions that have formed the basis for recent criticism are analyzed: First, the assumption that intact muscles possess invariant force-length characteristics (ICs). Second, that these ICs are of the same form in agonist-antagonist pairs. Third, that muscle control is monoparametric and that the control parameter, lambda, can be given a neurophysiological interpretation. Fourth, that reflex loop time delays and the known, asymmetric, nonlinear mechanical properties of muscles can be ignored. Mechanical and neurophysiological investigations of the neuromuscular system suggests that none of these assumptions is likely to be correct. This has been taken to mean that the EP hypothesis is oversimplified and a new approach is needed. It is argued that such an approach can be provided without rejecting the EP hypothesis, rather to regard it as an input-output description of muscle and associated segmental circuits. The operation of the segmental circuitry can be interpreted as having the function, at least in part, of compensating for a variety of nonlinearities and asymmetries such that the overall system implements the lambda-EP model equations.

Sitnikov cyclic configuration of N+1-body problem

NASA Astrophysics Data System (ADS)

Shahbaz Ullah, M.; Hassan, M. R.

2014-12-01

This manuscript deals with the generalisation of all previous works on series solutions and linear stability of equilibrium points of the Sitnikov problem. Following Giacaglia (1967), in Sect. 2 we have derived the equation of motion of the infinitesimal mass moving along the z-axis about which the plane of motion is rotating with unit angular velocity. In Sects. 3, 4 and 5 the series solutions of the Sitnikov problem have been developed by the method of MacMillan, Lindstedt-Poincaré and iteration of Green's function respectively. In Sect. 6 the three series solutions have been compared graphically by putting N=2, 3, 4. In Sect. 7 the coordinates of equilibrium points have been calculated. In Sect. 8 the linear stability of equilibrium points has been examined by the method of Murray and Dermott (Solar System Dynamics, Cambridge University Press, Cambridge, 1999) and it was found that the equilibrium points are stable in Sitnikov problem.

The Hand: Shall We Ever Understand How it Works?

PubMed

Latash, Mark L

2015-04-01

The target article presents a review of the neural control of the human hand. The review emphasizes the physical approach to motor control. It focuses on such concepts as equilibrium-point control, control with referent body configurations, uncontrolled manifold hypothesis, principle of abundance, hierarchical control, multidigit synergies, and anticipatory synergy adjustments. Changes in aspects of the hand neural control with age and neurological disorder are discussed. The target article is followed by six commentaries written by Alexander Aruin, Kelly Cole, Monica Perez, Robert Sainburg, Marco Sanello, and Wei Zhang.

Robust and novel two degree of freedom fractional controller based on two-loop topology for inverted pendulum.

PubMed

Dwivedi, Prakash; Pandey, Sandeep; Junghare, A S

2018-04-01

A rotary single inverted pendulum (RSIP) typically represents a space booster rocket, Segway and similar systems with unstable equilibrium. This paper proposes a novel two degree of freedom (2-DOF) fractional control strategy based on 2-loop topology for RSIP system which can be extended to control the systems with unstable equilibrium. It comprises feedback and feed-forward paths. Primary controller relates the perturbation attenuation while the secondary controller is accountable for set point tracking. To tune the parameters of proposed fractional controller a simple graphical tuning method based on frequency response is used. The study will serve the outstanding experimental results for both, stabilization and trajectory tracking tasks. The study will also serve to present a comparison of the performance of the proposed controller with the 1-DOF FOPID controller and sliding mode controller (SMC) for the RSIP system. Further to confirm the usability of the proposed controller and to avoid the random perturbations sensitivity, robustness, and stability analysis through fractional root-locus and Bode-plot is investigated. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

An Approach to Optimal Control of Electrodynamic Tethers in a Stochastically Varying Drag Environment

DTIC Science & Technology

2011-05-06

and used to help address some of the complications and drawbacks of chemical propulsion systems. One such technology is electric propulsion, which...in and out of the orbital plane around its equilibrium point. The motion is similar to a swinging pendulum . These librations are due to the

Posture and Movement

NASA Technical Reports Server (NTRS)

1997-01-01

Session TP3 includes short reports on: (1) Modification of Goal-Directed Arm Movements During Inflight Adaptation to Microgravity; (2) Quantitative Analysis of Motion control in Long Term Microgravity; (3) Does the Centre of Gravity Remain the Stabilised Reference during Complex Human Postural Equilibrium Tasks in Weightlessness?; and (4) Arm End-Point Trajectories Under Normal and Microgravity Environments.

Thermal equilibrium concentrations and effects of negatively charged Ga vacancies in n-type GaAs

NASA Astrophysics Data System (ADS)

Tan, T. Y.; You, H.-M.; Gösele, U. M.

1993-03-01

We have calculated the thermal equilibrium concentrations of the various negatively charged Ga vacancy species in GaAs. The triply-negatively-charged Ga vacancy, V {Ga/3-}, has been emphasized, since it dominates Ga self-diffusion and Ga-Al interdiffusion under intrinsic and n-doping conditions, as well as the diffusion of Si donor atoms occupying Ga sites. Under strong n-doping conditions, the thermal equilibrium V {Ga/3-}concentration, C_{V_{_{Ga} }^{3 - } }^{eq} (n), has been found to exhibit a temperature independence or a negative temperature dependence, i.e., the C_{V_{_{Ga} }^{3 - } }^{eq} (n) value is either unchanged or increases as the temperature is lowered. This is quite contrary to the normal point defect behavior for which the point defect thermal equilibrium concentration decreases as the temperature is lowered. This C_{V_{_{Ga} }^{3 - } }^{eq} (n) property provides explanations to a number of outstanding experimental results, either requiring the interpretation that V {Ga/3-}has attained its thermal equilibrium concentration at the onset of each experiment, or requiring mechanisms involving point defect non-equilibrium phenomena.

How the credit assignment problems in motor control could be solved after the cerebellum predicts increases in error.

PubMed

Verduzco-Flores, Sergio O; O'Reilly, Randall C

2015-01-01

We present a cerebellar architecture with two main characteristics. The first one is that complex spikes respond to increases in sensory errors. The second one is that cerebellar modules associate particular contexts where errors have increased in the past with corrective commands that stop the increase in error. We analyze our architecture formally and computationally for the case of reaching in a 3D environment. In the case of motor control, we show that there are synergies of this architecture with the Equilibrium-Point hypothesis, leading to novel ways to solve the motor error and distal learning problems. In particular, the presence of desired equilibrium lengths for muscles provides a way to know when the error is increasing, and which corrections to apply. In the context of Threshold Control Theory and Perceptual Control Theory we show how to extend our model so it implements anticipative corrections in cascade control systems that span from muscle contractions to cognitive operations.

How the credit assignment problems in motor control could be solved after the cerebellum predicts increases in error

PubMed Central

Verduzco-Flores, Sergio O.; O'Reilly, Randall C.

2015-01-01

We present a cerebellar architecture with two main characteristics. The first one is that complex spikes respond to increases in sensory errors. The second one is that cerebellar modules associate particular contexts where errors have increased in the past with corrective commands that stop the increase in error. We analyze our architecture formally and computationally for the case of reaching in a 3D environment. In the case of motor control, we show that there are synergies of this architecture with the Equilibrium-Point hypothesis, leading to novel ways to solve the motor error and distal learning problems. In particular, the presence of desired equilibrium lengths for muscles provides a way to know when the error is increasing, and which corrections to apply. In the context of Threshold Control Theory and Perceptual Control Theory we show how to extend our model so it implements anticipative corrections in cascade control systems that span from muscle contractions to cognitive operations. PMID:25852535

Stability and Optimal Harvesting of Modified Leslie-Gower Predator-Prey Model

NASA Astrophysics Data System (ADS)

Toaha, S.; Azis, M. I.

2018-03-01

This paper studies a modified of dynamics of Leslie-Gower predator-prey population model. The model is stated as a system of first order differential equations. The model consists of one predator and one prey. The Holling type II as a predation function is considered in this model. The predator and prey populations are assumed to be beneficial and then the two populations are harvested with constant efforts. Existence and stability of the interior equilibrium point are analysed. Linearization method is used to get the linearized model and the eigenvalue is used to justify the stability of the interior equilibrium point. From the analyses, we show that under a certain condition the interior equilibrium point exists and is locally asymptotically stable. For the model with constant efforts of harvesting, cost function, revenue function, and profit function are considered. The stable interior equilibrium point is then related to the maximum profit problem as well as net present value of revenues problem. We show that there exists a certain value of the efforts that maximizes the profit function and net present value of revenues while the interior equilibrium point remains stable. This means that the populations can live in coexistence for a long time and also maximize the benefit even though the populations are harvested with constant efforts.

Crystal-liquid-vapor equilibrium experiments at high temperature (less than or equal to 1800 C) and low, controlled oxygen and hydrogen pressure (10(-1) to 10(-9) PA)

NASA Technical Reports Server (NTRS)

Mysen, B. O.

1987-01-01

Evidence from carbonaceous chrondrites points to refractory oxides in the system CaO-MgO-Al2O3-TiO2-SiO2-Fe-O as being among the earliest phases to condense from the solar nebula. It is necessary to establish the equilibrium relationships between the relevant crystalline and amorphous phases before the chemical constraints can be meaningfully applied to models of solar system history. Preliminary experiments on earth show that such experiments are feasible. Earth-based experiments suffer from several unavoidable problems. These problems can be overcome by experimentation in the Space Station where the experiments can be conducted under near static pressure conditions and where total pressure equals the sum of controlled hydrogen and oxygen pressures and can be controlled for periods exceeding several hours.

Motion in a modified Chermnykh's restricted three-body problem with oblateness

NASA Astrophysics Data System (ADS)

Singh, Jagadish; Leke, Oni

2014-03-01

In this paper, the restricted problem of three bodies is generalized to include a case when the passively gravitating test particle is an oblate spheroid under effect of small perturbations in the Coriolis and centrifugal forces when the first primary is a source of radiation and the second one an oblate spheroid, coupled with the influence of the gravitational potential from the belt. The equilibrium points are found and it is seen that, in addition to the usual three collinear equilibrium points, there appear two new ones due to the potential from the belt and the mass ratio. Two triangular equilibrium points exist. These equilibria are affected by radiation of the first primary, small perturbation in the centrifugal force, oblateness of both the test particle and second primary and the effect arising from the mass of the belt. The linear stability of the equilibrium points is explored and the stability outcome of the collinear equilibrium points remains unstable. In the case of the triangular points, motion is stable with respect to some conditions which depend on the critical mass parameter; influenced by the small perturbations, radiating effect of the first primary, oblateness of the test body and second primary and the gravitational potential from the belt. The effects of each of the imposed free parameters are analyzed. The potential from the belt and small perturbation in the Coriolis force are stabilizing parameters while radiation, small perturbation in the centrifugal force and oblateness reduce the stable regions. The overall effect is that the region of stable motion increases under the combine action of these parameters. We have also found the frequencies of the long and short periodic motion around stable triangular points. Illustrative numerical exploration is rendered in the Sun-Jupiter and Sun-Earth systems where we show that in reality, for some values of the system parameters, the additional equilibrium points do not in general exist even when there is a belt to interact with.

A possible four-phase coexistence in a single-component system

NASA Astrophysics Data System (ADS)

Akahane, Kenji; Russo, John; Tanaka, Hajime

2016-08-01

For different phases to coexist in equilibrium at constant temperature T and pressure P, the condition of equal chemical potential μ must be satisfied. This condition dictates that, for a single-component system, the maximum number of phases that can coexist is three. Historically this is known as the Gibbs phase rule, and is one of the oldest and venerable rules of thermodynamics. Here we make use of the fact that, by varying model parameters, the Gibbs phase rule can be generalized so that four phases can coexist even in single-component systems. To systematically search for the quadruple point, we use a monoatomic system interacting with a Stillinger-Weber potential with variable tetrahedrality. Our study indicates that the quadruple point provides flexibility in controlling multiple equilibrium phases and may be realized in systems with tunable interactions, which are nowadays feasible in several soft matter systems such as patchy colloids.

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

NASA Astrophysics Data System (ADS)

Maiti, Atasi Patra; Dubey, B.

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

A possible four-phase coexistence in a single-component system

PubMed Central

Akahane, Kenji; Russo, John; Tanaka, Hajime

2016-01-01

For different phases to coexist in equilibrium at constant temperature T and pressure P, the condition of equal chemical potential μ must be satisfied. This condition dictates that, for a single-component system, the maximum number of phases that can coexist is three. Historically this is known as the Gibbs phase rule, and is one of the oldest and venerable rules of thermodynamics. Here we make use of the fact that, by varying model parameters, the Gibbs phase rule can be generalized so that four phases can coexist even in single-component systems. To systematically search for the quadruple point, we use a monoatomic system interacting with a Stillinger–Weber potential with variable tetrahedrality. Our study indicates that the quadruple point provides flexibility in controlling multiple equilibrium phases and may be realized in systems with tunable interactions, which are nowadays feasible in several soft matter systems such as patchy colloids. PMID:27558452

Independent control of joint stiffness in the framework of the equilibrium-point hypothesis.

PubMed

Latash, M L

1992-01-01

In the framework of the equilibrium-point hypothesis, virtual trajectories and joint stiffness patterns have been reconstructed during two motor tasks practiced against a constant bias torque. One task required a voluntary increase in joint stiffness while preserving the original joint position. The other task involved fast elbow flexions over 36 degrees. Joint stiffness gradually subsided after the termination of fast movements. In both tasks, the external torque could slowly and unexpectedly change. The subjects were required not to change their motor commands if the torque changed, i.e. "to do the same no matter what the motor did". In both tasks, changes in joint stiffness were accompanied by unchanged virtual trajectories that were also independent of the absolute value of the bias torque. By contrast, the intercept of the joint compliant characteristic with the angle axis, r(t)-function, has demonstrated a clear dependence upon both the level of coactivation and external load. We assume that a template virtual trajectory is generated at a certain level of the motor hierarchy and is later scaled taking into account some commonly changing dynamic factors of the movement execution, for example, external load. The scaling leads to the generation of commands to the segmental structures that can be expressed, according to the equilibrium-point hypothesis, as changes in the thresholds of the tonic stretch reflex for corresponding muscles.

Collocation of equilibria in gravitational field of triangular body via mass redistribution

NASA Astrophysics Data System (ADS)

Burov, Alexander A.; Guerman, Anna D.; Nikonov, Vasily I.

2018-05-01

We consider a gravitating system with triangular mass distribution that can be used as approximation of gravitational field for small irregular celestial bodies. In such system, the locations of equilibrium points, that is, the points where the gravitational forces are balanced, are analyzed. The goal is to find the mass distribution which provides equilibrium in a pre-assigned location near the triangular system, and to study the stability of this equilibrium.

Dynamics Analysis of Anti-predator Model on Intermediate Predator With Ratio Dependent Functional Responses

NASA Astrophysics Data System (ADS)

Savitri, D.

2018-01-01

This articel discusses a predator prey model with anti-predator on intermediate predator using ratio dependent functional responses. Dynamical analysis performed on the model includes determination of equilibrium point, stability and simulation. Three kinds of equilibrium points have been discussed, namely the extinction of prey point, the extinction of intermediate predator point and the extinction of predator point are exists under certain conditions. It can be shown that the result of numerical simulations are in accordance with analitical results

The relationship between control, kinematic and electromyographic variables in fast single-joint movements in humans.

PubMed

Feldman, A G; Adamovich, S V; Levin, M F

1995-01-01

Two versions of the hypothesis that discrete movements are produced by shifts in the system's equilibrium point are considered. The first suggests that shifts are monotonic and end near the peak velocity of movement, and the second presumes that they are nonmonotonic ("N-shaped") and proceed until the end of movement. The first version, in contrast to the second, predicts that movement time may be significantly reduced by opposing loads without changes in the control pattern. The purpose of the present study was to test the two hypotheses about the duration and shape of the shift in the equilibrium point based on their respective predictions concerning the effects of perturbations on kinematic and EMG patterns in fast elbow flexor movements. Subjects performed unopposed flexions of about 55-70 degrees (control trials) and, in random test trials, movements were opposed by spring-like loads generated by a torque motor. Subjects had no visual feedback and were instructed not to correct arm deflections in case of perturbations. After the end of the movement, the load was removed leading to a secondary movement to the same final position as that in control trials (equifinality). When the load was varied, the static arm positions before unloading and associated joint torques (ranging from 0 to 80-90% of maximum voluntary contraction) had a monotonic relationship. Test movements opposed by a high load (80-90% of maximal voluntary contraction) ended near the peak velocity of control movements. Phasic and tonic electromyographic patterns were load-dependent. In movements opposed by high loads, the first agonist burst was significantly prolonged and displayed a high level of tonic activity for as long as the load was maintained. In the same load conditions, the antagonist burst was suppressed during the dynamic and static phases of movement. The findings of suppression of the antagonist burst does not support the hypothesis of an N-shaped control signal. Equally, the substantial reduction in movement time by the introduction of an opposing load cannot be reconciled in this model. Instead, our data indicate that the shifts in the equilibrium point underlying fast flexor movements are of short duration, ending near the peak velocity of unopposed movement. This suggests that kinematic and electromyographic patterns represent a long-lasting oscillatory response of the system to the short-duration monotonic control pattern, external forces and proprioceptive feedback.

Equilibrium points and associated periodic orbits in the gravity of binary asteroid systems: (66391) 1999 KW4 as an example

NASA Astrophysics Data System (ADS)

Shi, Yu; Wang, Yue; Xu, Shijie

2018-04-01

The motion of a massless particle in the gravity of a binary asteroid system, referred as the restricted full three-body problem (RF3BP), is fundamental, not only for the evolution of the binary system, but also for the design of relevant space missions. In this paper, equilibrium points and associated periodic orbit families in the gravity of a binary system are investigated, with the binary (66391) 1999 KW4 as an example. The polyhedron shape model is used to describe irregular shapes and corresponding gravity fields of the primary and secondary of (66391) 1999 KW4, which is more accurate than the ellipsoid shape model in previous studies and provides a high-fidelity representation of the gravitational environment. Both of the synchronous and non-synchronous states of the binary system are considered. For the synchronous binary system, the equilibrium points and their stability are determined, and periodic orbit families emanating from each equilibrium point are generated by using the shooting (multiple shooting) method and the homotopy method, where the homotopy function connects the circular restricted three-body problem and RF3BP. In the non-synchronous binary system, trajectories of equivalent equilibrium points are calculated, and the associated periodic orbits are obtained by using the homotopy method, where the homotopy function connects the synchronous and non-synchronous systems. Although only the binary (66391) 1999 KW4 is considered, our methods will also be well applicable to other binary systems with polyhedron shape data. Our results on equilibrium points and associated periodic orbits provide general insights into the dynamical environment and orbital behaviors in proximity of small binary asteroids and enable the trajectory design and mission operations in future binary system explorations.

The research of the coupled orbital-attitude controlled motion of celestial body in the neighborhood of the collinear libration point L1

NASA Astrophysics Data System (ADS)

Shmyrov, A.; Shmyrov, V.; Shymanchuk, D.

2017-10-01

This article considers the motion of a celestial body within the restricted three-body problem of the Sun-Earth system. The equations of controlled coupled attitude-orbit motion in the neighborhood of collinear libration point L1 are investigated. The translational orbital motion of a celestial body is described using Hill's equations of circular restricted three-body problem of the Sun-Earth system. Rotational orbital motion is described using Euler's dynamic equations and quaternion kinematic equation. We investigate the problem of stability of celestial body rotational orbital motion in relative equilibrium positions and stabilization of celestial body rotational orbital motion with proposed control laws in the neighborhood of collinear libration point L1. To study stabilization problem, Lyapunov function is constructed in the form of the sum of the kinetic energy and special "kinematic function" of the Rodriguez-Hamiltonian parameters. Numerical modeling of the controlled rotational motion of a celestial body at libration point L1 is carried out. The numerical characteristics of the control parameters and rotational motion are given.

Local Stability of AIDS Epidemic Model Through Treatment and Vertical Transmission with Time Delay

NASA Astrophysics Data System (ADS)

Novi W, Cascarilla; Lestari, Dwi

2016-02-01

This study aims to explain stability of the spread of AIDS through treatment and vertical transmission model. Human with HIV need a time to positively suffer AIDS. The existence of a time, human with HIV until positively suffer AIDS can be delayed for a time so that the model acquired is the model with time delay. The model form is a nonlinear differential equation with time delay, SIPTA (susceptible-infected-pre AIDS-treatment-AIDS). Based on SIPTA model analysis results the disease free equilibrium point and the endemic equilibrium point. The disease free equilibrium point with and without time delay are local asymptotically stable if the basic reproduction number is less than one. The endemic equilibrium point will be local asymptotically stable if the time delay is less than the critical value of delay, unstable if the time delay is more than the critical value of delay, and bifurcation occurs if the time delay is equal to the critical value of delay.

Two Archetypes of Motor Control Research.

PubMed

Latash, Mark L

2010-07-01

This reply to the Commentaries is focused on two archetypes of motor control research, one based on physics and physiology and the other based on control theory and ideas of neural computations. The former approach, represented by the equilibrium-point hypothesis, strives to discover the physical laws and salient physiological variables that make purposeful coordinated movements possible. The latter approach, represented by the ideas of internal models and optimal control, tries to apply methods of control developed for man-made inanimate systems to the human body. Specific issues related to control with subthreshold membrane depolarization, motor redundancy, and the idea of synergies are briefly discussed.

Linear active disturbance rejection control of underactuated systems: the case of the Furuta pendulum.

PubMed

Ramírez-Neria, M; Sira-Ramírez, H; Garrido-Moctezuma, R; Luviano-Juárez, A

2014-07-01

An Active Disturbance Rejection Control (ADRC) scheme is proposed for a trajectory tracking problem defined on a nonfeedback linearizable Furuta Pendulum example. A desired rest to rest angular position reference trajectory is to be tracked by the horizontal arm while the unactuated vertical pendulum arm stays around its unstable vertical position without falling down during the entire maneuver and long after it concludes. A linear observer-based linear controller of the ADRC type is designed on the basis of the flat tangent linearization of the system around an arbitrary equilibrium. The advantageous combination of flatness and the ADRC method makes it possible to on-line estimate and cancels the undesirable effects of the higher order nonlinearities disregarded by the linearization. These effects are triggered by fast horizontal arm tracking maneuvers driving the pendulum substantially away from the initial equilibrium point. Convincing experimental results, including a comparative test with a sliding mode controller, are presented. © 2013 ISA. Published by ISA. All rights reserved.

Design and Integration of an All-Magnetic Attitude Control System for FASTSAT-HSV01's Multiple Pointing Objectives

NASA Technical Reports Server (NTRS)

DeKock, Brandon; Sanders, Devon; Vanzwieten, Tannen; Capo-Lugo, Pedro

2011-01-01

The FASTSAT-HSV01 spacecraft is a microsatellite with magnetic torque rods as it sole attitude control actuator. FASTSAT s multiple payloads and mission functions require the Attitude Control System (ACS) to maintain Local Vertical Local Horizontal (LVLH)-referenced attitudes without spin-stabilization, while the pointing errors for some attitudes be significantly smaller than the previous best-demonstrated for this type of control system. The mission requires the ACS to hold multiple stable, unstable, and non-equilibrium attitudes, as well as eject a 3U CubeSat from an onboard P-POD and recover from the ensuing tumble. This paper describes the Attitude Control System, the reasons for design choices, how the ACS integrates with the rest of the spacecraft, and gives recommendations for potential future applications of the work.

Control Model for Dampening Hand Vibrations Using Information of Internal and External Coordinates

PubMed Central

Togo, Shunta; Kagawa, Takahiro; Uno, Yoji

2015-01-01

In the present study, we investigate a control mechanism that dampens hand vibrations. Here, we propose a control method with two components to suppress hand vibrations. The first is a passive suppression method that lowers the joint stiffness to passively dampen the hand vibrations. The second is an active suppression method that adjusts an equilibrium point based on skyhook control to actively dampen the hand vibrations. In a simulation experiment, we applied these two methods to dampen hand vibrations during the shoulder’s horizontal oscillation. We also conducted a measurement experiment wherein a subject’s shoulder was sinusoidally oscillated by a platform that generated horizontal oscillations. The results of the measurement experiments showed that the jerk of each part of the arm in a task using a cup filled with water was smaller than the shoulder jerk and that in a task with a cup filled with stones was larger than the shoulder jerk. Moreover, the amplitude of the hand trajectory in both horizontal and vertical directions was smaller in a task using a cup filled with water than in a task using a cup filled with stones. The results of the measurement experiments were accurately reproduced by the active suppression method based on skyhook control. These results suggest that humans dampen hand vibrations by controlling the equilibrium point through the information of the external workspace and the internal body state rather than by lowering joint stiffness only by using internal information. PMID:25876037

Phase Equilibrium, Chemical Equilibrium, and a Test of the Third Law: Experiments for Physical Chemistry.

ERIC Educational Resources Information Center

Dannhauser, Walter

1980-01-01

Described is an experiment designed to provide an experimental basis for a unifying point of view (utilizing theoretical framework and chemistry laboratory experiments) for physical chemistry students. Three experiments are described: phase equilibrium, chemical equilibrium, and a test of the third law of thermodynamics. (Author/DS)

Dynamics of an eco-epidemiological model with saturated incidence rate

NASA Astrophysics Data System (ADS)

Suryanto, Agus

2017-03-01

In this paper we study the effect of prey infection on the modified Leslie-Gower predator-prey model with saturated incidence rate. The model will be analyzed dynamically to find the equilibria and their existence conditions as well as their local stability conditions. It is found that there are six type of equilibria, namely the extinction of both prey and predator point, the extinction of infective prey and predator point, the extinction of predator point, the extinction of prey point, the extinction of infective prey point and the interior point. The first four equilibrium points are always unstable, while the last two equilibria are conditionally stable. We also find that the system undergoes Hopf bifurcation around the interior point which is controlled by the rate of infection. To illustrate our analytical results, we show some numerical results.

Combining fungal biopesticides and insecticide-treated bednets to enhance malaria control.

PubMed

Hancock, Penelope A

2009-10-01

In developing strategies to control malaria vectors, there is increased interest in biological methods that do not cause instant vector mortality, but have sublethal and lethal effects at different ages and stages in the mosquito life cycle. These techniques, particularly if integrated with other vector control interventions, may produce substantial reductions in malaria transmission due to the total effect of alterations to multiple life history parameters at relevant points in the life-cycle and transmission-cycle of the vector. To quantify this effect, an analytically tractable gonotrophic cycle model of mosquito-malaria interactions is developed that unites existing continuous and discrete feeding cycle approaches. As a case study, the combined use of fungal biopesticides and insecticide treated bednets (ITNs) is considered. Low values of the equilibrium EIR and human prevalence were obtained when fungal biopesticides and ITNs were combined, even for scenarios where each intervention acting alone had relatively little impact. The effect of the combined interventions on the equilibrium EIR was at least as strong as the multiplicative effect of both interventions. For scenarios representing difficult conditions for malaria control, due to high transmission intensity and widespread insecticide resistance, the effect of the combined interventions on the equilibrium EIR was greater than the multiplicative effect, as a result of synergistic interactions between the interventions. Fungal biopesticide application was found to be most effective when ITN coverage was high, producing significant reductions in equilibrium prevalence for low levels of biopesticide coverage. By incorporating biological mechanisms relevant to vectorial capacity, continuous-time vector population models can increase their applicability to integrated vector management.

Asymptotic stability estimates near an equilibrium point

NASA Astrophysics Data System (ADS)

Dumas, H. Scott; Meyer, Kenneth R.; Palacián, Jesús F.; Yanguas, Patricia

2017-07-01

We use the error bounds for adiabatic invariants found in the work of Chartier, Murua and Sanz-Serna [3] to bound the solutions of a Hamiltonian system near an equilibrium over exponentially long times. Our estimates depend only on the linearized system and not on the higher order terms as in KAM theory, nor do we require any steepness or convexity conditions as in Nekhoroshev theory. We require that the equilibrium point where our estimate applies satisfy a type of formal stability called Lie stability.

Equilibrium and Stability of a Pendulum in an Orbiting Spaceship.

ERIC Educational Resources Information Center

Blitzer, Leon

1979-01-01

Investigates the behavior of a simple pendulum attached to a fixed point inside a satellite moving in a circular orbit about the earth. It is found that the number of equilibrium positions depends on the length of the pendulum and the location of the point of attachment. (HM)

Frozen Orbits-Near Constant or Beneficially Varying Orbital Parameters.

DTIC Science & Technology

1986-05-15

89 6.3 Equatorial Near-Circular Orbits ............................... 92 6.4 Stable and Unstable Equilibrium Points ...Angle Libration Period......................................... 78 5-2 Lunar Gravitational Effect on Near-Circular Orbits .................... 80 5-3...6-1 Period of Oscillation about the Stable Equilibrium Point ............... 102 FIGURES Figure 2.1 Orbital Parameters

Local stability of a five dimensional food chain model in the ocean

NASA Astrophysics Data System (ADS)

Kusumawinahyu, W. M.; Hidayatulloh, M. R.

2014-02-01

This paper discuss a food chain model on a microbiology ecosystem in the ocean, where predation process occurs. Four population growth rates are discussed, namely bacteria, phytoplankton, zooplankton, and protozoa growth rate. When the growth of nutrient density is also considered, the model is governed by a five dimensional dynamical system. The system considered in this paper is a modification of a model proposed by Hadley and Forbes [1], by taking Holling Type I as the functional response. For sake of simplicity, the model needs to be scaled. Dynamical behavior, such as existence condition of equilibrium points and their local stability are addressed. There are eight equilibrium points, where two of them exist under certain conditions. Three equilibrium points are unstable, while two points stable under certain conditions and the other three points are stable if the Ruth-Hurwitz criteria are satisfied. Numerical simulations are carried out to illustrate analytical findings.

Impulsive control of a financial model [rapid communication

NASA Astrophysics Data System (ADS)

Sun, Jitao; Qiao, Fei; Wu, Qidi

2005-02-01

In this Letter, several new theorems on the stability of impulsive control systems are presented. These theorem are then used to find the conditions under which an advertising strategy can be asymptotically control to the equilibrium point by using impulsive control. Given the parameters of the financial model and the impulsive control law, an estimation of the upper bound of the impulse interval is given, i.e., number of advert can been decreased (i.e., can decrease cost) for to obtain the equivalent advertising effect.The result is illustrated to be efficient through a numerical example.

An alternative extragradient projection method for quasi-equilibrium problems.

PubMed

Chen, Haibin; Wang, Yiju; Xu, Yi

2018-01-01

For the quasi-equilibrium problem where the players' costs and their strategies both depend on the rival's decisions, an alternative extragradient projection method for solving it is designed. Different from the classical extragradient projection method whose generated sequence has the contraction property with respect to the solution set, the newly designed method possesses an expansion property with respect to a given initial point. The global convergence of the method is established under the assumptions of pseudomonotonicity of the equilibrium function and of continuity of the underlying multi-valued mapping. Furthermore, we show that the generated sequence converges to the nearest point in the solution set to the initial point. Numerical experiments show the efficiency of the method.

Groundwater flux estimation in streams: A thermal equilibrium approach

USGS Publications Warehouse

Zhou, Yan; Fox, Garey A.; Miller, Ron B.; Mollenhauer, Robert; Brewer, Shannon K.

2018-01-01

Stream and groundwater interactions play an essential role in regulating flow, temperature, and water quality for stream ecosystems. Temperature gradients have been used to quantify vertical water movement in the streambed since the 1960s, but advancements in thermal methods are still possible. Seepage runs are a method commonly used to quantify exchange rates through a series of streamflow measurements but can be labor and time intensive. The objective of this study was to develop and evaluate a thermal equilibrium method as a technique for quantifying groundwater flux using monitored stream water temperature at a single point and readily available hydrological and atmospheric data. Our primary assumption was that stream water temperature at the monitored point was at thermal equilibrium with the combination of all heat transfer processes, including mixing with groundwater. By expanding the monitored stream point into a hypothetical, horizontal one-dimensional thermal modeling domain, we were able to simulate the thermal equilibrium achieved with known atmospheric variables at the point and quantify unknown groundwater flux by calibrating the model to the resulting temperature signature. Stream water temperatures were monitored at single points at nine streams in the Ozark Highland ecoregion and five reaches of the Kiamichi River to estimate groundwater fluxes using the thermal equilibrium method. When validated by comparison with seepage runs performed at the same time and reach, estimates from the two methods agreed with each other with an R2 of 0.94, a root mean squared error (RMSE) of 0.08 (m/d) and a Nash–Sutcliffe efficiency (NSE) of 0.93. In conclusion, the thermal equilibrium method was a suitable technique for quantifying groundwater flux with minimal cost and simple field installation given that suitable atmospheric and hydrological data were readily available.

Groundwater flux estimation in streams: A thermal equilibrium approach

NASA Astrophysics Data System (ADS)

Zhou, Yan; Fox, Garey A.; Miller, Ron B.; Mollenhauer, Robert; Brewer, Shannon

2018-06-01

Stream and groundwater interactions play an essential role in regulating flow, temperature, and water quality for stream ecosystems. Temperature gradients have been used to quantify vertical water movement in the streambed since the 1960s, but advancements in thermal methods are still possible. Seepage runs are a method commonly used to quantify exchange rates through a series of streamflow measurements but can be labor and time intensive. The objective of this study was to develop and evaluate a thermal equilibrium method as a technique for quantifying groundwater flux using monitored stream water temperature at a single point and readily available hydrological and atmospheric data. Our primary assumption was that stream water temperature at the monitored point was at thermal equilibrium with the combination of all heat transfer processes, including mixing with groundwater. By expanding the monitored stream point into a hypothetical, horizontal one-dimensional thermal modeling domain, we were able to simulate the thermal equilibrium achieved with known atmospheric variables at the point and quantify unknown groundwater flux by calibrating the model to the resulting temperature signature. Stream water temperatures were monitored at single points at nine streams in the Ozark Highland ecoregion and five reaches of the Kiamichi River to estimate groundwater fluxes using the thermal equilibrium method. When validated by comparison with seepage runs performed at the same time and reach, estimates from the two methods agreed with each other with an R2 of 0.94, a root mean squared error (RMSE) of 0.08 (m/d) and a Nash-Sutcliffe efficiency (NSE) of 0.93. In conclusion, the thermal equilibrium method was a suitable technique for quantifying groundwater flux with minimal cost and simple field installation given that suitable atmospheric and hydrological data were readily available.

Summary of Research 1997, Department of Mathematics.

DTIC Science & Technology

1999-01-01

problems. This capabil- ity is especially important at the present time when technology in general, and information operations in particular, are changing...compression algorithms, especially the Radiant TIN algorithm and its use on tactical imagery. SUMMARY: Several aspects of this problem were...points are not always the same, especially when bifurcation occurs. The equilibrium sets of control systems and their bifurcations are classified based

Diverse origins of Arctic and Subarctic methane point source emissions identified with multiply-substituted isotopologues

NASA Astrophysics Data System (ADS)

Douglas, P. M. J.; Stolper, D. A.; Smith, D. A.; Walter Anthony, K. M.; Paull, C. K.; Dallimore, S.; Wik, M.; Crill, P. M.; Winterdahl, M.; Eiler, J. M.; Sessions, A. L.

2016-09-01

Methane is a potent greenhouse gas, and there are concerns that its natural emissions from the Arctic could act as a substantial positive feedback to anthropogenic global warming. Determining the sources of methane emissions and the biogeochemical processes controlling them is important for understanding present and future Arctic contributions to atmospheric methane budgets. Here we apply measurements of multiply-substituted isotopologues, or clumped isotopes, of methane as a new tool to identify the origins of ebullitive fluxes in Alaska, Sweden and the Arctic Ocean. When methane forms in isotopic equilibrium, clumped isotope measurements indicate the formation temperature. In some microbial methane, however, non-equilibrium isotope effects, probably related to the kinetics of methanogenesis, lead to low clumped isotope values. We identify four categories of emissions in the studied samples: thermogenic methane, deep subsurface or marine microbial methane formed in isotopic equilibrium, freshwater microbial methane with non-equilibrium clumped isotope values, and mixtures of deep and shallow methane (i.e., combinations of the first three end members). Mixing between deep and shallow methane sources produces a non-linear variation in clumped isotope values with mixing proportion that provides new constraints for the formation environment of the mixing end-members. Analyses of microbial methane emitted from lakes, as well as a methanol-consuming methanogen pure culture, support the hypothesis that non-equilibrium clumped isotope values are controlled, in part, by kinetic isotope effects induced during enzymatic reactions involved in methanogenesis. Our results indicate that these kinetic isotope effects vary widely in microbial methane produced in Arctic lake sediments, with non-equilibrium Δ18 values spanning a range of more than 5‰.

Reaction paths and equilibrium end-points in solid-solution aqueous-solution systems

USGS Publications Warehouse

Glynn, P.D.; Reardon, E.J.; Plummer, Niel; Busenberg, E.

1990-01-01

Equations are presented describing equilibrium in binary solid-solution aqueous-solution (SSAS) systems after a dissolution, precipitation, or recrystallization process, as a function of the composition and relative proportion of the initial phases. Equilibrium phase diagrams incorporating the concept of stoichiometric saturation are used to interpret possible reaction paths and to demonstrate relations between stoichiometric saturation, primary saturation, and thermodynamic equilibrium states. The concept of stoichiometric saturation is found useful in interpreting and putting limits on dissolution pathways, but there currently is no basis for possible application of this concept to the prediction and/ or understanding of precipitation processes. Previously published dissolution experiments for (Ba, Sr)SO4 and (Sr, Ca)C??O3orth. solids are interpreted using equilibrium phase diagrams. These studies show that stoichiometric saturation can control, or at least influence, initial congruent dissolution pathways. The results for (Sr, Ca)CO3orth. solids reveal that stoichiometric saturation can also control the initial stages of incongruent dissolution, despite the intrinsic instability of some of the initial solids. In contrast, recrystallisation experiments in the highly soluble KCl-KBr-H2O system demonstrate equilibrium. The excess free energy of mixing calculated for K(Cl, Br) solids is closely modeled by the relation GE = ??KBr??KClRT[a0 + a1(2??KBr-1)], where a0 is 1.40 ?? 0.02, a1, is -0.08 ?? 0.03 at 25??C, and ??KBr and ??KCl are the mole fractions of KBr and KCl in the solids. The phase diagram constructed using this fit reveals an alyotropic maximum located at ??KBr = 0.676 and at a total solubility product, ???? = [K+]([Cl-] + [Br-]) = 15.35. ?? 1990.

Stability of Poisson Equilibria and Hamiltonian Relative Equilibria by Energy Methods

NASA Astrophysics Data System (ADS)

Patrick, George W.; Roberts, Mark; Wulff, Claudia

2004-12-01

We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum Methods. Using a topological generalisation of Lyapunov’s result that an extremal critical point of a conserved quantity is stable, we show that a Poisson equilibrium is stable if it is an isolated point in the intersection of a level set of a conserved function with a subset of the phase space that is related to the topology of the symplectic leaf space at that point. This criterion is applied to generalise the energy-momentum method to Hamiltonian systems which are invariant under non-compact symmetry groups for which the coadjoint orbit space is not Hausdorff. We also show that a G-stable relative equilibrium satisfies the stronger condition of being A-stable, where A is a specific group-theoretically defined subset of G which contains the momentum isotropy subgroup of the relative equilibrium. The results are illustrated by an application to the stability of a rigid body in an ideal irrotational fluid.

Effect of (social) media on the political figure fever model: Jokowi-fever model

NASA Astrophysics Data System (ADS)

Yong, Benny; Samat, Nor Azah

2016-02-01

In recent years, political figures begin to utilize social media as one of alternative to engage in communication with their supporters. Publics referred to Jokowi, one of the candidates in Indonesia presidential election in 2014, as the first politician in Indonesia to truly understand the power of social media. Social media is very important in shaping public opinion. In this paper, effect of social media on the Jokowi-fever model in a closed population will be discussed. Supporter population is divided into three class sub-population, i.e susceptible supporters, Jokowi infected supporters, and recovered supporters. For case no positive media, there are two equilibrium points; the Jokowi-fever free equilibrium point in which it locally stable if basic reproductive ratio less than one and the Jokowi-fever endemic equilibrium point in which it locally stable if basic reproductive ratio greater than one. For case no negative media, there is only the Jokowi-fever endemic equilibrium point in which it locally stable if the condition is satisfied. Generally, for case positive media proportion is positive, there is no Jokowi-fever free equilibrium point. The numerical result shows that social media gives significantly effect on Jokowi-fever model, a sharp increase or a sharp decrease in the number of Jokowi infected supporters. It is also shown that the boredom rate is one of the sensitive parameters in the Jokowi-fever model; it affects the number of Jokowi infected supporters.

Effect of Stellar Wind and Poynting-Robertson Drag on Photogravitational Elliptic Restricted Three Body Problem

NASA Astrophysics Data System (ADS)

Chakraborty, A.; Narayan, A.

2018-03-01

The existence and linear stability of the planar equilibrium points for photogravitational elliptical restricted three body problem is investigated in this paper. Assuming that the primaries, one of which is radiating are rotating in an elliptical orbit around their common center of mass. The effect of the radiation pressure, forces due to stellar wind and Poynting-Robertson drag on the dust particles are considered. The location of the five equilibrium points are found using analytical methods. It is observed that the collinear equilibrium points L 1, L 2 and L 3 do not lie on the line joining the primaries but are shifted along the y-coordinate. The instability of the libration points due to the presence of the drag forces is demonstrated by Lyapunov's first method of stability.

Geochemical behavior and dissolved species control in acid sand pit lakes, Sepetiba sedimentary basin, Rio de Janeiro, SE - Brazil

NASA Astrophysics Data System (ADS)

Marques, Eduardo D.; Sella, Sílvia M.; Bidone, Edison D.; Silva-Filho, Emmanoel V.

2010-12-01

This work shows the influence of pluvial waters on dissolved components and mineral equilibrium of four sand pit lakes, located in the Sepetiba sedimentary basin, SE Brazil. The sand mining activities promote sediment oxidation, lowering pH and increasing SO 4 contents. The relatively high acidity of these waters, similar to ore pit lakes environment and associated acid mine drainage, increases weathering rate, especially of silicate minerals, which produces high Al concentrations, the limiting factor for fish aquaculture. During the dry season, basic cations (Ca, Mg, K and Na), SiO 2 and Al show their higher values due to evapoconcentration and pH are buffered. In the beginning of the wet season, the dilution factor by rainwater increases SO 4 and decreases pH values. The aluminum monomeric forms (Al(OH) 2+ and Al(OH) 2+), the most toxic species for aquatic organisms, occur during the dry season, while AlSO 4+ species predominate during the wet season. Gibbsite, allophane, alunite and jurbanite are the reactive mineral phases indicated by PHREEQC modeling. During the dry season, hydroxialuminosilicate allophane is the main phase in equilibrium with the solution, while the sulphate salts alunite and jurbanite predominate in the rainy season due to the increasing of SO 4 values. Gibbsite is also in equilibrium with sand pit lakes waters, pointing out that hydrolysis reaction is a constant process in the system. Comparing to SiO 2, sulphate is the main Al retriever in the pit waters because the most samples (alunite and jurbanite) are in equilibrium with the solution in both seasons. This Al hydrochemical control allied to some precaution, like pH correction and fertilization of these waters, allows the conditions for fishpond culture. Equilibrium of the majority samples with kaolinite (Ca, Mg, Na diagrams) and primary minerals (K diagram) points to moderate weathering rate in sand pit sediments, which cannot be considered for the whole basin due to the anomalous acidification of the studied waters.

Local Voltage Control in Distribution Networks: A Game-Theoretic Perspective

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

Zhou, Xinyang; Tian, Jie; Chen, Lijun

Inverter-based voltage regulation is gaining importance to alleviate emerging reliability and power-quality concerns related to distribution systems with high penetration of photovoltaic (PV) systems. This paper seeks contribution in the domain of reactive power compensation by establishing stability of local Volt/VAr controllers. In lieu of the approximate linear surrogate used in the existing work, the paper establishes existence and uniqueness of an equilibrium point using nonlinear AC power flow model. Key to this end is to consider a nonlinear dynamical system with non-incremental local Volt/VAr control, cast the Volt/VAr dynamics as a game, and leverage the fixed-point theorem as wellmore » as pertinent contraction mapping argument. Numerical examples are provided to complement the analytical results.« less

Local Voltage Control in Distribution Networks: A Game-Theoretic Perspective: Preprint

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

Zhou, Xinyang; Tian, Jie; Chen, Lijun

Inverter-based voltage regulation is gaining importance to alleviate emerging reliability and power-quality concerns related to distribution systems with high penetration of photovoltaic (PV) systems. This paper seeks contribution in the domain of reactive power compensation by establishing stability of local Volt/VAr controllers. In lieu of the approximate linear surrogate used in the existing work, the paper establishes existence and uniqueness of an equilibrium point using nonlinear AC power flow model. Key to this end is to consider a nonlinear dynamical system with non-incremental local Volt/VAr control, cast the Volt/VAr dynamics as a game, and leverage the fixed-point theorem as wellmore » as pertinent contraction mapping argument. Numerical examples are provided to complement the analytical results.« less

High vacuum measurements and calibrations, molecular flow fluid transient effects

DOE PAGES

Leishear, Robert A.; Gavalas, Nickolas A.

2015-04-29

High vacuum pressure measurements and calibrations below 1 × 10 -8 Torr are problematic. Specifically, measurement accuracies change drastically for vacuum gauges when pressures are suddenly lowered in vacuum systems. How can gauges perform like this? A brief system description is first required to answer this question. Calibrations were performed using a vacuum calibration chamber with attached vacuum gauges. To control chamber pressures, vacuum pumps decreased the chamber pressure while nitrogen tanks increased the chamber pressure. By balancing these opposing pressures, equilibrium in the chamber was maintained at selected set point pressures to perform calibrations. When pressures were suddenly decreasedmore » during set point adjustments, a sudden rush of gas from the chamber also caused a surge of gas from the gauges to decrease the pressures in those gauges. Gauge pressures did not return to equilibrium as fast as chamber pressures due to the sparse distribution of gas molecules in the system. This disparity in the rate of pressure changes caused the pressures in different gauges to be different than expected. This discovery was experimentally proven to show that different gauge designs return to equilibrium at different rates, and that gauge accuracies vary for different gauge designs due to fluid transients in molecular flow.« less

Vertical Position and Current Profile Measurements by Faraday-effect Polarimetry On EAST tokamak

NASA Astrophysics Data System (ADS)

Ding, Weixing; Liu, H. Q.; Jie, Y. X.; Brower, D. L.; Qian, J. P.; Zou, Z. Y.; Lian, H.; Wang, S. X.; Luo, Z. P.; Xiao, B. J.; Ucla Team; Asipp Team

2017-10-01

A primary goal for ITER and prospective fusion power reactors is to achieve controlled long-pulse/steady-state burning plasmas. For elongated divertor plasmas, both the vertical position and current profile have to be precisely controlled to optimize performance and prevent disruptions. An eleven-channel laser-based POlarimeter-INTerferometer (POINT) system has been developed for measuring the internal magnetic field in the EAST tokamak and can be used to obtain the plasma current profile and vertical position. Current profiles are determined from equilibrium reconstruction including internal magnetic field measurements as internal constraints. Horizontally-viewing chords at/near the mid-plane allow us to determine plasma vertical position non-inductively with subcentimeter spatial resolution and time response up to 1 s. The polarimeter-based position measurement, which does not require equilibrium reconstruction, is benchmarked against conventional flux loop measurements and can be exploited for feedback control. Work supported by US DOE through Grants No. DE-FG02-01ER54615 and No. DC-SC0010469.

Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds.

PubMed

Lu, Haishu; Wang, Zhihua

2017-01-01

This paper deals with the abstract generalized vector quasi-equilibrium problem in noncompact Hadamard manifolds. We prove the existence of solutions to the abstract generalized vector quasi-equilibrium problem under suitable conditions and provide applications to an abstract vector quasi-equilibrium problem, a generalized scalar equilibrium problem, a scalar equilibrium problem, and a perturbed saddle point problem. Finally, as an application of the existence of solutions to the generalized scalar equilibrium problem, we obtain a weakly mixed variational inequality and two mixed variational inequalities. The results presented in this paper unify and generalize many known results in the literature.

Controlling dynamical quantum phase transitions

NASA Astrophysics Data System (ADS)

Kennes, D. M.; Schuricht, D.; Karrasch, C.

2018-05-01

We study the dynamics arising from a double quantum quench where the parameters of a given Hamiltonian are abruptly changed from being in an equilibrium phase A to a different phase B and back (A →B →A ). As prototype models, we consider the (integrable) transverse Ising field as well as the (nonintegrable) ANNNI model. The return amplitude features nonanalyticities after the first quench through the equilibrium quantum critical point (A →B ), which is routinely taken as a signature of passing through a so-called dynamical quantum phase transition. We demonstrate that nonanalyticities after the second quench (B →A ) can be avoided and reestablished in a recurring manner upon increasing the time T spent in phase B. The system retains an infinite memory of its past state, and one has the intriguing opportunity to control at will whether or not dynamical quantum phase transitions appear after the second quench.

Mathematical model of temephos resistance in Aedes aegypti mosquito population

NASA Astrophysics Data System (ADS)

Aldila, D.; Nuraini, N.; Soewono, E.; Supriatna, A. K.

2014-03-01

Aedes aegypti is the main vector of dengue disease in many tropical and sub-tropical countries. Dengue became major public concern in these countries due to the unavailability of vaccine or drugs for dengue disease in the market. Hence, the only way to control the spread of DF and DHF is by controlling the vectors carrying the disease, for instance with fumigation, temephos or genetic manipulation. Many previous studies conclude that Aedes aegypti may develop resistance to many kind of insecticide, including temephos. Mathematical model for transmission of temephos resistance in Aedes aegypti population is discussed in this paper. Nontrivial equilibrium point of the system and the corresponding existence are shown analytically. The model analysis have shown epidemiological trends condition that permits the coexistence of nontrivial equilibrium is given analytically. Numerical results are given to show parameter sensitivity and some cases of worsening effect values for illustrating possible conditions in the field.

Counting relative equilibrium configurations of the full two-body problem

NASA Astrophysics Data System (ADS)

Moeckel, Richard

2018-02-01

Consider a system of two rigid, massive bodies interacting according to their mutual gravitational attraction. In a relative equilibrium motion, the bodies rotate rigidly and uniformly about a fixed axis in R^3. This is possible only for special positions and orientations of the bodies. After fixing the angular momentum, these relative equilibrium configurations can be characterized as critical points of a smooth function on configuration space. The goal of this paper is to use Morse theory and Lusternik-Schnirelmann category theory to give lower bounds for the number of critical points when the angular momentum is sufficiently large. In addition, the exact number of critical points and their Morse indices are found in the limit as the angular momentum tends to infinity.

Dynamic Analysis of the Melanoma Model: From Cancer Persistence to Its Eradication

NASA Astrophysics Data System (ADS)

Starkov, Konstantin E.; Jimenez Beristain, Laura

In this paper, we study the global dynamics of the five-dimensional melanoma model developed by Kronik et al. This model describes interactions of tumor cells with cytotoxic T cells and respective cytokines under cellular immunotherapy. We get the ultimate upper and lower bounds for variables of this model, provide formulas for equilibrium points and present local asymptotic stability/hyperbolic instability conditions. Next, we prove the existence of the attracting set. Based on these results we come to global asymptotic melanoma eradication conditions via global stability analysis. Finally, we provide bounds for a locus of the melanoma persistence equilibrium point, study the case of melanoma persistence and describe conditions under which we observe global attractivity to the unique melanoma persistence equilibrium point.

