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.

Role of delay and screening in controlling AIDS

NASA Astrophysics Data System (ADS)

Chauhan, Sudipa; Bhatia, Sumit Kaur; Gupta, Surbhi

2016-06-01

We propose a non-linear HIV/ AIDS model to analyse the spread and control of HIV/AIDS. The population is divided into three classes, susceptible, infective and AIDS patients. The model is developed under the assumptions of vertical transmission and time delay in infective class. Time delay is also included to show sexual maturity period of infected newborns. We study dynamics of the model and obtain the reproduction number. Now to control the epidemic, we study the model where aware infective class is also added, i.e., people are made aware of their medical status by way of screening. To make the model more realistic, we consider the situation where aware infective class also interacts with other people. The model is analysed qualitatively by stability theory of ODE. Stability analysis of both disease-free and endemic equilibrium is studied based on reproduction number. Also, it is proved that if (R0)1, R1 ≤ 1 then, disease free equilibrium point is locally asymptotically stable and if (R0)1, R1 > 1 then, disease free equilibrium is unstable. Also, the stability analysis of endemic equilibrium point has been done and it is shown that for (R0)1 > 1 endemic equilibrium point is stable. Global stability analysis of endemic equilibrium point has also been done. At last, it is shown numerically that the delay in sexual maturity of infected individuals result in less number of AIDS patients.

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.

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.

Dynamics and control of high area-to-mass ratio spacecraft and its application to geomagnetic exploration

NASA Astrophysics Data System (ADS)

Luo, Tong; Xu, Ming; Colombo, Camilla

2018-04-01

This paper studies the dynamics and control of a spacecraft, whose area-to-mass ratio is increased by deploying a reflective orientable surface such as a solar sail or a solar panel. The dynamical system describing the motion of a non-zero attitude angle high area-to-mass ratio spacecraft under the effects of the Earth's oblateness and solar radiation pressure admits the existence of equilibrium points, whose number and the eccentricity values depend on the semi-major axis, the area-to-mass ratio and the attitude angle of the spacecraft together. When two out of three parameters are fixed, five different dynamical topologies successively occur through varying the third parameter. Two of these five topologies are critical cases characterized by the appearance of the bifurcation phenomena. A conventional Hamiltonian structure-preserving (HSP) controller and an improved HSP controller are both constructed to stabilize the hyperbolic equilibrium point. Through the use of a conventional HSP controller, a bounded trajectory around the hyperbolic equilibrium point is obtained, while an improved HSP controller allows the spacecraft to easily transfer to the hyperbolic equilibrium point and to follow varying equilibrium points. A bifurcation control using topologies and changes of behavior areas can also stabilize a spacecraft near a hyperbolic equilibrium point. Natural trajectories around stable equilibrium point and these stabilized trajectories around hyperbolic equilibrium point can all be applied to geomagnetic exploration.

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.

Biomechanical stability analysis of the lambda-model controlling one joint.

PubMed

Lan, L; Zhu, K Y

2007-06-01

Computer modeling and control of the human motor system might be helpful for understanding the mechanism of human motor system and for the diagnosis and treatment of neuromuscular disorders. In this paper, a brief view of the equilibrium point hypothesis for human motor system modeling is given, and the lambda-model derived from this hypothesis is studied. The stability of the lambda-model based on equilibrium and Jacobian matrix is investigated. The results obtained in this paper suggest that the lambda-model is stable and has a unique equilibrium point under certain conditions.

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.

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.

Do planetary seasons play a role in attaining stable climates?

NASA Astrophysics Data System (ADS)

Olsen, Kasper Wibeck; Bohr, Jakob

2018-05-01

A simple phenomenological account for planetary climate instabilities is presented. The description is based on the standard model where the balance of incoming stellar radiation and outward thermal radiation is described by the effective planet temperature. Often, it is found to have three different points, or temperatures, where the influx of radiation is balanced with the out-flux, even with conserved boundary conditions. Two of these points are relatively long-term stable, namely the point corresponding to a cold climate and the point corresponding to a hot climate. In a classical sense these points are equilibrium balance points. The hypothesis promoted in this paper is the possibility that the intermediate third point can become long-term stable by being driven dynamically. The initially unstable point is made relatively stable over a long period by the presence of seasonal climate variations.

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.

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

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.

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.

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.

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.

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.

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.

Approximating basins of attraction for dynamical systems via stable radial bases

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

Cavoretto, R.; De Rossi, A.; Perracchione, E.

2016-06-08

In applied sciences it is often required to model and supervise temporal evolution of populations via dynamical systems. In this paper, we focus on the problem of approximating the basins of attraction of such models for each stable equilibrium point. We propose to reconstruct the basins via an implicit interpolant using stable radial bases, obtaining the surfaces by partitioning the phase space into disjoint regions. An application to a competition model presenting jointly three stable equilibria is considered.

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.

On the asymptotic stability of nonlinear mechanical switched systems

NASA Astrophysics Data System (ADS)

Platonov, A. V.

2018-05-01

Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.

Equilibria, prudent compromises, and the "waiting" game.

PubMed

Sim, Kwang Mong

2005-08-01

While evaluation of many e-negotiation agents are carried out through empirical studies, this work supplements and complements existing literature by analyzing the problem of designing market-driven agents (MDAs) in terms of equilibrium points and stable strategies. MDAs are negotiation agents designed to make prudent compromises taking into account factors such as time preference, outside option, and rivalry. This work shows that 1) in a given market situation, an MDA negotiates optimally because it makes minimally sufficient concession, and 2) by modeling negotiation of MDAs as a game gamma of incomplete information, it is shown that the strategies adopted by MDAs are stable. In a bilateral negotiation, it is proven that the strategy pair of two MDAs forms a sequential equilibrium for gamma. In a multilateral negotiation, it is shown that the strategy profile of MDAs forms a market equilibrium for gamma.

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.

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.

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.

Algebraic and radical potential fields. Stability domains in coordinate and parametric space

NASA Astrophysics Data System (ADS)

Uteshev, Alexei Yu.

2018-05-01

A dynamical system d X/d t = F(X; A) is treated where F(X; A) is a polynomial (or some general type of radical contained) function in the vectors of state variables X ∈ ℝn and parameters A ∈ ℝm. We are looking for stability domains in both spaces, i.e. (a) domain ℙ ⊂ ℝm such that for any parameter vector specialization A ∈ ℙ, there exists a stable equilibrium for the dynamical system, and (b) domain 𝕊 ⊂ ℝn such that any point X* ∈ 𝕊 could be made a stable equilibrium by a suitable specialization of the parameter vector A.

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.

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.

Quantum Spin Stabilized Magnetic Levitation

NASA Astrophysics Data System (ADS)

Rusconi, C. C.; Pöchhacker, V.; Kustura, K.; Cirac, J. I.; Romero-Isart, O.

2017-10-01

We theoretically show that, despite Earnshaw's theorem, a nonrotating single magnetic domain nanoparticle can be stably levitated in an external static magnetic field. The stabilization relies on the quantum spin origin of magnetization, namely, the gyromagnetic effect. We predict the existence of two stable phases related to the Einstein-de Haas effect and the Larmor precession. At a stable point, we derive a quadratic Hamiltonian that describes the quantum fluctuations of the degrees of freedom of the system. We show that, in the absence of thermal fluctuations, the quantum state of the nanomagnet at the equilibrium point contains entanglement and squeezing.

Quantum Spin Stabilized Magnetic Levitation.

PubMed

Rusconi, C C; Pöchhacker, V; Kustura, K; Cirac, J I; Romero-Isart, O

2017-10-20

We theoretically show that, despite Earnshaw's theorem, a nonrotating single magnetic domain nanoparticle can be stably levitated in an external static magnetic field. The stabilization relies on the quantum spin origin of magnetization, namely, the gyromagnetic effect. We predict the existence of two stable phases related to the Einstein-de Haas effect and the Larmor precession. At a stable point, we derive a quadratic Hamiltonian that describes the quantum fluctuations of the degrees of freedom of the system. We show that, in the absence of thermal fluctuations, the quantum state of the nanomagnet at the equilibrium point contains entanglement and squeezing.

Non-equilibrium thermodynamical description of rhythmic motion patterns of active systems: a canonical-dissipative approach.

PubMed

Dotov, D G; Kim, S; Frank, T D

2015-02-01

We derive explicit expressions for the non-equilibrium thermodynamical variables of a canonical-dissipative limit cycle oscillator describing rhythmic motion patterns of active systems. These variables are statistical entropy, non-equilibrium internal energy, and non-equilibrium free energy. In particular, the expression for the non-equilibrium free energy is derived as a function of a suitable control parameter. The control parameter determines the Hopf bifurcation point of the deterministic active system and describes the effective pumping of the oscillator. In analogy to the equilibrium free energy of the Landau theory, it is shown that the non-equilibrium free energy decays as a function of the control parameter. In doing so, a similarity between certain equilibrium and non-equilibrium phase transitions is pointed out. Data from an experiment on human rhythmic movements is presented. Estimates for pumping intensity as well as the thermodynamical variables are reported. It is shown that in the experiment the non-equilibrium free energy decayed when pumping intensity was increased, which is consistent with the theory. Moreover, pumping intensities close to zero could be observed at relatively slow intended rhythmic movements. In view of the Hopf bifurcation underlying the limit cycle oscillator model, this observation suggests that the intended limit cycle movements were actually more similar to trajectories of a randomly perturbed stable focus. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

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.

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.

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.

Specific non-monotonous interactions increase persistence of ecological networks.

PubMed

Yan, Chuan; Zhang, Zhibin

2014-03-22

The relationship between stability and biodiversity has long been debated in ecology due to opposing empirical observations and theoretical predictions. Species interaction strength is often assumed to be monotonically related to population density, but the effects on stability of ecological networks of non-monotonous interactions that change signs have not been investigated previously. We demonstrate that for four kinds of non-monotonous interactions, shifting signs to negative or neutral interactions at high population density increases persistence (a measure of stability) of ecological networks, while for the other two kinds of non-monotonous interactions shifting signs to positive interactions at high population density decreases persistence of networks. Our results reveal a novel mechanism of network stabilization caused by specific non-monotonous interaction types through either increasing stable equilibrium points or reducing unstable equilibrium points (or both). These specific non-monotonous interactions may be important in maintaining stable and complex ecological networks, as well as other networks such as genes, neurons, the internet and human societies.

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.

Development of safe mechanism for surgical robots using equilibrium point control method.

PubMed

Park, Shinsuk; Lim, Hokjin; Kim, Byeong-sang; Song, Jae-bok

2006-01-01

This paper introduces a novel mechanism for surgical robotic systems to generate human arm-like compliant motion. The mechanism is based on the idea of the equilibrium point control hypothesis which claims that multi-joint limb movements are achieved by shifting the limbs' equilibrium positions defined by neuromuscular activity. The equilibrium point control can be implemented on a robot manipulator by installing two actuators at each joint of the manipulator, one to control the joint position, and the other to control the joint stiffness. This double-actuator mechanism allows us to arbitrarily manipulate the stiffness (or impedance) of a robotic manipulator as well as its position. Also, the force at the end-effector can be estimated based on joint stiffness and joint angle changes without using force transducers. A two-link manipulator and a three-link manipulator with the double-actuator units have been developed, and experiments and simulation results show the potential of the proposed approach. By creating the human arm-like behavior, this mechanism can improve the performance of robot manipulators to execute stable and safe movement in surgical environments by using a simple control scheme.

Evolutionary behaviour, trade-offs and cyclic and chaotic population dynamics.

PubMed

Hoyle, Andy; Bowers, Roger G; White, Andy

2011-05-01

Many studies of the evolution of life-history traits assume that the underlying population dynamical attractor is stable point equilibrium. However, evolutionary outcomes can change significantly in different circumstances. We present an analysis based on adaptive dynamics of a discrete-time demographic model involving a trade-off whose shape is also an important determinant of evolutionary behaviour. We derive an explicit expression for the fitness in the cyclic region and consequently present an adaptive dynamic analysis which is algebraic. We do this fully in the region of 2-cycles and (using a symbolic package) almost fully for 4-cycles. Simulations illustrate and verify our results. With equilibrium population dynamics, trade-offs with accelerating costs produce a continuously stable strategy (CSS) whereas trade-offs with decelerating costs produce a non-ES repellor. The transition to 2-cycles produces a discontinuous change: the appearance of an intermediate region in which branching points occur. The size of this region decreases as we move through the region of 2-cycles. There is a further discontinuous fall in the size of the branching region during the transition to 4-cycles. We extend our results numerically and with simulations to higher-period cycles and chaos. Simulations show that chaotic population dynamics can evolve from equilibrium and vice-versa.

Combining stable isotope isotope geochemistry and carbonic anhydrase activity to trace vital effect in carbonate precipitation experiments

NASA Astrophysics Data System (ADS)

Thaler, C.; Ader, M.; Menez, B.; Guyot, F. J.

2013-12-01

Carbonates precipitated by skeleton-forming eukaryotic organisms are often characterized by non-equilibrium isotopic signatures. This specificity is referred to as the "vital effect" and can be used as an isotopic evidence to trace life. Combining stable isotope geochemistry and enzymology (using the enzyme carbonic anhydrase) we aim to demonstrate that prokaryotes are also able to precipitate carbonate with a non-equilibrium d18OCaCO3. Indeed, if in an biomineralization experiment carbonates are precipitated with a vital effect, the addition of carbonic anhydrase should drive the system to isotope equilibrium, And provide a comparison point to estimate the vital effect range. This protocol allowed us to identify a -20‰ vital effect for the d18O of carbonates precipitated by Sporosarcina pasteurii, a bacterial model of carbonatogen metabolisms. This approach is thus a powerfull tool for the understanding of microbe carbonatogen activity and will probably bring new insights into the understanding of bacterial activity in subsurface and during diagenesis.

Polymorphism of phosphoric oxide

USGS Publications Warehouse

Hill, W.L.; Faust, G.T.; Hendricks, S.B.

1943-01-01

The melting points and monotropic relationship of three crystalline forms of phosphoric oxide were determined by the method of quenching. Previous vapor pressure data are discussed and interpreted to establish a pressure-temperature diagram (70 to 600??) for the one-component system. The system involves three triple points, at which solid, liquid and vapor (P4O10) coexist in equilibrium, namely: 420?? and 360 cm., 562?? and 43.7 cm. and 580?? and 55.5 cm., corresponding to the hexagonal, orthorhombic and stable polymorphs, respectively, and at least two distinct liquids, one a stable polymer of the other, which are identified with the melting of the stable form and the hexagonal modification, respectively. Indices of refraction of the polymorphs and glasses were determined. The density and the thermal, hygroscopic and structural properties of the several phases are discussed.

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.

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.

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.

From Wang-Chen System with Only One Stable Equilibrium to a New Chaotic System Without Equilibrium

NASA Astrophysics Data System (ADS)

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

2017-06-01

Wang-Chen system with only one stable equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang-Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one stable equilibrium to hidden attractors without equilibrium.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Nonlinear Dynamic Models in Advanced Life Support

NASA Technical Reports Server (NTRS)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

THE INTERSECTION OF STABLE AND NON-EQUILIBRIUM TETRAHEDRA IN A MUTUAL 7- COMPONENT SYSTEM OF Li, Na, Rb, T1/Br, C1, NO$sub 3$, SO$sub 4$ (in Russian)

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

Dombrovskaya, N.S.; Khakhlova, N.V.; Alekseeva, E.A.

1961-04-21

The most stable configuration of the mixture of the 16 salts formed from Li, Na, Rb, Tl/Br, Cl, NO/sub 3/, and S0/sub 4/ con ture which however interact, resulting in a stable mixture. On the basis of exchange reactions the following equation has been derived: LiBr + NaNO/sub 3/ + RbCl + 1/2Tl/sub 2/SO/sub 4/ = 1/ 2LiSO/sub 4/ + NaCl + RbNO/sub 3/ + TlBr. In addition, several binary complexes are also formed, such as Li/sub 2/SO/sub 4/ - Rb/sub 2/SO/sub 4/, 4Li/sub 2/SO/ sub 4/ - RbSO /sub 4/, RbCl - 2Li/sub 2/SO/sub 4/ and possible others. Inmore » view of the great interest, the intersection of stable and non-equilibrium tetrahedra consisting of components of both, was experimentally studied by thermai analysis. On the basis of cooling curves the following deflection points have been observed: 453 deg C, precipitation of the first Li/sub 2/SO/sub 4/ crystals; 409 deg , coprecipitation of Li/sub 2/SO/sub 4/ and NaCl; 391 deg , coprecipitation of Li/sub 2/SO/sub 4/, NaCl snd TlBr; and finally at 107 deg , formation of the quaternary eutectic with the previously mentioned salts + RbNO/sub 3/. The microstructures of the stable and non-equilibrium phases are quite similar. (TTT)« less

Dynamically stable magnetic suspension/bearing system

DOEpatents

Post, R.F.

1996-02-27

A magnetic bearing system contains magnetic subsystems which act together to support a rotating element in a state of dynamic equilibrium. However, owing to the limitations imposed by Earnshaw`s Theorem, the magnetic bearing systems to be described do not possess a stable equilibrium at zero rotational speed. Therefore, mechanical stabilizers are provided, in each case, to hold the suspended system in equilibrium until its speed has exceeded a low critical speed where dynamic effects take over, permitting the achievement of a stable equilibrium for the rotating object. A state of stable equilibrium is achieved above a critical speed by use of a collection of passive elements using permanent magnets to provide their magnetomotive excitation. The magnetic forces exerted by these elements, when taken together, levitate the rotating object in equilibrium against external forces, such as the force of gravity or forces arising from accelerations. At the same time, this equilibrium is made stable against displacements of the rotating object from its equilibrium position by using combinations of elements that possess force derivatives of such magnitudes and signs that they can satisfy the conditions required for a rotating body to be stably supported by a magnetic bearing system over a finite range of those displacements. 32 figs.

Dynamically stable magnetic suspension/bearing system

DOEpatents

Post, Richard F.

1996-01-01

A magnetic bearing system contains magnetic subsystems which act together to support a rotating element in a state of dynamic equilibrium. However, owing to the limitations imposed by Earnshaw's Theorem, the magnetic bearing systems to be described do not possess a stable equilibrium at zero rotational speed. Therefore, mechanical stabilizers are provided, in each case, to hold the suspended system in equilibrium until its speed has exceeded a low critical speed where dynamic effects take over, permitting the achievement of a stable equilibrium for the rotating object. A state of stable equilibrium is achieved above a critical speed by use of a collection of passive elements using permanent magnets to provide their magnetomotive excitation. The magnetic forces exerted by these elements, when taken together, levitate the rotating object in equilibrium against external forces, such as the force of gravity or forces arising from accelerations. At the same time, this equilibrium is made stable against displacements of the rotating object from its equilibrium position by using combinations of elements that possess force derivatives of such magnitudes and signs that they can satisfy the conditions required for a rotating body to be stably supported by a magnetic bearing system over a finite range of those displacements.

Local Nash equilibrium in social networks.

PubMed

Zhang, Yichao; Aziz-Alaoui, M A; Bertelle, Cyrille; Guan, Jihong

2014-08-29

Nash equilibrium is widely present in various social disputes. As of now, in structured static populations, such as social networks, regular, and random graphs, the discussions on Nash equilibrium are quite limited. In a relatively stable static gaming network, a rational individual has to comprehensively consider all his/her opponents' strategies before they adopt a unified strategy. In this scenario, a new strategy equilibrium emerges in the system. We define this equilibrium as a local Nash equilibrium. In this paper, we present an explicit definition of the local Nash equilibrium for the two-strategy games in structured populations. Based on the definition, we investigate the condition that a system reaches the evolutionary stable state when the individuals play the Prisoner's dilemma and snow-drift game. The local Nash equilibrium provides a way to judge whether a gaming structured population reaches the evolutionary stable state on one hand. On the other hand, it can be used to predict whether cooperators can survive in a system long before the system reaches its evolutionary stable state for the Prisoner's dilemma game. Our work therefore provides a theoretical framework for understanding the evolutionary stable state in the gaming populations with static structures.

Local Nash Equilibrium in Social Networks

PubMed Central

Zhang, Yichao; Aziz-Alaoui, M. A.; Bertelle, Cyrille; Guan, Jihong

2014-01-01

Nash equilibrium is widely present in various social disputes. As of now, in structured static populations, such as social networks, regular, and random graphs, the discussions on Nash equilibrium are quite limited. In a relatively stable static gaming network, a rational individual has to comprehensively consider all his/her opponents' strategies before they adopt a unified strategy. In this scenario, a new strategy equilibrium emerges in the system. We define this equilibrium as a local Nash equilibrium. In this paper, we present an explicit definition of the local Nash equilibrium for the two-strategy games in structured populations. Based on the definition, we investigate the condition that a system reaches the evolutionary stable state when the individuals play the Prisoner's dilemma and snow-drift game. The local Nash equilibrium provides a way to judge whether a gaming structured population reaches the evolutionary stable state on one hand. On the other hand, it can be used to predict whether cooperators can survive in a system long before the system reaches its evolutionary stable state for the Prisoner's dilemma game. Our work therefore provides a theoretical framework for understanding the evolutionary stable state in the gaming populations with static structures. PMID:25169150

Local Nash Equilibrium in Social Networks

NASA Astrophysics Data System (ADS)

Zhang, Yichao; Aziz-Alaoui, M. A.; Bertelle, Cyrille; Guan, Jihong

2014-08-01

Nash equilibrium is widely present in various social disputes. As of now, in structured static populations, such as social networks, regular, and random graphs, the discussions on Nash equilibrium are quite limited. In a relatively stable static gaming network, a rational individual has to comprehensively consider all his/her opponents' strategies before they adopt a unified strategy. In this scenario, a new strategy equilibrium emerges in the system. We define this equilibrium as a local Nash equilibrium. In this paper, we present an explicit definition of the local Nash equilibrium for the two-strategy games in structured populations. Based on the definition, we investigate the condition that a system reaches the evolutionary stable state when the individuals play the Prisoner's dilemma and snow-drift game. The local Nash equilibrium provides a way to judge whether a gaming structured population reaches the evolutionary stable state on one hand. On the other hand, it can be used to predict whether cooperators can survive in a system long before the system reaches its evolutionary stable state for the Prisoner's dilemma game. Our work therefore provides a theoretical framework for understanding the evolutionary stable state in the gaming populations with static structures.

Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation

PubMed Central

Garić-Demirović, M.; Kulenović, M. R. S.; Nurkanović, M.

2013-01-01

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x n+1 = x n−1 2/(ax n 2 + bx n x n−1 + cx n−1 2), n = 0,1, 2,…, where the parameters a,  b, and  c are positive numbers and the initial conditions x −1 and x 0 are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilibrium solution and the minimal period-two solution both of which are locally asymptotically stable. PMID:24369451

Complexity analysis of dual-channel game model with different managers' business objectives

NASA Astrophysics Data System (ADS)

Li, Ting; Ma, Junhai

2015-01-01

This paper considers dual-channel game model with bounded rationality, using the theory of bifurcations of dynamical system. The business objectives of retailers are assumed to be different, which is closer to reality than previous studies. We study the local stable region of Nash equilibrium point and find that business objectives can expand the stable region and play an important role in price strategy. One interesting finding is that a fiercer competition tends to stabilize the Nash equilibrium. Simulation shows the complex behavior of two dimensional dynamic system, we find period doubling bifurcation and chaos phenomenon. We measure performances of the model in different period by using the index of average profit. The results show that unstable behavior in economic system is often an unfavorable outcome. So this paper discusses the application of adaptive adjustment mechanism when the model exhibits chaotic behavior and then allows the retailers to eliminate the negative effects.

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.

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.

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.

Free oscillations in a climate model with ice-sheet dynamics

NASA Technical Reports Server (NTRS)

Kallen, E.; Crafoord, C.; Ghil, M.

1979-01-01

A study of stable periodic solutions to a simple nonlinear model of the ocean-atmosphere-ice system is presented. The model has two dependent variables: ocean-atmosphere temperature and latitudinal extent of the ice cover. No explicit dependence on latitude is considered in the model. Hence all variables depend only on time and the model consists of a coupled set of nonlinear ordinary differential equations. The globally averaged ocean-atmosphere temperature in the model is governed by the radiation balance. The reflectivity to incoming solar radiation, i.e., the planetary albedo, includes separate contributions from sea ice and from continental ice sheets. The major physical mechanisms active in the model are (1) albedo-temperature feedback, (2) continental ice-sheet dynamics and (3) precipitation-rate variations. The model has three-equilibrium solutions, two of which are linearly unstable, while one is linearly stable. For some choices of parameters, the stability picture changes and sustained, finite-amplitude oscillations obtain around the previously stable equilibrium solution. The physical interpretation of these oscillations points to the possibility of internal mechanisms playing a role in glaciation cycles.

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.

Coexistence of Multiple Attractors in an Active Diode Pair Based Chua’s Circuit

NASA Astrophysics Data System (ADS)

Bao, Bocheng; Wu, Huagan; Xu, Li; Chen, Mo; Hu, Wen

This paper focuses on the coexistence of multiple attractors in an active diode pair based Chua’s circuit with smooth nonlinearity. With dimensionless equations, dynamical properties, including boundness of system orbits and stability distributions of two nonzero equilibrium points, are investigated, and complex coexisting behaviors of multiple kinds of disconnected attractors of stable point attractors, limit cycles and chaotic attractors are numerically revealed. The results show that unlike the classical Chua’s circuit, the proposed circuit has two stable nonzero node-foci for the specified circuit parameters, thereby resulting in the emergence of multistability phenomenon. Based on two general impedance converters, the active diode pair based Chua’s circuit with an adjustable inductor and an adjustable capacitor is made in hardware, from which coexisting multiple attractors are conveniently captured.

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.

Equilibrium stable-isotope fractionation of thallium and mercury

NASA Astrophysics Data System (ADS)

Schauble, E. A.

2005-12-01

In this study first-principles quantum mechanical and empirical force-field models are used to estimate equilibrium mass-dependent isotopic fractionations among a variety of thallium and mercury compounds. High-precision MC-ICP-MS measurements have recently uncovered evidence of stable isotope fractionation for many elements, including 2-4‰ variability in the isotopic compositions of thallium[1] (atomic no. 81) and mercury[2] (atomic no. 80). The observed thallium- and mercury-isotope fractionations are remarkable, given that the magnitude of isotopic fractionation typically decreases as atomic number increases[3]. Stable isotope measurements could improve our understanding of geochemical and biogeochemical cycling of both elements, but little is known about the mechanisms driving these fractionations. A better understanding of the chemical processes controlling stable isotope compositions could help maximize the utility of these new geochemical tracers. Standard equilibrium stable isotope fractionation theory holds that the energy driving fractionation comes from isotopic effects on vibrational frequencies, which have generally not been measured. In the present study both quantum-mechanical and empirical force fields are used to estimate unknown frequencies. Results suggest that thallium and mercury fractionations of ≥ 0.5‰ are likely during the relevant redox reactions Tl+ ↔ Tl3+ and HgO ↔ Hg2+. Methyl-mercury and mercury-halide compounds like CH3HgCl will have ~ 1‰ higher 202Hg/198Hg than atomic vapor at room temperature. Fractionations between coexisting Hg2+ species appear to be much smaller, however. 205Tl/203Tl in Tl(H2O)_63+ is predicted to be ~0.5‰ higher than in coexisting Tl+-bearing substances. This result is in qualitative agreement with data from ferromanganese crusts [1], suggesting that Tl3+ in manganese-oxides will have higher 205Tl/203Tl than aqueous Tl+. Equilibrium fractionations for both elements are much smaller than the observed range of isotopic fractionations, however, which could point to a major role for kinetic-fractionation or Rayleigh-like distillation processes. Refs.: [1] Rehämper et al. (2002) EPSL 197:65. [2] Xie et al. (2005) J. Anal. Atomic Spectrom. 20:515. [3] Bigeleisen and Mayer (1947) J. Chem. Phys. 15:261.

Evolution and polymorphism in the multilocus Levene model with no or weak epistasis.

PubMed

Bürger, Reinhard

2010-09-01

Evolution and the maintenance of polymorphism under the multilocus Levene model with soft selection are studied. The number of loci and alleles, the number of demes, the linkage map, and the degree of dominance are arbitrary, but epistasis is absent or weak. We prove that, without epistasis and under mild, generic conditions, every trajectory converges to a stationary point in linkage equilibrium. Consequently, the equilibrium and stability structure can be determined by investigating the much simpler gene-frequency dynamics on the linkage-equilibrium manifold. For a haploid species an analogous result is shown. For weak epistasis, global convergence to quasi-linkage equilibrium is established. As an application, the maintenance of multilocus polymorphism is explored if the degree of dominance is intermediate at every locus and epistasis is absent or weak. If there are at least two demes, then arbitrarily many multiallelic loci can be maintained polymorphic at a globally asymptotically stable equilibrium. Because this holds for an open set of parameters, such equilibria are structurally stable. If the degree of dominance is not only intermediate but also deme independent, and loci are diallelic, an open set of parameters yielding an internal equilibrium exists only if the number of loci is strictly less than the number of demes. Otherwise, a fully polymorphic equilibrium exists only nongenerically, and if it exists, it consists of a manifold of equilibria. Its dimension is determined. In the absence of genotype-by-environment interaction, however, a manifold of equilibria occurs for an open set of parameters. In this case, the equilibrium structure is not robust to small deviations from no genotype-by-environment interaction. In a quantitative-genetic setting, the assumptions of no epistasis and intermediate dominance are equivalent to assuming that in every deme directional selection acts on a trait that is determined additively, i.e., by nonepistatic loci with dominance. Some of our results are exemplified in this quantitative-genetic context. Copyright 2010 Elsevier Inc. All rights reserved.

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.

How a small noise generates large-amplitude oscillations of volcanic plug and provides high seismicity

NASA Astrophysics Data System (ADS)

Alexandrov, Dmitri V.; Bashkirtseva, Irina A.; Ryashko, Lev B.

2015-04-01

A non-linear behavior of dynamic model of the magma-plug system under the action of N-shaped friction force and stochastic disturbances is studied. It is shown that the deterministic dynamics essentially depends on the mutual arrangement of an equilibrium point and the friction force branches. Variations of this arrangement imply bifurcations, birth and disappearance of stable limit cycles, changes of the stability of equilibria, system transformations between mono- and bistable regimes. A slope of the right increasing branch of the friction function is responsible for the formation of such regimes. In a bistable zone, the noise generates transitions between small and large amplitude stochastic oscillations. In a monostable zone with single stable equilibrium, a new dynamic phenomenon of noise-induced generation of large amplitude stochastic oscillations in the plug rate and pressure is revealed. A beat-type dynamics of the plug displacement under the influence of stochastic forcing is studied as well.

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.

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.

The information capacity of hypercycles.

PubMed

Silvestre, Daniel A M M; Fontanari, José F

2008-10-21

Hypercycles are information integration systems which are thought to overcome the information crisis of prebiotic evolution by ensuring the coexistence of several short templates. For imperfect template replication, we derive a simple expression for the maximum number of distinct templates n(m) that can coexist in a hypercycle and show that it is a decreasing function of the length L of the templates. In the case of high replication accuracy we find that the product n(m)L tends to a constant value, limiting thus the information content of the hypercycle. Template coexistence is achieved either as a stationary equilibrium (stable fixed point) or a stable periodic orbit in which the total concentration of functional templates is nonzero. For the hypercycle system studied here we find numerical evidence that the existence of an unstable fixed point is a necessary condition for the presence of periodic orbits.

Delay induced stability switch, multitype bistability and chaos in an intraguild predation model.

PubMed

Shu, Hongying; Hu, Xi; Wang, Lin; Watmough, James

2015-12-01

In many predator-prey models, delay has a destabilizing effect and induces oscillations; while in many competition models, delay does not induce oscillations. By analyzing a rather simple delayed intraguild predation model, which combines both the predator-prey relation and competition, we show that delay in intraguild predation models promotes very complex dynamics. The delay can induce stability switches exhibiting a destabilizing role as well as a stabilizing role. It is shown that three types of bistability are possible: one stable equilibrium coexists with another stable equilibrium (node-node bistability); one stable equilibrium coexists with a stable periodic solution (node-cycle bistability); one stable periodic solution coexists with another stable periodic solution (cycle-cycle bistability). Numerical simulations suggest that delay can also induce chaos in intraguild predation models.

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.

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.

3D Printing — The Basins of Tristability in the Lorenz System

NASA Astrophysics Data System (ADS)

Xiong, Anda; Sprott, Julien C.; Lyu, Jingxuan; Wang, Xilu

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists with a symmetric pair of stable equilibrium points, and the resulting tri-stable system has three intertwined basins of attraction. The advent of 3D printers now makes it possible to visualize the topology of such basins of attraction as the results presented here illustrate.

Adaptive behaviour and multiple equilibrium states in a predator-prey model.

PubMed

Pimenov, Alexander; Kelly, Thomas C; Korobeinikov, Andrei; O'Callaghan, Michael J A; Rachinskii, Dmitrii

2015-05-01

There is evidence that multiple stable equilibrium states are possible in real-life ecological systems. Phenomenological mathematical models which exhibit such properties can be constructed rather straightforwardly. For instance, for a predator-prey system this result can be achieved through the use of non-monotonic functional response for the predator. However, while formal formulation of such a model is not a problem, the biological justification for such functional responses and models is usually inconclusive. In this note, we explore a conjecture that a multitude of equilibrium states can be caused by an adaptation of animal behaviour to changes of environmental conditions. In order to verify this hypothesis, we consider a simple predator-prey model, which is a straightforward extension of the classic Lotka-Volterra predator-prey model. In this model, we made an intuitively transparent assumption that the prey can change a mode of behaviour in response to the pressure of predation, choosing either "safe" of "risky" (or "business as usual") behaviour. In order to avoid a situation where one of the modes gives an absolute advantage, we introduce the concept of the "cost of a policy" into the model. A simple conceptual two-dimensional predator-prey model, which is minimal with this property, and is not relying on odd functional responses, higher dimensionality or behaviour change for the predator, exhibits two stable co-existing equilibrium states with basins of attraction separated by a separatrix of a saddle point. Copyright © 2015 Elsevier Inc. All rights reserved.