Complete stability of delayed recurrent neural networks with Gaussian activation functions.

PubMed

Liu, Peng; Zeng, Zhigang; Wang, Jun

2017-01-01

This paper addresses the complete stability of delayed recurrent neural networks with Gaussian activation functions. By means of the geometrical properties of Gaussian function and algebraic properties of nonsingular M-matrix, some sufficient conditions are obtained to ensure that for an n-neuron neural network, there are exactly 3 k equilibrium points with 0≤k≤n, among which 2 k and 3 k -2 k equilibrium points are locally exponentially stable and unstable, respectively. Moreover, it concludes that all the states converge to one of the equilibrium points; i.e., the neural networks are completely stable. The derived conditions herein can be easily tested. Finally, a numerical example is given to illustrate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Noise-induced extinction for a ratio-dependent predator-prey model with strong Allee effect in prey

NASA Astrophysics Data System (ADS)

Mandal, Partha Sarathi

2018-04-01

In this paper, we study a stochastically forced ratio-dependent predator-prey model with strong Allee effect in prey population. In the deterministic case, we show that the model exhibits the stable interior equilibrium point or limit cycle corresponding to the co-existence of both species. We investigate a probabilistic mechanism of the noise-induced extinction in a zone of stable interior equilibrium point. Computational methods based on the stochastic sensitivity function technique are applied for the analysis of the dispersion of random states near stable interior equilibrium point. This method allows to construct a confidence domain and estimate the threshold value of the noise intensity for a transition from the coexistence to the extinction.

Experimental Investigation of Gas/Slag/Matte/Tridymite Equilibria in the Cu-Fe-O-S-Si System in Controlled Atmospheres: Development of Technique

NASA Astrophysics Data System (ADS)

Fallah-Mehrjardi, Ata; Hidayat, Taufiq; Hayes, Peter C.; Jak, Evgueni

2017-12-01

The majority of primary pyrometallurgical copper making processes involve the formation of two immiscible liquid phases, i.e., matte product and the slag phase. There are significant gaps and discrepancies in the phase equilibria data of the slag and the matte systems due to issues and difficulties in performing the experiments and phase analysis. The present study aims to develop an improved experimental methodology for accurate characterisation of gas/slag/matte/tridymite equilibria in the Cu-Fe-O-S-Si system under controlled atmospheres. The experiments involve high-temperature equilibration of synthetic mixtures on silica substrates in CO/CO2/SO2/Ar atmospheres, rapid quenching of samples into water, and direct composition measurement of the equilibrium phases using Electron Probe X-ray Microanalysis (EPMA). A four-point-test procedure was applied to ensure the achievement of equilibrium, which included the following: (i) investigation of equilibration as a function of time, (ii) assessment of phase homogeneity, (iii) confirmation of equilibrium by approaching from different starting conditions, and (iv) systematic analysis of the reactions specific to the system. An iterative improved experimental methodology was developed using this four-point-test approach to characterize the complex multi-component, multi-phase equilibria with high accuracy and precision. The present study is a part of a broader overall research program on the characterisation of the multi-component (Cu-Fe-O-S-Si-Al-Ca-Mg), multi-phase (gas/slag/matte/metal/solids) systems with minor elements (Pb, Zn, As, Bi, Sn, Sb, Ag, and Au).

Stability of equilibrium solutions of Hamiltonian systems with n-degrees of freedom and single resonance in the critical case

NASA Astrophysics Data System (ADS)

dos Santos, Fabio; Vidal, Claudio

2018-04-01

In this paper we give new results for the stability of one equilibrium solution of an autonomous analytic Hamiltonian system in a neighborhood of the equilibrium point with n-degrees of freedom. Our Main Theorem generalizes several results existing in the literature and mainly we give information in the critical cases (i.e., the condition of stability and instability is not fulfilled). In particular, our Main Theorem provides necessary and sufficient conditions for stability of the equilibrium solutions under the existence of a single resonance. Using analogous tools used in the Main Theorem for the critical case, we study the stability or instability of degenerate equilibrium points in Hamiltonian systems with one degree of freedom. We apply our results to the stability of Hamiltonians of the type of cosmological models as in planar as in the spatial case.

Multistability of second-order competitive neural networks with nondecreasing saturated activation functions.

PubMed

Nie, Xiaobing; Cao, Jinde

2011-11-01

In this paper, second-order interactions are introduced into competitive neural networks (NNs) and the multistability is discussed for second-order competitive NNs (SOCNNs) with nondecreasing saturated activation functions. Firstly, based on decomposition of state space, Cauchy convergence principle, and inequality technique, some sufficient conditions ensuring the local exponential stability of 2N equilibrium points are derived. Secondly, some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region. Thirdly, the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the SOCNNs can have (r+1)N locally exponentially stable equilibrium points. Even if there is no second-order interactions, the obtained results are less restrictive than those in some recent works. Finally, three examples with their simulations are presented to verify the theoretical analysis.

Anti-sway control of tethered satellite systems using attitude control of the main satellite

NASA Astrophysics Data System (ADS)

Yousefian, Peyman; Salarieh, Hassan

2015-06-01

In this study a new method is introduced to suppress libration of a tethered satellite system (TSS). It benefits from coupling between satellites and tether libration dynamics. The control concept uses the main satellite attitude maneuvers to suppress librational motion of the tether, and the main satellite's actuators for attitude control are used as the only actuation in the system. The study considers planar motion of a two body TSS system in a circular orbit and it is assumed that the tether's motion will not change it. Governing dynamic equations of motion are derived using the extended Lagrange method. Controllability of the system around the equilibrium state is studied and a linear LQG controller is designed to regulate libration of the system. Tether tension and satellite attitude are assumed as only measurable outputs of the system. The Extended Kalman Filter (EKF) is used to estimate states of the system to be used as feedback to the controller. The designed controller and observer are implemented to the nonlinear plant and simulations demonstrate that the controller lead to reduction of the tether libration propoerly. By the way, because the controller is linear, it is applicable only at low amplitudes in the vicinity of equilibrium point. To reach global stability, a nonlinear controller is demanded.

A Locust Phase Change Model with Multiple Switching States and Random Perturbation

NASA Astrophysics Data System (ADS)

Xiang, Changcheng; Tang, Sanyi; Cheke, Robert A.; Qin, Wenjie

2016-12-01

Insects such as locusts and some moths can transform from a solitarious phase when they remain in loose populations and a gregarious phase, when they may swarm. Therefore, the key to effective management of outbreaks of species such as the desert locust Schistocercagregaria is early detection of when they are in the threshold state between the two phases, followed by timely control of their hopper stages before they fledge because the control of flying adult swarms is costly and often ineffective. Definitions of gregarization thresholds should assist preventive control measures and avoid treatment of areas that might not lead to gregarization. In order to better understand the effects of the threshold density which represents the gregarization threshold on the outbreak of a locust population, we developed a model of a discrete switching system. The proposed model allows us to address: (1) How frequently switching occurs from solitarious to gregarious phases and vice versa; (2) When do stable switching transients occur, the existence of which indicate that solutions with larger amplitudes can switch to a stable attractor with a value less than the switching threshold density?; and (3) How does random perturbation influence the switching pattern? Our results show that both subsystems have refuge equilibrium points, outbreak equilibrium points and bistable equilibria. Further, the outbreak equilibrium points and bistable equilibria can coexist for a wide range of parameters and can switch from one to another. This type of switching is sensitive to the intrinsic growth rate and the initial values of the locust population, and may result in locust population outbreaks and phase switching once a small perturbation occurs. Moreover, the simulation results indicate that the switching transient patterns become identical after some generations, suggesting that the evolving process of the perturbation system is not related to the initial value after some fixed number of generations for the same stochastic processes. However, the switching frequency and outbreak patterns can be significantly affected by the intensity of noise and the intrinsic growth rate of the locust population.

Extreme multistability analysis of memristor-based chaotic system and its application in image decryption

NASA Astrophysics Data System (ADS)

Li, Chuang; Min, Fuhong; Jin, Qiusen; Ma, Hanyuan

2017-12-01

An active charge-controlled memristive Chua's circuit is implemented, and its basic properties are analyzed. Firstly, with the system trajectory starting from an equilibrium point, the dynamic behavior of multiple coexisting attractors depending on the memristor initial value and the system parameter is studied, which shows the coexisting behaviors of point, period, chaos, and quasic-period. Secondly, with the system motion starting from a non-equilibrium point, the dynamics of extreme multistability in a wide initial value domain are easily conformed by new analytical methods. Furthermore, the simulation results indicate that some strange chaotic attractors like multi-wing type and multi-scroll type are observed when the observed signals are extended from voltage and current to power and energy, respectively. Specially, when different initial conditions are taken, the coexisting strange chaotic attractors between the power and energy signals are exhibited. Finally, the chaotic sequences of the new system are used for encrypting color image to protect image information security. The encryption performance is analyzed by statistic histogram, correlation, key spaces and key sensitivity. Simulation results show that the new memristive chaotic system has high security in color image encryption.

Determining Equilibrium Position For Acoustical Levitation

NASA Technical Reports Server (NTRS)

Barmatz, M. B.; Aveni, G.; Putterman, S.; Rudnick, J.

1989-01-01

Equilibrium position and orientation of acoustically-levitated weightless object determined by calibration technique on Earth. From calibration data, possible to calculate equilibrium position and orientation in presence of Earth gravitation. Sample not levitated acoustically during calibration. Technique relies on Boltzmann-Ehrenfest adiabatic-invariance principle. One converts resonant-frequency-shift data into data on normalized acoustical potential energy. Minimum of energy occurs at equilibrium point. From gradients of acoustical potential energy, one calculates acoustical restoring force or torque on objects as function of deviation from equilibrium position or orientation.

Dynamical properties of a prey-predator-scavenger model with quadratic harvesting

NASA Astrophysics Data System (ADS)

Gupta, R. P.; Chandra, Peeyush

2017-08-01

In this paper, we propose and analyze an extended model for the prey-predator-scavenger in presence of harvesting to study the effects of harvesting of predator as well as scavenger. The positivity, boundedness and persistence conditions are derived for the proposed model. The model undergoes a Hopf-bifurcation around the co-existing equilibrium point. It is also observed that the model is capable of exhibiting period doubling route to chaos. It is pointed out that a suitable amount of harvesting of predator can control the chaotic dynamics and make the system stable. An extensive numerical simulation is performed to validate the analytic findings. The associated control problem for the proposed model has been analyzed for optimal harvesting.

Dynamics of tethered satellites in the vicinity of the Lagrangian point L2 of the Earth-Moon system

NASA Astrophysics Data System (ADS)

Baião, M. F.; Stuchi, T. J.

2017-08-01

This paper analyzes the dynamical evolution of satellites formed by two masses connected by a cable— tethered satellites. We derive the Lagrangian equations of motion in the neighborhood of the collinear equilibrium points, especially for the L2 , of the restricted problem of three bodies. The rigid body configuration is expanded in Legendre polynomials up to fourth degree. We present some numerical simulations of the influence of the parameters such as cable length, mass ratio and initial conditions in the behavior of the tethered satellites. The equation for the collinear equilibrium point is derived and numerically solved. The evolution of the equilibria with the variation of the cable length as a parameter is studied. We also present a discussion of the linear stability around these equilibria. Based on this analysis calculate some unstable Lyapunov orbits associated to these equilibrium points. We found periodic orbits in which the tether travels parallel to itself without involving the angular motion. The numerical applications are focused on the Earth-Moon system. However, the general character of the equations allows applications to the L1 equilibrium and obviously to systems other than the Earth-Moon.

Shifts in Key Time Points and Strategies for a Multisegment Motor Task in Healthy Aging Subjects.

PubMed

Casteran, Matthieu; Hilt, Pauline M; Mourey, France; Manckoundia, Patrick; French, Robert; Thomas, Elizabeth

2018-05-05

In this study, we compared key temporal points in the whole body pointing movement of healthy aging and young subjects. During this movement, subject leans forward from a standing position to reach a target. As it involves forward inclination of the trunk, the movement creates a risk for falling. We examined two strategic time points during the task-first, the crossover point where the velocity of the center of mass (CoM) in the vertical dimension outstripped the velocity in the anteroposterior dimension and secondly, the time to peak of the CoM velocity profile. Transitions to stabilizing postures occur at these time points. They both occurred earlier in aging subjects. The crossover point also showed adjustments with target distance in aging subjects, while this was not observed in younger subjects. The shifts in these key time points could not be attributed to differences in movement duration between the two groups. Investigation with an optimal control model showed that the temporal adjustment as a function of target distance in the healthy aging subjects fits into a strategy that emphasized equilibrium maintenance rather than absolute work as a control strategy.

Investigating Strategies to Increase Persistence and Success Rates among Anatomy & Physiology Students: A Case Study at Austin Community College District

NASA Astrophysics Data System (ADS)

Vedartham, Padmaja B.

Snap-through buckling provides an intricate force-displacement relationship for study. With the possibility for multiple limit points and pitchfork bifurcations and large regions of instability, experimental validation of numerical analysis can become difficult. This requires stabilization of unstable static equilibria, for which limited prior research exists. For all but the simplest cases, more than one actuator is needed, increasing the complexity of the experiment to the point of intractability without a control system. In this thesis, the necessary conditions for stabilization of a buckled beam with pinned boundaries under transverse loading were determined. By combining various nonlinear solution methods, a control system was created that could stabilize any branch of the force-displacement response. Experimental traversal of an unstable branch are presented along with other unstable static equilibrium configurations. The control system had numerical limitations, losing convergence near singular points. The groundwork for experimental stabilization was validated and demonstrated.

The gallium melting-point standard: its role in manufacture and quality control of electronic thermometers for the clinical laboratory.

PubMed

Sostman, H E

1977-01-01

I discuss the traceability of calibration of electronic thermometers to thermometric constants of nature or to the National Bureau of Standards, form a manufacturer's basic standards through the manufacturing process to the user's laboratory. Useful electrical temperature sensors, their advantages, and means for resolving their disadvantages are described. I summarize our development of a cell for realizing the melting phase equilibrium of pure gallium (at 29.770 degrees C) as a thermometer calibration fixed point, and enumerate its advantages in the routine calibration verification of electrical thermometers in the clinical chemistry laboratory.

Entropy in Collisionless Self-gravitating Systems

NASA Astrophysics Data System (ADS)

Barnes, Eric; Williams, L.

2010-01-01

Collisionless systems, like simulated dark matter halos or gas-less elliptical galaxies, often times have properties suggesting that a common physical principle controls their evolution. For example, N-body simulations of dark matter halos present nearly scale-free density/velocity-cubed profiles. In an attempt to understand the origins of such relationships, we adopt a thermodynamics approach. While it is well-known that self-gravitating systems do not have physically realizable thermal equilibrium configurations, we are interested in the behavior of entropy as mechanical equilibrium is acheived. We will discuss entropy production in these systems from a kinetic theory point of view. This material is based upon work supported by the National Aeronautics and Space Administration under grant NNX07AG86G issued through the Science Mission Directorate.

Contour-time approach to the Bose-Hubbard model in the strong coupling regime: Studying two-point spatio-temporal correlations at the Hartree-Fock-Bogoliubov level

NASA Astrophysics Data System (ADS)

Fitzpatrick, Matthew R. C.; Kennett, Malcolm P.

2018-05-01

We develop a formalism that allows the study of correlations in space and time in both the superfluid and Mott insulating phases of the Bose-Hubbard Model. Specifically, we obtain a two particle irreducible effective action within the contour-time formalism that allows for both equilibrium and out of equilibrium phenomena. We derive equations of motion for both the superfluid order parameter and two-point correlation functions. To assess the accuracy of this formalism, we study the equilibrium solution of the equations of motion and compare our results to existing strong coupling methods as well as exact methods where possible. We discuss applications of this formalism to out of equilibrium situations.

Pulse-density modulation control of chemical oscillation far from equilibrium in a droplet open-reactor system

PubMed Central

Sugiura, Haruka; Ito, Manami; Okuaki, Tomoya; Mori, Yoshihito; Kitahata, Hiroyuki; Takinoue, Masahiro

2016-01-01

The design, construction and control of artificial self-organized systems modelled on dynamical behaviours of living systems are important issues in biologically inspired engineering. Such systems are usually based on complex reaction dynamics far from equilibrium; therefore, the control of non-equilibrium conditions is required. Here we report a droplet open-reactor system, based on droplet fusion and fission, that achieves dynamical control over chemical fluxes into/out of the reactor for chemical reactions far from equilibrium. We mathematically reveal that the control mechanism is formulated as pulse-density modulation control of the fusion–fission timing. We produce the droplet open-reactor system using microfluidic technologies and then perform external control and autonomous feedback control over autocatalytic chemical oscillation reactions far from equilibrium. We believe that this system will be valuable for the dynamical control over self-organized phenomena far from equilibrium in chemical and biomedical studies. PMID:26786848

Pulse-density modulation control of chemical oscillation far from equilibrium in a droplet open-reactor system.

PubMed

Sugiura, Haruka; Ito, Manami; Okuaki, Tomoya; Mori, Yoshihito; Kitahata, Hiroyuki; Takinoue, Masahiro

2016-01-20

The design, construction and control of artificial self-organized systems modelled on dynamical behaviours of living systems are important issues in biologically inspired engineering. Such systems are usually based on complex reaction dynamics far from equilibrium; therefore, the control of non-equilibrium conditions is required. Here we report a droplet open-reactor system, based on droplet fusion and fission, that achieves dynamical control over chemical fluxes into/out of the reactor for chemical reactions far from equilibrium. We mathematically reveal that the control mechanism is formulated as pulse-density modulation control of the fusion-fission timing. We produce the droplet open-reactor system using microfluidic technologies and then perform external control and autonomous feedback control over autocatalytic chemical oscillation reactions far from equilibrium. We believe that this system will be valuable for the dynamical control over self-organized phenomena far from equilibrium in chemical and biomedical studies.

Adaptation, Learning, and the Art of War: A Cybernetic Perspective

DTIC Science & Technology

2014-05-14

William Ross Ashby and contemporary cybernetic thought, the study modeled the adaptive systems as control loops and the processes of adaptive systems...as a Markov process . Using this model , the study concluded that systems would return to the same relative equilibrium point, expressed in terms of...uncertain and ever-changing environment. Drawing from the works of William Ross Ashby and contemporary cybernetic thought, the study modeled the adaptive

Stages in Learning Motor Synergies: A View Based on the Equilibrium-Point Hypothesis

PubMed Central

Latash, Mark L.

2009-01-01

This review describes a novel view on stages in motor learning based on recent developments of the notion of synergies, the uncontrolled manifold hypothesis, and the equilibrium-point hypothesis (referent configuration) that allow to merge these notions into a single scheme of motor control. The principle of abundance and the principle of minimal final action form the foundation for analyses of natural motor actions performed by redundant sets of elements. Two main stages of motor learning are introduced corresponding to (1) discovery and strengthening of motor synergies stabilizing salient performance variable(s), and (2) their weakening when other aspects of motor performance are optimized. The first stage may be viewed as consisting of two steps, the elaboration of an adequate referent configuration trajectory and the elaboration of multi-joint (multi-muscle) synergies stabilizing the referent configuration trajectory. Both steps are expected to lead to more variance in the space of elemental variables that is compatible with a desired time profile of the salient performance variable (“good variability”). Adjusting control to other aspects of performance during the second stage (for example, esthetics, energy expenditure, time, fatigue, etc.) may lead to a drop in the “good variability”. Experimental support for the suggested scheme is reviewed. PMID:20060610

Stages in learning motor synergies: a view based on the equilibrium-point hypothesis.

PubMed

Latash, Mark L

2010-10-01

This review describes a novel view on stages in motor learning based on recent developments of the notion of synergies, the uncontrolled manifold hypothesis, and the equilibrium-point hypothesis (referent configuration) that allow to merge these notions into a single scheme of motor control. The principle of abundance and the principle of minimal final action form the foundation for analyses of natural motor actions performed by redundant sets of elements. Two main stages of motor learning are introduced corresponding to (1) discovery and strengthening of motor synergies stabilizing salient performance variable(s) and (2) their weakening when other aspects of motor performance are optimized. The first stage may be viewed as consisting of two steps, the elaboration of an adequate referent configuration trajectory and the elaboration of multi-joint (multi-muscle) synergies stabilizing the referent configuration trajectory. Both steps are expected to lead to more variance in the space of elemental variables that is compatible with a desired time profile of the salient performance variable ("good variability"). Adjusting control to other aspects of performance during the second stage (for example, esthetics, energy expenditure, time, fatigue, etc.) may lead to a drop in the "good variability". Experimental support for the suggested scheme is reviewed. Copyright © 2009 Elsevier B.V. All rights reserved.

Abnormal motor patterns in the framework of the equilibrium-point hypothesis: a cause for dystonic movements?

PubMed

Latash, M L; Gutman, S R

1994-01-01

Until now, the equilibrium-point hypothesis (lambda model) of motor control has assumed nonintersecting force-length characteristics of the tonic stretch reflex for individual muscles. Limited data from animal experiments suggest, however, that such intersections may occur. We have assumed the possibility of intersection of the characteristics of the tonic stretch reflex and performed a computer simulation of movement trajectories and electromyographic patterns. The simulation has demonstrated, in particular, that a transient change in the slope of the characteristic of an agonist muscle may lead to temporary movement reversals, hesitations, oscillations, and multiple electromyographic bursts that are typical of movements of patients with dystonia. The movement patterns of three patients with idiopathic dystonia during attempts at fast single-joint movements (in the elbow, wrist, and ankle) were recorded and compared with the results of the computer simulation. This approach considers that motor disorders in dystonia result from faulty control patterns that may not correlate with any morphological or neurophysiological changes. It provides a basis for the high variability of dystonic movements. The uniqueness of abnormal motor patterns in dystonia, that precludes statistical analysis across patients, may result from subtle differences in the patterns of intersecting characteristics of the tonic stretch reflex. The applicability of our analysis to disordered multijoint movement patterns is discussed.

An Overview on Aerospatiale Magnetic Bearing Products for Spacecraft Attitude Control and for Industry

NASA Technical Reports Server (NTRS)

Samuel, Alain; Lechable, Bernard

1996-01-01

Aerospatiale magnetic bearings are based on the use of permanent magnets and on the control of the rotor around a zero force equilibrium point. The present developments of magnetic bearing wheels for space applications focus on the versatility of a basic design which leads to a family of reaction and momentum wheels with tailored torque and kinetic momentum, leading to competitive mass and cost. The present industrial applications concern kinetic energy accumulators, medical x-ray rotating devices, avionics equipment, cryotechnic compressors and vacuum pumps.

Thermal equilibrium concentration of intrinsic point defects in heavily doped silicon crystals - Theoretical study of formation energy and formation entropy in area of influence of dopant atoms-

NASA Astrophysics Data System (ADS)

Kobayashi, K.; Yamaoka, S.; Sueoka, K.; Vanhellemont, J.

2017-09-01

It is well known that p-type, neutral and n-type dopants affect the intrinsic point defect (vacancy V and self-interstitial I) behavior in single crystal Si. By the interaction with V and/or I, (1) growing Si crystals become more V- or I-rich, (2) oxygen precipitation is enhanced or retarded, and (3) dopant diffusion is enhanced or retarded, depending on the type and concentration of dopant atoms. Since these interactions affect a wide range of Si properties ranging from as-grown crystal quality to LSI performance, numerical simulations are used to predict and to control the behavior of both dopant atoms and intrinsic point defects. In most cases, the thermal equilibrium concentrations of dopant-point defect pairs are evaluated using the mass action law by taking only the binding energy of closest pair to each other into account. The impacts of dopant atoms on the formation of V and I more distant than 1st neighbor and on the change of formation entropy are usually neglected. In this study, we have evaluated the thermal equilibrium concentrations of intrinsic point defects in heavily doped Si crystals. Density functional theory (DFT) calculations were performed to obtain the formation energy (Ef) of the uncharged V and I at all sites in a 64-atom supercell around a substitutional p-type (B, Ga, In, and Tl), neutral (C, Ge, and Sn) and n-type (P, As, and Sb) dopant atom. The formation (vibration) entropies (Sf) of free I, V and I, V at 1st neighboring site from B, C, Sn, P and As atoms were also calculated with the linear response method. The dependences of the thermal equilibrium concentrations of trapped and total intrinsic point defects (sum of free I or V and I or V trapped with dopant atoms) on the concentrations of B, C, Sn, P and As in Si were obtained. Furthermore, the present evaluations well explain the experimental results of the so-called ;Voronkov criterion; in B and C doped Si, and also the observed dopant dependent void sizes in P and As doped Si crystals. The expressions obtained in the present work are very useful for the numerical simulation of grown-in defect behavior, oxygen precipitation and dopant diffusion in heavily doped Si. DFT calculations also showed that Coulomb interaction reaches approximately 30 Å from p (n)-type dopant atoms to I (V) in Si.

Optimal control of predator-prey mathematical model with infection and harvesting on prey

NASA Astrophysics Data System (ADS)

Diva Amalia, R. U.; Fatmawati; Windarto; Khusnul Arif, Didik

2018-03-01

This paper presents a predator-prey mathematical model with infection and harvesting on prey. The infection and harvesting only occur on the prey population and it assumed that the prey infection would not infect predator population. We analysed the mathematical model of predator-prey with infection and harvesting in prey. Optimal control, which is a prevention of the prey infection, also applied in the model and denoted as U. The purpose of the control is to increase the susceptible prey. The analytical result showed that the model has five equilibriums, namely the extinction equilibrium (E 0), the infection free and predator extinction equilibrium (E 1), the infection free equilibrium (E 2), the predator extinction equilibrium (E 3), and the coexistence equilibrium (E 4). The extinction equilibrium (E 0) is not stable. The infection free and predator extinction equilibrium (E 1), the infection free equilibrium (E 2), also the predator extinction equilibrium (E 3), are locally asymptotically stable with some certain conditions. The coexistence equilibrium (E 4) tends to be locally asymptotically stable. Afterwards, by using the Maximum Pontryagin Principle, we obtained the existence of optimal control U. From numerical simulation, we can conclude that the control could increase the population of susceptible prey and decrease the infected prey.

Linear control of the flywheel inverted pendulum.

PubMed

Olivares, Manuel; Albertos, Pedro

2014-09-01

The flywheel inverted pendulum is an underactuated mechanical system with a nonlinear model but admitting a linear approximation around the unstable equilibrium point in the upper position. Although underactuated systems usually require nonlinear controllers, the easy tuning and understanding of linear controllers make them more attractive for designers and final users. In a recent paper, a simple PID controller was proposed by the authors, leading to an internally unstable controlled plant. To achieve global stability, two options are developed here: first by introducing an internal stabilizing controller and second by replacing the PID controller by an observer-based state feedback control. Simulation and experimental results show the effectiveness of the design. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Unsteady steady-states: Central causes of unintentional force drift

PubMed Central

Ambike, Satyajit; Mattos, Daniela; Zatsiorsky, Vladimir M.; Latash, Mark L.

2016-01-01

We applied the theory of synergies to analyze the processes that lead to unintentional decline in isometric fingertip force when visual feedback of the produced force is removed. We tracked the changes in hypothetical control variables involved in single fingertip force production based on the equilibrium-point hypothesis, namely, the fingertip referent coordinate (RFT) and its apparent stiffness (CFT). The system's state is defined by a point in the {RFT; CFT} space. We tested the hypothesis that, after visual feedback removal, this point (1) moves along directions leading to drop in the output fingertip force, and (2) has even greater motion along directions that leaves the force unchanged. Subjects produced a prescribed fingertip force using visual feedback, and attempted to maintain this force for 15 s after the feedback was removed. We used the “inverse piano” apparatus to apply small and smooth positional perturbations to fingers at various times after visual feedback removal. The time courses of RFT and CFT showed that force drop was mostly due to a drift in RFT towards the actual fingertip position. Three analysis techniques, namely, hyperbolic regression, surrogate data analysis, and computation of motor-equivalent and non-motor-equivalent motions, suggested strong co-variation in RFT and CFT stabilizing the force magnitude. Finally, the changes in the two hypothetical control variables {RFT; CFT} relative to their average trends also displayed covariation. On the whole the findings suggest that unintentional force drop is associated with (a) a slow drift of the referent coordinate that pulls the system towards a low-energy state, and (b) a faster synergic motion of RFT and CFT that tends to stabilize the output fingertip force about the slowly-drifting equilibrium point. PMID:27540726

Unsteady steady-states: central causes of unintentional force drift.

PubMed

Ambike, Satyajit; Mattos, Daniela; Zatsiorsky, Vladimir M; Latash, Mark L

2016-12-01

We applied the theory of synergies to analyze the processes that lead to unintentional decline in isometric fingertip force when visual feedback of the produced force is removed. We tracked the changes in hypothetical control variables involved in single fingertip force production based on the equilibrium-point hypothesis, namely the fingertip referent coordinate (R FT ) and its apparent stiffness (C FT ). The system's state is defined by a point in the {R FT ; C FT } space. We tested the hypothesis that, after visual feedback removal, this point (1) moves along directions leading to drop in the output fingertip force, and (2) has even greater motion along directions that leaves the force unchanged. Subjects produced a prescribed fingertip force using visual feedback and attempted to maintain this force for 15 s after the feedback was removed. We used the "inverse piano" apparatus to apply small and smooth positional perturbations to fingers at various times after visual feedback removal. The time courses of R FT and C FT showed that force drop was mostly due to a drift in R FT toward the actual fingertip position. Three analysis techniques, namely hyperbolic regression, surrogate data analysis, and computation of motor-equivalent and non-motor-equivalent motions, suggested strong covariation in R FT and C FT stabilizing the force magnitude. Finally, the changes in the two hypothetical control variables {R FT ; C FT } relative to their average trends also displayed covariation. On the whole, the findings suggest that unintentional force drop is associated with (a) a slow drift of the referent coordinate that pulls the system toward a low-energy state and (b) a faster synergic motion of R FT and C FT that tends to stabilize the output fingertip force about the slowly drifting equilibrium point.

Coriolis-force-induced trajectory and endpoint deviations in the reaching movements of labyrinthine-defective subjects

NASA Technical Reports Server (NTRS)

DiZio, P.; Lackner, J. R.

2001-01-01

When reaching movements are made during passive constant velocity body rotation, inertial Coriolis accelerations are generated that displace both movement paths and endpoints in their direction. These findings directly contradict equilibrium point theories of movement control. However, it has been argued that these movement errors relate to subjects sensing their body rotation through continuing vestibular activity and making corrective movements. In the present study, we evaluated the reaching movements of five labyrinthine-defective subjects (lacking both semicircular canal and otolith function) who cannot sense passive body rotation in the dark and five age-matched, normal control subjects. Each pointed 40 times in complete darkness to the location of a just extinguished visual target before, during, and after constant velocity rotation at 10 rpm in the center of a fully enclosed slow rotation room. All subjects, including the normal controls, always felt completely stationary when making their movements. During rotation, both groups initially showed large deviations of their movement paths and endpoints in the direction of the transient Coriolis forces generated by their movements. With additional per-rotation movements, both groups showed complete adaptation of movement curvature (restoration of straight-line reaches) during rotation. The labyrinthine-defective subjects, however, failed to regain fully accurate movement endpoints after 40 reaches, unlike the control subjects who did so within 11 reaches. Postrotation, both groups' movements initially had mirror image curvatures to their initial per-rotation reaches; the endpoint aftereffects were significantly different from prerotation baseline for the control subjects but not for the labyrinthine-defective subjects reflecting the smaller amount of endpoint adaptation they achieved during rotation. The labyrinthine-defective subjects' movements had significantly lower peak velocity, higher peak elevation, lower terminal velocity, and a more vertical touchdown than those of the control subjects. Thus the way their reaches terminated denied them the somatosensory contact cues necessary for full endpoint adaptation. These findings fully contradict equilibrium point theories of movement control. They emphasize the importance of contact cues in adaptive movement control and indicate that movement errors generated by Coriolis perturbations of limb movements reveal characteristics of motor planning and adaptation in both healthy and clinical populations.

Shape-retainment control using an antagonistic shape memory alloy system

NASA Astrophysics Data System (ADS)

Ikeda, T.; Sawamura, K.; Senba, A.; Tamayama, M.

2015-04-01

Since shape memory alloy (SMA) actuators can generate large force per unit weight, they are expected as one of the next generation actuators for aircraft. To keep a position of conventional control surfaces or morphing wings with SMA actuators, the SMA actuators must keep being heated, and the heating energy is not small. To save the energy, a new control method proposed for piezoelectric actuators utilizing hysteresis in deformation [Ikeda and Takahashi, Proc. SPIE 8689 (2013), 86890C] is applied to an antagonistic SMA system. By using the control method any position can be an equilibrium point within hysteresis of stress-strain diagrams. To confirm a feasibility of the control method, a fundamental experiment is performed. The SMA wires are heated by applying electric current to the wires. When a pulsed current is applied to the two SMA wires alternately, the equilibrium position changes between two positions alternately, and when a series of pulse whose amplitude increases gradually is applied to one SMA wire, the equilibrium position changes like a staircase. However, just after the pulse the position returns slightly, that is, overshoot takes place. To investigate such a behavior of the system, numerical simulation is also performed. The one-dimensional phase transformation model [Ikeda, Proc. SPIE 5757 (2005), 344-352] is used for a constitutive model of the SMA wires. The simulated result agrees with the experiment qualitatively, including the overshoot. By examining volume fraction of each phase, it is found that the overshoot is caused by that austenite phase transforms into stress-induced martensite phase during the cooling process after the pulse.

Adaptive attitude control and momentum management for large-angle spacecraft maneuvers

NASA Technical Reports Server (NTRS)

Parlos, Alexander G.; Sunkel, John W.

1992-01-01

The fully coupled equations of motion are systematically linearized around an equilibrium point of a gravity gradient stabilized spacecraft, controlled by momentum exchange devices. These equations are then used for attitude control system design of an early Space Station Freedom flight configuration, demonstrating the errors caused by the improper approximation of the spacecraft dynamics. A full state feedback controller, incorporating gain-scheduled adaptation of the attitude gains, is developed for use during spacecraft on-orbit assembly or operations characterized by significant mass properties variations. The feasibility of the gain adaptation is demonstrated via a Space Station Freedom assembly sequence case study. The attitude controller stability robustness and transient performance during gain adaptation appear satisfactory.

Reconstruction of equilibrium trajectories during whole-body movements.

PubMed

Domen, K; Latash, M L; Zatsiorsky, V M

1999-03-01

The framework of the equilibrium-point hypothesis was used to reconstruct equilibrium trajectories (ETs) of the ankle, hip and body center of mass during quick voluntary hip flexions ('Japanese courtesy bow') by standing subjects. Different spring loads applied to the subject's back were used to introduce smooth perturbations that are necessary to reconstruct ETs based on a series of trials at the same task. Time patterns of muscle torques were calculated using inverse dynamics techniques. A second-order linear model was employed to calculate the instantaneous position of the spring-like joint or center of mass characteristic at different times during the movement. ETs of the joints and of the center of mass had significantly different shapes from the actual trajectories. Integral measures of electromyographic bursts of activity in postural muscles demonstrated a relation to muscle length corresponding to the equilibrium-point hypothesis.

Coexistence and local μ-stability of multiple equilibrium points for memristive neural networks with nonmonotonic piecewise linear activation functions and unbounded time-varying delays.

PubMed

Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde

2016-12-01

In this paper, the coexistence and dynamical behaviors of multiple equilibrium points are discussed for a class of memristive neural networks (MNNs) with unbounded time-varying delays and nonmonotonic piecewise linear activation functions. By means of the fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis, it is proven that under some conditions, such n-neuron MNNs can have 5 n equilibrium points located in ℜ n , and 3 n of them are locally μ-stable. As a direct application, some criteria are also obtained on the multiple exponential stability, multiple power stability, multiple log-stability and multiple log-log-stability. All these results reveal that the addressed neural networks with activation functions introduced in this paper can generate greater storage capacity than the ones with Mexican-hat-type activation function. Numerical simulations are presented to substantiate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Searching for artificial equilibrium points to place satellites "above and below" L3 in the Sun-Earth system

NASA Astrophysics Data System (ADS)

de Almeida, A. K., Jr.; Prado, A. F. B. A.; Sanchez, D. M.; Yokoyama, T.

2017-10-01

Regarding practical applications of L3 of the Sun-Earth system, there are few studies with the goal of placing a spacecraft at this point, or in orbit around it. One of the main problems in placing a spacecraft near this equilibrium point is the fact that it is located behind the Sun with respect to the Earth. The Sun would be blocking direct communication between the spacecraft and the Earth. The present research gives several options to solve this problem by using a solar sail to place one or two spacecraft above and/or below the Ecliptic plane. This sail could also be used for the mission itself, to collect energy or particles. By using an adequate size, location and attitude of the solar sail, the equilibrium point can be moved from its original location to allow communications between the spacecraft and the Earth. A preliminary study of a solar sail that uses this strategy is shown here.

SOL Thermal Instability due to Radial Blob Convection

NASA Astrophysics Data System (ADS)

D'Ippolito, D. A.

2005-10-01

C-Mod datafootnotetextM. Greenwald, Plasma Phys. Contr. Fusion 44, R27 (2002). suggests a density limit when rapid perpendicular convection dominates SOL heat transport. This is supported by a recent analysisfootnotetextD.A. Russell et al., Phys. Rev. Lett. 93, 265001 (2004). of BOUT code turbulence simulations, which shows that rapid outwards convection of plasma by turbulent blobs is enhanced when the X-point collisionality is large, resulting in a synergistic effect between blob convection and X-point cooling. This work motivates the present analysis of SOL thermal equilibrium and instability including an RX-regime modelfootnotetextJ.R. Myra and D.A. D'Ippolito, Lodestar Report LRC-05-105 (2005). of blob particle and heat transport. Two-point (midplane, X-point) SOL thermal equilibrium and stability models are considered including both two-field (T) and four-field (n,T) treatments. The conditions under which loss of thermal equilibrium or thermal instabilities occur are established, and relations to the C-Mod data are described.

Dynamic Analysis of a Reaction-Diffusion Rumor Propagation Model

NASA Astrophysics Data System (ADS)

Zhao, Hongyong; Zhu, Linhe

2016-06-01

The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. Rumor propagation in social networks has brought new challenges to network security and social stability. This paper, based on partial differential equations (PDEs), proposes a new SIS rumor propagation model by considering the effect of the communication between the different rumor infected users on rumor propagation. The stabilities of a nonrumor equilibrium point and a rumor-spreading equilibrium point are discussed by linearization technique and the upper and lower solutions method, and the existence of a traveling wave solution is established by the cross-iteration scheme accompanied by the technique of upper and lower solutions and Schauder’s fixed point theorem. Furthermore, we add the time delay to rumor propagation and deduce the conditions of Hopf bifurcation and stability switches for the rumor-spreading equilibrium point by taking the time delay as the bifurcation parameter. Finally, numerical simulations are performed to illustrate the theoretical results.

Tangential acceleration feedback control of friction induced vibration

NASA Astrophysics Data System (ADS)

Nath, Jyayasi; Chatterjee, S.

2016-09-01

Tangential control action is studied on a phenomenological mass-on-belt model exhibiting friction-induced self-excited vibration attributed to the low-velocity drooping characteristics of friction which is also known as Stribeck effect. The friction phenomenon is modelled by the exponential model. Linear stability analysis is carried out near the equilibrium point and local stability boundary is delineated in the plane of control parameters. The system is observed to undergo a Hopf bifurcation as the eigenvalues determined from the linear stability analysis are found to cross the imaginary axis transversally from RHS s-plane to LHS s-plane or vice-versa as one varies the control parameters, namely non-dimensional belt velocity and the control gain. A nonlinear stability analysis by the method of Averaging reveals the subcritical nature of the Hopf bifurcation. Thus, a global stability boundary is constructed so that any choice of control parameters from the globally stable region leads to a stable equilibrium. Numerical simulations in a MATLAB SIMULINK model and bifurcation diagrams obtained in AUTO validate these analytically obtained results. Pole crossover design is implemented to optimize the filter parameters with an independent choice of belt velocity and control gain. The efficacy of this optimization (based on numerical results) in the delicate low velocity region is also enclosed.

A hyperjerk memristive system with infinite equilibrium points

NASA Astrophysics Data System (ADS)

Prousalis, Dimitrios A.; Volos, Christos K.; Stouboulos, Ioannis N.; Kyprianidis, Ioannis M.

2017-09-01

A novel 4-D dynamical memristive system is presented in this work. The specificity of the model is that it develops a line of equilibrium points and it has hyperjerk dynamics in a particular range of the parameters space. The behavior of the suggested system is investigated through numerical simulations, by using phase portraits, Lyapunov exponents, bifurcation diagrams. Also, its circuital implementation confirms the memristive system's expected dynamics.

Equilibrium points of the tilted perfect fluid Bianchi VIh state space

NASA Astrophysics Data System (ADS)

Apostolopoulos, Pantelis S.

2005-05-01

We present the full set of evolution equations for the spatially homogeneous cosmologies of type VIh filled with a tilted perfect fluid and we provide the corresponding equilibrium points of the resulting dynamical state space. It is found that only when the group parameter satisfies h > -1 a self-similar solution exists. In particular we show that for h > -{1/9} there exists a self-similar equilibrium point provided that γ ∈ ({2(3+sqrt{-h})/5+3sqrt{-h}},{3/2}) whereas for h < -{frac 19} the state parameter belongs to the interval γ ∈(1,{2(3+sqrt{-h})/5+3sqrt{-h}}). This family of new exact self-similar solutions belongs to the subclass nαα = 0 having non-zero vorticity. In both cases the equilibrium points have a six-dimensional stable manifold and may act as future attractors at least for the models satisfying nαα = 0. Also we give the exact form of the self-similar metrics in terms of the state and group parameter. As an illustrative example we provide the explicit form of the corresponding self-similar radiation model (γ = {frac 43}), parametrised by the group parameter h. Finally we show that there are no tilted self-similar models of type III and irrotational models of type VIh.

Rare behavior of growth processes via umbrella sampling of trajectories

NASA Astrophysics Data System (ADS)

Klymko, Katherine; Geissler, Phillip L.; Garrahan, Juan P.; Whitelam, Stephen

2018-03-01

We compute probability distributions of trajectory observables for reversible and irreversible growth processes. These results reveal a correspondence between reversible and irreversible processes, at particular points in parameter space, in terms of their typical and atypical trajectories. Thus key features of growth processes can be insensitive to the precise form of the rate constants used to generate them, recalling the insensitivity to microscopic details of certain equilibrium behavior. We obtained these results using a sampling method, inspired by the "s -ensemble" large-deviation formalism, that amounts to umbrella sampling in trajectory space. The method is a simple variant of existing approaches, and applies to ensembles of trajectories controlled by the total number of events. It can be used to determine large-deviation rate functions for trajectory observables in or out of equilibrium.

Complex Nonlinear Dynamic System of Oligopolies Price Game with Heterogeneous Players Under Noise

NASA Astrophysics Data System (ADS)

Liu, Feng; Li, Yaguang

A nonlinear four oligopolies price game with heterogeneous players, that are boundedly rational and adaptive, is built using two different special demand costs. Based on the theory of complex discrete dynamical system, the stability and the existing equilibrium point are investigated. The complex dynamic behavior is presented via bifurcation diagrams, the Lyapunov exponents to show equilibrium state, bifurcation and chaos with the variation in parameters. As disturbance is ubiquitous in economic systems, this paper focuses on the analysis of delay feedback control method under noise circumstances. Stable dynamics is confirmed to depend mainly on the low price adjustment speed, and if all four players have limited opportunities to stabilize the market, the new adaptive player facing profits of scale are found to be higher than the incumbents of bounded rational.

Orbiter entry trajectory corridors: 32000 pound payload, 67.5 percent center of gravity. [glide path data compilation

NASA Technical Reports Server (NTRS)

Treybig, J. H.

1975-01-01

Thermal and equilibrium glide boundaries were used to analyze and/or design shuttle orbiter entry trajectories. Plots are presented of orbiter thermal and equilibrium glide boundaries in the drag/mass-relative velocity dynamic pressure-relative velocity, and altitude-relative velocity planes for an orbiter having a 32,000 pound payload and a 67.5% center of gravity location. These boundaries were defined for control points 1 through 4 of the shuttle orbiter for 40 deg-30 deg and 38 deg-28 deg ramped angle of attack entry profiles and 40 deg, 38 deg, 35 deg, 30 deg, 28 deg, and 25 deg constant angle of attack entry profiles each at 20 deg, 15 deg, and 10 deg constant body flap settings.

Multistability and hidden attractors in a relay system with hysteresis

NASA Astrophysics Data System (ADS)

Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Rubanov, Vasily G.; Nabokov, Roman A.

2015-06-01

For nonlinear dynamic systems with switching control, the concept of a "hidden attractor" naturally applies to a stable dynamic state that either (1) coexists with the stable switching cycle or (2), if the switching cycle is unstable, has a basin of attraction that does not intersect with the neighborhood of that cycle. We show how the equilibrium point of a relay system disappears in a boundary-equilibrium bifurcation as the system enters the region of autonomous switching dynamics and demonstrate experimentally how a relay system can exhibit large amplitude chaotic oscillations at high values of the supply voltage. By investigating a four-dimensional model of the experimental relay system we finally show how a variety of hidden periodic, quasiperiodic and chaotic attractors arise, transform and disappear through different bifurcations.

Tuning the sapphire EFG process to the growth of Al2O3/YAG/ZrO2:Y eutectic

NASA Astrophysics Data System (ADS)

Carroz, L.; Duffar, T.

2018-05-01

In this work, a model is proposed, in order to analytically study the working point of the Edge defined Film-fed Growth (EFG) pulling of crystal plates. The model takes into account the heat equilibrium at the interface and the pressure equilibrium across the meniscus. It is validated on an industrial device dedicated to the pulling of sapphire ribbons. Then, the model is applied to pulling ceramic alloy plates, of the ternary eutectic Al2O3/YAG/ZrO2:Y. This allowed understanding the experimental difficulties of pulling this new material and suggested improvements of the control software. From these results, pulling net shaped ceramic alloy plates was successful in the same industrial equipment as used for sapphire.

Dynamics of a Delayed HIV-1 Infection Model with Saturation Incidence Rate and CTL Immune Response

NASA Astrophysics Data System (ADS)

Guo, Ting; Liu, Haihong; Xu, Chenglin; Yan, Fang

2016-12-01

In this paper, we investigate the dynamics of a five-dimensional virus model incorporating saturation incidence rate, CTL immune response and three time delays which represent the latent period, virus production period and immune response delay, respectively. We begin this model by proving the positivity and boundedness of the solutions. Our model admits three possible equilibrium solutions, namely the infection-free equilibrium E0, the infectious equilibrium without immune response E1 and the infectious equilibrium with immune response E2. Moreover, by analyzing corresponding characteristic equations, the local stability of each of the feasible equilibria and the existence of Hopf bifurcation at the equilibrium point E2 are established, respectively. Further, by using fluctuation lemma and suitable Lyapunov functionals, it is shown that E0 is globally asymptotically stable when the basic reproductive numbers for viral infection R0 is less than unity. When the basic reproductive numbers for immune response R1 is less than unity and R0 is greater than unity, the equilibrium point E1 is globally asymptotically stable. Finally, some numerical simulations are carried out for illustrating the theoretical results.

Critical viewpoints on the methods of realizing the metal freezing points of the ITS-90

NASA Astrophysics Data System (ADS)

Ma, C. K.

1995-08-01

The time-honored method for realizing the freezing point tf of a metal (in practice necessarily a dilute alloy) is that of continuous, slow freezing where the plateau temperature (which is the result of solidifying material's being so pure that its phase-transition temperature is observably constant) is measured. The freezing point being an equilibrium temperature, Ancsin considers this method to be inappropriate in principle: equilibrium between the solid and liquid phases cannot be achieved while the solid is being cooled to dispose of the releasing latent heat and while it is accreting at the expense of the liquid. In place of the continuous freezing method he has employed the pulse-heating method (in which the sample is allowed to approach equilibrium after each heat pulse) in his study of Ag; his measurements suggest that freezing can produce non-negligible errors. Here we examine both methods and conclude that the freezing method, employing an inside solid-liquid interface thermally isolated by an outside interface, can provide realizations of the highest accuracy; in either method, perturbation, by inducing solid-liquid phase transition continuously or intermittently, is essential for detecting equilibrium thermally. The respective merits and disadvantages of these two methods and also of the inner-melt method are discussed. We conclude that in a freezing-point measurement what is being measured is in effect the however minutely varying phase transition, and nonconstitutional equilibrium, temperature ti at the solid-liquid interface. The objective is then to measure the ti that is the best measure of tf, which is, normally, the plateau temperature.

Freezing point depression in model Lennard-Jones solutions

NASA Astrophysics Data System (ADS)

Koschke, Konstantin; Jörg Limbach, Hans; Kremer, Kurt; Donadio, Davide

2015-09-01

Crystallisation of liquid solutions is of uttermost importance in a wide variety of processes in materials, atmospheric and food science. Depending on the type and concentration of solutes the freezing point shifts, thus allowing control on the thermodynamics of complex fluids. Here we investigate the basic principles of solute-induced freezing point depression by computing the melting temperature of a Lennard-Jones fluid with low concentrations of solutes, by means of equilibrium molecular dynamics simulations. The effect of solvophilic and weakly solvophobic solutes at low concentrations is analysed, scanning systematically the size and the concentration. We identify the range of parameters that produce deviations from the linear dependence of the freezing point on the molal concentration of solutes, expected for ideal solutions. Our simulations allow us also to link the shifts in coexistence temperature to the microscopic structure of the solutions.

Symmetric and Asymmetric Tendencies in Stable Complex Systems

PubMed Central

Tan, James P. L.

2016-01-01

A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by obtaining eigenvalue bounds of the Jacobian, we show that stable complex systems will favor mutualistic and competitive relationships that are asymmetrical (non-reciprocative) and trophic relationships that are symmetrical (reciprocative). Additionally, we define a measure called the interdependence diversity that quantifies how distributed the dependencies are between the dynamical variables in the system. We find that increasing interdependence diversity has a destabilizing effect on the equilibrium point, and the effect is greater for trophic relationships than for mutualistic and competitive relationships. These predictions are consistent with empirical observations in ecology. More importantly, our findings suggest stabilization algorithms that can apply very generally to a variety of complex systems. PMID:27545722

Symmetric and Asymmetric Tendencies in Stable Complex Systems.

PubMed

Tan, James P L

2016-08-22

A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by obtaining eigenvalue bounds of the Jacobian, we show that stable complex systems will favor mutualistic and competitive relationships that are asymmetrical (non-reciprocative) and trophic relationships that are symmetrical (reciprocative). Additionally, we define a measure called the interdependence diversity that quantifies how distributed the dependencies are between the dynamical variables in the system. We find that increasing interdependence diversity has a destabilizing effect on the equilibrium point, and the effect is greater for trophic relationships than for mutualistic and competitive relationships. These predictions are consistent with empirical observations in ecology. More importantly, our findings suggest stabilization algorithms that can apply very generally to a variety of complex systems.

An Impact Triggered Runaway Greenhouse on Mars

NASA Technical Reports Server (NTRS)

Segura, T. L.; McKay, C. P.; Toon, O. B.

2004-01-01

When a planet is in radiative equilibrium, the incoming solar flux balances the outgoing longwave flux. If something were to perturb the system slightly, say the incoming solar flux increased, the planet would respond by radiating at a higher surface temperature. Since any radiation that comes in must go out, if the incoming is increased, the outgoing must also increase, and this increase manifests itself as a warmer equilibrium temperature. The increase in solar flux would correspond to an increase in temperature, which would increase the amount of water vapor in the atmosphere due to increased evaporation. Since water vapor is a greenhouse gas, it would absorb more radiation in the atmosphere leading to a yet warmer equilibrium temperature. The planet would reach radiative equilibrium at this new temperature. There exists a point, however, past which this positive feedback leads to a "runaway" situation. In this case, the planet does not simply evaporate a little more water and eventually come to a slightly higher equilibrium temperature. Instead, the planet keeps evaporating more and more water until all of the planet's available liquid and solid water is in the atmosphere. The reason for this is generally understood. If the planet's temperature increases, evaporation of water increases, and the absorption of radiation increases. This increases the temperature and the feedback continues until all water is in the atmosphere. The resulting equilibrium temperature is very high, much higher than the equilibrium temperature of a point with slightly lower solar flux. One can picture that as solar flux increases, planetary temperature also increases until the runaway point where temperature suddenly "jumps" to a higher value, in response to all the available water now residing in the atmosphere. This new equilibrium is called a "runaway greenhouse" and it has been theorized that this is what happened to the planet Venus, where the surface temperature is more than 700 K (427 C).

The Absolute Stability Analysis in Fuzzy Control Systems with Parametric Uncertainties and Reference Inputs

NASA Astrophysics Data System (ADS)

Wu, Bing-Fei; Ma, Li-Shan; Perng, Jau-Woei

This study analyzes the absolute stability in P and PD type fuzzy logic control systems with both certain and uncertain linear plants. Stability analysis includes the reference input, actuator gain and interval plant parameters. For certain linear plants, the stability (i.e. the stable equilibriums of error) in P and PD types is analyzed with the Popov or linearization methods under various reference inputs and actuator gains. The steady state errors of fuzzy control systems are also addressed in the parameter plane. The parametric robust Popov criterion for parametric absolute stability based on Lur'e systems is also applied to the stability analysis of P type fuzzy control systems with uncertain plants. The PD type fuzzy logic controller in our approach is a single-input fuzzy logic controller and is transformed into the P type for analysis. In our work, the absolute stability analysis of fuzzy control systems is given with respect to a non-zero reference input and an uncertain linear plant with the parametric robust Popov criterion unlike previous works. Moreover, a fuzzy current controlled RC circuit is designed with PSPICE models. Both numerical and PSPICE simulations are provided to verify the analytical results. Furthermore, the oscillation mechanism in fuzzy control systems is specified with various equilibrium points of view in the simulation example. Finally, the comparisons are also given to show the effectiveness of the analysis method.

The sensitivity of tokamak magnetohydrodynamics stability on the edge equilibrium

NASA Astrophysics Data System (ADS)

Zheng, L. J.; Kotschenreuther, M. T.; Valanju, P.

2017-10-01

Due to the X-point singularity, the safety factor tends to infinity as approaching to the last closed flux surface. The numerical treatments of the near X-point behavior become challenging both for equilibrium and stability. The usual solution is to cut off a small fraction of edge region for system stability evaluation or simply use an up-down symmetric equilibrium without X-point as an approximation. In this work, we assess the sensitivity of this type of equilibrium treatments on the stability calculation. It is found that the system stability can depend strongly on the safety factor value (qa) at the edge after the cutting-off. When the edge safety factor value falls in the vicinity of a rational mode number (referred to as the resonant gap), the system becomes quite unstable due to the excitation of the peeling type modes. Instead, when the edge safety factor is outside the resonant gaps, the system is much more stable and the predominant modes become the usual external kink (or ballooning and infernal) type. It is also found that the resonant gaps become smaller and smaller as qa increases. The ideal magnetohydrodynamic peeling ballooning stability diagram is widely used to explain the experimental observations, and the current results indicate that the conventional peeling ballooning stability diagram based on the simplified equilibrium needs to be reexamined.

Thermodynamic Investigation of the Effect of Interface Curvature on the Solid-Liquid Equilibrium and Eutectic Point of Binary Mixtures.

PubMed

Liu, Fanghui; Zargarzadeh, Leila; Chung, Hyun-Joong; Elliott, Janet A W

2017-10-12

Thermodynamic phase behavior is affected by curved interfaces in micro- and nanoscale systems. For example, capillary freezing point depression is associated with the pressure difference between the solid and liquid phases caused by interface curvature. In this study, the thermal, mechanical, and chemical equilibrium conditions are derived for binary solid-liquid equilibrium with a curved solid-liquid interface due to confinement in a capillary. This derivation shows the equivalence of the most general forms of the Gibbs-Thomson and Ostwald-Freundlich equations. As an example, the effect of curvature on solid-liquid equilibrium is explained quantitatively for the water/glycerol system. Considering the effect of a curved solid-liquid interface, a complete solid-liquid phase diagram is developed over a range of concentrations for the water/glycerol system (including the freezing of pure water or precipitation of pure glycerol depending on the concentration of the solution). This phase diagram is compared with the traditional phase diagram in which the assumption of a flat solid-liquid interface is made. We show the extent to which nanoscale interface curvature can affect the composition-dependent freezing and precipitating processes, as well as the change in the eutectic point temperature and concentration with interface curvature. Understanding the effect of curvature on solid-liquid equilibrium in nanoscale capillaries has applications in the food industry, soil science, cryobiology, nanoporous materials, and various nanoscience fields.

Adaptive backstepping sliding mode control with fuzzy monitoring strategy for a kind of mechanical system.

PubMed

Song, Zhankui; Sun, Kaibiao

2014-01-01

A novel adaptive backstepping sliding mode control (ABSMC) law with fuzzy monitoring strategy is proposed for the tracking-control of a kind of nonlinear mechanical system. The proposed ABSMC scheme combining the sliding mode control and backstepping technique ensure that the occurrence of the sliding motion in finite-time and the trajectory of tracking-error converge to equilibrium point. To obtain a better perturbation rejection property, an adaptive control law is employed to compensate the lumped perturbation. Furthermore, we introduce fuzzy monitoring strategy to improve adaptive capacity and soften the control signal. The convergence and stability of the proposed control scheme are proved by using Lyaponov's method. Finally, numerical simulations demonstrate the effectiveness of the proposed control scheme. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Stability analysis and nonstandard Grünwald-Letnikov scheme for a fractional order predator-prey model with ratio-dependent functional response

NASA Astrophysics Data System (ADS)

Suryanto, Agus; Darti, Isnani

2017-12-01

In this paper we discuss a fractional order predator-prey model with ratio-dependent functional response. The dynamical properties of this model is analyzed. Here we determine all equilibrium points of this model including their existence conditions and their stability properties. It is found that the model has two type of equilibria, namely the predator-free point and the co-existence point. If there is no co-existence equilibrium, i.e. when the coefficient of conversion from the functional response into the growth rate of predator is less than the death rate of predator, then the predator-free point is asymptotically stable. On the other hand, if the co-existence point exists then this equilibrium is conditionally stable. We also construct a nonstandard Grnwald-Letnikov (NSGL) numerical scheme for the propose model. This scheme is a combination of the Grnwald-Letnikov approximation and the nonstandard finite difference scheme. This scheme is implemented in MATLAB and used to perform some simulations. It is shown that our numerical solutions are consistent with the dynamical properties of our fractional predator-prey model.

Inactivation of tumor suppressor genes and cancer therapy: An evolutionary game theory approach.

PubMed

Khadem, Heydar; Kebriaei, Hamed; Veisi, Zahra

2017-06-01

Inactivation of alleles in tumor suppressor genes (TSG) is one of the important issues resulting in evolution of cancerous cells. In this paper, the evolution of healthy, one and two missed allele cells is modeled using the concept of evolutionary game theory and replicator dynamics. The proposed model also takes into account the interaction rates of the cells as designing parameters of the system. Different combinations of the equilibrium points of the parameterized nonlinear system is studied and categorized into some cases. In each case, the interaction rates' values are suggested in a way that the equilibrium points of the replicator dynamics are located on an appropriate region of the state space. Based on the suggested interaction rates, it is proved that the system doesn't have any undesirable interior equilibrium point as well. Therefore, the system will converge to the desirable region, where there is a scanty level of cancerous cells. In addition, the proposed conditions for interaction rates guarantee that, when a trajectory of the system reaches the boundaries, then it will stay there forever which is a desirable property since the equilibrium points have been already located on the boundaries, appropriately. The simulation results show the effectiveness of the suggestions in the elimination of the cancerous cells in different scenarios. Copyright © 2017 Elsevier Inc. All rights reserved.

"Squishy capacitor" model for electrical double layers and the stability of charged interfaces.

PubMed

Partenskii, Michael B; Jordan, Peter C

2009-07-01

Negative capacitance (NC), predicted by various electrical double layer (EDL) theories, is critically reviewed. Physically possible for individual components of the EDL, the compact or diffuse layer, it is strictly prohibited for the whole EDL or for an electrochemical cell with two electrodes. However, NC is allowed for the artificial conditions of sigma control, where an EDL is described by the equilibrium electric response of electrolyte to a field of fixed, and typically uniform, surface charge-density distributions, sigma. The contradiction is only apparent; in fact local sigma cannot be set independently, but is established by the equilibrium response to physically controllable variables, i.e., applied voltage phi (phi control) or total surface charge q (q control). NC predictions in studies based on sigma control signify potential instabilities and phase transitions for physically realizable conditions. Building on our previous study of phi control [M. B. Partenskii and P. C. Jordan, Phys. Rev. E 77, 061117 (2008)], here we analyze critical behavior under q control, clarifying the basic picture using an exactly solvable "squishy capacitor" toy model. We find that phi can change discontinuously in the presence of a lateral transition, specify stability conditions for an electrochemical cell, analyze the origin of the EDL's critical point in terms of compact and diffuse serial contributions, and discuss perspectives and challenges for theoretical studies not limited by sigma control.

On the magnetic attitude control for spacecraft via the ɛ-strategies method

NASA Astrophysics Data System (ADS)

Smirnov, Georgi V.; Ovchinnikov, Mikhail; Miranda, Francisco

2008-09-01

We develop a new approach to stabilization problems based on a combination of the Lyapunov functions method with local controllability properties. The stabilizability is understood in the sense of ɛ-strategies introduced by Pontryagin in the frame of differential games theory. To illustrate the possibilities of our approach we consider a satellite with two magnetic coils directed along its principal inertia axes. Its circular orbit is neither polar nor equatorial. We show that there exists an ɛ-strategy stabilizing an Earth pointing satellite, whenever the deviations from the equilibrium position are small enough.

Multiple points of equilibrium for active magnetic regenerators using first order magnetocaloric material

NASA Astrophysics Data System (ADS)

Niknia, I.; Trevizoli, P. V.; Govindappa, P.; Christiaanse, T. V.; Teyber, R.; Rowe, A.

2018-05-01

First order transition material (FOM) usually exhibits magnetocaloric effects in a narrow temperature range which complicates their use in an active magnetic regenerator (AMR) refrigerator. In addition, the magnetocaloric effect in first order materials can vary with field and temperature history of the material. This study examines the behavior of a MnFe(P,Si) FOM sample in an AMR cycle using a numerical model and experimental measurements. For certain operating conditions, multiple points of equilibrium (MPE) exist for a fixed hot rejection temperature. Stable and unstable points of equilibriums (PEs) are identified and the impacts of heat loads, operating conditions, and configuration losses on the number of PEs are discussed. It is shown that the existence of multiple PEs can affect the performance of an AMR significantly for certain operating conditions. In addition, the points where MPEs exist appear to be linked to the device itself, not just the material, suggesting the need to layer a regenerator in a way that avoids MPE conditions and to layer with a specific device in mind.

Multistability of neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays.

PubMed

Nie, Xiaobing; Zheng, Wei Xing

2015-05-01

This paper is concerned with the problem of coexistence and dynamical behaviors of multiple equilibrium points for neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays. The fixed point theorem and other analytical tools are used to develop certain sufficient conditions that ensure that the n-dimensional discontinuous neural networks with time-varying delays can have at least 5(n) equilibrium points, 3(n) of which are locally stable and the others are unstable. The importance of the derived results is that it reveals that the discontinuous neural networks can have greater storage capacity than the continuous ones. Moreover, different from the existing results on multistability of neural networks with discontinuous activation functions, the 3(n) locally stable equilibrium points obtained in this paper are located in not only saturated regions, but also unsaturated regions, due to the non-monotonic structure of discontinuous activation functions. A numerical simulation study is conducted to illustrate and support the derived theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Phase diagram for a two-dimensional, two-temperature, diffusive XY model.

PubMed

Reichl, Matthew D; Del Genio, Charo I; Bassler, Kevin E

2010-10-01

Using Monte Carlo simulations, we determine the phase diagram of a diffusive two-temperature conserved order parameter XY model. When the two temperatures are equal the system becomes the equilibrium XY model with the continuous Kosterlitz-Thouless (KT) vortex-antivortex unbinding phase transition. When the two temperatures are unequal the system is driven by an energy flow from the higher temperature heat-bath to the lower temperature one and reaches a far-from-equilibrium steady state. We show that the nonequilibrium phase diagram contains three phases: A homogenous disordered phase and two phases with long range, spin texture order. Two critical lines, representing continuous phase transitions from a homogenous disordered phase to two phases of long range order, meet at the equilibrium KT point. The shape of the nonequilibrium critical lines as they approach the KT point is described by a crossover exponent φ=2.52±0.05. Finally, we suggest that the transition between the two phases with long-range order is first-order, making the KT-point where all three phases meet a bicritical point.

Applicability of Markets to Global Scheduling in Grids: Critical Examination of General Equilibrium Theory and Market Folklore

NASA Technical Reports Server (NTRS)

Nakai, Junko; VanDerWijngaart, Rob F.

2003-01-01

Markets are often considered superior to other global scheduling mechanisms for distributed computing systems. This claim is supported by: a casual observation from our every-day life that markets successfully equilibrate supply and demand, and the features of markets which originate in the general equilibrium theory, e.g., efficiency and the lack of necessity of 2 central controller. This paper describes why such beliefs in markets are not warranted. It does so by examining the general equilibrium theory, in terms of scope, abstraction, and interpretation. Not only does the general equilibrium theory fail to provide a satisfactory explanation of actual economies, including a computing-resource economy, it also falls short of supplying theoretical foundations for commonly held views of market desirability. This paper also points out that the argument for the desirability of markets involves circular reasoning and that the desirability can be established only vis-a-vis a scheduling goal. Finally, recasting the conclusion of Arrow's Impossibility Theorem as that for global scheduling, we conclude that there exists no market-based scheduler that is rational (in the sense defined in microeconomic theory), takes into account utility of more than one user, and yet yields a Pareto-optimal outcome for arbitrary user utility functions.

Thermally driven ratchet motion of a skyrmion microcrystal and topological magnon Hall effect

NASA Astrophysics Data System (ADS)

Mochizuki, M.; Yu, X. Z.; Seki, S.; Kanazawa, N.; Koshibae, W.; Zang, J.; Mostovoy, M.; Tokura, Y.; Nagaosa, N.

2014-03-01

Spontaneously emergent chirality is an issue of fundamental importance across the natural sciences. It has been argued that a unidirectional (chiral) rotation of a mechanical ratchet is forbidden in thermal equilibrium, but becomes possible in systems out of equilibrium. Here we report our finding that a topologically nontrivial spin texture known as a skyrmion—a particle-like object in which spins point in all directions to wrap a sphere—constitutes such a ratchet. By means of Lorentz transmission electron microscopy we show that micrometre-sized crystals of skyrmions in thin films of Cu2OSeO3 and MnSi exhibit a unidirectional rotation motion. Our numerical simulations based on a stochastic Landau-Lifshitz-Gilbert equation suggest that this rotation is driven solely by thermal fluctuations in the presence of a temperature gradient, whereas in thermal equilibrium it is forbidden by the Bohr-van Leeuwen theorem. We show that the rotational flow of magnons driven by the effective magnetic field of skyrmions gives rise to the skyrmion rotation, therefore suggesting that magnons can be used to control the motion of these spin textures.

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

NASA Astrophysics Data System (ADS)

Panday, Pijush; Pal, Nikhil; Samanta, Sudip; Chattopadhyay, Joydev

In the present paper, we investigate the impact of fear in a tri-trophic food chain model. We propose a three-species food chain model, where the growth rate of middle predator is reduced due to the cost of fear of top predator, and the growth rate of prey is suppressed due to the cost of fear of middle predator. Mathematical properties such as equilibrium analysis, stability analysis, bifurcation analysis and persistence have been investigated. We also describe the global stability analysis of the equilibrium points. Our numerical simulations reveal that cost of fear in basal prey may exhibit bistability by producing unstable limit cycles, however, fear in middle predator can replace unstable limit cycles by a stable limit cycle or a stable interior equilibrium. We observe that fear can stabilize the system from chaos to stable focus through the period-halving phenomenon. We conclude that chaotic dynamics can be controlled by the fear factors. We apply basic tools of nonlinear dynamics such as Poincaré section and maximum Lyapunov exponent to identify the chaotic behavior of the system.

Calculation of point defect concentration in Cu2ZnSnS4: Insights into the high-temperature equilibrium and quenching

NASA Astrophysics Data System (ADS)

Kosyak, V.; Postnikov, A. V.; Scragg, J.; Scarpulla, M. A.; Platzer-Björkman, C.

2017-07-01

Herein, we study the native point defect equilibrium in Cu2ZnSnS4 (CZTS) by applying a statistical thermodynamic model. The stable chemical-potential space (SCPS) of CZTS at an elevated temperature was estimated directly, on the basis of deviations from stoichiometry calculated for the different combinations of chemical potential of the components. We show that the SCPS is narrow due to high concentration of (" separators="|VCu --ZnC u + ) complex which is dominant over other complexes and isolated defects. The CZTS was found to have p-type conductivity for both stoichiometric and Cu-poor/Zn-rich composition. It is established that the reason for this is that the majority of donor-like ZnC u + antisites are involved in the formation of (" separators="|VCu --ZnC u + ) complex making CuZ n - dominant and providing p-type conductivity even for Cu-poor/Zn-rich composition. However, our calculation reveals that the hole concentration is almost insensitive to the variation of the chemical composition within the composition region of the single-phase CZTS due to nearly constant concentration of dominant charged defects. The calculations for the full equilibrium and quenching indicate that hole concentration is strongly dependent on the annealing temperature and decreases substantially after the drastic cooling. This means that the precise control of annealing temperature and post-annealing cooling rate are critical for tuning the electrical properties of CZTS.

Stochastic driven systems far from equilibrium

NASA Astrophysics Data System (ADS)

Kim, Kyung Hyuk

We study the dynamics and steady states of two systems far from equilibrium: a 1-D driven lattice gas and a driven Brownian particle with inertia. (1) We investigate the dynamical scaling behavior of a 1-D driven lattice gas model with two species of particles hopping in opposite directions. We confirm numerically that the dynamic exponent is equal to z = 1.5. We show analytically that a quasi-particle representation relates all phase points to a special phase line directly related to the single-species asymmetric simple exclusion process. Quasi-particle two-point correlations decay exponentially, and in such a manner that quasi-particles of opposite charge dynamically screen each other with a special balance. The balance encompasses all over the phase space. These results indicate that the model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. (2) We investigate the non-equilibrium thermodynamics of a Brownian particle with inertia under feedback control of its inertia. We find such open systems can act as a molecular refrigerator due to an entropy pumping mechanism. We extend the fluctuation theorems to the refrigerator. The entropy pumping modifies both the Jarzynski equality and the fluctuation theorems. We discover that the entropy pumping has a dual role of work and heat. We also investigate the thermodynamics of the particle under a hydrodynamic interaction described by a Langevin equation with a multiplicative noise. The Stratonovich stochastic integration prescription involved in the definition of heat is shown to be the unique physical choice.

A New Chaotic Flow with Hidden Attractor: The First Hyperjerk System with No Equilibrium

NASA Astrophysics Data System (ADS)

Ren, Shuili; Panahi, Shirin; Rajagopal, Karthikeyan; Akgul, Akif; Pham, Viet-Thanh; Jafari, Sajad

2018-02-01

Discovering unknown aspects of non-equilibrium systems with hidden strange attractors is an attractive research topic. A novel quadratic hyperjerk system is introduced in this paper. It is noteworthy that this non-equilibrium system can generate hidden chaotic attractors. The essential properties of such systems are investigated by means of equilibrium points, phase portrait, bifurcation diagram, and Lyapunov exponents. In addition, a fractional-order differential equation of this new system is presented. Moreover, an electronic circuit is also designed and implemented to verify the feasibility of the theoretical model.

On the dynamics aspects for the plane motion of a particle under the action of potential forces in the presence of a magnetic field

NASA Astrophysics Data System (ADS)

Mnasri, C.; Elmandouh, A. A.

2018-06-01

This article deals with the general motion of a particle moving in the Euclidean plane under the influence of a conservative potential force in the presence of a magnetic field perpendicular to the plane of the motion. We introduce the conditions for which this motion is not algebraically integrable by using Kowalevski's exponents. We present the equilibrium positions and study their stability and moreover, we clarify that the existence of the magnetic field acts as a stabilizer for maximum unstable equilibrium points for the effective potential. We employ Lyapunov theorem to construct the periodic solutions near the equilibrium points. The allowed regions of motion are specified and illustrated graphically.

Analytical Study on the Saturated Polarization Under Electric Field and Phase Equilibrium of Three-Phase Polycrystalline Ferroelectrics by Using the Generalized Inverse-Pole-Figure Model

NASA Astrophysics Data System (ADS)

Ju, Kyong-Sik; Ryo, Hyok-Su; Pak, Sung-Nam; Pak, Chang-Su; Ri, Sung-Guk; Ri, Dok-Hwan

2018-07-01

By using the generalized inverse-pole-figure model, the numbers of crystalline particles involved in different domain-switching near the triple tetragonal-rhombohedral-orthorhombic (T-R-O) points of three-phase polycrystalline ferroelectrics have been analytically calculated and domain-switching which can bring out phase transformations has been considered. Through polarization by an electric field, different numbers of crystalline particles can be involved in different phase transformations. According to the phase equilibrium conditions, the phase equilibrium compositions of the three phases coexisting near the T-R-O triple point have been evaluated from the results of the numbers of crystalline particles involved in different phase transformations.

Information spread in networks: Games, optimal control, and stabilization

NASA Astrophysics Data System (ADS)

Khanafer, Ali

This thesis focuses on designing efficient mechanisms for controlling information spread in networks. We consider two models for information spread. The first one is the well-known distributed averaging dynamics. The second model is a nonlinear one that describes virus spread in computer and biological networks. We seek to design optimal, robust, and stabilizing controllers under practical constraints. For distributed averaging networks, we study the interaction between a network designer and an adversary. We consider two types of attacks on the network. In Attack-I, the adversary strategically disconnects a set of links to prevent the nodes from reaching consensus. Meanwhile, the network designer assists the nodes in reaching consensus by changing the weights of a limited number of links in the network. We formulate two problems to describe this competition where the order in which the players act is reversed in the two problems. Although the canonical equations provided by the Pontryagin's Maximum Principle (MP) seem to be intractable, we provide an alternative characterization for the optimal strategies that makes connection to potential theory. Further, we provide a sufficient condition for the existence of a saddle-point equilibrium (SPE) for the underlying zero-sum game. In Attack-II, the designer and the adversary are both capable of altering the measurements of all nodes in the network by injecting global signals. We impose two constraints on both players: a power constraint and an energy constraint. We assume that the available energy to each player is not sufficient to operate at maximum power throughout the horizon of the game. We show the existence of an SPE and derive the optimal strategies in closed form for this attack scenario. As an alternative to the "network designer vs. adversary" framework, we investigate the possibility of stabilizing unknown network diffusion processes using a distributed mechanism, where the uncertainty is due to an attack on the network. To this end, we propose a distributed version of the classical logic-based supervisory control scheme. Given a network of agents whose dynamics contain unknown parameters, the distributed supervisory control scheme is used to assist the agents to converge to a certain set-point without requiring them to have explicit knowledge of that set-point. Unlike the classical supervisory control scheme where a centralized supervisor makes switching decisions among the candidate controllers, in our scheme, each agent is equipped with a local supervisor that switches among the available controllers. The switching decisions made at a certain agent depend only on the information from its neighboring agents. We provide sufficient conditions for stabilization and apply our framework to the distributed averaging problem in the presence of large modeling uncertainty. For infected networks, we study the stability properties of a susceptible-infected-susceptible (SIS) diffusion model, so-called the n-intertwined Markov model, over arbitrary network topologies. Similar to the majority of infection spread dynamics, this model exhibits a threshold phenomenon. When the curing rates in the network are high, the all-healthy state is the unique equilibrium over the network. Otherwise, an endemic equilibrium state emerges, where some infection remains within the network. Using notions from positive systems theory, we provide conditions for the global asymptotic stability of the equilibrium points in both cases over strongly and weakly connected directed networks based on the value of the basic reproduction number, a fundamental quantity in the study of epidemics. Furthermore, we demonstrate that the n-intertwined Markov model can be viewed as a best-response dynamical system of a concave game among the nodes. This characterization allows us to cast new infection spread dynamics; additionally, we provide a sufficient condition, for the global convergence to the all-healthy state, that can be checked in a distributed fashion. Moreover, we investigate the problem of stabilizing the network when the curing rates of a limited number of nodes can be controlled. In particular, we characterize the number of controllers required for a class of undirected graphs. We also design optimal controllers capable of minimizing the total infection in the network at minimum cost. Finally, we outline a set of open problems in the area of information spread control.

Dynamics of eco-epidemiological model with harvesting

NASA Astrophysics Data System (ADS)

Purnomo, Anna Silvia; Darti, Isnani; Suryanto, Agus

2017-12-01

In this paper, we study an eco-epidemiology model which is derived from S I epidemic model with bilinear incidence rate and modified Leslie Gower predator-prey model with harvesting on susceptible prey. Existence condition and stability of all equilibrium points are discussed for the proposed model. Furthermore, we show that the model exhibits a Hopf bifurcation around interior equilibrium point which is driven by the rate of infection. Our numerical simulations using some different value of parameters confirm our analytical analysis.

Chemical equilibrium of ablation materials including condensed species

NASA Technical Reports Server (NTRS)

Stroud, C. W.; Brinkley, K. L.

1975-01-01

Equilibrium is determined by finding chemical composition with minimum free energy. Method of steepest descent is applied to quadratic representation of free-energy surface. Solution is initiated by selecting arbitrary set of mole fractions, from which point on free-energy surface is computed.

Universal Off-Equilibrium Scaling of Critical Cumulants in the QCD Phase Diagram

DOE PAGES

Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi

2016-11-23

Exploiting the universality between the QCD critical point and the three-dimensional Ising model, closed form expressions derived for nonequilibrium critical cumulants on the crossover side of the critical point reveal that they can differ in both magnitude and sign from equilibrium expectations. Here, we demonstrate here that key elements of the Kibble-Zurek framework of nonequilibrium phase transitions can be employed to describe the dynamics of these critical cumulants. Lastly, our results suggest that observables sensitive to critical dynamics in heavy-ion collisions should be expressible as universal scaling functions, thereby providing powerful model-independent guidance in searches for the QCD critical point.

The dynamics and control of large flexible space structures, part 11

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Reddy, A. S. S. R; Diarra, Cheick M.; Li, Feiyue

1988-01-01

A mathematical model is developed to predict the dynamics of the proposed Spacecraft Control Laboratory Experiment during the stationkeeping phase. The Shuttle and reflector are assumed to be rigid, while the mass connecting the Shuttle to the reflector is assumed to be flexible with elastic deformations small as compared with its length. It is seen that in the presence of gravity-gradient torques, the system assumes a new equilibrium position primarily due to the offset in the mass attachment point to the reflector from the reflector's mass center. Control is assumed to be provided through the Shuttle's three torquers and throught six actuators located by painrs at two points on the mass and at the reflector mass center. Numerical results confirm the robustness of an LQR derived control strategy during stationkeeping with maximum control efforts significantly below saturation levels. The linear regulator theory is also used to derive control laws for the linearized model of the rigidized SCOLE configuration where the mast flexibility is not included. It is seen that this same type of control strategy can be applied for the rapid single axis slewing of the SCOLE through amplitudes as large as 20 degrees. These results provide a definite trade-off between the slightly larger slewing times with the considerable reduction in over-all control effort as compared with the results of the two point boundary value problem application of Pontryagin's Maximum Principle.

Stabilisation problem in biaxial platform

NASA Astrophysics Data System (ADS)

Lindner, Tymoteusz; Rybarczyk, Dominik; Wyrwał, Daniel

2016-12-01

The article describes investigation of rolling ball stabilization problem on a biaxial platform. The aim of the control system proposed here is to stabilize ball moving on a plane in equilibrium point. The authors proposed a control algorithm based on cascade PID and they compared it with another control method. The article shows the results of the accuracy of ball stabilization and influence of applied filter on the signal waveform. The application used to detect the ball position measured by digital camera has been written using a cross platform .Net wrapper to the OpenCV image processing library - EmguCV. The authors used the bipolar stepper motor with dedicated electronic controller. The data between the computer and the designed controller are sent with use of the RS232 standard. The control stand is based on ATmega series microcontroller.

On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system

NASA Astrophysics Data System (ADS)

Hajipour, Ahamad; Hajipour, Mojtaba; Baleanu, Dumitru

2018-05-01

This manuscript mainly focuses on the construction, dynamic analysis and control of a new fractional-order financial system. The basic dynamical behaviors of the proposed system are studied such as the equilibrium points and their stability, Lyapunov exponents, bifurcation diagrams, phase portraits of state variables and the intervals of system parameters. It is shown that the system exhibits hyperchaotic behavior for a number of system parameters and fractional-order values. To stabilize the proposed hyperchaotic fractional system with uncertain dynamics and disturbances, an efficient adaptive sliding mode controller technique is developed. Using the proposed technique, two hyperchaotic fractional-order financial systems are also synchronized. Numerical simulations are presented to verify the successful performance of the designed controllers.

An assessment of mean-field mixed semiclassical approaches: Equilibrium populations and algorithm stability

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

Bellonzi, Nicole; Jain, Amber; Subotnik, Joseph E.

2016-04-21

We study several recent mean-field semiclassical dynamics methods, focusing on the ability to recover detailed balance for long time (equilibrium) populations. We focus especially on Miller and Cotton’s [J. Phys. Chem. A 117, 7190 (2013)] suggestion to include both zero point electronic energy and windowing on top of Ehrenfest dynamics. We investigate three regimes: harmonic surfaces with weak electronic coupling, harmonic surfaces with strong electronic coupling, and anharmonic surfaces with weak electronic coupling. In most cases, recent additions to Ehrenfest dynamics are a strong improvement upon mean-field theory. However, for methods that include zero point electronic energy, we show thatmore » anharmonic potential energy surfaces often lead to numerical instabilities, as caused by negative populations and forces. We also show that, though the effect of negative forces can appear hidden in harmonic systems, the resulting equilibrium limits do remain dependent on any windowing and zero point energy parameters.« less

Pollutant threshold concentration determination in marine ecosystems using an ecological interaction endpoint.

PubMed

Wang, Changyou; Liang, Shengkang; Guo, Wenting; Yu, Hua; Xing, Wenhui

2015-09-01

The threshold concentrations of pollutants are determined by extrapolating single-species effect data to community-level effects. This assumes the most sensitive endpoint of the life cycle of individuals and the species sensitivity distribution from single-species toxic effect tests, thus, ignoring the ecological interactions. The uncertainties due to this extrapolation can be partially overcome using the equilibrium point of a customized ecosystem. This method incorporates ecological interactions and integrates the effects on growth, survival, and ingestion into a single effect measure, the equilibrium point excursion in the customized ecosystem, in order to describe the toxic effects on plankton. A case study showed that the threshold concentration of copper calculated with the endpoint of the equilibrium point was 10 μg L(-1), which is significantly different from the threshold calculated with a single-species endpoint. The endpoint calculated using this method provides a more relevant measure of the ecological impact than any single individual-level endpoint. Copyright © 2015 Elsevier Ltd. All rights reserved.

Adaptive Dynamic Programming for Discrete-Time Zero-Sum Games.

PubMed

Wei, Qinglai; Liu, Derong; Lin, Qiao; Song, Ruizhuo

2018-04-01

In this paper, a novel adaptive dynamic programming (ADP) algorithm, called "iterative zero-sum ADP algorithm," is developed to solve infinite-horizon discrete-time two-player zero-sum games of nonlinear systems. The present iterative zero-sum ADP algorithm permits arbitrary positive semidefinite functions to initialize the upper and lower iterations. A novel convergence analysis is developed to guarantee the upper and lower iterative value functions to converge to the upper and lower optimums, respectively. When the saddle-point equilibrium exists, it is emphasized that both the upper and lower iterative value functions are proved to converge to the optimal solution of the zero-sum game, where the existence criteria of the saddle-point equilibrium are not required. If the saddle-point equilibrium does not exist, the upper and lower optimal performance index functions are obtained, respectively, where the upper and lower performance index functions are proved to be not equivalent. Finally, simulation results and comparisons are shown to illustrate the performance of the present method.

SEIIrR: Drug abuse model with rehabilitation

NASA Astrophysics Data System (ADS)

Sutanto, Azizah, Afina; Widyaningsih, Purnami; Saputro, Dewi Retno Sari

2017-05-01

Drug abuse in the world quite astonish and tend to increase. The increase and decrease on the number of drug abusers showed a pattern of spread that had the same characteristics with patterns of spread of infectious disease. The susceptible infected removed (SIR) and susceptible exposed infected removed (SEIR) epidemic models for infectious disease was developed to study social epidemic. In this paper, SEIR model for disease epidemic was developed to study drug abuse epidemic with rehabilitation treatment. The aims of this paper were to analogize susceptible exposed infected isolated recovered (SEIIrR) model on the drug abusers, to determine solutions of the model, to determine equilibrium point, and to do simulation on β. The solutions of SEIIrR model was determined by using fourth order of Runge-Kutta algorithm, equilibrium point obtained was free-drug equilibrium point. Solutions of SEIIrR showed that the model was able to suppress the spread of drug abuse. The increasing value of contact rate was not affect the number of infected individuals due to rehabilitation treatment.

The equilibrium of overpressurized polytropes

NASA Astrophysics Data System (ADS)

Huré, J.-M.; Hersant, F.; Nasello, G.

2018-03-01

We investigate the impact of an external pressure on the structure of self-gravitating polytropes for axially symmetric ellipsoids and rings. The confinement of the fluid by photons is accounted for through a boundary condition on the enthalpy H. Equilibrium configurations are determined numerically from a generalized `self-consistent-field' method. The new algorithm incorporates an intraloop re-scaling operator R(H), which is essential for both convergence and getting self-normalized solutions. The main control parameter is the external-to-core enthalpy ratio. In the case of uniform rotation rate and uniform surrounding pressure, we compute the mass, the volume, the rotation rate and the maximum enthalpy. This is repeated for a few polytropic indices, n. For a given axial ratio, overpressurization globally increases all output quantities, and this is more pronounced for large n. Density profiles are flatter than in the absence of an external pressure. When the control parameter asymptotically tends to unity, the fluid converges towards the incompressible solution, whatever the index, but becomes geometrically singular. Equilibrium sequences, obtained by varying the axial ratio, are built. States of critical rotation are greatly exceeded or even disappear. The same trends are observed with differential rotation. Finally, the typical response to a photon point source is presented. Strong irradiation favours sharp edges. Applications concern star-forming regions and matter orbiting young stars and black holes.

Time Reparametrization Group and the Long Time Behavior in Quantum Glassy Systems

NASA Astrophysics Data System (ADS)

Kennett, Malcolm P.; Chamon, Claudio

2001-02-01

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations; in this language the long time behavior of this model is controlled by a reparametrization group ( RpG) fixed point of the classical dynamics. The irrelevance of quantum terms in the dynamical equations in the aging regime explains the classical nature of the out of equilibrium fluctuation-dissipation relation.

Global Stability and Control Analysis of Aircraft at High Angles-of-Attack.

DTIC Science & Technology

1977-06-30

500 deg/sec to 500 deg/sec and com - puting the eigenvalues of the linearized system around different equilibrium points for 6e = 2°. It is noticed...SYSTEMS, INC. 0" -114- 2 Ä»" • + + + + + _+ + + + + + + + + M I o o o a i i 8 8 in 8 8 XNXX * x x» x x x< x...history com - parisons show significant improvement in dynamic response and performance using the BACTM ARI gain, as opposed to nulling the rudder

Chaotic Dynamics in a Low-Energy Transfer Strategy to the Equilateral Equilibrium Points in the Earth-Moon System

NASA Astrophysics Data System (ADS)

Salazar, F. J. T.; Macau, E. E. N.; Winter, O. C.

In the frame of the equilateral equilibrium points exploration, numerous future space missions will require maximization of payload mass, simultaneously achieving reasonable transfer times. To fulfill this request, low-energy non-Keplerian orbits could be used to reach L4 and L5 in the Earth-Moon system instead of high energetic transfers. Previous studies have shown that chaos in physical systems like the restricted three-body Earth-Moon-particle problem can be used to direct a chaotic trajectory to a target that has been previously considered. In this work, we propose to transfer a spacecraft from a circular Earth Orbit in the chaotic region to the equilateral equilibrium points L4 and L5 in the Earth-Moon system, exploiting the chaotic region that connects the Earth with the Moon and changing the trajectory of the spacecraft (relative to the Earth) by using a gravity assist maneuver with the Moon. Choosing a sequence of small perturbations, the time of flight is reduced and the spacecraft is guided to a proper trajectory so that it uses the Moon's gravitational force to finally arrive at a desired target. In this study, the desired target will be an orbit about the Lagrangian equilibrium points L4 or L5. This strategy is not only more efficient with respect to thrust requirement, but also its time transfer is comparable to other known transfer techniques based on time optimization.

Anomaly on Superspace of Time Series Data

NASA Astrophysics Data System (ADS)

Capozziello, Salvatore; Pincak, Richard; Kanjamapornkul, Kabin

2017-11-01

We apply the G-theory and anomaly of ghost and antighost fields in the theory of supersymmetry to study a superspace over time series data for the detection of hidden general supply and demand equilibrium in the financial market. We provide proof of the existence of a general equilibrium point over 14 extradimensions of the new G-theory compared with the M-theory of the 11 dimensions model of Edward Witten. We found that the process of coupling between nonequilibrium and equilibrium spinor fields of expectation ghost fields in the superspace of time series data induces an infinitely long exact sequence of cohomology from a short exact sequence of moduli state space model. If we assume that the financial market is separated into two topological spaces of supply and demand as the D-brane and anti-D-brane model, then we can use a cohomology group to compute the stability of the market as a stable point of the general equilibrium of the interaction between D-branes of the market. We obtain the result that the general equilibrium will exist if and only if the 14th Batalin-Vilkovisky cohomology group with the negative dimensions underlying 14 major hidden factors influencing the market is zero.

Thermal Equilibrium of a Macroscopic Quantum System in a Pure State.

PubMed

Goldstein, Sheldon; Huse, David A; Lebowitz, Joel L; Tumulka, Roderich

2015-09-04

We consider the notion of thermal equilibrium for an individual closed macroscopic quantum system in a pure state, i.e., described by a wave function. The macroscopic properties in thermal equilibrium of such a system, determined by its wave function, must be the same as those obtained from thermodynamics, e.g., spatial uniformity of temperature and chemical potential. When this is true we say that the system is in macroscopic thermal equilibrium (MATE). Such a system may, however, not be in microscopic thermal equilibrium (MITE). The latter requires that the reduced density matrices of small subsystems be close to those obtained from the microcanonical, equivalently the canonical, ensemble for the whole system. The distinction between MITE and MATE is particularly relevant for systems with many-body localization for which the energy eigenfuctions fail to be in MITE while necessarily most of them, but not all, are in MATE. We note, however, that for generic macroscopic systems, including those with MBL, most wave functions in an energy shell are in both MATE and MITE. For a classical macroscopic system, MATE holds for most phase points on the energy surface, but MITE fails to hold for any phase point.

A THERMODYNAMIC ANALYSIS OF MITOTIC SPINDLE EQUILIBRIUM AT ACTIVE METAPHASE

PubMed Central

Stephens, R. E.

1973-01-01

The mitotic apparatus of first-division metaphase eggs of the sea urchin Strongylocentrotus drobachiensis was observed by means of polarization microscopy under controlled temperature conditions. Eggs were fertilized and grown at two temperature extremes in order to produce two different sizes of available spindle pool. Slow division time allowed successive samples of such cells to be observed at the same point in metaphase but at different equilibrium temperatures, yielding curves of metaphase equilibrium birefringence vs. observational temperature. Using the plateau value of birefringence at higher temperatures as a measure of total available spindle pool and the observed birefringence at lower temperatures as a measure of polymerized material at equilibrium, the spindle protein association was evaluated according to the method of Inoué. Both pool conditions produced linear van't Hoff functions. Analysis of these functions yielded enthalpy and entropy changes of +55–65 kcal/mol and +197–233 entropy units (eu), respectively. These values for active mitotic metaphase are quite comparable to those obtained by Inoué and co-workers for arrested meiotic metaphase cells. When other equilibrium treatments were considered, the best fit to the experimental data was still that of Inoué, a treatment which theoretically involves first-order polymerization and dissociation kinetics. Treatment of metaphase cells with D2O by direct immersion drove the equilibrium to completion regardless of temperature, attaining or exceeding a birefringence value equal to the cell's characteristic pool size; perfusion with D2O appeared to erase the original temperature-determined pool size differences for the two growth conditions, attaining a maximum value characteristic of the larger pool condition. These data confirm Inoué's earlier contention that D2O treatment can modify the available spindle pool. PMID:4734864

Optimal Sunshade Configurations for Space-Based Geoengineering near the Sun-Earth L1 Point.

PubMed

Sánchez, Joan-Pau; McInnes, Colin R

2015-01-01

Within the context of anthropogenic climate change, but also considering the Earth's natural climate variability, this paper explores the speculative possibility of large-scale active control of the Earth's radiative forcing. In particular, the paper revisits the concept of deploying a large sunshade or occulting disk at a static position near the Sun-Earth L1 Lagrange equilibrium point. Among the solar radiation management methods that have been proposed thus far, space-based concepts are generally seen as the least timely, albeit also as one of the most efficient. Large occulting structures could potentially offset all of the global mean temperature increase due to greenhouse gas emissions. This paper investigates optimal configurations of orbiting occulting disks that not only offset a global temperature increase, but also mitigate regional differences such as latitudinal and seasonal difference of monthly mean temperature. A globally resolved energy balance model is used to provide insights into the coupling between the motion of the occulting disks and the Earth's climate. This allows us to revise previous studies, but also, for the first time, to search for families of orbits that improve the efficiency of occulting disks at offsetting climate change on both global and regional scales. Although natural orbits exist near the L1 equilibrium point, their period does not match that required for geoengineering purposes, thus forced orbits were designed that require small changes to the disk attitude in order to control its motion. Finally, configurations of two occulting disks are presented which provide the same shading area as previously published studies, but achieve reductions of residual latitudinal and seasonal temperature changes.

Optimal Sunshade Configurations for Space-Based Geoengineering near the Sun-Earth L1 Point

PubMed Central

Sánchez, Joan-Pau; McInnes, Colin R.

2015-01-01

Within the context of anthropogenic climate change, but also considering the Earth’s natural climate variability, this paper explores the speculative possibility of large-scale active control of the Earth’s radiative forcing. In particular, the paper revisits the concept of deploying a large sunshade or occulting disk at a static position near the Sun-Earth L1 Lagrange equilibrium point. Among the solar radiation management methods that have been proposed thus far, space-based concepts are generally seen as the least timely, albeit also as one of the most efficient. Large occulting structures could potentially offset all of the global mean temperature increase due to greenhouse gas emissions. This paper investigates optimal configurations of orbiting occulting disks that not only offset a global temperature increase, but also mitigate regional differences such as latitudinal and seasonal difference of monthly mean temperature. A globally resolved energy balance model is used to provide insights into the coupling between the motion of the occulting disks and the Earth’s climate. This allows us to revise previous studies, but also, for the first time, to search for families of orbits that improve the efficiency of occulting disks at offsetting climate change on both global and regional scales. Although natural orbits exist near the L1 equilibrium point, their period does not match that required for geoengineering purposes, thus forced orbits were designed that require small changes to the disk attitude in order to control its motion. Finally, configurations of two occulting disks are presented which provide the same shading area as previously published studies, but achieve reductions of residual latitudinal and seasonal temperature changes. PMID:26309047

Steps toward identifying a biogeochemical signal in non-equilibrium methane clumped isotope measurements

NASA Astrophysics Data System (ADS)

Douglas, P. M.; Eiler, J. M.; Sessions, A. L.; Dawson, K.; Walter Anthony, K. M.; Smith, D. A.; Lloyd, M. K.; Yanay, E.

2016-12-01

Microbially produced methane is a globally important greenhouse gas, energy source, and biological substrate. Methane clumped isotope measurements have recently been developed as a new analytical tool for understanding the source of methane in different environments. When methane forms in isotopic equilibrium clumped isotope values are determined by formation temperature, but in many cases microbial methane clumped isotope values deviate strongly from expected equilibrium values. Indeed, we observe a very wide range of clumped isotope values in microbial methane, which are likely strongly influenced by kinetic isotope effects, but thus far the biological and environmental parameters controlling this variability are not understood. We will present data from both culture experiments and natural environments to explore patterns of variability in non-equilibrium clumped isotope values on temporal and spatial scales. In methanogen batch cultures sampled at different time points along a growth curve we observe significant variability in clumped isotope values, with values decreasing from early to late exponential growth. Clumped isotope values then increase during stationary growth. This result is consistent with previous work suggesting that differences in the reversibility of methanogenesis related to metabolic rates control non-equilibrium clumped isotope values. Within single lakes in Alaska and Sweden we observe substantial variability in clumped isotope values on the order of 5‰. Lower clumped isotope values are associated with larger 2H isotopic fractionation between water and methane, which is also consistent with a kinetic isotope effect determined by the reversibility of methanogenesis. Finally, we analyzed a time-series clumped isotope compositions of methane emitted from two seeps in an Alaskan lake over several months. Temporal variability in these seeps is on the order of 2‰, which is much less than the observed spatial variability within the lake. Comparing carbon isotope fractionation between CO2 and CH4 with clumped isotope data suggests the temporal variability may result from changes in methane oxidation.

On the freestream matching condition for stagnation point turbulent flows

NASA Technical Reports Server (NTRS)

Speziale, C. G.

1989-01-01

The problem of plane stagnation point flow with freestream turbulence is examined from a basic theoretical standpoint. It is argued that the singularity which arises from the standard kappa-epsilon model is not due to a defect in the model but results from the use of an inconsistent freestream boundary condition. The inconsistency lies in the implementation of a production equals dissipation equilibrium hypothesis in conjunction with a freestream mean velocity field that corresponds to homogeneous plane strain - a turbulent flow which does not reach such a simple equilibrium. Consequently, the adjustment that has been made in the constants of the epsilon-transport equation to eliminate this singularity is not self-consistent since it is tantamount to artificially imposing an equilibrium structure on a turbulent flow which is known not to have one.

Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays.

PubMed

Zhang, Zhengqiu; Liu, Wenbin; Zhou, Dongming

2012-01-01

In this paper, we first discuss the existence of a unique equilibrium point of a generalized Cohen-Grossberg BAM neural networks of neutral type delays by means of the Homeomorphism theory and inequality technique. Then, by applying the existence result of an equilibrium point and constructing a Lyapunov functional, we study the global asymptotic stability of the equilibrium solution to the above Cohen-Grossberg BAM neural networks of neutral type. In our results, the hypothesis for boundedness in the existing paper, which discussed Cohen-Grossberg neural networks of neutral type on the activation functions, are removed. Finally, we give an example to demonstrate the validity of our global asymptotic stability result for the above neural networks. Copyright © 2011 Elsevier Ltd. All rights reserved.

Distributed Multiple Access Control for the Wireless Mesh Personal Area Networks

NASA Astrophysics Data System (ADS)

Park, Moo Sung; Lee, Byungjoo; Rhee, Seung Hyong

Mesh networking technologies for both high-rate and low-rate wireless personal area networks (WPANs) are under development by several standardization bodies. They are considering to adopt distributed TDMA MAC protocols to provide seamless user mobility as well as a good peer-to-peer QoS in WPAN mesh. It has been, however, pointed out that the absence of a central controller in the wireless TDMA MAC may cause a severe performance degradation: e. g., fair allocation, service differentiation, and admission control may be hard to achieve or can not be provided. In this paper, we suggest a new framework of resource allocation for the distributed MAC protocols in WPANs. Simulation results show that our algorithm achieves both a fair resource allocation and flexible service differentiations in a fully distributed way for mesh WPANs where the devices have high mobility and various requirements. We also provide an analytical modeling to discuss about its unique equilibrium and to compute the lengths of reserved time slots at the stable point.

Implementation Of Fuzzy Automated Brake Controller Using TSK Algorithm

NASA Astrophysics Data System (ADS)

Mittal, Ruchi; Kaur, Magandeep

2010-11-01

In this paper an application of Fuzzy Logic for Automatic Braking system is proposed. Anti-blocking system (ABS) brake controllers pose unique challenges to the designer: a) For optimal performance, the controller must operate at an unstable equilibrium point, b) Depending on road conditions, the maximum braking torque may vary over a wide range, c) The tire slippage measurement signal, crucial for controller performance, is both highly uncertain and noisy. A digital controller design was chosen which combines a fuzzy logic element and a decision logic network. The controller identifies the current road condition and generates a command braking pressure signal Depending upon the speed and distance of train. This paper describes design criteria, and the decision and rule structure of the control system. The simulation results present the system's performance depending upon the varying speed and distance of the train.

Optimal harvesting policy of predator-prey model with free fishing and reserve zones

NASA Astrophysics Data System (ADS)

Toaha, Syamsuddin; Rustam

2017-03-01

The present paper deals with an optimal harvesting of predator-prey model in an ecosystem that consists of two zones, namely the free fishing and prohibited zones. The dynamics of prey population in the ecosystem can migrate from the free fishing to the prohibited zone and vice versa. The predator and prey populations in the free fishing zone are then harvested with constant efforts. The existence of the interior equilibrium point is analyzed and its stability is determined using Routh-Hurwitz stability test. The stable interior equilibrium point is then related to the problem of maximum profit and the problem of present value of net revenue. We follow the Pontryagin's maximal principle to get the optimal harvesting policy of the present value of the net revenue. From the analysis, we found a critical point of the efforts that makes maximum profit. There also exists certain conditions of the efforts that makes the present value of net revenue becomes maximal. In addition, the interior equilibrium point is locally asymptotically stable which means that the optimal harvesting is reached and the unharvested prey, harvested prey, and harvested predator populations remain sustainable. Numerical examples are given to verify the analytical results.

Direct recording of cardiac output- and venous return-curves in the dog heart-lung preparation for a graphical analysis of the effects of cardioactive drugs.