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.

Combined passive magnetic bearing element and vibration damper

DOEpatents

Post, Richard F.

2001-01-01

A magnetic bearing system contains magnetic subsystems which act together to support a rotating element in a state of dynamic equilibrium and dampen transversely directed vibrations. Mechanical stabilizers are provided to hold the suspended system in equilibrium until its speed has exceeded a low critical speed where dynamic effects take over, permitting the achievement of a stable equilibrium for the rotating object. A state of stable equilibrium is achieved above a critical speed by use of a collection of passive elements using permanent magnets to provide their magnetomotive excitation. In a improvement over U.S. Pat. No. 5,495,221, a magnetic bearing element is combined with a vibration damping element to provide a single upper stationary dual-function element. The magnetic forces exerted by such an element, enhances levitation of the rotating object in equilibrium against external forces, such as the force of gravity or forces arising from accelerations, and suppresses the effects of unbalance or inhibits the onset of whirl-type rotor-dynamic instabilities. Concurrently, this equilibrium is made stable against displacement-dependent drag forces of the rotating object from its equilibrium position.

Regarding `Information Preservation and Weather Forecasting for Black Holes' by S. W. Hawking

NASA Astrophysics Data System (ADS)

Winterberg, Friedwardt

2014-06-01

It is proposed that the `apparent horizons' assumed by Hawking to resolve the black hole information paradox, are in reality the regions where in Lorentzian relativity the absolute velocity against a preferred reference system at rest with the zero point vacuum energy reaches the velocity of light, and where an elliptical differential equation holding matter in a stable equilibrium goes over a transluminal Euler-Tricomi equation into a hyperbolic differential equation where such an equilibrium is not more possible, with matter in approaching this region disintegrating into radiation. Hawking's proposal depends on the anti-de Sitter/conformal field theory (AdS/CFT) conjecture which in turn depends on string/M theory which in the absence of super-symmetry will not work.

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.

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.

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.

On the global dynamics of a chronic myelogenous leukemia model

NASA Astrophysics Data System (ADS)

Krishchenko, Alexander P.; Starkov, Konstantin E.

2016-04-01

In this paper we analyze some features of global dynamics of a three-dimensional chronic myelogenous leukemia (CML) model with the help of the stability analysis and the localization method of compact invariant sets. The behavior of CML model is defined by concentrations of three cellpopulations circulating in the blood: naive T cells, effector T cells specific to CML and CML cancer cells. We prove that the dynamics of the CML system around the tumor-free equilibrium point is unstable. Further, we compute ultimate upper bounds for all three cell populations and provide the existence conditions of the positively invariant polytope. One ultimate lower bound is obtained as well. Moreover, we describe the iterative localization procedure for refining localization bounds; this procedure is based on cyclic using of localizing functions. Applying this procedure we obtain conditions under which the internal tumor equilibrium point is globally asymptotically stable. Our theoretical analyses are supplied by results of the numerical simulation.

Stability of the Einstein static universe in Einstein-Cartan theory

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

Atazadeh, K., E-mail: atazadeh@azaruniv.ac.ir

The existence and stability of the Einstein static solution have been built in the Einstein-Cartan gravity. We show that this solution in the presence of perfect fluid with spin density satisfying the Weyssenhoff restriction is cyclically stable around a center equilibrium point. Thus, study of this solution is interesting because it supports non-singular emergent cosmological models in which the early universe oscillates indeterminately about an initial Einstein static solution and is thus past eternal.

On Nash-Equilibria of Approximation-Stable Games

NASA Astrophysics Data System (ADS)

Awasthi, Pranjal; Balcan, Maria-Florina; Blum, Avrim; Sheffet, Or; Vempala, Santosh

One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ɛ-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ɛ-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximation-stable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ɛ,Δ) approximation-stable games must have an ɛ-equilibrium of support O(Δ^{2-o(1)}/ɛ2{log n}), yielding an immediate n^{O(Δ^{2-o(1)}/ɛ^2log n)}-time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ɛ are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.

Chaotic Behavior of a Generalized Sprott E Differential System

NASA Astrophysics Data System (ADS)

Oliveira, Regilene; Valls, Claudia

A chaotic system with only one equilibrium, a stable node-focus, was introduced by Wang and Chen [2012]. This system was found by adding a nonzero constant b to the Sprott E system [Sprott, 1994]. The coexistence of three types of attractors in this autonomous system was also considered by Braga and Mello [2013]. Adding a second parameter to the Sprott E differential system, we get the autonomous system ẋ = ayz + b,ẏ = x2 - y,ż = 1 - 4x, where a,b ∈ ℝ are parameters and a≠0. In this paper, we consider theoretically some global dynamical aspects of this system called here the generalized Sprott E differential system. This polynomial differential system is relevant because it is the first polynomial differential system in ℝ3 with two parameters exhibiting, besides the point attractor and chaotic attractor, coexisting stable limit cycles, demonstrating that this system is truly complicated and interesting. More precisely, we show that for b sufficiently small this system can exhibit two limit cycles emerging from the classical Hopf bifurcation at the equilibrium point p = (1/4, 1/16, 0). We also give a complete description of its dynamics on the Poincaré sphere at infinity by using the Poincaré compactification of a polynomial vector field in ℝ3, and we show that it has no first integrals in the class of Darboux functions.

Noise-induced transitions and shifts in a climate-vegetation feedback model.

PubMed

Alexandrov, Dmitri V; Bashkirtseva, Irina A; Ryashko, Lev B

2018-04-01

Motivated by the extremely important role of the Earth's vegetation dynamics in climate changes, we study the stochastic variability of a simple climate-vegetation system. In the case of deterministic dynamics, the system has one stable equilibrium and limit cycle or two stable equilibria corresponding to two opposite (cold and warm) climate-vegetation states. These states are divided by a separatrix going across a point of unstable equilibrium. Some possible stochastic scenarios caused by different externally induced natural and anthropogenic processes inherit properties of deterministic behaviour and drastically change the system dynamics. We demonstrate that the system transitions across its separatrix occur with increasing noise intensity. The climate-vegetation system therewith fluctuates, transits and localizes in the vicinity of its attractor. We show that this phenomenon occurs within some critical range of noise intensities. A noise-induced shift into the range of smaller global average temperatures corresponding to substantial oscillations of the Earth's vegetation cover is revealed. Our analysis demonstrates that the climate-vegetation interactions essentially contribute to climate dynamics and should be taken into account in more precise and complex models of climate variability.

Stability of triangular points in the elliptic restricted three-body problem with oblateness up to zonal harmonic J4 of both primaries

NASA Astrophysics Data System (ADS)

Singh, Jagadish; Tyokyaa, Richard K.

2016-10-01

In this paper, we study the locations and stability of triangular points in the elliptic restricted three-body problem when both primaries are taken as oblate spheroids with oblateness up to J4. The positions of the triangular points are seen to be affected by oblateness of the primaries and the eccentricity of their orbits. The triangular points are conditionally stable for 0<μ<μc0<μ<μc and unstable for μc≤μ≤12μc≤μ≤12, where μcμc is the critical mass parameter depending on the oblateness coefficients J2iJ2i (i =1,2) and the eccentricity of the orbits. We further observe that both coefficients J2 and J4, semi-major axis and the eccentricity have destabilizing tendencies resulting in a decrease in the size of the region of stability with an increase in the parameters involved. Knowing that, in general, the triangular equilibrium points are stable for 0<μ<μc0<μ<μc, in particular systems (Alpha Centauri, X1X1 Bootis, Sirius and Kruger 60) this does not hold and such points are unstable.

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.

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.

Horseshoes in a Chaotic System with Only One Stable Equilibrium

NASA Astrophysics Data System (ADS)

Huan, Songmei; Li, Qingdu; Yang, Xiao-Song

To confirm the numerically demonstrated chaotic behavior in a chaotic system with only one stable equilibrium reported by Wang and Chen, we resort to Poincaré map technique and present a rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoes theory.

Trapped fast particle destabilization of internal kink mode for the locally flattened q-profile with an inflection point

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

Wang, Xian-Qu; Zhang, Rui-Bin; Meng, Guo

2016-07-15

The destabilization of ideal internal kink modes by trapped fast particles in tokamak plasmas with a “shoulder”-like equilibrium current is investigated. It is found that energetic particle branch of the mode is unstable with the driving of fast-particle precession drifts and corresponds to a precessional fishbone. The mode with a low stability threshold is also more easily excited than the conventional precessional fishbone. This is different from earlier studies for the same equilibrium in which the magnetohydrodynamic (MHD) branch of the mode is stable. Furthermore, the stability and characteristic frequency of the mode are analyzed by solving the dispersion relationmore » and comparing with the conventional fishbone. The results suggest that an equilibrium with a locally flattened q-profile, may be modified by localized current drive (or bootstrap current, etc.), is prone to the onset of the precessional fishbone branch of the mode.« less

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.

Stability analysis of the phytoplankton effect model on changes in nitrogen concentration on integrated multi-trophic aquaculture systems

NASA Astrophysics Data System (ADS)

Widowati; Putro, S. P.; Silfiana

2018-05-01

Integrated Multi-Trophic Aquaculture (IMTA) is a polyculture with several biotas maintained in it to optimize waste recycling as a food source. The interaction between phytoplankton and nitrogen as waste in fish cultivation including ammonia, nitrite, and nitrate studied in the form of mathematical models. The form model is non-linear systems of differential equations with the four variables. The analytical analysis was used to study the dynamic behavior of this model. Local stability analysis is performed at the equilibrium point with the first step linearized model by using Taylor series, then determined the Jacobian matrix. If all eigenvalues have negative real parts, then the equilibrium of the system is locally asymptotic stable. Some numerical simulations were also demonstrated to verify our analytical result.

Two-dimensional heteroclinic attractor in the generalized Lotka-Volterra system

NASA Astrophysics Data System (ADS)

Afraimovich, Valentin S.; Moses, Gregory; Young, Todd

2016-05-01

We study a simple dynamical model exhibiting sequential dynamics. We show that in this model there exist sets of parameter values for which a cyclic chain of saddle equilibria, O k , k=1,\\ldots,p , have two-dimensional unstable manifolds that contain orbits connecting each O k to the next two equilibrium points O k+1 and O k+2 in the chain ({{O}p+1}={{O}1} ). We show that the union of these equilibria and their unstable manifolds form a two-dimensional surface with a boundary that is homeomorphic to a cylinder if p is even and a Möbius strip if p is odd. If, further, each equilibrium in the chain satisfies a condition called ‘dissipativity’, then this surface is asymptotically stable.

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.

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.

Sustained and transient oscillations and chaos induced by delayed antiviral immune response in an immunosuppressive infection model.

PubMed

Shu, Hongying; Wang, Lin; Watmough, James

2014-01-01

Sustained and transient oscillations are frequently observed in clinical data for immune responses in viral infections such as human immunodeficiency virus, hepatitis B virus, and hepatitis C virus. To account for these oscillations, we incorporate the time lag needed for the expansion of immune cells into an immunosuppressive infection model. It is shown that the delayed antiviral immune response can induce sustained periodic oscillations, transient oscillations and even sustained aperiodic oscillations (chaos). Both local and global Hopf bifurcation theorems are applied to show the existence of periodic solutions, which are illustrated by bifurcation diagrams and numerical simulations. Two types of bistability are shown to be possible: (i) a stable equilibrium can coexist with another stable equilibrium, and (ii) a stable equilibrium can coexist with a stable periodic solution.

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

The Existence and Stability Analysis of the Equilibria in Dengue Disease Infection Model

NASA Astrophysics Data System (ADS)

Anggriani, N.; Supriatna, A. K.; Soewono, E.

2015-06-01

In this paper we formulate an SIR (Susceptible - Infective - Recovered) model of Dengue fever transmission with constant recruitment. We found a threshold parameter K0, known as the Basic Reproduction Number (BRN). This model has two equilibria, disease-free equilibrium and endemic equilibrium. By constructing suitable Lyapunov function, we show that the disease- free equilibrium is globally asymptotic stable whenever BRN is less than one and when it is greater than one, the endemic equilibrium is globally asymptotic stable. Numerical result shows the dynamic of each compartment together with effect of multiple bio-agent intervention as a control to the dengue transmission.

Stochastic dynamics and stable equilibrium of evolutionary optional public goods game in finite populations

NASA Astrophysics Data System (ADS)

Quan, Ji; Liu, Wei; Chu, Yuqing; Wang, Xianjia

2018-07-01

Continuous noise caused by mutation is widely present in evolutionary systems. Considering the noise effects and under the optional participation mechanism, a stochastic model for evolutionary public goods game in a finite size population is established. The evolutionary process of strategies in the population is described as a multidimensional ergodic and continuous time Markov process. The stochastic stable state of the system is analyzed by the limit distribution of the stochastic process. By numerical experiments, the influences of the fixed income coefficient for non-participants and the investment income coefficient of the public goods on the stochastic stable equilibrium of the system are analyzed. Through the numerical calculation results, we found that the optional participation mechanism can change the evolutionary dynamics and the equilibrium of the public goods game, and there is a range of parameters which can effectively promote the evolution of cooperation. Further, we obtain the accurate quantitative relationship between the parameters and the probabilities for the system to choose different stable equilibriums, which can be used to realize the control of cooperation.

Multiscale deformation of a liquid surface in interaction with a nanoprobe

NASA Astrophysics Data System (ADS)

Ledesma-Alonso, R.; Tordjeman, P.; Legendre, D.

2012-06-01

The interaction between a nanoprobe and a liquid surface is studied. The surface deformation depends on physical and geometric parameters, which are depicted by employing three dimensionless parameters: Bond number Bo, modified Hamaker number Ha, and dimensionless separation distance D*. The evolution of the deformation is described by a strongly nonlinear partial differential equation, which is solved by means of numerical methods. The dynamic analysis of the liquid profile points out the existence of a critical distance Dmin*, below which the irreversible wetting process of the nanoprobe happens. For D*≥Dmin*, the numerical results show the existence of two deformation profiles, one stable and another unstable from the energetic point of view. Different deformation length-scales, characterizing the stable liquid equilibrium interface, define the near- and the far-field deformation zones, where self-similar profiles are found. Finally, our results allow us to provide simple relationships between the parameters, which leads to determine the optimal conditions when performing atomic force microscope measurements over liquids.

Plasmon-mediated binding forces on gold or silver homodimer and heterodimer

NASA Astrophysics Data System (ADS)

Liaw, Jiunn-Woei; Kuo, Ting-Yu; Kuo, Mao-Kuen

2016-02-01

This study theoretically investigates plasmon-mediated optical binding forces, which are exerted on metal homo or heterodimers, induced by the normal illumination of a linearly polarized plane wave or Gaussian beam. Using the multiple multipole method, we analyzed the optical force in terms of Maxwell's stress tensor for various interparticle distance at some specific wavelengths. Numerical results show that for a given wavelength there are several stable equilibrium distances between two nanoparticles (NPs) of a homodimer, which are slightly shorter than some integer multiples of the wavelength in medium, such that metal dimer acts as bonded together. At these specific interparticle distances, the optical force between dimer is null and serves a restoring force, which is repulsive and attractive, respectively, as the two NPs are moving closer to and away from each other. The spring constant of the restoring force at the first stable equilibrium is always the largest, indicating that the first stable equilibrium distance is the most stable one. Moreover, the central line (orientation) of a dimer tends to be perpendicular to the polarization of light. For the cases of heterodimers, the phenomenon of stable equilibrium interparticle distance still exists, except there is an extra net photophoretic force drifting the heterodimer as one. Moreover, gradient force provided by a Gaussian beam may reduce the stability of these equilibriums, so larger NPs are preferred to stabilize a dimer under illumination of Gaussian beam. The finding may pave the way for using optical manipulation on the gold or silver colloidal self-assembly.

Harvesting in delayed food web model with omnivory

NASA Astrophysics Data System (ADS)

Collera, Juancho A.

2016-02-01

We consider a tri-trophic community module called intraguild predation (IGP) that includes a prey and its predator which share a common basal resource for their sustenance. The growth of the basal resource in the absence of predation follows the Hutchinson's equation where the delay parameter arises, while functional responses in our model are of Lotka-Volterra type. Moreover, the basal resource is harvested for its economic value with a constant harvesting rate. This work generalizes the previous works on the same model with no harvesting and no time delay. We show that the harvesting rate has to be small enough in order for the equilibria to exist. Moreover, we show that by increasing the delay parameter the stability of the equilibrium solutions may change, and periodic solutions may emerge through Hopf bifurcations. In the case of the positive equilibrium solution, multiple stability switches are obtained, and numerical continuation shows that a stable branch of periodic solutions emerges once the positive equilibrium loses its stability at the first Hopf bifurcation point. This result is important because it gives an alternative for the coexistence of all three species, avoiding extinction of one or more species when the positive equilibrium becomes unstable.

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.

Chemical properties of ground water and their corrosion and encrustation effects on wells

USGS Publications Warehouse

Barnes, Ivan; Clarke, Frank Eldridge

1969-01-01

Well waters in Egypt, Nigeria, and West Pakistan were studied for their chemical properties and corrosive or encrusting behavior. From the chemical composition of the waters, reaction states with reference to equilibrium were tested for 29 possible coexisting oxides, carbonates, sulfides, and elements. Of the 29 solids considered, only calcite, CaCO3, and ferric hydroxide, Fe(OH)3, showed any correlation with the corrosiveness of the waters to mild steel (iron metal). All 39 of the waters tested were out of equilibrium with iron metal, but those waters in equilibrium or supersaturated with both calcite and ferric hydroxide were the least corrosive. Supersaturation with other solid phases apparently was unrelated to corrosion. A number of solids may form surface deposits in wells and lead to decreased yields by fouling well intakes (screens and gravel packs) or increasing friction losses in casings. Calcite, CaCO3; ferric hydroxide, Fe(OH)3; magnetite, Fe3O4; siderite, FeCO3; hausmannite, Mn304 (tetragonal); manganese spinel, Mn3O4 (isometric); three iron sulfides mackinawite, FeS (tetragonal); greigite, Fe3S4 (isometric); and smythite, Fe3S4 (rhombohedral)-copper hydroxide, Co(OH)2; and manganese hydroxide, Mn(OH)2, were all at least tentatively identified in the deposits sampled. Of geochemical interest is the demonstration that simple stable equilibrium models fail in nearly every case to predict compositions of water yielded by the wells studied. Only one stable phase (calcite) was found to exhibit behavior approximately predictable from stable equilibrium considerations. No other stable phase was found to behave as would be predicted from equilibrium considerations. All the solids found to precipitate (except calcite) are metastable in that they are not the least soluble phases possible in the systems studied. In terms of metastable equilibrium, siderite and ferric hydroxide behave approximately as would be predicted from equilibrium considerations, but both are metastable and the presence of neither would be anticipated if only the most stable phases were considered. The behaviors of none of the other solids would be predictable from either stable or metastable equilibrium considerations. An unanswered problem raised by the study reported here is how, or by what paths, truly stable phases form if first precipitates are generally metastable.The utility of the findings in well design and operation is in no way impaired by the general lack of equilibrium. Conditions leading to either corrosion (which is related to lack of supersaturation with protective phases), or encrustation (supersaturation with phases that were found to precipitate), or both, apparently can be identified. The application of the methods described can be of great importance in developing unexploited ground-water resources in that certain practical problems can be identified before extensive well construction and unnecessary well failure.

Analysis of A Virus Dynamics Model

NASA Astrophysics Data System (ADS)

Zhang, Baolin; Li, Jianquan; Li, Jia; Zhao, Xin

2018-03-01

In order to more accurately characterize the virus infection in the host, a virus dynamics model with latency and virulence is established and analyzed in this paper. The positivity and boundedness of the solution are proved. After obtaining the basic reproduction number and the existence of infected equilibrium, the Lyapunov method and the LaSalle invariance principle are used to determine the stability of the uninfected equilibrium and infected equilibrium by constructing appropriate Lyapunov functions. We prove that, when the basic reproduction number does not exceed 1, the uninfected equilibrium is globally stable, the virus can be cleared eventually; when the basic reproduction number is more than 1, the infected equilibrium is globally stable, the virus will persist in the host at a certain level. The effect of virulence and latency on infection is also discussed.

The annealing mechanism of the radiation-induced vacancy-oxygen defect in silicon

NASA Astrophysics Data System (ADS)

Voronkov, V. V.; Falster, R.; Londos, C. A.

2012-06-01

Annealing experiments on the VO defect (the A-centre) produced by radiation in silicon—reported long ago—have been re-examined in order to deduce the two most important properties of VO: its diffusivity and the equilibrium constant for VO dissociation into V + O. The loss rate of VO is accounted for by two major reactions. One is the conventional reaction of the trapping of mobile VO by oxygen, thus producing VO2. The other is an annihilation of vacancies, which coexist in an equilibrium ratio with VO, by radiation-produced interstitial point defects. In some cases, a minor reaction, VO + V, should also be taken into account. The emerging minor defects V2O are also highly mobile. They partially dissociate back and partially get trapped by oxygen producing stable V2O2 defects.

Global asymptotic stability of density dependent integral population projection models.

PubMed

Rebarber, Richard; Tenhumberg, Brigitte; Townley, Stuart

2012-02-01

Many stage-structured density dependent populations with a continuum of stages can be naturally modeled using nonlinear integral projection models. In this paper, we study a trichotomy of global stability result for a class of density dependent systems which include a Platte thistle model. Specifically, we identify those systems parameters for which zero is globally asymptotically stable, parameters for which there is a positive asymptotically stable equilibrium, and parameters for which there is no asymptotically stable equilibrium. Copyright © 2011 Elsevier Inc. All rights reserved.

Variational energy principle for compressible, baroclinic flow. 2: Free-energy form of Hamilton's principle

NASA Technical Reports Server (NTRS)

Schmid, L. A.

1977-01-01

The first and second variations are calculated for the irreducible form of Hamilton's Principle that involves the minimum number of dependent variables necessary to describe the kinetmatics and thermodynamics of inviscid, compressible, baroclinic flow in a specified gravitational field. The form of the second variation shows that, in the neighborhood of a stationary point that corresponds to physically stable flow, the action integral is a complex saddle surface in parameter space. There exists a form of Hamilton's Principle for which a direct solution of a flow problem is possible. This second form is related to the first by a Friedrichs transformation of the thermodynamic variables. This introduces an extra dependent variable, but the first and second variations are shown to have direct physical significance, namely they are equal to the free energy of fluctuations about the equilibrium flow that satisfies the equations of motion. If this equilibrium flow is physically stable, and if a very weak second order integral constraint on the correlation between the fluctuations of otherwise independent variables is satisfied, then the second variation of the action integral for this free energy form of Hamilton's Principle is positive-definite, so the action integral is a minimum, and can serve as the basis for a direct trail and error solution. The second order integral constraint states that the unavailable energy must be maximum at equilibrium, i.e. the fluctuations must be so correlated as to produce a second order decrease in the total unavailable energy.

Effect of electromagnetic field on Kordylewski clouds formation

NASA Astrophysics Data System (ADS)

Salnikova, Tatiana; Stepanov, Sergey

2018-05-01

In previous papers the authors suggest a clarification of the phenomenon of appearance-disappearance of Kordylewski clouds - accumulation of cosmic dust mass in the vicinity of the triangle libration points of the Earth-Moon system. Under gravi-tational and light perturbation of the Sun the triangle libration points aren't the points of relative equilibrium. However, there exist the stable periodic motion of the particles, surrounding every of the triangle libration points. Due to this fact we can consider a probabilistic model of the dust clouds formation. These clouds move along the periodical orbits in small vicinity of the point of periodical orbit. To continue this research we suggest a mathematical model to investigate also the electromagnetic influences, arising under consideration of the charged dust particles in the vicinity of the triangle libration points of the Earth-Moon system. In this model we take under consideration the self-unduced force field within the set of charged particles, the probability distribution density evolves according to the Vlasov equation.

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

2016-01-01

A new engine cycle analysis tool, called Pycycle, was recently built using the OpenMDAO framework. This tool uses equilibrium chemistry based thermodynamics, and provides analytic derivatives. This allows for stable and efficient use of gradient-based optimization and sensitivity analysis methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a multi-point turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Stable and unstable singularities in the unforced Hele-Shaw cell

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

Almgren, R.; Bertozzi, A.; Brenner, M.P.

We study singularity formation in the lubrication model for the unforced Hele-Shaw system, describing the breaking in two of a fluid droplet confined between two narrowly spaced glass plates. By varying the initial data, we exhibit four different scenarios: (1) the droplet breaks in finite time, with two pinch points moving toward each other and merging at the singular time; (2) the droplet breaks in finite time, with two asymmetric pinch points propagating away from each other; (3) the droplet breaks in finite time, with a single symmetric pinch point; or (4) the droplet relaxes to a stable equilibrium shapemore » without a finite time breakup. Each of the three singular scenarios has a self-similar structure with different scaling laws; the first scenario has not been observed before in other Hele-Shaw studies. We demonstrate instabilities of the second and third scenarios, in which the solution changes its behavior at a thickness that can be arbitrarily small depending on the initial condition. These transitions can be identified by examining the structure of the solution in the intermediate scaling region. {copyright} {ital 1996 American Institute of Physics.}« less

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.

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.

Motion of the moonlet in the binary system 243 Ida

NASA Astrophysics Data System (ADS)

Lan, L.; Ni, Y.; Jiang, Y.; Li, J.

2018-02-01

The motion of the moonlet Dactyl in the binary system 243 Ida is investigated in this paper. First, periodic orbits in the vicinity of the primary are calculated, including the orbits around the equilibrium points and large-scale orbits. The Floquet multipliers' topological cases of periodic orbits are calculated to study the orbits' stabilities. During the continuation of the retrograde near-circular orbits near the equatorial plane, two period-doubling bifurcations and one Neimark-Sacker bifurcation occur one by one, leading to two stable regions and two unstable regions. Bifurcations occur at the boundaries of these regions. Periodic orbits in the stable regions are all stable, but in the unstable regions are all unstable. Moreover, many quasi-periodic orbits exist near the equatorial plane. Long-term integration indicates that a particle in a quasi-periodic orbit runs in a space like a tire. Quasi-periodic orbits in different regions have different styles of motion indicated by the Poincare sections. There is the possibility that moonlet Dactyl is in a quasi-periodic orbit near the stable region I, which is enlightening for the stability of the binary system.

Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations

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

Rinaldi, Massimiliano, E-mail: massimiliano.rinaldi@unitn.it

We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to mattermore » domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.« less

Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations

NASA Astrophysics Data System (ADS)

Rinaldi, Massimiliano

2015-10-01

We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to matter domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.

Theory of Dust Voids in Plasmas

NASA Technical Reports Server (NTRS)

Goree, J.; Morfill, G. E.; Tsytovich, V. N.; Vladimirov, S. V.

1999-01-01

Dusty plasmas in a gas discharge often feature a stable void, i.e., a dust-free region inside the dust cloud. This occurs under conditions relevant to both plasma processing discharges and plasma crystal experiments. The void results from a balance of the electrostatic and ion drag forces on a dust particle. The ion drag force is driven by a flow of ions outward from an ionization source and toward the surrounding dust cloud, which has a negative space charge. In equilibrium the force balance for dust particles requires that the boundary with the dust cloud be sharp, provided that the particles are cold and monodispersive. Numerical solutions of the one-dimensional nonlinear fluid equations are carried out including dust charging and dust-neutral collisions, but not ion-neutral collisions. The regions of parameter space that allow stable void equilibria are identified. There is a minimum ionization rate that can sustain a void. Spatial profiles of plasma parameters in the void are reported. In the absence of ion-neutral collisions, the ion flow enters the dust cloud's edge at Mach number M = 1. Phase diagrams for expanding or contracting voids reveal a stationary point corresponding to a single stable equilibrium void size, provided the ionization rate is constant. Large voids contract and small voids expand until they attain this stationary void size. On the other hand, if the ionization rate is not constant, the void size can oscillate. Results are compared to recent laboratory and microgravity experiments.

The roles of non-extensivity and dust concentration as bifurcation parameters in dust-ion acoustic traveling waves in magnetized dusty plasma

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

Narayan Ghosh, Uday; Kumar Mandal, Pankaj, E-mail: pankajwbmsd@gmail.com; Chatterjee, Prasanta

Dust ion-acoustic traveling waves are studied in a magnetized dusty plasma in presence of static dust and non-extensive distributed electrons in the framework of Zakharov-Kuznesstov-Burgers (ZKB) equation. System of coupled nonlinear ordinary differential equations is derived from ZKB equation, and equilibrium points are obtained. Nonlinear wave phenomena are studied numerically using fourth order Runge-Kutta method. The change from unstable to stable solution and consequently to asymptotic stable of dust ion acoustic traveling waves is studied through dynamical system approach. It is found that some dramatical features emerge when the non-extensive parameter and the dust concentration parameters are varied. Behavior ofmore » the solution of the system changes from unstable to stable and stable to asymptotic stable depending on the value of the non-extensive parameter. It is also observed that when the dust concentration is increased the solution pattern is changed from oscillatory shocks to periodic solution. Thus, non-extensive and dust concentration parameters play crucial roles in determining the nature of the stability behavior of the system. Thus, the non-extensive parameter and the dust concentration parameters can be treated as bifurcation parameters.« less

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.

Design and Construction of Multi-Variable Vortex-Ring Bubble Generator for Use in Interactive Exhibit

DTIC Science & Technology

2013-12-01

providing the opportunity to teach complex subjects related to stable and unstable equilibrium, stochastic systems, and conservation laws. The...bubbles through adjustment of three variables. The seal pressure, actuating pressure, and cycle time of the triggering solenoid valve each contribute to...stable and unstable equilibrium, stochastic systems, and conservation laws. The diaphragm valve designed in this thesis provides the centerpiece for

Parametric changes in response equilibrium during an intra-cranial self stimulation (ICSS) task: can reward value be assessed independently of absolute threshold?

PubMed

Easterling, K W; Holtzman, S G

1997-01-01

Traditional ICSS methodologies have attempted to evaluate changes in the rewarding value of brain stimulation by assessing the lowest value of the stimulation that will support responding. However, orderly changes in suprathreshold indicants of hedonic magnitude such as titration point have been shown. In the present experiments, rats were trained to respond on two ICSS autotitration schedules in which every response on one lever produced stimulation of the medial forebrain bundle, and every Xth response decreased either the stimulation current or the stimulation frequency. At any time, a response on a second "reset" lever restored the stimulation current or frequency available on the stimulation lever to its starting level and operationally defined changes in "reward value". In order to study this titration point measure, two response requirements (responses/stepdown; step size) and two stimulation parameters (initial stimulation level; train duration) were systematically varied. Under both current and frequency titration schedules, data indicated that response rate and titration point remained stable over repeated trials and multiple testing days--parameters being constant. Across all conditions, compared to the frequency titration schedule, subjects responding under the current titration schedule showed significantly higher titration points and lower rates of responding. Indicating the independence of rate and titration point data, parametric manipulations did not affect titration point and rate data concurrently. Results support the conclusion that titration point is a relative measure of "reward value" that is generally independent of response rate, but that is affected by manipulations that alter the amount of stimulation available between "resets". Additional work is needed in order to determine the relationship between the magnitude of stimulation needed to maintain minimal responding and that needed to maintain response equilibrium in an autotitration task.

Tuning the phase diagram of colloid-polymer mixtures via Yukawa interactions

NASA Astrophysics Data System (ADS)

González García, Álvaro; Tuinier, Remco

2016-12-01

Theory that predicts the phase behavior of interacting Yukawa spheres in a solution containing nonadsorbing polymer is presented. Our approach accounts for multiple overlap of depletion zones. It is found that additional Yukawa interactions beyond hard core interactions strongly affect the location and presence of coexistence regions and phase states. The theoretical phase diagrams are compared with Monte Carlo simulations. The agreement between the two approaches supports the validity of the theoretical approximations made and confirms that, by choosing the parameters of the interaction potentials, tuning of the binodals is possible. The critical end point characterizes the phase diagram topology. It is demonstrated how an additional Yukawa interaction shifts this point with respect to the hard sphere case. Provided a certain depletant-to-colloid size ratio for which a stable colloidal gas-liquid phase coexistence takes place for hard spheres, added direct interactions turn this into a metastable gas-liquid equilibrium. The opposite case, the induction of a stable gas-liquid coexistence where only fluid-solid was present for hard spheres, is also reported.

Curvature induced phase stability of an intensely heated liquid

NASA Astrophysics Data System (ADS)

Sasikumar, Kiran; Liang, Zhi; Cahill, David G.; Keblinski, Pawel

2014-06-01

We use non-equilibrium molecular dynamics simulations to study the heat transfer around intensely heated solid nanoparticles immersed in a model Lennard-Jones fluid. We focus our studies on the role of the nanoparticle curvature on the liquid phase stability under steady-state heating. For small nanoparticles we observe a stable liquid phase near the nanoparticle surface, which can be at a temperature well above the boiling point. Furthermore, for particles with radius smaller than a critical radius of 2 nm we do not observe formation of vapor even above the critical temperature. Instead, we report the existence of a stable fluid region with a density much larger than that of the vapor phase. We explain the stability in terms of the Laplace pressure associated with the formation of a vapor nanocavity and the associated effect on the Gibbs free energy.

THE EFFECT OF METASTABLE EQUILIBRIUM STATES ON THE PARTITIONING OF NITRATE BETWEEN THE GAS AND AEROSOL PHASES. (R824793)

EPA Science Inventory

With the aid of three atmospheric aerosol equilibrium models, we quantify the effect of metastable equilibrium states (efflorescence branch) in comparison to stable (deliquescence branch) on the partitioning of total nitrate between the gas and aerosol phases. On average, efflore...

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.