PubMed

Ishikawa, N; Taki, K; Hojo, Y; Hagino, Y; Shigei, T

1978-09-01

The dog heart-lung preparations were prepared. The "equilibrium point", which could be defined as the point at which the cardiac output (CO)-curve and the venous return (VR)-curve crossed, when the CO and VR were plotted against the right atrial pressure, was recorded directly by utilizing an X-Y recorder. The CO-curve was obtained, as a locus of the equilibrium point, by raising and lowering the level of blood in the venous reservoir (competence test). The meaning of the procedure was shown to increase or decrease the mean systemic pressure, and to cause the corresponding parallel shift in the VR-curve. The VR-curve was obtained by changing myocardial contractility. When heart failure was induced by pentobarbital or by chloroform, the equilibrium point shifted downwards to the right, depicting the VR-curve. During development of the failure, the slopes of CO-curves decreased gradually. Effects of cinobufagin and norepinephrine were also analyzed. Utilization of the X-Y recorder enabled us to settle the uniform experimental conditions more easily, and to follow the effects of drugs continuously on a diagram equating the CO- and VR-curves (Gyton's scheme).

Optimal intravenous infusion to decrease the haematocrit level in patient of DHF infection

NASA Astrophysics Data System (ADS)

Handayani, D.; Nuraini, N.; Saragih, R.; Wijaya, K. P.; Naiborhu, J.

2014-02-01

The optimal control of infusion model for Dengue Hemorrhagic Fever (DHF) infection is formulated here. The infusion model will be presented in form of haematocrit level. The input control aim to normalize the haematocrit level and is expressed as infusion volume on mL/day. The stability near the equilibrium points will be analyzed. Numerical simulation shows the dynamic of each infection compartments which gives a description of within-host dynamic of dengue virus. These results show particularly that infected compartments tend to be vanished in ±15days after the onset of the virus. In fact, without any control added, the haematocrit level will decrease but not up to the normal level. Therefore the effective haematocrit normalization should be done with the treatment control. Control treatment for a fixed time using a control input can bring haematocrit level to normal range 42-47%. The optimal control in this paper is divided into three cases, i.e. fixed end point, constrained input, and tracking haematocrit state. Each case shows different infection condition in human body. However, all cases require that the haematocrit level to be in normal range in fixed final time.

Nonlinear Differential Equations and Feedback Control Design for the Urban-Rural Resident Pension Insurance in China

NASA Astrophysics Data System (ADS)

Wang, Lijian

2015-12-01

Facing many problems of the urban-rural resident pension insurance system in China, one should firstly make sure that this system can be optimized. This paper, based on the modern control theory, sets up differential equations as models to describe the urban-rural resident pension insurance system, and discusses the globally asymptotic stability in the sense of Liapunov for the urban-rural resident pension insurance system in the new equilibrium point. This research sets the stage for our further discussion, and it is theoretically important and convenient for optimizing the urban-rural resident pension insurance system.

Mathematical Model of Three Species Food Chain Interaction with Mixed Functional Response

NASA Astrophysics Data System (ADS)

Ws, Mada Sanjaya; Mohd, Ismail Bin; Mamat, Mustafa; Salleh, Zabidin

In this paper, we study mathematical model of ecology with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Holling type-III functional response for predator and super predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviors of this model are investigated. Models for biologically reasonable parameter values, exhibits stable, unstable periodic and limit cycles. The dynamical behavior is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.

A Class of Solvable Stopping Games

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

Alvarez, Luis H. R.

We consider a class of Dynkin games in the case where the underlying process evolves according to a one-dimensional but otherwise general diffusion. We establish general conditions under which both the value and the saddle point equilibrium exist and under which the exercise boundaries characterizing the saddle point strategy can be explicitly characterized in terms of a pair of standard first order necessary conditions for optimality. We also analyze those cases where an extremal pair of boundaries exists and investigate the overall impact of increased volatility on the equilibrium stopping strategies and their values.

Iterative algorithms for computing the feedback Nash equilibrium point for positive systems

NASA Astrophysics Data System (ADS)

Ivanov, I.; Imsland, Lars; Bogdanova, B.

2017-03-01

The paper studies N-player linear quadratic differential games on an infinite time horizon with deterministic feedback information structure. It introduces two iterative methods (the Newton method as well as its accelerated modification) in order to compute the stabilising solution of a set of generalised algebraic Riccati equations. The latter is related to the Nash equilibrium point of the considered game model. Moreover, we derive the sufficient conditions for convergence of the proposed methods. Finally, we discuss two numerical examples so as to illustrate the performance of both of the algorithms.

Anomalous behavior of 1/f noise in graphene near the charge neutrality point

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

Takeshita, Shunpei; Tanaka, Takahiro; Arakawa, Tomonori

2016-03-07

We investigate the noise in single layer graphene devices from equilibrium to far-from equilibrium and found that the 1/f noise shows an anomalous dependence on the source-drain bias voltage (V{sub SD}). While the Hooge's relation is not the case around the charge neutrality point, we found that it is recovered at very low V{sub SD} region. We propose that the depinning of the electron-hole puddles is induced at finite V{sub SD}, which may explain this anomalous noise behavior.

Stability of equilibrium points in intraguild predation model with disease with SI model

NASA Astrophysics Data System (ADS)

Hassan, Aimi Nuraida binti Ali; Bujang, Noriham binti; Mahdi, Ahmad Faisal Bin

2017-04-01

Intraguild Predation (IGP) is classified as killing and eating among potential competitors. Intraguild Predation is a universal interaction, differing from competition or predation. Lotka Volterra competition model and Intraguild predation model has been analyze. The assumption for this model is no any immigration or migration involves. This paper is only considered IGP model for susceptible and infective (SI) only. The analysis of stability of the equilibrium points of Intraguild Predation Models with disease using Routh Hurwitz criteria will be illustrated using some numerical example.

Nakedly singular non-vacuum gravitating equilibrium states

NASA Astrophysics Data System (ADS)

Woszczyna, Andrzej; Kutschera, Marek; Kubis, Sebastian; Czaja, Wojciech; Plaszczyk, Piotr; Golda, Zdzisław A.

2016-01-01

Non-vacuum static spherically symmetric spacetimes with central point-like repulsive gravity sources are investigated. Both the symmetries of spacetime and the degree of irregularity of curvature invariants, are the same as for the Schwarzschild case. The equilibrium configurations are modelled using the neutron star polytrope equation of state.

How Stable Is Stable?

ERIC Educational Resources Information Center

Baehr, Marie

1994-01-01

Provides a problem where students are asked to find the point at which a soda can floating in some liquid changes its equilibrium between stable and unstable as the soda is removed from the can. Requires use of Newton's first law, center of mass, Archimedes' principle, stable and unstable equilibrium, and buoyant force position. (MVL)

Discretization and control of an SEIR epidemic model under equilibrium Wiener noise disturbances

NASA Astrophysics Data System (ADS)

Alonso, Santiago; De la Sen, Manuel; Nistal, Raul; Ibeas, Asier

2017-11-01

A discretized SEIR epidemic model, subject to Wiener noise disturbances of the equilibrium points, is studied. The discrete-time model is got from a general discretization technique applied to its continuous-time counterpart so that its behaviour be close to its continuous-time counterpart irrespective of the size of the discretization period. The positivity and stability of a normalized version of such a discrete-time model are emphasized. The paper also proposes the design of a periodic impulsive vaccination which is periodically injected to the susceptible subpopulation in order to eradicate the propagation of the disease or, at least, to reduce its unsuitable infective effects within the potentially susceptible subpopulation. The existence and asymptotic stability of a disease-free periodic solution are proved. In particular, both the exposed and infectious subpopulations converge asymptotically to zero as time tends to infinity while the normalized subpopulations of susceptible and recovered by immunization oscillate.

A new equilibrium torus solution and GRMHD initial conditions

NASA Astrophysics Data System (ADS)

Penna, Robert F.; Kulkarni, Akshay; Narayan, Ramesh

2013-11-01

Context. General relativistic magnetohydrodynamic (GRMHD) simulations are providing influential models for black hole spin measurements, gamma ray bursts, and supermassive black hole feedback. Many of these simulations use the same initial condition: a rotating torus of fluid in hydrostatic equilibrium. A persistent concern is that simulation results sometimes depend on arbitrary features of the initial torus. For example, the Bernoulli parameter (which is related to outflows), appears to be controlled by the Bernoulli parameter of the initial torus. Aims: In this paper, we give a new equilibrium torus solution and describe two applications for the future. First, it can be used as a more physical initial condition for GRMHD simulations than earlier torus solutions. Second, it can be used in conjunction with earlier torus solutions to isolate the simulation results that depend on initial conditions. Methods: We assume axisymmetry, an ideal gas equation of state, constant entropy, and ignore self-gravity. We fix an angular momentum distribution and solve the relativistic Euler equations in the Kerr metric. Results: The Bernoulli parameter, rotation rate, and geometrical thickness of the torus can be adjusted independently. Our torus tends to be more bound and have a larger radial extent than earlier torus solutions. Conclusions: While this paper was in preparation, several GRMHD simulations appeared based on our equilibrium torus. We believe it will continue to provide a more realistic starting point for future simulations.

Generating one to four-wing hidden attractors in a novel 4D no-equilibrium chaotic system with extreme multistability.

PubMed

Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le

2018-01-01

By using a simple state feedback controller in a three-dimensional chaotic system, a novel 4D chaotic system is derived in this paper. The system state equations are composed of nine terms including only one constant term. Depending on the different values of the constant term, this new proposed system has a line of equilibrium points or no equilibrium points. Compared with other similar chaotic systems, the newly presented system owns more abundant and complicated dynamic properties. What interests us is the observation that if the value of the constant term of the system is nonzero, it has no equilibria, and therefore, the Shil'nikov theorem is not suitable to verify the existence of chaos for the lack of heteroclinic or homoclinic trajectory. However, one-wing, two-wing, three-wing, and four-wing hidden attractors can be obtained from this new system. In addition, various coexisting hidden attractors are obtained and the complex transient transition behaviors are also observed. More interestingly, the unusual and striking dynamic behavior of the coexistence of infinitely many hidden attractors is revealed by selecting the different initial values of the system, which means that extreme multistability arises. The rich and complex hidden dynamic characteristics of this system are investigated by phase portraits, bifurcation diagrams, Lyapunov exponents, and so on. Finally, the new system is implemented by an electronic circuit. A very good agreement is observed between the experimental results and the numerical simulations of the same system on the Matlab platform.

Generating one to four-wing hidden attractors in a novel 4D no-equilibrium chaotic system with extreme multistability

NASA Astrophysics Data System (ADS)

Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le

2018-01-01

By using a simple state feedback controller in a three-dimensional chaotic system, a novel 4D chaotic system is derived in this paper. The system state equations are composed of nine terms including only one constant term. Depending on the different values of the constant term, this new proposed system has a line of equilibrium points or no equilibrium points. Compared with other similar chaotic systems, the newly presented system owns more abundant and complicated dynamic properties. What interests us is the observation that if the value of the constant term of the system is nonzero, it has no equilibria, and therefore, the Shil'nikov theorem is not suitable to verify the existence of chaos for the lack of heteroclinic or homoclinic trajectory. However, one-wing, two-wing, three-wing, and four-wing hidden attractors can be obtained from this new system. In addition, various coexisting hidden attractors are obtained and the complex transient transition behaviors are also observed. More interestingly, the unusual and striking dynamic behavior of the coexistence of infinitely many hidden attractors is revealed by selecting the different initial values of the system, which means that extreme multistability arises. The rich and complex hidden dynamic characteristics of this system are investigated by phase portraits, bifurcation diagrams, Lyapunov exponents, and so on. Finally, the new system is implemented by an electronic circuit. A very good agreement is observed between the experimental results and the numerical simulations of the same system on the Matlab platform.

External Source of Infection and Nutritional Efficiency Control Chaos in a Predator-Prey Model with Disease in the Predator

NASA Astrophysics Data System (ADS)

Pada Das, Krishna; Roy, Prodip; Ghosh, Subhabrata; Maiti, Somnath

This paper deals with an eco-epidemiological approach with disease circulating through the predator species. Disease circulation in the predator species can be possible by contact as well as by external sources. Here, we try to discuss the role of external source of infection along with nutritional value on system dynamics. To establish our findings, we have worked out the local and global stability analysis of the equilibrium points with Hopf bifurcation analysis associated with interior equilibrium point. The ecological consequence by ecological basic reproduction number as well as the disease basic reproduction number or basic reproductive ratio are obtained and we have analyzed the community structure of the particular system with the help of ecological and disease basic reproduction numbers. Further we pay attention to the chaotic dynamics which is produced by disease circulating in predator species by contact. Our numerical simulations reveal that eco-epidemiological system without external source of infection induced chaotic dynamics for increasing force of infection due to contact, whereas in the presence of external source of infection, it exhibits stable solution. It is also observed that nutritional value can prevent chaotic dynamics. We conclude that chaotic dynamics can be controlled by the external source of infection as well as nutritional value. We apply basic tools of nonlinear dynamics such as Poincare section and maximum Lyapunov exponent to investigate chaotic behavior of the system.

Transport spectroscopy of induced superconductivity in the three-dimensional topological insulator HgTe

NASA Astrophysics Data System (ADS)

Wiedenmann, Jonas; Liebhaber, Eva; Kübert, Johannes; Bocquillon, Erwann; Burset, Pablo; Ames, Christopher; Buhmann, Hartmut; Klapwijk, Teun M.; Molenkamp, Laurens W.

2017-10-01

The proximity-induced superconducting state in the three-dimensional topological insulator HgTe has been studied using electronic transport of a normal metal-superconducting point contact as a spectroscopic tool (Andreev point-contact spectroscopy). By analyzing the conductance as a function of voltage for various temperatures, magnetic fields, and gate voltages, we find evidence, in equilibrium, for an induced order parameter in HgTe of 70 µeV and a niobium order parameter of 1.1 meV. To understand the full conductance curve as a function of applied voltage we suggest a non-equilibrium-driven transformation of the quantum transport process where the relevant scattering region and equilibrium reservoirs change with voltage. This change implies that the spectroscopy probes the superconducting correlations at different positions in the sample, depending on the bias voltage.

Integrated Power and Attitude Control for a Spacecraft with Flywheels and Control Moment Gyroscopes

NASA Technical Reports Server (NTRS)

Roithmayr, Carlos M.; Karlgaard, Christopher D.; Kumar, Renjith R.; Bose, David M.

2003-01-01

A law is designed for simultaneous control of the orientation of an Earth-pointing spacecraft, the energy stored by counter-rotating flywheels, and the angular momentum of the flywheels and control moment gyroscopes used together as all integrated set of actuators for attitude control. General. nonlinear equations of motion are presented in vector-dyadic form, and used to obtain approximate expressions which are then linearized in preparation for design of control laws that include feedback of flywheel kinetic energy error as it means of compensating for damping exerted by rotor bearings. Two flywheel 'steering laws' are developed such that torque commanded by all attitude control law is achieved while energy is stored or discharged at the required rate. Using the International Space Station as an example, numerical simulations are performed to demonstrate control about a torque equilibrium attitude and illustrate the benefits of kinetic energy error feedback.

Quasi-Linear Parameter Varying Representation of General Aircraft Dynamics Over Non-Trim Region

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob

2007-01-01

For applying linear parameter varying (LPV) control synthesis and analysis to a nonlinear system, it is required that a nonlinear system be represented in the form of an LPV model. In this paper, a new representation method is developed to construct an LPV model from a nonlinear mathematical model without the restriction that an operating point must be in the neighborhood of equilibrium points. An LPV model constructed by the new method preserves local stabilities of the original nonlinear system at "frozen" scheduling parameters and also represents the original nonlinear dynamics of a system over a non-trim region. An LPV model of the motion of FASER (Free-flying Aircraft for Subscale Experimental Research) is constructed by the new method.

Linear control of oscillator and amplifier flows*

NASA Astrophysics Data System (ADS)

Schmid, Peter J.; Sipp, Denis

2016-08-01

Linear control applied to fluid systems near an equilibrium point has important applications for many flows of industrial or fundamental interest. In this article we give an exposition of tools and approaches for the design of control strategies for globally stable or unstable flows. For unstable oscillator flows a feedback configuration and a model-based approach is proposed, while for stable noise-amplifier flows a feedforward setup and an approach based on system identification is advocated. Model reduction and robustness issues are addressed for the oscillator case; statistical learning techniques are emphasized for the amplifier case. Effective suppression of global and convective instabilities could be demonstrated for either case, even though the system-identification approach results in a superior robustness to off-design conditions.

Resonant behaviour of MHD waves on magnetic flux tubes. III - Effect of equilibrium flow

NASA Technical Reports Server (NTRS)

Goossens, Marcel; Hollweg, Joseph V.; Sakurai, Takashi

1992-01-01

The Hollweg et al. (1990) analysis of MHD surface waves in a stationary equilibrium is extended. The conservation laws and jump conditions at Alfven and slow resonance points obtained by Sakurai et al. (1990) are generalized to include an equilibrium flow, and the assumption that the Eulerian perturbation of total pressure is constant is recovered as the special case of the conservation law for an equilibrium with straight magnetic field lines and flow along the magnetic field lines. It is shown that the conclusions formulated by Hollweg et al. are still valid for the straight cylindrical case. The effect of curvature is examined.

Effect of stirring on the safety of flammable liquid mixtures.

PubMed

Liaw, Horng-Jang; Gerbaud, Vincent; Chen, Chan-Cheng; Shu, Chi-Min

2010-05-15

Flash point is the most important variable employed to characterize fire and explosion hazard of liquids. The models developed for predicting the flash point of partially miscible mixtures in the literature to date are all based on the assumption of liquid-liquid equilibrium. In real-world environments, however, the liquid-liquid equilibrium assumption does not always hold, such as the collection or accumulation of waste solvents without stirring, where complete stirring for a period of time is usually used to ensure the liquid phases being in equilibrium. This study investigated the effect of stirring on the flash-point behavior of binary partially miscible mixtures. Two series of partially miscible binary mixtures were employed to elucidate the effect of stirring. The first series was aqueous-organic mixtures, including water+1-butanol, water+2-butanol, water+isobutanol, water+1-pentanol, and water+octane; the second series was the mixtures of two flammable solvents, which included methanol+decane, methanol+2,2,4-trimethylpentane, and methanol+octane. Results reveal that for binary aqueous-organic solutions the flash-point values of unstirred mixtures were located between those of the completely stirred mixtures and those of the flammable component. Therefore, risk assessment could be done based on the flammable component flash-point value. However, for the assurance of safety, it is suggested to completely stir those mixtures before handling to reduce the risk. Copyright (c) 2010 Elsevier B.V. All rights reserved.

Late-time behaviour of the tilted Bianchi type VIh models

NASA Astrophysics Data System (ADS)

Hervik, S.; van den Hoogen, R. J.; Lim, W. C.; Coley, A. A.

2007-08-01

We study tilted perfect fluid cosmological models with a constant equation of state parameter in spatially homogeneous models of Bianchi type VIh using dynamical systems methods and numerical experimentation, with an emphasis on their future asymptotic evolution. We determine all of the equilibrium points of the type VIh state space (which correspond to exact self-similar solutions of the Einstein equations, some of which are new), and their stability is investigated. We find that there are vacuum plane-wave solutions that act as future attractors. In the parameter space, a 'loophole' is shown to exist in which there are no stable equilibrium points. We then show that a Hopf-bifurcation can occur resulting in a stable closed orbit (which we refer to as the Mussel attractor) corresponding to points both inside the loophole and points just outside the loophole; in the former case the closed curves act as late-time attractors while in the latter case these attracting curves will co-exist with attracting equilibrium points. In the special Bianchi type III case, centre manifold theory is required to determine the future attractors. Comprehensive numerical experiments are carried out to complement and confirm the analytical results presented. We note that the Bianchi type VIh case is of particular interest in that it contains many different subcases which exhibit many of the different possible future asymptotic behaviours of Bianchi cosmological models.

Determination of flash point in air and pure oxygen using an equilibrium closed bomb apparatus.

PubMed

Kong, Dehong; am Ende, David J; Brenek, Steven J; Weston, Neil P

2003-08-29

The standard closed testers for flash point measurements may not be feasible for measuring flash point in special atmospheres like oxygen because the test atmosphere cannot be maintained due to leakage and the laboratory safety can be compromised. To address these limitations we developed a new "equilibrium closed bomb" (ECB). The ECB generally gives lower flash point values than standard closed cup testers as shown by the results of six flammable liquids. The present results are generally in good agreement with the values calculated from the reported lower flammability limits and the vapor pressures. Our measurements show that increased oxygen concentration had little effect on the flash points of the tested flammable liquids. While generally regarded as non-flammable because of the lack of observed flash point in standard closed cup flash point testers, dichloromethane is known to form flammable mixtures. The flash point of dichloromethane in oxygen measured in the ECB is -7.1 degrees C. The flash point of dichloromethane in air is dependent on the type and energy of the ignition source. Further research is being carried out to establish the relationship between the flash point of dichloromethane and the energy of the ignition source.

Modified NASA-Lewis chemical equilibrium code for MHD applications

NASA Technical Reports Server (NTRS)

Sacks, R. A.; Geyer, H. K.; Grammel, S. J.; Doss, E. D.

1979-01-01

A substantially modified version of the NASA-Lewis Chemical Equilibrium Code was recently developed. The modifications were designed to extend the power and convenience of the Code as a tool for performing combustor analysis for MHD systems studies. The effect of the programming details is described from a user point of view.

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

PubMed

Wang, Zhen; Campbell, Sue Ann

2017-11-01

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

A Floating Cylinder on an Unbounded Bath

NASA Astrophysics Data System (ADS)

Chen, Hanzhe; Siegel, David

2018-03-01

In this paper, we reconsider a circular cylinder horizontally floating on an unbounded reservoir in a gravitational field directed downwards, which was studied by Bhatnagar and Finn (Phys Fluids 18(4):047103, 2006). We follow their approach but with some modifications. We establish the relation between the total energy E_T relative to the undisturbed state and the total force F_T , that is, F_T = -dE_T/dh , where h is the height of the center of the cylinder relative to the undisturbed fluid level. There is a monotone relation between h and the wetting angle φ _0 . We study the number of equilibria, the floating configurations and their stability for all parameter values. We find that the system admits at most two equilibrium points for arbitrary contact angle γ , the one with smaller φ _0 is stable and the one with larger φ _0 is unstable. Since the one-sided solution can be translated horizontally, the fluid interfaces may intersect. We show that the stable equilibrium point never lies in the intersection region, while the unstable equilibrium point may lie in the intersection region.

Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy.

PubMed

Schättler, Heinz; Ledzewicz, Urszula; Amini, Behrooz

2016-04-01

A minimally parameterized mathematical model for low-dose metronomic chemotherapy is formulated that takes into account angiogenic signaling between the tumor and its vasculature and tumor inhibiting effects of tumor-immune system interactions. The dynamical equations combine a model for tumor development under angiogenic signaling formulated by Hahnfeldt et al. with a model for tumor-immune system interactions by Stepanova. The dynamical properties of the model are analyzed. Depending on the parameter values, the system encompasses a variety of medically realistic scenarios that range from cases when (i) low-dose metronomic chemotherapy is able to eradicate the tumor (all trajectories converge to a tumor-free equilibrium point) to situations when (ii) tumor dormancy is induced (a unique, globally asymptotically stable benign equilibrium point exists) to (iii) multi-stable situations that have both persistent benign and malignant behaviors separated by the stable manifold of an unstable equilibrium point and finally to (iv) situations when tumor growth cannot be overcome by low-dose metronomic chemotherapy. The model forms a basis for a more general study of chemotherapy when the main components of a tumor's microenvironment are taken into account.

Legendre submanifolds in contact manifolds as attractors and geometric nonequilibrium thermodynamics

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

Goto, Shin-itiro, E-mail: sgoto@ims.ac.jp

It has been proposed that equilibrium thermodynamics is described on Legendre submanifolds in contact geometry. It is shown in this paper that Legendre submanifolds embedded in a contact manifold can be expressed as attractors in phase space for a certain class of contact Hamiltonian vector fields. By giving a physical interpretation that points outside the Legendre submanifold can represent nonequilibrium states of thermodynamic variables, in addition to that points of a given Legendre submanifold can represent equilibrium states of the variables, this class of contact Hamiltonian vector fields is physically interpreted as a class of relaxation processes, in which thermodynamicmore » variables achieve an equilibrium state from a nonequilibrium state through a time evolution, a typical nonequilibrium phenomenon. Geometric properties of such vector fields on contact manifolds are characterized after introducing a metric tensor field on a contact manifold. It is also shown that a contact manifold and a strictly convex function induce a lower dimensional dually flat space used in information geometry where a geometrization of equilibrium statistical mechanics is constructed. Legendre duality on contact manifolds is explicitly stated throughout.« less

Analysis of gene network robustness based on saturated fixed point attractors

PubMed Central

2014-01-01

The analysis of gene network robustness to noise and mutation is important for fundamental and practical reasons. Robustness refers to the stability of the equilibrium expression state of a gene network to variations of the initial expression state and network topology. Numerical simulation of these variations is commonly used for the assessment of robustness. Since there exists a great number of possible gene network topologies and initial states, even millions of simulations may be still too small to give reliable results. When the initial and equilibrium expression states are restricted to being saturated (i.e., their elements can only take values 1 or −1 corresponding to maximum activation and maximum repression of genes), an analytical gene network robustness assessment is possible. We present this analytical treatment based on determination of the saturated fixed point attractors for sigmoidal function models. The analysis can determine (a) for a given network, which and how many saturated equilibrium states exist and which and how many saturated initial states converge to each of these saturated equilibrium states and (b) for a given saturated equilibrium state or a given pair of saturated equilibrium and initial states, which and how many gene networks, referred to as viable, share this saturated equilibrium state or the pair of saturated equilibrium and initial states. We also show that the viable networks sharing a given saturated equilibrium state must follow certain patterns. These capabilities of the analytical treatment make it possible to properly define and accurately determine robustness to noise and mutation for gene networks. Previous network research conclusions drawn from performing millions of simulations follow directly from the results of our analytical treatment. Furthermore, the analytical results provide criteria for the identification of model validity and suggest modified models of gene network dynamics. The yeast cell-cycle network is used as an illustration of the practical application of this analytical treatment. PMID:24650364

Automated realization of the gallium melting and triple points

NASA Astrophysics Data System (ADS)

Yan, X.; Duan, Y.; Zhang, J. T.; Wang, W.

2013-09-01

In order to improve the automation and convenience of the process involved in realizing the gallium fixed points, an automated apparatus, based on thermoelectric and heat pipe technologies, was designed and developed. This paper describes the apparatus design and procedures for freezing gallium mantles and realizing gallium melting and triple points. Also, investigations on the melting behavior of a gallium melting point cell and of gallium triple point cells were carried out while controlling the temperature outside the gallium point cells at 30 °C, 30.5 °C, 31 °C, and 31.5 °C. The obtained melting plateau curves show dentate temperature oscillations on the melting plateaus for the gallium point cells when thermal couplings occurred between the outer and inner liquid-solid interfaces. The maximum amplitude of the temperature fluctuations was about 1.5 mK. Therefore, the temperature oscillations can be used to indicate the ending of the equilibrium phase transitions. The duration and amplitude of such temperature oscillations depend on the temperature difference between the setting temperature and the gallium point temperature; the smaller the temperature difference, the longer the duration of both the melting plateaus and the temperature fluctuations.

An enhanced velocity-based algorithm for safe implementations of gain-scheduled controllers

NASA Astrophysics Data System (ADS)

Lhachemi, H.; Saussié, D.; Zhu, G.

2017-09-01

This paper presents an enhanced velocity-based algorithm to implement gain-scheduled controllers for nonlinear and parameter-dependent systems. A new scheme including pre- and post-filtering is proposed with the assumption that the time-derivative of the controller inputs is not available for feedback control. It is shown that the proposed control structure can preserve the input-output properties of the linearised closed-loop system in the neighbourhood of each equilibrium point, avoiding the emergence of the so-called hidden coupling terms. Moreover, it is guaranteed that this implementation will not introduce unobservable or uncontrollable unstable modes, and hence the internal stability will not be affected. A case study dealing with the design of a pitch-axis missile autopilot is carried out and the numerical simulation results confirm the validity of the proposed approach.

Time-varying sliding-coefficient-based decoupled terminal sliding-mode control for a class of fourth-order systems.

PubMed

Bayramoglu, Husnu; Komurcugil, Hasan

2014-07-01

A time-varying sliding-coefficient-based decoupled terminal sliding mode control strategy is presented for a class of fourth-order systems. First, the fourth-order system is decoupled into two second-order subsystems. The sliding surface of each subsystem was designed by utilizing time-varying coefficients. Then, the control target of one subsystem to another subsystem was embedded. Thereafter, a terminal sliding mode control method was utilized to make both subsystems converge to their equilibrium points in finite time. The simulation results on the inverted pendulum system demonstrate that the proposed method exhibits a considerable improvement in terms of a faster dynamic response and lower IAE and ITAE values as compared with the existing decoupled control methods. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Isolation strategy of a two-strain avian influenza model using optimal control

NASA Astrophysics Data System (ADS)

Mardlijah, Ariani, Tika Desi; Asfihani, Tahiyatul

2017-08-01

Avian influenza has killed many victims of both birds and humans. Most cases of avian influenza infection in humans have resulted transmission from poultry to humans. To prevent or minimize the patients of avian influenza can be done by pharmaceutical and non-pharmaceutical measures such as the use of masks, isolation, etc. We will be analyzed two strains of avian influenza models that focus on treatment of symptoms with insulation, then investigate the stability of the equilibrium point by using Routh-Hurwitz criteria. We also used optimal control to reduce the number of humans infected by making the isolation level as the control then proceeds optimal control will be simulated. The completion of optimal control used in this study is the Pontryagin Minimum Principle and for simulation we are using Runge Kutta method. The results obtained showed that the application of two control is more optimal compared to apply one control only.

Multivariable control altitude demonstration on the F100 turbofan engine

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Dehoff, R. L.; Hackney, R. D.

1979-01-01

The F100 Multivariable control synthesis (MVCS) program, was aimed at demonstrating the benefits of LGR synthesis theory in the design of a multivariable engine control system for operation throughout the flight envelope. The advantages of such procedures include: (1) enhanced performance from cross-coupled controls, (2) maximum use of engine variable geometry, and (3) a systematic design procedure that can be applied efficiently to new engine systems. The control system designed, under the MVCS program, for the Pratt & Whitney F100 turbofan engine is described. Basic components of the control include: (1) a reference value generator for deriving a desired equilibrium state and an approximate control vector, (2) a transition model to produce compatible reference point trajectories during gross transients, (3) gain schedules for producing feedback terms appropriate to the flight condition, and (4) integral switching logic to produce acceptable steady-state performance without engine operating limit exceedance.

Information-theoretic equilibrium and observable thermalization

NASA Astrophysics Data System (ADS)

Anzà, F.; Vedral, V.

2017-03-01

A crucial point in statistical mechanics is the definition of the notion of thermal equilibrium, which can be given as the state that maximises the von Neumann entropy, under the validity of some constraints. Arguing that such a notion can never be experimentally probed, in this paper we propose a new notion of thermal equilibrium, focused on observables rather than on the full state of the quantum system. We characterise such notion of thermal equilibrium for an arbitrary observable via the maximisation of its Shannon entropy and we bring to light the thermal properties that it heralds. The relation with Gibbs ensembles is studied and understood. We apply such a notion of equilibrium to a closed quantum system and show that there is always a class of observables which exhibits thermal equilibrium properties and we give a recipe to explicitly construct them. Eventually, an intimate connection with the Eigenstate Thermalisation Hypothesis is brought to light.

Information-theoretic equilibrium and observable thermalization

PubMed Central

Anzà, F.; Vedral, V.

2017-01-01

A crucial point in statistical mechanics is the definition of the notion of thermal equilibrium, which can be given as the state that maximises the von Neumann entropy, under the validity of some constraints. Arguing that such a notion can never be experimentally probed, in this paper we propose a new notion of thermal equilibrium, focused on observables rather than on the full state of the quantum system. We characterise such notion of thermal equilibrium for an arbitrary observable via the maximisation of its Shannon entropy and we bring to light the thermal properties that it heralds. The relation with Gibbs ensembles is studied and understood. We apply such a notion of equilibrium to a closed quantum system and show that there is always a class of observables which exhibits thermal equilibrium properties and we give a recipe to explicitly construct them. Eventually, an intimate connection with the Eigenstate Thermalisation Hypothesis is brought to light. PMID:28266646

Information-theoretic equilibrium and observable thermalization.

PubMed

Anzà, F; Vedral, V

2017-03-07

A crucial point in statistical mechanics is the definition of the notion of thermal equilibrium, which can be given as the state that maximises the von Neumann entropy, under the validity of some constraints. Arguing that such a notion can never be experimentally probed, in this paper we propose a new notion of thermal equilibrium, focused on observables rather than on the full state of the quantum system. We characterise such notion of thermal equilibrium for an arbitrary observable via the maximisation of its Shannon entropy and we bring to light the thermal properties that it heralds. The relation with Gibbs ensembles is studied and understood. We apply such a notion of equilibrium to a closed quantum system and show that there is always a class of observables which exhibits thermal equilibrium properties and we give a recipe to explicitly construct them. Eventually, an intimate connection with the Eigenstate Thermalisation Hypothesis is brought to light.

Artificial gravity as a countermeasure in long-duration space flight

NASA Technical Reports Server (NTRS)

Lackner, J. R.; DiZio, P.

2000-01-01

Long-duration exposure to weightlessness results in bone demineralization, muscle atrophy, cardiovascular deconditioning, altered sensory-motor control, and central nervous system reorganizations. Exercise countermeasures and body loading methods so far employed have failed to prevent these changes. A human mission to Mars might last 2 or 3 years and without effective countermeasures could result in dangerous levels of bone and muscle loss. Artificial gravity generated by rotation of an entire space vehicle or of an inner chamber could be used to prevent structural changes. Some of the physical characteristics of rotating environments are outlined along with their implications for human performance. Artificial gravity is the centripetal force generated in a rotating vehicle and is proportional to the product of the square of angular velocity and the radius of rotation. Thus, for a particular g-level, there is a tradeoff between velocity of rotation and radius. Increased radius is vastly more expensive to achieve than velocity, so it is important to know the highest rotation rates to which humans can adapt. Early studies suggested that 3 rpm might be the upper limit because movement control and orientation were disrupted at higher velocities and motion sickness and chronic fatigue were persistent problems. Recent studies, however, are showing that, if the terminal velocity is achieved over a series of gradual steps and many body movements are made at each dwell velocity, then full adaptation of head, arm, and leg movements is possible. Rotation rates as high as 7.5-10 rpm are likely feasible. An important feature of the new studies is that they provide compelling evidence that equilibrium point theories of movement control are inadequate. The central principles of equilibrium point theories lead to the equifinality prediction, which is violated by movements made in rotating reference frames. Copyright 2000 Wiley-Liss, Inc.

Achieving Radiation Tolerance through Non-Equilibrium Grain Boundary Structures.

PubMed

Vetterick, Gregory A; Gruber, Jacob; Suri, Pranav K; Baldwin, Jon K; Kirk, Marquis A; Baldo, Pete; Wang, Yong Q; Misra, Amit; Tucker, Garritt J; Taheri, Mitra L

2017-09-25

Many methods used to produce nanocrystalline (NC) materials leave behind non-equilibrium grain boundaries (GBs) containing excess free volume and higher energy than their equilibrium counterparts with identical 5 degrees of freedom. Since non-equilibrium GBs have increased amounts of both strain and free volume, these boundaries may act as more efficient sinks for the excess interstitials and vacancies produced in a material under irradiation as compared to equilibrium GBs. The relative sink strengths of equilibrium and non-equilibrium GBs were explored by comparing the behavior of annealed (equilibrium) and as-deposited (non-equilibrium) NC iron films on irradiation. These results were coupled with atomistic simulations to better reveal the underlying processes occurring on timescales too short to capture using in situ TEM. After irradiation, NC iron with non-equilibrium GBs contains both a smaller number density of defect clusters and a smaller average defect cluster size. Simulations showed that excess free volume contribute to a decreased survival rate of point defects in cascades occurring adjacent to the GB and that these boundaries undergo less dramatic changes in structure upon irradiation. These results suggest that non-equilibrium GBs act as more efficient sinks for defects and could be utilized to create more radiation tolerant materials in future.

Solute transport with multiple equilibrium-controlled or kinetically controlled chemical reactions

USGS Publications Warehouse

Friedly, John C.; Rubin, Jacob

1992-01-01

A new approach is applied to the problem of modeling solute transport accompanied by many chemical reactions. The approach, based on concepts of the concentration space and its stoichiometric subspaces, uses elements of the subspaces as primary dependent variables. It is shown that the resulting model equations are compact in form, isolate the chemical reaction expressions from flow expressions, and can be used for either equilibrium or kinetically controlled reactions. The implications of the results on numerical algorithms for solving the equations are discussed. The application of the theory is illustrated throughout with examples involving a simple but broadly representative set of reactions previously considered in the literature. Numerical results are presented for four interconnected reactions: a homogeneous complexation reaction, two sorption reactions, and a dissolution/precipitation reaction. Three cases are considered: (1) four kinetically controlled reactions, (2) four equilibrium-controlled reactions, and (3) a system with two kinetically controlled reactions and two equilibrium-controlled reactions.

Non-Equilibrium Plasma Applications for Water Purification Supporting Human Spaceflight and Terrestrial Point-of-Use

NASA Technical Reports Server (NTRS)

Blankson, Isaiah M.; Foster, John E.; Adamovsky, Grigory

2016-01-01

2016 NASA Glenn Technology Day Panel Presentation on May 24, 2016. The panel description is: Environmental Impact: NASA Glenn Water Capabilities Both global water scarcity and water treatment concerns are two of the most predominant environmental issues of our time. Glenn researchers share insights on a snow sensing technique, hyper spectral imaging of Lake Erie algal blooms, and a discussion on non-equilibrium plasma applications for water purification supporting human spaceflight and terrestrial point-of-use. The panel moderator will be Bryan Stubbs, Executive Director of the Cleveland Water Alliance.

Linear and quadratic static response functions and structure functions in Yukawa liquids.

PubMed

Magyar, Péter; Donkó, Zoltán; Kalman, Gabor J; Golden, Kenneth I

2014-08-01

We compute linear and quadratic static density response functions of three-dimensional Yukawa liquids by applying an external perturbation potential in molecular dynamics simulations. The response functions are also obtained from the equilibrium fluctuations (static structure factors) in the system via the fluctuation-dissipation theorems. The good agreement of the quadratic response functions, obtained in the two different ways, confirms the quadratic fluctuation-dissipation theorem. We also find that the three-point structure function may be factorizable into two-point structure functions, leading to a cluster representation of the equilibrium triplet correlation function.

Dynamics and circuit of a chaotic system with a curve of equilibrium points

NASA Astrophysics Data System (ADS)

Pham, Viet-Thanh; Volos, Christos; Kapitaniak, Tomasz; Jafari, Sajad; Wang, Xiong

2018-03-01

Although chaotic systems have been intensively studied since the 1960s, new systems with mysterious features are still of interest. A novel chaotic system including hyperbolic functions is proposed in this work. Especially, the system has an infinite number of equilibrium points. Dynamics of the system are investigated by using non-linear tools such as phase portrait, bifurcation diagram, and Lyapunov exponent. It is interesting that the system can display coexisting chaotic attractors. An electronic circuit for realising the chaotic system has been implemented. Experimental results show a good agreement with theoretical ones.

Linear stability of collinear equilibrium points around an asteroid as a two-connected-mass: Application to fast rotating Asteroid 2000EB 14

NASA Astrophysics Data System (ADS)

Hirabayashi, Masatoshi; Morimoto, Mutsuko Y.; Yano, Hajime; Kawaguchi, Jun'ichiro; Bellerose, Julie

2010-04-01

This note discusses the stability of collinear equilibrium points around a rotating system composed of two masses rigidly connected by a massless rod in the case, where the centripetal force outweighs the gravitational force. It is found that a stable region appears at L1 when the ratio of gravitational to centripetal acceleration is less than 0.125, and that there is always no stable area at L2 and L3; the result is applied to the fast rotating Asteroid 2000EB 14.

Students' Understanding of Equilibrium and Stability: The Case of Dynamic Systems

ERIC Educational Resources Information Center

Canu, Michaël; de Hosson, Cécile; Duque, Mauricio

2016-01-01

Engineering students in control courses have been observed to lack an understanding of equilibrium and stability, both of which are crucial concepts in this discipline. The introduction of these concepts is generally based on the study of classical examples from Newtonian mechanics supplemented with a control system. Equilibrium and stability are…

Decentralized learning in Markov games.

PubMed

Vrancx, Peter; Verbeeck, Katja; Nowé, Ann

2008-08-01

Learning automata (LA) were recently shown to be valuable tools for designing multiagent reinforcement learning algorithms. One of the principal contributions of the LA theory is that a set of decentralized independent LA is able to control a finite Markov chain with unknown transition probabilities and rewards. In this paper, we propose to extend this algorithm to Markov games--a straightforward extension of single-agent Markov decision problems to distributed multiagent decision problems. We show that under the same ergodic assumptions of the original theorem, the extended algorithm will converge to a pure equilibrium point between agent policies.

13-Moment System with Global Hyperbolicity for Quantum Gas

NASA Astrophysics Data System (ADS)

Di, Yana; Fan, Yuwei; Li, Ruo

2017-06-01

We point out that the quantum Grad's 13-moment system (Yano in Physica A 416:231-241, 2014) is lack of global hyperbolicity, and even worse, the thermodynamic equilibrium is not an interior point of the hyperbolicity region of the system. To remedy this problem, by fully considering Grad's expansion, we split the expansion into the equilibrium part and the non-equilibrium part, and propose a regularization for the system with the help of the new hyperbolic regularization theory developed in Cai et al. (SIAM J Appl Math 75(5):2001-2023, 2015) and Fan et al. (J Stat Phys 162(2):457-486, 2016). This provides us a new model which is hyperbolic for all admissible thermodynamic states, and meanwhile preserves the approximate accuracy of the original system. It should be noted that this procedure is not a trivial application of the hyperbolic regularization theory.

Equilibrium radiative heating tables for aerobraking in the Martian atmosphere

NASA Astrophysics Data System (ADS)

Hartung, Lin C.; Sutton, Kenneth; Brauns, Frank

1990-05-01

Studies currently underway for Mars missions often envision the use of aerobraking for orbital capture at Mars. These missions generally involve blunt-nosed vehicles to dissipate the excess energy of the interplanetary transfer. Radiative heating may be of importance in these blunt-body flows because of the highly energetic shock layer around the blunt nose. In addition, the Martian atmosphere contains CO2, whose dissociation products are known to include strong radiators. An inviscid, equilibrium, stagnation point, radiation-coupled flow-field code has been developed for investigating blunt-body atmospheric entry. The method has been compared with ground-based and flight data for air, and reasonable agreement has been found. In the present work, the method was applied to a matrix of conditions in the Martian atmosphere. These conditions encompass most trajectories of interest for Mars exploration spacecraft. The predicted equilibrium radiative heating to the stagnation point of the vehicle is presented.

Equilibrium radiative heating tables for aerobraking in the Martian atmosphere

NASA Technical Reports Server (NTRS)

Hartung, Lin C.; Sutton, Kenneth; Brauns, Frank

1990-01-01

Studies currently underway for Mars missions often envision the use of aerobraking for orbital capture at Mars. These missions generally involve blunt-nosed vehicles to dissipate the excess energy of the interplanetary transfer. Radiative heating may be of importance in these blunt-body flows because of the highly energetic shock layer around the blunt nose. In addition, the Martian atmosphere contains CO2, whose dissociation products are known to include strong radiators. An inviscid, equilibrium, stagnation point, radiation-coupled flow-field code has been developed for investigating blunt-body atmospheric entry. The method has been compared with ground-based and flight data for air, and reasonable agreement has been found. In the present work, the method was applied to a matrix of conditions in the Martian atmosphere. These conditions encompass most trajectories of interest for Mars exploration spacecraft. The predicted equilibrium radiative heating to the stagnation point of the vehicle is presented.

Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory

PubMed Central

Zhuang, Qian; Di, Zengru; Wu, Jinshan

2014-01-01

Using the Logit quantal response form as the response function in each step, the original definition of static quantal response equilibrium (QRE) is extended into an iterative evolution process. QREs remain as the fixed points of the dynamic process. However, depending on whether such fixed points are the long-term solutions of the dynamic process, they can be classified into stable (SQREs) and unstable (USQREs) equilibriums. This extension resembles the extension from static Nash equilibriums (NEs) to evolutionary stable solutions in the framework of evolutionary game theory. The relation between SQREs and other solution concepts of games, including NEs and QREs, is discussed. Using experimental data from other published papers, we perform a preliminary comparison between SQREs, NEs, QREs and the observed behavioral outcomes of those experiments. For certain games, we determine that SQREs have better predictive power than QREs and NEs. PMID:25157502

Access point selection game with mobile users using correlated equilibrium.

PubMed

Sohn, Insoo

2015-01-01

One of the most important issues in wireless local area network (WLAN) systems with multiple access points (APs) is the AP selection problem. Game theory is a mathematical tool used to analyze the interactions in multiplayer systems and has been applied to various problems in wireless networks. Correlated equilibrium (CE) is one of the powerful game theory solution concepts, which is more general than the Nash equilibrium for analyzing the interactions in multiplayer mixed strategy games. A game-theoretic formulation of the AP selection problem with mobile users is presented using a novel scheme based on a regret-based learning procedure. Through convergence analysis, we show that the joint actions based on the proposed algorithm achieve CE. Simulation results illustrate that the proposed algorithm is effective in a realistic WLAN environment with user mobility and achieves maximum system throughput based on the game-theoretic formulation.

Access Point Selection Game with Mobile Users Using Correlated Equilibrium

PubMed Central

Sohn, Insoo

2015-01-01

One of the most important issues in wireless local area network (WLAN) systems with multiple access points (APs) is the AP selection problem. Game theory is a mathematical tool used to analyze the interactions in multiplayer systems and has been applied to various problems in wireless networks. Correlated equilibrium (CE) is one of the powerful game theory solution concepts, which is more general than the Nash equilibrium for analyzing the interactions in multiplayer mixed strategy games. A game-theoretic formulation of the AP selection problem with mobile users is presented using a novel scheme based on a regret-based learning procedure. Through convergence analysis, we show that the joint actions based on the proposed algorithm achieve CE. Simulation results illustrate that the proposed algorithm is effective in a realistic WLAN environment with user mobility and achieves maximum system throughput based on the game-theoretic formulation. PMID:25785726

Multiscale System for Environmentally-Driven Infectious Disease with Threshold Control Strategy

NASA Astrophysics Data System (ADS)

Sun, Xiaodan; Xiao, Yanni

A multiscale system for environmentally-driven infectious disease is proposed, in which control measures at three different scales are implemented when the number of infected hosts exceeds a certain threshold. Our coupled model successfully describes the feedback mechanisms of between-host dynamics on within-host dynamics by employing one-scale variable guided enhancement of interventions on other scales. The modeling approach provides a novel idea of how to link the large-scale dynamics to small-scale dynamics. The dynamic behaviors of the multiscale system on two time-scales, i.e. fast system and slow system, are investigated. The slow system is further simplified to a two-dimensional Filippov system. For the Filippov system, we study the dynamics of its two subsystems (i.e. free-system and control-system), the sliding mode dynamics, the boundary equilibrium bifurcations, as well as the global behaviors. We prove that both subsystems may undergo backward bifurcations and the sliding domain exists. Meanwhile, it is possible that the pseudo-equilibrium exists and is globally stable, or the pseudo-equilibrium, the disease-free equilibrium and the real equilibrium are tri-stable, or the pseudo-equilibrium and the real equilibrium are bi-stable, or the pseudo-equilibrium and disease-free equilibrium are bi-stable, which depends on the threshold value and other parameter values. The global stability of the pseudo-equilibrium reveals that we may maintain the number of infected hosts at a previously given value. Moreover, the bi-stability and tri-stability indicate that whether the number of infected individuals tends to zero or a previously given value or other positive values depends on the parameter values and the initial states of the system. These results highlight the challenges in the control of environmentally-driven infectious disease.

Flash Points of Secondary Alcohol and n-Alkane Mixtures.

PubMed

Esina, Zoya N; Miroshnikov, Alexander M; Korchuganova, Margarita R

2015-11-19

The flash point is one of the most important characteristics used to assess the ignition hazard of mixtures of flammable liquids. To determine the flash points of mixtures of secondary alcohols with n-alkanes, it is necessary to calculate the activity coefficients. In this paper, we use a model that allows us to obtain enthalpy of fusion and enthalpy of vaporization data of the pure components to calculate the liquid-solid equilibrium (LSE) and vapor-liquid equilibrium (VLE). Enthalpy of fusion and enthalpy of vaporization data of secondary alcohols in the literature are limited; thus, the prediction of these characteristics was performed using the method of thermodynamic similarity. Additionally, the empirical models provided the critical temperatures and boiling temperatures of the secondary alcohols. The modeled melting enthalpy and enthalpy of vaporization as well as the calculated LSE and VLE flash points were determined for the secondary alcohol and n-alkane mixtures.

Results of using the NSTX-U Plasma Control System for scenario development

NASA Astrophysics Data System (ADS)

Boyer, M. D.; Battaglia, D. J.; Gates, D. A.; Gerhardt, S.; Menard, J.; Mueller, D.; Myers, C. E.; Ferron, J.; Sabbagh, S.; NSTX-U Team

2016-10-01

To best use the new capabilities of NSTX-U (e.g., higher toroidal field and additional, more distributed heating and current drive sources) and to achieve the operational goals of the program, major upgrades to the Plasma Control System have been made. These include improvements to vertical control, real-time equilibrium reconstruction, and plasma boundary shape control and the addition of flexible algorithms for beam modulation and gas injection to control the upgraded actuators in real-time, enabling their use in algorithms for stored energy and profile control. Control system commissioning activities have so far focused on vertical position and shape control. The upgraded controllers have been used to explore the vertical stability limits in inner wall limited and diverted discharges, and control of X-point and strike point locations has been demonstrated and is routinely used. A method for controlling the mid-plane inner gap, a challenge for STs, has also been added to improve reproducible control of diverted discharges. A supervisory shutdown handling algorithm has also been commissioned to ramp the plasma down and safely turn off actuators after an event such as loss of vertical control. Use of the upgrades has contributed to achieving 1MA, 0.65T scenarios with greater than 1s pulse length. Work supported by U.S. D.O.E. Contract No. DE-AC02-09CH11466.

Pilot study on quantitative assessment of muscle imbalance: differences of muscle synergies, equilibrium-point trajectories, and endpoint stiffness in normal and pathological upper-limb movements.

PubMed

Oku, Takanori; Uno, Kanna; Nishi, Tomoki; Kageyama, Masayuki; Phatiwuttipat, Pipatthana; Koba, Keitaro; Yamashita, Yuto; Murakami, Kenta; Uemura, Mitsunori; Hirai, Hiroaki; Miyazaki, Fumio; Naritomi, Hiroaki

2014-01-01

This paper proposes a novel method for assessment of muscle imbalance based on muscle synergy hypothesis and equilibrium point (EP) hypothesis of motor control. We explain in detail the method for extracting muscle synergies under the concept of agonist-antagonist (AA) muscle pairs and for estimating EP trajectories and endpoint stiffness of human upper limbs in a horizontal plane using an electromyogram. The results of applying this method to the reaching movement of one normal subject and one hemiplegic subject suggest that (1) muscle synergies (the balance among coactivation of AA muscle pairs), particularly the synergies that contributes to the angular directional kinematics of EP and the limb stiffness, are quite different between the normal subject and the hemiplegic subject; (2) the concomitant EP trajectory is also different between the normal and hemiplegic subjects, corresponding to the difference of muscle synergies; and (3) the endpoint (hand) stiffness ellipse of the hemiplegic subject becomes more elongated and orientation of the major axis rotates clockwise more than that of the normal subject. The level of motor impairment would be expected to be assessed from a comparison of these differences of muscle synergies, EP trajectories, and endpoint stiffness among normal and pathological subjects using the method.

Efficiency and temperature dependence of water removal by membrane dryers

NASA Technical Reports Server (NTRS)

Leckrone, K. J.; Hayes, J. M.

1997-01-01

The vapor pressure of water in equilibrium with sorption sites within a Nafion membrane is given by log P(WN) = -3580/T + 10.01, where P(WN) is expressed in Torr and T is the membrane temperature, in kelvin. The efficiency of dryers based on selective permeation of water through Nafion can thus be enhanced by cooling the membrane. Residual water in effluents exceeds equilibrium levels if insufficient time is allowed for water to diffuse to the membrane surface as gas passes through the dryer. For tubular configurations, this limitation can be avoided if L > or = Fc(10(3.8)/120 pi D), where L is the length of the tubular membrane, in centimeters, Fc is the gas flow rate, in mL/ min, and D is the diffusion coefficient for water in the carrier gas at the operating temperature of the dryer, in cm2/s. An efficient dryer that at room temperature dries gas to a dew point of -61 degrees C is described; the same dryer maintained at 0 degrees C yields a dew point of -80 degrees C and removes water as effectively as Mg(ClO4)2 or a dry ice/acetone slush. The use of Nafion membranes to construct devices capable of delivering gas streams with low but precisely controlled humidities is discussed.

Optimal Equilibria and Plasma Parameter Evolutions for the Ignitor Experiment*

NASA Astrophysics Data System (ADS)

Airoldi, A.; Cenacchi, G.; Coppi, B.

2011-10-01

In view of the operation of the Ignitor machine in both the H and the I-regime, optimal equilibrium configurations that can sustain plasma currents Ip up to 10 MA with a double X-point have been identified. In fact, the emergence of the I-regime in double X-point configurations has not been observed experimentally yet. The characteristics of the magnetic equilibrium configurations that can be produced play a crucial role in the performance of the machine. Therefore, particular care has been devoted to the study of plasma equilibria relevant to the main phases of the discharge evolution. A series of simulations to be utilized for the control of the relevant (sub-ignited) plasma parameters has been carried out using the JETTO transport code considering different values of the plasma current and, correspondingly, of the magnetic field. Special attention has been devoted to non-igniting experiments with Ip = 5 MA and BT = 8 T, where BT is the toroidal magnetic field, as they can be performed with much better duty cycles and longer duration than experiments aimed at reaching the most extreme plasma parameters and ignition in particular. The results of the relevant analyses with a discussion of the adopted transport coefficients is presented. * Sponsored in part by ENEA and the U.S. DOE.

Venus climate stability and volcanic resurfacing rates

NASA Technical Reports Server (NTRS)

Bullock, M. A.; Grinspoon, D. H.; Pollack, J. B.

1994-01-01

The climate of Venus is to a large degree controlled by the radiative properties of its massive atmosphere. In addition, outgassing due to volcanic activity, exospheric escape processes, and surface/atmosphere interactions may all be important in moderating the abundances of atmospheric CO2 and other volatiles. We have developed an evolutionary climate model for Venus using a systems approach that emphasizes feedbacks between elements in the climate system. Modules for atmospheric radiative transfer, surface/atmosphere interactions, tropospheric chemistry, and exospheric escape processes have so far been developed. Climate feedback loops result from interconnections between modules, in the form of the environmental parameters pressure, temperature, and atmospheric mixing ratios. The radiative transfer module has been implemented by using Rosseland mean opacities in a one dimensional grey radiative-convective model. The model has been solved for the static (time independent) case to determine climate equilibrium points. The dynamics of the model have also been explored by employing reaction/diffusion kinetics for possible surface atmosphere heterogeneous reactions over geologic timescales. It was found that under current conditions, the model predicts that the climate of Venus is at or near an unstable equilibrium point. The effects of constant rate volcanism and corresponding exsolution of volatiles on the stability of the climate model were also explored.

Application of optimal control strategies to HIV-malaria co-infection dynamics

NASA Astrophysics Data System (ADS)

Fatmawati; Windarto; Hanif, Lathifah

2018-03-01

This paper presents a mathematical model of HIV and malaria co-infection transmission dynamics. Optimal control strategies such as malaria preventive, anti-malaria and antiretroviral (ARV) treatments are considered into the model to reduce the co-infection. First, we studied the existence and stability of equilibria of the presented model without control variables. The model has four equilibria, namely the disease-free equilibrium, the HIV endemic equilibrium, the malaria endemic equilibrium, and the co-infection equilibrium. We also obtain two basic reproduction ratios corresponding to the diseases. It was found that the disease-free equilibrium is locally asymptotically stable whenever their respective basic reproduction numbers are less than one. We also conducted a sensitivity analysis to determine the dominant factor controlling the transmission. sic reproduction numbers are less than one. We also conducted a sensitivity analysis to determine the dominant factor controlling the transmission. Then, the optimal control theory for the model was derived analytically by using Pontryagin Maximum Principle. Numerical simulations of the optimal control strategies are also performed to illustrate the results. From the numerical results, we conclude that the best strategy is to combine the malaria prevention and ARV treatments in order to reduce malaria and HIV co-infection populations.

Nash equilibrium in differential games and the construction of the programmed iteration method

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

Averboukh, Yurii V

This work is devoted to the study of nonzero-sum differential games. The set of payoffs in a situation of Nash equilibrium is examined. It is shown that the set of payoffs in a situation of Nash equilibrium coincides with the set of values of consistent functions which are fixed points of the program absorption operator. A condition for functions to be consistent is given in terms of the weak invariance of the graph of the functions under a certain differential inclusion. Bibliography: 18 titles.

Quantum gambling based on Nash-equilibrium

NASA Astrophysics Data System (ADS)

Zhang, Pei; Zhou, Xiao-Qi; Wang, Yun-Long; Liu, Bi-Heng; Shadbolt, Pete; Zhang, Yong-Sheng; Gao, Hong; Li, Fu-Li; O'Brien, Jeremy L.

2017-06-01

The problem of establishing a fair bet between spatially separated gambler and casino can only be solved in the classical regime by relying on a trusted third party. By combining Nash-equilibrium theory with quantum game theory, we show that a secure, remote, two-party game can be played using a quantum gambling machine which has no classical counterpart. Specifically, by modifying the Nash-equilibrium point we can construct games with arbitrary amount of bias, including a game that is demonstrably fair to both parties. We also report a proof-of-principle experimental demonstration using linear optics.

An implicit flux-split algorithm to calculate hypersonic flowfields in chemical equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1987-01-01

An implicit, finite-difference, shock-capturing algorithm that calculates inviscid, hypersonic flows in chemical equilibrium is presented. The flux vectors and flux Jacobians are differenced using a first-order, flux-split technique. The equilibrium composition of the gas is determined by minimizing the Gibbs free energy at every node point. The code is validated by comparing results over an axisymmetric hemisphere against previously published results. The algorithm is also applied to more practical configurations. The accuracy, stability, and versatility of the algorithm have been promising.

Excito-oscillatory dynamics as a mechanism of ventricular fibrillation.

PubMed

Gray, Richard A; Huelsing, Delilah J

2008-04-01

The instabilities associated with reentrant spiral waves are of paramount importance to the initiation and maintenance of tachyarrhythmias, especially ventricular fibrillation (VF). In addition to tissue heterogeneities, there are only a few basic purported mechanisms of spiral wave breakup, most notably restitution. We test the hypothesis that oscillatory membrane properties act to destabilize spiral waves. We recorded transmembrane potential (V(m)) from isolated rabbit myocytes using a constant current stimulation protocol. We developed a mathematical model that included both the stable excitable equilibrium point at resting V(m) (-80 mV) and the unstable oscillatory equilibrium point at elevated V(m) (-10 mV). Spiral wave dynamics were studied in 2-dimensional grids using variants of the model. All models showed restitution and reproduced the experimental values of transmembrane resistance at rest and during the action potential plateau. Stable spiral waves were observed when the model showed only 1 equilibrium point. However, spatio-temporal complexity was observed if the model showed both excitable and oscillatory equilibrium points (i.e., excito-oscillatory models). The initial wave breaks resulted from oscillatory waves expanding in all directions; after a few beats, the patterns were characterized by a combination of unstable spiral waves and target patterns consistent with the patterns observed on the heart surface during VF. In our model, this VF-like activity only occurred when the single cell period of V(m) oscillations was within a specific range. The VF-like patterns observed in our excito-oscillatory models could not be explained by the existing proposed instability mechanisms. Our results introduce the important suggestion that membrane dynamics responsible for V(m) oscillations at elevated V(m) levels can destabilize spiral waves and thus may be a novel therapeutic target for preventing VF.

Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field

NASA Astrophysics Data System (ADS)

Feng, Jinglang; Hou, Xiyun

2017-07-01

Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circular restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.

Quantum oligopoly

NASA Astrophysics Data System (ADS)

Lo, C. F.; Kiang, D.

2003-12-01

Based upon a modification of Li et al.'s "minimal" quantization rules (Phys. Lett. A306(2002) 73), we investigate the quantum version of the Cournot and Bertrand oligopoly. In the Cournot oligopoly, the profit of each of the N firms at the Nash equilibrium point rises monotonically with the measure of the quantum entanglement. Only at maximal entanglement, however, does the Nash equilibrium point coincide with the Pareto optimal point. In the Bertrand case, the Bertrand Paradox remains for finite entanglement (i.e., the perfectly competitive stage is reached for any N>=2), whereas with maximal entanglement each of the N firms will still have a non-zero shared profit. Hence, the Bertrand Paradox is completely resolved. Furthermore, a perfectly competitive market is reached asymptotically for N → ∞ in both the Cournot and Bertrand oligopoly.

TIME-DEPENDENT COROTATION RESONANCE IN BARRED GALAXIES

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

Wu, Yu-Ting; Taam, Ronald E.; Pfenniger, Daniel, E-mail: ytwu@asiaa.sinica.edu.tw, E-mail: daniel.pfenniger@unige.ch, E-mail: taam@asiaa.sinica.edu.tw

2016-10-20

The effective potential neighboring the corotation resonance region in barred galaxies is shown to be strongly time-dependent in any rotating frame, due to the competition of nearby perturbations of similar strengths with differing rotation speeds. Contrary to the generally adopted assumption that in the bar rotating frame the corotation region should possess four stationary equilibrium points (Lagrange points), with high quality N -body simulations, we localize the instantaneous equilibrium points (EPs) and find that they circulate or oscillate broadly in azimuth with respect to the pattern speeds of the inner or outer perturbations. This implies that at the particle levelmore » the Jacobi integral is not well conserved around the corotation radius. That is, angular momentum exchanges decouple from energy exchanges, enhancing the chaotic diffusion of stars through the corotation region.« less

Reactive species in non-equilibrium atmospheric-pressure plasmas: Generation, transport, and biological effects

NASA Astrophysics Data System (ADS)

Lu, X.; Naidis, G. V.; Laroussi, M.; Reuter, S.; Graves, D. B.; Ostrikov, K.

2016-05-01

Non-equilibrium atmospheric-pressure plasmas have recently become a topical area of research owing to their diverse applications in health care and medicine, environmental remediation and pollution control, materials processing, electrochemistry, nanotechnology and other fields. This review focuses on the reactive electrons and ionic, atomic, molecular, and radical species that are produced in these plasmas and then transported from the point of generation to the point of interaction with the material, medium, living cells or tissues being processed. The most important mechanisms of generation and transport of the key species in the plasmas of atmospheric-pressure plasma jets and other non-equilibrium atmospheric-pressure plasmas are introduced and examined from the viewpoint of their applications in plasma hygiene and medicine and other relevant fields. Sophisticated high-precision, time-resolved plasma diagnostics approaches and techniques are presented and their applications to monitor the reactive species and plasma dynamics in the plasma jets and other discharges, both in the gas phase and during the plasma interaction with liquid media, are critically reviewed. The large amount of experimental data is supported by the theoretical models of reactive species generation and transport in the plasmas, surrounding gaseous environments, and plasma interaction with liquid media. These models are presented and their limitations are discussed. Special attention is paid to biological effects of the plasma-generated reactive oxygen and nitrogen (and some other) species in basic biological processes such as cell metabolism, proliferation, survival, etc. as well as plasma applications in bacterial inactivation, wound healing, cancer treatment and some others. Challenges and opportunities for theoretical and experimental research are discussed and the authors' vision for the emerging convergence trends across several disciplines and application domains is presented to stimulate critical discussions and collaborations in the future.

Thermodynamic behavior of a phase transition in a model for sympatric speciation

NASA Astrophysics Data System (ADS)

Luz-Burgoa, K.; Moss de Oliveira, S.; Schwämmle, Veit; Sá Martins, J. S.

2006-08-01

We investigate the macroscopic effects of the ingredients that drive the origin of species through sympatric speciation. In our model, sympatric speciation is obtained as we tune up the strength of competition between individuals with different phenotypes. As a function of this control parameter, we can characterize, through the behavior of a macroscopic order parameter, a phase transition from a nonspeciation to a speciation state of the system. The behavior of the first derivative of the order parameter with respect to the control parameter is consistent with a phase transition and exhibits a sharp peak at the transition point. For different resources distribution, the transition point is shifted, an effect similar to pressure in a PVT system. The inverse of the parameter related to a sexual selection strength behaves like an external field in the system and, as thus, is also a control parameter. The macroscopic effects of the biological parameters used in our model are a reminiscent of the behavior of thermodynamic quantities in a phase transition of an equilibrium physical system.

Global stability and optimal control of epidemic spreading on multiplex networks with nonlinear mutual interaction

NASA Astrophysics Data System (ADS)

Jia, Nan; Ding, Li; Liu, Yu-Jing; Hu, Ping

2018-07-01

In this paper, we consider two interacting pathogens spreading on multiplex networks. Each pathogen spreads only on its single layer, and different layers have the same individuals but different network topology. A state-dependent infectious rate is proposed to describe the nonlinear mutual interaction during the propagation of two pathogens. Then a novel epidemic spreading model incorporating treatment control strategy is established. We investigate the global asymptotic stability of the equilibrium points by using Dulac's criterion, Poincaré-Bendixson theorem and Lyapunov method. Furthermore, we discuss an optimal strategy to minimize the total number of the infected individuals and the cost associated with treatment control for both spreading of two pathogens. Finally, numerical simulations are presented to show the validity and efficiency of our results.

Leading bureaucracies to the tipping point: An alternative model of multiple stable equilibrium levels of corruption

PubMed Central

Caulkins, Jonathan P.; Feichtinger, Gustav; Grass, Dieter; Hartl, Richard F.; Kort, Peter M.; Novak, Andreas J.; Seidl, Andrea

2013-01-01

We present a novel model of corruption dynamics in the form of a nonlinear optimal dynamic control problem. It has a tipping point, but one whose origins and character are distinct from that in the classic Schelling (1978) model. The decision maker choosing a level of corruption is the chief or some other kind of authority figure who presides over a bureaucracy whose state of corruption is influenced by the authority figure’s actions, and whose state in turn influences the pay-off for the authority figure. The policy interpretation is somewhat more optimistic than in other tipping models, and there are some surprising implications, notably that reforming the bureaucracy may be of limited value if the bureaucracy takes its cues from a corrupt leader. PMID:23565027

Leading bureaucracies to the tipping point: An alternative model of multiple stable equilibrium levels of corruption.

PubMed

Caulkins, Jonathan P; Feichtinger, Gustav; Grass, Dieter; Hartl, Richard F; Kort, Peter M; Novak, Andreas J; Seidl, Andrea

2013-03-16

We present a novel model of corruption dynamics in the form of a nonlinear optimal dynamic control problem. It has a tipping point, but one whose origins and character are distinct from that in the classic Schelling (1978) model. The decision maker choosing a level of corruption is the chief or some other kind of authority figure who presides over a bureaucracy whose state of corruption is influenced by the authority figure's actions, and whose state in turn influences the pay-off for the authority figure. The policy interpretation is somewhat more optimistic than in other tipping models, and there are some surprising implications, notably that reforming the bureaucracy may be of limited value if the bureaucracy takes its cues from a corrupt leader.

Ranking nano-enabled hybrid media for simultaneous removal of contaminants with different chemistries: Pseudo-equilibrium sorption tests versus column tests.

PubMed

Custodio, Tomas; Garcia, Jose; Markovski, Jasmina; McKay Gifford, James; Hristovski, Kiril D; Olson, Larry W

2017-12-15

The underlying hypothesis of this study was that pseudo-equilibrium and column testing conditions would provide the same sorbent ranking trends although the values of sorbents' performance descriptors (e.g. sorption capacity) may vary because of different kinetics and competition effects induced by the two testing approaches. To address this hypothesis, nano-enabled hybrid media were fabricated and its removal performances were assessed for two model contaminants under multi-point batch pseudo-equilibrium and continuous-flow conditions. Calculation of simultaneous removal capacity indices (SRC) demonstrated that the more resource demanding continuous-flow tests are able to generate the same performance rankings as the ones obtained by conducing the simpler pseudo-equilibrium tests. Furthermore, continuous overlap between the 98% confidence boundaries for each SRC index trend, not only validated the hypothesis that both testing conditions provide the same ranking trends, but also pointed that SRC indices are statistically the same for each media, regardless of employed method. In scenarios where rapid screening of new media is required to obtain the best performing synthesis formulation, use of pseudo-equilibrium tests proved to be reliable. Considering that kinetics induced effects on sorption capacity must not be neglected, more resource demanding column test could be conducted only with the top performing media that exhibit the highest sorption capacity. Copyright © 2017 Elsevier B.V. All rights reserved.

Variable Structure Control of a Hand-Launched Glider

NASA Technical Reports Server (NTRS)

Anderson, Mark R.; Waszak, Martin R.

2005-01-01

Variable structure control system design methods are applied to the problem of aircraft spin recovery. A variable structure control law typically has two phases of operation. The reaching mode phase uses a nonlinear relay control strategy to drive the system trajectory to a pre-defined switching surface within the motion state space. The sliding mode phase involves motion along the surface as the system moves toward an equilibrium or critical point. Analysis results presented in this paper reveal that the conventional method for spin recovery can be interpreted as a variable structure controller with a switching surface defined at zero yaw rate. Application of Lyapunov stability methods show that deflecting the ailerons in the direction of the spin helps to insure that this switching surface is stable. Flight test results, obtained using an instrumented hand-launched glider, are used to verify stability of the reaching mode dynamics.

Design of an adaptive super-twisting decoupled terminal sliding mode control scheme for a class of fourth-order systems.

PubMed

Ashtiani Haghighi, Donya; Mobayen, Saleh

2018-04-01

This paper proposes an adaptive super-twisting decoupled terminal sliding mode control technique for a class of fourth-order systems. The adaptive-tuning law eliminates the requirement of the knowledge about the upper bounds of external perturbations. Using the proposed control procedure, the state variables of cart-pole system are converged to decoupled terminal sliding surfaces and their equilibrium points in the finite time. Moreover, via the super-twisting algorithm, the chattering phenomenon is avoided without affecting the control performance. The numerical results demonstrate the high stabilization accuracy and lower performance indices values of the suggested method over the other ones. The simulation results on the cart-pole system as well as experimental validations demonstrate that the proposed control technique exhibits a reasonable performance in comparison with the other methods. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

The Stability of Tidal Equilibrium for Hierarchical Star-Planet-Moon Systems

NASA Astrophysics Data System (ADS)

Adams, Fred C.

2018-04-01

Motivated by the current search for exomoons, this talk considers the stability of tidal equilibrium for hierarchical three-body systems containing a star, a planet, and a moon. In this treatment, the energy and angular momentum budgets include contributions from the planetary orbit, lunar orbit, stellar spin, planetary spin, and lunar spin. The goal is to determine the optimized energy state of the system subject to the constraint of constant angular momentum. Due to the lack of a closed form solution for the full three-body problem, however, we must use use an approximate description of the orbits. We first consider the Keplerian limit and find that the critical energy states are saddle points, rather than minima, so that these hierarchical systems have no stable tidal equilibrium states. We then generalize the calculation so that the lunar orbit is described by a time-averaged version of the circular restricted three-body problem. In this latter case, the critical energy state is a shallow minimum, so that a tidal equilibrium state exists. In both cases, however, the lunar orbit for the critical point lies outside the boundary (roughly half the Hill radius) where (previous) numerical simulations indicate dynamical instability.

Individual-based models for adaptive diversification in high-dimensional phenotype spaces.

PubMed

Ispolatov, Iaroslav; Madhok, Vaibhav; Doebeli, Michael

2016-02-07

Most theories of evolutionary diversification are based on equilibrium assumptions: they are either based on optimality arguments involving static fitness landscapes, or they assume that populations first evolve to an equilibrium state before diversification occurs, as exemplified by the concept of evolutionary branching points in adaptive dynamics theory. Recent results indicate that adaptive dynamics may often not converge to equilibrium points and instead generate complicated trajectories if evolution takes place in high-dimensional phenotype spaces. Even though some analytical results on diversification in complex phenotype spaces are available, to study this problem in general we need to reconstruct individual-based models from the adaptive dynamics generating the non-equilibrium dynamics. Here we first provide a method to construct individual-based models such that they faithfully reproduce the given adaptive dynamics attractor without diversification. We then show that a propensity to diversify can be introduced by adding Gaussian competition terms that generate frequency dependence while still preserving the same adaptive dynamics. For sufficiently strong competition, the disruptive selection generated by frequency-dependence overcomes the directional evolution along the selection gradient and leads to diversification in phenotypic directions that are orthogonal to the selection gradient. Copyright © 2015 Elsevier Ltd. All rights reserved.

MAGNETAR GIANT FLARES AND THEIR PRECURSORS-FLUX ROPE ERUPTIONS WITH CURRENT SHEETS

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

Yu Cong; Huang Lei, E-mail: cyu@ynao.ac.cn, E-mail: muduri@shao.ac.cn

2013-07-10

We propose a catastrophic magnetospheric model for magnetar precursors and their successive giant flares. Axisymmetric models of the magnetosphere, which contain both a helically twisted flux rope and a current sheet, are established based on force-free field configurations. In this model, the helically twisted flux rope would lose its equilibrium and erupt abruptly in response to the slow and quasi-static variations at the ultra-strongly magnetized neutron star's surface. In a previous model without current sheets, only one critical point exists in the flux rope equilibrium curve. New features show up in the equilibrium curves for the flux rope when currentmore » sheets appear in the magnetosphere. The causal connection between the precursor and the giant flare, as well as the temporary re-entry of the quiescent state between the precursor and the giant flare, can be naturally explained. Magnetic energy would be released during the catastrophic state transitions. The detailed energetics of the model are also discussed. The current sheet created by the catastrophic loss of equilibrium of the flux rope provides an ideal place for magnetic reconnection. We point out the importance of magnetic reconnection for further enhancement of the energy release during eruptions.« less

Mixed-order phase transition in a minimal, diffusion-based spin model.

PubMed

Fronczak, Agata; Fronczak, Piotr

2016-07-01

In this paper we exactly solve, within the grand canonical ensemble, a minimal spin model with the hybrid phase transition. We call the model diffusion based because its Hamiltonian can be recovered from a simple dynamic procedure, which can be seen as an equilibrium statistical mechanics representation of a biased random walk. We outline the derivation of the phase diagram of the model, in which the triple point has the hallmarks of the hybrid transition: discontinuity in the average magnetization and algebraically diverging susceptibilities. At this point, two second-order transition curves meet in equilibrium with the first-order curve, resulting in a prototypical mixed-order behavior.

Laser fusion neutron source employing compression with short pulse lasers

DOEpatents

Sefcik, Joseph A; Wilks, Scott C

2013-11-05

A method and system for achieving fusion is provided. The method includes providing laser source that generates a laser beam and a target that includes a capsule embedded in the target and filled with DT gas. The laser beam is directed at the target. The laser beam helps create an electron beam within the target. The electron beam heats the capsule, the DT gas, and the area surrounding the capsule. At a certain point equilibrium is reached. At the equilibrium point, the capsule implodes and generates enough pressure on the DT gas to ignite the DT gas and fuse the DT gas nuclei.

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

Pugliese, D.; Stuchlík, Z., E-mail: d.pugliese.physics@gmail.com, E-mail: zdenek.stuchlik@physics.cz

We analyze the possibility that several instability points may be formed, due to the Paczyński mechanism of violation of mechanical equilibrium, in the orbiting matter around a supermassive Kerr black hole. We consider a recently proposed model of a ringed accretion disk, made up by several tori (rings) that can be corotating or counter-rotating relative to the Kerr attractor due to the history of the accretion process. Each torus is governed by the general relativistic hydrodynamic Boyer condition of equilibrium configurations of rotating perfect fluids. We prove that the number of the instability points is generally limited and depends onmore » the dimensionless spin of the rotating attractor.« less

A novel grid multiwing chaotic system with only non-hyperbolic equilibria

NASA Astrophysics Data System (ADS)

Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le

2018-05-01

The structure of the chaotic attractor of a system is mainly determined by the nonlinear functions in system equations. By using a new saw-tooth wave function and a new stair function, a novel complex grid multiwing chaotic system which belongs to non-Shil'nikov chaotic system with non-hyperbolic equilibrium points is proposed in this paper. It is particularly interesting that the complex grid multiwing attractors are generated by increasing the number of non-hyperbolic equilibrium points, which are different from the traditional methods of realising multiwing attractors by adding the index-2 saddle-focus equilibrium points in double-wing chaotic systems. The basic dynamical properties of the new system, such as dissipativity, phase portraits, the stability of the equilibria, the time-domain waveform, power spectrum, bifurcation diagram, Lyapunov exponents, and so on, are investigated by theoretical analysis and numerical simulations. Furthermore, the corresponding electronic circuit is designed and simulated on the Multisim platform. The Multisim simulation results and the hardware experimental results are in good agreement with the numerical simulations of the same system on Matlab platform, which verify the feasibility of this new grid multiwing chaotic system.

The phenotypic equilibrium of cancer cells: From average-level stability to path-wise convergence.

PubMed

Niu, Yuanling; Wang, Yue; Zhou, Da

2015-12-07

The phenotypic equilibrium, i.e. heterogeneous population of cancer cells tending to a fixed equilibrium of phenotypic proportions, has received much attention in cancer biology very recently. In the previous literature, some theoretical models were used to predict the experimental phenomena of the phenotypic equilibrium, which were often explained by different concepts of stabilities of the models. Here we present a stochastic multi-phenotype branching model by integrating conventional cellular hierarchy with phenotypic plasticity mechanisms of cancer cells. Based on our model, it is shown that: (i) our model can serve as a framework to unify the previous models for the phenotypic equilibrium, and then harmonizes the different kinds of average-level stabilities proposed in these models; and (ii) path-wise convergence of our model provides a deeper understanding to the phenotypic equilibrium from stochastic point of view. That is, the emergence of the phenotypic equilibrium is rooted in the stochastic nature of (almost) every sample path, the average-level stability just follows from it by averaging stochastic samples. Copyright © 2015 Elsevier Ltd. All rights reserved.

Bifurcation and Stability Analysis of the Equilibrium States in Thermodynamic Systems in a Small Vicinity of the Equilibrium Values of Parameters

NASA Astrophysics Data System (ADS)

Barsuk, Alexandr A.; Paladi, Florentin

2018-04-01

The dynamic behavior of thermodynamic system, described by one order parameter and one control parameter, in a small neighborhood of ordinary and bifurcation equilibrium values of the system parameters is studied. Using the general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, we performed an exhaustive analysis of the order parameter dependences on the control parameter in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameter (bifurcation diagrams). The peculiarities of the transition to an unstable state of the system are discussed, and the estimates of the transition time to the unstable state in the neighborhood of ordinary and bifurcation equilibrium values of parameters are given. The influence of an external field on the dynamic behavior of thermodynamic system is analyzed, and the peculiarities of the system dynamic behavior are discussed near the ordinary and bifurcation equilibrium values of parameters in the presence of external field. The dynamic process of magnetization of a ferromagnet is discussed by using the general methods of bifurcation and stability analysis presented in the paper.

Plasma Equilibrium Control in Nuclear Fusion Devices 2. Plasma Control in Magnetic Confinement Devices 2.1 Plasma Control in Tokamaks

NASA Astrophysics Data System (ADS)

Fukuda, Takeshi

The plasma control technique for use in large tokamak devices has made great developmental strides in the last decade, concomitantly with progress in the understanding of tokamak physics and in part facilitated by the substantial advancement in the computing environment. Equilibrium control procedures have thereby been established, and it has been pervasively recognized in recent years that the real-time feedback control of physical quantities is indispensable for the improvement and sustainment of plasma performance in a quasi-steady-state. Further development is presently undertaken to realize the “advanced plasma control” concept, where integrated fusion performance is achieved by the simultaneous feedback control of multiple physical quantities, combined with equilibrium control.

Creation and protection of entanglement in systems out of thermal equilibrium

NASA Astrophysics Data System (ADS)

Bellomo, Bruno; Antezza, Mauro

2013-11-01

We investigate the creation of entanglement between two quantum emitters interacting with a realistic common stationary electromagnetic field out of thermal equilibrium. In the case of two qubits we show that the absence of equilibrium allows the generation of steady entangled states, which is inaccessible at thermal equilibrium and is realized without any further external action on the two qubits. We first give a simple physical interpretation of the phenomenon in a specific case and then we report a detailed investigation on the dependence of the entanglement dynamics on the various physical parameters involved. Sub- and super-radiant effects are discussed, and qualitative differences in the dynamics concerning both creation and protection of entanglement according to the initial two-qubit state are pointed out.

The Painting-Sponging Analogy for Chemical Equilibrium

NASA Astrophysics Data System (ADS)

Gamitz, Adoni

1997-05-01

An analogy for chemical equilibrium is presented, in which high school or younger students can follow the advance towards equilibrium and its final dynamic nature. The relative opposition between forward and backward processes in a real chemical reaction is exemplified by the distance of a road line that is painted by one person and erased by another, both with different skills and working speeds. The graphical results of the progress of the line distance is entirely similar to the increasing of products concentration in a chemical reaction starting from the reactants. In the analogy, the final equilibrium position is independent of the starting point, as well as in a real chemical process. A simple basic program is included for interactive learning purposes.

A dynamical systems approach to the tilted Bianchi models of solvable type

NASA Astrophysics Data System (ADS)

Coley, Alan; Hervik, Sigbjørn

2005-02-01

We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VIh and VIIh) with a perfect fluid and a linear barotropic γ-law equation of state. In particular, we study the late-time behaviour of tilted Bianchi models, with an emphasis on the existence of equilibrium points and their stability properties. We briefly discuss the tilting Bianchi type V models and the late-time asymptotic behaviour of irrotational Bianchi type VII0 models. We prove the important result that for non-inflationary Bianchi type VIIh models vacuum plane-wave solutions are the only future attracting equilibrium points in the Bianchi type VIIh invariant set. We then investigate the dynamics close to the plane-wave solutions in more detail, and discover some new features that arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of tilt. We point out that in a tiny open set of parameter space in the type IV model (the loophole) there exist closed curves which act as attracting limit cycles. More interestingly, in the Bianchi type VIIh models there is a bifurcation in which a set of equilibrium points turns into closed orbits. There is a region in which both sets of closed curves coexist, and it appears that for the type VIIh models in this region the solution curves approach a compact surface which is topologically a torus.

A Mathematical Model with Quarantine States for the Dynamics of Ebola Virus Disease in Human Populations.

PubMed

Ngwa, Gideon A; Teboh-Ewungkem, Miranda I

2016-01-01

A deterministic ordinary differential equation model for the dynamics and spread of Ebola Virus Disease is derived and studied. The model contains quarantine and nonquarantine states and can be used to evaluate transmission both in treatment centres and in the community. Possible sources of exposure to infection, including cadavers of Ebola Virus victims, are included in the model derivation and analysis. Our model's results show that there exists a threshold parameter, R 0, with the property that when its value is above unity, an endemic equilibrium exists whose value and size are determined by the size of this threshold parameter, and when its value is less than unity, the infection does not spread into the community. The equilibrium state, when it exists, is locally and asymptotically stable with oscillatory returns to the equilibrium point. The basic reproduction number, R 0, is shown to be strongly dependent on the initial response of the emergency services to suspected cases of Ebola infection. When intervention measures such as quarantining are instituted fully at the beginning, the value of the reproduction number reduces and any further infections can only occur at the treatment centres. Effective control measures, to reduce R 0 to values below unity, are discussed.

A Mathematical Model with Quarantine States for the Dynamics of Ebola Virus Disease in Human Populations

PubMed Central

Ngwa, Gideon A.

2016-01-01

A deterministic ordinary differential equation model for the dynamics and spread of Ebola Virus Disease is derived and studied. The model contains quarantine and nonquarantine states and can be used to evaluate transmission both in treatment centres and in the community. Possible sources of exposure to infection, including cadavers of Ebola Virus victims, are included in the model derivation and analysis. Our model's results show that there exists a threshold parameter, R 0, with the property that when its value is above unity, an endemic equilibrium exists whose value and size are determined by the size of this threshold parameter, and when its value is less than unity, the infection does not spread into the community. The equilibrium state, when it exists, is locally and asymptotically stable with oscillatory returns to the equilibrium point. The basic reproduction number, R 0, is shown to be strongly dependent on the initial response of the emergency services to suspected cases of Ebola infection. When intervention measures such as quarantining are instituted fully at the beginning, the value of the reproduction number reduces and any further infections can only occur at the treatment centres. Effective control measures, to reduce R 0 to values below unity, are discussed. PMID:27579053

A numerical analysis of heat and mass transfer during the steam reforming process of ethane

NASA Astrophysics Data System (ADS)

Tomiczek, Marcin; Kaczmarczyk, Robert; Mozdzierz, Marcin; Brus, Grzegorz

2017-11-01

This paper presents a numerical analysis of heat and mass transfer during the steam reforming of ethane. From a chemical point of view, the reforming process of heavy hydrocarbons, such as ethane, is complex. One of the main issue is a set of undesired chemical reactions that causes the deposition of solid carbon and consequently blocks the catalytic property of a reactor. In the literature a carbon deposition regime is selected by thermodynamical analysis to design safe operation conditions. In the case of Computational Fluid Dynamic (CFD, hereafter) models each control volume should be investigated to determinate if carbon deposition is thermodynamically favourable. In this paper the authors combine equilibrium and kinetics analysis to simulate the steam reforming of methane-ethane rich fuel. The results of the computations were juxtaposed with experimental data for methane steam reforming, and good agreement was found. An analysis based on the kinetics of reactions was conducted to predict the influence of temperature drop and non-equilibrium composition on solid carbon deposition. It was found that strong non-uniform temperature distribution in the reactor causes conditions favourable for carbon deposition at the inlet of the reformer. It was shown that equilibrium calculations, often used in the literature, are insufficient.

Equilibrium Polymerization of Butyl Methacrylate in Bulk and in Nanopore Confinement

NASA Astrophysics Data System (ADS)

Tian, Qian; Simon, Sindee

The equilibrium between monomer and polymer in free radical polymerization can be shifted towards monomer under nanoconfinement. This decrease in ceiling temperature is due to a decrease in the entropy associated with the constrained polymer chains, resulting in a larger negative change in entropy of reaction. Here, we investigate the equilibrium polymerization of butyl methacrylate (BMA) in bulk and in nanopore confinement with differential scanning calorimetry (DSC) using di-tert-butyl peroxide (DTBP) as initiator. This system has several advantages compare to the previously studied system of methyl methacrylate (MMA) initiated with 2,2'-azo-bis-isobutyronitrile (AIBN), namely, a reduced rate of reaction, higher boiling point of monomer, and higher initiator utilization temperature range, all of which facilitate the study of the reaction at high temperatures near the ceiling temperature. Interestingly, for BMA, there is no change in limiting conversion between material reacted in bulk and that in controlled pore glass having pore diameters of 7.5 and 50 nm. This unexpected result may be due to the greater flexibility of the PBMA chains compared to PMMA, suggesting that in the BMA/PBMA system, the degree of confinement is relatively low. Future studies will continue to investigate how the entropy change on reaction is affected by confinement.

Morphology Controls on Calcite Recrystallization.

PubMed

Heberling, Frank; Paulig, Leonie; Nie, Zhe; Schild, Dieter; Finck, Nicolas

2016-11-01

Environmental scientists and geoscientists working in different fields regard the reactivity of calcite and corresponding changes in its trace elemental- or isotopic composition from diametrically opposed points of view. As one extreme, calcite based environmental remediation strategies rely on the fast recrystallization of calcite and the concurrent uptake and immobilization of pollutants. Paleo-ecological investigations denote the other extreme, and rely on the invariability of calcite composition over geological periods of time. We use long-term radiotracer experiments to quantify recrystallization rates of seven types of calcite powder with diverse morphology and particle size distribution. On the one hand our results demonstrate the long-term metastability of calcite with equilibrated crystal surfaces even at isotopic dis-equilibrium. On the other hand, we document the extremely high reactivity and interfacial free energy of freshly ground, rough calcite. Our results indicate that bulk calcite recrystallization is an interfacial free energy driven Ostwald-ripening process, in which particle roughness effects dominate over the effect of crystal habitus and particle size. We confirm that the dynamic equilibrium exchange of crystal constituents between kink sites involves an activation barrier of about 25 kJ/mol. At room temperature the equilibrium exchange is limited to a near surface region and proceeds at a rate of (3.6 ± 1.4)·10 -13 mol/(m 2 ·s).

Nonlinear dynamics of attractive magnetic bearings

NASA Technical Reports Server (NTRS)

Hebbale, K. V.; Taylor, D. L.

1987-01-01

The nonlinear dynamics of a ferromagnetic shaft suspended by the force of attraction of 1, 2, or 4 independent electromagnets is presented. Each model includes a state variable feedback controller which has been designed using the pole placement method. The constitutive relationships for the magnets are derived analytically from magnetic circuit theory, and the effects of induced eddy currents due to the rotation of the journal are included using Maxwell's field relations. A rotor suspended by four electro-magnets with closed loop feedback is shown to have nine equilibrium points within the bearing clearance space. As the rotor spin speed increases, the system is shown to pass through a Hopf bifurcation (a flutter instability). Using center manifold theory, this bifurcation can be shown to be of the subcritical type, indicating an unstable limit cycle below the critical speed. The bearing is very sensitive to initial conditions, and the equilibrium position is easily upset by transient excitation. The results are confirmed by numerical simulation.

Phase Transitions and Scaling in Systems Far from Equilibrium

NASA Astrophysics Data System (ADS)

Täuber, Uwe C.

2017-03-01

Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were extended to continuous phase transitions separating distinct nonequilibrium stationary states in driven classical and quantum systems. In concordance with detailed numerical simulations and laboratory experiments, several prominent dynamical universality classes have emerged that govern large-scale, long-time scaling properties both near and far from thermal equilibrium. These pertain to genuine specific critical points as well as entire parameter space regions for steady states that display generic scale invariance. The exploration of nonstationary relaxation properties and associated physical aging scaling constitutes a complementary potent means to characterize cooperative dynamics in complex out-of-equilibrium systems. This review describes dynamic scaling features through paradigmatic examples that include near-equilibrium critical dynamics, driven lattice gases and growing interfaces, correlation-dominated reaction-diffusion systems, and basic epidemic models.

Revealing missing charges with generalised quantum fluctuation relations.

PubMed

Mur-Petit, J; Relaño, A; Molina, R A; Jaksch, D

2018-05-22

The non-equilibrium dynamics of quantum many-body systems is one of the most fascinating problems in physics. Open questions range from how they relax to equilibrium to how to extract useful work from them. A critical point lies in assessing whether a system has conserved quantities (or 'charges'), as these can drastically influence its dynamics. Here we propose a general protocol to reveal the existence of charges based on a set of exact relations between out-of-equilibrium fluctuations and equilibrium properties of a quantum system. We apply these generalised quantum fluctuation relations to a driven quantum simulator, demonstrating their relevance to obtain unbiased temperature estimates from non-equilibrium measurements. Our findings will help guide research on the interplay of quantum and thermal fluctuations in quantum simulation, in studying the transition from integrability to chaos and in the design of new quantum devices.

Adapting and Modifying the Apparatus for Students to Accurately Determine the Freezing Point of a Solvent and Solution

ERIC Educational Resources Information Center

Li, Shirong; Guo, Jianzhong; Wang, Kewang; Chen, Lin; Hu, Daodao; Bai, Yunshan

2017-01-01

An improved apparatus for measuring freezing points has been developed. Compared to the traditional Beckmann freezing point instrument, the improved one overcame prior difficulties with solidification of liquid and made the solid-liquid equilibrium reversible with heat compensation from a heating tube. The reliability and accuracy were carefully…

Soap Films and GeoGebra in the Study of Fermat and Steiner Points

ERIC Educational Resources Information Center

Flores, Alfinio; Park, Jungeun

2018-01-01

We discuss how mathematics and secondary mathematics education majors developed an understanding of Fermat points for the triangle as well as Steiner points for the square and regular pentagon, and also of soap film configurations between parallel plates where forces are in equilibrium. The activities included the use of soap films and the…

Linking point scale process non-linearity, catchment organization and linear system dynamics in a thermodynamic state space

NASA Astrophysics Data System (ADS)

Zehe, Erwin; Loritz, Ralf; Ehret, Uwe; Westhoff, Martijn; Kleidon, Axel; Savenije, Hubert

2017-04-01

It is flabbergasting to note that catchment systems often behave almost linearly, despite of the strong non-linearity of point scale soil water characteristics. In the present study we provide evidence that a thermodynamic treatment of environmental system dynamics is the key to understand how particularly a stronger spatial organization of catchments leads to a more linear rainfall runoff behavior. Our starting point is that water fluxes in a catchment are associated with fluxes of kinetic and potential energy while changes in subsurface water stocks go along with changes in potential energy and chemical energy of subsurface water. Steady state/local equilibrium of the entire system can be defined as a state of minimum free energy, reflecting an equilibrium subsurface water storage, which is determined catchment topography, soil water characteristics and water levels in the stream. Dynamics of the entire system, i.e. deviations from equilibrium storage, are 'pseudo' oscillations in a thermodynamic state space. Either to an excess potential energy in case of wetting while subsequent relaxation back to equilibrium requires drainage/water export. Or to an excess in capillary binding energy in case of driving, while relaxation back to equilibrium requires recharge of the subsurface water stock. While system dynamics is highly non-linear on the 'too dry branch' it is essentially linear on the 'too wet branch' in case of potential energy excess. A steepened topography, which reflects a stronger spatial organization, reduces the equilibrium storage of the catchment system to smaller values, thereby it increases the range of states where the systems behaves linearly due to an excess in potential energy. Contrarily to this a shift to finer textured soils increases the equilibrium storage, which implies that the range of states where the systems behaves linearly is reduced. In this context it is important to note that an increased internal organization of the system due to an elevated density of the preferential flow paths, imply a less non-linear system behavior. This is because they avoid persistence of very dry states system states by facilitating recharge of the soil moisture stock. Based on the proposed approach we compare dynamics of four distinctly different catchments in their respective state space and demonstrate the feasibility of the approach to explain differences and similarities in their rainfall runoff regimes.

BINARY CORRELATIONS IN IONIZED GASES

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

Balescu, R.; Taylor, H.S.

1961-01-01

An equation of evolution for the binary distribution function in a classical homogeneous, nonequilibrium plasma was derived. It is shown that the asymptotic (long-time) solution of this equation is the Debye distribution, thus providing a rigorous dynamical derivation of the equilibrium distribution. This proof is free from the fundamental conceptual difficulties of conventional equilibrium derivations. Out of equilibrium, a closed formula was obtained for the long living correlations, in terms of the momentum distribution function. These results should form an appropriate starting point for a rigorous theory of transport phenomena in plasmas, including the effect of molecular correlations. (auth)

Equilibrium and nonequilibrium models on Solomon networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2016-05-01

We investigate the critical properties of the equilibrium and nonequilibrium systems on Solomon networks. The equilibrium and nonequilibrium systems studied here are the Ising and Majority-vote models, respectively. These systems are simulated by applying the Monte Carlo method. We calculate the critical points, as well as the critical exponents ratio γ/ν, β/ν and 1/ν. We find that both systems present identical exponents on Solomon networks and are of different universality class as the regular two-dimensional ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

Algorithm For Hypersonic Flow In Chemical Equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.

Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field

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

Feng, Jinglang; Hou, Xiyun, E-mail: jinglang@nju.edu.cn, E-mail: silence@nju.edu.cn

2017-07-01

Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circularmore » restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.« less

Equilibrium between cell division and apoptosis in immortal cells as an alternative to the G1 restriction mechanism in mammalian cells.

PubMed

Dedov, Vadim N; Dedova, Irina V; Nicholson, Garth A

2004-04-01

Starvation arrests cultured mammalian cells in the G(1) restriction point of the cell cycle, whereas cancer cells generally lose the regulatory control of the cell cycle. Human lymphocytes, infected with Epstein-Barr virus (EBV), also lose their cell cycle control and produce immortal lymphoblastoid cell lines. We show that during starvation, EBV-lymphoblasts override the cell cycle arrest in the G(1) restriction point and continue cell division. Simultaneously, starvation activates apoptosis in an approximately half of the daughter cells in each cell generation. Continuos cell division and partial removal of cells by apoptosis results in stabilization of viable cell numbers, where a majority of viable cells are in the G(1) phase of the cell cycle. In contrast to starvation, anticancer drug etoposide activates apoptosis indiscriminately in all EBV-lymphoblasts and convertes all the viable cells into apoptotic. We conclude that the removal of surplus cells by apoptosis may represent a survival mechanism of transformed (i.e., cancer) cell population in nutrient restricted conditions, whereas nontransformed mammalian cells are arrested in the G(1) restriction point of the cell cycle.

Optimal control of diarrhea transmission in a flood evacuation zone

NASA Astrophysics Data System (ADS)

Erwina, N.; Aldila, D.; Soewono, E.

2014-03-01

Evacuation of residents and diarrhea disease outbreak in evacuation zone have become serious problem that frequently happened during flood periods. Limited clean water supply and infrastructure in evacuation zone contribute to a critical spread of diarrhea. Transmission of diarrhea disease can be reduced by controlling clean water supply and treating diarrhea patients properly. These treatments require significant amount of budget, which may not be fulfilled in the fields. In his paper, transmission of diarrhea disease in evacuation zone using SIRS model is presented as control optimum problem with clean water supply and rate of treated patients as input controls. Existence and stability of equilibrium points and sensitivity analysis are investigated analytically for constant input controls. Optimum clean water supply and rate of treatment are found using optimum control technique. Optimal results for transmission of diarrhea and the corresponding controls during the period of observation are simulated numerically. The optimum result shows that transmission of diarrhea disease can be controlled with proper combination of water supply and rate of treatment within allowable budget.

Design and analysis of adaptive Super-Twisting sliding mode control for a microgyroscope.

PubMed

Feng, Zhilin; Fei, Juntao

2018-01-01

This paper proposes a novel adaptive Super-Twisting sliding mode control for a microgyroscope under unknown model uncertainties and external disturbances. In order to improve the convergence rate of reaching the sliding surface and the accuracy of regulating and trajectory tracking, a high order Super-Twisting sliding mode control strategy is employed, which not only can combine the advantages of the traditional sliding mode control with the Super-Twisting sliding mode control, but also guarantee that the designed control system can reach the sliding surface and equilibrium point in a shorter finite time from any initial state and avoid chattering problems. In consideration of unknown parameters of micro gyroscope system, an adaptive algorithm based on Lyapunov stability theory is designed to estimate the unknown parameters and angular velocity of microgyroscope. Finally, the effectiveness of the proposed scheme is demonstrated by simulation results. The comparative study between adaptive Super-Twisting sliding mode control and conventional sliding mode control demonstrate the superiority of the proposed method.

Students' and Teachers' Misapplication of Le Chatelier's Principle: Implications for the Teaching of Chemical Equilibrium.

ERIC Educational Resources Information Center

Quilez-Pardo, Juan; Solaz-Portoles, Joan Josep

1995-01-01

Study of strategies and procedures of 170 students and 40 teachers when solving chemical equilibrium problems found misconceptions emerging through: misapplication of Le Chatelier's Principle, use of rote-learning recall, incorrect control of variables, limited use of chemical equilibrium law, lack of mastery of chemical equilibrium principles,…

Dynamical System Analysis of Reynolds Stress Closure Equations

NASA Technical Reports Server (NTRS)

Girimaji, Sharath S.

1997-01-01

In this paper, we establish the causality between the model coefficients in the standard pressure-strain correlation model and the predicted equilibrium states for homogeneous turbulence. We accomplish this by performing a comprehensive fixed point analysis of the modeled Reynolds stress and dissipation rate equations. The results from this analysis will be very useful for developing improved pressure-strain correlation models to yield observed equilibrium behavior.

Chemical vapor deposition modeling: An assessment of current status

NASA Technical Reports Server (NTRS)

Gokoglu, Suleyman A.

1991-01-01

The shortcomings of earlier approaches that assumed thermochemical equilibrium and used chemical vapor deposition (CVD) phase diagrams are pointed out. Significant advancements in predictive capabilities due to recent computational developments, especially those for deposition rates controlled by gas phase mass transport, are demonstrated. The importance of using the proper boundary conditions is stressed, and the availability and reliability of gas phase and surface chemical kinetic information are emphasized as the most limiting factors. Future directions for CVD are proposed on the basis of current needs for efficient and effective progress in CVD process design and optimization.

Numerically derived parametrisation of optimal RMP coil phase as a guide to experiments on ASDEX Upgrade

NASA Astrophysics Data System (ADS)

Ryan, D. A.; Liu, Y. Q.; Li, L.; Kirk, A.; Dunne, M.; Dudson, B.; Piovesan, P.; Suttrop, W.; Willensdorfer, M.; the ASDEX Upgrade Team; the EUROfusion MST1 Team

2017-02-01

Edge localised modes (ELMs) are a repetitive MHD instability, which may be mitigated or suppressed by the application of resonant magnetic perturbations (RMPs). In tokamaks which have an upper and lower set of RMP coils, the applied spectrum of the RMPs can be tuned for optimal ELM control, by introducing a toroidal phase difference {{Δ }}{{Φ }} between the upper and lower rows. The magnitude of the outermost resonant component of the RMP field | {b}{{res}}1| (other proposed criteria are discussed herein) has been shown experimentally to correlate with mitigated ELM frequency, and to be controllable by {{Δ }}{{Φ }} (Kirk et al 2013 Plasma Phys. Control. Fusion 53 043007). This suggests that ELM mitigation may be optimised by choosing {{Δ }}{{Φ }}={{Δ }}{{{Φ }}}{{opt}}, such that | {b}{{res}}1| is maximised. However it is currently impractical to compute {{Δ }}{{{Φ }}}{{opt}} in advance of experiments. This motivates this computational study of the dependence of the optimal coil phase difference {{Δ }}{{{Φ }}}{{opt}}, on global plasma parameters {β }N and q 95, in order to produce a simple parametrisation of {{Δ }}{{{Φ }}}{{opt}}. In this work, a set of tokamak equilibria spanning a wide range of ({β }N, q 95) is produced, based on a reference equilibrium from an ASDEX Upgrade experiment. The MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681) is then used to compute {{Δ }}{{{Φ }}}{{opt}} across this equilibrium set for toroidal mode numbers n = 1-4, both for the vacuum field and including the plasma response. The computational scan finds that for fixed plasma boundary shape, rotation profiles and toroidal mode number n, {{Δ }}{{{Φ }}}{{opt}} is a smoothly varying function of ({β }N, q 95). A 2D quadratic function in ({β }N, q 95) is used to parametrise {{Δ }}{{{Φ }}}{{opt}}, such that for given ({β }N, q 95) and n, an estimate of {{Δ }}{{{Φ }}}{{opt}} may be made without requiring a plasma response computation. To quantify the uncertainty of the parametrisation relative to a plasma response computation, {{Δ }}{{{Φ }}}{{opt}} is also computed using MARS-F for a set of benchmarking points. Each benchmarking point consists of a distinct free boundary equilibrium reconstructed from an ASDEX Upgrade RMP experiment, and set of experimental kinetic profiles and coil currents. Comparing the MARS-F predictions of {{Δ }}{{{Φ }}}{{opt}} for these benchmarking points to predictions of the 2D quadratic, shows that relative to a plasma response computation with MARS-F the 2D quadratic is accurate to 26.5° for n = 1, and 20.6° for n = 2. Potential sources for uncertainty are assessed.

Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem

NASA Astrophysics Data System (ADS)

Lei, Hanlun; Xu, Bo; Circi, Christian

2018-05-01

In this work, the single-mode motions around the collinear and triangular libration points in the circular restricted three-body problem are studied. To describe these motions, we adopt an invariant manifold approach, which states that a suitable pair of independent variables are taken as modal coordinates and the remaining state variables are expressed as polynomial series of them. Based on the invariant manifold approach, the general procedure on constructing polynomial expansions up to a certain order is outlined. Taking the Earth-Moon system as the example dynamical model, we construct the polynomial expansions up to the tenth order for the single-mode motions around collinear libration points, and up to order eight and six for the planar and vertical-periodic motions around triangular libration point, respectively. The application of the polynomial expansions constructed lies in that they can be used to determine the initial states for the single-mode motions around equilibrium points. To check the validity, the accuracy of initial states determined by the polynomial expansions is evaluated.

Prediction of boiling points of organic compounds by QSPR tools.

PubMed

Dai, Yi-min; Zhu, Zhi-ping; Cao, Zhong; Zhang, Yue-fei; Zeng, Ju-lan; Li, Xun

2013-07-01

The novel electro-negativity topological descriptors of YC, WC were derived from molecular structure by equilibrium electro-negativity of atom and relative bond length of molecule. The quantitative structure-property relationships (QSPR) between descriptors of YC, WC as well as path number parameter P3 and the normal boiling points of 80 alkanes, 65 unsaturated hydrocarbons and 70 alcohols were obtained separately. The high-quality prediction models were evidenced by coefficient of determination (R(2)), the standard error (S), average absolute errors (AAE) and predictive parameters (Qext(2),RCV(2),Rm(2)). According to the regression equations, the influences of the length of carbon backbone, the size, the degree of branching of a molecule and the role of functional groups on the normal boiling point were analyzed. Comparison results with reference models demonstrated that novel topological descriptors based on the equilibrium electro-negativity of atom and the relative bond length were useful molecular descriptors for predicting the normal boiling points of organic compounds. Copyright © 2013 Elsevier Inc. All rights reserved.

Estimating the population size and colony boundary of subterranean termites by using the density functions of directionally averaged capture probability.

PubMed

Su, Nan-Yao; Lee, Sang-Hee

2008-04-01

Marked termites were released in a linear-connected foraging arena, and the spatial heterogeneity of their capture probabilities was averaged for both directions at distance r from release point to obtain a symmetrical distribution, from which the density function of directionally averaged capture probability P(x) was derived. We hypothesized that as marked termites move into the population and given sufficient time, the directionally averaged capture probability may reach an equilibrium P(e) over the distance r and thus satisfy the equal mixing assumption of the mark-recapture protocol. The equilibrium capture probability P(e) was used to estimate the population size N. The hypothesis was tested in a 50-m extended foraging arena to simulate the distance factor of field colonies of subterranean termites. Over the 42-d test period, the density functions of directionally averaged capture probability P(x) exhibited four phases: exponential decline phase, linear decline phase, equilibrium phase, and postequilibrium phase. The equilibrium capture probability P(e), derived as the intercept of the linear regression during the equilibrium phase, correctly projected N estimates that were not significantly different from the known number of workers in the arena. Because the area beneath the probability density function is a constant (50% in this study), preequilibrium regression parameters and P(e) were used to estimate the population boundary distance 1, which is the distance between the release point and the boundary beyond which the population is absent.

Nanoscale Correlated Disorder in Out-of-Equilibrium Myelin Ultrastructure.

PubMed

Campi, Gaetano; Di Gioacchino, Michael; Poccia, Nicola; Ricci, Alessandro; Burghammer, Manfred; Ciasca, Gabriele; Bianconi, Antonio

2018-01-23

Ultrastructural fluctuations at nanoscale are fundamental to assess properties and functionalities of advanced out-of-equilibrium materials. We have taken myelin as a model of supramolecular assembly in out-of-equilibrium living matter. Myelin sheath is a simple stable multilamellar structure of high relevance and impact in biomedicine. Although it is known that myelin has a quasi-crystalline ultrastructure, there is no information on its fluctuations at nanoscale in different states due to limitations of the available standard techniques. To overcome these limitations, we have used scanning micro X-ray diffraction, which is a unique non-invasive probe of both reciprocal and real space to visualize statistical fluctuations of myelin order of the sciatic nerve of Xenopus laevis. The results show that the ultrastructure period of the myelin is stabilized by large anticorrelated fluctuations at nanoscale, between hydrophobic and hydrophilic layers. The ratio between the total thickness of hydrophilic and hydrophobic layers defines the conformational parameter, which describes the different states of myelin. Our key result is that myelin in its out-of-equilibrium functional state fluctuates point-to-point between different conformations showing a correlated disorder described by a Levy distribution. As the system approaches the thermodynamic equilibrium in an aged state, the disorder loses its correlation degree and the structural fluctuation distribution changes to Gaussian. In a denatured state at low pH, it changes to a completely disordered stage. Our results aim to clarify the degradation mechanism in biological systems by associating these states with ultrastructural dynamic fluctuations at nanoscale.

Regulatory T cells in the control of host-microorganism interactions (*).

PubMed

Belkaid, Yasmine; Tarbell, Kristin

2009-01-01

Each microenvironment requires a specific set of regulatory elements that are finely and constantly tuned to maintain local homeostasis. Various populations of regulatory T cells contribute to the maintenance of this equilibrium and establishment of controlled immune responses. In particular, regulatory T cells limit the magnitude of effector responses, which may result in failure to adequately control infection. However, regulatory T cells also help limit collateral tissue damage caused by vigorous antimicrobial immune responses against pathogenic microbes as well as commensals. In this review, we describe various situations in which the balance between regulatory T cells and effector immune functions influence the outcome of host-microorganism coexistence and discuss current hypotheses and points of polemic associated with the origin, target, and antigen specificity of both endogenous and induced regulatory T cells during these interactions.

Impedance learning for robotic contact tasks using natural actor-critic algorithm.

PubMed

Kim, Byungchan; Park, Jooyoung; Park, Shinsuk; Kang, Sungchul

2010-04-01

Compared with their robotic counterparts, humans excel at various tasks by using their ability to adaptively modulate arm impedance parameters. This ability allows us to successfully perform contact tasks even in uncertain environments. This paper considers a learning strategy of motor skill for robotic contact tasks based on a human motor control theory and machine learning schemes. Our robot learning method employs impedance control based on the equilibrium point control theory and reinforcement learning to determine the impedance parameters for contact tasks. A recursive least-square filter-based episodic natural actor-critic algorithm is used to find the optimal impedance parameters. The effectiveness of the proposed method was tested through dynamic simulations of various contact tasks. The simulation results demonstrated that the proposed method optimizes the performance of the contact tasks in uncertain conditions of the environment.

Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field

NASA Astrophysics Data System (ADS)

Moawad, S. M.; Moawad

2013-10-01

The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

Marginal states in a cubic autocatalytic reaction

NASA Astrophysics Data System (ADS)

Das, Debojyoti; Ghosh, Pushpita; Ray, Deb Shankar

2011-09-01

Marginal steady state belongs to a special class of states in nonlinear dynamics. To realize this state we consider a cubic autocatalytic reaction A + 2B → 3B in a continuous-stirred-tank-reactor, where the flow rate of the reactant A can be controlled to manipulate the dynamical behavior of the open system. We demonstrate that when the flow rate is weakly noisy the autocatalytic reaction admits of a steady state which is marginal in nature and is surrounded by infinite number of periodic trajectories. When the uncatalyzed reaction A → B is included in the reaction scheme, there exists a marginal steady state which is a critical state corresponding to the point of transition between the flow branch and the equilibrium branch, similar to gas-liquid critical point of transition. This state loses its stability in the weak noise limit.

Retinal image quality and visual stimuli processing by simulation of partial eye cataract

NASA Astrophysics Data System (ADS)

Ozolinsh, Maris; Danilenko, Olga; Zavjalova, Varvara

2016-10-01

Visual stimuli were demonstrated on a 4.3'' mobile phone screen inside a "Virtual Reality" adapter that allowed separation of the left and right eye visual fields. Contrast of the retina image thus can be controlled by the image on the phone screen and parallel to that at appropriate geometry by the AC voltage applied to scattering PDLC cell inside the adapter. Such optical pathway separation allows to demonstrate to both eyes spatially variant images, that after visual binocular fusion acquire their characteristic indications. As visual stimuli we used grey and different color (two opponent components to vision - red-green in L*a*b* color space) spatially periodical stimuli for left and right eyes; and with spatial content that by addition or subtraction resulted as clockwise or counter clockwise slanted Gabor gratings. We performed computer modeling with numerical addition or subtraction of signals similar to processing in brain via stimuli input decomposition in luminance and color opponency components. It revealed the dependence of the perception psychophysical equilibrium point between clockwise or counter clockwise perception of summation on one eye image contrast and color saturation, and on the strength of the retinal aftereffects. Existence of a psychophysical equilibrium point in perception of summation is only in the presence of a prior adaptation to a slanted periodical grating and at the appropriate slant orientation of adaptation grating and/or at appropriate spatial grating pattern phase according to grating nods. Actual observer perception experiments when one eye images were deteriorated by simulated cataract approved the shift of mentioned psychophysical equilibrium point on the degree of artificial cataract. We analyzed also the mobile devices stimuli emission spectra paying attention to areas sensitive to macula pigments absorption spectral maxima and blue areas where the intense irradiation can cause in abnormalities in periodic melatonin regeneration and deviations in regular circadian rhythms. Therefore participants in vision studies using "Virtual Reality" appliances with fixed vision fields and emitting a spike liked spectral bands (on basis of OLED and AMOLED diodes) different from spectra of ambient illuminators should be accordingly warned about potential health risks.

Gas-kinetic unified algorithm for hypersonic flows covering various flow regimes solving Boltzmann model equation in nonequilibrium effect

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

Li, Zhihui; Ma, Qiang; Wu, Junlin

2014-12-09

Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinatemore » points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.« less

Torque equilibrium attitude control for Skylab reentry

NASA Technical Reports Server (NTRS)

Glaese, J. R.; Kennel, H. F.

1979-01-01

All the available torque equilibrium attitudes (most were useless from the standpoint of lack of electrical power) and the equilibrium seeking method are presented, as well as the actual successful application during the 3 weeks prior to Skylab reentry.

Sedimentation dynamics and equilibrium profiles in multicomponent mixtures of colloidal particles.

PubMed

Spruijt, E; Biesheuvel, P M

2014-02-19

In this paper we give a general theoretical framework that describes the sedimentation of multicomponent mixtures of particles with sizes ranging from molecules to macroscopic bodies. Both equilibrium sedimentation profiles and the dynamic process of settling, or its converse, creaming, are modeled. Equilibrium profiles are found to be in perfect agreement with experiments. Our model reconciles two apparently contradicting points of view about buoyancy, thereby resolving a long-lived paradox about the correct choice of the buoyant density. On the one hand, the buoyancy force follows necessarily from the suspension density, as it relates to the hydrostatic pressure gradient. On the other hand, sedimentation profiles of colloidal suspensions can be calculated directly using the fluid density as apparent buoyant density in colloidal systems in sedimentation-diffusion equilibrium (SDE) as a result of balancing gravitational and thermodynamic forces. Surprisingly, this balance also holds in multicomponent mixtures. This analysis resolves the ongoing debate of the correct choice of buoyant density (fluid or suspension): both approaches can be used in their own domain. We present calculations of equilibrium sedimentation profiles and dynamic sedimentation that show the consequences of these insights. In bidisperse mixtures of colloids, particles with a lower mass density than the homogeneous suspension will first cream and then settle, whereas particles with a suspension-matched mass density form transient, bimodal particle distributions during sedimentation, which disappear when equilibrium is reached. In all these cases, the centers of the distributions of the particles with the lowest mass density of the two, regardless of their actual mass, will be located in equilibrium above the so-called isopycnic point, a natural consequence of their hard-sphere interactions. We include these interactions using the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state. Finally, we demonstrate that our model is not limited to hard spheres, by extending it to charged spherical particles, and to dumbbells, trimers and short chains of connected beads.

A note on AB INITIO semiconductor band structures

NASA Astrophysics Data System (ADS)

Fiorentini, Vincenzo

1992-09-01

We point out that only the internal features of the DFT ab initio theoretical picture of a crystal should be used in a consistent ab initio calculation of the band structure. As a consequence, we show that ground-state band structure calculations should be performed for the system in equilibrium at zero pressure, i.e. at the computed equilibrium cell volume ω th. Examples of consequences of this attitude are considered.

Nonlinear dynamic behaviors of permanent magnet synchronous motors in electric vehicles caused by unbalanced magnetic pull

NASA Astrophysics Data System (ADS)

Xiang, Changle; Liu, Feng; Liu, Hui; Han, Lijin; Zhang, Xun

2016-06-01

Unbalanced magnetic pull (UMP) plays a key role in nonlinear dynamic behaviors of permanent magnet synchronous motors (PMSM) in electric vehicles. Based on Jeffcott rotor model, the stiffness characteristics of the rotor system of the PMSM are analyzed and the nonlinear dynamic behaviors influenced by UMP are investigated. In free vibration study, eigenvalue-based stability analysis for multiple equilibrium points is performed which offers an insight in system stiffness. Amplitude modulation effects are discovered of which the mechanism is explained and the period of modulating signal is carried out by phase analysis and averaging method. The analysis indicates that the effects are caused by the interaction of the initial phases of forward and backward whirling motions. In forced vibration study, considering dynamic eccentricity, frequency characteristics revealing softening type are obtained by harmonic balance method, and the stability of periodic solution is investigated by Routh-Hurwitz criterion. The frequency characteristics analysis indicates that the response amplitude is limited in the range between the amplitudes of the two kinds of equilibrium points. In the vicinity of the continuum of equilibrium points, the system hardly provides resistance to bending, and hence external disturbances easily cause loss of stability. It is useful for the design of the PMSM with high stability and low vibration and acoustic noise.

Multiple μ-stability of neural networks with unbounded time-varying delays.

PubMed

Wang, Lili; Chen, Tianping

2014-05-01

In this paper, we are concerned with a class of recurrent neural networks with unbounded time-varying delays. Based on the geometrical configuration of activation functions, the phase space R(n) can be divided into several Φη-type subsets. Accordingly, a new set of regions Ωη are proposed, and rigorous mathematical analysis is provided to derive the existence of equilibrium point and its local μ-stability in each Ωη. It concludes that the n-dimensional neural networks can exhibit at least 3(n) equilibrium points and 2(n) of them are μ-stable. Furthermore, due to the compatible property, a set of new conditions are presented to address the dynamics in the remaining 3(n)-2(n) subset regions. As direct applications of these results, we can get some criteria on the multiple exponential stability, multiple power stability, multiple log-stability, multiple log-log-stability and so on. In addition, the approach and results can also be extended to the neural networks with K-level nonlinear activation functions and unbounded time-varying delays, in which there can store (2K+1)(n) equilibrium points, (K+1)(n) of them are locally μ-stable. Numerical examples are given to illustrate the effectiveness of our results. Copyright © 2014 Elsevier Ltd. All rights reserved.

Simulations of Dissipative Circular Restricted Three-body Problems Using the Velocity-scaling Correction Method

NASA Astrophysics Data System (ADS)

Wang, Shoucheng; Huang, Guoqing; Wu, Xin

2018-02-01

In this paper, we survey the effect of dissipative forces including radiation pressure, Poynting–Robertson drag, and solar wind drag on the motion of dust grains with negligible mass, which are subjected to the gravities of the Sun and Jupiter moving in circular orbits. The effect of the dissipative parameter on the locations of five Lagrangian equilibrium points is estimated analytically. The instability of the triangular equilibrium point L4 caused by the drag forces is also shown analytically. In this case, the Jacobi constant varies with time, whereas its integral invariant relation still provides a probability for the applicability of the conventional fourth-order Runge–Kutta algorithm combined with the velocity scaling manifold correction scheme. Consequently, the velocity-only correction method significantly suppresses the effects of artificial dissipation and a rapid increase in trajectory errors caused by the uncorrected one. The stability time of an orbit, regardless of whether it is chaotic or not in the conservative problem, is apparently longer in the corrected case than in the uncorrected case when the dissipative forces are included. Although the artificial dissipation is ruled out, the drag dissipation leads to an escape of grains. Numerical evidence also demonstrates that more orbits near the triangular equilibrium point L4 escape as the integration time increases.

Examples of equilibrium and non-equilibrium behavior in evolutionary systems

NASA Astrophysics Data System (ADS)

Soulier, Arne

With this thesis, we want to shed some light into the darkness of our understanding of simply defined statistical mechanics systems and the surprisingly complex dynamical behavior they exhibit. We will do so by presenting in turn one equilibrium and then one non-equilibrium system with evolutionary dynamics. In part 1, we will present the seceder-model, a newly developed system that cannot equilibrate. We will then study several properties of the system and obtain an idea of the richness of the dynamics of the seceder model, which is particular impressive given the minimal amount of modeling necessary in its setup. In part 2, we will present extensions to the directed polymer in random media problem on a hypercube and its connection to the Eigen model of evolution. Our main interest will be the influence of time-dependent and time-independent changes in the fitness landscape viewed by an evolving population. This part contains the equilibrium dynamics. The stochastic models and the topic of evolution and non-equilibrium in general will allow us to point out similarities to the various lines of thought in game theory.

Convergence of neural networks for programming problems via a nonsmooth Lojasiewicz inequality.

PubMed

Forti, Mauro; Nistri, Paolo; Quincampoix, Marc

2006-11-01

This paper considers a class of neural networks (NNs) for solving linear programming (LP) problems, convex quadratic programming (QP) problems, and nonconvex QP problems where an indefinite quadratic objective function is subject to a set of affine constraints. The NNs are characterized by constraint neurons modeled by ideal diodes with vertical segments in their characteristic, which enable to implement an exact penalty method. A new method is exploited to address convergence of trajectories, which is based on a nonsmooth Lojasiewicz inequality for the generalized gradient vector field describing the NN dynamics. The method permits to prove that each forward trajectory of the NN has finite length, and as a consequence it converges toward a singleton. Furthermore, by means of a quantitative evaluation of the Lojasiewicz exponent at the equilibrium points, the following results on convergence rate of trajectories are established: (1) for nonconvex QP problems, each trajectory is either exponentially convergent, or convergent in finite time, toward a singleton belonging to the set of constrained critical points; (2) for convex QP problems, the same result as in (1) holds; moreover, the singleton belongs to the set of global minimizers; and (3) for LP problems, each trajectory converges in finite time to a singleton belonging to the set of global minimizers. These results, which improve previous results obtained via the Lyapunov approach, are true independently of the nature of the set of equilibrium points, and in particular they hold even when the NN possesses infinitely many nonisolated equilibrium points.

Space and time in the context of equilibrium-point theory.

PubMed

Feldman, Anatol G

2011-05-01

Advances to the equilibrium-point (EP) theory and solutions to several classical problems of action and perception are suggested and discussed. Among them are (1) the posture-movement problem of how movements away from a stable posture can be made without evoking resistance of posture-stabilizing mechanisms resulting from intrinsic muscle and reflex properties; (2) the problem of kinesthesia or why our sense of limb position is fairly accurate despite ambiguous positional information delivered by proprioceptive and cutaneous signals; (3) the redundancy problems in the control of multiple muscles and degrees of freedom. Central to the EP hypothesis is the notion that there are specific neural structures that represent spatial frames of reference (FRs) selected by the brain in a task-specific way from a set of available FRs. The brain is also able to translate or/and rotate the selected FRs by modifying their major attributes-the origin, metrics, and orientation-and thus substantially influence, in a feed-forward manner, action and perception. The brain does not directly solve redundancy problems: it only limits the amount of redundancy by predetermining where, in spatial coordinates, a task-specific action should emerge and allows all motor elements, including the environment, to interact to deliver a unique action, thus solving the redundancy problem (natural selection of action). The EP theory predicts the existence of specific neurons associated with the control of different attributes of FRs and explains the role of mirror neurons in the inferior frontal gyrus and place cells in the hippocampus. WIREs Cogni Sci 2011 2 287-304 DOI: 10.1002/wcs.108 For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.

Equilibrium positions on stationary orbits and planetary principal inertia axis orientations for the Solar System

NASA Astrophysics Data System (ADS)

Romero, Pilar; Barderas, Gonzalo; Mejuto, Javier

2018-05-01

We present a qualitative analysis in a phase space to determine the longitudinal equilibrium positions on the planetary stationary orbits by applying an analytical model that considers linear gravitational perturbations. We discuss how these longitudes are related with the orientation of the planetary principal inertia axes with respect to their Prime Meridians, and then we use this determination to derive their positions with respect to the International Celestial Reference Frame. Finally, a numerical analysis of the non-linear effects of the gravitational fields on the equilibrium point locations is developed and their correlation with gravity field anomalies shown.

Blurring out hydrogen: The dynamical structure of teflic acid

NASA Astrophysics Data System (ADS)

Herbers, S.; Obenchain, D. A.; Kraus, P.; Wachsmuth, D.; Grabow, J.-U.

2018-05-01

The microwave spectra of 10 teflic acid isotopologues were recorded in the frequency range of 3-25 GHz using supersonic jet-expansion Fourier transform microwave spectroscopy. Despite being asymmetric in its equilibrium structure, the delocalization of the hydrogen atom leads to a symmetric top vibrational ground state structure. In this work, we present the zero point structure obtained from the experimental rotational constants and an approach to determine the semi-experimental equilibrium structure aided by ab initio data. The Te-O bond length determined in the equilibrium structure is accurate to the picometer and can be used as a benchmark for computational methods treating relativistic effects.

Network Aggregation in Transportation Planning : Volume II : A Fixed Point Method for Treating Traffic Equilibria

DOT National Transportation Integrated Search

1978-04-01

Volume 2 defines a new algorithm for the network equilibrium model that works in the space of path flows and is based on the theory of fixed point method. The goals of the study were broadly defined as the identification of aggregation practices and ...

Under What Conditions Can Equilibrium Gas-Particle Partitioning Be Expected to Hold in the Atmosphere?

PubMed

Mai, Huajun; Shiraiwa, Manabu; Flagan, Richard C; Seinfeld, John H

2015-10-06

The prevailing treatment of secondary organic aerosol formation in atmospheric models is based on the assumption of instantaneous gas-particle equilibrium for the condensing species, yet compelling experimental evidence indicates that organic aerosols can exhibit the properties of highly viscous, semisolid particles, for which gas-particle equilibrium may be achieved slowly. The approach to gas-particle equilibrium partitioning is controlled by gas-phase diffusion, interfacial transport, and particle-phase diffusion. Here we evaluate the controlling processes and the time scale to achieve gas-particle equilibrium as a function of the volatility of the condensing species, its surface accommodation coefficient, and its particle-phase diffusivity. For particles in the size range of typical atmospheric organic aerosols (∼50-500 nm), the time scale to establish gas-particle equilibrium is generally governed either by interfacial accommodation or particle-phase diffusion. The rate of approach to equilibrium varies, depending on whether the bulk vapor concentration is constant, typical of an open system, or decreasing as a result of condensation into the particles, typical of a closed system.

Intermittent muscle activity in the feedback loop of postural control system during natural quiet standing.

PubMed

Tanabe, Hiroko; Fujii, Keisuke; Kouzaki, Motoki

2017-09-06

The origin of continual body oscillation during quiet standing is a neural-muscular-skeletal closed feedback loop system that includes insufficient joint stiffness and a time delay. Thus, muscle activity and joint oscillations are nonlinear during quiet standing, making it difficult to demonstrate the muscular-skeletal relationship experimentally. Here we experimentally revealed this relationship using intermittent control theory, in which non-actuation works to stabilize the skeletal system towards equilibrium. We found that leg muscles were activated/inactivated when the state point was located in the opposite/same direction as the direction of anatomical action, which was associated with joint torque actuating the body towards equilibrium. The derivative values of stability index defined in the phase space approximately 200 ms before muscle inactivation were also larger than those before activation for some muscles. These results indicate that bipedal standing might be achieved by monitoring the rate of change of stability/instability components and generating joint torque to stabilize the body. In conclusion, muscles are likely to activate in an event-driven manner during quiet standing and a possible metric for on/off switching is SI dot, and our methodology of EMG processing could allows us to extract such event-driven intermittent muscle activities.

Power exhaust scenarios and control for projected high-power NSTX-U operation

NASA Astrophysics Data System (ADS)

Menard, Jonathan; Gerhardt, S. P.; Myers, C. E.; Reinke, M. L.; Brooks, A.; Mardenfeld, M.; NSTX Upgrade Team

2017-10-01

An important goal of the NSTX Upgrade (NSTX-U) research program is to characterize energy confinement in the low-aspect-ratio spherical tokamak configuration over a significantly expanded range of plasma current, toroidal field, and heating power, while increasing flattop durations up to 5 seconds. However, the narrowing of the scrape-off layer at higher current combined with an improved understanding of expected halo-current loads has motivated a significant re-design of NSTX-U plasma facing components in the high-heat-flux regions of the divertor. In order to reduce the expected divertor heat flux to acceptable levels, a combination of mitigation techniques will be used: increased divertor poloidal flux expansion, increased divertor radiation, and controlled strike-point sweeping. The machine requirements for these various mitigation techniques are studied here using a newly implemented reduced heat-flux model. Systematic equilibrium scans are used to quantify the required divertor coil currents and to verify vertical stability for a range of plasma shapes. Free-boundary control schemes to constrain the strike-point location and field-line angle-of-incidence will also be discussed. Work supported by DOE contract DE-AC02- 09CH11466.

Dangerous nutrients: evolution of phytoplankton resource uptake subject to virus attack.

PubMed

Menge, Duncan N L; Weitz, Joshua S

2009-03-07

Phytoplankton need multiple resources to grow and reproduce (such as nitrogen, phosphorus, and iron), but the receptors through which they acquire resources are, in many cases, the same channels through which viruses attack. Therefore, phytoplankton can face a bottom-up vs. top-down tradeoff in receptor allocation: Optimize resource uptake or minimize virus attack? We investigate this top-down vs. bottom-up tradeoff using an evolutionary ecology model of multiple essential resources, specialist viruses that attack through the resource receptors, and a phytoplankton population that can evolve to alter the fraction of receptors used for each resource/virus type. Without viruses present the singular continuously stable strategy is to allocate receptors such that resources are co-limiting, which also minimizes the equilibrium concentrations of both resources. Only one virus type can be present at equilibrium (because phytoplankton, in this model, are a single resource for viruses), and when a virus type is present, it controls the equilibrium phytoplankton population size. Despite this top-down control on equilibrium densities, bottom-up control determines the evolutionary outcome. Regardless of which virus type is present, the allocation strategy that yields co-limitation between the two resources is continuously stable. This is true even when the virus type attacking through the limiting resource channel is present, even though selection for co-limitation in this case decreases the equilibrium phytoplankton population and does not decrease the equilibrium concentration of the limiting resource. Therefore, although moving toward co-limitation and decreasing the equilibrium concentration of the limiting resource often co-occur in models, it is co-limitation, and not necessarily the lowest equilibrium concentration of the limiting resource, that is the result of selection. This result adds to the growing body of literature suggesting that co-limitation at equilibrium is a winning strategy.

The ESS and replicator equation in matrix games under time constraints.

PubMed

Garay, József; Cressman, Ross; Móri, Tamás F; Varga, Tamás

2018-06-01

Recently, we introduced the class of matrix games under time constraints and characterized the concept of (monomorphic) evolutionarily stable strategy (ESS) in them. We are now interested in how the ESS is related to the existence and stability of equilibria for polymorphic populations. We point out that, although the ESS may no longer be a polymorphic equilibrium, there is a connection between them. Specifically, the polymorphic state at which the average strategy of the active individuals in the population is equal to the ESS is an equilibrium of the polymorphic model. Moreover, in the case when there are only two pure strategies, a polymorphic equilibrium is locally asymptotically stable under the replicator equation for the pure-strategy polymorphic model if and only if it corresponds to an ESS. Finally, we prove that a strict Nash equilibrium is a pure-strategy ESS that is a locally asymptotically stable equilibrium of the replicator equation in n-strategy time-constrained matrix games.

Phase-space dynamics of opposition control in wall-bounded turbulent flows

NASA Astrophysics Data System (ADS)

Hwang, Yongyun; Ibrahim, Joseph; Yang, Qiang; Doohan, Patrick

2017-11-01

The phase-space dynamics of wall-bounded shear flow in the presence of opposition control is explored by examining the behaviours of a pair of nonlinear equilibrium solutions (exact coherent structures), edge state and life time of turbulence at low Reynolds numbers. While the control modifies statistics and phase-space location of the edge state and the lower-branch equilibrium solution very little, it is also found to regularise the periodic orbit on the edge state by reverting a period-doubling bifurcation. Only the upper-branch equilibrium solution and mean turbulent state are significantly modified by the control, and, in phase space, they gradually approach the edge state on increasing the control gain. It is found that this behaviour results in a significant reduction of the life time of turbulence, indicating that the opposition control significantly increases the probability that the turbulent solution trajectory passes through the edge state. Finally, it is shown that the opposition control increases the critical Reynolds number of the onset of the equilibrium solutions, indicating its capability of transition delay. This work is sponsored by the Engineering and Physical Sciences Research Council (EPSRC) in the UK (EP/N019342/1).

Thermal equilibrium control by frequent bang-bang modulation.

PubMed

Yang, Cheng-Xi; Wang, Xiang-Bin

2010-05-01

In this paper, we investigate the non-Markovian heat transfer between a weakly damped harmonic oscillator (system) and a thermal bath. When the system is initially in a thermal state and not correlated with the environment, the mean energy of the system always first increases, then oscillates, and finally reaches equilibrium with the bath, no matter what the initial temperature of the system is. Moreover, the heat transfer between the system and the bath can be controlled by fast bang-bang modulation. This modulation does work on the system, and temporarily inverts the direction of heat flow. In this case, the common sense that heat always transfers from hot to cold does not hold any more. At the long time scale, a new dynamic equilibrium is established between the system and the bath. At this equilibrium, the energy of the system can be either higher or lower than its normal equilibrium value. A comprehensive analysis of the relationship between the dynamic equilibrium and the parameters of the modulation as well as the environment is presented.

Elimination of carbon vacancies in 4H-SiC employing thermodynamic equilibrium conditions at moderate temperatures

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

Ayedh, H. M.; Svensson, B. G.; Nipoti, R.

The carbon vacancy (V{sub C}) is a major point defect in high-purity 4H-SiC epitaxial layers limiting the minority charge carrier lifetime. In layers grown by chemical vapor deposition techniques, the V{sub C} concentration is typically in the range of 10{sup 12 }cm{sup −3}, and after device processing at temperatures approaching 2000 °C, it can be enhanced by several orders of magnitude. In the present study, both as-grown layers and a high-temperature processed one have been annealed at 1500 °C and the V{sub C} concentration is demonstrated to be strongly reduced, exhibiting a value of only a few times 10{sup 11 }cm{sup −3} as determinedmore » by deep-level transient spectroscopy measurements. The value is reached already after annealing times on the order of 1 h and is evidenced to reflect thermodynamic equilibrium under C-rich ambient conditions. The physical processes controlling the kinetics for establishment of the V{sub C} equilibrium are estimated to have an activation energy below ∼3 eV and both in-diffusion of carbon interstitials and out-diffusion of V{sub C}'s are discussed as candidates. This concept of V{sub C} elimination is flexible and readily integrated in a materials and device processing sequence.« less

Nonequilibrium Tricritical Point in a System with Long-Range Interactions

NASA Astrophysics Data System (ADS)

Antoniazzi, Andrea; Fanelli, Duccio; Ruffo, Stefano; Yamaguchi, Yoshiyuki Y.

2007-07-01

Systems with long-range interactions display a short-time relaxation towards quasistationary states whose lifetime increases with system size. With reference to the Hamiltonian mean field model, we here show that a maximum entropy principle, based on Lynden-Bell’s pioneering idea of “violent relaxation,” predicts the presence of out-of-equilibrium phase transitions separating the relaxation towards homogeneous (zero magnetization) or inhomogeneous (nonzero magnetization) quasistationary states. When varying the initial condition within a family of “water bags” with different initial magnetization and energy, first- and second-order phase transition lines are found that merge at an out-of-equilibrium tricritical point. Metastability is theoretically predicted and numerically checked around the first-order phase transition line.

Study of chaos in chaotic satellite systems

NASA Astrophysics Data System (ADS)

Khan, Ayub; Kumar, Sanjay

2018-01-01

In this paper, we study the qualitative behaviour of satellite systems using bifurcation diagrams, Poincaré section, Lyapunov exponents, dissipation, equilibrium points, Kaplan-Yorke dimension etc. Bifurcation diagrams with respect to the known parameters of satellite systems are analysed. Poincaré sections with different sowing axes of the satellite are drawn. Eigenvalues of Jacobian matrices for the satellite system at different equilibrium points are calculated to justify the unstable regions. Lyapunov exponents are estimated. From these studies, chaos in satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the considered system.

Space and time renormalization in phase transition dynamics

DOE PAGES

Francuz, Anna; Dziarmaga, Jacek; Gardas, Bartłomiej; ...

2016-02-18

Here, when a system is driven across a quantum critical point at a constant rate, its evolution must become nonadiabatic as the relaxation time τ diverges at the critical point. According to the Kibble-Zurek mechanism (KZM), the emerging post-transition excited state is characterized by a finite correlation length ξˆ set at the time tˆ=τˆ when the critical slowing down makes it impossible for the system to relax to the equilibrium defined by changing parameters. This observation naturally suggests a dynamical scaling similar to renormalization familiar from the equilibrium critical phenomena. We provide evidence for such KZM-inspired spatiotemporal scaling by investigatingmore » an exact solution of the transverse field quantum Ising chain in the thermodynamic limit.« less

Trajectory-Based Loads for the Ares I-X Test Flight Vehicle

NASA Technical Reports Server (NTRS)

Vause, Roland F.; Starr, Brett R.

2011-01-01

In trajectory-based loads, the structural engineer treats each point on the trajectory as a load case. Distributed aero, inertial, and propulsion forces are developed for the structural model which are equivalent to the integrated values of the trajectory model. Free-body diagrams are then used to solve for the internal forces, or loads, that keep the applied aero, inertial, and propulsion forces in dynamic equilibrium. There are several advantages to using trajectory-based loads. First, consistency is maintained between the integrated equilibrium equations of the trajectory analysis and the distributed equilibrium equations of the structural analysis. Second, the structural loads equations are tied to the uncertainty model for the trajectory systems analysis model. Atmosphere, aero, propulsion, mass property, and controls uncertainty models all feed into the dispersions that are generated for the trajectory systems analysis model. Changes in any of these input models will affect structural loads response. The trajectory systems model manages these inputs as well as the output from the structural model over thousands of dispersed cases. Large structural models with hundreds of thousands of degrees of freedom would execute too slowly to be an efficient part of several thousand system analyses. Trajectory-based loads provide a means for the structures discipline to be included in the integrated systems analysis. Successful applications of trajectory-based loads methods for the Ares I-X vehicle are covered in this paper. Preliminary design loads were based on 2000 trajectories using Monte Carlo dispersions. Range safety loads were tied to 8423 malfunction turn trajectories. In addition, active control system loads were based on 2000 preflight trajectories using Monte Carlo dispersions.

Region stability analysis and tracking control of memristive recurrent neural network.

PubMed

Bao, Gang; Zeng, Zhigang; Shen, Yanjun

2018-02-01

Memristor is firstly postulated by Leon Chua and realized by Hewlett-Packard (HP) laboratory. Research results show that memristor can be used to simulate the synapses of neurons. This paper presents a class of recurrent neural network with HP memristors. Firstly, it shows that memristive recurrent neural network has more compound dynamics than the traditional recurrent neural network by simulations. Then it derives that n dimensional memristive recurrent neural network is composed of [Formula: see text] sub neural networks which do not have a common equilibrium point. By designing the tracking controller, it can make memristive neural network being convergent to the desired sub neural network. At last, two numerical examples are given to verify the validity of our result. Copyright © 2017 Elsevier Ltd. All rights reserved.

Temperature anisotropy at equilibrium reveals nonlocal entropic contributions to interfacial properties.

PubMed

Wilhelmsen, Øivind; Trinh, Thuat T; Lervik, Anders

2018-01-01

Density gradient theory for fluids has played a key role in the study of interfacial phenomena for a century. In this work, we revisit its fundamentals by examining the vapor-liquid interface of argon, represented by the cut and shifted Lennard-Jones fluid. The starting point has traditionally been a Helmholtz energy functional using mass densities as arguments. By using rather the internal energy as starting point and including the entropy density as an additional argument, following thereby the phenomenological approach from classical thermodynamics, the extended theory suggests that the configurational part of the temperature has different contributions from the parallel and perpendicular directions at the interface, even at equilibrium. We find a similar anisotropy by examining the configurational temperature in molecular dynamics simulations and obtain a qualitative agreement between theory and simulations. The extended theory shows that the temperature anisotropy originates in nonlocal entropic contributions, which are currently missing from the classical theory. The nonlocal entropic contributions discussed in this work are likely to play a role in the description of both equilibrium and nonequilibrium properties of interfaces. At equilibrium, they influence the temperature- and curvature-dependence of the surface tension. Across the vapor-liquid interface of the Lennard Jones fluid, we find that the maximum in the temperature anisotropy coincides precisely with the maximum in the thermal resistivity relative to the equimolar surface, where the integral of the thermal resistivity gives the Kapitza resistance. This links the temperature anisotropy at equilibrium to the Kapitza resistance of the vapor-liquid interface at nonequilibrium.

Temperature anisotropy at equilibrium reveals nonlocal entropic contributions to interfacial properties

NASA Astrophysics Data System (ADS)

Wilhelmsen, Øivind; Trinh, Thuat T.; Lervik, Anders

2018-01-01

Density gradient theory for fluids has played a key role in the study of interfacial phenomena for a century. In this work, we revisit its fundamentals by examining the vapor-liquid interface of argon, represented by the cut and shifted Lennard-Jones fluid. The starting point has traditionally been a Helmholtz energy functional using mass densities as arguments. By using rather the internal energy as starting point and including the entropy density as an additional argument, following thereby the phenomenological approach from classical thermodynamics, the extended theory suggests that the configurational part of the temperature has different contributions from the parallel and perpendicular directions at the interface, even at equilibrium. We find a similar anisotropy by examining the configurational temperature in molecular dynamics simulations and obtain a qualitative agreement between theory and simulations. The extended theory shows that the temperature anisotropy originates in nonlocal entropic contributions, which are currently missing from the classical theory. The nonlocal entropic contributions discussed in this work are likely to play a role in the description of both equilibrium and nonequilibrium properties of interfaces. At equilibrium, they influence the temperature- and curvature-dependence of the surface tension. Across the vapor-liquid interface of the Lennard Jones fluid, we find that the maximum in the temperature anisotropy coincides precisely with the maximum in the thermal resistivity relative to the equimolar surface, where the integral of the thermal resistivity gives the Kapitza resistance. This links the temperature anisotropy at equilibrium to the Kapitza resistance of the vapor-liquid interface at nonequilibrium.

Isometric torque-angle relationship and movement-related activity of human elbow flexors: implications for the equilibrium-point hypothesis.

PubMed

Hasan, Z; Enoka, R M

1985-01-01

Since the moment arms for the elbow-flexor muscles are longest at intermediate positions of the elbow and shorter at the extremes of the range of motion, it was expected that the elbow torque would also show a peak at an intermediate angle provided the activity of the flexor muscles remained constant. We measured the isometric elbow torque at different elbow angles while the subject attempted to keep constant the electromyographic activity (EMG) of the brachioradialis muscle. The torque-angle relationship thus obtained exhibited a peak, as expected, but the shape of the relationship varied widely among subjects. This was due in part to differences in the variation of the biceps brachii EMG with elbow angle among the different subjects. The implications of these observations for the equilibrium-point hypothesis of movement were investigated as follows. The subject performed elbow movements in the presence of an external torque (which tended to extend the elbow joint) provided by a weight-and-pulley arrangement. We found in the case of flexion movements that invariably there was a transient increase in flexor EMG, as would seem necessary for initiating the movement. However, the steady-state EMG after the movement could be greater or less than the pre-movement EMG. Specifically, the least flexor EMG was required for equilibrium in the intermediate range of elbow angles, compared to the extremes of the range of motion. The EMG-angle relationship, however, varied with the muscle and the subject. The observation that the directions of change in the transient and the steady-state EMG are independent of each other militates against the generality of the equilibrium-point hypothesis. However, a form of the hypothesis which includes the effects of the stretch reflex is not contradicted by this observation.

Adaptation in a rotating artificial gravity environment

NASA Technical Reports Server (NTRS)

Lackner, J. R.; DiZio, P.

1998-01-01

The centripetal force generated by a rotating space vehicle is a potential source of artificial gravity. Minimizing the cost of such a vehicle dictates using the smallest radius and highest rotation rate possible, but head movements made at high rotation rates generate disorienting, nauseogenic cross-coupled semicircular canal stimulation. Early studies suggested 3 or 4 rpm as the highest rate at which humans could adapt to this vestibular stimulus. These studies neglected the concomitant Coriolis force actions on the head/neck system. We assessed non-vestibular Coriolis effects by measuring arm and leg movements made in the center of a rotating room turning at 10 rpm and found that movement endpoints and trajectories are initially deviated; however, subjects readily adapt with 10-20 additional movements, even without seeing their errors. Equilibrium point theories of motor control errantly predict that Coriolis forces will not cause movement endpoint errors so that subjects will not have to adapt their reaching movements during rotation. Adaptation of movement trajectory acquired during Coriolis force perturbations of one arm transfers to the unexposed arm but there is no intermanual transfer of endpoint adaptation indicating that neuromotor representations of movement endpoint and trajectory are separable and can adapt independently, also contradictory to equilibrium point theories. Touching a surface at the end of reaching movements is required for complete endpoint adaptation in darkness but trajectory adapts completely with or without terminal contact. We have also made the first kinematic measurements of unconstrained head movements during rotation, these movements show rapid adaptation to Coriolis force perturbations. Our results point to methods for achieving full compensation for rotation up to 10 rpm. Copyright 1998 Published by Elsevier Science B.V.

Adaptation in a rotating artificial gravity environment.

PubMed

Lackner, J R; DiZio, P

1998-11-01

The centripetal force generated by a rotating space vehicle is a potential source of artificial gravity. Minimizing the cost of such a vehicle dictates using the smallest radius and highest rotation rate possible, but head movements made at high rotation rates generate disorienting, nauseogenic cross-coupled semicircular canal stimulation. Early studies suggested 3 or 4 rpm as the highest rate at which humans could adapt to this vestibular stimulus. These studies neglected the concomitant Coriolis force actions on the head/neck system. We assessed non-vestibular Coriolis effects by measuring arm and leg movements made in the center of a rotating room turning at 10 rpm and found that movement endpoints and trajectories are initially deviated; however, subjects readily adapt with 10-20 additional movements, even without seeing their errors. Equilibrium point theories of motor control errantly predict that Coriolis forces will not cause movement endpoint errors so that subjects will not have to adapt their reaching movements during rotation. Adaptation of movement trajectory acquired during Coriolis force perturbations of one arm transfers to the unexposed arm but there is no intermanual transfer of endpoint adaptation indicating that neuromotor representations of movement endpoint and trajectory are separable and can adapt independently, also contradictory to equilibrium point theories. Touching a surface at the end of reaching movements is required for complete endpoint adaptation in darkness but trajectory adapts completely with or without terminal contact. We have also made the first kinematic measurements of unconstrained head movements during rotation, these movements show rapid adaptation to Coriolis force perturbations. Our results point to methods for achieving full compensation for rotation up to 10 rpm. Copyright 1998 Published by Elsevier Science B.V.

Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

NASA Astrophysics Data System (ADS)

Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

2018-07-01

The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

Understanding resistant effect of mosquito on fumigation strategy in dengue control program

NASA Astrophysics Data System (ADS)

Aldila, D.; Situngkir, N.; Nareswari, K.

2018-01-01

A mathematical model of dengue disease transmission will be introduced in this talk with involving fumigation intervention into mosquito population. Worsening effect of uncontrolled fumigation in the form of resistance of mosquito to fumigation chemicals will also be included into the model to capture the reality in the field. Deterministic approach in a 9 dimensional of ordinary differential equation will be used. Analytical result about the existence and local stability of the equilibrium points followed with the basic reproduction number will be discussed. Some numerical result will be performed for some scenario to give a better interpretation for the analytical results.

Control of Low Melting Point Mno-Sio2-Al2o3 Inclusions in Low Carbon Thin-Strip Continuous Casting Steel

NASA Astrophysics Data System (ADS)

Chen, Jing; Zhu, Qing; Huang, Di; Zheng, Shaobo; Zhang, Jieyu; Li, Huigai

2017-09-01

There is a significant difference in the demand for molten steel quality between thin-strip continuous casting and traditional continuous casting. In order to make sure the better surface quality of the thin strips, to generate an oxidation film on the surface of cooling roller is required. This will require that the higher oxygen potential in molten steel and inclusions with low melting point. In this article, the possibility of producing low-melting inclusions which is mainly consisted of SiO2 and MnO is studied by controlling the initial oxygen potential and addition order of deoxidizing alloys. The interaction activity between each component in the ternary system of Al2O3-SiO2-MnO is obtained by Action Concentration model. The equal [Mn], [Si], [O], [Al] curve under the temperature of 1823K and equilibrium condition in ternary system of Al2O3-SiO2-MnO is obtained by relative thermodynamic calculation as well. The control method for getting the low-melting point inclusion is as below. While the weight percentage of Si is 0.35% and the one of Mn is 0.90%, in order to maintain the melting point of inclusion around 1200°C, the free oxygen potential in melted steel F[O] should be maintained between 0.002% ∼ 0.004%. On the contrary, the requirement for acid dissolved [Al] content in melted steel is as low as 0.0001% ∼ 0.0005%.

Perspectives: Black Holes

NASA Technical Reports Server (NTRS)

Dolan, Joseph F.; Fisher, Richard R. (Technical Monitor)

2001-01-01

When asked to discuss Cyg XR-1, E. E. Salpeter once concluded, 'A black hole in Cyg X(R)-1 is the most conservative hypothesis.' Recent observations now make it likely that a black hole in Cyg XR-1 is the only hypothesis tenable. Chandrasekhar first showed that compact stars - those with the inward force of gravity on their outer layers balanced by the pressure generated by the Pauli exclusion principle acting on its electrons (in white dwarfs) or nucleons (in neutron stars) - have a maximum mass. Equilibrium is achieved at a minimum of the total energy of the star, which is the sum of the positive Fermi energy and the negative gravitational energy. The maximum mass attainable in equilibrium is found by setting E = 0: M(max) = 1.5 M(Sun). If the mass of the star is larger than this, then E can be decreased without bound by decreasing the star's radius and increasing its (negative) gravitational energy. No equilibrium value of the radius exist, and general relativity predicts that gravitational collapse to a point occurs. This point singularity is a black hole.

Equation of state of detonation products based on statistical mechanical theory

NASA Astrophysics Data System (ADS)

Zhao, Yanhong; Liu, Haifeng; Zhang, Gongmu; Song, Haifeng

2015-06-01

The equation of state (EOS) of gaseous detonation products is calculated using Ross's modification of hard-sphere variation theory and the improved one-fluid van der Waals mixture model. The condensed phase of carbon is a mixture of graphite, diamond, graphite-like liquid and diamond-like liquid. For a mixed system of detonation products, the free energy minimization principle is used to calculate the equilibrium compositions of detonation products by solving chemical equilibrium equations. Meanwhile, a chemical equilibrium code is developed base on the theory proposed in this article, and then it is used in the three typical calculations as follow: (i) Calculation for detonation parameters of explosive, the calculated values of detonation velocity, the detonation pressure and the detonation temperature are in good agreement with experimental ones. (ii) Calculation for isentropic unloading line of RDX explosive, whose starting points is the CJ point. Comparison with the results of JWL EOS it is found that the calculated value of gamma is monotonically decreasing using the presented theory in this paper, while double peaks phenomenon appears using JWL EOS.

Equation of state of detonation products based on statistical mechanical theory

NASA Astrophysics Data System (ADS)

Zhao, Yanhong; Liu, Haifeng; Zhang, Gongmu; Song, Haifeng; Iapcm Team

2013-06-01

The equation of state (EOS) of gaseous detonation products is calculated using Ross's modification of hard-sphere variation theory and the improved one-fluid van der Waals mixture model. The condensed phase of carbon is a mixture of graphite, diamond, graphite-like liquid and diamond-like liquid. For a mixed system of detonation products, the free energy minimization principle is used to calculate the equilibrium compositions of detonation products by solving chemical equilibrium equations. Meanwhile, a chemical equilibrium code is developed base on the theory proposed in this article, and then it is used in the three typical calculations as follow: (i) Calculation for detonation parameters of explosive, the calculated values of detonation velocity, the detonation pressure and the detonation temperature are in good agreement with experimental ones. (ii) Calculation for isentropic unloading line of RDX explosive, whose starting points is the CJ point. Comparison with the results of JWL EOS it is found that the calculated value of gamma is monotonically decreasing using the presented theory in this paper, while double peaks phenomenon appears using JWL EOS.

Punishment in a complementarity game

NASA Astrophysics Data System (ADS)

Li, W.; Cai, X.; Wang, Q. A.

2006-05-01

We study the effects arisen from the punishment in an evolutionary complementarity game. Each round one member of population “buyers” deals with a randomly chosen member of population “sellers”. When the buyer's offer is greater than the seller's, a deal is done and both players are rewarded by gaining some points. Otherwise the transaction is not successful and both will lose certain points as punishment. Our simulations indicate that the resulting equilibrium of the game with punishment embedded is remarkably time-delayed compared to the counterpart of the non-punishment game. However, the median fee and the success rate of deals at the equilibrium remain nearly unchanged in various cases of games with different degrees of punishment, whether severe or not. Symmetry, between the two populations, and the equilibrium value can still be maintained when the members of both of them are punished fairly in any failed transaction. If they are done in a different manner, namely, the members of one population are subject to very severe punishment whereas their opponents receive less or no punishment at all, the latter in most cases will be better off.