Numerical Solution of Dyson Brownian Motion and a Sampling Scheme for Invariant Matrix Ensembles

NASA Astrophysics Data System (ADS)

Li, Xingjie Helen; Menon, Govind

2013-12-01

The Dyson Brownian Motion (DBM) describes the stochastic evolution of N points on the line driven by an applied potential, a Coulombic repulsion and identical, independent Brownian forcing at each point. We use an explicit tamed Euler scheme to numerically solve the Dyson Brownian motion and sample the equilibrium measure for non-quadratic potentials. The Coulomb repulsion is too singular for the SDE to satisfy the hypotheses of rigorous convergence proofs for tamed Euler schemes (Hutzenthaler et al. in Ann. Appl. Probab. 22(4):1611-1641, 2012). Nevertheless, in practice the scheme is observed to be stable for time steps of O(1/ N 2) and to relax exponentially fast to the equilibrium measure with a rate constant of O(1) independent of N. Further, this convergence rate appears to improve with N in accordance with O(1/ N) relaxation of local statistics of the Dyson Brownian motion. This allows us to use the Dyson Brownian motion to sample N× N Hermitian matrices from the invariant ensembles. The computational cost of generating M independent samples is O( MN 4) with a naive scheme, and O( MN 3log N) when a fast multipole method is used to evaluate the Coulomb interaction.

Le Chatelier's principle in replicator dynamics

NASA Astrophysics Data System (ADS)

Allahverdyan, Armen E.; Galstyan, Aram

2011-10-01

The Le Chatelier principle states that physical equilibria are not only stable, but they also resist external perturbations via short-time negative-feedback mechanisms: a perturbation induces processes tending to diminish its results. The principle has deep roots, e.g., in thermodynamics it is closely related to the second law and the positivity of the entropy production. Here we study the applicability of the Le Chatelier principle to evolutionary game theory, i.e., to perturbations of a Nash equilibrium within the replicator dynamics. We show that the principle can be reformulated as a majorization relation. This defines a stability notion that generalizes the concept of evolutionary stability. We determine criteria for a Nash equilibrium to satisfy the Le Chatelier principle and relate them to mutualistic interactions (game-theoretical anticoordination) showing in which sense mutualistic replicators can be more stable than (say) competing ones. There are globally stable Nash equilibria, where the Le Chatelier principle is violated even locally: in contrast to the thermodynamic equilibrium a Nash equilibrium can amplify small perturbations, though both types of equilibria satisfy the detailed balance condition.

Le Chatelier's principle in replicator dynamics.

PubMed

Allahverdyan, Armen E; Galstyan, Aram

2011-10-01

The Le Chatelier principle states that physical equilibria are not only stable, but they also resist external perturbations via short-time negative-feedback mechanisms: a perturbation induces processes tending to diminish its results. The principle has deep roots, e.g., in thermodynamics it is closely related to the second law and the positivity of the entropy production. Here we study the applicability of the Le Chatelier principle to evolutionary game theory, i.e., to perturbations of a Nash equilibrium within the replicator dynamics. We show that the principle can be reformulated as a majorization relation. This defines a stability notion that generalizes the concept of evolutionary stability. We determine criteria for a Nash equilibrium to satisfy the Le Chatelier principle and relate them to mutualistic interactions (game-theoretical anticoordination) showing in which sense mutualistic replicators can be more stable than (say) competing ones. There are globally stable Nash equilibria, where the Le Chatelier principle is violated even locally: in contrast to the thermodynamic equilibrium a Nash equilibrium can amplify small perturbations, though both types of equilibria satisfy the detailed balance condition.

A piecewise smooth model of evolutionary game for residential mobility and segregation

NASA Astrophysics Data System (ADS)

Radi, D.; Gardini, L.

2018-05-01

The paper proposes an evolutionary version of a Schelling-type dynamic system to model the patterns of residential segregation when two groups of people are involved. The payoff functions of agents are the individual preferences for integration which are empirically grounded. Differently from Schelling's model, where the limited levels of tolerance are the driving force of segregation, in the current setup agents benefit from integration. Despite the differences, the evolutionary model shows a dynamics of segregation that is qualitatively similar to the one of the classical Schelling's model: segregation is always a stable equilibrium, while equilibria of integration exist only for peculiar configurations of the payoff functions and their asymptotic stability is highly sensitive to parameter variations. Moreover, a rich variety of integrated dynamic behaviors can be observed. In particular, the dynamics of the evolutionary game is regulated by a one-dimensional piecewise smooth map with two kink points that is rigorously analyzed using techniques recently developed for piecewise smooth dynamical systems. The investigation reveals that when a stable internal equilibrium exists, the bimodal shape of the map leads to several different kinds of bifurcations, smooth, and border collision, in a complicated interplay. Our global analysis can give intuitions to be used by a social planner to maximize integration through social policies that manipulate people's preferences for integration.

Earthquake nucleation in a stochastic fault model of globally coupled units with interaction delays

NASA Astrophysics Data System (ADS)

Vasović, Nebojša; Kostić, Srđan; Franović, Igor; Todorović, Kristina

2016-09-01

In present paper we analyze dynamics of fault motion by considering delayed interaction of 100 all-to-all coupled blocks with rate-dependent friction law in presence of random seismic noise. Such a model sufficiently well describes a real fault motion, whose prevailing stochastic nature is implied by surrogate data analysis of available GPS measurements of active fault movement. Interaction of blocks in an analyzed model is studied as a function of time delay, observed both for dynamics of individual faults and phenomenological models. Analyzed model is examined as a system of all-to-all coupled blocks according to typical assumption of compound faults as complex of globally coupled segments. We apply numerical methods to show that there are local bifurcations from equilibrium state to periodic oscillations, with an occurrence of irregular aperiodic behavior when initial conditions are set away from the equilibrium point. Such a behavior indicates a possible existence of a bi-stable dynamical regime, due to effect of the introduced seismic noise or the existence of global attractor. The latter assumption is additionally confirmed by analyzing the corresponding mean-field approximated model. In this bi-stable regime, distribution of event magnitudes follows Gutenberg-Richter power law with satisfying statistical accuracy, including the b-value within the real observed range.

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.

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.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

NASA Astrophysics Data System (ADS)

Broche, Rita de Cássia D. S.; de Oliveira, Luiz Augusto F.

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem.

Global stability of a multiple infected compartments model for waterborne diseases

NASA Astrophysics Data System (ADS)

Wang, Yi; Cao, Jinde

2014-10-01

In this paper, mathematical analysis is carried out for a multiple infected compartments model for waterborne diseases, such as cholera, giardia, and rotavirus. The model accounts for both person-to-person and water-to-person transmission routes. Global stability of the equilibria is studied. In terms of the basic reproduction number R0, we prove that, if R0⩽1, then the disease-free equilibrium is globally asymptotically stable and the infection always disappears; whereas if R0>1, there exists a unique endemic equilibrium which is globally asymptotically stable for the corresponding fast-slow system. Numerical simulations verify our theoretical results and present that the decay rate of waterborne pathogens has a significant impact on the epidemic growth rate. Also, we observe numerically that the unique endemic equilibrium is globally asymptotically stable for the whole system. This statement indicates that the present method need to be improved by other techniques.

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.

THE EFFECT OF METASTABLE EQUILIBRIUM STATES ON THE PARTITIONING OF NITRATE BETWEEN THE GAS AND AEROSOL PHASES. (R826371C005)

EPA Science Inventory

With the aid of three atmospheric aerosol equilibrium models, we quantify the effect of metastable equilibrium states (efflorescence branch) in comparison to stable (deliquescence branch) on the partitioning of total nitrate between the gas and aerosol phases. On average, effl...

Ribosome flow model with positive feedback

PubMed Central

Margaliot, Michael; Tuller, Tamir

2013-01-01

Eukaryotic mRNAs usually form a circular structure; thus, ribosomes that terminatae translation at the 3′ end can diffuse with increased probability to the 5′ end of the transcript, initiating another cycle of translation. This phenomenon describes ribosomal flow with positive feedback—an increase in the flow of ribosomes terminating translating the open reading frame increases the ribosomal initiation rate. The aim of this paper is to model and rigorously analyse translation with feedback. We suggest a modified version of the ribosome flow model, called the ribosome flow model with input and output. In this model, the input is the initiation rate and the output is the translation rate. We analyse this model after closing the loop with a positive linear feedback. We show that the closed-loop system admits a unique globally asymptotically stable equilibrium point. From a biophysical point of view, this means that there exists a unique steady state of ribosome distributions along the mRNA, and thus a unique steady-state translation rate. The solution from any initial distribution will converge to this steady state. The steady-state distribution demonstrates a decrease in ribosome density along the coding sequence. For the case of constant elongation rates, we obtain expressions relating the model parameters to the equilibrium point. These results may perhaps be used to re-engineer the biological system in order to obtain a desired translation rate. PMID:23720534

Analytic Approximation of Carbon Condensation Issues in Type ii Supernovae

NASA Astrophysics Data System (ADS)

Clayton, Donald D.

2013-01-01

I present analytic approximations for some issues related to condensation of graphite, TiC, and silicon carbide in oxygen-rich cores of supernovae of Type II. Increased understanding, which mathematical analysis can support, renders researchers more receptive to condensation in O-rich supernova gases. Taking SN 1987A as typical, my first analysis shows why the abundance of CO molecules reaches an early maximum in which free carbon remains more abundant than CO. This analysis clarifies why O-rich gas cannot oxidize C if 56Co radioactivity is as strong as in SN 1987A. My next analysis shows that the CO abundance could be regarded as being in chemical equilibrium if the CO molecule is given an effective binding energy rather than its laboratory dissociation energy. The effective binding energy makes the thermal dissociation rate of CO equal to its radioactive dissociation rate. This preserves possible relevance for the concept of chemical equilibrium. My next analysis shows that the observed abundances of CO and SiO molecules in SN 1987A rule out frequent suggestions that equilibrium condensation of SUNOCONs has occurred following atomic mixing of the He-burning shell with more central zones in such a way as to reproduce roughly the observed spectrum of isotopes in SUNOCONs while preserving C/O > 1. He atoms admixed along with the excess carbon would destroy CO and SiO molecules, leaving their observed abundances unexplained. The final analysis argues that a chemical quasiequilibrium among grains (but not gas) may exist approximately during condensation, so that its computational use is partially justified as a guide to which mineral phases would be stable against reactions with gas. I illustrate this point with quasiequilibrium calculations by Ebel & Grossman that have shown that graphite is stable even when O/C >1 if prominent molecules are justifiably excluded from the calculation of chemical equilibrium.

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.

Global stability of an SIR model with differential infectivity on complex networks

NASA Astrophysics Data System (ADS)

Yuan, Xinpeng; Wang, Fang; Xue, Yakui; Liu, Maoxing

2018-06-01

In this paper, an SIR model with birth and death on complex networks is analyzed, where infected individuals are divided into m groups according to their infection and contact between human is treated as a scale-free social network. We obtain the basic reproduction number R0 as well as the effects of various immunization schemes. The results indicate that the disease-free equilibrium is locally and globally asymptotically stable in some conditions, otherwise disease-free equilibrium is unstable and exists an unique endemic equilibrium that is globally asymptotically stable. Our theoretical results are confirmed by numerical simulations and a promising way for infectious diseases control is suggested.

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

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

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

2016-04-15

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

Polymorphism in the two-locus Levene model with nonepistatic directional selection.

PubMed

Bürger, Reinhard

2009-11-01

For the Levene model with soft selection in two demes, the maintenance of polymorphism at two diallelic loci is studied. Selection is nonepistatic and dominance is intermediate. Thus, there is directional selection in every deme and at every locus. We assume that selection is in opposite directions in the two demes because otherwise no polymorphism is possible. If at one locus there is no dominance, then a complete analysis of the dynamical and equilibrium properties is performed. In particular, a simple necessary and sufficient condition for the existence of an internal equilibrium and sufficient conditions for global asymptotic stability are obtained. These results are extended to deme-independent degree of dominance at one locus. A perturbation analysis establishes structural stability within the full parameter space. In the absence of genotype-environment interaction, which requires deme-independent dominance at both loci, nongeneric equilibrium behavior occurs, and the introduction of arbitrarily small genotype-environment interaction changes the equilibrium structure and may destroy stable polymorphism. The volume of the parameter space for which a (stable) two-locus polymorphism is maintained is computed numerically. It is investigated how this volume depends on the strength of selection and on the dominance relations. If the favorable allele is (partially) dominant in its deme, more than 20% of all parameter combinations lead to a globally asymptotically stable, fully polymorphic equilibrium.

Non-equilibrium Microwave Plasma for Efficient High Temperature Chemistry.

PubMed

van den Bekerom, Dirk; den Harder, Niek; Minea, Teofil; Gatti, Nicola; Linares, Jose Palomares; Bongers, Waldo; van de Sanden, Richard; van Rooij, Gerard

2017-08-01

A flowing microwave plasma based methodology for converting electric energy into internal and/or translational modes of stable molecules with the purpose of efficiently driving non-equilibrium chemistry is discussed. The advantage of a flowing plasma reactor is that continuous chemical processes can be driven with the flexibility of startup times in the seconds timescale. The plasma approach is generically suitable for conversion/activation of stable molecules such as CO2, N2 and CH4. Here the reduction of CO2 to CO is used as a model system: the complementary diagnostics illustrate how a baseline thermodynamic equilibrium conversion can be exceeded by the intrinsic non-equilibrium from high vibrational excitation. Laser (Rayleigh) scattering is used to measure the reactor temperature and Fourier Transform Infrared Spectroscopy (FTIR) to characterize in situ internal (vibrational) excitation as well as the effluent composition to monitor conversion and selectivity.

Magnetar giant flares in multipolar magnetic fields. I. Fully and partially open eruptions of flux ropes

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

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

2014-04-01

We propose a catastrophic eruption model for the enormous energy release of magnetars during giant flares, in which a toroidal and helically twisted flux rope is embedded within a force-free magnetosphere. The flux rope stays in stable equilibrium states initially and evolves quasi-statically. Upon the loss of equilibrium, the flux rope cannot sustain the stable equilibrium states and erupts catastrophically. During the process, the magnetic energy stored in the magnetosphere is rapidly released as the result of destabilization of global magnetic topology. The magnetospheric energy that could be accumulated is of vital importance for the outbursts of magnetars. We carefullymore » establish the fully open fields and partially open fields for various boundary conditions at the magnetar surface and study the relevant energy thresholds. By investigating the magnetic energy accumulated at the critical catastrophic point, we find that it is possible to drive fully open eruptions for dipole-dominated background fields. Nevertheless, it is hard to generate fully open magnetic eruptions for multipolar background fields. Given the observational importance of the multipolar magnetic fields in the vicinity of the magnetar surface, it would be worthwhile to explore the possibility of the alternative eruption approach in multipolar background fields. Fortunately, we find that flux ropes may give rise to partially open eruptions in the multipolar fields, which involve only partial opening of background fields. The energy release fractions are greater for cases with central-arcaded multipoles than those with central-caved multipoles that emerged in background fields. Eruptions would fail only when the centrally caved multipoles become extremely strong.« less

Stability of choice in the honey bee nest-site selection process.

PubMed

Nevai, Andrew L; Passino, Kevin M; Srinivasan, Parthasarathy

2010-03-07

We introduce a pair of compartment models for the honey bee nest-site selection process that lend themselves to analytic methods. The first model represents a swarm of bees deciding whether a site is viable, and the second characterizes its ability to select between two viable sites. We find that the one-site assessment process has two equilibrium states: a disinterested equilibrium (DE) in which the bees show no interest in the site and an interested equilibrium (IE) in which bees show interest. In analogy with epidemic models, we define basic and absolute recruitment numbers (R(0) and B(0)) as measures of the swarm's sensitivity to dancing by a single bee. If R(0) is less than one then the DE is locally stable, and if B(0) is less than one then it is globally stable. If R(0) is greater than one then the DE is unstable and the IE is stable under realistic conditions. In addition, there exists a critical site quality threshold Q(*) above which the site can attract some interest (at equilibrium) and below which it cannot. We also find the existence of a second critical site quality threshold Q(**) above which the site can attract a quorum (at equilibrium) and below which it cannot. The two-site discrimination process, in which we examine a swarm's ability to simultaneously consider two sites differing in both site quality and discovery time, has a stable DE if and only if both sites' individual basic recruitment numbers are less than one. Numerical experiments are performed to study the influences of site quality on quorum time and the outcome of competition between a lower quality site discovered first and a higher quality site discovered second. 2009 Elsevier Ltd. All rights reserved.

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.

Stability and thermal behavior of molybdenum disulfide nanotubes: Nonequilibrium molecular dynamics simulation using REBO potential

NASA Astrophysics Data System (ADS)

Ahadi, Zohreh; Shadman Lakmehsari, Muhammad; Kumar Singh, Sandeep; Davoodi, Jamal

2017-12-01

This study is an attempt to perform equilibrium molecular dynamics and non-equilibrium molecular dynamics (NEMD) to evaluate the stability and thermal behavior of molybdenum disulfide nanotubes (MoS2NTs) by reactive empirical bond order potential. The stability of nanotubes, cohesive energy, isobaric heat capacity, and enthalpies of fusion in armchair and zigzag structures with different radii were calculated. The observed results illustrate that SWMoS2NTs, which have larger diameters, are more stable with more negative energy than the smaller ones. Moreover, it was found that the melting point is increased with an increase in the nanotube's radius. During the melting process, the structural transformation of nanotubes was investigated using a mean-square displacement and radial distribution function diagrams. Afterwards, using a NEMD simulation, the thermal conductivity of nanotubes with various diameters was calculated at a constant nanotube length. The obtained results show that the thermal conductivity coefficient increases with increasing nanotube diameters when the nanotube length is constant.

Equilibrium p-T Phase Diagram of Boron: Experimental Study and Thermodynamic Analysis

PubMed Central

Solozhenko, Vladimir L.; Kurakevych, Oleksandr O.

2013-01-01

Solid-state phase transformations and melting of high-purity crystalline boron have been in situ and ex situ studied at pressures to 20 GPa in the 1500–2500 K temperature range where diffusion processes become fast and lead to formation of thermodynamically stable phases. The equilibrium phase diagram of boron has been constructed based on thermodynamic analysis of experimental and literature data. The high-temperature part of the diagram contains p-T domains of thermodynamic stability of rhombohedral β-B106, orthorhombic γ-B28, pseudo-cubic (tetragonal) t'-B52, and liquid boron (L). The positions of two triple points have been experimentally estimated, i.e. β–t'–L at ~ 8.0 GPa and ~ 2490 K; and β–γ–t' at ~ 9.6 GPa and ~ 2230 K. Finally, the proposed phase diagram explains all thermodynamic aspects of boron allotropy and significantly improves our understanding of the fifth element. PMID:23912523

Evolution of conducting states and the maximum dissipated power

NASA Astrophysics Data System (ADS)

Bezryadin, A.; Tinkham, M.

1998-03-01

Evolution of conducting states in adaptable systems below the percolation threshold is studied experimentally. The sample consists of a pair of metal electrodes immersed into a colloidal suspension of conducting graphite nanoparticles in an electrically insulating liquid (toluene, mineral oil). When this initially homogeneous system is driven far from equilibrium by biasing the electrodes with a high DC voltage, a breaking of translational symmetry occurs and the conductivity increases by many orders of magnitude. Two qualitatively different conducting states are observed. The first is a self-organized critical state characterized by a sequence of avalanches with a 1/f^α power spectrum. In the process of evolution this state may transform into the second, ordered stable state with higher conductivity. The transition into the stable state occurs only if the system reaches the point when the power dissipated in the suspension is the maximum allowed by the bias voltage and series resistor. The critical states decay within a few hours while the stable states, which are characterized by visible strings of particles connecting the electrodes, exist much longer.

Early warning signals for critical transitions in a thermoacoustic system

PubMed Central

Gopalakrishnan, E. A.; Sharma, Yogita; John, Tony; Dutta, Partha Sharathi; Sujith, R. I.

2016-01-01

Dynamical systems can undergo critical transitions where the system suddenly shifts from one stable state to another at a critical threshold called the tipping point. The decrease in recovery rate to equilibrium (critical slowing down) as the system approaches the tipping point can be used to identify the proximity to a critical transition. Several measures have been adopted to provide early indications of critical transitions that happen in a variety of complex systems. In this study, we use early warning indicators to predict subcritical Hopf bifurcation occurring in a thermoacoustic system by analyzing the observables from experiments and from a theoretical model. We find that the early warning measures perform as robust indicators in the presence and absence of external noise. Thus, we illustrate the applicability of these indicators in an engineering system depicting critical transitions. PMID:27767065

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.

Statistical mechanics of self-driven Carnot cycles.

PubMed

Smith, E

1999-10-01

The spontaneous generation and finite-amplitude saturation of sound, in a traveling-wave thermoacoustic engine, are derived as properties of a second-order phase transition. It has previously been argued that this dynamical phase transition, called "onset," has an equivalent equilibrium representation, but the saturation mechanism and scaling were not computed. In this work, the sound modes implementing the engine cycle are coarse-grained and statistically averaged, in a partition function derived from microscopic dynamics on criteria of scale invariance. Self-amplification performed by the engine cycle is introduced through higher-order modal interactions. Stationary points and fluctuations of the resulting phenomenological Lagrangian are analyzed and related to background dynamical currents. The scaling of the stable sound amplitude near the critical point is derived and shown to arise universally from the interaction of finite-temperature disorder, with the order induced by self-amplification.

Numerical Experiments Based on the Catastrophe Model of Solar Eruptions

NASA Astrophysics Data System (ADS)

Xie, X. Y.; Ziegler, U.; Mei, Z. X.; Wu, N.; Lin, J.

2017-11-01

On the basis of the catastrophe model developed by Isenberg et al., we use the NIRVANA code to perform the magnetohydrodynamics (MHD) numerical experiments to look into various behaviors of the coronal magnetic configuration that includes a current-carrying flux rope used to model the prominence levitating in the corona. These behaviors include the evolution in equilibrium heights of the flux rope versus the change in the background magnetic field, the corresponding internal equilibrium of the flux rope, dynamic properties of the flux rope after the system loses equilibrium, as well as the impact of the referential radius on the equilibrium heights of the flux rope. In our calculations, an empirical model of the coronal density distribution given by Sittler & Guhathakurta is used, and the physical diffusion is included. Our experiments show that the deviation of simulations in the equilibrium heights from the theoretical results exists, but is not apparent, and the evolutionary features of the two results are similar. If the flux rope is initially locate at the stable branch of the theoretical equilibrium curve, the flux rope will quickly reach the equilibrium position in the simulation after several rounds of oscillations as a result of the self-adjustment of the system; and the flux rope lose the equilibrium if the initial location of the flux rope is set at the critical point on the theoretical equilibrium curve. Correspondingly, the internal equilibrium of the flux rope can be reached as well, and the deviation from the theoretical results is somewhat apparent since the approximation of the small radius of the flux rope is lifted in our experiments, but such deviation does not affect the global equilibrium in the system. The impact of the referential radius on the equilibrium heights of the flux rope is consistent with the prediction of the theory. Our calculations indicate that the motion of the flux rope after the loss of equilibrium is consistent with which is predicted by the Lin-Forbes model and observations. Formation of the fast mode shock ahead of the flux rope is observed in our experiments. Outward motions of the flux rope are smooth, and magnetic energy is continuously converted into the other types of energy because both the diffusions are considered in calculations, and magnetic reconnection is allowed to occur successively in the current sheet behind the flux rope.

On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem

PubMed Central

Li, Jiawei; Kendall, Graham

2015-01-01

In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games. PMID:26288088

Magnetar giant flares in multipolar magnetic fields. II. Flux rope eruptions with current sheets

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

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

2014-11-20

We propose a physical mechanism to explain giant flares and radio afterglows in terms of a magnetospheric model containing both a helically twisted flux rope and a current sheet (CS). With the appearance of a CS, we solve a mixed boundary value problem to get the magnetospheric field based on a domain decomposition method. We investigate properties of the equilibrium curve of the flux rope when the CS is present in background multipolar fields. In response to the variations at the magnetar surface, it quasi-statically evolves in stable equilibrium states. The loss of equilibrium occurs at a critical point and,more » beyond that point, it erupts catastrophically. New features show up when the CS is considered. In particular, we find two kinds of physical behaviors, i.e., catastrophic state transition and catastrophic escape. Magnetic energy would be released during state transitions. This released magnetic energy is sufficient to drive giant flares, and the flux rope would, therefore, go away from the magnetar quasi-statically, which is inconsistent with the radio afterglow. Fortunately, in the latter case, i.e., the catastrophic escape, the flux rope could escape the magnetar and go to infinity in a dynamical way. This is more consistent with radio afterglow observations of giant flares. We find that the minor radius of the flux rope has important implications for its eruption. Flux ropes with larger minor radii are more prone to erupt. We stress that the CS provides an ideal place for magnetic reconnection, which would further enhance the energy release during eruptions.« less

Humans as holobionts: implications for prevention and therapy.

PubMed

van de Guchte, Maarten; Blottière, Hervé M; Doré, Joël

2018-05-01

The human gut microbiota is increasingly recognized for its important or even decisive role in health. As it becomes clear that microbiota and host mutually affect and depend on each other in an intimate relationship, a holistic view of the gut microbiota-host association imposes itself. Ideally, a stable state of equilibrium, homeostasis, is maintained and serves health, but signs are that perturbation of this equilibrium beyond the limits of resilience can propel the system into an alternative stable state, a pre-disease state, more susceptible to the development of chronic diseases. The microbiota-host equilibrium of a large and growing proportion of individuals in Western society may represent such a pre-disease state and explain the explosive development of chronic diseases such as inflammatory bowel disease, obesity, and other inflammatory diseases. These diseases themselves represent other alternative stable states again and are therefore hard to cure. The holistic view of the microbiota-host association where feedback loops between microbiota and host are thought to maintain the system in a stable state-be it a healthy, pre-disease, or disease state-implies that integrated approaches, addressing host processes and microbiota, should be used to treat or prevent (pre-)disease.

A model-based approach to stabilizing crutch supported paraplegic standing by artificial hip joint stiffness.

PubMed

van der Spek, Jaap H; Veltink, Peter H; Hermens, Hermie J; Koopman, Bart F J M; Boom, Herman B K

2003-12-01

The prerequisites for stable crutch supported standing were analyzed in this paper. For this purpose, a biomechanical model of crutch supported paraplegic stance was developed assuming the patient was standing with extended knees. When using crutches during stance, the crutches will put a position constraint on the shoulder, thus reducing the number of degrees of freedom. Additional hip-joint stiffness was applied to stabilize the hip joint and, therefore, to stabilize stance. The required hip-joint stiffness for changing crutch placement and hip-joint offset angle was studied under static and dynamic conditions. Modeling results indicate that, by using additional hip-joint stiffness, stable crutch supported paraplegic standing can be achieved, both under static as well as dynamic situations. The static equilibrium postures and the stability under perturbations were calculated to be dependent on crutch placement and stiffness applied. However, postures in which the hip joint was in extension (C postures) appeared to the most stable postures. Applying at least 60 N x m/rad hip-joint stiffness gave stable equilibrium postures in all cases. Choosing appropriate hip-joint offset angles, the static equilibrium postures changed to more erect postures, without causing instability or excessive arm forces to occur.

Solid-phase Microextraction (SPME) with Stable Isotope Calibration for Measuring Bioavailability of Hydrophobic Organic Contaminants

PubMed Central

Cui, Xinyi; Bao, Lianjun; Gan, Jay

2014-01-01

Solid-phase microextraction (SPME) is a biomimetic tool ideally suited for measuring bioavailability of hydrophobic organic compounds (HOCs) in sediment and soil matrices. However, conventional SPME sampling requires the attainment of equilibrium between the fiber and sample matrix, which may take weeks or months, greatly limiting its applicability. In this study, we explored the preloading of polydimethylsiloxane fiber with stable isotope labeled analogs (SI-SPME) to circumvent the need for long sampling time, and evaluated the performance of SI-SPME against the conventional equilibrium SPME (Eq-SPME) using a range of sediments and conditions. Desorption of stable isotope-labeled analogs and absorption of PCB-52, PCB-153, bifenthrin and cis-permethrin were isotropic, validating the assumption for SI-SPME. Highly reproducible preloading was achieved using acetone-water (1:4, v/v) as the carrier. Compared to Eq-SPME that required weeks or even months, the fiber concentrations (Cf) under equilibrium could be reliably estimated by SI-SPME in 1 d under agitated conditions or 20 d under static conditions in spiked sediments. The Cf values predicted by SI-SPME were statistically identical to those determined by Eq-SPME. The SI-SPME method was further applied successfully to field sediments contaminated with PCB 52, PCB 153, and bifenthrin. The increasing availability of stable isotope labeled standards and mass spectrometry nowadays makes SI-SPME highly feasible, allowing the use of SPME under non-equilibrium conditions with much shorter or flexible sampling time. PMID:23930601

Stability boundaries for command augmentation systems

NASA Technical Reports Server (NTRS)

Shrivastava, P. C.

1987-01-01

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

Polymorphism of paracetamol: relative stabilities of the monoclinic and orthorhombic phases inferred from topological pressure-temperature and temperature-volume phase diagrams.

PubMed

Espeau, Philippe; Céolin, René; Tamarit, Josep-Lluis; Perrin, Marc-Antoine; Gauchi, Jean-Pierre; Leveiller, Franck

2005-03-01

The thermodynamic relationships between the two known polymorphs of paracetamol have been investigated, and the subsequent pressure-temperature and temperature-volume phase diagrams were constructed using data from crystallographic and calorimetric measurements as a function of the temperature. Irrespective of temperature, monoclinic Form I and orthorhombic Form II are stable phases at ordinary and high pressures, respectively. The I and II phase regions in the pressure-temperature diagram are bordered by the I-II equilibrium curve, for which a negative slope (dp/dT approximately -0.3 MPa x K(-1)) was determined although it was not observed experimentally. This curve goes through the I-II-liquid triple point whose coordinates (p approximately 234 MPa, T approximately 505 K) correspond to the crossing point of the melting curves, for which dp/dT values of +3.75 MPa x K(-1) (I) and +3.14 MPa x K(-1) (II) were calculated from enthalpy and volume changes upon fusion. More generally, this case exemplifies how the stability hierarchy of polymorphs may be inferred from the difference in their sublimation curves, as topologically positioned with respect to each other, using the phase rule and simple inferences resorting to Gibbs equilibrium thermodynamics. Copyright 2004 Wiley-Liss, Inc. and the American Pharmacists Association.

Black Hole Firewalls and Lorentzian Relativity

NASA Astrophysics Data System (ADS)

Winterberg, Friedwardt

2013-04-01

In a paper published (Z. f. Naturforsch. 56a, 889, 2001) I had shown that the pre-Einstein theory of relativity by Lorentz and Poincare, extended to the general theory of relativity and quantum mechanics, predicts the disintegration of matter by passing through the event horizon. The zero point vacuum energy is there cut-off at the Planck energy, but Lorentz-invariant all the way up to this energy. The cut-off creates a distinguished reference system in which this energy is at rest. For non-relativistic velocities relative to this reference system, the special and general relativity remain a good approximations, with matter held together in a stable equilibrium by electrostatic forces (or forces acting like them) as a solution of an elliptic partial differential equation derived from Maxwell's equation. But in approaching and crossing the velocity of light in the distinguished reference system, which is equivalent in approaching and crossing of the event horizon, the elliptic differential equation goes over into a hyperbolic differential equation (as in fluid dynamics from subsonic to supersonic flow), and there is no such equilibrium. According to Schwarzschild's interior solution, the event horizon of a collapsing mass appears first as a point in its center, thereafter moving radially outwards, thereby converting all the mass into energy, explaining the observed gamma ray bursters.

Andriy Zakutayev | NREL

Science.gov Websites

technologies using materials-by-design methods. The basic direction involves research on non-equilibrium doping in semiconductors Materials by Design and Materials Genome Non-equilibrium and metastable . 5, 1117 (2014) "Theoretical Prediction and Experimental Realization of New Stable Inorganic

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

Maintenance of equilibrium point control during an unexpectedly loaded rapid limb movement.

PubMed

Simmons, R W; Richardson, C

1984-06-08

Two experiments investigated whether the equilibrium point hypothesis or the mass-spring model of motor control subserves positioning accuracy during spring loaded, rapid, bi-articulated movement. For intact preparations, the equilibrium point hypothesis predicts response accuracy to be determined by a mixture of afferent and efferent information, whereas the mass-spring model predicts positioning to be under a direct control system. Subjects completed a series of load-resisted training trials to a spatial target. The magnitude of a sustained spring load was unexpectedly increased on selected trials. Results indicated positioning accuracy and applied force varied with increases in load, which suggests that the original efferent commands are modified by afferent information during the movement as predicted by the equilibrium point hypothesis.

Kinetics and Equilibrium of Age-Induced Precipitation in Cu-4 At. Pct Ti Binary Alloy

NASA Astrophysics Data System (ADS)

Semboshi, Satoshi; Amano, Shintaro; Fu, Jie; Iwase, Akihiro; Takasugi, Takayuki

2017-03-01

Transformation kinetics and phase equilibrium of metastable and stable precipitates in age-hardenable Cu-4 at. pct Ti binary alloy have been investigated by monitoring the microstructural evolution during isothermal aging at temperatures between 693 K (420 °C) and 973 K (700 °C). The microstructure of the supersaturated solid solution evolves in four stages: compositional modulation due to spinodal decomposition, continuous precipitation of the needle-shaped metastable β'-Cu4Ti with a tetragonal structure, discontinuous precipitation of cellular components containing stable β-Cu4Ti lamellae with an orthorhombic structure, and eventually precipitation saturation at equilibrium. In specimens aged below 923 K (650 °C), the stable β-Cu4Ti phase is produced only due to the cellular reaction, whereas it can be also directly obtained from the intergranular needle-shaped β'-Cu4Ti precipitates in specimens aged at 973 K (700 °C). The precipitation kinetics and phase equilibrium observed for the specimens aged between 693 K (420 °C) and 973 K (700 °C) were characterized in accordance with a time-temperature-transformation (TTT) diagram and a Cu-Ti partial phase diagram, which were utilized to determine the alloy microstructure, strength, and electrical conductivity.

Stochastic evolutionary voluntary public goods game with punishment in a Quasi-birth-and-death process.

PubMed

Quan, Ji; Liu, Wei; Chu, Yuqing; Wang, Xianjia

2017-11-23

Traditional replication dynamic model and the corresponding concept of evolutionary stable strategy (ESS) only takes into account whether the system can return to the equilibrium after being subjected to a small disturbance. In the real world, due to continuous noise, the ESS of the system may not be stochastically stable. In this paper, a model of voluntary public goods game with punishment is studied in a stochastic situation. Unlike the existing model, we describe the evolutionary process of strategies in the population as a generalized quasi-birth-and-death process. And we investigate the stochastic stable equilibrium (SSE) instead. By numerical experiments, we get all possible SSEs of the system for any combination of parameters, and investigate the influence of parameters on the probabilities of the system to select different equilibriums. It is found that in the stochastic situation, the introduction of the punishment and non-participation strategies can change the evolutionary dynamics of the system and equilibrium of the game. There is a large range of parameters that the system selects the cooperative states as its SSE with a high probability. This result provides us an insight and control method for the evolution of cooperation in the public goods game in stochastic situations.

Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse.

PubMed

Ren, Shanjing

In this paper, an SEIR epidemic model for an imperfect treatment disease with age-dependent latency and relapse is proposed. The model is well-suited to model tuberculosis. The basic reproduction number R0 is calculated. We obtain the global behavior of the model in terms of R0. If R0< 1, the disease-free equilibrium is globally asymptotically stable, whereas if R0>1, a Lyapunov functional is used to show that the endemic equilibrium is globally stable amongst solutions for which the disease is present.

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

LONG-TERM STABLE EQUILIBRIA FOR SYNCHRONOUS BINARY ASTEROIDS

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

Jacobson, Seth A.; Scheeres, Daniel J.

Synchronous binary asteroids may exist in a long-term stable equilibrium, where the opposing torques from mutual body tides and the binary YORP (BYORP) effect cancel. Interior of this equilibrium, mutual body tides are stronger than the BYORP effect and the mutual orbit semimajor axis expands to the equilibrium; outside of the equilibrium, the BYORP effect dominates the evolution and the system semimajor axis will contract to the equilibrium. If the observed population of small (0.1-10 km diameter) synchronous binaries are in static configurations that are no longer evolving, then this would be confirmed by a null result in the observationalmore » tests for the BYORP effect. The confirmed existence of this equilibrium combined with a shape model of the secondary of the system enables the direct study of asteroid geophysics through the tidal theory. The observed synchronous asteroid population cannot exist in this equilibrium if described by the canonical 'monolithic' geophysical model. The 'rubble pile' geophysical model proposed by Goldreich and Sari is sufficient, however it predicts a tidal Love number directly proportional to the radius of the asteroid, while the best fit to the data predicts a tidal Love number inversely proportional to the radius. This deviation from the canonical and Goldreich and Sari models motivates future study of asteroid geophysics. Ongoing BYORP detection campaigns will determine whether these systems are in an equilibrium, and future determination of secondary shapes will allow direct determination of asteroid geophysical parameters.« less

The dynamics of the de Sitter resonance

NASA Astrophysics Data System (ADS)

Celletti, Alessandra; Paita, Fabrizio; Pucacco, Giuseppe

2018-02-01

We study the dynamics of the de Sitter resonance, namely the stable equilibrium configuration of the first three Galilean satellites. We clarify the relation between this family of configurations and the more general Laplace resonant states. In order to describe the dynamics around the de Sitter stable equilibrium, a one-degree-of-freedom Hamiltonian normal form is constructed and exploited to identify initial conditions leading to the two families. The normal form Hamiltonian is used to check the accuracy in the location of the equilibrium positions. Besides, it gives a measure of how sensitive it is with respect to the different perturbations acting on the system. By looking at the phase plane of the normal form, we can identify a Laplace-like configuration, which highlights many substantial aspects of the observed one.

Nanoscale heat transfer and phase transformation surrounding intensely heated nanoparticles

NASA Astrophysics Data System (ADS)

Sasikumar, Kiran

Over the last decade there has been significant ongoing research to use nanoparticles for hyperthermia-based destruction of cancer cells. In this regard, the investigation of highly non-equilibrium thermal systems created by ultrafast laser excitation is a particularly challenging and important aspect of nanoscale heat transfer. It has been observed experimentally that noble metal nanoparticles, illuminated by radiation at the plasmon resonance wavelength, can act as localized heat sources at nanometer-length scales. Achieving biological response by delivering heat via nanoscale heat sources has also been demonstrated. However, an understanding of the thermal transport at these scales and associated phase transformations is lacking. A striking observation made in several laser-heating experiments is that embedded metal nanoparticles heated to extreme temperatures may even melt without an associated boiling of the surrounding fluid. This unusual phase stability is not well understood and designing experiments to understand the physics of this phenomenon is a challenging task. In this thesis, we will resort to molecular dynamics (MD) simulations, which offer a powerful tool to investigate this phenomenon, without assumptions underlying continuum-level model formulations. We present the results from a series of steady state and transient non-equilibrium MD simulations performed on an intensely heated nanoparticle immersed in a model liquid. For small nanoparticles (1-10 nm in diameter) we observe a stable liquid phase near the nanoparticle surface, which can be at a temperature well above the boiling point. Furthermore, we report the existence of a critical nanoparticle size (4 nm in diameter) below which we do not observe formation of vapor even when local fluid temperatures exceed the critical temperature. Instead, we report the existence of a stable fluid region with a density much larger than that of the vapor phase. We explain this stability in terms of the Laplace pressure associated with the formation of a vapor nanocavity and the associated effect on the Gibbs free energy. Separately, we also demonstrate the role of extreme temperature gradients (108-1010 K/m) in elevating the boiling point of liquids. We show that, assuming local thermal equilibrium, the observed elevation of the boiling point is associated with the interplay between the "bulk" driving force for the phase change and surface tension of the liquid-vapor interface that suppresses the transformation. In transient simulations that mimic laser-heating experiments we observe the formation and collapse of vapor bubbles around the nanoparticles beyond a threshold. Detailed analysis of the cavitation dynamics indicates adiabatic formation followed by an isothermal final stage of growth and isothermal collapse.

An automated and efficient conformation search of L-cysteine and L,L-cystine using the scaled hypersphere search method

NASA Astrophysics Data System (ADS)

Kishimoto, Naoki; Waizumi, Hiroki

2017-10-01

Stable conformers of L-cysteine and L,L-cystine were explored using an automated and efficient conformational searching method. The Gibbs energies of the stable conformers of L-cysteine and L,L-cystine were calculated with G4 and MP2 methods, respectively, at 450, 298.15, and 150 K. By assuming thermodynamic equilibrium and the barrier energies for the conformational isomerization pathways, the estimated ratios of the stable conformers of L-cysteine were compared with those determined by microwave spectroscopy in a previous study. Equilibrium structures of 1:1 and 2:1 cystine-Fe complexes were also calculated, and the energy of insertion of Fe into the disulfide bond was obtained.

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.

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

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.

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.

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 global phase diagram of the Gay-Berne model

NASA Astrophysics Data System (ADS)

de Miguel, Enrique; Vega, Carlos

2002-10-01

The phase diagram of the Gay-Berne model with anisotropy parameters κ=3, κ'=5 has been evaluated by means of computer simulations. For a number of temperatures, NPT simulations were performed for the solid phase leading to the determination of the free energy of the solid at a reference density. Using the equation of state and free energies of the isotropic and nematic phases available in the existing literature the fluid-solid equilibrium was calculated for the temperatures selected. Taking these fluid-solid equilibrium results as the starting points, the fluid-solid equilibrium curve was determined for a wide range of temperatures using Gibbs-Duhem integration. At high temperatures the sequence of phases encountered on compression is isotropic to nematic, and then nematic to solid. For reduced temperatures below T=0.85 the sequence is from the isotropic phase directly to the solid state. In view of this we locate the isotropic-nematic-solid triple point at TINS=0.85. The present results suggest that the high-density phase designated smectic B in previous simulations of the model is in fact a molecular solid and not a smectic liquid crystal. It seems that no thermodynamically stable smectic phase appears for the Gay-Berne model with the choice of parameters used in this work. We locate the vapor-isotropic liquid-solid triple point at a temperature TVIS=0.445. Considering that the critical temperatures is Tc=0.473, the Gay-Berne model used in this work presents vapor-liquid separation over a rather narrow range of temperatures. It is suggested that the strong lateral attractive interactions present in the Gay-Berne model stabilizes the layers found in the solid phase. The large stability of the solid phase, particularly at low temperatures, would explain the unexpectedly small liquid range observed in the vapor-liquid region.

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

Third-Order Memristive Morris-Lecar Model of Barnacle Muscle Fiber

NASA Astrophysics Data System (ADS)

Rajamani, Vetriveeran; Sah, Maheshwar Pd.; Mannan, Zubaer Ibna; Kim, Hyongsuk; Chua, Leon

This paper presents a detailed analysis of various oscillatory behaviors observed in relation to the calcium and potassium ions in the third-order Morris-Lecar model of giant barnacle muscle fiber. Since, both the calcium and potassium ions exhibit all of the characteristics of memristor fingerprints, we claim that the time-varying calcium and potassium ions in the third-order Morris-Lecar model are actually time-invariant calcium and potassium memristors in the third-order memristive Morris-Lecar model. We confirmed the existence of a small unstable limit cycle oscillation in both the second-order and the third-order Morris-Lecar model by numerically calculating the basin of attraction of the asymptotically stable equilibrium point associated with two subcritical Hopf bifurcation points. We also describe a comprehensive analysis of the generation of oscillations in third-order memristive Morris-Lecar model via small-signal circuit analysis and a subcritical Hopf bifurcation phenomenon.

Equilibrium contact angle or the most-stable contact angle?

PubMed

Montes Ruiz-Cabello, F J; Rodríguez-Valverde, M A; Cabrerizo-Vílchez, M A

2014-04-01

It is well-established that the equilibrium contact angle in a thermodynamic framework is an "unattainable" contact angle. Instead, the most-stable contact angle obtained from mechanical stimuli of the system is indeed experimentally accessible. Monitoring the susceptibility of a sessile drop to a mechanical stimulus enables to identify the most stable drop configuration within the practical range of contact angle hysteresis. Two different stimuli may be used with sessile drops: mechanical vibration and tilting. The most stable drop against vibration should reveal the changeless contact angle but against the gravity force, it should reveal the highest resistance to slide down. After the corresponding mechanical stimulus, once the excited drop configuration is examined, the focus will be on the contact angle of the initial drop configuration. This methodology needs to map significantly the static drop configurations with different stable contact angles. The most-stable contact angle, together with the advancing and receding contact angles, completes the description of physically realizable configurations of a solid-liquid system. Since the most-stable contact angle is energetically significant, it may be used in the Wenzel, Cassie or Cassie-Baxter equations accordingly or for the surface energy evaluation. © 2013 Elsevier B.V. All rights reserved.

Frequency-Dependent Selection: The High Potential for Permanent Genetic Variation in the Diallelic, Pairwise Interaction Model

PubMed Central

Asmussen, M. A.; Basnayake, E.

1990-01-01

A detailed analytic and numerical study is made of the potential for permanent genetic variation in frequency-dependent models based on pairwise interactions among genotypes at a single diallelic locus. The full equilibrium structure and qualitative gene-frequency dynamics are derived analytically for a symmetric model, in which pairwise fitnesses are chiefly determined by the genetic similarity of the individuals involved. This is supplemented by an extensive numerical investigation of the general model, the symmetric model, and nine other special cases. Together the results show that there is a high potential for permanent genetic diversity in the pairwise interaction model, and provide insight into the extent to which various forms of genotypic interactions enhance or reduce this potential. Technically, although two stable polymorphic equilibria are possible, the increased likelihood of maintaining both alleles, and the poor performance of protected polymorphism conditions as a measure of this likelihood, are primarily due to a greater variety and frequency of equilibrium patterns with one stable polymorphic equilibrium, in conjunction with a disproportionately large domain of attraction for stable internal equilibria. PMID:2341034

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

Numerical simulation of a two-sex human papillomavirus (HPV) vaccination model

NASA Astrophysics Data System (ADS)

Suryani, I.; Adi-Kusumo, F.

2014-02-01

Human Papillomavirus (HPV) is a major cause of cervical cancer, precancerous lesions, cancer and other disease. HPV is the most common sexually transmitted infection. Although HPV virus primarily affects woman but it can also affects man because it cause of cancer of the anus, vulva, vagina, penis and some other cancers. HPV vaccines now used to prevent cervical cancer and genital warts because the vaccine protect against four types of HPV that most commonly cause disease are types 6, 11, 16, and 18. This paper is sequel work of Elbasha (2008). Difference with Elbasha (2008) are give alternative proof global stability, numerical simulation and interpretation. Global stability of the equilibrium on the model of a two-sex HPV vaccination were explored by using Lyapunov. Although we use the same lyapunov function, we use the largest invariant set to proof the global stability. The result show that the global stability of the equilibrium depends on the effective reproduction number (R). If R < 1 then the infection-free equilibrium is asymptotically stable globally. If R > 1 then endemic equilibrium have globally asymptotically stable properties. Then equilibrium proceed with the interpretation of numerical simulation.

Teaching the Concept of Gibbs Energy Minimization through Its Application to Phase-Equilibrium Calculation

ERIC Educational Resources Information Center

Privat, Romain; Jaubert, Jean-Noe¨l; Berger, Etienne; Coniglio, Lucie; Lemaitre, Ce´cile; Meimaroglou, Dimitrios; Warth, Vale´rie

2016-01-01

Robust and fast methods for chemical or multiphase equilibrium calculation are routinely needed by chemical-process engineers working on sizing or simulation aspects. Yet, while industrial applications essentially require calculation tools capable of discriminating between stable and nonstable states and converging to nontrivial solutions,…

Space Instrument Optimization by Implementing of Generic Three Bodies Circular Restricted Problem

NASA Astrophysics Data System (ADS)

Nejat, Cyrus

2011-01-01

In this study, the main discussion emphasizes on the spacecraft operation with a concentration on stationary points in space. To achieve these objectives, the circular restricted problem was solved for selected approaches. The equations of motion of three body restricted problem was demonstrated to apply in cases other than Lagrange's (1736-1813 A.D.) achievements, by means of the purposed CN (Cyrus Nejat) theorem along with appropriate comments. In addition to five Lagrange, two other points, CN1 and CN2 were found to be in unstable equilibrium points in a very large distance respect to Lagrange points, but stable at infinity. A very interesting simulation of Milky Way Galaxy and Andromeda Galaxy were created to find the Lagrange points, CN points (Cyrus Nejat Points), and CN lines (Cyrus Nejat Lines). The equations of motion were rearranged such a way that the transfer trajectory would be conical, by means of decoupling concept. The main objective was to make a halo orbit transfer about CN lines. The author purposes therefore that all of the corresponding sizing design that they must be developed by optimization techniques would be considered in future approaches. The optimization techniques are sufficient procedures to search for the most ideal response of a system.

Equilibrium-point control hypothesis examined by measured arm stiffness during multijoint movement.

PubMed

Gomi, H; Kawato

1996-04-05

For the last 20 years, it has been hypothesized that well-coordinated, multijoint movements are executed without complex computation by the brain, with the use of springlike muscle properties and peripheral neural feedback loops. However, it has been technically and conceptually difficult to examine this "equilibrium-point control" hypothesis directly in physiological or behavioral experiments. A high-performance manipulandum was developed and used here to measure human arm stiffness, the magnitude of which during multijoint movement is important for this hypothesis. Here, the equilibrium-point trajectory was estimated from the measured stiffness, the actual trajectory, and the generated torque. Its velocity profile differed from that of the actual trajectory. These results argue against the hypothesis that the brain sends as a motor command only an equilibrium-point trajectory similar to the actual trajectory.

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.

Concentrated dispersions of equilibrium protein nanoclusters that reversibly dissociate into active monomers

NASA Astrophysics Data System (ADS)

Truskett, Thomas M.; Johnston, Keith; Maynard, Jennifer; Borwankar, Ameya; Miller, Maria; Wilson, Brian; Dinin, Aileen; Khan, Tarik; Kaczorowski, Kevin

2012-02-01

Stabilizing concentrated protein solutions is of wide interest in drug delivery. However, a major challenge is how to reliably formulate concentrated, low viscosity (i.e., syringeable) solutions of biologically active proteins. Unfortunately, proteins typically undergo irreversible aggregation at intermediate concentrations of 100-200 mg/ml. In this talk, I describe how they can effectively avoid these intermediate concentrations by reversibly assembling into nanoclusters. Nanocluster assembly is achieved by balancing short-ranged, cosolute-induced attractions with weak, longer-ranger electrostatic repulsions near the isoelectric point. Theory predicts that native proteins are stabilized by a self-crowding mechanism within the concentrated environment of the nanoclusters, while weak cluster-cluster interactions can result in colloidally-stable dispersions with moderate viscosities. I present experimental results where this strategy is used to create concentrated antibody dispersions (up to 260 mg/ml) comprising nanoclusters of proteins [monoclonal antibody 1B7, polyclonal sheep Immunoglobin G and bovine serum albumin], which upon dilution in vitro or administration in vivo, are conformationally stable and retain activity.

Complexity dynamics and Hopf bifurcation analysis based on the first Lyapunov coefficient about 3D IS-LM macroeconomics system

NASA Astrophysics Data System (ADS)

Ma, Junhai; Ren, Wenbo; Zhan, Xueli

2017-04-01

Based on the study of scholars at home and abroad, this paper improves the three-dimensional IS-LM model in macroeconomics, analyzes the equilibrium point of the system and stability conditions, focuses on the parameters and complex dynamic characteristics when Hopf bifurcation occurs in the three-dimensional IS-LM macroeconomics system. In order to analyze the stability of limit cycles when Hopf bifurcation occurs, this paper further introduces the first Lyapunov coefficient to judge the limit cycles, i.e. from a practical view of the business cycle. Numerical simulation results show that within the range of most of the parameters, the limit cycle of 3D IS-LM macroeconomics is stable, that is, the business cycle is stable; with the increase of the parameters, limit cycles becomes unstable, and the value range of the parameters in this situation is small. The research results of this paper have good guide significance for the analysis of macroeconomics system.

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.

Dynamic Interaction of TTDA with TFIIH Is Stabilized by Nucleotide Excision Repair in Living Cells

PubMed Central

Theil, Arjan F; Mari, Pierre-Olivier; Hoogstraten, Deborah; Ng, Jessica M. Y; Dinant, Christoffel; Hoeijmakers, Jan H. J

2006-01-01

Transcription/repair factor IIH (TFIIH) is essential for RNA polymerase II transcription and nucleotide excision repair (NER). This multi-subunit complex consists of ten polypeptides, including the recently identified small 8-kDa trichothiodystrophy group A (TTDA)/ hTFB5 protein. Patients belonging to the rare neurodevelopmental repair syndrome TTD-A carry inactivating mutations in the TTDA/hTFB5 gene. One of these mutations completely inactivates the protein, whereas other TFIIH genes only tolerate point mutations that do not compromise the essential role in transcription. Nevertheless, the severe NER-deficiency in TTD-A suggests that the TTDA protein is critical for repair. Using a fluorescently tagged and biologically active version of TTDA, we have investigated the involvement of TTDA in repair and transcription in living cells. Under non-challenging conditions, TTDA is present in two distinct kinetic pools: one bound to TFIIH, and a free fraction that shuttles between the cytoplasm and nucleus. After induction of NER-specific DNA lesions, the equilibrium between these two pools dramatically shifts towards a more stable association of TTDA to TFIIH. Modulating transcriptional activity in cells did not induce a similar shift in this equilibrium. Surprisingly, DNA conformations that only provoke an abortive-type of NER reaction do not result into a more stable incorporation of TTDA into TFIIH. These findings identify TTDA as the first TFIIH subunit with a primarily NER-dedicated role in vivo and indicate that its interaction with TFIIH reflects productive NER. PMID:16669699

Stability hierarchy between Piracetam forms I, II, and III from experimental pressure-temperature diagrams and topological inferences.

PubMed

Toscani, Siro; Céolin, René; Minassian, Léon Ter; Barrio, Maria; Veglio, Nestor; Tamarit, Josep-Lluis; Louër, Daniel; Rietveld, Ivo B

2016-01-30

The trimorphism of the active pharmaceutical ingredient piracetam is a famous case of polymorphism that has been frequently revisited by many researchers. The phase relationships between forms I, II, and III were ambiguous because they seemed to depend on the heating rate of the DSC and on the history of the samples or they have not been observed at all (equilibrium II-III). In the present paper, piezo-thermal analysis and high-pressure differential thermal analysis have been used to elucidate the positions of the different solid-solid and solid-liquid equilibria. The phase diagram, involving the three solid phases, the liquid phase and the vapor phase, has been constructed. It has been shown that form III is the high-pressure, low-temperature form and the stable form at room temperature. Form II is stable under intermediary conditions and form I is the low pressure, high temperature form, which possesses a stable melting point. The present paper demonstrates the strength of the topological approach based on the Clapeyron equation and the alternation rule when combined with high-pressure measurements. Copyright © 2015 Elsevier B.V. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

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

Criticality of the random field Ising model in and out of equilibrium: A nonperturbative functional renormalization group description

NASA Astrophysics Data System (ADS)

Balog, Ivan; Tarjus, Gilles; Tissier, Matthieu

2018-03-01

We show that, contrary to previous suggestions based on computer simulations or erroneous theoretical treatments, the critical points of the random-field Ising model out of equilibrium, when quasistatically changing the applied source at zero temperature, and in equilibrium are not in the same universality class below some critical dimension dD R≈5.1 . We demonstrate this by implementing a nonperturbative functional renormalization group for the associated dynamical field theory. Above dD R, the avalanches, which characterize the evolution of the system at zero temperature, become irrelevant at large distance, and hysteresis and equilibrium critical points are then controlled by the same fixed point. We explain how to use computer simulation and finite-size scaling to check the correspondence between in and out of equilibrium criticality in a far less ambiguous way than done so far.

Bifurcation Gaps in Asymmetric and High-Dimensional Hypercycles

NASA Astrophysics Data System (ADS)

Puig, Júlia; Farré, Gerard; Guillamon, Antoni; Fontich, Ernest; Sardanyés, Josep

Hypercycles are catalytic systems with cyclic architecture. These systems have been suggested to play a key role in the maintenance and increase of information in prebiotic replicators. It is known that for a large enough number of hypercycle species (n > 4) the coexistence of all hypercycle members is governed by a stable periodic orbit. Previous research has characterized saddle-node (s-n) bifurcations involving abrupt transitions from stable hypercycles to extinction of all hypercycle members, or, alternatively, involving the outcompetition of the hypercycle by so-called mutant sequences or parasites. Recently, the presence of a bifurcation gap between a s-n bifurcation of periodic orbits and a s-n of fixed points has been described for symmetric five-member hypercycles. This gap was found between the value of the replication quality factor Q from which the periodic orbit vanishes (QPO) and the value where two unstable (nonzero) equilibrium points collide (QSS). Here, we explore the persistence of this gap considering asymmetries in replication rates in five-member hypercycles as well as considering symmetric, larger hypercycles. Our results indicate that both the asymmetry in Malthusian replication constants and the increase in hypercycle members enlarge the size of this gap. The implications of this phenomenon are discussed in the context of delayed transitions associated to the so-called saddle remnants.

New concepts and new design of permanent maglev rotary artificial heart blood pumps.

PubMed

Qian, K X; Zeng, P; Ru, W M; Yuan, H Y

2006-05-01

According to tradition, permanent maglev cannot achieve stable equilibrium. The authors have developed, to the contrary, two stable permanent maglev impeller blood pumps. The first pump is an axially driven uni-ventricular assist pump, in which the rotor with impeller is radially supported by two passive magnetic bearings, but has one point contact with the stator axially at standstill. As the pump raises its rotating speed, the increasing hydrodynamic force of fluid acting on the impeller will make the rotor taking off from contacting point and disaffiliate from the stator. Then the rotor becomes fully suspended. The second pump is a radially driven bi-ventricular assist pump, i.e., an impeller total artificial heart. Its rotor with two impellers on both ends is supported by two passive magnetic bearings, which counteract the attractive force between rotor magnets and stator coil iron core. The rotor is affiliated to the stator radially at standstill and becomes levitated during rotation. Therefore, the rotor keeps concentric with stator during rotation but eccentric at standstill, as is confirmed by rotor position detection with Honeywell sensors. It concludes that the permanent maglev needs action of a non-magnetic force to achieve stability but a rotating magnetic levitator with high speed and large inertia can maintain its stability merely with passive magnetic bearings.

Generation of Strategies for Environmental Deception in Two-Player Normal-Form Games

DTIC Science & Technology

2015-06-18

found in the literature is pre- sented by Kohlberg and Mertens [23]. A stable equilibrium by their definition is an equi- librium in an extensive-form...the equilibrium in this state provides them with an increased payoff. While interesting, Kohlberg and Mertens’ defi- 13 nition of equilibrium...stability used by Kohlberg and Mertens. Arsham’s work focuses on determining the amount by which a mixed-strategy Nash equilibrium’s payoff values can

Stable carbon and hydrogen isotope fractionation of dissolved organic groundwater pollutants by equilibrium sorption.

PubMed

Höhener, Patrick; Yu, Xianjing

2012-03-15

Linear free energy relationships (LFERs) were established which relate equilibrium vapor-liquid isotope effects to stable carbon and hydrogen isotope enrichment factors for equilibrium sorption to geosorbents. The LFERs were established for normal, cyclic or branched alkanes, monoaromatic hydrocarbons, and chloroethenes. These LFERs predict that isotopic light compounds sorb more strongly than their heavy counterparts. Defining fractionation as in classical literature by "heavy divided by light", carbon enrichment factors for equilibrium sorption were derived which ranged from -0.13±0.04‰ (benzene) to -0.52±0.19‰ (trichloroethene at 5-15 °C). Hydrogen enrichment factors for sorption of 14 different compounds were between -2.4 and -9.2‰. For perdeuterated hydrocarbons the predicted enrichment factors ranged from -19±5.4‰ (benzene) to -64±30‰ (cyclohexane). Equilibrium sorption experiments with a soil and activated carbon as sorbents were performed in the laboratory for perdeuterocyclohexane and perdeuterotoluene. The measured D/H enrichments agreed with the LFER prediction for both compounds and both sorbents within the uncertainty estimate of the prediction. The results of this work suggest that equilibrium sorption does create only very small isotope shifts for (13)C in groundwater pollutants in aquifers. It is also suggested that deuterium shifts are expected to be higher, especially for strongly sorbing pollutants. Copyright © 2011 Elsevier B.V. All rights reserved.

Fostering cooperation of selfish agents through public goods in relation to the loners

NASA Astrophysics Data System (ADS)

Zhang, Jianlei; Chen, Zengqiang; Liu, Zhongxin

2016-03-01

Altruistic behaviors in multiplayer groups have obtained great attention in the context of the public goods game, which poses a riddle from the evolutionary viewpoint. Here we focus on a particular type of public goods game model in which the benefits of cooperation are either discounted or synergistically enhanced at the appearance of multiple cooperators in a group. Moreover, we focus on the three-strategies profile by adding the role of loners, besides the often-used cooperation and defection. Using the replicator dynamic equations, we investigate a range of dynamical portraits that characterizes the properties of the steady state. Analysis results indicate that loners and cooperators both have chances to be the stable equilibrium points in the presence of perturbations, while defectors fail to do so in this three-strategy competition. Moreover, the coexistence state, in which all three strategies exist in equilibrium, can be led by suitable parameters and stabilized for perturbations. These results elucidate the interplay between the characteristics of the public goods game and evolutionary dynamics in well-mixed systems.

Onset of Cooperative Dynamics in an Equilibrium Glass-Forming Metallic Liquid

DOE PAGES

Jaiswal, Abhishek; O’Keeffe, Stephanie; Mills, Rebecca; ...

2016-01-22

Onset of cooperative dynamics has been observed in many molecular liquids, colloids, and granular materials in the metastable regime on approaching their respective glass or jamming transition points, and is considered to play a significant role in the emergence of the slow dynamics. However, the nature of such dynamical cooperativity remains elusive in multicomponent metallic liquids characterized by complex many-body interactions and high mixing entropy. Herein, we report evidence of onset of cooperative dynamics in an equilibrium glass-forming metallic liquid (LM601: Zr 51Cu 36Ni 4Al 9). This is revealed by deviation of the mean effective diffusion coefficient from its high-temperaturemore » Arrhenius behavior below T A ≈ 1300 K, i.e., a crossover from uncorrelated dynamics above T A to landscape-influenced correlated dynamics below T A. Moreover, the onset/ crossover temperature T A in such a multicomponent bulk metallic glass-forming liquid is observed at approximately twice of its calorimetric glass transition temperature (T g ≈ 697 K) and in its stable liquid phase, unlike many molecular liquids.« less

Solubility behavior of lamivudine crystal forms in recrystallization solvents.

PubMed

Jozwiakowski, M J; Nguyen, N A; Sisco, J M; Spancake, C W

1996-02-01

Lamivudine can be obtained as acicular crystals (form I, 0.2 hydrate) from water or methanol and as bipyramidal crystals (form II, nonsolvated) from many nonaqueous solvents. Form II is thermodynamically favored in the solid state (higher melting point and greater density than form I) at ambient relative humidities. Solubility measurements on both forms versus solvent and temperature was used to determine whether entropy or enthalpy was the driving force for solubility. Solution calorimetry data indicated that form I is favored (less soluble) in all solvents studied on the basis of enthalpy alone. In higher alcohols and other organic solvents, form I has a larger entropy of solution than form II, which compensates for the enthalpic factors and results in physical stability for form II in these systems. The metastable crystal form solubility at 25 degrees C was estimated to be 1.2-2.3 times as high as the equilibrium solubility of the stable form, depending on the temperature, solvent, and crystal form. Binary solvent studies showed that > 18-20% water must be present in ethanol to convert the excess solid to form I at equilibrium.

Velocity-based planning of rapid elbow movements expands the control scheme of the equilibrium point hypothesis.

PubMed

Suzuki, Masataka; Yamazaki, Yoshihiko

2005-01-01

According to the equilibrium point hypothesis of voluntary motor control, control action of muscles is not explicitly computed, but rather arises as a consequence of interaction between moving equilibrium position, current kinematics and stiffness of the joint. This approach is attractive as it obviates the need to explicitly specify the forces controlling limb movements. However, many debatable aspects of this hypothesis remain in the manner of specification of the equilibrium point trajectory and muscle activation (or its stiffness), which elicits a restoring force toward the planned equilibrium trajectory. In this study, we expanded the framework of this hypothesis by assuming that the control system uses the velocity measure as the origin of subordinate variables scaling descending commands. The velocity command is translated into muscle control inputs by second order pattern generators, which yield reciprocal command and coactivation commands, and create alternating activation of the antagonistic muscles during movement and coactivation in the post-movement phase, respectively. The velocity command is also integrated to give a position command specifying a moving equilibrium point. This model is purely kinematics-dependent, since the descending commands needed to modulate the visco-elasticity of muscles are implicitly given by simple parametric specifications of the velocity command alone. The simulated movements of fast elbow single-joint movements corresponded well with measured data performed over a wide range of movement distances, in terms of both muscle excitations and kinematics. Our proposal on a synthesis for the equilibrium point approach and velocity command, may offer some insights into the control scheme of the single-joint arm movements.

Using chromium stable isotope ratios to quantify Cr(VI) reduction: Lack of sorption effects

USGS Publications Warehouse

Ellis, A.S.; Johnson, T.M.; Bullen, T.D.

2004-01-01

Chromium stable isotope values can be effectively used to monitor reduction of Cr(VI) in natural waters. We investigate effects of sorption during transport of Cr(VI) which may also shift Cr isotopes values, complicating efforts to quantify reduction. This study shows that Cr stable isotope fractionation caused by sorption is negligible. Equilibrium fractionation of Cr stable isotopes between dissolved Cr-(VI) and Cr(VI) adsorbed onto ??-Al2O3 and goethite is less than 0.04???. (53Cr/52Cr) under environmentally relevant pH conditions. Batch experiments at pH 4.0 and pH 6.0 were conducted in series to sequentially magnify small isotope fractionations. A simple transport model suggests that adsorption may cause amplification of a small isotope fractionation along extreme fringes of a plume, leading to shifts in 53Cr/52Cr values. We therefore suggest that isotope values at extreme fringes of Cr plumes be critically evaluated for sorption effects. A kinetic effect was observed in experiments with goethite at pH 4 where apparently lighter isotopes diffuse into goethite clumps at a faster rate before eventually reaching equilibrium. This observed kinetic effect may be important in a natural system that has not attained equilibrium and is in need of further study. Cr isotope fractionation caused by speciation of Cr(VI) between HCrO4- and CrO42- was also examined, and we conclude that it is not measurable. In the absence of isotope fractionation caused by equilibrium speciation and sorption, most of the variation in ??53 Cr values may be attributed to reduction, and reliable estimates of Cr reduction can be made.

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)

Thermodynamics and kinetics of vesicles formation processes.

PubMed

Guida, Vincenzo

2010-12-15

Vesicles are hollow aggregates, composed of bilayers of amphiphilic molecules, dispersed into and filled with a liquid solvent. These aggregates can be formed either as equilibrium or as out of equilibrium meta-stable structures and they exhibit a rich variety of different morphologies. The surprising richness of structures, the vast range of industrial applications and the presence of vesicles in a number of biological systems have attracted the interest of numerous researchers and scientists. In this article, we review both the thermodynamics and the kinetics aspects of the phenomena of formation of vesicles. We start presenting the thermodynamics of bilayer membranes formation and deformation, with the aim of deriving the conditions for the existence of equilibrium vesicles. Specifically, we use the results from continuum thermodynamics to discuss the possibility of formation of stable equilibrium vesicles, from both mixed amphiphiles and single component systems. We also link the bilayer membrane properties to the molecular structure of the starting amphiphiles. In the second part of this article, we focus on the dynamics and kinetics of vesiculation. We review the process of vesicles formation both from planar lamellar phase under shear and from isotropic micelles. In order to clarify the physical mechanisms of vesicles formation, we continuously draw a parallel between emulsification and vesiculation processes. Specifically, we compare the experimental results, the driving forces and the relative scaling laws identified for the two processes. Describing the dynamics of vesicles formation, we also discuss why non equilibrium vesicles can be formed by kinetics control and why they are meta-stable. Understanding how to control the properties, the stability and the formation process of vesicles is of fundamental importance for a vast number of industrial applications. Copyright © 2009. Published by Elsevier B.V.