Equilibrium control of nonlinear verticum-type systems, applied to integrated pest control.

PubMed

Molnár, S; Gámez, M; López, I; Cabello, T

2013-08-01

Linear verticum-type control and observation systems have been introduced for modelling certain industrial systems, consisting of subsystems, vertically connected by certain state variables. Recently the concept of verticum-type observation systems and the corresponding observability condition have been extended by the authors to the nonlinear case. In the present paper the general concept of a nonlinear verticum-type control system is introduced, and a sufficient condition for local controllability to equilibrium is obtained. In addition to a usual linearization, the basic idea is a decomposition of the control of the whole system into the control of the subsystems. Starting from the integrated pest control model of Rafikov and Limeira (2012) and Rafikov et al. (2012), a nonlinear verticum-type model has been set up an equilibrium control is obtained. Furthermore, a corresponding bioeconomical problem is solved minimizing the total cost of integrated pest control (combining chemical control with a biological one). Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

The change of steel surface chemistry regarding oxygen partial pressure and dew point

NASA Astrophysics Data System (ADS)

Norden, Martin; Blumenau, Marc; Wuttke, Thiemo; Peters, Klaus-Josef

2013-04-01

By investigating the surface state of a Ti-IF, TiNb-IF and a MnCr-DP after several series of intercritical annealing, the impact of the annealing gas composition on the selective oxidation process is discussed. On behalf of the presented results, it can be concluded that not the general oxygen partial pressure in the annealing furnace, which is a result of the equilibrium reaction of water and hydrogen, is the main driving force for the selective oxidation process. It is shown that the amounts of adsorbed gases at the strip surface and the effective oxygen partial pressure resulting from the adsorbed gases, which is mainly dependent on the water content of the annealing furnace, is driving the selective oxidation processes occurring during intercritical annealing. Thus it is concluded, that for industrial applications the dew point must be the key parameter value for process control.

Accelerated Self-Replication under Non-Equilibrium, Periodic Energy Delivery

NASA Astrophysics Data System (ADS)

Zhang, Rui; Olvera de La Cruz, Monica

2014-03-01

Self-replication is a remarkable phenomenon in nature that has fascinated scientists for decades. In a self-replicating system, the original units are attracted to a template, which induce their binding. In equilibrium, the energy required to disassemble the newly assembled copy from the mother template is supplied by thermal energy. The possibility of optimizing self-replication is explored by controlling the frequency at which energy is supplied to the system. A model system inspired by a class of light switchable colloids is considered where light is used to control the interactions. Conditions under which self-replication can be significantly more effective under non-equilibrium, cyclic energy delivery than under equilibrium constant energy conditions are identified. Optimal self-replication does not require constant energy expenditure. Instead, the proper timing at which energy is delivered to the system is an essential controllable parameter to induce high replication rates. This work was supported by the Non-Equilibrium Energy Research Center (NERC), which is an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0000989.

Soil-moisture constants and their variation

Treesearch

Walter M. Broadfoot; Hubert D. Burke

1958-01-01

"Constants" like field capacity, liquid limit, moisture equivalent, and wilting point are used by most students and workers in soil moisture. These constants may be equilibrium points or other values that describe soil moisture. Their values under specific soil and cover conditions have been discussed at length in the literature, but few general analyses and...

Artificial equilibrium points in binary asteroid systems with continuous low-thrust

NASA Astrophysics Data System (ADS)

Bu, Shichao; Li, Shuang; Yang, Hongwei

2017-08-01

The positions and dynamical characteristics of artificial equilibrium points (AEPs) in the vicinity of a binary asteroid with continuous low-thrust are studied. The restricted ellipsoid-ellipsoid model of binary system is employed for the binary asteroid system. The positions of AEPs are obtained by this model. It is found that the set of the point L1 or L2 forms a shape of an ellipsoid while the set of the point L3 forms a shape like a "banana". The effect of the continuous low-thrust on the feasible region of motion is analyzed by zero velocity curves. Because of using the low-thrust, the unreachable region can become reachable. The linearized equations of motion are derived for stability's analysis. Based on the characteristic equation of the linearized equations, the stability conditions are derived. The stable regions of AEPs are investigated by a parametric analysis. The effect of the mass ratio and ellipsoid parameters on stable region is also discussed. The results show that the influence of the mass ratio on the stable regions is more significant than the parameters of ellipsoid.

Diffusion in jammed particle packs

NASA Astrophysics Data System (ADS)

Bolintineanu, Dan S.; Silbert, Leonardo E.; Grest, Gary S.; Lechman, Jeremy B.

2015-03-01

Diffusive transport in jammed particle packs is of interest for a number of applications, as well as being a potential indicator of structural properties near the jamming point. To this end, we report stochastic simulations of equilibrium diffusion through monodisperse sphere packs near the jamming point in the limit of a perfectly insulating surrounding medium. The time dependence of various diffusion properties is resolved over several orders of magnitude. Two time regimes of expected Fickian diffusion are observed, separated by an intermediate regime of anomalous diffusion. This intermediate regime grows as the particle volume fraction approaches the critical jamming transition. The diffusion behavior is fully controlled by the extent of the contacts between neighboring particles, which in turn depend on proximity to the jamming point. In particular, the mean first passage time associated with the escape of random walkers between neighboring particles is shown to control both the time to recover Fickian diffusion and the long time diffusivity. Scaling laws are established that relate these quantities to the difference between the actual and critical jamming volume fractions. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's NNSA under Contract DE- AC04-94AL85000.

Energy flow in non-equilibrium conformal field theory

NASA Astrophysics Data System (ADS)

Bernard, Denis; Doyon, Benjamin

2012-09-01

We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.

Minimal energy configurations of gravitationally interacting rigid bodies

NASA Astrophysics Data System (ADS)

Moeckel, Richard

2017-05-01

Consider a collection of n rigid, massive bodies interacting according to their mutual gravitational attraction. A relative equilibrium motion is one where the entire configuration rotates rigidly and uniformly about a fixed axis in R^3. Such a motion is possible only for special positions and orientations of the bodies. A minimal energy motion is one which has the minimum possible energy in its fixed angular momentum level. While every minimal energy motion is a relative equilibrium motion, the main result here is that a relative equilibrium motion of n≥3 disjoint rigid bodies is never an energy minimizer. This generalizes a known result about point masses to the case of rigid bodies.

A General Method for Automatic Computation of Equilibrium Compositions and Theoretical Rocket Performance of Propellants

NASA Technical Reports Server (NTRS)

Gordon, Sanford; Zeleznik, Frank J.; Huff, Vearl N.

1959-01-01

A general computer program for chemical equilibrium and rocket performance calculations was written for the IBM 650 computer with 2000 words of drum storage, 60 words of high-speed core storage, indexing registers, and floating point attachments. The program is capable of carrying out combustion and isentropic expansion calculations on a chemical system that may include as many as 10 different chemical elements, 30 reaction products, and 25 pressure ratios. In addition to the equilibrium composition, temperature, and pressure, the program calculates specific impulse, specific impulse in vacuum, characteristic velocity, thrust coefficient, area ratio, molecular weight, Mach number, specific heat, isentropic exponent, enthalpy, entropy, and several thermodynamic first derivatives.

Equilibrium and nonequilibrium models on solomon networks with two square lattices

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios γ/ν, β/ν, and 1/ν. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

Realization of atomistic transitions with colloidal nanoparticles using an ultrafast laser

NASA Astrophysics Data System (ADS)

Akguc, Gursoy; Ilday, Serim; Ilday, Omer; Gulseren, Oguz; Makey, Ghaith; Yavuz, Koray

We report on realization of rapid atomistic transitions with colloidal nanoparticles in a setting that constitutes a dissipative far-from-equilibrium system subject to stochastic forces. Large colloidal crystals (comprising hundreds of particles) can be formed and transitions between solid-liquid-gas phases can be observed effortlessly and within seconds. Furthermore, this system allows us to form and dynamically arrest metastable phases such as glassy structures and to controllably transform a crystal pattern from square to hexagonal lattices and vice versa as well as to observe formation and propagation of crystal defects (i.e. line defects, point defects, planar defects). The mechanism largely relies on an interplay between convective forces induced by femtosecond pulses and strong Brownian motion; the former drags the colloids to form and reinforce the crystal and the latter is analogous to lattice vibrations, which makes it possible to observe phase transitions, defect formation and propagation and lattice transformation. This unique system can help us get insight into the mechanisms underlying various solid state phenomena that were previously studied under slowly evolving (within hours/days), near-equilibrium colloidal systems.

Disorder-mediated crowd control in an active matter system

NASA Astrophysics Data System (ADS)

Pinçe, Erçağ; Velu, Sabareesh K. P.; Callegari, Agnese; Elahi, Parviz; Gigan, Sylvain; Volpe, Giovanni; Volpe, Giorgio

2016-03-01

Living active matter systems such as bacterial colonies, schools of fish and human crowds, display a wealth of emerging collective and dynamic behaviours as a result of far-from-equilibrium interactions. The dynamics of these systems are better understood and controlled considering their interaction with the environment, which for realistic systems is often highly heterogeneous and disordered. Here, we demonstrate that the presence of spatial disorder can alter the long-term dynamics in a colloidal active matter system, making it switch between gathering and dispersal of individuals. At equilibrium, colloidal particles always gather at the bottom of any attractive potential; however, under non-equilibrium driving forces in a bacterial bath, the colloids disperse if disorder is added to the potential. The depth of the local roughness in the environment regulates the transition between gathering and dispersal of individuals in the active matter system, thus inspiring novel routes for controlling emerging behaviours far from equilibrium.

A Synthesis of Equilibrium and Historical Models of Landform Development.

ERIC Educational Resources Information Center

Renwick, William H.

1985-01-01

The synthesis of two approaches that can be used in teaching geomorphology is described. The equilibrium approach explains landforms and landform change in terms of equilibrium between landforms and controlling processes. The historical approach draws on climatic geomorphology to describe the effects of Quaternary climatic and tectonic events on…

Lunar Navigation with Libration Point Orbiters and GPS

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2004-01-01

NASA is currently studying a Vision for Space Exploration based on spiral development of robotic and piloted missions to the moon and Mars, but research into how to perform such missions has continued ever since the first era of lunar exploration. One area of study that a number of researchers have pursued is libration point navigation and communication relay concepts. These concepts would appear to support many of NASA's current requirements for navigation and communications coverage for human and robotic spacecraft operating in lunar space and beyond. In trading libration point concepts against other options, designers must consider issues such as the number of spacecraft, required to provide coverage, insertion and stationkeeping costs, power and data rate requirements, frequency allocations, and many others. The libration points, along with a typical cis-lunar trajectory, are equilibrium locations for an infinitesimal mass in the rotating coordinate system that follows the motion of two massive bodies in circular orbits with respect to their common barycenter. There are three co-linear points along the line connecting the massive bodies: between the bodies, beyond the secondary body, and beyond the primary body. The relative distances of these points along the line connecting the bodies depend on the mass ratios. There are also two points that form equilateral triangles with the massive bodies. Ideally, motion in the neighborhood of the co-linear points is unstable, while motion near the equilibrium points is stable. However, in the real world, the motions are highly perturbed so that a satellite will require stationkeeping maneuvers.

Basic and Applied Studies of the RAM Accelerator as a Hypervelocity Projectile Launcher

DTIC Science & Technology

1993-12-10

The quasi-steady, one-dimensional "blackbox" model of thermally choked ram accelerator performance 18 that has been widely used by the authors and...the thermal choke point is assumed to be in equilibrium, the conditions can be determined by an equilibrium chemistry combustion routine. This model ...to operation, the details of the flow field must be examined. I The simplest model of the thermally choked ram accelerator flow field treats the flow

Integrable structure in discrete shell membrane theory

PubMed Central

Schief, W. K.

2014-01-01

We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory. PMID:24808755

Integrable structure in discrete shell membrane theory.

PubMed

Schief, W K

2014-05-08

We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory.

Nonlinear Dynamics and Nucleation Kinetics in Near-Critical Liquids

NASA Technical Reports Server (NTRS)

Patashinski, Alexander Z.; Ratner, Mark A.; Pines, Vladimir

1996-01-01

The objective of our study is to model the nonlinear behavior of a near-critical liquid following a rapid change of the temperature and/or other thermodynamic parameters (pressure, external electric or gravitational field). The thermodynamic critical point is manifested by large, strongly correlated fluctuations of the order parameter (particle density in liquid-gas systems, concentration in binary solutions) in the critical range of scales. The largest critical length scale is the correlation radius r(sub c). According to the scaling theory, r(sub c) increases as r(sub c) = r(sub 0)epsilon(exp -alpha) when the nondimensional distance epsilon = (T - T(sub c))/T(sub c) to the critical point decreases. The normal gravity alters the nature of correlated long-range fluctuations when one reaches epsilon approximately equal to 10(exp -5), and correspondingly the relaxation time, tau(r(sub c)), is approximately equal to 10(exp -3) seconds; this time is short when compared to the typical experimental time. Close to the critical point, a rapid, relatively small temperature change may perturb the thermodynamic equilibrium on many scales. The critical fluctuations have a hierarchical structure, and the relaxation involves many length and time scales. Above the critical point, in the one-phase region, we consider the relaxation of the liquid following a sudden temperature change that simultaneously violates the equilibrium on many scales. Below T(sub c), a non-equilibrium state may include a distribution of small scale phase droplets; we consider the relaxation of such a droplet following a temperature change that has made the phase of the matrix stable.

Bifurcation Analysis Using Rigorous Branch and Bound Methods

NASA Technical Reports Server (NTRS)

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

2014-01-01

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

A unified model of shoot tropism in plants: photo-, gravi- and Propio-ception.

PubMed

Bastien, Renaud; Douady, Stéphane; Moulia, Bruno

2015-02-01

Land plants rely mainly on gravitropism and phototropism to control their posture and spatial orientation. In natural conditions, these two major tropisms act concurrently to create a photogravitropic equilibrium in the responsive organ. Recently, a parsimonious model was developed that accurately predicted the complete gravitropic and proprioceptive control over the movement of different organs in different species in response to gravitational stimuli. Here we show that the framework of this unifying graviproprioceptive model can be readily extended to include phototropism. The interaction between gravitropism and phototropism results in an alignment of the apical part of the organ toward a photogravitropic set-point angle. This angle is determined by a combination of the two directional stimuli, gravity and light, weighted by the ratio between the gravi- and photo-sensitivities of the plant organ. In the model, two dimensionless numbers, the graviproprioceptive number B and the photograviceptive number M, control the dynamics and the shapes of the movement. The extended model agrees well with two sets of detailed quantitative data on photogravitropic equilibrium in oat coleoptiles. It is demonstrated that the influence of light intensity I can be included in the model in a power-law-dependent relationship M(I). The numbers B and M and the related photograviceptive number D are all quantitative genetic traits that can be measured in a straightforward manner, opening the way to the phenotyping of molecular and mechanical aspects of shoot tropism.

A Unified Model of Shoot Tropism in Plants: Photo-, Gravi- and Propio-ception

PubMed Central

Bastien, Renaud; Douady, Stéphane; Moulia, Bruno

2015-01-01

Land plants rely mainly on gravitropism and phototropism to control their posture and spatial orientation. In natural conditions, these two major tropisms act concurrently to create a photogravitropic equilibrium in the responsive organ. Recently, a parsimonious model was developed that accurately predicted the complete gravitropic and proprioceptive control over the movement of different organs in different species in response to gravitational stimuli. Here we show that the framework of this unifying graviproprioceptive model can be readily extended to include phototropism. The interaction between gravitropism and phototropism results in an alignment of the apical part of the organ toward a photogravitropic set-point angle. This angle is determined by a combination of the two directional stimuli, gravity and light, weighted by the ratio between the gravi- and photo-sensitivities of the plant organ. In the model, two dimensionless numbers, the graviproprioceptive number B and the photograviceptive number M, control the dynamics and the shapes of the movement. The extended model agrees well with two sets of detailed quantitative data on photogravitropic equilibrium in oat coleoptiles. It is demonstrated that the influence of light intensity I can be included in the model in a power-law-dependent relationship M(I). The numbers B and M and the related photograviceptive number D are all quantitative genetic traits that can be measured in a straightforward manner, opening the way to the phenotyping of molecular and mechanical aspects of shoot tropism. PMID:25692607

Non-equilibrium freezing behaviour of aqueous systems.

PubMed

MacKenzie, A P

1977-03-29

The tendencies to non-equilibrium freezing behaviour commonly noted in representative aqueous systems derive from bulk and surface properties according to the circumstances. Supercooling and supersaturation are limited by heterogeneous nucleation in the presence of solid impurities. Homogeneous nucleation has been observed in aqueous systems freed from interfering solids. Once initiated, crystal growth is ofter slowed and, very frequently, terminated with increasing viscosity. Nor does ice first formed always succeed in assuming its most stable crystalline form. Many of the more significant measurements on a given systeatter permitting the simultaneous representation of thermodynamic and non-equilibrium properties. The diagram incorporated equilibrium melting points, heterogeneous nucleation temperatures, homogeneous nucleation temperatures, glass transition and devitrification temperatures, recrystallization temperatures, and, where appropriate, solute solubilities and eutectic temperatures. Taken together, the findings on modle systems aid the identification of the kinetic and thermodynamic factors responsible for the freezing-thawing survival of living cells.

Phylogenies support out-of-equilibrium models of biodiversity.

PubMed

Manceau, Marc; Lambert, Amaury; Morlon, Hélène

2015-04-01

There is a long tradition in ecology of studying models of biodiversity at equilibrium. These models, including the influential Neutral Theory of Biodiversity, have been successful at predicting major macroecological patterns, such as species abundance distributions. But they have failed to predict macroevolutionary patterns, such as those captured in phylogenetic trees. Here, we develop a model of biodiversity in which all individuals have identical demographic rates, metacommunity size is allowed to vary stochastically according to population dynamics, and speciation arises naturally from the accumulation of point mutations. We show that this model generates phylogenies matching those observed in nature if the metacommunity is out of equilibrium. We develop a likelihood inference framework that allows fitting our model to empirical phylogenies, and apply this framework to various mammalian families. Our results corroborate the hypothesis that biodiversity dynamics are out of equilibrium. © 2015 John Wiley & Sons Ltd/CNRS.

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

NASA Technical Reports Server (NTRS)

Glass, Christopher E.

1990-01-01

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

NASA Astrophysics Data System (ADS)

Glass, Christopher E.

1990-08-01

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

A comparative study of the adsorption equilibrium of progesterone by a carbon black and a commercial activated carbon

NASA Astrophysics Data System (ADS)

Valenzuela-Calahorro, Cristóbal; Navarrete-Guijosa, Antonio; Stitou, Mostafa; Cuerda-Correa, Eduardo M.

2007-04-01

In this paper the adsorption process of a natural steroid hormone (progesterone) by a carbon black and a commercial activated carbon has been studied. The corresponding equilibrium isotherms have been analyzed according to a previously proposed model which establishes a kinetic law satisfactorily fitting the C versus t isotherms. The analysis of the experimental data points out the existence of two well-defined sections in the equilibrium isotherms. A general equation including these two processes has been proposed, the global adsorption process being fitted to such equation. From the values of the kinetic equilibrium constant so obtained, values of standard average adsorption enthalpy ( ΔH°) and entropy ( ΔS°) have been calculated. Finally, information related to variations of differential adsorption enthalpy ( ΔH) and entropy ( ΔS) with the surface coverage fraction ( θ) was obtained by using the corresponding Clausius-Clapeyron equations.

Control of Chemical Equilibrium by Solvent: A Basis for Teaching Physical Chemistry of Solutions

ERIC Educational Resources Information Center

Prezhdo, Oleg V.; Craig, Colleen F.; Fialkov, Yuriy; Prezhdo, Victor V.

2007-01-01

The study demonstrates that the solvent present in a system can highly alter and control the chemical equilibrium of a system. The results show that the dipole moment and polarizibility of a system can be highly altered by using different mixed solvents.

Analysis of the dynamics of multi-team Bertrand game with heterogeneous players

NASA Astrophysics Data System (ADS)

Ding, Zhanwen; Hang, Qinglan; Yang, Honglin

2011-06-01

In this article, we study the dynamics of a two-team Bertrand game with players having heterogeneous expectations. We study the equilibrium solutions and the conditions of their locally asymptotic stability. Numerical simulations are used to illustrate the complex behaviours of the proposed model of the Bertrand game. We demonstrate that some parameters of the model have great influence on the stability of Nash equilibrium and on the speed of convergence to Nash equilibrium. The chaotic behaviour of the model has been controlled by using feedback control method.

Controlling Metastable Native Point-Defect Populations in Cu(In,Ga)Se 2 and Cu 2ZnSnSe 4 Materials and Solar Cells through Voltage-Bias Annealing

DOE PAGES

Teeter, Glenn; Harvey, Steve P.; Johnston, Steve

2017-01-30

Our contribution describes the influence of low-temperature annealing with and without applied voltage bias on thin-film Cu 2ZnSnSe 4 (CZTSe), Cu(In,Ga)Se 2 (CIGS), and CdS material properties and solar cell performance. In order to quantify the effects of cation disorder on CZTSe device performance, completed devices were annealed under open-circuit conditions at various temperatures from 110 degrees C to 215 degrees C and subsequently quenched. Measurements on these devices document systematic, reversible changes in solar-cell performance consistent with a reduction in CZTSe band tails at lower annealing temperatures. CIGS and CZTSe solar cells were also annealed at various temperatures (200more » degrees C for CIGS and 110 degrees C-215 degrees C for CZTSe) and subsequently quenched with continuously applied voltage bias to explore the effects of non-equilibrium annealing conditions. For both absorbers, large reversible changes in device characteristics correlated with the magnitude and sign of the applied voltage bias were observed. For CZTSe devices, the voltage-bias annealing (VBA) produced reversible changes in open-circuit voltage (VOC) from 289 meV to 446 meV. For CIGS solar cells, even larger changes were observed in device performance: photovoltaic (PV) conversion efficiency of the CIGS device varied from below 3% to above 15%, with corresponding changes in CIGS hole density of about three orders of magnitude. Findings from these VBA experiments are interpreted in terms of changes to the metastable point-defect populations that control key properties in the absorber layers, and in the CdS buffer layer. Computational device modeling was performed to assess the impacts of cation disorder on the CZTSe VOC deficit, and to elucidate the effects of VBA treatments on metastable point defect populations in CZTSe, CIGS, and CdS. Our results indicate that band tails impose important limitations on CZTSe device performance. Device modeling results also indicate that non-equilibrium processing conditions including the effects of voltage bias can dramatically alter point-defect-mediated opto-electronic properties of semiconductors. Implications for optimization of PV materials and connections to long-term stability of PV devices are discussed.« less

Controlling metastable native point-defect populations in Cu(In,Ga)Se2 and Cu2ZnSnSe4 materials and solar cells through voltage-bias annealing

NASA Astrophysics Data System (ADS)

Teeter, G.; Harvey, S. P.; Johnston, S.

2017-01-01

This contribution describes the influence of low-temperature annealing with and without applied voltage bias on thin-film Cu2ZnSnSe4 (CZTSe), Cu(In,Ga)Se2 (CIGS), and CdS material properties and solar cell performance. To quantify the effects of cation disorder on CZTSe device performance, completed devices were annealed under open-circuit conditions at various temperatures from 110 °C to 215 °C and subsequently quenched. Measurements on these devices document systematic, reversible changes in solar-cell performance consistent with a reduction in CZTSe band tails at lower annealing temperatures. CIGS and CZTSe solar cells were also annealed at various temperatures (200 °C for CIGS and 110 °C-215 °C for CZTSe) and subsequently quenched with continuously applied voltage bias to explore the effects of non-equilibrium annealing conditions. For both absorbers, large reversible changes in device characteristics correlated with the magnitude and sign of the applied voltage bias were observed. For CZTSe devices, the voltage-bias annealing (VBA) produced reversible changes in open-circuit voltage (VOC) from 289 meV to 446 meV. For CIGS solar cells, even larger changes were observed in device performance: photovoltaic (PV) conversion efficiency of the CIGS device varied from below 3% to above 15%, with corresponding changes in CIGS hole density of about three orders of magnitude. Findings from these VBA experiments are interpreted in terms of changes to the metastable point-defect populations that control key properties in the absorber layers, and in the CdS buffer layer. Computational device modeling was performed to assess the impacts of cation disorder on the CZTSe VOC deficit, and to elucidate the effects of VBA treatments on metastable point defect populations in CZTSe, CIGS, and CdS. Results indicate that band tails impose important limitations on CZTSe device performance. Device modeling results also indicate that non-equilibrium processing conditions including the effects of voltage bias can dramatically alter point-defect-mediated opto-electronic properties of semiconductors. Implications for optimization of PV materials and connections to long-term stability of PV devices are discussed.

Controlling Metastable Native Point-Defect Populations in Cu(In,Ga)Se 2 and Cu 2ZnSnSe 4 Materials and Solar Cells through Voltage-Bias Annealing

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

Teeter, Glenn; Harvey, Steve P.; Johnston, Steve

Our contribution describes the influence of low-temperature annealing with and without applied voltage bias on thin-film Cu 2ZnSnSe 4 (CZTSe), Cu(In,Ga)Se 2 (CIGS), and CdS material properties and solar cell performance. In order to quantify the effects of cation disorder on CZTSe device performance, completed devices were annealed under open-circuit conditions at various temperatures from 110 degrees C to 215 degrees C and subsequently quenched. Measurements on these devices document systematic, reversible changes in solar-cell performance consistent with a reduction in CZTSe band tails at lower annealing temperatures. CIGS and CZTSe solar cells were also annealed at various temperatures (200more » degrees C for CIGS and 110 degrees C-215 degrees C for CZTSe) and subsequently quenched with continuously applied voltage bias to explore the effects of non-equilibrium annealing conditions. For both absorbers, large reversible changes in device characteristics correlated with the magnitude and sign of the applied voltage bias were observed. For CZTSe devices, the voltage-bias annealing (VBA) produced reversible changes in open-circuit voltage (VOC) from 289 meV to 446 meV. For CIGS solar cells, even larger changes were observed in device performance: photovoltaic (PV) conversion efficiency of the CIGS device varied from below 3% to above 15%, with corresponding changes in CIGS hole density of about three orders of magnitude. Findings from these VBA experiments are interpreted in terms of changes to the metastable point-defect populations that control key properties in the absorber layers, and in the CdS buffer layer. Computational device modeling was performed to assess the impacts of cation disorder on the CZTSe VOC deficit, and to elucidate the effects of VBA treatments on metastable point defect populations in CZTSe, CIGS, and CdS. Our results indicate that band tails impose important limitations on CZTSe device performance. Device modeling results also indicate that non-equilibrium processing conditions including the effects of voltage bias can dramatically alter point-defect-mediated opto-electronic properties of semiconductors. Implications for optimization of PV materials and connections to long-term stability of PV devices are discussed.« less

Surfactant-enhanced remediation of a trichloroethene-contaminated aquifer. 1. Transport of triton X-100

USGS Publications Warehouse

Smith, J.A.; Sahoo, D.; Mclellan, H.M.; Imbrigiotta, T.E.

1997-01-01

Transport of a nonionic surfactant (Triton X-100) at aqueous concentrations less than 400 mg/L through a trichloroethene-contaminated sand-and-gravel aquifer at Picatinny Arsenal, NJ, has been studied through a series of laboratory and field experiments. In the laboratory, batch and column experiments were conducted to quantify the rate and amount of Triton X-100 sorption to the aquifer sediments. In the field, a 400 mg/L aqueous Triton X-100 solution was injected into the aquifer at a rate of 26.5 L/min for a 35-d period. The transport of Triton X-100 was monitored by sampling and analysis of groundwater at six locations surrounding the injection well. Equilibrium batch sorption experiments showed that Triton X-100 sorbs strongly and nonlinearly to the field soil with the sharpest inflection point of the isotherm occurring at an equilibrium aqueous Triton X-100 concentration close to critical micelle concentration. Batch, soil column, and field experimental data were analyzed with zero-, one-, and two- dimensional (respectively) transient solute transport models with either equilibrium or rate-limited sorption. These analyses reveal that Triton X- 100 sorption to the aquifer solids is slow relative to advective and dispersive transport and that an equilibrium sorption model cannot simulate accurately the observed soil column and field data. Comparison of kinetic sorption parameters from batch, column, and field transport data indicate that both physical heterogeneities and Triton X-100 mass transfer between water and soil contribute to the kinetic transport effects.Transport of a nonionic surfactant (Triton X-100) at aqueous concentrations less than 400 mg/L through a trichloroethene-contaminated sand-and-gravel aquifer was studied. Equilibrium batch sorption experiments showed that Triton X-100 sorbs strongly and nonlinearly to the field soil with the sharpest inflection point of the isotherm occurring at an equilibrium aqueous Triton X-100 concentration close to critical micelle concentration. Batch, soil column, and field experimental data were analyzed with zero-, one-, and two-dimensional transient solute transport models with either equilibrium or rate-limited sorption. These analyses revealed that Triton X-100 sorption to the aquifer solids was slow relative to advective and dispersive transport.

Development of an anaesthetized-rat model of exercise hyperpnoea: an integrative model of respiratory control using an equilibrium diagram.

PubMed

Miyamoto, Tadayoshi; Manabe, Kou; Ueda, Shinya; Nakahara, Hidehiro

2018-05-01

What is the central question of this study? The lack of useful small-animal models for studying exercise hyperpnoea makes it difficult to investigate the underlying mechanisms of exercise-induced ventilatory abnormalities in various disease states. What is the main finding and its importance? We developed an anaesthetized-rat model for studying exercise hyperpnoea, using a respiratory equilibrium diagram for quantitative characterization of the respiratory chemoreflex feedback system. This experimental model will provide an opportunity to clarify the major determinant mechanisms of exercise hyperpnoea, and will be useful for understanding the mechanisms responsible for abnormal ventilatory responses to exercise in disease models. Exercise-induced ventilatory abnormalities in various disease states seem to arise from pathological changes of respiratory regulation. Although experimental studies in small animals are essential to investigate the pathophysiological basis of various disease models, the lack of an integrated framework for quantitatively characterizing respiratory regulation during exercise prevents us from resolving these problems. The purpose of this study was to develop an anaesthetized-rat model for studying exercise hyperpnoea for quantitative characterization of the respiratory chemoreflex feedback system. In 24 anaesthetized rats, we induced muscle contraction by stimulating bilateral distal sciatic nerves at low and high voltage to mimic exercise. We recorded breath-by-breath respiratory gas analysis data and cardiorespiratory responses while running two protocols to characterize the controller and plant of the respiratory chemoreflex. The controller was characterized by determining the linear relationship between end-tidal CO 2 pressure (P ETC O2) and minute ventilation (V̇E), and the plant by the hyperbolic relationship between V̇E and P ETC O2. During exercise, the controller curve shifted upward without change in controller gain, accompanying increased oxygen uptake. The hyperbolic plant curve shifted rightward and downward depending on exercise intensity as predicted by increased metabolism. Exercise intensity-dependent changes in operating points (V̇E and P ETC O2) were estimated by integrating the controller and plant curves in a respiratory equilibrium diagram. In conclusion, we developed an anaesthetized-rat model for studying exercise hyperpnoea, using systems analysis for quantitative characterization of the respiratory system. This novel experimental model will be useful for understanding the mechanisms responsible for abnormal ventilatory responses to exercise in disease models. © 2018 Morinomiya University of Medical Sciences. Experimental Physiology © 2018 The Physiological Society.

Universal relations for differentially rotating relativistic stars at the threshold to collapse

NASA Astrophysics Data System (ADS)

Bozzola, Gabriele; Stergioulas, Nikolaos; Bauswein, Andreas

2018-03-01

A binary neutron star merger produces a rapidly and differentially rotating compact remnant whose lifespan heavily affects the electromagnetic and gravitational emissions. Its stability depends on both the equation of state (EOS) and the rotation law and it is usually investigated through numerical simulations. Nevertheless, by means of a sufficient criterion for secular instability, equilibrium sequences can be used as a computational inexpensive way to estimate the onset of dynamical instability, which, in general, is close to the secular one. This method works well for uniform rotation and relies on the location of turning points: stellar models that are stationary points in a sequence of equilibrium solutions with constant rest mass or angular momentum. Here, we investigate differentially rotating models (using a large number of EOSs and different rotation laws) and find that several universal relations between properly scaled gravitational mass, rest mass and angular momentum of the turning-point models that are valid for uniform rotation are insensitive to the degree of differential rotation, to high accuracy.

Tidal evolution of close binary stars. I - Revisiting the theory of the equilibrium tide

NASA Technical Reports Server (NTRS)

Zahn, J.-P.

1989-01-01

The theory of the equilibrium tide in stars that possess a convective envelope is reexamined critically, taking recent developments into account and treating thermal convection in the most consistent way within the mixing-length approach. The weak points are identified and discussed, in particular, the reduction of the turbulent viscosity when the tidal period becomes shorter than the convective turnover time. An improved version is derived for the secular equations governing the dynamical evolution of close binaries of such type.

Condensation of helium in aerogel and athermal dynamics of the random-field Ising model.

PubMed

Aubry, Geoffroy J; Bonnet, Fabien; Melich, Mathieu; Guyon, Laurent; Spathis, Panayotis; Despetis, Florence; Wolf, Pierre-Etienne

2014-08-22

High resolution measurements reveal that condensation isotherms of (4)He in high porosity silica aerogel become discontinuous below a critical temperature. We show that this behavior does not correspond to an equilibrium phase transition modified by the disorder induced by the aerogel structure, but to the disorder-driven critical point predicted for the athermal out-of-equilibrium dynamics of the random-field Ising model. Our results evidence the key role of nonequilibrium effects in the phase transitions of disordered systems.

Analysis of three-phase equilibrium conditions for methane hydrate by isometric-isothermal molecular dynamics simulations.

PubMed

Yuhara, Daisuke; Brumby, Paul E; Wu, David T; Sum, Amadeu K; Yasuoka, Kenji

2018-05-14

To develop prediction methods of three-phase equilibrium (coexistence) conditions of methane hydrate by molecular simulations, we examined the use of NVT (isometric-isothermal) molecular dynamics (MD) simulations. NVT MD simulations of coexisting solid hydrate, liquid water, and vapor methane phases were performed at four different temperatures, namely, 285, 290, 295, and 300 K. NVT simulations do not require complex pressure control schemes in multi-phase systems, and the growth or dissociation of the hydrate phase can lead to significant pressure changes in the approach toward equilibrium conditions. We found that the calculated equilibrium pressures tended to be higher than those reported by previous NPT (isobaric-isothermal) simulation studies using the same water model. The deviations of equilibrium conditions from previous simulation studies are mainly attributable to the employed calculation methods of pressure and Lennard-Jones interactions. We monitored the pressure in the methane phase, far from the interfaces with other phases, and confirmed that it was higher than the total pressure of the system calculated by previous studies. This fact clearly highlights the difficulties associated with the pressure calculation and control for multi-phase systems. The treatment of Lennard-Jones interactions without tail corrections in MD simulations also contributes to the overestimation of equilibrium pressure. Although improvements are still required to obtain accurate equilibrium conditions, NVT MD simulations exhibit potential for the prediction of equilibrium conditions of multi-phase systems.

Analysis of three-phase equilibrium conditions for methane hydrate by isometric-isothermal molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Yuhara, Daisuke; Brumby, Paul E.; Wu, David T.; Sum, Amadeu K.; Yasuoka, Kenji

2018-05-01

To develop prediction methods of three-phase equilibrium (coexistence) conditions of methane hydrate by molecular simulations, we examined the use of NVT (isometric-isothermal) molecular dynamics (MD) simulations. NVT MD simulations of coexisting solid hydrate, liquid water, and vapor methane phases were performed at four different temperatures, namely, 285, 290, 295, and 300 K. NVT simulations do not require complex pressure control schemes in multi-phase systems, and the growth or dissociation of the hydrate phase can lead to significant pressure changes in the approach toward equilibrium conditions. We found that the calculated equilibrium pressures tended to be higher than those reported by previous NPT (isobaric-isothermal) simulation studies using the same water model. The deviations of equilibrium conditions from previous simulation studies are mainly attributable to the employed calculation methods of pressure and Lennard-Jones interactions. We monitored the pressure in the methane phase, far from the interfaces with other phases, and confirmed that it was higher than the total pressure of the system calculated by previous studies. This fact clearly highlights the difficulties associated with the pressure calculation and control for multi-phase systems. The treatment of Lennard-Jones interactions without tail corrections in MD simulations also contributes to the overestimation of equilibrium pressure. Although improvements are still required to obtain accurate equilibrium conditions, NVT MD simulations exhibit potential for the prediction of equilibrium conditions of multi-phase systems.

Equilibrium econophysics: A unified formalism for neoclassical economics and equilibrium thermodynamics

NASA Astrophysics Data System (ADS)

Sousa, Tânia; Domingos, Tiago

2006-11-01

We develop a unified conceptual and mathematical structure for equilibrium econophysics, i.e., the use of concepts and tools of equilibrium thermodynamics in neoclassical microeconomics and vice versa. Within this conceptual structure the results obtained in microeconomic theory are: (1) the definition of irreversibility in economic behavior; (2) the clarification that the Engel curve and the offer curve are not descriptions of real processes dictated by the maximization of utility at constant endowment; (3) the derivation of a relation between elasticities proving that economic elasticities are not all independent; (4) the proof that Giffen goods do not exist in a stable equilibrium; (5) the derivation that ‘economic integrability’ is equivalent to the generalized Le Chatelier principle and (6) the definition of a first order phase transition, i.e., a transition between separate points in the utility function. In thermodynamics the results obtained are: (1) a relation between the non-dimensional isothermal and adiabatic compressibilities and the increase or decrease in the thermodynamic potentials; (2) the distinction between mathematical integrability and optimization behavior and (3) the generalization of the Clapeyron equation.

A new PIC noise reduction technique

NASA Astrophysics Data System (ADS)

Barnes, D. C.

2014-10-01

Numerical solution of the Vlasov equation is considered in a general situation in which there is an underlying static solution (equilibrium). There are no further assumptions about dimensionality, smallenss of orbits, or disparate time scales. The semi-characteristic (SC) method for Vlasov solution is described. The usual characteristics of the equation, which are the single particle orbits, are modified in such a way that the equilibrium phase-space flow is removed. In this way, the shot noise introduced by the usual discrete particle representation of the equilibrium is static in time and can be removed completely by subtraction. An almost exact algorithm for this is based on the observation that a (infinitesimal or) discrete time step of any equilibrium MC realization is again a realization of the equilibrium, building up strings of associated simulation particles. In this way, the only added discretization error arises from the need to extrapolate backward in time the chain end points one dt using a canonical transformation. Previously developed energy-conserving time-implicit methods are applied without modification. 1D ES examples of Landau damping and velocity-space instability are given to illustrate the method.

Leaf Uptake of Nitrogen Dioxide (NO2) Under Different Environmental Conditions.

NASA Astrophysics Data System (ADS)

Chaparro-Suarez, I.; Thielmann, A.; Meixner, F. X.; Kesselmeier, J.

2005-12-01

The chemical budget of Ozone in the troposphere is largely determined by the concentration of NOx (NO, NO2) within a photostationary equilibrium. It is well known that atmospheric concentration is strongly influenced by the bi-directional exchange of NO2. However, there is some debate about the magnitude of the compensation point. Therefore, we investigated the uptake of atmospheric NO2 by trees in relation to atmospheric NO2 concentrations. Using the dynamic chamber technique and a sensitive and specific NO-analysator (CLD 780, Eco Physics) we measured the uptake of NO2 by four different tree species (Betula pendula, Fagus sylvatica, Quercus ilex und Pinus sylvestris) under field and laboratory conditions. Simultaneous measurements of CO2 exchange and transpiration were performed to track photosynthesis and stomatal conductance. Depending on tree species we found the exchange to be controlled by very low NO2 compensation points sometimes reaching zero values (no emission) under laboratory conditions. In the field a high compensation point for European beech (Fagus sylvatica) was observed, which is understood as a result of complex atmospheric conditions.

Recovery of postural equilibrium control following spaceflight

NASA Technical Reports Server (NTRS)

Paloski, W. H.; Reschke, M. F.; Black, F. O.; Doxey, D. D.; Harm, D. L.

1992-01-01

Decreased postural stability is observed in most astronauts immediately following spaceflight. Because ataxia may present postflight operational hazards, it is important to determine the incidence of postural instability immediately following landing and the dynamics of recovery of normal postural equilibrium control. It is postulated that postflight postural instability results from in-flight adaptive changes in central nervous system (CNS) processing of sensory information from the visual, vestibular, and proprioceptive systems. The purpose of the present investigation was to determine the magnitude and time course of postflight recovery of postural equilibrium control and, hence, readaptation of CNS processing of sensory information. Thirteen crew members from six spaceflight missions were studied pre- and postflight using a modified commercial posturography system. Postural equilibrium control was found to be seriously disrupted immediately following spaceflight in all subjects. Readaptation to the terrestrial environment began immediately upon landing, proceeded rapidly for the first 10-12 hours, and then proceeded much more slowly for the subsequent 2-4 days until preflight stability levels were reachieved. It is concluded that the overall postflight recovery of postural stability follows a predictable time course.

Universal ideal behavior and macroscopic work relation of linear irreversible stochastic thermodynamics

NASA Astrophysics Data System (ADS)

Ma, Yi-An; Qian, Hong

2015-06-01

We revisit the Ornstein-Uhlenbeck (OU) process as the fundamental mathematical description of linear irreversible phenomena, with fluctuations, near an equilibrium. By identifying the underlying circulating dynamics in a stationary process as the natural generalization of classical conservative mechanics, a bridge between a family of OU processes with equilibrium fluctuations and thermodynamics is established through the celebrated Helmholtz theorem. The Helmholtz theorem provides an emergent macroscopic ‘equation of state’ of the entire system, which exhibits a universal ideal thermodynamic behavior. Fluctuating macroscopic quantities are studied from the stochastic thermodynamic point of view and a non-equilibrium work relation is obtained in the macroscopic picture, which may facilitate experimental study and application of the equalities due to Jarzynski, Crooks, and Hatano and Sasa.

Physical analysis of the process of cavitation in xylem sap.

PubMed

Shen, Fanyi; Gao, Rongfu; Liu, Wenji; Zhang, Wenjie

2002-06-01

Recent studies have confirmed that cavitation in xylem is caused by air bubbles. We analyzed expansion of a preexistent bubble adhering to a crack in a conduit wall and a bubble formed by the passage of air through a pore of a pit membrane, a process known as air seeding. We consider that there are two equilibrium states for a very small air bubble in the xylem: one is temporarily stable with a bubble radius r1 at point s1 on the curve P(r) relating pressure within the bubble (P) with bubble radius (r); the other is unstable with a bubble radius r2 at point s2 on Pr (where r1 < r2). In each equilibrium state, the bubble collapse pressure (2sigma/r, where sigma is surface tension of water) is balanced by the pressure difference across its surface. In the case of a bubble from a crack in a conduit wall, which is initially at point s1, expansion will occur steadily as water potential decreases. The bubble will burst only if the xylem pressure drops below a threshold value. A formula giving the threshold pressure for bubble bursting is proposed. In the case of an air seed entering a xylem conduit through a pore in a pit membrane, its initial radius may be r2 (i.e., the radius of the pore by which the air seed entered the vessel) at point s2 on Pr. Because the bubble is in an unstable equilibrium when entering the conduit, it can either expand or contract to point s1. As water vaporizes into the air bubble at s2, P rises until it exceeds the gas pressure that keeps the bubble in equilibrium, at which point the bubble will burst and induce a cavitation event in accordance with the air-seeding hypothesis. However, other possible perturbations could make the air-seeded bubble contract to s1, in which case the bubble will burst at a threshold pressure proposed for a bubble expanding from a crack in a conduit wall. For this reason some cavitation events may take place at a xylem threshold pressure (Pl'*) other than that determined by the formula, Plp'* = -2sigma/rp, proposed by Sperry and Tyree (1988), which is applicable only to air-seeded bubbles at s2. The more general formula we propose for calculating the threshold pressure for bubble breaking is consistent with the results of published experiments.

Motion of the angular momentum vector in body coordinates for torque-free dual-spin spacecraft

NASA Technical Reports Server (NTRS)

Fedor, J. V.

1981-01-01

The motion of the angular momentum vector in body coordinates for torque free, asymmetric dual spin spacecraft without and, for a special case, with energy dissipation on the main spacecraft is investigated. Without energy dissipation, two integrals can be obtained from the Euler equations of motion. Using the classical method of elimination of variable, the motion about the equilibrium points (six for the general case) are derived with these integrals. For small nutation angle, theta, the trajectories about the theta = 0 deg and theta = 180 deg points readily show the requirements for stable motion about these points. Also the conditions needed to eliminate stable motion about the theta = 180 deg point as well as the other undesireable equilibrium points follow directly from these equations. For the special case where the angular momentum vector moves about the principal axis which contains the momentum wheel, the notion of 'free variable' azimuth angle is used. Physically this angle must vary from 0 to 2 pi in a circular periodic fashion. Expressions are thus obtained for the nutation angle in terms of the free variable and other spacecraft parameters. Results show that in general there are two separate trajectory expressions that govern the motion of the angular momentum vector in body coordinates.

Electric-Field Instrument With Ac-Biased Corona Point

NASA Technical Reports Server (NTRS)

Markson, R.; Anderson, B.; Govaert, J.

1993-01-01

Measurements indicative of incipient lightning yield additional information. New instrument gives reliable readings. High-voltage ac bias applied to needle point through high-resistance capacitance network provides corona discharge at all times, enabling more-slowly-varying component of electrostatic potential of needle to come to equilibrium with surrounding air. High resistance of high-voltage coupling makes instrument insensitive to wind. Improved corona-point instrument expected to yield additional information assisting in safety-oriented forecasting of lighting.

A Course of Lectures on Statistical Mechanics

DTIC Science & Technology

2010-06-01

of mathematics goes a long way to making it tractable. In particular for doing problems in thermodynamics , we’ll stress the following point . For any...disentangle temperature from k. This is done by setting T = 273.16 K at the triple point of water (’ 0.01◦C). Note that the SI unit of the Kelvin...energy, 11 of harmonic oscillator, 66 thermal equilibrium, 19 thermal resistance, 27 triple point of water, 19 ultraviolet catastrophe, 71 validity

Influence of Hall Effect on Magnetic Control of Stagnation Point Heat Transfer

NASA Astrophysics Data System (ADS)

Poggie, Jonathan; Gaitonde, Datta

2001-11-01

Electromagnetic control is an appealing possibility for mitigating the thermal loads that occur in hypersonic flight. There was extensive research on this technique in the past (up to about 1970), but enthusiasm waned because of problems of system cost and weight. Renewed interest has arisen recently due to developments in the technology of super-conducting magnets and the understanding of the physics of weakly-ionized, non-equilibrium plasmas. A problem of particular interest is the reduction of stagnation point heating during atmospheric entry by magnetic deceleration of the flow in the shock layer. For the case of hypersonic flow over a sphere, a reduction in heat flux has been observed with the application of a dipole magnetic field (Poggie and Gaitonde, AIAA Paper 2001-0196). The Hall effect has a detrimental influence on this control scheme, tending to rotate the current vector out of the circumferential direction and to reduce the impact of the applied magnetic field on the fluid. In the present work we re-examine this problem by using modern computational methods to simulate flow past a hemispherical-nosed vehicle in which a axially-oriented magnetic dipole has been placed. The deleterious effects of the Hall current are characterized, and are observed to diminish when the surface of the vehicle is conducting.

Editorial: Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems

NASA Astrophysics Data System (ADS)

Cazalilla, M. A.; Rigol, M.

2010-05-01

The dynamics and thermalization of classical systems have been extensively studied in the past. However, the corresponding quantum phenomena remain, to a large extent, uncharted territory. Recent experiments with ultracold quantum gases have at last allowed exploration of the coherent dynamics of isolated quantum systems, as well as observation of non-equilibrium phenomena that challenge our current understanding of the dynamics of quantum many-body systems. These experiments have also posed many new questions. How can we control the dynamics to engineer new states of matter? Given that quantum dynamics is unitary, under which conditions can we expect observables of the system to reach equilibrium values that can be predicted by conventional statistical mechanics? And, how do the observables dynamically approach their statistical equilibrium values? Could the approach to equilibrium be hampered if the system is trapped in long-lived metastable states characterized, for example, by a certain distribution of topological defects? How does the dynamics depend on the way the system is perturbed, such as changing, as a function of time and at a given rate, a parameter across a quantum critical point? What if, conversely, after relaxing to a steady state, the observables cannot be described by the standard equilibrium ensembles of statistical mechanics? How would they depend on the initial conditions in addition to the other properties of the system, such as the existence of conserved quantities? The search for answers to questions like these is fundamental to a new research field that is only beginning to be explored, and to which researchers with different backgrounds, such as nuclear, atomic, and condensed-matter physics, as well as quantum optics, can make, and are making, important contributions. This body of knowledge has an immediate application to experiments in the field of ultracold atomic gases, but can also fundamentally change the way we approach and understand many-body quantum systems. This focus issue of New Journal Physics brings together both experimentalists and theoreticians working on these problems to provide a comprehensive picture of the state of the field. Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems Contents Spin squeezing of high-spin, spatially extended quantum fields Jay D Sau, Sabrina R Leslie, Marvin L Cohen and Dan M Stamper-Kurn Thermodynamic entropy of a many-body energy eigenstate J M Deutsch Ground states and dynamics of population-imbalanced Fermi condensates in one dimension Masaki Tezuka and Masahito Ueda Relaxation dynamics in the gapped XXZ spin-1/2 chain Jorn Mossel and Jean-Sébastien Caux Canonical thermalization Peter Reimann Minimally entangled typical thermal state algorithms E M Stoudenmire and Steven R White Manipulation of the dynamics of many-body systems via quantum control methods Julie Dinerman and Lea F Santos Multimode analysis of non-classical correlations in double-well Bose-Einstein condensates Andrew J Ferris and Matthew J Davis Thermalization in a quasi-one-dimensional ultracold bosonic gas I E Mazets and J Schmiedmayer Two simple systems with cold atoms: quantum chaos tests and non-equilibrium dynamics Cavan Stone, Yassine Ait El Aoud, Vladimir A Yurovsky and Maxim Olshanii On the speed of fluctuations around thermodynamic equilibrium Noah Linden, Sandu Popescu, Anthony J Short and Andreas Winter A quantum central limit theorem for non-equilibrium systems: exact local relaxation of correlated states M Cramer and J Eisert Quantum quench dynamics of the sine-Gordon model in some solvable limits A Iucci and M A Cazalilla Nonequilibrium quantum dynamics of atomic dark solitons A D Martin and J Ruostekoski Quantum quenches in the anisotropic spin-1⁄2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium Peter Barmettler, Matthias Punk, Vladimir Gritsev, Eugene Demler and Ehud Altman Crossover from adiabatic to sudden interaction quenches in the Hubbard model: prethermalization and non-equilibrium dynamics Michael Moeckel and Stefan Kehrein Quantum quenches in integrable field theories Davide Fioretto and Giuseppe Mussardo Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point A Bermudez, L Amico and M A Martin-Delgado Thermometry with spin-dependent lattices D McKay and B DeMarco Near-adiabatic parameter changes in correlated systems: influence of the ramp protocol on the excitation energy Martin Eckstein and Marcus Kollar Sudden change of the thermal contact between two quantum systems J Restrepo and S Camalet Reflection of a Lieb-Liniger wave packet from the hard-wall potential D Jukić and H Buljan Probing interaction-induced ferromagnetism in optical superlattices J von Stecher, E Demler, M D Lukin and A M Rey Sudden interaction quench in the quantum sine-Gordon model Javier Sabio and Stefan Kehrein Dynamics of an inhomogeneous quantum phase transition Jacek Dziarmaga and Marek M Rams

Influence of Two-Phase Thermocapillary Flow on Cryogenic Liquid Retention in Microscopic Pores

NASA Technical Reports Server (NTRS)

Schmidt, G. R.; Nadarajah, A.; Chung, T. J.; Karr, G. R.