Using computer algebra and SMT-solvers to analyze a mathematical model of cholera propagation

NASA Astrophysics Data System (ADS)

Trujillo Arredondo, Mariana

2014-06-01

We analyze a mathematical model for the transmission of cholera. The model is already defined and involves variables such as the pathogen agent, which in this case is the bacterium Vibrio cholera, and the human population. The human population is divided into three classes: susceptible, infectious and removed. Using Computer Algebra, specifically Maple we obtain two equilibrium states: the disease free state and the endemic state. Using Maple it is possible to prove that the disease free state is locally asymptotically stable if and only if R0 < 1. Using Maple it is possible to prove that the endemic equilibrium state is locally stable when it exists, it is to say when R0 > 1. Using the package Red-Log of the Computer algebra system Reduce and the SMT-Solver Z3Py it is possible to obtain numerical conditions for the model. The formula for the basic reproductive number makes a synthesis with all epidemic parameters in the model. Also it is possible to make numerical simulations which are very illustrative about the epidemic patters that are expected to be observed in real situations. We claim that these kinds of software are very useful in the analysis of epidemic models given that the symbolic computation provides algebraic formulas for the basic reproductive number and such algebraic formulas are very useful to derive control measures. For other side, computer algebra software is a powerful tool to make the stability analysis for epidemic models given that the all steps in the stability analysis can be made automatically: finding the equilibrium points, computing the jacobian, computing the characteristic polynomial for the jacobian, and applying the Routh-Hurwitz theorem to the characteristic polynomial. Finally, using SMT-Solvers is possible to make automatically checks of satisfiability, validity and quantifiers elimination being these computations very useful to analyse complicated epidemic models.

Preparation and Relaxation of Very Stable Glassy States of a Simulated Liquid

NASA Astrophysics Data System (ADS)

Jack, Robert L.; Hedges, Lester O.; Garrahan, Juan P.; Chandler, David

2011-12-01

We prepare metastable glassy states in a model glass former made of Lennard-Jones particles by sampling biased ensembles of trajectories with low dynamical activity. These trajectories form an inactive dynamical phase whose “fast” vibrational degrees of freedom are maintained at thermal equilibrium by contact with a heat bath, while the “slow” structural degrees of freedom are located in deep valleys of the energy landscape. We examine the relaxation to equilibrium and the vibrational properties of these metastable states. The glassy states we prepare by our trajectory sampling method are very stable to thermal fluctuations and also more mechanically rigid than low-temperature equilibrated configurations.

Characterization of Weak Convergence of Probability-Valued Solutions of General One-Dimensional Kinetic Equations

NASA Astrophysics Data System (ADS)

Perversi, Eleonora; Regazzini, Eugenio

2015-05-01

For a general inelastic Kac-like equation recently proposed, this paper studies the long-time behaviour of its probability-valued solution. In particular, the paper provides necessary and sufficient conditions for the initial datum in order that the corresponding solution converges to equilibrium. The proofs rest on the general CLT for independent summands applied to a suitable Skorokhod representation of the original solution evaluated at an increasing and divergent sequence of times. It turns out that, roughly speaking, the initial datum must belong to the standard domain of attraction of a stable law, while the equilibrium is presentable as a mixture of stable laws.

Punctuated equilibrium as an emergent process and its modified thermodynamic characterization.

PubMed

Wosniack, M E; da Luz, M G E; Schulman, L S

2017-01-07

We address evolutionary dynamics and consider under which conditions the ecosystem interaction network allows punctuated equilibrium (i.e., alternation between hectic and quasi-stable phases). We focus on the links connecting various species and on the strength and sign of those links. For this study we consider the Tangled Nature model, which allows considerable flexibility and plasticity in the analysis of interspecies interactions. We find that it is necessary to have a proper balance of connectivity and interaction intensities so as to establish the kind of mutual cooperation and competition found in nature. It suggests evolutionary punctuated equilibrium as an emergent process, thus displaying features of complex systems. To explicitly demonstrate this fact we consider an extended form of thermodynamics, defining (for the present context) relevant out-of-equilibrium "collective" functions. We then show how to characterize the punctuated equilibrium through entropy-like and free energy-like quantities. Finally, from a close analogy to thermodynamic systems, we propose a protocol similar to simulated annealing. It is based on controlling the species' rate of mutation during the hectic periods, in this way enhancing the exploration of the genome space (similar to the known behavior of bacteria in stressful environments). This allows the system to more rapidly converge to long-duration quasi-stable phases. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

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.

Balancing Eggs

ERIC Educational Resources Information Center

Mills, Allan

2014-01-01

Theory predicts that an egg-shaped body should rest in stable equilibrium when on its side, balance vertically in metastable equilibrium on its broad end and be completely unstable on its narrow end. A homogeneous solid egg made from wood, clay or plastic behaves in this way, but a real egg will not stand on either end. It is shown that this…

Exploring the Clapeyron Equation and the Phase Rule Using a Mechanical Drawing Toy

ERIC Educational Resources Information Center

Darvesh, Katherine V.

2013-01-01

The equilibrium between phases is a key concept from the introductory physical chemistry curriculum. Phase diagrams display which phase is the most stable at a given temperature and pressure. If more than one phase has the lowest Gibbs energy, then those phases are in equilibrium under those conditions. An activity designed to demonstrate the…

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

Non-covalent interaction between Cu-phthalocyanine and methanato borondifluoride derivatives in two different medium

NASA Astrophysics Data System (ADS)

Pal, Chiranjit; Chaudhuri, Tandrima; Chattopdhyay, Subrata; Banerjee, Manas

2017-04-01

This study sort out chemical physics of non-covalent interaction between Copper phthalocyanine (CuPC) with Methanato borondifluoride derivatives (MBDF) in chloroform and ethanol. Formation of isosbestic points indicated stable ground state equilibrium between CuPC and MBDF, association ability were more pronounced in less polar chloroform. Interesting overall parallel orientation of MBDF over CuPC in gas phase geometries indicated that fluorine centre of MBDF lying just above the Cu-centre of CuPC. Thus strong interaction between Cu(II)- and F- centre could not be overruled and was also established by NBO calculation. TDDFT along with FMO features and heat of reaction values clearly designated the existence of π-π interaction and effect of solvent polarity on that interaction.

Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays.

PubMed

Huang, Haiying; Du, Qiaosheng; Kang, Xibing

2013-11-01

In this paper, a class of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. At first, the existence of equilibrium point for the addressed neural networks is studied. By utilizing the Lyapunov stability theory, stochastic analysis theory and linear matrix inequality (LMI) technique, new delay-dependent stability criteria are presented in terms of linear matrix inequalities to guarantee the neural networks to be globally exponentially stable in the mean square. Numerical simulations are carried out to illustrate the main results. © 2013 ISA. Published by ISA. All rights reserved.

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.

Artificial tektites: an experimental technique for capturing the shapes of spinning drops

NASA Astrophysics Data System (ADS)

Baldwin, K. A.

2014-12-01

Tektites are small stones formed from rapidly cooling drops of molten rock ejected from high velocity asteroid impacts with the Earth, that freeze into a myriad of shapes during flight. Many splash-form tektites have an elongated or dumb-bell shape owing to their rotation prior to solidification[1]. Here we present a novel method for creating 'artificial tektites' from spinning drops of molten wax, using diamagnetic levitation to suspend the drops[2]. We find that the solid wax models produced this way are the stable equilibrium shapes of a spinning liquid droplet held together by surface tension. In addition to the geophysical interest in tektite formation, the stable equilibrium shapes of liquid drops have implications for many physical phenomena, covering a wide range of length scales, from nuclear physics (e.g. in studies of rapidly rotating atomic nuclei), to astrophysics (e.g. in studies of the shapes of astronomical bodies such as asteroids, rapidly rotating stars and event horizons of rotating black holes). For liquid drops bound by surface tension, analytical and numerical methods predict a series of stable equilibrium shapes with increasing angular momentum. Slowly spinning drops have an oblate-like shape. With increasing angular momentum these shapes become secularly unstable to a series of triaxial pseudo-ellipsoids that then evolve into a family of two-lobed 'dumb-bell' shapes as the angular momentum is increased still further. Our experimental method allows accurate measurements of the drops to be taken, which are useful to validate numerical models. This method has provided a means for observing tektite formation, and has additionally confirmed experimentally the stable equilibrium shapes of liquid drops, distinct from the equivalent shapes of rotating astronomical bodies. Potentially, this technique could be applied to observe the non-equilibrium dynamic processes that are also important in real tektite formation, involving, e.g. viscoelastic effects, non-uniform solidification, surface wrinkling (Schlieren), and rapid separation/fission of dumb-bells via the Rayleigh-Plateau instability. [1] M. R. Stauffer and S. L. Butler, Earth Moon Planets, 107, 169 (2009). [2] R. J. A. Hill and L. Eaves, Phys. Rev. Lett. 101, 234501 (2008).

Resonance and Capture of Jupiter Comets

NASA Astrophysics Data System (ADS)

Koon, W. S.; Lo, M. W.; Marsden, J. E.; Ross, S. D.

A number of Jupiter family comets such as Oterma and Gehrels 3 make a rapid transition from heliocentric orbits outside the orbit of Jupiter to heliocentric orbits inside the orbit of Jupiter and vice versa. During this transition, the comet can be captured temporarily by Jupiter for one to several orbits around Jupiter. The interior heliocentric orbit is typically close to the 3:2 resonance while the exterior heliocentric orbit is near the 2:3 resonance. An important feature of the dynamics of these comets is that during the transition, the orbit passes close to the libration points L_1 and L_2, two of the equilibrium points for the restricted three-body problem for the Sun-Jupiter system. Studying the libration point invariant manifold structures for L_1 and L_2 is a starting point for understanding the capture and resonance transition of these comets. For example, the recently discovered heteroclinic connection between pairs of unstable periodic orbits (one around the L_1 and the other around L_2) implies a complicated dynamics for comets in a certain energy range. Furthermore, the stable and unstable invariant manifold `tubes' associated to libration point periodic orbits, of which the heteroclinic connections are a part, are phase space conduits transporting material to and from Jupiter and between the interior and exterior of Jupiter's orbit.

Equilibrium and stability of axisymmetric drops on a conical substrate under gravity

NASA Astrophysics Data System (ADS)

Nurse, A. K.; Colbert-Kelly, S.; Coriell, S. R.; McFadden, G. B.

2015-08-01

Motivated by recent investigations of toroidal tissue clusters that are observed to climb conical obstacles after self-assembly [Nurse et al., "A model of force generation in a three-dimensional toroidal cluster of cells," J. Appl. Mech. 79, 051013 (2012)], we study a related problem of the determination of the equilibrium and stability of axisymmetric drops on a conical substrate in the presence of gravity. A variational principle is used to characterize equilibrium shapes that minimize surface energy and gravitational potential energy subject to a volume constraint, and the resulting Euler equation is solved numerically using an angle/arclength formulation. The resulting equilibria satisfy a Laplace-Young boundary condition that specifies the contact angle at the three-phase trijunction. The vertical position of the equilibrium drops on the cone is found to vary significantly with the dimensionless Bond number that represents the ratio of gravitational and capillary forces; a global force balance is used to examine the conditions that affect the drop positions. In particular, depending on the contact angle and the cone half-angle, we find that the vertical position of the drop can either increase ("the drop climbs the cone") or decrease due to a nominal increase in the gravitational force. Most of the equilibria correspond to upward-facing cones and are analogous to sessile drops resting on a planar surface; however, we also find equilibria that correspond to downward facing cones that are instead analogous to pendant drops suspended vertically from a planar surface. The linear stability of the drops is determined by solving the eigenvalue problem associated with the second variation of the energy functional. The drops with positive Bond number are generally found to be unstable to non-axisymmetric perturbations that promote a tilting of the drop. Additional points of marginal stability are found that correspond to limit points of the axisymmetric base state. Drops that are far from the tip are subject to azimuthal instabilities with higher mode numbers that are analogous to the Rayleigh instability of a cylindrical interface. We have also found a range of completely stable solutions that correspond to small contact angles and cone half-angles.

The equilibrium point hypothesis and its application to speech motor control.

PubMed

Perrier, P; Ostry, D J; Laboissière, R

1996-04-01

In this paper, we address a number of issues in speech research in the context of the equilibrium point hypothesis of motor control. The hypothesis suggests that movements arise from shifts in the equilibrium position of the limb or the speech articulator. The equilibrium is a consequence of the interaction of central neural commands, reflex mechanisms, muscle properties, and external loads, but it is under the control of central neural commands. These commands act to shift the equilibrium via centrally specified signals acting at the level of the motoneurone (MN) pool. In the context of a model of sagittal plane jaw and hyoid motion based on the lambda version of the equilibrium point hypothesis, we consider the implications of this hypothesis for the notion of articulatory targets. We suggest that simple linear control signals may underlie smooth articulatory trajectories. We explore as well the phenomenon of intraarticulator coarticulation in jaw movement. We suggest that even when no account is taken of upcoming context, that apparent anticipatory changes in movement amplitude and duration may arise due to dynamics. We also present a number of simulations that show in different ways how variability in measured kinematics can arise in spite of constant magnitude speech control signals.

Interaction between fiscal and monetary policy in a dynamic nonlinear model.

PubMed

Bertella, Mario A; Rego, Henio A; Neris, Celso; Silva, Jonathas N; Podobnik, Boris; Stanley, H Eugene

2015-01-01

The objective of this study is to verify the dynamics between fiscal policy, measured by public debt, and monetary policy, measured by a reaction function of a central bank. Changes in monetary policies due to deviations from their targets always generate fiscal impacts. We examine two policy reaction functions: the first related to inflation targets and the second related to economic growth targets. We find that the condition for stable equilibrium is more restrictive in the first case than in the second. We then apply our simulation model to Brazil and United Kingdom and find that the equilibrium is unstable in the Brazilian case but stable in the UK case.

Interaction between Fiscal and Monetary Policy in a Dynamic Nonlinear Model

PubMed Central

Bertella, Mario A.; Rego, Henio A.; Neris, Celso; Silva, Jonathas N.; Podobnik, Boris; Stanley, H. Eugene

2015-01-01

The objective of this study is to verify the dynamics between fiscal policy, measured by public debt, and monetary policy, measured by a reaction function of a central bank. Changes in monetary policies due to deviations from their targets always generate fiscal impacts. We examine two policy reaction functions: the first related to inflation targets and the second related to economic growth targets. We find that the condition for stable equilibrium is more restrictive in the first case than in the second. We then apply our simulation model to Brazil and United Kingdom and find that the equilibrium is unstable in the Brazilian case but stable in the UK case. PMID:25799581

Does media coverage influence the spread of drug addiction?

NASA Astrophysics Data System (ADS)

Ma, Mingju; Liu, Sanyang; Li, Jun

2017-09-01

In this paper, a three dimensional drug model is constructed to investigate the impact of media coverage on the spread and control of drug addiction. The dynamical behavior of the model is studied by using the basic reproduction number R0. The drug-free equilibrium is globally asymptotically stable if R0 < 1 and the drug addiction equilibrium is locally stable if R0 > 1. The results demonstrate that the media effect in human population cannot change the stabilities of equilibria but can affect the number of drug addicts. Sensitivity analyses are performed to seek for effective control measures for drug treatment. Numerical simulations are given to support the theoretical results.

Adolescents' Body Image Trajectories: A Further Test of the Self-Equilibrium Hypothesis

ERIC Educational Resources Information Center

Morin, Alexandre J. S.; Maïano, Christophe; Scalas, L. Francesca; Janosz, Michel; Litalien, David

2017-01-01

The self-equilibrium hypothesis underlines the importance of having a strong core self, which is defined as a high and developmentally stable self-concept. This study tested this hypothesis in relation to body image (BI) trajectories in a sample of 1,006 adolescents (M[subscript age] = 12.6, including 541 males and 465 females) across a 4-year…

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.

Competitive Exclusion and Coexistence of Pathogens in a Homosexually-Transmitted Disease Model

PubMed Central

Chai, Caichun; Jiang, Jifa

2011-01-01

A sexually-transmitted disease model for two strains of pathogen in a one-sex, heterogeneously-mixing population has been studied completely by Jiang and Chai in (J Math Biol 56:373–390, 2008). In this paper, we give a analysis for a SIS STD with two competing strains, where populations are divided into three differential groups based on their susceptibility to two distinct pathogenic strains. We investigate the existence and stability of the boundary equilibria that characterizes competitive exclusion of the two competing strains; we also investigate the existence and stability of the positive coexistence equilibrium, which characterizes the possibility of coexistence of the two strains. We obtain sufficient and necessary conditions for the existence and global stability about these equilibria under some assumptions. We verify that there is a strong connection between the stability of the boundary equilibria and the existence of the coexistence equilibrium, that is, there exists a unique coexistence equilibrium if and only if the boundary equilibria both exist and have the same stability, the coexistence equilibrium is globally stable or unstable if and only if the two boundary equilibria are both unstable or both stable. PMID:21347222

Equilibrium-disequilibrium relations in the Monte Rosa Granite, Western Alps: Petrological, Rb-Sr and stable isotope data

USGS Publications Warehouse

Frey, M.; Hunziker, J.C.; O'Neil, J.R.; Schwander, H.W.

1976-01-01

Nine samples from the Monte Rosa Granite have been investigated by microscopic, X-ray, wet chemical, electron microprobe, stable isotope and Rb-Sr and K-Ar methods. Two mineral assemblages have been distinguished by optical methods and dated as Permian and mid-Tertiary by means of Rb-Sr age determinations. The Permian assemblage comprises quartz, orthoclase, oligoclase, biotite, and muscovite whereas the Alpine assemblage comprises quartz, microcline, albite+epidote or oligoclase, biotite, and phengite. Disequilibrium between the Permian and Alpine mineral assemblages is documented by the following facts: (i) Two texturally distinguishable generations of white K-mica are 2 M muscovite (Si=3.1-3.2) and 2 M or 3 T phengite (Si=3.3-3.4). Five muscovites show Permian Rb-Sr ages and oxygen isotope fractionations indicating temperatures between 520 and 560 ?? C; however, K-Ar ages are mixed or rejuvenated. Phengite always shows mid-Tertiary Rb-Sr ages, (ii) Two biotite generations can be recognized, although textural evidence is often ambiguous. Three out of four texturally old biotites show mid-Tertiary Rb-Sr cooling ages while the oxygen isotopic fractionations point to Permian, mixed or Alpine temperatures, (iii) Comparison of radiogenic and stable isotope relations indicates that the radiogenic isotopes in the interlayer positions of the micas were mobilized during Alpine time without recrystallization, that is, without breaking Al-O or Si-O bonds. High Ti contents in young muscovites and biotites also indicate that the octahedral (and tetrahedral) sites remained undisturbed during rejuvenation. (iv) 'Isotopic reversals' in the order of O18 enrichment between K-feldspar and albite exist. Arguments for equilibrium during Permian time are meagre because of Alpine overprinting effects. Texturally old muscovites show high temperatures and Permian Rb-Sr ages in concordancy with Rb-Sr whole rock ages. For the tectonically least affected samples, excellent concordance between quartz-muscovite and quartz-biotite 'Permian temperatures' implies oxygen isotope equilibrium in Permian time which was undisturbed during Alpine metamorphism. Arguments for equilibrium during the mid-Tertiary metamorphism are as follows: (i) Mid-Tertiary Rb-Sr mineral isochrons of up to six minerals exist, (ii) Oxygen isotope temperatures of coexisting Alpine phengites and biotites are concordant. The major factor for the adjustment of the Permian assemblages to Alpine conditions was the degree of Alpine tectonic overprinting rather than the maximum temperatures reached during the mid-Tertiary Alpine metamorphism. The lack of exchange with externally introduced fluid phases in the samples least affected by tectonism indicates that the Monte Rosa Granite 'stewed in its own juices'. This seems to be the major cause for the persistence of Permian ages and corresponding temperatures. ?? 1976 Springer-Verlag.

A rumor transmission model with incubation in social networks

NASA Astrophysics Data System (ADS)

Jia, Jianwen; Wu, Wenjiang

2018-02-01

In this paper, we propose a rumor transmission model with incubation period and constant recruitment in social networks. By carrying out an analysis of the model, we study the stability of rumor-free equilibrium and come to the local stable condition of the rumor equilibrium. We use the geometric approach for ordinary differential equations for showing the global stability of the rumor equilibrium. And when ℜ0 = 1, the new model occurs a transcritical bifurcation. Furthermore, numerical simulations are used to support the analysis. At last, some conclusions are presented.

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)

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.

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.

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)

Plant interspecies competition for sunlight: a mathematical model of canopy partitioning.

PubMed

Nevai, Andrew L; Vance, Richard R

2007-07-01

We examine the influence of canopy partitioning on the outcome of competition between two plant species that interact only by mutually shading each other. This analysis is based on a Kolmogorov-type canopy partitioning model for plant species with clonal growth form and fixed vertical leaf profiles (Vance and Nevai in J. Theor. Biol., 2007, to appear). We show that canopy partitioning is necessary for the stable coexistence of the two competing plant species. We also use implicit methods to show that, under certain conditions, the species' nullclines can intersect at most once. We use nullcline endpoint analysis to show that when the nullclines do intersect, and in such a way that they cross, then the resulting equilibrium point is always stable. We also construct surfaces that divide parameter space into regions within which the various outcomes of competition occur, and then study parameter dependence in the locations of these surfaces. The analysis presented here and in a companion paper (Nevai and Vance, The role of leaf height in plant competition for sunlight: analysis of a canopy partitioning model, in review) together shows that canopy partitioning is both necessary and, under appropriate parameter values, sufficient for the stable coexistence of two hypothetical plant species whose structure and growth are described by our model.

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

NASA Astrophysics Data System (ADS)

Yu, Yue; Zhang, Zhengdi; Han, Xiujing

2018-03-01

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

Fluctuations around equilibrium laws in ergodic continuous-time random walks.

PubMed

Schulz, Johannes H P; Barkai, Eli

2015-06-01

We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.

Origin, evolution, and population genetics of the selfish Segregation Distorter gene duplication in European and African populations of Drosophila melanogaster.

PubMed

Brand, Cara L; Larracuente, Amanda M; Presgraves, Daven C

2015-05-01

Meiotic drive elements are a special class of evolutionarily "selfish genes" that subvert Mendelian segregation to gain preferential transmission at the expense of homologous loci. Many drive elements appear to be maintained in populations as stable polymorphisms, their equilibrium frequencies determined by the balance between drive (increasing frequency) and selection (decreasing frequency). Here we show that a classic, seemingly balanced, drive system is instead characterized by frequent evolutionary turnover giving rise to dynamic, rather than stable, equilibrium frequencies. The autosomal Segregation Distorter (SD) system of the fruit fly Drosophila melanogaster is a selfish coadapted meiotic drive gene complex in which the major driver corresponds to a partial duplication of the gene Ran-GTPase activating protein (RanGAP). SD chromosomes segregate at similar, low frequencies of 1-5% in natural populations worldwide, consistent with a balanced polymorphism. Surprisingly, our population genetic analyses reveal evidence for parallel, independent selective sweeps of different SD chromosomes in populations on different continents. These findings suggest that, rather than persisting at a single stable equilibrium, SD chromosomes turn over frequently within populations. © 2015 The Author(s). Evolution published by Wiley Periodicals, Inc. on behalf of The Society for the Study of Evolution.

Generation of zonal flows through symmetry breaking of statistical homogeneity

NASA Astrophysics Data System (ADS)

Parker, Jeffrey B.; Krommes, John A.

2014-03-01

In geophysical and plasma contexts, zonal flows (ZFs) are well known to arise out of turbulence. We elucidate the transition from homogeneous turbulence without ZFs to inhomogeneous turbulence with steady ZFs. Starting from the equation for barotropic flow on a β plane, we employ both the quasilinear approximation and a statistical average, which retains a great deal of the qualitative behavior of the full system. Within the resulting framework known as CE2, we extend recent understanding of the symmetry-breaking zonostrophic instability and show that it is an example of a Type {{\\text{I}}_{s}} instability within the pattern formation literature. The broken symmetry is statistical homogeneity. Near the bifurcation point, the slow dynamics of CE2 are governed by a well-known amplitude equation. The important features of this amplitude equation, and therefore of the CE2 system, are multiple. First, the ZF wavelength is not unique. In an idealized, infinite system, there is a continuous band of ZF wavelengths that allow a nonlinear equilibrium. Second, of these wavelengths, only those within a smaller subband are stable. Unstable wavelengths must evolve to reach a stable wavelength; this process manifests as merging jets. These behaviors are shown numerically to hold in the CE2 system. We also conclude that the stability of the equilibria near the bifurcation point, which is governed by the Eckhaus instability, is independent of the Rayleigh-Kuo criterion.

Stability analysis of an HIV/AIDS epidemic model with treatment

NASA Astrophysics Data System (ADS)

Cai, Liming; Li, Xuezhi; Ghosh, Mini; Guo, Baozhu

2009-07-01

An HIV/AIDS epidemic model with treatment is investigated. The model allows for some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. We first establish the ODE treatment model with two infective stages. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are completely determined by the basic reproduction number [real]0. If [real]0<=1, the disease-free equilibrium is globally stable, whereas the unique infected equilibrium is globally asymptotically stable if [real]0>1. Then, we introduce a discrete time delay to the model to describe the time from the start of treatment in the symptomatic stage until treatment effects become visible. The effect of the time delay on the stability of the endemically infected equilibrium is investigated. Moreover, the delay model exhibits Hopf bifurcations by using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results.

Tough Supramolecular Hydrogel Based on Strong Hydrophobic Interactions in a Multiblock Segmented Copolymer

PubMed Central

2017-01-01

We report the preparation and structural and mechanical characterization of a tough supramolecular hydrogel, based exclusively on hydrophobic association. The system consists of a multiblock, segmented copolymer of hydrophilic poly(ethylene glycol) (PEG) and hydrophobic dimer fatty acid (DFA) building blocks. A series of copolymers containing 2K, 4K, and 8K PEG were prepared. Upon swelling in water, a network is formed by self-assembly of hydrophobic DFA units in micellar domains, which act as stable physical cross-link points. The resulting hydrogels are noneroding and contain 75–92 wt % of water at swelling equilibrium. Small-angle neutron scattering (SANS) measurements showed that the aggregation number of micelles ranges from 2 × 102 to 6 × 102 DFA units, increasing with PEG molecular weight. Mechanical characterization indicated that the hydrogel containing PEG 2000 is mechanically very stable and tough, possessing a tensile toughness of 4.12 MJ/m3. The high toughness, processability, and ease of preparation make these hydrogels very attractive for applications where mechanical stability and load bearing features of soft materials are required. PMID:28469284

Sensitivity of glacier mass balance and equilibrium line altitude to climatic change on King George Island, Antarctic Peninsula.

NASA Astrophysics Data System (ADS)

Falk, Ulrike; Lopez, Damian; Silva-Busso, Adrian

2017-04-01

The South Shetland Islands are located at the northern tip of the Antarctic Peninsula which is among the fastest warming regions on Earth. Surface air temperature increases (ca. 3 K in 50 years) are concurrent with retreating glacier fronts, an increase in melt areas, ice surface lowering and rapid break-up and disintegration of ice shelves. Observed surface air temperature lapse rates show a high variability during winter months (standard deviations up to ±1.0 K/100 m), and a distinct spatial heterogeneity reflecting the impact of synoptic weather patterns especially during winter glacial mass accumulation periods. The increased mesocyclonic activity during the winter time in the study area results in intensified advection of warm, moist air with high temperatures and rain, and leads to melt conditions on the ice cap, fixating surface air temperatures to the melting point. The impact on winter accumulation results in even more negative mass balance estimates. Six years of glaciological measurements on mass balance stake transects are used with a glacier melt model to assess changes in melt water input to the coastal waters, glacier surface mass balance and the equilibrium line altitude. The average equilibrium line altitude (ELA) calculated from own glaciological observations for KGI over the time period 2010 - 2015 amounts to ELA=330±100 m. Published studies suggest rather stable condition slightly negative glacier mass balance until the mid 80's with an ELA of approx. 150 m. The calculated accumulation area ratio suggests rather dramatic changes in extension of the inland ice cap for the South Shetland Islands until an equilibrium with concurrent climate conditions is reached.

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

Determining osmotic pressure of drug solutions by air humidity in equilibrium method.

PubMed

Zhan, Xiancheng; Li, Hui; Yu, Lan; Wei, Guocui; Li, Chengrong

2014-06-01

To establish a new osmotic pressure measuring method with a wide measuring range. The osmotic pressure of drug solutions is determined by measuring the relative air humidity in equilibrium with the solution. The freezing point osmometry is used as a control. The data obtained by the proposed method are comparable to those by the control method, and the measuring range of the proposed method is significantly wider than that of the control method. The proposed method is performed in an isothermal and equilibrium state, so it overcomes the defects of the freezing point and dew point osmometries which result from the heterothermal process in the measurement, and therefore is not limited to diluted solutions.

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.

MAGNETAR GIANT FLARES-FLUX ROPE ERUPTIONS IN MULTIPOLAR MAGNETOSPHERIC MAGNETIC FIELDS

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

Yu Cong, E-mail: cyu@ynao.ac.cn

2012-09-20

We address a primary question regarding the physical mechanism that triggers the energy release and initiates the onset of eruptions in the magnetar magnetosphere. Self-consistent stationary, axisymmetric models of the magnetosphere are constructed based on force-free magnetic field configurations that contain a helically twisted force-free flux rope. Depending on the surface magnetic field polarity, there exist two kinds of magnetic field configurations, inverse and normal. For these two kinds of configurations, variations of the flux rope equilibrium height in response to gradual surface physical processes, such as flux injections and crust motions, are carefully examined. We find that equilibrium curvesmore » contain two branches: one represents a stable equilibrium branch, and the other an unstable equilibrium branch. As a result, the evolution of the system shows a catastrophic behavior: when the magnetar surface magnetic field evolves slowly, the height of the flux rope would gradually reach a critical value beyond which stable equilibriums can no longer be maintained. Subsequently, the flux rope would lose equilibrium and the gradual quasi-static evolution of the magnetosphere will be replaced by a fast dynamical evolution. In addition to flux injections, the relative motion of active regions would give rise to the catastrophic behavior and lead to magnetic eruptions as well. We propose that a gradual process could lead to a sudden release of magnetosphere energy on a very short dynamical timescale, without being initiated by a sudden fracture in the crust of the magnetar. Some implications of our model are also discussed.« less

Non-equilibrium relaxation in a stochastic lattice Lotka-Volterra model

NASA Astrophysics Data System (ADS)

Chen, Sheng; Täuber, Uwe C.

2016-04-01

We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. Holding all other rates fixed, we investigate the non-equilibrium relaxation of the predator density in the vicinity of the critical predation rate. As expected, we observe critical slowing-down, i.e., a power law dependence of the relaxation time on the predation rate, and algebraic decay of the predator density at the extinction critical point. The numerically determined critical exponents are in accord with the established values of the directed percolation universality class. Following a sudden predation rate change to its critical value, one finds critical aging for the predator density autocorrelation function that is also governed by universal scaling exponents. This aging scaling signature of the active-to-absorbing state phase transition emerges at significantly earlier times than the stationary critical power laws, and could thus serve as an advanced indicator of the (predator) population’s proximity to its extinction threshold.

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.

Floating liquid phase in sedimenting colloid-polymer mixtures.

PubMed

Schmidt, Matthias; Dijkstra, Marjolein; Hansen, Jean-Pierre

2004-08-20

Density functional theory and computer simulation are used to investigate sedimentation equilibria of colloid-polymer mixtures within the Asakura-Oosawa-Vrij model of hard sphere colloids and ideal polymers. When the ratio of buoyant masses of the two species is comparable to the ratio of differences in density of the coexisting bulk (colloid) gas and liquid phases, a stable "floating liquid" phase is found, i.e., a thin layer of liquid sandwiched between upper and lower gas phases. The full phase diagram of the mixture under gravity shows coexistence of this floating liquid phase with a single gas phase or a phase involving liquid-gas equilibrium; the phase coexistence lines meet at a triple point. This scenario remains valid for general asymmetric binary mixtures undergoing bulk phase separation.

Periodic Trojan-type orbits in the earth-sun system

NASA Technical Reports Server (NTRS)

Weissman, P. R.; Wetherill, G. W.

1974-01-01

Periodic orbits about the triangular equilibrium points are found for the planar restricted three-body problem using the earth-sun system. The maximum semimajor axis for tadpole orbits ranges from the infinitesimal orbit at 1.000 AU to the near-limiting orbit at 1.00285 AU. Horseshoe orbits are found for 1.0029 to 1.0080 AU, larger horseshoes being unstable because of close approaches to the earth. Using stability tests devised by Rabe (1961, 1962), the limit of stability for nonperiodic orbits is found to occur for maximum semimajor axes near 1.0020 AU. In addition, near-periodic tadpole orbits appear to be stable against perturbations by Jupiter and Venus for periods of at least 10,000 yr. The possibility that minor planets actually exist in such orbits is considered.

CellTrans: An R Package to Quantify Stochastic Cell State Transitions.

PubMed

Buder, Thomas; Deutsch, Andreas; Seifert, Michael; Voss-Böhme, Anja

2017-01-01

Many normal and cancerous cell lines exhibit a stable composition of cells in distinct states which can, e.g., be defined on the basis of cell surface markers. There is evidence that such an equilibrium is associated with stochastic transitions between distinct states. Quantifying these transitions has the potential to better understand cell lineage compositions. We introduce CellTrans, an R package to quantify stochastic cell state transitions from cell state proportion data from fluorescence-activated cell sorting and flow cytometry experiments. The R package is based on a mathematical model in which cell state alterations occur due to stochastic transitions between distinct cell states whose rates only depend on the current state of a cell. CellTrans is an automated tool for estimating the underlying transition probabilities from appropriately prepared data. We point out potential analytical challenges in the quantification of these cell transitions and explain how CellTrans handles them. The applicability of CellTrans is demonstrated on publicly available data on the evolution of cell state compositions in cancer cell lines. We show that CellTrans can be used to (1) infer the transition probabilities between different cell states, (2) predict cell line compositions at a certain time, (3) predict equilibrium cell state compositions, and (4) estimate the time needed to reach this equilibrium. We provide an implementation of CellTrans in R, freely available via GitHub (https://github.com/tbuder/CellTrans).

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.

On habitable Trojan worlds in exoplanetary systems

NASA Astrophysics Data System (ADS)

Schwarz, Richard; Eggl, Siegfried; Akos, Bazso; Funk, Barbara

2016-09-01

When astronomers look for life on planets in exoplanetary systems (EPS), they use the concept of the habitable zone (HZ) for the search of life in the universe. In many EPS a giant planet moves in the HZ and makes the existence of another habitable planet impossible, because of the gravitational interaction with a gas giant (GG). Therefore the investigation of the Trojan configuration provides another opportunity for an additional habitable planet. The configuration is the following, when a GG (like Jupiter or larger) moves in the HZ, a terrestrial Trojan planet may move in a stable orbit around the Lagrangian equilibrium points L4 or L5. Trojans are moving either close to 60° ahead or 60° behind the GG with nearly the same semi-major axis as the planet (as shown in the figure for the circular case). Former studies (Schwarz et al. 2009 and Schwarz et al 2014) could show that this configuration is not only stable for small bodies like asteroids (e.g. Jupiter Trojans), but also for larger ones (Earth-mass). We investigate the stability of possible Trojan planets in several known extra-solar planetary systems, by using the planar 3 and N-body problem as dynamical model considering the eccentricity of the planets. For our numerical simulations we use the Lie-integration method with an automatic step-size control to solve the equations of motion (Eggl and Dvorak 2010). In our study, we have concentrated on the extension of the stability region around the Lagrangian points and the influence of additional outer or inner GG. Finally we present a list of candidates of EPS where a massive GG (3-10 Jupiter masses) moves almost or fully in the HZ and an additional possible Trojan planet can have stable motion.

Direct Detection of a Chemical Equilibrium between a Localized Singlet Diradical and Its σ-Bonded Species by Time-Resolved UV/Vis and IR Spectroscopy.

PubMed

Yoshidomi, Shohei; Mishima, Megumi; Seyama, Shin; Abe, Manabu; Fujiwara, Yoshihisa; Ishibashi, Taka-Aki

2017-03-06

Localized singlet diradicals are key intermediates in bond homolyses. The singlet diradicals are energetically much less stable than the σ-bonded species. In general, only one-way reactions from diradicals to σ-bonded species are observed. In this study, a thermal equilibrium between a singlet 1,2-diazacyclopentane-3,5-diyl diradical and the corresponding σ-bonded species was directly observed. The singlet diradical was more stable than the σ-bonded species. The solvent effect clarified key features, such as the zwitterionic character of the singlet diradical. The effect of the nitrogen atoms is discussed in detail. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

On Budyko curve as a consequence of climate-soil-vegetation equilibrium hypothesis

NASA Astrophysics Data System (ADS)

Pande, S.

2012-04-01

A hypothesis that Budyko curve is a consequence of stable equilibriums of climate-soil-vegetation co-evolution is tested at biome scale. We assume that i) distribution of vegetation, soil and climate within a biome is a distribution of equilibriums of similar soil-vegetation dynamics and that this dynamics is different across different biomes and ii) soil and vegetation are in dynamic equilibrium with climate while in static equilibrium with each other. In order to test the hypothesis, a two stage regression is considered using MOPEX/Hydrologic Synthesis Project dataset for basins in eastern United States. In the first stage, multivariate regression (Seemingly Unrelated Regression) is performed for each biome with soil (estimated porosity and slope of soil water retention curve) and vegetation characteristics (5-week NDVI gradient) as dependent variables and aridity index, vegetation and soil characteristics as independent variables for respective dependent variables. The regression residuals of the first stage along with aridity index then serve as second stage independent variables while actual vaporization to precipitation ratio (vapor index) serving as dependent variable. Insignificance, if revealed, of a first stage parameter allows us to reject the role of corresponding soil or vegetation characteristics in the co-evolution hypothesis. Meanwhile the significance of second stage regression parameter corresponding to a first stage residual allow us to reject the hypothesis that Budyko curve is a locus "solely" of climate-soil-vegetation co-evolution equilibrium points. Results suggest lack of evidence for soil-vegetation co-evolution in Prairies and Mixed/SouthEast Forests (unlike in Deciduous Forests) though climate plays a dominant role in explaining within biome soil and vegetation characteristics across all the biomes. Preliminary results indicate absence of effects beyond climate-soil-vegetation co-evolution in explaining the ratio of annual total minimum monthly flows to precipitation in Deciduous Forests though other three biome types show presence of effects beyond co-evolutionary. Such an analysis can yield insights into the nature of hydrologic change when assessed along the Budyko curve as well as non co-evolutionary effects such as anthropogenic effects on basin scale annual water balances.

Stability of lava lakes

NASA Astrophysics Data System (ADS)

Witham, Fred; Llewellin, Edward W.

2006-11-01

A physical model of a generic lava lake system is developed. We derive the requisite conditions for the existence of an 'equilibrium lava lake' in which magmastatic pressure at the base of the conduit balances the pressure in the underlying magmatic reservoir. The stability of this lava lake system is tested by investigating the response of the system to perturbation. We develop a graphical method, based on the system's pressure-depth profile, to predict the subsequent behaviour of the system. Despite the simplicity of the modelled system, we find a broad behavioural spectrum. Initially, the rise of bubbles through the magma is ignored. In this case, both stable, long-lived lava lakes, and unstable lakes that are prone to sudden draining, are predicted. The stability of the system is shown to be controlled by lake-conduit geometry, the solubility and gas expansion laws and the magma's volatile content. We show that an unstable lake must collapse to a new, stable equilibrium. Subsequent recharge of the system by, for example, conduit overturn, would promote a return to the original equilibrium, giving rise to cyclic behaviour. Such a mechanism is consistent with lava lake behaviour during the 1983-1984 Pu'u 'O'o eruption of Kilauea. When the rise of bubbles through the magma is considered, our model predicts that stable lakes must drain over time. We, therefore, deduce that persistently degassing, stable lava lakes, such as those observed at Mt. Erebus, Antarctica, and Mauna Ulu, Kilauea, Hawaii, must have an effective conduit convection mechanism or an exogenous supply of bubbles from depth.

Trapping Phenomenon Attenuates the Consequences of Tipping Points for Limit Cycles

NASA Astrophysics Data System (ADS)

Medeiros, Everton S.; Caldas, Iberê L.; Baptista, Murilo S.; Feudel, Ulrike

2017-02-01

Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the system’s parameters abruptly shift the system to an alternative state with a contrasting dynamical behavior. While tipping in a fold bifurcation of an equilibrium is well understood, much less is known about tipping of oscillations (limit cycles) though this dynamics are the typical response of many natural systems to a periodic external forcing, like e.g. seasonal forcing in ecology and climate sciences. We provide a detailed analysis of tipping phenomena in periodically forced systems and show that, when limit cycles are considered, a transient structure, so-called channel, plays a fundamental role in the transition. Specifically, we demonstrate that trajectories crossing such channel conserve, for a characteristic time, the twisting behavior of the stable limit cycle destroyed in the fold bifurcation of cycles. As a consequence, this channel acts like a “ghost” of the limit cycle destroyed in the critical transition and instead of the expected abrupt transition we find a smooth one. This smoothness is also the reason that it is difficult to precisely determine the transition point employing the usual indicators of tipping points, like critical slowing down and flickering.

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.

Investigation of island formation due to RMPs in DIII-D plasmas with the SIESTA resistive MHD equilibrium code

NASA Astrophysics Data System (ADS)

Hirshman, S. P.; Shafer, M. W.; Seal, S. K.; Canik, J. M.

2016-04-01

> The SIESTA magnetohydrodynamic (MHD) equilibrium code has been used to compute a sequence of ideally stable equilibria resulting from numerical variation of the helical resonant magnetic perturbation (RMP) applied to an axisymmetric DIII-D plasma equilibrium. Increasing the perturbation strength at the dominant , resonant surface leads to lower MHD energies and increases in the equilibrium island widths at the (and sidebands) surfaces, in agreement with theoretical expectations. Island overlap at large perturbation strengths leads to stochastic magnetic fields which correlate well with the experimentally inferred field structure. The magnitude and spatial phase (around the dominant rational surfaces) of the resonant (shielding) component of the parallel current are shown to change qualitatively with the magnetic island topology.

Melting processes of oligomeric α and β isotactic polypropylene crystals at ultrafast heating rates

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

Ji, Xiaojing; He, Xuehao, E-mail: xhhe@tju.edu.cn, E-mail: scjiang@tju.edu.cn; Jiang, Shichun, E-mail: xhhe@tju.edu.cn, E-mail: scjiang@tju.edu.cn

The melting behaviors of α (stable) and β (metastable) isotactic polypropylene (iPP) crystals at ultrafast heating rates are simulated with atomistic molecular dynamics method. Quantitative information about the melting processes of α- and β-iPP crystals at atomistic level is achieved. The result shows that the melting process starts from the interfaces of lamellar crystal through random dislocation of iPP chains along the perpendicular direction of lamellar crystal structure. In the melting process, the lamellar crystal gradually expands but the corresponding thickness decreases. The analysis shows that the system expansion lags behind the crystallinity decreasing and the lagging extents for α-more » and β-iPP are significantly different. The apparent melting points of α- and β-iPP crystals rise with the increase of the heating rate and lamellar crystal thickness. The apparent melting point of α-iPP crystal is always higher than that of β-iPP at differently heating rates. Applying the Gibbs-Thomson rule and the scaling property of the melting kinetics, the equilibrium melting points of perfect α- and β-iPP crystals are finally predicted and it shows a good agreement with experimental result.« less

Basin stability measure of different steady states in coupled oscillators

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Intermediate states and structure evolution in the free-falling process of the dislocation in graphene

NASA Astrophysics Data System (ADS)

Wang, Shaofeng; Yao, Yin; Bai, Jianhui; Wang, Rui

2017-04-01

This paper investigated the intermediate states and the structure evolution of the dislocation in graphene when it falls freely from the saddle point of the energy landscape. The O-type dislocation, an unstable equilibrium structure located at the saddle point, is obtained from the lattice theory of the dislocation structure and improved by the ab initio calculation to take the buckling into account. Intermediate states along the kinetics path in the falling process are obtained from the ab initio simulation. Once the dislocation falls from the saddle point to the energy valley, this O-type dislocation transforms into the stable structure that is referred to as the B-type dislocation, and in the meantime, it moves a distance that equals half a Burgers vector. The structure evolution and the energy variation in the free-falling process are revealed explicitly. It is observed that rather than smooth change, a platform manifests itself in the energy curve. The unusual behaviour in the energy curve is mainly originated from symmetry breaking and bond formation in the dislocation core. The results can provide deep insight in the mechanism of the brittle feature of covalent materials.

Turbulent mixing of a critical fluid: The non-perturbative renormalization

NASA Astrophysics Data System (ADS)

Hnatič, M.; Kalagov, G.; Nalimov, M.

2018-01-01

Non-perturbative Renormalization Group (NPRG) technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi 〉 ∼ (Pji⊥ + αPji∥) /k d + ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there is a new nonequilibrium regime (universality class) associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ) of possible scaling regimes in the system. The physical point d = 3, ζ = 4 / 3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α ≲ 2.26. Otherwise, in the case of "strong compressibility" α ≳ 2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

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.

Dynamics and Physiological Roles of Stochastic Firing Patterns Near Bifurcation Points

NASA Astrophysics Data System (ADS)

Jia, Bing; Gu, Huaguang

2017-06-01

Different stochastic neural firing patterns or rhythms that appeared near polarization or depolarization resting states were observed in biological experiments on three nervous systems, and closely matched those simulated near bifurcation points between stable equilibrium point and limit cycle in a theoretical model with noise. The distinct dynamics of spike trains and interspike interval histogram (ISIH) of these stochastic rhythms were identified and found to build a relationship to the coexisting behaviors or fixed firing frequency of four different types of bifurcations. Furthermore, noise evokes coherence resonances near bifurcation points and plays important roles in enhancing information. The stochastic rhythms corresponding to Hopf bifurcation points with fixed firing frequency exhibited stronger coherence degree and a sharper peak in the power spectrum of the spike trains than those corresponding to saddle-node bifurcation points without fixed firing frequency. Moreover, the stochastic firing patterns changed to a depolarization resting state as the extracellular potassium concentration increased for the injured nerve fiber related to pathological pain or static blood pressure level increased for aortic depressor nerve fiber, and firing frequency decreased, which were different from the physiological viewpoint that firing frequency increased with increasing pressure level or potassium concentration. This shows that rhythms or firing patterns can reflect pressure or ion concentration information related to pathological pain information. Our results present the dynamics of stochastic firing patterns near bifurcation points, which are helpful for the identification of both dynamics and physiological roles of complex neural firing patterns or rhythms, and the roles of noise.

Adaptive Topographies and Equilibrium Selection in an Evolutionary Game

PubMed Central

Osinga, Hinke M.; Marshall, James A. R.

2015-01-01

It has long been known in the field of population genetics that adaptive topographies, in which population equilibria maximise mean population fitness for a trait regardless of its genetic bases, do not exist. Whether one chooses to model selection acting on a single locus or multiple loci does matter. In evolutionary game theory, analysis of a simple and general game involving distinct roles for the two players has shown that whether strategies are modelled using a single ‘locus’ or one ‘locus’ for each role, the stable population equilibria are unchanged and correspond to the fitness-maximising evolutionary stable strategies of the game. This is curious given the aforementioned population genetical results on the importance of the genetic bases of traits. Here we present a dynamical systems analysis of the game with roles detailing how, while the stable equilibria in this game are unchanged by the number of ‘loci’ modelled, equilibrium selection may differ under the two modelling approaches. PMID:25706762

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.

A Fundamental Approach to Developing Aluminium based Bulk Amorphous Alloys based on Stable Liquid Metal Structures and Electronic Equilibrium - 154041

DTIC Science & Technology

2017-03-28

AFRL-AFOSR-JP-TR-2017-0027 A Fundamental Approach to Developing Aluminium-based Bulk Amorphous Alloys based on Stable Liquid -Metal Structures and...to 16 Dec 2016 4.  TITLE AND SUBTITLE A Fundamental Approach to Developing Aluminium-based Bulk Amorphous Alloys based on Stable Liquid -Metal...including Al, Cu, Ni, Zr, Mg, Pd, Ga , Ca. Many new Al-based amorphous alloys were found within the numerous alloy systems studied in this project, and

Examination of the gamma equilibrium point hypothesis when applied to single degree of freedom movements performed with different inertial loads.

PubMed

Bellomo, A; Inbar, G

1997-01-01

One of the theories of human motor control is the gamma Equilibrium Point Hypothesis. It is an attractive theory since it offers an easy control scheme where the planned trajectory shifts monotionically from an initial to a final equilibrium state. The feasibility of this model was tested by reconstructing the virtual trajectory and the stiffness profiles for movements performed with different inertial loads and examining them. Three types of movements were tested: passive movements, targeted movements, and repetitive movements. Each of the movements was performed with five different inertial loads. Plausible virtual trajectories and stiffness profiles were reconstructed based on the gamma Equilibrium Point Hypothesis for the three different types of movements performed with different inertial loads. However, the simple control strategy supported by the model, where the planned trajectory shifts monotonically from an initial to a final equilibrium state, could not be supported for targeted movements performed with added inertial load. To test the feasibility of the model further we must examine the probability that the human motor control system would choose a trajectory more complicated than the actual trajectory to control.

Benchmarking kinetic calculations of resistive wall mode stability

NASA Astrophysics Data System (ADS)

Berkery, J. W.; Liu, Y. Q.; Wang, Z. R.; Sabbagh, S. A.; Logan, N. C.; Park, J.-K.; Manickam, J.; Betti, R.

2014-05-01

Validating the calculations of kinetic resistive wall mode (RWM) stability is important for confidently predicting RWM stable operating regions in ITER and other high performance tokamaks for disruption avoidance. Benchmarking the calculations of the Magnetohydrodynamic Resistive Spectrum—Kinetic (MARS-K) [Y. Liu et al., Phys. Plasmas 15, 112503 (2008)], Modification to Ideal Stability by Kinetic effects (MISK) [B. Hu et al., Phys. Plasmas 12, 057301 (2005)], and Perturbed Equilibrium Nonambipolar Transport PENT) [N. Logan et al., Phys. Plasmas 20, 122507 (2013)] codes for two Solov'ev analytical equilibria and a projected ITER equilibrium has demonstrated good agreement between the codes. The important particle frequencies, the frequency resonance energy integral in which they are used, the marginally stable eigenfunctions, perturbed Lagrangians, and fluid growth rates are all generally consistent between the codes. The most important kinetic effect at low rotation is the resonance between the mode rotation and the trapped thermal particle's precession drift, and MARS-K, MISK, and PENT show good agreement in this term. The different ways the rational surface contribution was treated historically in the codes is identified as a source of disagreement in the bounce and transit resonance terms at higher plasma rotation. Calculations from all of the codes support the present understanding that RWM stability can be increased by kinetic effects at low rotation through precession drift resonance and at high rotation by bounce and transit resonances, while intermediate rotation can remain susceptible to instability. The applicability of benchmarked kinetic stability calculations to experimental results is demonstrated by the prediction of MISK calculations of near marginal growth rates for experimental marginal stability points from the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)].

Invasion resistance arises in strongly interacting species-rich model competition communities.

PubMed Central

Case, T J

1990-01-01

I assemble stable multispecies Lotka-Volterra competition communities that differ in resident species number and average strength (and variance) of species interactions. These are then invaded with randomly constructed invaders drawn from the same distribution as the residents. The invasion success rate and the fate of the residents are determined as a function of community-and species-level properties. I show that the probability of colonization success for an invader decreases with community size and the average strength of competition (alpha). Communities composed of many strongly interacting species limit the invasion possibilities of most similar species. These communities, even for a superior invading competitor, set up a sort of "activation barrier" that repels invaders when they invade at low numbers. This "priority effect" for residents is not assumed a priori in my description for the individual population dynamics of these species; rather it emerges because species-rich and strongly interacting species sets have alternative stable states that tend to disfavor species at low densities. These models point to community-level rather than invader-level properties as the strongest determinant of differences in invasion success. The probability of extinction for a resident species increases with community size, and the probability of successful colonization by the invader decreases. Thus an equilibrium community size results wherein the probability of a resident species' extinction just balances the probability of an invader's addition. Given the distribution of alpha it is now possible to predict the equilibrium species number. The results provide a logical framework for an island-biogeographic theory in which species turnover is low even in the face of persistent invasions and for the protection of fragile native species from invading exotics. PMID:11607132

Study of Second Stability for Global ITG Modes in MHD-stable Equilibria

NASA Astrophysics Data System (ADS)

Fivaz, Mathieu; Sauter, Olivier; Appert, Kurt; Tran, Trach-Minh; Vaclavik, Jan

1997-11-01

We study finite pressure effects on the Ion Temperature Gradient (ITG) instabilities; these modes are stabilized when the magnetic field gradient is reversed at high β [1]. This second stability regime for ITG modes is studied in details with a global linear gyrokinetic Particle-In-Cell code which takes the full toroidal MHD equilibrium data from the equilibrium solver CHEASE [2]. Both the trapped-ion and the toroidal ITG regimes are explored. In contrast to second stability for MHD ballooning modes, low magnetic shear and high values of the safety factor do not facilitate strongly the access to the second-stable ITG regime. The consequences for anomalous ion heat transport in tokamaks are explored. We use the results to find optimized configurations that are stable to ideal MHD modes for both the long (kink) and short (ballooning) wavelengths and where the ITG modes are stable or have very low growth rates; such configurations might present very low level of anomalous transport. [1] M. Fivaz, T.M. Tran, K. Appert, J. Vaclavik and S. E. Parker, Phys. Rev. Lett. 78, 1997, p. 3471 [2] H. Lütjens, A. Bondeson and O. Sauter, Comput. Phys. Commun. 97, 1996, p. 219

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.

A New Equilibrium State for Singly Synchronous Binary Asteroids

NASA Astrophysics Data System (ADS)

Golubov, Oleksiy; Unukovych, Vladyslav; Scheeres, Daniel J.

2018-04-01

The evolution of rotation states of small asteroids is governed by the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect, nonetheless some asteroids can stop their YORP evolution by attaining a stable equilibrium. The same is true for binary asteroids subjected to the binary YORP (BYORP) effect. Here we discuss a new type of equilibrium that combines these two, which is possible in a singly synchronous binary system. This equilibrium occurs when the normal YORP, the tangential YORP, and the BYORP compensate each other, and tidal torques distribute the angular momentum between the components of the system and dissipate energy. If unperturbed, such a system would remain singly synchronous in perpetuity with constant spin and orbit rates, as the tidal torques dissipate the incoming energy from impinging sunlight at the same rate. The probability of the existence of this kind of equilibrium in a binary system is found to be on the order of a few percent.

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.

Stability Analysis of an Encapsulated Microbubble against Gas Diffusion

PubMed Central

Katiyar, Amit; Sarkar, Kausik

2009-01-01

Linear stability analysis is performed for a mathematical model of diffusion of gases from an encapsulated microbubble. It is an Epstein-Plesset model modified to account for encapsulation elasticity and finite gas permeability. Although, bubbles, containing gases other than air is considered, the final stable bubble, if any, contains only air, and stability is achieved only when the surrounding medium is saturated or oversaturated with air. In absence of encapsulation elasticity, only a neutral stability is achieved for zero surface tension, the other solution being unstable. For an elastic encapsulation, different equilibrium solutions are obtained depending on the saturation level and whether the surface tension is smaller or higher than the elasticity. For an elastic encapsulation, elasticity can stabilize the bubble. However, imposing a non-negativity condition on the effective surface tension (consisting of reference surface tension and the elastic stress) leads to an equilibrium radius which is only neutrally stable. If the encapsulation can support net compressive stress, it achieves actual stability. The linear stability results are consistent with our recent numerical findings. Physical mechanisms for the stability or instability of various equilibriums are provided. PMID:20005522

Tautomerism, molecular structure, intramolecular hydrogen bond, and enol-enol equilibrium of para halo substituted 4,4,4-trifluoro-1-phenyl-1,3-butanedione; Experimental and theoretical studies

NASA Astrophysics Data System (ADS)

Darugar, V. R.; Vakili, M.; Nekoei, A. R.; Tayyari, S. F.; Afzali, R.

2017-12-01

Para halo, X = F, Cl, and Br, substitution effect on tautomerism, keto-enol content, molecular structure, intramolecular hydrogen bonding, and enol-enol equilibrium constants of 4,4,4-trifluoro-1-phenyl-1,3-butanedione, known as trifluorobenzoylacetone (TFBA), have been investigated by means of density functional theory calculations and NMR, IR, and UV-Vis spectroscopic methods. Comparing the calculated and experimental results suggests coexisting of two stable cis-enol forms of titled molecules in comparable proportions in the sample. The theoretical and experimental results show that the equilibrium constants between both stable cis-enol forms of the studied molecules are similar, about 1.1-1.2. According to the AIM calculated results performed at the B3LYP/6-311++G∗∗ level, the target para halo molecules have a hydrogen bond strength of about 18.6 kcal/mol, as a medium hydrogen bond, similar to that of TFBA. The theoretical and experimental results indicate that there is no considerable difference between the hydrogen bond strength of the X-substituted titled molecules.

Ab initio atomic recombination reaction energetics on model heat shield surfaces

NASA Technical Reports Server (NTRS)

Senese, Fredrick; Ake, Robert

1992-01-01

Ab initio quantum mechanical calculations on small hydration complexes involving the nitrate anion are reported. The self-consistent field method with accurate basis sets has been applied to compute completely optimized equilibrium geometries, vibrational frequencies, thermochemical parameters, and stable site labilities of complexes involving 1, 2, and 3 waters. The most stable geometries in the first hydration shell involve in-plane waters bridging pairs of nitrate oxygens with two equal and bent hydrogen bonds. A second extremely labile local minimum involves out-of-plane waters with a single hydrogen bond and lies about 2 kcal/mol higher. The potential in the region of the second minimum is extremely flat and qualitatively sensitive to changes in the basis set; it does not correspond to a true equilibrium structure.

A tether tension control law for tethered subsatellites deployed along local vertical. [space shuttle orbiters - satellite control/towed bodies

NASA Technical Reports Server (NTRS)

Rupp, C. C.

1975-01-01

A tethered subsatellite deployed along the local vertical is in stable equilibrium. This applies equally to subsatellites deployed in the direction towards the earth from the main spacecraft or away from the earth. Momentary perturbations from this stable equilibrium will result in a swinging motion, which decays very slowly if passive means are relied upon to provide damping. A control law is described which actively damps the swinging motion by employing a reel, or other mechanism, to apply appropriate tension as a function of tetherline length, rate of change of length, and desired length. The same control law is shown to be useful for deployment and retrieval of tethered subsatellites in addition to damping to steady state.

A simple nonlinear model for the return to isotropy in turbulence

NASA Technical Reports Server (NTRS)

Sarkar, Sutanu; Speziale, Charles G.

1990-01-01

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed. The model is shown to satisfy realizability and to give rise to no stable nontrivial equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. The absence of stable nontrivial equilibrium solutions is a necessary condition to ensure that the model predicts a return to isotropy for all relaxational turbulent flows. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Direct comparisons are also made with the predictions of the Rotta model and the Lumley model.

Unitarity limits on the mass and radius of dark matter particles

NASA Technical Reports Server (NTRS)

Griest, Kim; Kamionkowski, Marc

1989-01-01

Using partial wave unitarity and the observed density of the Universe, it is show that a stable elementary particle which was once in thermal equilibrium cannot have a mass greater than 340 TeV. An extended object which was once in thermal equilibrium cannot have a radius less than 7.5 x 10(exp -7) fm. A lower limit to the relic abundance of such particles is also found.

Equilibria of oligomeric proteins under high pressure - A theoretical description.

PubMed

Ingr, Marek; Kutálková, Eva; Hrnčiřík, Josef; Lange, Reinhard

2016-12-21

High pressure methods have become a useful tool for studying protein structure and stability. Using them, various physico-chemical processes including protein unfolding, aggregation, oligomer dissociation or enzyme-activity decrease were studied on many different proteins. Oligomeric protein dissociation is a process that can perfectly utilize the potential of high-pressure techniques, as the high pressure shifts the equilibria to higher concentrations making them better observable by spectroscopic methods. This can be especially useful when the oligomeric form is highly stable at atmospheric pressure. These applications may be, however, hindered by less intensive experimental response as well as interference of the oligomerization equilibria with unfolding or aggregation of the subunits, but also by more complex theoretical description. In this study we develop mathematical models describing different kinds of oligomerization equilibria, both closed (equilibrium of monomer and the highest possible oligomer without any intermediates) and consecutive. Closed homooligomer equilibria are discussed for any oligomerization degree, while the more complex heterooligomer equilibria and the consecutive equilibria in both homo- and heterooligomers are taken into account only for dimers and trimers. In all the cases, fractions of all the relevant forms are evaluated as functions of pressure and concentration. Significant points (inflection points and extremes) of the resulting transition curves, that can be determined experimentally, are evaluated as functions of pressure and/or concentration. These functions can be further used in order to evaluate the thermodynamic parameters of the system, i.e. atmospheric-pressure equilibrium constants and volume changes of the individual steps of the oligomer-dissociation processes. Copyright © 2016 Elsevier Ltd. All rights reserved.

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

NASA Astrophysics Data System (ADS)

Behtash, Alireza; Cruz-Camacho, C. N.; Martinez, M.

2018-02-01

The nonequilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed nonplanar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second-order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansions diverge and use resurgence techniques to perform the resummation of these divergences. We also comment on a possible link between the manifold of steepest descent paths in path integrals and the basin of attraction for the attractors via Lyapunov functions that opens a new horizon toward an effective field theory description of hydrodynamics. Our findings indicate that the reorganization of the expansion series carried out by anisotropic hydrodynamics resums the Knudsen and inverse Reynolds numbers to all orders and thus, it can be understood as an effective theory for the far-from-equilibrium fluid dynamics.

First passage analysis of the folding of a β-sheet miniprotein: is it more realistic than the standard equilibrium approach?

PubMed

Kalgin, Igor V; Chekmarev, Sergei F; Karplus, Martin

2014-04-24

Simulations of first-passage folding of the antiparallel β-sheet miniprotein beta3s, which has been intensively studied under equilibrium conditions by A. Caflisch and co-workers, show that the kinetics and dynamics are significantly different from those for equilibrium folding. Because the folding of a protein in a living system generally corresponds to the former (i.e., the folded protein is stable and unfolding is a rare event), the difference is of interest. In contrast to equilibrium folding, the Ch-curl conformations become very rare because they contain unfavorable parallel β-strand arrangements, which are difficult to form dynamically due to the distant N- and C-terminal strands. At the same time, the formation of helical conformations becomes much easier (particularly in the early stage of folding) due to short-range contacts. The hydrodynamic descriptions of the folding reaction have also revealed that while the equilibrium flow field presented a collection of local vortices with closed "streamlines", the first-passage folding is characterized by a pronounced overall flow from the unfolded states to the native state. The flows through the locally stable structures Cs-or and Ns-or, which are conformationally close to the native state, are negligible due to detailed balance established between these structures and the native state. Although there are significant differences in the general picture of the folding process from the equilibrium and first-passage folding simulations, some aspects of the two are in agreement. The rate of transitions between the clusters of characteristic protein conformations in both cases decreases approximately exponentially with the distance between the clusters in the hydrogen bond distance space of collective variables, and the folding time distribution in the first-passage segments of the equilibrium trajectory is in good agreement with that for the first-passage folding simulations.

First Passage Analysis of the Folding of a β-Sheet Miniprotein: Is it More Realistic Than the Standard Equilibrium Approach?

PubMed Central

2015-01-01

Simulations of first-passage folding of the antiparallel β-sheet miniprotein beta3s, which has been intensively studied under equilibrium conditions by A. Caflisch and co-workers, show that the kinetics and dynamics are significantly different from those for equilibrium folding. Because the folding of a protein in a living system generally corresponds to the former (i.e., the folded protein is stable and unfolding is a rare event), the difference is of interest. In contrast to equilibrium folding, the Ch-curl conformations become very rare because they contain unfavorable parallel β-strand arrangements, which are difficult to form dynamically due to the distant N- and C-terminal strands. At the same time, the formation of helical conformations becomes much easier (particularly in the early stage of folding) due to short-range contacts. The hydrodynamic descriptions of the folding reaction have also revealed that while the equilibrium flow field presented a collection of local vortices with closed ”streamlines”, the first-passage folding is characterized by a pronounced overall flow from the unfolded states to the native state. The flows through the locally stable structures Cs-or and Ns-or, which are conformationally close to the native state, are negligible due to detailed balance established between these structures and the native state. Although there are significant differences in the general picture of the folding process from the equilibrium and first-passage folding simulations, some aspects of the two are in agreement. The rate of transitions between the clusters of characteristic protein conformations in both cases decreases approximately exponentially with the distance between the clusters in the hydrogen bond distance space of collective variables, and the folding time distribution in the first-passage segments of the equilibrium trajectory is in good agreement with that for the first-passage folding simulations. PMID:24669953

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.

Is the Reaction Equilibrium Composition in Non-ideal Mixtures Uniquely Determined by the Initial Composition?

NASA Astrophysics Data System (ADS)

Sefcik, Jan

1998-05-01

Reaction equilibrium can be mathematically described by the equilibrium equation and the reaction equilibrium composition can be calculated by solving this equation. It can be proved by non-elementary thermodynamic arguments that for a generic system with given initial composition, temperature and pressure there is a unique stable equilibrium state corresponding to the global minimum of the Gibbs free energy function. However, when the concept of equilibrium is introduced in undergraduate chemistry and chemical engineering courses, such arguments are generally not accessible. When there is a single reaction equilibrium among mixture components and the components form an ideal mixture, it has been demonstrated by a simple, elegant mathematical argument that there is a unique composition satisfying the equilibrium equation. It has been also suggested that this particular argument extends to non-ideal mixtures by simply incorporating activity coefficients. We show that the argument extension to non-ideal systems is not generally valid. Increasing non-ideality can result in non-monotonicity of the function crucial for the simple uniqueness argument, and only later it leads to non-uniqueness and hence phase separation. The main feature responsible for this is a composition dependence of activity coefficients in non-ideal mixtures.

Communication: Microphase equilibrium and assembly dynamics.

PubMed

Zhuang, Yuan; Charbonneau, Patrick

2017-09-07

Despite many attempts, ordered equilibrium microphases have yet to be obtained in experimental colloidal suspensions. The recent computation of the equilibrium phase diagram of a microscopic, particle-based microphase former [Zhuang et al., Phys. Rev. Lett. 116, 098301 (2016)] has nonetheless found such mesoscale assemblies to be thermodynamically stable. Here, we consider their equilibrium and assembly dynamics. At intermediate densities above the order-disorder transition, we identify four different dynamical regimes and the structural changes that underlie the dynamical crossovers from one disordered regime to the next. Below the order-disorder transition, we also find that periodic lamellae are the most dynamically accessible of the periodic microphases. Our analysis thus offers a comprehensive view of the dynamics of disordered microphases and a route to the assembly of periodic microphases in a putative well-controlled, experimental system.

Exploring the Stability of Ligand Binding Modes to Proteins by Molecular Dynamics Simulations: A Cross-docking Study.