1994-01-01

Previous experiments indicate that the bubble point pressure of spacecraft liquid hydrogen acquisition devices is reduced substantially when the ullage is pressurized with heated hydrogen vapor. The objective is to determine whether the two-phase thermocapillary convection arising from thermodynamic non-equilibrium along the porous surfaces of such devices could lead to this observed degradation in retention performance. We also examine why retention capability appears to be unaffected by pressurization with heated helium or direct heating through the porous structure. Computational assessments based on coupled solution of the flowfield and liquid free surface indicate that for highly wetting fluids in small pores, dynamic pressure and vapor recoil dictate surface morphology and drive meniscus deformation. With superheating, the two terms exert the same influence on curvature and promote mechanical equilibrium, but with subcooling, the pressure distribution produces a suction about the pore center-line that degrades retention. This result points to thermocapillary-induced deformation arising from condensation as the cause for retention loss. It also indicates that increasing the level of non-equilibrium by reducing accommodation coefficient restricts deformation and explains why retention failure does not occur with direct screen heating or helium pressurization.

Ergodic Theory, Interpretations of Probability and the Foundations of Statistical Mechanics

NASA Astrophysics Data System (ADS)

van Lith, Janneke

The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of these two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well known that this account is problematic. This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented.

Global stability analysis of two-strain epidemic model with bilinear and non-monotone incidence rates

NASA Astrophysics Data System (ADS)

Baba, Isa Abdullahi; Hincal, Evren

2017-05-01

In this article we studied an epidemic model consisting of two strains with different types of incidence rates; bilinear and non-monotone. The model consists of four equilibrium points: disease-free equilibrium, endemic with respect to strain 1, endemic with respect to strain 2, and endemic with respect to both strains. The global stability analysis of the equilibrium points was carried out through the use of Lyapunov functions. Two basic reproduction ratios R 1 0 and R 2 0 are found, and we have shown that if both are less than one, the disease dies out, and if both are greater than one epidemic occurs. Furthermore, epidemics occur with respect to any strain with a basic reproduction ratio greater than one and disease dies out with respect to any strain with a basic reproduction ratio less than one. It was also shown that any strain with highest basic reproduction ratio will automatically outperform the other strain, thereby eliminating it. Numerical simulations were carried out to support the analytic result and to show the effect of the parameter k in the non-monotone incidence rate, which describes the psychological effect of general public towards infection.

Dynamics and Control of Attitude, Power, and Momentum for a Spacecraft Using Flywheels and Control Moment Gyroscopes

NASA Technical Reports Server (NTRS)

Roithmayr, Carlos M.; Karlgaard, Christopher D.; Kumar, Renjith R.; Seywald, Hans; Bose, David M.

2003-01-01

Several laws are designed for simultaneous control of the orientation of an Earth-pointing spacecraft, the energy stored by counter-rotating flywheels, and the angular momentum of the flywheels and control moment gyroscopes used together as an integrated set of actuators for attitude control. General, nonlinear equations of motion are presented in vector-dyadic form, and used to obtain approximate expressions which are then linearized in preparation for design of control laws that include feedback of flywheel kinetic energy error as a means of compensating for damping exerted by rotor bearings. Two flywheel steering laws are developed such that torque commanded by an attitude control law is achieved while energy is stored or discharged at the required rate. Using the International Space Station as an example, numerical simulations are performed to demonstrate control about a torque equilibrium attitude, and illustrate the benefits of kinetic energy error feedback. Control laws for attitude hold are also developed, and used to show the amount of propellant that can be saved when flywheels assist the CMGs. Nonlinear control laws for large-angle slew maneuvers perform well, but excessive momentum is required to reorient a vehicle like the International Space Station.

Local Equilibrium and Retardation Revisited.

PubMed

Hansen, Scott K; Vesselinov, Velimir V

2018-01-01

In modeling solute transport with mobile-immobile mass transfer (MIMT), it is common to use an advection-dispersion equation (ADE) with a retardation factor, or retarded ADE. This is commonly referred to as making the local equilibrium assumption (LEA). Assuming local equilibrium, Eulerian textbook treatments derive the retarded ADE, ostensibly exactly. However, other authors have presented rigorous mathematical derivations of the dispersive effect of MIMT, applicable even in the case of arbitrarily fast mass transfer. We resolve the apparent contradiction between these seemingly exact derivations by adopting a Lagrangian point of view. We show that local equilibrium constrains the expected time immobile, whereas the retarded ADE actually embeds a stronger, nonphysical, constraint: that all particles spend the same amount of every time increment immobile. Eulerian derivations of the retarded ADE thus silently commit the gambler's fallacy, leading them to ignore dispersion due to mass transfer that is correctly modeled by other approaches. We then present a particle tracking simulation illustrating how poor an approximation the retarded ADE may be, even when mobile and immobile plumes are continually near local equilibrium. We note that classic "LEA" (actually, retarded ADE validity) criteria test for insignificance of MIMT-driven dispersion relative to hydrodynamic dispersion, rather than for local equilibrium. Published 2017. This article is a U.S. Government work and is in the public domain in the USA.

Synthesis and amphiphilic properties of decanoyl esters of tri- and tetraethylene glycol.

PubMed

Zhu, Ying; Molinier, Valérie; Queste, Sébastien; Aubry, Jean-Marie

2007-08-15

Well-defined decanoyl triethylene glycol ester and decanoyl tetraethylene glycol ester were synthesized and compared to their ether counterparts (C(10)E(4) and C(10)E(3)). Their physicochemical properties i.e. critical micelle concentrations (CMC), cloud points, and equilibrium surface tensions were determined. Binary water-surfactant phase behavior was also studied by polarized optical microscopy. The stability of the ester bond was determined by investigating alkaline hydrolysis of the compounds. It was found that CMC, cloud point and equilibrium surface tension are roughly the same for corresponding ethers and esters. In the binary diagram, the esters form only lamellar phases, the area of which is smaller than that of the ether counterparts. These different behaviors can be related to the modification of the molecular conformation induced by the replacement of the ether group by the ester group.

Upwind MacCormack Euler solver with non-equilibrium chemistry

NASA Technical Reports Server (NTRS)

Sherer, Scott E.; Scott, James N.

1993-01-01

A computer code, designated UMPIRE, is currently under development to solve the Euler equations in two dimensions with non-equilibrium chemistry. UMPIRE employs an explicit MacCormack algorithm with dissipation introduced via Roe's flux-difference split upwind method. The code also has the capability to employ a point-implicit methodology for flows where stiffness is introduced through the chemical source term. A technique consisting of diagonal sweeps across the computational domain from each corner is presented, which is used to reduce storage and execution requirements. Results depicting one dimensional shock tube flow for both calorically perfect gas and thermally perfect, dissociating nitrogen are presented to verify current capabilities of the program. Also, computational results from a chemical reactor vessel with no fluid dynamic effects are presented to check the chemistry capability and to verify the point implicit strategy.

Design and implementation of grid multi-scroll fractional-order chaotic attractors

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

Chen, Liping, E-mail: lip-chenhut@126.com; Pan, Wei; Wu, Ranchao

2016-08-15

This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most.more » Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.« less

Stability Analysis of Continuous-Time and Discrete-Time Quaternion-Valued Neural Networks With Linear Threshold Neurons.

PubMed

Chen, Xiaofeng; Song, Qiankun; Li, Zhongshan; Zhao, Zhenjiang; Liu, Yurong

2018-07-01

This paper addresses the problem of stability for continuous-time and discrete-time quaternion-valued neural networks (QVNNs) with linear threshold neurons. Applying the semidiscretization technique to the continuous-time QVNNs, the discrete-time analogs are obtained, which preserve the dynamical characteristics of their continuous-time counterparts. Via the plural decomposition method of quaternion, homeomorphic mapping theorem, as well as Lyapunov theorem, some sufficient conditions on the existence, uniqueness, and global asymptotical stability of the equilibrium point are derived for the continuous-time QVNNs and their discrete-time analogs, respectively. Furthermore, a uniform sufficient condition on the existence, uniqueness, and global asymptotical stability of the equilibrium point is obtained for both continuous-time QVNNs and their discrete-time version. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.

Dynamic analysis of trapping and escaping in dual beam optical trap

NASA Astrophysics Data System (ADS)

Li, Wenqiang; Hu, Huizhu; Su, Heming; Li, Zhenggang; Shen, Yu

2016-10-01

In this paper, we simulate the dynamic movement of a dielectric sphere in optical trap. This dynamic analysis can be used to calibrate optical forces, increase trapping efficiency and measure viscous coefficient of surrounding medium. Since an accurate dynamic analysis is based on a detailed force calculation, we calculate all forces a sphere receives. We get the forces of dual-beam gradient radiation pressure on a micron-sized dielectric sphere in the ray optics regime and utilize Einstein-Ornstein-Uhlenbeck to deal with its Brownian motion forces. Hydrodynamic viscous force also exists when the sphere moves in liquid. Forces from buoyance and gravity are also taken into consideration. Then we simulate trajectory of a sphere when it is subject to all these forces in a dual optical trap. From our dynamic analysis, the sphere can be trapped at an equilibrium point in static water, although it permanently fluctuates around the equilibrium point due to thermal effects. We go a step further to analyze the effects of misalignment of two optical traps. Trapping and escaping phenomena of the sphere in flowing water are also simulated. In flowing water, the sphere is dragged away from the equilibrium point. This dragging distance increases with the decrease of optical power, which results in escaping of the sphere with optical power below a threshold. In both trapping and escaping process we calculate the forces and position of the sphere. Finally, we analyze a trapping region in dual optical tweezers.

Active Learning Session Based on Didactical Engineering Framework for Conceptual Change in Students' Equilibrium and Stability Understanding

ERIC Educational Resources Information Center

Canu, Michael; Duque, Mauricio; de Hosson, Cécile

2017-01-01

Engineering students on control courses lack a deep understanding of equilibrium and stability that are crucial concepts in this discipline. Several studies have shown that students find it difficult to understand simple familiar or academic static equilibrium cases as well as dynamic ones from mechanics even if they know the discipline's criteria…

On Social Optima of Non-Cooperative Mean Field Games

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

Li, Sen; Zhang, Wei; Zhao, Lin

This paper studies the social optima in noncooperative mean-field games for a large population of agents with heterogeneous stochastic dynamic systems. Each agent seeks to maximize an individual utility functional, and utility functionals of different agents are coupled through a mean field term that depends on the mean of the population states/controls. The paper has the following contributions. First, we derive a set of control strategies for the agents that possess *-Nash equilibrium property, and converge to the mean-field Nash equilibrium as the population size goes to infinity. Second, we study the social optimal in the mean field game. Wemore » derive the conditions, termed the socially optimal conditions, under which the *-Nash equilibrium of the mean field game maximizes the social welfare. Third, a primal-dual algorithm is proposed to compute the *-Nash equilibrium of the mean field game. Since the *-Nash equilibrium of the mean field game is socially optimal, we can compute the equilibrium by solving the social welfare maximization problem, which can be addressed by a decentralized primal-dual algorithm. Numerical simulations are presented to demonstrate the effectiveness of the proposed approach.« less

Aerospace Applications of Non-Equilibrium Plasma

NASA Technical Reports Server (NTRS)

Blankson, Isaiah M.

2016-01-01

Nonequilibrium plasma/non-thermal plasma/cold plasmas are being used in a wide range of new applications in aeronautics, active flow control, heat transfer reduction, plasma-assisted ignition and combustion, noise suppression, and power generation. Industrial applications may be found in pollution control, materials surface treatment, and water purification. In order for these plasma processes to become practical, efficient means of ionization are necessary. A primary challenge for these applications is to create a desired non-equilibrium plasma in air by preventing the discharge from transitioning into an arc. Of particular interest is the impact on simulations and experimental data with and without detailed consideration of non-equilibrium effects, and the consequences of neglecting non-equilibrium. This presentation will provide an assessment of the presence and influence of non-equilibrium phenomena for various aerospace needs and applications. Specific examples to be considered will include the forward energy deposition of laser-induced non-equilibrium plasmoids for sonic boom mitigation, weakly ionized flows obtained from pulsed nanosecond discharges for an annular Hall type MHD generator duct for turbojet energy bypass, and fundamental mechanisms affecting the design and operation of novel plasma-assisted reactive systems in dielectric liquids (water purification, in-pipe modification of fuels, etc.).

Theories and applications of second-order correlation of longitudinal velocity increments at three points in isotropic turbulence

NASA Astrophysics Data System (ADS)

Wu, J. Z.; Fang, L.; Shao, L.; Lu, L. P.

2018-06-01

In order to introduce new physics to traditional two-point correlations, we define the second-order correlation of longitudinal velocity increments at three points and obtain the analytical expressions in isotropic turbulence. By introducing the Kolmogorov 4/5 law, this three-point correlation explicitly contains velocity second- and third-order moments, which correspond to energy and energy transfer respectively. The combination of them then shows additional information of non-equilibrium turbulence by comparing to two-point correlations. Moreover, this three-point correlation shows the underlying inconsistency between numerical interpolation and three-point scaling law in numerical calculations, and inspires a preliminary model to correct this problem in isotropic turbulence.

Equilibrium charge distribution on a finite straight one-dimensional wire

NASA Astrophysics Data System (ADS)

Batle, Josep; Ciftja, Orion; Abdalla, Soliman; Elhoseny, Mohamed; Alkhambashi, Majid; Farouk, Ahmed

2017-09-01

The electrostatic properties of uniformly charged regular bodies are prominently discussed on college-level electromagnetism courses. However, one of the most basic problems of electrostatics that deals with how a continuous charge distribution reaches equilibrium is rarely mentioned at this level. In this work we revisit the problem of equilibrium charge distribution on a straight one-dimensional (1D) wire with finite length. The majority of existing treatments in the literature deal with the 1D wire as a limiting case of a higher-dimensional structure that can be treated analytically for a Coulomb interaction potential between point charges. Surprisingly, different models (for instance, an ellipsoid or a cylinder model) may lead to different results, thus there is even some ambiguity on whether the problem is well-posed. In this work we adopt a different approach where we do not start with any higher-dimensional body that reduces to a 1D wire in the appropriate limit. Instead, our starting point is the obvious one, a finite straight 1D wire that contains charge. However, the new tweak in the model is the assumption that point charges interact with each other via a non-Coulomb power-law interaction potential. This potential is well-behaved, allows exact analytical results and approaches the standard Coulomb interaction potential as a limit. The results originating from this approach suggest that the equilibrium charge distribution for a finite straight 1D wire is a uniform charge density when the power-law interaction potential approaches the Coulomb interaction potential as a suitable limit. We contrast such a finding to results obtained using a different regularised logarithmic interaction potential which allows exact treatment in 1D. The present self-contained material may be of interest to instructors teaching electromagnetism as well as students who will discover that simple-looking problems may sometimes pose important scientific challenges.

Linear dynamics of classical spin as Mobius transformation

DOE PAGES

Galda, Alexey; Vinokur, Valerii М.

2017-04-26

Though the overwhelming majority of natural processes occur far from the equilibrium, general theoretical approaches to non-equilibrium phase transitions remain scarce. Recent breakthroughs introduced a description of open dissipative systems in terms of non-Hermitian quantum mechanics enabling the identification of a class of non-equilibrium phase transitions associated with the loss of combined parity (reflection) and time-reversal symmetries. Here we report that the time evolution of a single classical spin (e.g. monodomain ferromagnet) governed by the Landau-Lifshitz-Gilbert-Slonczewski equation in the absence of magnetic anisotropy terms is described by a Mobius transformation in complex stereographic coordinates. We identify the parity-time symmetry-breaking phasemore » transition occurring in spin-transfer torque-driven linear spin systems as a transition between hyperbolic and loxodromic classes of Mobius transformations, with the critical point of the transition corresponding to the parabolic transformation. However, this establishes the understanding of non-equilibrium phase transitions as topological transitions in configuration space.« less

Does shaking increase the pressure inside a bottle of champagne?

PubMed

Vreme, A; Pouligny, B; Nadal, F; Liger-Belair, G

2015-02-01

Colas, beers and sparkling wines are all concentrated solutions of carbon dioxide in aqueous solvents. Any such carbonated liquid is ordinarily conditioned inside a closed bottle or a metal can as a liquid-gas 2-phase system. At thermodynamic equilibrium, the partial pressure of carbon-dioxide in the gas phase and its concentration in the liquid are proportional (Henry's law). In practical conditions and use (transport, opening of the container, exterior temperature change, etc.), Henry's equilibrium can be perturbed. The goal of this paper is to describe and understand how the system responds to such perturbations and evolves towards a new equilibrium state. Formally, we investigate the dynamics around Henry's equilibrium of a closed system, through dedicated experiments and modeling. We focus on the response to a sudden pressure change and to mechanical shaking (the latter point inspired the article's title). Observations are rationalized through basic considerations including molecular diffusion, bubble dynamics (based on Epstein-Plesset theory) and chemi-convective hydrodynamic instabilities. Copyright © 2014 Elsevier Inc. All rights reserved.

Statistical approach to partial equilibrium analysis

NASA Astrophysics Data System (ADS)

Wang, Yougui; Stanley, H. E.

2009-04-01

A statistical approach to market equilibrium and efficiency analysis is proposed in this paper. One factor that governs the exchange decisions of traders in a market, named willingness price, is highlighted and constitutes the whole theory. The supply and demand functions are formulated as the distributions of corresponding willing exchange over the willingness price. The laws of supply and demand can be derived directly from these distributions. The characteristics of excess demand function are analyzed and the necessary conditions for the existence and uniqueness of equilibrium point of the market are specified. The rationing rates of buyers and sellers are introduced to describe the ratio of realized exchange to willing exchange, and their dependence on the market price is studied in the cases of shortage and surplus. The realized market surplus, which is the criterion of market efficiency, can be written as a function of the distributions of willing exchange and the rationing rates. With this approach we can strictly prove that a market is efficient in the state of equilibrium.

Viscous-shock-layer solutions with coupled radiation and ablation injection for earth entry

NASA Technical Reports Server (NTRS)

Gupta, Roop N.; Lee, Kam-Pui; Moos, James N.; Sutton, Kenneth

1990-01-01

Results are obtained for the forebody of a planetary exploration vehicle entering the earth's atmosphere. A viscous-shock-layer analysis is used assuming the flow to be laminar and in chemical equilibrium. Presented results include coupled radiation and ablation injection. This study further includes the effect of different transport and thermodynamic properties and radiation models. A Lewis number of 1.4 appears adequate for the radiation-dominated flows. Five velocities corresponding to different possible trajectory points at an altitude of 70 km have been further analyzed in detail. Sublimation and radiative equilibrium wall temperatures are employed for cases with and without coupled injection, respectively. For the cases analyzed here, the mass injection rates are small. However, the rates could become large if a lower altitude is used for aerobraking and/or the body size is increased. A comparison of the equilibrium results with finite-rate chemistry calculation shows the flowfield to be in chemical equilibrium.

Bus-based park-and-ride system: a stochastic model on multimodal network with congestion pricing schemes

NASA Astrophysics Data System (ADS)

Liu, Zhiyuan; Meng, Qiang

2014-05-01

This paper focuses on modelling the network flow equilibrium problem on a multimodal transport network with bus-based park-and-ride (P&R) system and congestion pricing charges. The multimodal network has three travel modes: auto mode, transit mode and P&R mode. A continuously distributed value-of-time is assumed to convert toll charges and transit fares to time unit, and the users' route choice behaviour is assumed to follow the probit-based stochastic user equilibrium principle with elastic demand. These two assumptions have caused randomness to the users' generalised travel times on the multimodal network. A comprehensive network framework is first defined for the flow equilibrium problem with consideration of interactions between auto flows and transit (bus) flows. Then, a fixed-point model with unique solution is proposed for the equilibrium flows, which can be solved by a convergent cost averaging method. Finally, the proposed methodology is tested by a network example.

Analysis of Steady, Two-Dimensional Chemically Reacting Nonequilibrium Flow by an Unsteady, Asymptotically Consistent Technique. Volume I. Theoretical Development.

DTIC Science & Technology

1982-09-01

wall, and exit points are know,, collectively as boundary points. In the following discussion, thi numerical treatment used for each type of mesh point...and fiozen solutions and that it matches the ODK solution 6 [Reference (10)] quite well. Also note that in this case, there is only a small departure...shows the results of the H-F system analysis. The mass-averaged temperature profile falls between the equilibrium and frozen solutions and matches the ODK

An Investigation of Spinup Dynamics of Axial Gyrostats Using Elliptic Integrals and the Method of Averaging

DTIC Science & Technology

1991-01-01

is a gyrostat near one of the five libration points . She identified the equilibria and determined their stability regions. Also, Mavraga- nis [71] has...defines a family of periodic orbits , depending on how close the all-spun motion is to an equilibrium point of the equations of motion for a single...determined by the relationship between the mission orbit and the object the platform is supposed to track. As a limiting case, one might wish to point

Muscle Co-activation: Definitions, Mechanisms, and Functions.

PubMed

Latash, Mark L

2018-03-28

The phenomenon of agonist-antagonist muscle co-activation is discussed with respect to its consequences for movement mechanics (such as increasing joint apparent stiffness, facilitating faster movements, and effects on action stability), implication for movement optimization, and involvement of different neurophysiological structures. Effects of co-activation on movement stability are ambiguous and depend on the effector representing a kinematic chain with a fixed origin or free origin. Further, co-activation is discussed within the framework of the equilibrium-point hypothesis and the idea of hierarchical control with spatial referent coordinates. Relations of muscle co-activation to changes in one of the basic commands, the c-command, are discussed and illustrated. A hypothesis is suggested that agonist-antagonist co-activation reflects a deliberate neural control strategy to preserve effector-level control and avoid making it degenerate and facing the necessity to control at the level of signals to individual muscles. This strategy, in particular, allows stabilizing motor actions by co-varied adjustments in spaces of control variables. This hypothesis is able to account for higher levels of co-activation in young healthy persons performing challenging tasks and across various populations with movement impairments.

Self-assembled materials and supramolecular chemistry within microfluidic environments: from common thermodynamic states to non-equilibrium structures.

PubMed

Sevim, S; Sorrenti, A; Franco, C; Furukawa, S; Pané, S; deMello, A J; Puigmartí-Luis, J

2018-05-01

Self-assembly is a crucial component in the bottom-up fabrication of hierarchical supramolecular structures and advanced functional materials. Control has traditionally relied on the use of encoded building blocks bearing suitable moieties for recognition and interaction, with targeting of the thermodynamic equilibrium state. On the other hand, nature leverages the control of reaction-diffusion processes to create hierarchically organized materials with surprisingly complex biological functions. Indeed, under non-equilibrium conditions (kinetic control), the spatio-temporal command of chemical gradients and reactant mixing during self-assembly (the creation of non-uniform chemical environments for example) can strongly affect the outcome of the self-assembly process. This directly enables a precise control over material properties and functions. In this tutorial review, we show how the unique physical conditions offered by microfluidic technologies can be advantageously used to control the self-assembly of materials and of supramolecular aggregates in solution, making possible the isolation of intermediate states and unprecedented non-equilibrium structures, as well as the emergence of novel functions. Selected examples from the literature will be used to confirm that microfluidic devices are an invaluable toolbox technology for unveiling, understanding and steering self-assembly pathways to desired structures, properties and functions, as well as advanced processing tools for device fabrication and integration.

Chemical equilibrium. [maximizing entropy of gas system to derive relations between thermodynamic variables

NASA Technical Reports Server (NTRS)

1976-01-01

The entropy of a gas system with the number of particles subject to external control is maximized to derive relations between the thermodynamic variables that obtain at equilibrium. These relations are described in terms of the chemical potential, defined as equivalent partial derivatives of entropy, energy, enthalpy, free energy, or free enthalpy. At equilibrium, the change in total chemical potential must vanish. This fact is used to derive the equilibrium constants for chemical reactions in terms of the partition functions of the species involved in the reaction. Thus the equilibrium constants can be determined accurately, just as other thermodynamic properties, from a knowledge of the energy levels and degeneracies for the gas species involved. These equilibrium constants permit one to calculate the equilibrium concentrations or partial pressures of chemically reacting species that occur in gas mixtures at any given condition of pressure and temperature or volume and temperature.

Equilibrium properties of the Skylab CMG rotation law

NASA Technical Reports Server (NTRS)

Elrod, B. D.; Anderson, G. M.

1972-01-01

The equilibrium properties of the control moment gyroscopes of the Skylab are discussed. A rotation law is developed to produce gimbal rates which distribute the angular momentum contributions among the control moment gyroscopes to avoid gimbal stop encounters. The implications for gimbal angle management under various angular momentum situations are described. Conditions were obtained for the existence of equilibria and corresponding stability properties.

Linearized theory of inhomogeneous multiple 'water-bag' plasmas

NASA Technical Reports Server (NTRS)

Bloomberg, H. W.; Berk, H. L.

1973-01-01

Equations are derived for describing the inhomogeneous equilibrium and small deviations from the equilibrium, giving particular attention to systems with trapped particles. An investigation is conducted of periodic systems with a single trapped-particle water bag, taking into account the behavior of the perturbation equations at the turning points. An outline is provided concerning a procedure for obtaining the eigenvalues. The results of stability calculations connected with the sideband effects are considered along with questions regarding the general applicability of the multiple water-bag approach in stability calculations.

Extrapolation to Nonequilibrium from Coarse-Grained Response Theory

NASA Astrophysics Data System (ADS)

Basu, Urna; Helden, Laurent; Krüger, Matthias

2018-05-01

Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many-body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse-grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far-from-equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many-body systems. It is illustrated in a four-state model and in the near critical Ising model.

Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

NASA Astrophysics Data System (ADS)

Zheng, Da-Chuan; Tong, Ning-Hua

2017-06-01

Using the bosonic numerical renormalization group method, we studied the equilibrium dynamical correlation function C(ω) of the spin operator σ z for the biased sub-Ohmic spin-boson model. The small-ω behavior C(ω )\\propto {ω }s is found to be universal and independent of the bias ɛ and the coupling strength α (except at the quantum critical point α ={α }{{c}} and ɛ = 0). Our NRG data also show C(ω )\\propto {χ }2{ω }s for a wide range of parameters, including the biased strong coupling regime (\\varepsilon \

Design of an Integrated Plasma Control System and Extension of XSCTools to Ignitor

NASA Astrophysics Data System (ADS)

Albanese, R.; Ambrosino, G.; Artaserse, G.; Pironti, A.; Rubinacci, G.; Villone, F.; Ramogida, G.

2010-11-01

The performance of the integrated system for vertical stability, shape and plasma current control for the Ignitor machine has been assessed by means of the CREATELlinearized model of plasma responseootnotetextR. Albanese, F. Villone, Nucl. Fusion 38, 723 (1998) against a set of disturbances for the reference 11 MA limiter configuration and the 9 MA Double Null configuration. A new design, based on the methodology of the eXtreme Shape Controller (XSC) at JET, has been tested : by using all the shape control circuits with the exception of those used to control the vertical stability is possible to control up to four independent linear combinations of the 36 plasma-wall gaps. The results point out a substantial improvement in shape recovery, especially in the presence of a disturbance in li. The new shape controller can also automatically generate, via feedback control, new plasma shapes in the proximity of a given equilibrium configuration. The XSC ToolsootnotetextG. Ambrosino, R. Albanese et al., Fus. Eng.& Des. 74, 521 (2005) have been adapted and extended to develop linearized Ignitor models including 2D eddy currents and to solve inverse linearized plasma equilibria.

Prediction of U-Mo dispersion nuclear fuels with Al-Si alloy using artificial neural network

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

Susmikanti, Mike, E-mail: mike@batan.go.id; Sulistyo, Jos, E-mail: soj@batan.go.id

2014-09-30

Dispersion nuclear fuels, consisting of U-Mo particles dispersed in an Al-Si matrix, are being developed as fuel for research reactors. The equilibrium relationship for a mixture component can be expressed in the phase diagram. It is important to analyze whether a mixture component is in equilibrium phase or another phase. The purpose of this research it is needed to built the model of the phase diagram, so the mixture component is in the stable or melting condition. Artificial neural network (ANN) is a modeling tool for processes involving multivariable non-linear relationships. The objective of the present work is to developmore » code based on artificial neural network models of system equilibrium relationship of U-Mo in Al-Si matrix. This model can be used for prediction of type of resulting mixture, and whether the point is on the equilibrium phase or in another phase region. The equilibrium model data for prediction and modeling generated from experimentally data. The artificial neural network with resilient backpropagation method was chosen to predict the dispersion of nuclear fuels U-Mo in Al-Si matrix. This developed code was built with some function in MATLAB. For simulations using ANN, the Levenberg-Marquardt method was also used for optimization. The artificial neural network is able to predict the equilibrium phase or in the phase region. The develop code based on artificial neural network models was built, for analyze equilibrium relationship of U-Mo in Al-Si matrix.« less

Study of Globus-M Tokamak Poloidal System and Plasma Position Control

NASA Astrophysics Data System (ADS)

Dokuka, V. N.; Korenev, P. S.; Mitrishkin, Yu. V.; Pavlova, E. A.; Patrov, M. I.; Khayrutdinov, R. R.

2017-12-01

In order to provide efficient performance of tokamaks with vertically elongated plasma position, control systems for limited and diverted plasma configuration are required. The accuracy, stability, speed of response, and reliability of plasma position control as well as plasma shape and current control depend on the performance of the control system. Therefore, the problem of the development of such systems is an important and actual task in modern tokamaks. In this study, the measured signals from the magnetic loops and Rogowski coils are used to reconstruct the plasma equilibrium, for which linear models in small deviations are constructed. We apply methods of the H∞-optimization theory to the synthesize control system for vertical and horizontal position of plasma capable to working with structural uncertainty of the models of the plant. These systems are applied to the plasma-physical DINA code which is configured for the tokamak Globus-M plasma. The testing of the developed systems applied to the DINA code with Heaviside step functions have revealed the complex dynamics of plasma magnetic configurations. Being close to the bifurcation point in the parameter space of unstable plasma has made it possible to detect an abrupt change in the X-point position from the top to the bottom and vice versa. Development of the methods for reconstruction of plasma magnetic configurations and experience in designing plasma control systems with feedback for tokamaks provided an opportunity to synthesize new digital controllers for plasma vertical and horizontal position stabilization. It also allowed us to test the synthesized digital controllers in the closed loop of the control system with the DINA code as a nonlinear model of plasma.

Constant speed control of four-stroke micro internal combustion swing engine

NASA Astrophysics Data System (ADS)

Gao, Dedong; Lei, Yong; Zhu, Honghai; Ni, Jun

2015-09-01

The increasing demands on safety, emission and fuel consumption require more accurate control models of micro internal combustion swing engine (MICSE). The objective of this paper is to investigate the constant speed control models of four-stroke MICSE. The operation principle of the four-stroke MICSE is presented based on the description of MICSE prototype. A two-level Petri net based hybrid model is proposed to model the four-stroke MICSE engine cycle. The Petri net subsystem at the upper level controls and synchronizes the four Petri net subsystems at the lower level. The continuous sub-models, including breathing dynamics of intake manifold, thermodynamics of the chamber and dynamics of the torque generation, are investigated and integrated with the discrete model in MATLAB Simulink. Through the comparison of experimental data and simulated DC voltage output, it is demonstrated that the hybrid model is valid for the four-stroke MICSE system. A nonlinear model is obtained from the cycle average data via the regression method, and it is linearized around a given nominal equilibrium point for the controller design. The feedback controller of the spark timing and valve duration timing is designed with a sequential loop closing design approach. The simulation of the sequential loop closure control design applied to the hybrid model is implemented in MATLAB. The simulation results show that the system is able to reach its desired operating point within 0.2 s, and the designed controller shows good MICSE engine performance with a constant speed. This paper presents the constant speed control models of four-stroke MICSE and carries out the simulation tests, the models and the simulation results can be used for further study on the precision control of four-stroke MICSE.

Communication: A method to compute the transport coefficient of pure fluids diffusing through planar interfaces from equilibrium molecular dynamics simulations.

PubMed

Vermorel, Romain; Oulebsir, Fouad; Galliero, Guillaume

2017-09-14

The computation of diffusion coefficients in molecular systems ranks among the most useful applications of equilibrium molecular dynamics simulations. However, when dealing with the problem of fluid diffusion through vanishingly thin interfaces, classical techniques are not applicable. This is because the volume of space in which molecules diffuse is ill-defined. In such conditions, non-equilibrium techniques allow for the computation of transport coefficients per unit interface width, but their weak point lies in their inability to isolate the contribution of the different physical mechanisms prone to impact the flux of permeating molecules. In this work, we propose a simple and accurate method to compute the diffusional transport coefficient of a pure fluid through a planar interface from equilibrium molecular dynamics simulations, in the form of a diffusion coefficient per unit interface width. In order to demonstrate its validity and accuracy, we apply our method to the case study of a dilute gas diffusing through a smoothly repulsive single-layer porous solid. We believe this complementary technique can benefit to the interpretation of the results obtained on single-layer membranes by means of complex non-equilibrium methods.

Conformal field theory out of equilibrium: a review

NASA Astrophysics Data System (ADS)

Bernard, Denis; Doyon, Benjamin

2016-06-01

We provide a pedagogical review of the main ideas and results in non-equilibrium conformal field theory and connected subjects. These concern the understanding of quantum transport and its statistics at and near critical points. Starting with phenomenological considerations, we explain the general framework, illustrated by the example of the Heisenberg quantum chain. We then introduce the main concepts underlying conformal field theory (CFT), the emergence of critical ballistic transport, and the CFT scattering construction of non-equilibrium steady states. Using this we review the theory for energy transport in homogeneous one-dimensional critical systems, including the complete description of its large deviations and the resulting (extended) fluctuation relations. We generalize some of these ideas to one-dimensional critical charge transport and to the presence of defects, as well as beyond one-dimensional criticality. We describe non-equilibrium transport in free-particle models, where connections are made with generalized Gibbs ensembles, and in higher-dimensional and non-integrable quantum field theories, where the use of the powerful hydrodynamic ideas for non-equilibrium steady states is explained. We finish with a list of open questions. The review does not assume any advanced prior knowledge of conformal field theory, large-deviation theory or hydrodynamics.

On the dynamics of a spinning top under the influence of rotation: Resonant relative equilibrium states

NASA Astrophysics Data System (ADS)

Sheheitli, H.; Touma, J. R.

2018-06-01

We investigate the dynamics of a spinning top driven by a turntable that rotates with a given angular speed Ω. The pivot point of the top is at a fixed distance from the center of the turntable. We show that such a setup leads to resonance where the spinning top is locked in a state of relative equilibrium: precessing with an angular speed equal to that of the turntable while maintaining a constant nutation angle. Bifurcation diagrams are presented to depict how the stability of these relative equilibria, along with the corresponding value of the nutation angle, depends on the two parameters: the initial spin angular momentum and Ω. We discuss the classical spinning top, that is, the Ω = 0 case, and address the relation of the "sleeping top" state to the aforementioned relative equilibria. We also relate the dynamics to that of a spherical pendulum on a rotary arm and show that the latter can be viewed as a special case of the system at hand. Finally, we illustrate how the relative equilibria can be exploited for the attitude control of the top through resonance capture while slowly varying the turnable angular speed, Ω.

Kinetic Monte Carlo simulations for transient thermal fields: Computational methodology and application to the submicrosecond laser processes in implanted silicon.

PubMed

Fisicaro, G; Pelaz, L; Lopez, P; La Magna, A

2012-09-01

Pulsed laser irradiation of damaged solids promotes ultrafast nonequilibrium kinetics, on the submicrosecond scale, leading to microscopic modifications of the material state. Reliable theoretical predictions of this evolution can be achieved only by simulating particle interactions in the presence of large and transient gradients of the thermal field. We propose a kinetic Monte Carlo (KMC) method for the simulation of damaged systems in the extremely far-from-equilibrium conditions caused by the laser irradiation. The reference systems are nonideal crystals containing point defect excesses, an order of magnitude larger than the equilibrium density, due to a preirradiation ion implantation process. The thermal and, eventual, melting problem is solved within the phase-field methodology, and the numerical solutions for the space- and time-dependent thermal field were then dynamically coupled to the KMC code. The formalism, implementation, and related tests of our computational code are discussed in detail. As an application example we analyze the evolution of the defect system caused by P ion implantation in Si under nanosecond pulsed irradiation. The simulation results suggest a significant annihilation of the implantation damage which can be well controlled by the laser fluence.

Implications of low mechanical impedance in upper limb reaching motion.

PubMed

Popescu, Florin C; Rymeri, W Zev

2003-10-01

The equilibrium point hypothesis (EPH), much discussed in recent years, is central in a class of theories that posits an important role for muscular mechanical and reflex properties in the control of voluntary movement. We review briefly the findings of our studies testing the idea of equifinality, a major tenet of the EPH, which predicts that terminal limb position will be achieved regardless of transient perturbations in initial position or during ongoing movement. Our observations do not support this prediction of equifinality. We also report our findings that joint viscosity and elastic stiffness estimated during ballistic motion are unexpectedly low, limiting their potential contributions to the regulation either of limb movement trajectory or of limb stability. Taken together, our results imply that neuromuscular mechanical properties are unlikely to be used for regulating voluntary motion, and that other control strategies, most notably the use of feedforward controllers in which muscles act as force generators acting primarily on inertial loads, are more consistent with our observations.

Polynomial Method for PLL Controller Optimization†

PubMed Central

Wang, Ta-Chung; Lall, Sanjay; Chiou, Tsung-Yu

2011-01-01

The Phase-Locked Loop (PLL) is a key component of modern electronic communication and control systems. PLL is designed to extract signals from transmission channels. It plays an important role in systems where it is required to estimate the phase of a received signal, such as carrier tracking from global positioning system satellites. In order to robustly provide centimeter-level accuracy, it is crucial for the PLL to estimate the instantaneous phase of an incoming signal which is usually buried in random noise or some type of interference. This paper presents an approach that utilizes the recent development in the semi-definite programming and sum-of-squares field. A Lyapunov function will be searched as the certificate of the pull-in range of the PLL system. Moreover, a polynomial design procedure is proposed to further refine the controller parameters for system response away from the equilibrium point. Several simulation results as well as an experiment result are provided to show the effectiveness of this approach. PMID:22163973

Spontaneous Droplet Motion on a Periodically Compliant Substrate.

PubMed

Liu, Tianshu; Nadermann, Nichole; He, Zhenping; Strogatz, Steven H; Hui, Chung-Yuen; Jagota, Anand

2017-05-23

Droplet motion arises in many natural phenomena, ranging from the familiar gravity-driven slip and arrest of raindrops on windows to the directed transport of droplets for water harvesting by plants and animals under dry conditions. Deliberate transportation and manipulation of droplets are also important in many technological applications, including droplet-based microfluidic chemical reactors and for thermal management. Droplet motion usually requires gradients of surface energy or temperature or external vibration to overcome contact angle hysteresis. Here, we report a new phenomenon in which a drying droplet placed on a periodically compliant surface undergoes spontaneous, erratic motion in the absence of surface energy gradients and external stimuli such as vibration. By modeling the droplet as a mass-spring system on a substrate with periodically varying compliance, we show that the stability of equilibrium depends on the size of the droplet. Specifically, if the center of mass of the drop lies at a stable equilibrium point of the system, it will stay there until evaporation reduces its size and this fixed point becomes unstable; with any small perturbation, the droplet then moves to one of its neighboring fixed points.

Configuration maintaining control of three-body ring tethered system based on thrust compensation

NASA Astrophysics Data System (ADS)

Huang, Panfeng; Liu, Binbin; Zhang, Fan

2016-06-01

Space multi-tethered systems have shown broad prospects in remote observation missions. This paper mainly focuses on the dynamics and configuration maintaining control of space spinning three-body ring tethered system for such mission. Firstly, we establish the spinning dynamic model of the three-body ring tethered system considering the elasticity of the tether using Newton-Euler method, and then validate the suitability of this model by numerical simulation. Subsequently, LP (Likins-Pringle) initial equilibrium conditions for the tethered system are derived based on rigid body's equilibrium theory. Simulation results show that tether slack, snapping and interaction between the tethers exist in the three-body ring system, and its' configuration can not be maintained without control. Finally, a control strategy based on thrust compensation, namely thrust to simulate tether compression under LP initial equilibrium conditions is designed to solve the configuration maintaining control problem. Control effects are verified by numerical simulation compared with uncontrolled situation. Simulation results show that the configuration of the three-body ring tethered system could maintain under this active control strategy.

Multi-period equilibrium/near-equilibrium in electricity markets based on locational marginal prices

NASA Astrophysics Data System (ADS)

Garcia Bertrand, Raquel

In this dissertation we propose an equilibrium procedure that coordinates the point of view of every market agent resulting in an equilibrium that simultaneously maximizes the independent objective of every market agent and satisfies network constraints. Therefore, the activities of the generating companies, consumers and an independent system operator are modeled: (1) The generating companies seek to maximize profits by specifying hourly step functions of productions and minimum selling prices, and bounds on productions. (2) The goals of the consumers are to maximize their economic utilities by specifying hourly step functions of demands and maximum buying prices, and bounds on demands. (3) The independent system operator then clears the market taking into account consistency conditions as well as capacity and line losses so as to achieve maximum social welfare. Then, we approach this equilibrium problem using complementarity theory in order to have the capability of imposing constraints on dual variables, i.e., on prices, such as minimum profit conditions for the generating units or maximum cost conditions for the consumers. In this way, given the form of the individual optimization problems, the Karush-Kuhn-Tucker conditions for the generating companies, the consumers and the independent system operator are both necessary and sufficient. The simultaneous solution to all these conditions constitutes a mixed linear complementarity problem. We include minimum profit constraints imposed by the units in the market equilibrium model. These constraints are added as additional constraints to the equivalent quadratic programming problem of the mixed linear complementarity problem previously described. For the sake of clarity, the proposed equilibrium or near-equilibrium is first developed for the particular case considering only one time period. Afterwards, we consider an equilibrium or near-equilibrium applied to a multi-period framework. This model embodies binary decisions, i.e., on/off status for the units, and therefore optimality conditions cannot be directly applied. To avoid limitations provoked by binary variables, while retaining the advantages of using optimality conditions, we define the multi-period market equilibrium using Benders decomposition, which allows computing binary variables through the master problem and continuous variables through the subproblem. Finally, we illustrate these market equilibrium concepts through several case studies.

Point Defect Distributions in ZnSe Crystals: Effects of Gravity Vector Orientation During Physical Vapor Transport Growth

NASA Technical Reports Server (NTRS)

Su, Ching-Hua; Feth, S.; Hirschfeld, D.; Smith, T. M.; Wang, Ling Jun; Volz, M. P.; Lehoczky, S. L.

1999-01-01

ZnSe crystals were grown by the physical vapor transport technique under horizontal and vertical (stabilized and destabilized) configurations. Secondary ion mass spectroscopy and photoluminescence measurements were performed on the grown ZnSe samples to map the distributions of [Si], [Fe], [Cu], [Al] and [Li or Na] impurities as well as Zn vacancy, [V (sub Zn)]. Annealings of ZnSe under controlled Zn pressures were studied to correlate the measured photoluminescence emission intensity to the equilibrium Zn partial pressure. In the horizontal grown crystals the segregations of [Si], [Fe], [Al] and [V (sub Zn)] were observed along the gravity vector direction whereas in the vertically stabilized grown crystal the segregation of these point defects was radially symmetrical. No apparent pattern was observed on the measured distributions in the vertically destabilized grown crystal. The observed segregations in the three growth configurations were interpreted based on the possible buoyancy-driven convection in the vapor phase.

Controlled chemical stabilization of polyvinyl precursor fiber, and high strength carbon fiber produced therefrom

DOEpatents

Naskar, Amit K.

2016-12-27

Method for the preparation of carbon fiber, which comprises: (i) immersing functionalized polyvinyl precursor fiber into a liquid solution having a boiling point of at least 60.degree. C.; (ii) heating the liquid solution to a first temperature of at least 25.degree. C. at which the functionalized precursor fiber engages in an elimination-addition equilibrium while a tension of at least 0.1 MPa is applied to the fiber; (iii) gradually raising the first temperature to a final temperature that is at least 20.degree. C. above the first temperature and up to the boiling point of the liquid solution for sufficient time to convert the functionalized precursor fiber to a pre-carbonized fiber; and (iv) subjecting the pre-carbonized fiber produced according to step (iii) to high temperature carbonization conditions to produce the final carbon fiber. Articles and devices containing the fibers, including woven and non-woven mats or paper forms of the fibers, are also described.

Statistical prescission point model of fission fragment angular distributions

NASA Astrophysics Data System (ADS)

John, Bency; Kataria, S. K.

1998-03-01

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

Effects of 2D and 3D Error Fields on the SAS Divertor Magnetic Topology

NASA Astrophysics Data System (ADS)

Trevisan, G. L.; Lao, L. L.; Strait, E. J.; Guo, H. Y.; Wu, W.; Evans, T. E.

2016-10-01

The successful design of plasma-facing components in fusion experiments is of paramount importance in both the operation of future reactors and in the modification of operating machines. Indeed, the Small Angle Slot (SAS) divertor concept, proposed for application on the DIII-D experiment, combines a small incident angle at the plasma strike point with a progressively opening slot, so as to better control heat flux and erosion in high-performance tokamak plasmas. Uncertainty quantification of the error fields expected around the striking point provides additional useful information in both the design and the modeling phases of the new divertor, in part due to the particular geometric requirement of the striking flux surfaces. The presented work involves both 2D and 3D magnetic error field analysis on the SAS strike point carried out using the EFIT code for 2D equilibrium reconstruction, V3POST for vacuum 3D computations and the OMFIT integrated modeling framework for data analysis. An uncertainty in the magnetic probes' signals is found to propagate non-linearly as an uncertainty in the striking point and angle, which can be quantified through statistical analysis to yield robust estimates. Work supported by contracts DE-FG02-95ER54309 and DE-FC02-04ER54698.

Orbital Maneuvers for Spacecrafts Travelling to/from the Lagrangian Points

NASA Astrophysics Data System (ADS)

Bertachini, A.

The well-known Lagrangian points that appear in the planar restricted three-body problem (Szebehely, 1967) are very important for astronautical applications. They are five points of equilibrium in the equations of motion, what means that a particle located at one of those points with zero velocity will remain there indefinitely. The collinear points (L1, L2 and L3) are always unstable and the triangular points (L4 and L5) are stable in the present case studied (Sun-Earth system). They are all very good points to locate a space-station, since they require a small amount of V (and fuel), the control to be used for station-keeping. The triangular points are specially good for this purpose, since they are stable equilibrium points. In this paper, the planar restricted three-body problem is regularized (using Lemaître regularization) and combined with numerical integration and gradient methods to solve the two point boundary value problem (the Lambert's three-body problem). This combination is applied to the search of families of transfer orbits between the Lagrangian points and the Earth, in the Sun-Earth system, with the minimum possible cost of the control used. So, the final goal of this paper is to find the magnitude and direction of the two impulses to be applied in the spacecraft to complete the transfer: the first one when leaving/arriving at the Lagrangian point and the second one when arriving/living at the Earth. This paper is a continuation of two previous papers that studied transfers in the Earth-Moon system: Broucke (1979), that studied transfer orbits between the Lagrangian points and the Moon and Prado (1996), that studied transfer orbits between the Lagrangian points and the Earth. So, the equations of motion are: whereis the pseudo-potential given by: To solve the TPBVP in the regularized variables the following steps are used: i) Guess a initial velocity Vi, so together with the initial prescribed position ri the complete initial state is known; ii) Guess a final regularized time f and integrate the regularized equations of motion from 0 = 0 until f; iii) Check the final position rf obtained from the numerical integration with the prescribed final position and the final real time with the specified time of flight. If there is an agreement (difference less than a specified error allowed) the solution is found and the process can stop here. If there is no agreement, an increment in the initial guessed velocity Vi and in the guessed final regularized time is made and the process goes back to step i). The method used to find the increment in the guessed variables is the standard gradient method, as described in Press et. al., 1989. The routines available in this reference are also used in this research with minor modifications. After that this algorithm is implemented, the Lambert's three-body problem between the Earth and the Lagrangian points is solved for several values of the time of flight. Since the regularized system is used to solve this problem, there is no need to specify the final position of M3 as lying in an primary's parking orbit (to avoid the singularity). Then, to make a comparison with previous papers (Broucke, 1979 and Prado, 1996) the centre of the primary is used as the final position for M3. The results are organized in plots of the energy and the initial flight path angle (the control to be used) in the rotating frame against the time of flight. The definition of the angle is such that the zero is in the "x" axis, (pointing to the positive direction) and it increases in the counter-clock-wise sense. This problem, as well as the Lambert's original version, has two solutions for a given transfer time: one in the counter-clock-wise direction and one in the clock-wise direction in the inertial frame. In this paper, emphasis is given in finding the families with the smallest possible energy (and velocity), although many other families do exist. Broucke, R., (1979) Travelling Between the Lagrange Points and the Moon, Journal of Guidance and Control, Vol. 2, Prado, A.F.B.A., (1969) Travelling Between the Lagrangian Points and the Earth, Acta Astronautica, Vol. 39, No. 7, pp. Press, W. H.; B. P. Flannery; S. A. Teukolsky and W. T. Vetterling (1989), Numerical Recipes, Cambridge University Szebehely, V., (1967), Theory of Orbits, Academic Press, New York.

Population and prehistory II: Space-limited human populations in constant environments

PubMed Central

Puleston, Cedric O.; Tuljapurkar, Shripad

2010-01-01

We present a population model to examine the forces that determined the quality and quantity of human life in early agricultural societies where cultivable area is limited. The model is driven by the non-linear and interdependent relationships between the age distribution of a population, its behavior and technology, and the nature of its environment. The common currency in the model is the production of food, on which age-specific rates of birth and death depend. There is a single nontrivial equilibrium population at which productivity balances caloric needs. One of the most powerful controls on equilibrium hunger level is fertility control. Gains against hunger are accompanied by decreases in population size. Increasing worker productivity does increase equilibrium population size but does not improve welfare at equilibrium. As a case study we apply the model to the population of a Polynesian valley before European contact. PMID:18598711

Population and prehistory II: space-limited human populations in constant environments.

PubMed

Puleston, Cedric O; Tuljapurkar, Shripad

2008-09-01

We present a population model to examine the forces that determined the quality and quantity of human life in early agricultural societies where cultivable area is limited. The model is driven by the non-linear and interdependent relationships between the age distribution of a population, its behavior and technology, and the nature of its environment. The common currency in the model is the production of food, on which age-specific rates of birth and death depend. There is a single non-trivial equilibrium population at which productivity balances caloric needs. One of the most powerful controls on equilibrium hunger level is fertility control. Gains against hunger are accompanied by decreases in population size. Increasing worker productivity does increase equilibrium population size but does not improve welfare at equilibrium. As a case study we apply the model to the population of a Polynesian valley before European contact.