PubMed

Liu, Kai; Kokubo, Hironori

2017-10-23

Docking has become an indispensable approach in drug discovery research to predict the binding mode of a ligand. One great challenge in docking is to efficiently refine the correct pose from various putative docking poses through scoring functions. We recently examined the stability of self-docking poses under molecular dynamics (MD) simulations and showed that equilibrium MD simulations have some capability to discriminate between correct and decoy poses. Here, we have extended our previous work to cross-docking studies for practical applications. Three target proteins (thrombin, heat shock protein 90-alpha, and cyclin-dependent kinase 2) of pharmaceutical interest were selected. Three comparable poses (one correct pose and two decoys) for each ligand were then selected from the docking poses. To obtain the docking poses for the three target proteins, we used three different protocols, namely: normal docking, induced fit docking (IFD), and IFD against the homology model. Finally, five parallel MD equilibrium runs were performed on each pose for the statistical analysis. The results showed that the correct poses were generally more stable than the decoy poses under MD. The discrimination capability of MD depends on the strategy. The safest way was to judge a pose as being stable if any one run among five parallel runs was stable under MD. In this case, 95% of the correct poses were retained under MD, and about 25-44% of the decoys could be excluded by the simulations for all cases. On the other hand, if we judge a pose as being stable when any two or three runs were stable, with the risk of incorrectly excluding some correct poses, approximately 31-53% or 39-56% of the two decoys could be excluded by MD, respectively. Our results suggest that simple equilibrium simulations can serve as an effective filter to exclude decoy poses that cannot be distinguished by docking scores from the computationally expensive free-energy calculations.

Stable carbon and sulfur isotopes as records of the early biosphere

NASA Technical Reports Server (NTRS)

Desmarais, David J.

1989-01-01

The abundance ratios of the stable isotopes of light elements such as carbon and sulfur can differ between various naturally-occurring chemical compounds. If coexisting compounds have achieved mutual chemical and isotopic equilibrium, then the relative isotopic composition can record the conditions at which equilibrium was last maintained. If coexisting chemical compounds indeed formed simultaneously but had not achieved mutual equilibrium, then their relative isotopic compositions often reflect the conditions and mechanisms associated with the kinetically controlled reactions responsible for their production. In the context of Mars, the stable isotopic compositions of various minerals might record not only the earlier environmental conditions of the planet, but also whether or not the chemistry of life ever occurred there. Two major geochemical reservoirs occur in Earth's crust, both for carbon and sulfur. In rocks formed in low temperature sedimentary environments, the oxidized forms of these elements tend to be enriched in the isotope having the larger mass, relative to the reduced forms. In sediments where the organics and sulfides were formed by biological processes, these isotopic contrasts were caused by the processes of biological CO2 fixation and dissimilatory sulfate reduction. Such isotopic contrasts between oxidized and reduced forms of carbon and sulfur are permitted by thermodynamics at ambient temperatures. However, nonbiological chemical reactions associated with the production of organic matter and the reduction of organics and sulfides are extremely slow at ambient temperatures. Thus the synthesis of organics and sulfides under ambient conditions illustrates life's profound role as a chemical catalyst that has altered the chemistry of Earth's crust. Because the stable isotopes of carbon and sulfur can reflect their chemistry, they are useful probes of the Martian surface.

Formation mechanism of a basin of attraction for passive dynamic walking induced by intrinsic hyperbolicity

PubMed Central

Aoi, Shinya; Tsuchiya, Kazuo; Kokubu, Hiroshi

2016-01-01

Passive dynamic walking is a useful model for investigating the mechanical functions of the body that produce energy-efficient walking. The basin of attraction is very small and thin, and it has a fractal-like shape; this explains the difficulty in producing stable passive dynamic walking. The underlying mechanism that produces these geometric characteristics was not known. In this paper, we consider this from the viewpoint of dynamical systems theory, and we use the simplest walking model to clarify the mechanism that forms the basin of attraction for passive dynamic walking. We show that the intrinsic saddle-type hyperbolicity of the upright equilibrium point in the governing dynamics plays an important role in the geometrical characteristics of the basin of attraction; this contributes to our understanding of the stability mechanism of bipedal walking. PMID:27436971

Dynamical Evolution and Momentum Transfer for Binary Asteroid Systems

NASA Astrophysics Data System (ADS)

Bellerose, Julie

Over the past decade, robotic missions have been sent to small bodies, providing a basic understanding of their environment. Some of these small systems are found to be in pairs, orbiting each other, which are thought to represent about 16% of the near-Earth asteroid population. It is fair to assume that a mission will target a binary asteroid system in the near future as they can enable scientific insight into both the geology and dynamics of asteroids. In previous work, the dynamical evolution of binary systems was investigated for an ellipsoidsphere model. From the dynamics of two celestial bodies, equilibrium configurations and their stability were analyzed. For a given value of angular momentum, it was shown that there are in general two relative equilibrium configurations which are opposite in stability. When perturbations are introduced, we found that the equilibrium states are the minimum energy points of nearby periodic families. General dynamics from unstable to stable configurations were investigated for binaries in close proximity. Accounting for the dynamics of binaries, the dynamics of particles in this gravitational field were also studied. The location of the analogue Lagrangian points and energy associated with them were characterized. The L1 region is a key element for transfers between the bodies. It was shown that L1 can be situated between or inside the bodies depending on the free parameters of the system modifying the transfer possibilities since L1 has a hyperbolic manifold associated with it. In the current work, we look at the L1 region for binary system where the bodies are in relative equilibrium, close to each other. We find that L1 transits from outside to inside the ellipsoid when the mass ratio is larger than 0.6. For binary systems in close proximity with L1 being inside the ellipsoidal body, simulations show that particles on the surface tend to move away from the ellipsoid, toward the spherical primary. We can relate this to the Roche limit of binaries which affect the distribution of mass between the bodies. Other parameters such as the spin rate of a larger spherical primary may also influence particle distribution. Hence, we can map and characterize the mass distribution and momentum exchange that may occur within a closely formed binary systems.

Superheating of ice crystals in antifreeze protein solutions

PubMed Central

Celik, Yeliz; Graham, Laurie A.; Mok, Yee-Foong; Bar, Maya; Davies, Peter L.; Braslavsky, Ido

2010-01-01

It has been argued that for antifreeze proteins (AFPs) to stop ice crystal growth, they must irreversibly bind to the ice surface. Surface-adsorbed AFPs should also prevent ice from melting, but to date this has been demonstrated only in a qualitative manner. Here we present the first quantitative measurements of superheating of ice in AFP solutions. Superheated ice crystals were stable for hours above their equilibrium melting point, and the maximum superheating obtained was 0.44 °C. When melting commenced in this superheated regime, rapid melting of the crystals from a point on the surface was observed. This increase in melting temperature was more appreciable for hyperactive AFPs compared to the AFPs with moderate antifreeze activity. For each of the AFP solutions that exhibited superheating, the enhancement of the melting temperature was far smaller than the depression of the freezing temperature. The present findings clearly show that AFPs adsorb to ice surfaces as part of their mechanism of action, and this absorption leads to protection of ice against melting as well as freezing. PMID:20215465

Redefining the utility of the three-isotope method

NASA Astrophysics Data System (ADS)

Cao, Xiaobin; Bao, Huiming

2017-09-01

The equilibrium isotope fractionation factor αeq is a fundamental parameter in the study of stable isotope effects. Experimentally, it has been difficult to establish that a system has attained equilibrium. The three-isotope method, using the initial trajectory of changing isotope ratios (e.g. 16O, 17O, and 18O) to deduce the final equilibrium point of isotope exchange, has long been hailed as the most rigorous experimental approach. However, over the years some researchers have cautioned on the limitations of this method, but the foundation of three-isotope method has not been properly examined and the method is still widely used in calibrating αeq for both traditional and increasingly non-traditional isotope systems today. Here, using water-water and dissolved CO2-water oxygen exchange as model systems, we conduct an isotopologues-specific kinetic analysis of the exchange processes and explore the underlying assumptions and validity of the three-isotope method. We demonstrate that without knowing the detailed exchange kinetics a priori the three-isotope method cannot lead to a reliable αeq. For a two-reservoir exchanging system, α determined by this method may be αeq, kinetic isotope effect, or apparent kinetic isotope effect, which can all bear different values. When multiple reservoirs exist during exchange, the evolving trajectory can be complex and hard to predict. Instead of being a tool for αeq determination, three-isotope method should be used as a tool for studying kinetic isotope effect, apparent kinetic isotope effect, and detailed exchange kinetics in diverse systems.

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

Dynamical stability of plutonium alloys

NASA Astrophysics Data System (ADS)

Torrent, Marc; Dorado, Boris; Bieder, Jordan

Plutonium sits at the center of the actinide series and marks the transition between localization and delocalization of the 5 f electrons. From a metallurgical standpoint, the monoclinic α phase (stable at low T) is brittle, not suitable for engineering applications, as opposed to the ductile fcc δ phase (stable at 580K). The δ - α transition can be avoided by alloying δ-Pu with ''deltagen'' elements. There is a wide unexplored area for Pu when it comes to lattice dynamics. Due to the changes in the composition, the dynamical stability of is constantly challenged. Displ. cascades are created in the material, which in turn produce numerous of point defects. Therefore, the accumulation of defects preclude a thermodynamic equilibrium. Given the importance for engineering applications, it is crucial that we understand the mechanisms that lead to stabilization with respect to the alloy composition. We use first-principles calculations to provide evidence of the effect of defects/impurities (C, O, Al, Fe, Ni, Ga, Ce, U, Am) on the dynamical stability of δ-Pu. We show that this phase is dynamically unstable at low T and that it depends on the 5 f orbital occupancies. We investigate how defects affect the stability by comparing the phonon DoS.

When Does Frequency-Independent Selection Maintain Genetic Variation?

PubMed

Novak, Sebastian; Barton, Nicholas H

2017-10-01

Frequency-independent selection is generally considered as a force that acts to reduce the genetic variation in evolving populations, yet rigorous arguments for this idea are scarce. When selection fluctuates in time, it is unclear whether frequency-independent selection may maintain genetic polymorphism without invoking additional mechanisms. We show that constant frequency-independent selection with arbitrary epistasis on a well-mixed haploid population eliminates genetic variation if we assume linkage equilibrium between alleles. To this end, we introduce the notion of frequency-independent selection at the level of alleles, which is sufficient to prove our claim and contains the notion of frequency-independent selection on haploids. When selection and recombination are weak but of the same order, there may be strong linkage disequilibrium; numerical calculations show that stable equilibria are highly unlikely. Using the example of a diallelic two-locus model, we then demonstrate that frequency-independent selection that fluctuates in time can maintain stable polymorphism if linkage disequilibrium changes its sign periodically. We put our findings in the context of results from the existing literature and point out those scenarios in which the possible role of frequency-independent selection in maintaining genetic variation remains unclear. Copyright © 2017 by the Genetics Society of America.

Headwater peatland channels in south-eastern Australia; the attainment of equilibrium

NASA Astrophysics Data System (ADS)

Nanson, R. A.; Cohen, T. J.

2014-05-01

Many small headwater catchments (< 50 km2) in temperate south-eastern Australia store sediment in valley fills. While accumulation in some of these systems commenced up to 30,000 years ago, most did not commence filling with peat or clastic material until at least the mid Holocene. In such headwater settings, many clastic valley fills develop cut-and-fill channels, which contrast to some peatland settings where sinuous equilibrium channels have evolved. Four peatland systems within this dataset demonstrate stable channel systems which span nearly the full spectrum of observed valley-floor slopes. We assess new and published longitudinal data from these four channels and demonstrate that each of these channels has achieved equilibrium profiles. New and published flow and survey data are synthesised to demonstrate how these peatland systems have attained equilibrium. Low rates of sediment supply and exceptionally high bank strengths have resulted in low width to depth ratios which accommodate rapid changes in flow velocity and depth with changes in discharge. In small peatland channels, planform adjustments have been sufficient to counter the energy provided by these hydraulically efficient cross-sections and have enabled the achievement of regime energy-slopes. In larger and higher energy peatland channels, large, armoured, stable, bedforms have developed. These bedforms integrate with planform adjustments to maintain a condition of minimum variance in energy losses as represented by the slope profiles and, therefore, a uniform increase in downstream entropy.

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.

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.

Materials Discovery across Technological Readiness Levels | Materials

Science.gov Websites

and experimental realization of new stable inorganic materials using Inverse Design approach, A , E. Tea, S. Lany, J. Phys. Chem. Lett. 5, 1117 (2014). Non-equilibrium origin of high electrical

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

Travesset, Alex

An extensive characterization of the low temperature phase diagram of particles interacting with power law or Lennard-Jones potentials is provided from Lattice Dynamical Theory. For power law systems, only two lattice structures are stable for certain values of the exponent (or softness) (A15, body centered cube (bcc)) and two more (face centered cubic (fcc), hexagonal close packed (hcp)) are always stable. Among them, only the fcc and bcc are equilibrium states. For Lennard-Jones systems, the equilibrium states are either hcp or fcc, with a coexistence curve in pressure and temperature that shows reentrant behavior. The hcp solid never coexists withmore » the liquid. In all cases analyzed, for both power law and Lennard-Jones potentials, the fcc crystal has higher entropy than the hcp. The role of anharmonic terms is thoroughly analyzed and a general thermodynamic integration to account for them is proposed.« less

How to control chaotic behaviour and population size with proportional feedback

NASA Astrophysics Data System (ADS)

Liz, Eduardo

2010-01-01

We study the control of chaos in one-dimensional discrete maps as they often occur in modelling population dynamics. For managing the population, we seek to suppress any possible chaotic behavior, leading the system to a stable equilibrium. In this Letter, we make a rigorous analysis of the proportional feedback method under certain conditions fulfilled by a wide family of maps. We show that it is possible to stabilize the chaotic dynamics towards a globally stable positive equilibrium, that can be chosen among a broad range of possible values. In particular, the size of the population can be enhanced by control in form of population reduction. This paradoxical phenomenon is known as the hydra effect, and it has important implications in the design of strategies in such areas as fishing, pest management, and conservation biology.

A simple nonlinear model for the return to isotropy in turbulence

NASA Technical Reports Server (NTRS)

Sarkar, Sutanu; Speziale, Charles G.

1989-01-01

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed. The model is shown to satisfy realizability and to give rise to no stable non-trivial equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. The absence of stable non-trivial equilibrium solutions is a necessary condition to ensure that the model predicts a return to isotropy for all relaxational turbulent flows. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Direct comparisons are also made with the predictions of the Rotta model and the Lumley model.

Packings of a charged line on a sphere.

PubMed

Alben, Silas

2008-12-01

We find equilibrium configurations of open and closed lines of charge on a sphere, and track them with respect to varying sphere radius. Closed lines transition from a circle to a spiral-like shape through two low-wave-number bifurcations-"baseball seam" and "twist"-which minimize Coulomb energy. The spiral shape is the unique stable equilibrium of the closed line. Other unstable equilibria arise through tip-splitting events. An open line transitions smoothly from an arc of a great circle to a spiral as the sphere radius decreases. Under repulsive potentials with faster-than-Coulomb power-law decay, the spiral is tighter in initial stages of sphere shrinkage, but at later stages of shrinkage the equilibria for all repulsive potentials converge on a spiral with uniform spacing between turns. Multiple stable equilibria of the open line are observed.

Does the centre of mass remain stable during complex human postural equilibrium tasks in weightlessness?

NASA Astrophysics Data System (ADS)

Stapley, Paul; Pozzo, Thierry

In normal gravity conditions the execution of voluntary movement involves the displacement of body segments as well as the maintenance of a stable reference value for equilibrium control. It has been suggested that centre of mass (CM) projection within the supporting base (BS) is the stabilised reference for voluntary action, and is conserved in weightlessness. The purpose of this study was to determine if the CM is stabilised during whole body reaching movements executed in weightlessness. The reaching task was conducted by two cosmonauts aboard the Russian orbital station MIR, during the Franco-Russian mission ALTAIR, 1993. Movements of reflective markers were recorded using a videocamera, successive images being reconstructed by computer every 40ms. The position of the CM, ankle joint torques and shank and thigh angles were computed for each subject pre- in- and post-flight using a 7-link mathematical model. Results showed that both cosmonauts adopted a backward leaning posture prior to reaching movements. Inflight, the CM was displaced throughout values in the horizontal axis three times those of pre-flight measures. In addition, ankle dorsi flexor torques inflight increased to values double those of pre- and post-flight tests. This study concluded that CM displacements do not remain stable during complex postural equilibrium tasks executed in weightlessness. Furthermore, in the absence of gravity, subjects changed their strategy for producing ankle torque during spaceflight from a forward to a backward leaning posture.

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.

An equilibrium ab initio atomistic thermodynamics study of chlorine adsorption on the Cu(001) surface.

PubMed

Suleiman, Ibrahim A; Radny, Marian W; Gladys, Michael J; Smith, Phillip V; Mackie, John C; Kennedy, Eric M; Dlugogorski, Bogdan Z

2011-06-07

The effect of chlorine (Cl) chemisorption on the energetics and atomic structure of the Cu(001) surface over a wide range of chlorine pressures and temperatures has been studied using equilibrium ab initio atomistic thermodynamics to elucidate the formation of cuprous chloride (CuCl) as part of the Deacon reaction on copper metal. The calculated surface free energies show that the 1/2 monolayer (ML) c(2 × 2)-Cl phase with chlorine atoms adsorbed at the hollow sites is the most stable structure for a wide range of Cl chemical potential, in agreement with experimental observations. It is also found that at very low pressure and exposure, but elevated temperature, the 1/9 ML and 1/4 ML phases become the most stable. By contrast, a high coverage of Cl does not lead to thermodynamically stable geometries. The subsurface adsorption of Cl atoms, however, dramatically increases the stability of the 1 ML and 2 ML adsorption configurations providing a possible pathway for the formation of the bulk-chloride surface phases in the kinetic regime.

Investigation of island formation due to RMPs in DIII-D plasmas with the SIESTA resistive MHD equilibrium code

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

Hirshman, S. P.; Shafer, M. W.; Seal, S. K.

The SIESTA magnetohydrodynamic (MHD) equilibrium code has been used to compute a sequence of ideally stable equilibria resulting from numerical variation of the helical resonant magnetic perturbation (RMP) applied to an axisymmetric DIII-D plasma equilibrium. Increasing the perturbation strength at the dominant m=2, n=-1 , resonant surface leads to lower MHD energies and increases in the equilibrium island widths at the m=2 (and sidebands) surfaces, in agreement with theoretical expectations. Island overlap at large perturbation strengths leads to stochastic magnetic fields which correlate well with the experimentally inferred field structure. The magnitude and spatial phase (around the dominant rational surfaces)more » of the resonant (shielding) component of the parallel current are shown to change qualitatively with the magnetic island topology.« less

Investigation of island formation due to RMPs in DIII-D plasmas with the SIESTA resistive MHD equilibrium code

DOE PAGES

Hirshman, S. P.; Shafer, M. W.; Seal, S. K.; ...

2016-03-03

The SIESTA magnetohydrodynamic (MHD) equilibrium code has been used to compute a sequence of ideally stable equilibria resulting from numerical variation of the helical resonant magnetic perturbation (RMP) applied to an axisymmetric DIII-D plasma equilibrium. Increasing the perturbation strength at the dominant m=2, n=-1 , resonant surface leads to lower MHD energies and increases in the equilibrium island widths at the m=2 (and sidebands) surfaces, in agreement with theoretical expectations. Island overlap at large perturbation strengths leads to stochastic magnetic fields which correlate well with the experimentally inferred field structure. The magnitude and spatial phase (around the dominant rational surfaces)more » of the resonant (shielding) component of the parallel current are shown to change qualitatively with the magnetic island topology.« less

The possibility of a tipping point in the Arctic sea ice cover, and associated early-warning signals

NASA Astrophysics Data System (ADS)

Jastamin Steene, Rebekka

2017-04-01

As the Arctic sea ice has become one of the primer indicators of global climate change, with a seemingly accelerated loss in both ice extent and volume the latest decades, the existence of a tipping point related to the Arctic sea ice cover has been widely debated. Several observed and potential abrupt transitions in the climate system may be interpreted as bifurcations in randomly driven dynamical systems. This means that a system approaching a bifurcation point shifts from one stable state to another, and we say that the system is subject to a critical transition. As the equilibrium states become unstable in the vicinity of a bifurcation point the characteristic relaxation times increases, and the system is said to experience a "critical slowing down". This makes it plausible to observe so called early-warning signals (EWS) when approaching a critical transition. In the Arctic non-linear mechanisms like the temperature response of the ice-albedo feedback can potentially cause a sudden shift to an ice-free Arctic Ocean. Using bifurcation theory and potential analyses we examine time series of observational data of the Arctic sea ice, investigating the possibility of multiple states in the behavior of the ice cover. We further debate whether a shift between states is irreversible, and whether it can be preluded by early-warning signals.

First-principles investigations of equilibrium Ca, Mg, Si and O isotope fractionations between silicate melts and minerals

NASA Astrophysics Data System (ADS)

Qi, Y.; Liu, X.; Kang, J.; He, L.

2017-12-01

Equilibrium isotope fractionation factors are essential for using stable isotope data to study many geosciences processes such as planetary differentiation and mantle evolution. The mass-dependent equilibrium isotope fractionation is primarily controlled by the difference in bond energies triggered by the isotope substitution. With the recent advances in computational capabilities, first-principles calculation has become a reliable tool to investigate equilibrium isotopic fractionations, greatly improving our understanding of the factors controlling isotope fractionations. It is important to understand the isotope fractionation between melts and minerals because magmatism is critical for creating and shaping the Earth. However, because isotope fractionation between melts and minerals is small at high temperature, it is difficult to experimentally calibrate such small signature. Due to the disordered and dynamic character of melts, calculations of equilibrium isotope fractionation of melts are more challenging than that for gaseous molecules or minerals. Here, we apply first-principles molecular dynamics method to calculate equilibrium Ca, Mg, Si, and O isotope fractionations between silicate melts and minerals. Our results show that equilibrium Mg, Si, and O isotope fractionations between olivine and pure Mg2SiO4 melt are close to zero at high temperature (e.g. δ26Mgmelt-ol = 0.03 ± 0.04‰, δ30Simelt-ol = -0.06 ± 0.07‰, δ18Omelt-ol = 0.07‰ ± 0.08 at 1500 K). Equilibrium Ca, Mg, Si, and O isotope fractionations between diopside and basalt melt (67% CaMgSi2O6 + 33% CaAl2Si2O8) are also negligible at high temperature (e.g. δ44/40Camelt-cpx = -0.01 ± 0.02‰, δ26Mgmelt-cpx = -0.05 ± 0.14‰, δ30Simelt-cpx = 0.04 ± 0.04‰, δ18Omelt-cpx = 0.03 ± 0.07‰ at 1500 K). These results are consistent with the observations in natural samples that there is no significant Ca, Mg, Si, and O isotope fractionation during mantle partial melting, demonstrating the reliability of our methods. Thus, our results can be used to understand stable isotope fractionation during partial melting of mantle peridotite or fractional crystallization during magmatic differentiation. The first-principles molecular dynamics method is a promising tool to obtain equilibrium fractionation of more isotope systems for complicate liquids.

Computational methods for reactive transport modeling: A Gibbs energy minimization approach for multiphase equilibrium calculations

NASA Astrophysics Data System (ADS)

Leal, Allan M. M.; Kulik, Dmitrii A.; Kosakowski, Georg

2016-02-01

We present a numerical method for multiphase chemical equilibrium calculations based on a Gibbs energy minimization approach. The method can accurately and efficiently determine the stable phase assemblage at equilibrium independently of the type of phases and species that constitute the chemical system. We have successfully applied our chemical equilibrium algorithm in reactive transport simulations to demonstrate its effective use in computationally intensive applications. We used FEniCS to solve the governing partial differential equations of mass transport in porous media using finite element methods in unstructured meshes. Our equilibrium calculations were benchmarked with GEMS3K, the numerical kernel of the geochemical package GEMS. This allowed us to compare our results with a well-established Gibbs energy minimization algorithm, as well as their performance on every mesh node, at every time step of the transport simulation. The benchmark shows that our novel chemical equilibrium algorithm is accurate, robust, and efficient for reactive transport applications, and it is an improvement over the Gibbs energy minimization algorithm used in GEMS3K. The proposed chemical equilibrium method has been implemented in Reaktoro, a unified framework for modeling chemically reactive systems, which is now used as an alternative numerical kernel of GEMS.

AEDT: A new concept for ecological dynamics in the ever-changing world.

PubMed

Chesson, Peter

2017-05-01

The important concept of equilibrium has always been controversial in ecology, but a new, more general concept, an asymptotic environmentally determined trajectory (AEDT), overcomes many concerns with equilibrium by realistically incorporating long-term climate change while retaining much of the predictive power of a stable equilibrium. A population or ecological community is predicted to approach its AEDT, which is a function of time reflecting environmental history and biology. The AEDT invokes familiar questions and predictions but in a more realistic context in which consideration of past environments and a future changing profoundly due to human influence becomes possible. Strong applications are also predicted in population genetics, evolution, earth sciences, and economics.

Carbonic Anhydrase, Calcification Dynamics and Stable Isotope Vital Effects: Deep Sea Corals and Beyond

NASA Astrophysics Data System (ADS)

Chen, S.; Gagnon, A. C.; Adkins, J. F.

2017-12-01

The stable isotope compositions of biogenic carbonates have been used for paleoceanographic and paleoclimatic reconstructions for decades, and produced some of the most iconic records in the field. However, we still lack a fully mechanistic understanding of the stable isotope proxies, especially the biological overprint on the environmental signals termed "vital effects". A ubiquitous feature of stable isotope vital effects in marine calcifying organisms is a strong correlation between δ18O and δ13C in a range of values that are depleted from equilibrium. Two mechanisms have been proposed to explain this correlation, one based on kinetic isotope effects during CO2(aq)-HCO3- inter-conversion, the other based on equilibrium isotope exchange during pH dependent speciation of the dissolved inorganic carbon pool. Neither mechanism explains all the stable isotope features observed in biogenic carbonates. Here we present a fully kinetic model of biomineralization and its isotope effects using deep sea corals as a test organism. A key component of our model is the consideration of the enzyme carbonic anhydrase in catalyzing the CO2(aq)-HCO3- inter-conversion reactions in the extracellular calcifying fluid (ECF). We find that the amount of carbonic anhydrase not only modulates the carbonate chemistry of the calcifying fluid, but also helps explain the slope of the δ18O-δ13C correlation. With this model, we are not only able to fit deep sea coral data, but also explain the stable isotope vital effects of other calcifying organisms. This fully kinetic model of stable isotope vital effects and the underlying calcification dynamics may also help us better understand mechanisms of other paleoceanographic tracers in biogenic carbonates, including boron isotopes and trace metal proxies.

Turing-Hopf bifurcations in a predator-prey model with herd behavior, quadratic mortality and prey-taxis

NASA Astrophysics Data System (ADS)

Liu, Xia; Zhang, Tonghua; Meng, Xinzhu; Zhang, Tongqian

2018-04-01

In this paper, we propose a predator-prey model with herd behavior and prey-taxis. Then, we analyze the stability and bifurcation of the positive equilibrium of the model subject to the homogeneous Neumann boundary condition. By using an abstract bifurcation theory and taking prey-tactic sensitivity coefficient as the bifurcation parameter, we obtain a branch of stable nonconstant solutions bifurcating from the positive equilibrium. Our results show that prey-taxis can yield the occurrence of spatial patterns.

Coupled Inverted Pendula Model of Competition and Cooperation

NASA Astrophysics Data System (ADS)

Yoshida, Katsutoshi; Ohta, Hiroki

A coupled inverted pendula model of competition and cooperation is proposed to develop a purely mechanical implementation comparable to the Lotka-Volterra competition model. It is shown numerically that the proposed model can produce the four stable equilibriums analogous to ecological coexistence, two states of dominance, and scramble. The authors also propose two types of open-loop strategies to switch the equilibriums. The proposed strategies can be associated with an attack and a counter attack of agents through a metaphor of martial arts.

General equilibrium characteristics of a dual-lift helicopter system

NASA Technical Reports Server (NTRS)

Cicolani, L. S.; Kanning, G.

1986-01-01

The equilibrium characteristics of a dual-lift helicopter system are examined. The system consists of the cargo attached by cables to the endpoints of a spreader bar which is suspended by cables below two helicopters. Results are given for the orientation angles of the suspension system and its internal forces, and for the helicopter thrust vector requirements under general circumstances, including nonidentical helicopters, any accelerating or static equilibrium reference flight condition, any system heading relative to the flight direction, and any distribution of the load to the two helicopters. Optimum tether angles which minimize the sum of the required thrust magnitudes are also determined. The analysis does not consider the attitude degrees of freedom of the load and helicopters in detail, but assumes that these bodies are stable, and that their aerodynamic forces in equilibrium flight can be determined independently as functions of the reference trajectory. The ranges of these forces for sample helicopters and loads are examined and their effects on the equilibrium characteristics are given parametrically in the 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.

The dynamical environment of asteroid 21 Lutetia according to different internal models

NASA Astrophysics Data System (ADS)

Aljbaae, S.; Chanut, T. G. G.; Carruba, V.; Souchay, J.; Prado, A. F. B. A.; Amarante, A.

2017-01-01

One of the most accurate models currently used to represent the gravity field of irregular bodies is the polyhedral approach. In this model, the mass of the body is assumed to be homogeneous, which may not be true for a real object. The main goal of the this paper is to study the dynamical effects induced by three different internal structures (uniform, three- and four-layered) of asteroid (21) Lutetia, an object that recent results from space probe suggest being at least partially differentiated. The Mascon gravity approach used in the this work consists of dividing each tetrahedron into eight parts to calculate the gravitational field around the asteroid. The zero-velocity curves show that the greatest displacement of the equilibrium points occurs in the position of the E4 point for the four-layered structure and the smallest one occurs in the position of the E3 point for the three-layered structure. Moreover, stability against impact shows that the planar limit gets slightly closer to the body with the four-layered structure. We then investigated the stability of orbital motion in the equatorial plane of (21) Lutetia and propose numerical stability criteria to map the region of stable motions. Layered structures could stabilize orbits that were unstable in the homogeneous model.

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 analysis of composite laminated beams using a 2D interpolating meshless technique

NASA Astrophysics Data System (ADS)

Sadek, S. H. M.; Belinha, J.; Parente, M. P. L.; Natal Jorge, R. M.; de Sá, J. M. A. César; Ferreira, A. J. M.

2018-02-01

Laminated composite materials are widely implemented in several engineering constructions. For its relative light weight, these materials are suitable for aerospace, military, marine, and automotive structural applications. To obtain safe and economical structures, the modelling analysis accuracy is highly relevant. Since meshless methods in the recent years achieved a remarkable progress in computational mechanics, the present work uses one of the most flexible and stable interpolation meshless technique available in the literature—the Radial Point Interpolation Method (RPIM). Here, a 2D approach is considered to numerically analyse composite laminated beams. Both the meshless formulation and the equilibrium equations ruling the studied physical phenomenon are presented with detail. Several benchmark beam examples are studied and the results are compared with exact solutions available in the literature and the results obtained from a commercial finite element software. The results show the efficiency and accuracy of the proposed numeric technique.

Dynamics and profiles of a diffusive host-pathogen system with distinct dispersal rates

NASA Astrophysics Data System (ADS)

Wu, Yixiang; Zou, Xingfu

2018-04-01

In this paper, we investigate a diffusive host-pathogen model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected hosts. We first prove that the solution of the model exists globally and the model system possesses a global attractor. We then identify the basic reproduction number R0 for the model and prove its threshold role: if R0 ≤ 1, the disease free equilibrium is globally asymptotically stable; if R0 > 1, the solution of the model is uniformly persistent and there exists a positive (pathogen persistent) steady state. Finally, we study the asymptotic profiles of the positive steady state as the dispersal rate of the susceptible or infected hosts approaches zero. Our result suggests that the infected hosts concentrate at certain points which can be characterized as the pathogen's most favoured sites when the mobility of the infected host is limited.

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.

Calculation of three-dimensional compressible laminar and turbulent boundary layers. An implicit finite-difference procedure for solving the three-dimensional compressible laminar, transitional, and turbulent boundary-layer equations

NASA Technical Reports Server (NTRS)

Harris, J. E.

1975-01-01

An implicit finite-difference procedure is presented for solving the compressible three-dimensional boundary-layer equations. The method is second-order accurate, unconditionally stable (conditional stability for reverse cross flow), and efficient from the viewpoint of computer storage and processing time. The Reynolds stress terms are modeled by (1) a single-layer mixing length model and (2) a two-layer eddy viscosity model. These models, although simple in concept, accurately predicted the equilibrium turbulent flow for the conditions considered. Numerical results are compared with experimental wall and profile data for a cone at an angle of attack larger than the cone semiapex angle. These comparisons clearly indicate that the numerical procedure and turbulence models accurately predict the experimental data with as few as 21 nodal points in the plane normal to the wall boundary.

Analysis on the crime model using dynamical approach

NASA Astrophysics Data System (ADS)

Mohammad, Fazliza; Roslan, Ummu'Atiqah Mohd

2017-08-01

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

Surface tension of evaporating nanofluid droplets

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

Chen, Ruey-Hung; Phuoc, Tran X.; Martello, Donald

2011-05-01

Measurements of nanofluid surface tension were made using the pendant droplet method. Three different types of nanoparticles were used - laponite, silver and Fe 2O 3 - with de-ionized water (DW) as the base fluid. The reported results focus on the following categories; (1) because some nanoparticles require surfactants to form stable colloids, the individual effects of the surfactant and the particles were investigated; (2) due to evaporation of the pendant droplet, the particle concentration increases, affecting the apparent surface tension; (3) because of the evaporation process, a hysteresis was found where the evaporating droplet can only achieve lower valuesmore » of surface tension than that of nanofluids at the same prepared concentrations: and (4) the Stefan equation relating the apparent surface tension and heat of evaporation was found to be inapplicable for nanofluids investigated. Comparisons with findings for sessile droplets are also discussed, pointing to additional effects of nanoparticles other than the non-equilibrium evaporation process.« less

Fragile-to-fragile liquid transition at Tg and stable-glass phase nucleation rate maximum at the Kauzmann temperature TK

NASA Astrophysics Data System (ADS)

Tournier, Robert F.

2014-12-01

An undercooled liquid is unstable. The driving force of the glass transition at Tg is a change of the undercooled-liquid Gibbs free energy. The classical Gibbs free energy change for a crystal formation is completed including an enthalpy saving. The crystal growth critical nucleus is used as a probe to observe the Laplace pressure change Δp accompanying the enthalpy change -Vm×Δp at Tg where Vm is the molar volume. A stable glass-liquid transition model predicts the specific heat jump of fragile liquids at T≤Tg, the Kauzmann temperature TK where the liquid entropy excess with regard to crystal goes to zero, the equilibrium enthalpy between TK and Tg, the maximum nucleation rate at TK of superclusters containing magic atom numbers, and the equilibrium latent heats at Tg and TK. Strong-to-fragile and strong-to-strong liquid transitions at Tg are also described and all their thermodynamic parameters are determined from their specific heat jumps. The existence of fragile liquids quenched in the amorphous state, which do not undergo liquid-liquid transition during heating preceding their crystallization, is predicted. Long ageing times leading to the formation at TK of a stable glass composed of superclusters containing up to 147 atom, touching and interpenetrating, are evaluated from nucleation rates. A fragile-to-fragile liquid transition occurs at Tg without stable-glass formation while a strong glass is stable after transition.

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.

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.

A Method of Determining the Equilibrium Performance and the Stability of an Engine Equipped with an Exhaust Turbosupercharger

NASA Technical Reports Server (NTRS)

Rea, James Buchanan

1941-01-01

The performance of an exhaust turbine driving a supercharger is investigated by means of a sample calculation based on reasonable assumptions for the purpose of determining whether the assumed installation is stable with respect to changes in the mass of gas handled, boost pressure, etc. The arrangement was found to be stable throughout the entire range of operation. The method developed can be generally applied.

A 3-Component System of Competition and Diffusion.

DTIC Science & Technology

1983-08-01

assume * that the distribution of the populations are determined by competition of’ Lotka - Volterra - * Gause type and simple diffusion. Suppose ui(t,x...diffusive Lotka - Volterra system with three species can have a stable non-constant equilibrium solutions. J. Math. Biol., (in press). [7] Kishimoto, K., Mimura...M. and Yoshida, K., Stable spatlo-temporal oscillations of diffusive Lotka - Volterra systems with three or more species, to appear in J. Math. Biol

Some General Thoughts about Broken Symmetry.

DTIC Science & Technology

1981-01-21

to what extent one may generalize to random systems and to ’dissipative structures’. Thermal equilibrium broken symmetry is characterized by an order...stable defects. We conjecture what may be the consequences of relaxing these assumptions. (Author)

Thermodynamics of Surface Nanobubbles.

PubMed

Zargarzadeh, Leila; Elliott, Janet A W

2016-11-01

In this paper, we examine the thermodynamic stability of surface nanobubbles. The appropriate free energy is defined for the system of nanobubbles on a solid surface submerged in a supersaturated liquid solution at constant pressure and temperature, under conditions where an individual nanobubble is not in diffusive contact with a gas phase outside of the system or with other nanobubbles on the time scale of the experiment. The conditions under which plots of free energy versus the radius of curvature of the nanobubbles show a global minimum, which denotes the stable equilibrium state, are explored. Our investigation shows that supersaturation and an anomalously high contact angle (measured through the liquid) are required to have stable surface nanobubbles. In addition, the anomalously high contact angle of surface nanobubbles is discussed from the standpoint of a framework recently proposed by Koch, Amirfazli, and Elliott that relates advancing and receding contact angles to thermodynamic equilibrium contact angles, combined with the existence of a gas enrichment layer.

Global stability of an age-structure epidemic model with imperfect vaccination and relapse

NASA Astrophysics Data System (ADS)

Cao, Bin; Huo, Hai-Feng; Xiang, Hong

2017-11-01

A new age-structured epidemic model with imperfect vaccination and relapse is proposed. The total population of our model is partitioned into five subclasses: susceptible class S, vaccinated class V, exposed class E, infectious class I and removed class R. Age-structures are equipped with in exposed and recovered classes. Furthermore, imperfect vaccination is also introduced in our model. The basic reproduction number R0 is defined and proved as a threshold parameter of the model. Asymptotic smoothness of solutions and uniform persistence of the system are showed via reformulating the system as a system of Volterra integral equation. Furthermore, by constructing proper Volterra-type Lyapunov functional we get when R0 < 1, the disease-free equilibrium is globally asymptotically stable. When R0 > 1, the endemic equilibrium is globally stable. Our results show that to increase the efficiency of vaccination and reduce influence of relapse are vital essential for controlling epidemic.

The surface stability and morphology of tobermorite 11 Å from first principles

NASA Astrophysics Data System (ADS)

Mutisya, Sylvia M.; Miranda, Caetano R.

2018-06-01

Tobermorite minerals are important in many industrial processes typically occurring in hydrous environment. Their functionality is therefore governed in various aspects by their morphology and surface stability/reactivity. Here, we present the results of the surface energies and morphology of normal tobermorite 11 Å in a water vapor environment investigated by employing first principles atomistic thermodynamic calculations. For the low index tobermorite surfaces studied, the calculated surface energies fall within a narrow range (0.41-0.97 J/m2) with the (0 0 4) surface being the most stable. The equilibrium morphology is a thin pseudohexagonal plate elongated along the b axis. The hydrated surfaces are more stable at high water vapor chemical potentials with the stability enhanced as the water partial pressures are varied from ambient to supercritical hydrothermal conditions. Increasing the water vapor chemical potential gives rise to a smaller size of the tobermorite crystal, with the equilibrium morphology remaining unaltered.

Stability of an SAIRS alcoholism model on scale-free networks

NASA Astrophysics Data System (ADS)

Xiang, Hong; Liu, Ying-Ping; Huo, Hai-Feng

2017-05-01

A new SAIRS alcoholism model with birth and death on complex heterogeneous networks is proposed. The total population of our model is partitioned into four compartments: the susceptible individual, the light problem alcoholic, the heavy problem alcoholic and the recovered individual. The spread of alcoholism threshold R0 is calculated by the next generation matrix method. When R0 < 1, the alcohol free equilibrium is globally asymptotically stable, then the alcoholics will disappear. When R0 > 1, the alcoholism equilibrium is global attractivity, then the number of alcoholics will remain stable and alcoholism will become endemic. Furthermore, the modified SAIRS alcoholism model on weighted contact network is introduced. Dynamical behavior of the modified model is also studied. Numerical simulations are also presented to verify and extend theoretical results. Our results show that it is very important to treat alcoholics to control the spread of the alcoholism.

Non-Gaussian, non-dynamical stochastic resonance

NASA Astrophysics Data System (ADS)

Szczepaniec, Krzysztof; Dybiec, Bartłomiej

2013-11-01

The classical model revealing stochastic resonance is a motion of an overdamped particle in a double-well fourth order potential when combined action of noise and external periodic driving results in amplifying of weak signals. Resonance behavior can also be observed in non-dynamical systems. The simplest example is a threshold triggered device. It consists of a periodic modulated input and noise. Every time an output crosses the threshold the signal is recorded. Such a digitally filtered signal is sensitive to the noise intensity. There exists the optimal value of the noise intensity resulting in the "most" periodic output. Here, we explore properties of the non-dynamical stochastic resonance in non-equilibrium situations, i.e. when the Gaussian noise is replaced by an α-stable noise. We demonstrate that non-equilibrium α-stable noises, depending on noise parameters, can either weaken or enhance the non-dynamical stochastic resonance.

Analysis of a Fishery Model with two competing prey species in the presence of a predator species for Optimal Harvesting

NASA Astrophysics Data System (ADS)

Sutimin; Khabibah, Siti; Munawwaroh, Dita Anis

2018-02-01

A harvesting fishery model is proposed to analyze the effects of the presence of red devil fish population, as a predator in an ecosystem. In this paper, we consider an ecological model of three species by taking into account two competing species and presence of a predator (red devil), the third species, which incorporates the harvesting efforts of each fish species. The stability of the dynamical system is discussed and the existence of biological and bionomic equilibrium is examined. The optimal harvest policy is studied and the solution is derived in the equilibrium case applying Pontryagin's maximal principle. The simulation results is presented to simulate the dynamical behavior of the model and show that the optimal equilibrium solution is globally asymptotically stable. The results show that the optimal harvesting effort is obtained regarding to bionomic and biological equilibrium.

Ultrafast saturable absorption in TiS2 induced by non-equilibrium electrons and the generation of a femtosecond mode-locked laser.

PubMed

Tian, Xiangling; Wei, Rongfei; Liu, Meng; Zhu, Chunhui; Luo, Zhichao; Wang, Fengqiu; Qiu, Jianrong

2018-05-24

Non-equilibrium electrons induced by ultrafast laser excitation in a correlated electron material can disturb the Fermi energy as well as optical nonlinearity. Here, non-equilibrium electrons translate a semiconductor TiS2 material into a plasma to generate broad band nonlinear optical saturable absorption with a sub-picosecond recovery time of ∼768 fs (corresponding to modulation frequencies over 1.3 THz) and a modulation response up to ∼145%. Based on this optical nonlinear modulator, a stable femtosecond mode-locked pulse with a pulse duration of ∼402 fs and a pulse train with a period of ∼175.5 ns is observed in the all-optical system. The findings indicate that non-equilibrium electrons can promote a TiS2-based saturable absorber to be an ultrafast switch for a femtosecond pulse output.

Spreading of a pendant liquid drop underneath a textured substrate

NASA Astrophysics Data System (ADS)

Mistry, Aashutosh; Muralidhar, K.

2018-04-01

A pendant drop spreading underneath a partially wetting surface from an initial shape to its final equilibrium configuration and contact angle is studied. A mathematical formulation that quantifies spreading behavior of liquid drops over textured surfaces is discussed. The drop volume and the equilibrium contact angle are treated as parameters in the study. The unbalanced force at the three-phase contact line is modeled as being proportional to the degree of departure from the equilibrium state. Model predictions are verified against the available experimental data in the literature. Results show that the flow dynamics is strongly influenced by the fluid properties, drop volume, and contact angle of the liquid with the partially wetting surface. The drop exhibits rich dynamical behavior including inertial oscillations and gravitational instability, given that gravity tries to detach the drop against wetting contributions. Flow characteristics of drop motion, namely, the radius of the footprint, slip length, and dynamic contact angle in the pendant configuration are presented. Given the interplay among the competing time-dependent forces, a spreading drop can momentarily be destabilized and not achieve a stable equilibrium shape. Instability is then controlled by the initial drop shape as well. The spreading model is used to delineate stable and unstable regimes in the parameter space. Predictions of the drop volume based on the Young-Laplace equation are seen to be conservative relative to the estimates of the dynamical model discussed in the present study.

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.

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.

Super heavy element Copernicium: Cohesive and electronic properties revisited

NASA Astrophysics Data System (ADS)

Gyanchandani, Jyoti; Mishra, Vinayak; Dey, G. K.; Sikka, S. K.

2018-01-01

First principles scalar relativistic (SR) calculations with and without including the spin orbit (SO) interactions have been performed for solid Copernicium (Cn) to determine its ground state equilibrium structure, volume, bulk modulus, pressure derivative of the bulk modulus, density of states and band structure. Both SR and SR+SO calculations have been performed with 6p levels treated as part of core electrons and also as part of valence electrons. These calculations have been performed for the rhombohedral, BCT, FCC, HCP, BCC and SC structures. Results have been compared with the results for Hg which is lighter homologue of Cn in the periodic table. We find hcp to be the stable crystal structure at SR level of theory and also at SR+SO level of theory when the 6p electrons are treated as part of core electrons. With 6p as part of valence electrons, SR+SO level of computations, however, yield bcc structure to be the most stable structure. Equilibrium volume (V0) of the most stable crystal structure at SR level of theory viz. hcp structure is 188.66 a.u.3whereas its value for the bcc structure, the equilibrium ground state structure at SR+SO level of theory is 165.71 a.u.3 i.e a large change due to relativistic effects is seen. The density of states at Fermi level is much smaller in Cn than in Hg, making it a poorer metal than mercury. In addition the cohesive energy of Cn is computed to be almost two times that of Hg for SR+SO case.

Long-time behavior and Turing instability induced by cross-diffusion in a three species food chain model with a Holling type-II functional response.

PubMed

Haile, Dawit; Xie, Zhifu

2015-09-01

In this paper, we study a strongly coupled reaction-diffusion system describing three interacting species in a food chain model, where the third species preys on the second one and simultaneously the second species preys on the first one. An intra-species competition b2 among the second predator is introduced to the food chain model. This parameter produces some very interesting result in linear stability and Turing instability. We first show that the unique positive equilibrium solution is locally asymptotically stable for the corresponding ODE system when the intra-species competition exists among the second predator. The positive equilibrium solution remains linearly stable for the reaction diffusion system without cross diffusion, hence it does not belong to the classical Turing instability scheme. But it becomes linearly unstable only when cross-diffusion also plays a role in the reaction-diffusion system, hence the instability is driven solely from the effect of cross diffusion. Our results also exhibit some interesting combining effects of cross-diffusion, intra-species competitions and inter-species interactions. Numerically, we conduct a one parameter analysis which illustrate how the interactions change the existence of stable equilibrium, limit cycle, and chaos. Some interesting dynamical phenomena occur when we perform analysis of interactions in terms of self-production of prey and intra-species competition of the middle predator. By numerical simulations, it illustrates the existence of nonuniform steady solutions and new patterns such as spot patterns, strip patterns and fluctuations due to the diffusion and cross diffusion in two-dimension. Published by Elsevier Inc.

Flow characteristics and longitudinal sorting patterns associated with stable alluvial-bedrock and bedrock-alluvial transitions

NASA Astrophysics Data System (ADS)

Jafarinik, S.; Viparelli, E.

2017-12-01

Recent research recognized the existence of bedrock channels in low-slope rivers, but little is known about the morphodynamics of bedrock-alluvial and alluvial-bedrock transitions in these systems. Bedrock-alluvial and alluvial-bedrock transitions are fluvial features separating bedrock and alluvial reaches. In the bedrock reach the river bed is partially covered with alluvium. An increase in sediment supply to an alluvial reach results in channel bed aggradation. An increase in sediment supply to a bedrock reach, on the other hand, results in a reduction of the exposed bedrock. Mathematical modeling of the alluvial morphodynamics of bedrock reaches reveals that these transitions can characterize transient or equilibrium conditions. Model results show that the magnitude of the alluvial equilibrium slope and the depth of the bedrock surface relative to the downstream water surface base level have a primary control on the equilibrium conditions. Further, numerical results show that when a stable bedrock-alluvial transition forms, the bed material transport capacity in bedrock reach decreases in the flow direction. On the contrary, when a stable alluvial-bedrock transition forms the bed material transport capacity in the bedrock reach increases in the flow direction. These spatial changes in bed material transport capacity are associated with spatial changes in alluvial cover and flow hydrodynamics. Here we present a one-dimensional formulation of alluvial morphodynamics that accounts for the non-uniformity of the bed material and for the spatial change in flow resistances associated with the spatial and temporal changes in flow hydrodynamics of the bedrock reaches. This change in flow resistances can be associated with 1) changes in skin friction due to longitudinal changes in the grain size distribution of the bed surface, and/or 2) changes in bedform geometry associated with the interaction between the alluvial cover and the underlying bedrock. The model has been validated against laboratory experiments with stable alluvial-bedrock transitions and is applied to describe the spatial changes in flow characteristics and sediment sorting patterns upstream of a stable bedrock-alluvial transition.

Cocrystal solubility product analysis - Dual concentration-pH mass action model not dependent on explicit solubility equations.

PubMed

Avdeef, Alex

2017-12-15

A novel general computational approach is described to address many aspects of cocrystal (CC) solubility product (K sp ) determination of drug substances. The CC analysis program, pDISOL-X, was developed and validated with published model systems of various acid-base combinations of active pharmaceutical ingredients (APIs) and coformers: (i) carbamazepine cocrystal systems with 4-aminobenzoic acid, cinnamic acid, saccharin, and salicylic acid, (ii) for indomethacin with saccharin, (iii) for nevirapine with maleic acid, saccharin, and salicylic acid, and (iv) for gabapentin with 3-hydroxybenzoic acid. In all systems but gabapentin, the coformer is much more soluble than the API. The model systems selected are those with available published dual concentration-pH data, one set for the API and one set for the coformer, generally measured at eutectic points (thermodynamically-stable three phases: solution, cocrystal, and crystalline API or coformer). The carbamazepine-cinnamic acid CC showed a substantial elevation in the API equilibrium concentration above pH5, consistent with the formation of a complex between carbamazepine and cinnamate anion. The analysis of the gabapentin:3-hydroxybenzoic acid 1:1 CC system indicated four zones of solid suspensions: coformer (pH<3.25), coformer and cocrystal eutectic (pH3.25-4.44), cocrystal (pH4.44-5.62), and API (pH>5.62). The general approach allows for testing of many possible equilibrium models, including those comprising drug-coformer complexation. The program calculates the ionic strength at each pH. From this, the equilibrium constants are adjusted for activity effects, based on the Stokes-Robinson hydration theory. The complete speciation analysis of the CC systems may provide useful insights into pH-sensitive dissolution effects that could potentially influence bioavailability. Copyright © 2017 Elsevier B.V. All rights reserved.

Population-genetic models of sex-limited genomic imprinting.

PubMed

Kelly, S Thomas; Spencer, Hamish G

2017-06-01

Genomic imprinting is a form of epigenetic modification involving parent-of-origin-dependent gene expression, usually the inactivation of one gene copy in some tissues, at least, for some part of the diploid life cycle. Occurring at a number of loci in mammals and flowering plants, this mode of non-Mendelian expression can be viewed more generally as parentally-specific differential gene expression. The effects of natural selection on genetic variation at imprinted loci have previously been examined in a several population-genetic models. Here we expand the existing one-locus, two-allele population-genetic models of viability selection with genomic imprinting to include sex-limited imprinting, i.e., imprinted expression occurring only in one sex, and differential viability between the sexes. We first consider models of complete inactivation of either parental allele and these models are subsequently generalized to incorporate differential expression. Stable polymorphic equilibrium was possible without heterozygote advantage as observed in some prior models of imprinting in both sexes. In contrast to these latter models, in the sex-limited case it was critical whether the paternally inherited or maternally inherited allele was inactivated. The parental origin of inactivated alleles had a different impact on how the population responded to the different selection pressures between the sexes. Under the same fitness parameters, imprinting in the other sex altered the number of possible equilibrium states and their stability. When the parental origin of imprinted alleles and the sex in which they are inactive differ, an allele cannot be inactivated in consecutive generations. The system dynamics became more complex with more equilibrium points emerging. Our results show that selection can interact with epigenetic factors to maintain genetic variation in previously unanticipated ways. Copyright © 2017 Elsevier Inc. All rights reserved.

Distributed Synchronization in Communication Networks

DTIC Science & Technology

2018-01-24

synchronization. Secondly, it is known that identical oscillators with sin() coupling functions are guaranteed to synchronize in phase on a complete...provide sufficient conditions for phase- locking , i.e., convergence to a stable equilibrium almost surely. We additionally find conditions when the

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.

There and back again: Two views on the protein folding puzzle.

PubMed

Finkelstein, Alexei V; Badretdin, Azat J; Galzitskaya, Oxana V; Ivankov, Dmitry N; Bogatyreva, Natalya S; Garbuzynskiy, Sergiy O

2017-07-01

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured folding times of single-domain globular proteins range from microseconds to hours: the difference (10-11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the universe. This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: "U-to-N" and "N-to-U". In the theory of protein folding rates a special role is played by the point of thermodynamic (and kinetic) equilibrium between the native and unfolded state of the chain; here, the theory obtains the simplest form. Paradoxically, a theoretical estimate of the folding time is easier to get from consideration of protein unfolding (the "N-to-U" transition) rather than folding, because it is easier to outline a good unfolding pathway of any structure than a good folding pathway that leads to the stable fold, which is yet unknown to the folding protein chain. And since the rates of direct and reverse reactions are equal at the equilibrium point (as follows from the physical "detailed balance" principle), the estimated folding time can be derived from the estimated unfolding time. Theoretical analysis of the "N-to-U" transition outlines the range of protein folding rates in a good agreement with experiment. Theoretical analysis of folding (the "U-to-N" transition), performed at the level of formation and assembly of protein secondary structures, outlines the upper limit of protein folding times (i.e., of the time of search for the most stable fold). Both theories come to essentially the same results; this is not a surprise, because they describe overcoming one and the same free-energy barrier, although the way to the top of this barrier from the side of the unfolded state is very different from the way from the side of the native state; and both theories agree with experiment. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control and explain the observed maximal size of the "foldable" protein domains. Copyright © 2017 Elsevier B.V. All rights reserved.

There and back again: Two views on the protein folding puzzle

NASA Astrophysics Data System (ADS)

Finkelstein, Alexei V.; Badretdin, Azat J.; Galzitskaya, Oxana V.; Ivankov, Dmitry N.; Bogatyreva, Natalya S.; Garbuzynskiy, Sergiy O.

2017-07-01

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured folding times of single-domain globular proteins range from microseconds to hours: the difference (10-11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the universe. This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: ;U-to-N; and ;N-to-U;. In the theory of protein folding rates a special role is played by the point of thermodynamic (and kinetic) equilibrium between the native and unfolded state of the chain; here, the theory obtains the simplest form. Paradoxically, a theoretical estimate of the folding time is easier to get from consideration of protein unfolding (the ;N-to-U; transition) rather than folding, because it is easier to outline a good unfolding pathway of any structure than a good folding pathway that leads to the stable fold, which is yet unknown to the folding protein chain. And since the rates of direct and reverse reactions are equal at the equilibrium point (as follows from the physical ;detailed balance; principle), the estimated folding time can be derived from the estimated unfolding time. Theoretical analysis of the ;N-to-U; transition outlines the range of protein folding rates in a good agreement with experiment. Theoretical analysis of folding (the ;U-to-N; transition), performed at the level of formation and assembly of protein secondary structures, outlines the upper limit of protein folding times (i.e., of the time of search for the most stable fold). Both theories come to essentially the same results; this is not a surprise, because they describe overcoming one and the same free-energy barrier, although the way to the top of this barrier from the side of the unfolded state is very different from the way from the side of the native state; and both theories agree with experiment. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control and explain the observed maximal size of the ;foldable; protein domains.

Arctic Ocean Cyclostratigraphy: An Alternative to Marine Oxygen Isotope curves as measures of Cryospheric and Sea-Level History

NASA Astrophysics Data System (ADS)

Cronin, T. M.; Marzen, R.; O'Regan, M.; Dwyer, G. S.

2016-12-01

The stable isotope compositions of biogenic carbonates have been used for paleoceanographic and paleoclimatic reconstructions for decades, and produced some of the most iconic records in the field. However, we still lack a fully mechanistic understanding of the stable isotope proxies, especially the biological overprint on the environmental signals termed "vital effects". A ubiquitous feature of stable isotope vital effects in marine calcifying organisms is a strong correlation between δ18O and δ13C in a range of values that are depleted from equilibrium. Two mechanisms have been proposed to explain this correlation, one based on kinetic isotope effects during CO2(aq)-HCO3- inter-conversion, the other based on equilibrium isotope exchange during pH dependent speciation of the dissolved inorganic carbon pool. Neither mechanism explains all the stable isotope features observed in biogenic carbonates. Here we present a fully kinetic model of biomineralization and its isotope effects using deep sea corals as a test organism. A key component of our model is the consideration of the enzyme carbonic anhydrase in catalyzing the CO2(aq)-HCO3- inter-conversion reactions in the extracellular calcifying fluid (ECF). We find that the amount of carbonic anhydrase not only modulates the carbonate chemistry of the calcifying fluid, but also helps explain the slope of the δ18O-δ13C correlation. With this model, we are not only able to fit deep sea coral data, but also explain the stable isotope vital effects of other calcifying organisms. This fully kinetic model of stable isotope vital effects and the underlying calcification dynamics may also help us better understand mechanisms of other paleoceanographic tracers in biogenic carbonates, including boron isotopes and trace metal proxies.

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.

Applying the new HIT results to tokamak and solar plasmas

NASA Astrophysics Data System (ADS)

Jarboe, Thomas; Sutherland, Derek; Hossack, Aaron; Nelson, Brian; Morgan, Kyle; Chris, Hansen; Benedett, Thomas; Everson, Chris; Penna, James

2016-10-01

Understanding sustainment of stable equilibria with helicity injection in HIT-SI has led to a simple picture of several tokamak features. Perturbations cause a viscous-like force on the current that flattens the λ profile, which sustains and stabilizes the equilibrium. An explanation of the mechanism is based on two properties of stable, ideal, two-fluid, magnetized plasma. First, the electron fluid is frozen to magnetic fields and, therefore, current flow is also magnetic field flow. Second, for a stable equilibrium the structure perpendicular to the flux surface resists deformation. Thus toroidal current is from electrons frozen in nested, rotating resilient flux surfaces. Only symmetric flux surfaces allow free differential current flow. Perturbations cause interference of the flux surfaces. Thus, perturbations cause forces that oppose differential electron rotation and forced differential flow produces a symmetrizing force against perturbations and instability. This mechanism can explain the level of field error that spoils tokamak performance and the rate of poloidal flux loss in argon-induced disruptions in DIII-D. This new understanding has led to an explanation of the source of the solar magnetic fields and the power source for the chromosphere, solar wind and corona. Please place in spheromak and FRC section with other HIT posters.

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.

Entropic Description of Gas Hydrate Ice-Liquid Equilibrium via Enhanced Sampling of Coexisting Phases

NASA Astrophysics Data System (ADS)

Małolepsza, Edyta; Kim, Jaegil; Keyes, Tom

2015-05-01

Metastable β ice holds small guest molecules in stable gas hydrates, so its solid-liquid equilibrium is of interest. However, aqueous crystal-liquid transitions are very difficult to simulate. A new molecular dynamics algorithm generates trajectories in a generalized N P T ensemble and equilibrates states of coexisting phases with a selectable enthalpy. With replicas spanning the range between β ice and liquid water, we find the statistical temperature from the enthalpy histograms and characterize the transition by the entropy, introducing a general computational procedure for first-order transitions.

Entropic description of gas hydrate ice/liquid equilibrium via enhanced sampling of coexisting phases

DOE PAGES

Malolepsza, Edyta; Kim, Jaegil; Keyes, Tom

2015-04-28

Metastable β ice holds small guest molecules in stable gas hydrates, so its solid/liquid equilibrium is of interest. However, aqueous crystal/liquid transitions are very difficult to simulate. A new MD algorithm generates trajectories in a generalized NPT ensemble and equilibrates states of coexisting phases with a selectable enthalpy. Furthermore, with replicas spanning the range between β ice and liquid water we find the statistical temperature from the enthalpy histograms and characterize the transition by the entropy, introducing a general computational procedure for first-order transitions.

Erasing no-man’s land by thermodynamically stabilizing the liquid-liquid transition in tetrahedral particles

NASA Astrophysics Data System (ADS)

Smallenburg, Frank; Filion, Laura; Sciortino, Francesco

2014-09-01

One of the most controversial hypotheses for explaining the origin of the thermodynamic anomalies characterizing liquid water postulates the presence of a metastable second-order liquid-liquid critical point located in the `no-man’s land’. In this scenario, two liquids with distinct local structure emerge near the critical temperature. Unfortunately, as spontaneous crystallization is rapid in this region, experimental support for this hypothesis relies on significant extrapolations, either from the metastable liquid or from amorphous solid water. Although the liquid-liquid transition is expected to feature in many tetrahedrally coordinated liquids, including silicon, carbon and silica, even numerical studies of atomic and molecular models have been unable to conclusively prove the existence of this transition. Here we provide such evidence for a model in which it is possible to continuously tune the softness of the interparticle interaction and the flexibility of the bonds, the key ingredients controlling the existence of the critical point. We show that conditions exist where the full coexistence is thermodynamically stable with respect to crystallization. Our work offers a basis for designing colloidal analogues of water exhibiting liquid-liquid transitions in equilibrium, opening the way for experimental confirmation of the original hypothesis.

Variable threshold algorithm for division of labor analyzed as a dynamical system.

PubMed

Castillo-Cagigal, Manuel; Matallanas, Eduardo; Navarro, Iñaki; Caamaño-Martín, Estefanía; Monasterio-Huelin, Félix; Gutiérrez, Álvaro

2014-12-01

Division of labor is a widely studied aspect of colony behavior of social insects. Division of labor models indicate how individuals distribute themselves in order to perform different tasks simultaneously. However, models that study division of labor from a dynamical system point of view cannot be found in the literature. In this paper, we define a division of labor model as a discrete-time dynamical system, in order to study the equilibrium points and their properties related to convergence and stability. By making use of this analytical model, an adaptive algorithm based on division of labor can be designed to satisfy dynamic criteria. In this way, we have designed and tested an algorithm that varies the response thresholds in order to modify the dynamic behavior of the system. This behavior modification allows the system to adapt to specific environmental and collective situations, making the algorithm a good candidate for distributed control applications. The variable threshold algorithm is based on specialization mechanisms. It is able to achieve an asymptotically stable behavior of the system in different environments and independently of the number of individuals. The algorithm has been successfully tested under several initial conditions and number of individuals.

Theoretical investigation of flash vaporisation in a screw expander

NASA Astrophysics Data System (ADS)

Vasuthevan, Hanushan; Brümmer, Andreas

2017-08-01

In the present study flash vaporisation of liquid injection in a twin screw expander for a Trilateral Flash Cycle (TFC) is examined theoretically. The TFC process comprises a pressure increase in the working fluid, followed by heating the liquid close to boiling point. The hot liquid is injected into the working chamber of a screw expander. During this process the pressure of the liquid drops below the saturation pressure, while the temperature of the liquid remains virtually constant. Hence the liquid is superheated and in a metastable state. The liquid jet seeks to achieve a stable state in thermodynamic equilibrium and is therefore partially vaporised. This effect is referred to as flash vaporisation. Accordingly, a two-phase mixture, consisting of vapour and liquid, exists in the working chamber. Thermodynamic simulations were carried out using water as the working fluid for representative screw expander geometry. The simulations presented are performed from two different aspects during the filling process of a screw expander. The first case is the vaporisation of the injected liquid in a state of thermodynamic equilibrium, whereby the two-phase mixture is treated entirely as a compressible and homogeneous gas. The second case considers flashing efficiency. It describes the quantity of flashed vapour and consists of a liquid and vapour domain. Both models are compared and analysed with respect to the operational behaviour of a screw expander.

Equilibrium-Based Movement Endpoints Elicited from Primary Motor Cortex Using Repetitive Microstimulation

PubMed Central

Van Acker, Gustaf M.; Amundsen, Sommer L.; Messamore, William G.; Zhang, Hongyu Y.; Luchies, Carl W.

2014-01-01

High-frequency, long-duration intracortical microstimulation (HFLD-ICMS) is increasingly being used to deduce how the brain encodes coordinated muscle activity and movement. However, the full movement repertoire that can be elicited from the forelimb representation of primary motor cortex (M1) using this method has not been systematically determined. Our goal was to acquire a comprehensive M1 forelimb representational map of movement endpoints elicited with HFLD-ICMS, using stimulus parameters optimal for evoking stable forelimb spatial endpoints. The data reveal a 3D forelimb movement endpoint workspace that is represented in a patchwork fashion on the 2D M1 cortical surface. Although cortical maps of movement endpoints appear quite disorderly with respect to movement space, we show that the endpoint locations in the workspace evoked with HFLD-ICMS of two adjacent cortical points are closer together than would be expected if the organization were random. Although there were few obvious consistencies in the endpoint maps across the two monkeys tested, one notable exception was endpoints bringing the hand to the mouth, which was located at the boundary between the hand and face representation. Endpoints at the extremes of the monkey's workspace and locations above the head were largely absent. Our movement endpoints are best explained as resulting from coactivation of agonist and antagonist muscles driving the joints toward equilibrium positions determined by the length–tension relationships of the muscles. PMID:25411500

Assessment of the accuracy of plasma shape reconstruction by the Cauchy condition surface method in JT-60SA

NASA Astrophysics Data System (ADS)

Miyata, Y.; Suzuki, T.; Takechi, M.; Urano, H.; Ide, S.

2015-07-01

For the purpose of stable plasma equilibrium control and detailed analysis, it is essential to reconstruct an accurate plasma boundary on the poloidal cross section in tokamak devices. The Cauchy condition surface (CCS) method is a numerical approach for calculating the spatial distribution of the magnetic flux outside a hypothetical surface and reconstructing the plasma boundary from the magnetic measurements located outside the plasma. The accuracy of the plasma shape reconstruction has been assessed by comparing the CCS method and an equilibrium calculation in JT-60SA with a high elongation and triangularity of plasma shape. The CCS, on which both Dirichlet and Neumann conditions are unknown, is defined as a hypothetical surface located inside the real plasma region. The accuracy of the plasma shape reconstruction is sensitive to the CCS free parameters such as the number of unknown parameters and the shape in JT-60SA. It is found that the optimum number of unknown parameters and the size of the CCS that minimizes errors in the reconstructed plasma shape are in proportion to the plasma size. Furthermore, it is shown that the accuracy of the plasma shape reconstruction is greatly improved using the optimum number of unknown parameters and shape of the CCS, and the reachable reconstruction errors in plasma shape and locations of strike points are within the target ranges in JT-60SA.

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.

Population-level consequences of antipredator behavior: a metaphysiological model based on the functional ecology of the leaf-eared mouse.

PubMed

Ramos-Jiliberto, Rodrigo; González-Olivares, Eduardo; Bozinovic, Francisco

2002-08-01

We present a predator-prey metaphysiological model, based on the available behavioral and physiological information of the sigmodontine rodent Phyllotis darwini. The model is focused on the population-level consequences of the antipredator behavior, performed by the rodent population, which is assumed to be an inducible response of predation avoidance. The decrease in vulnerability is explicitly considered to have two associated costs: a decreasing foraging success and an increasing metabolic loss. The model analysis was carried out on a reduced form of the system by means of numerical and analytical tools. We evaluated the stability properties of equilibrium points in the phase plane, and carried out bifurcation analyses of rodent equilibrium density under varying conditions of three relevant parameters. The bifurcation parameters chosen represent predator avoidance effectiveness (A), foraging cost of antipredator behavior (C(1)'), and activity-metabolism cost (C(4)'). Our analysis suggests that the trade-offs involved in antipredator behavior plays a fundamental role in the stability properties of the system. Under conditions of high foraging cost, stability decreases as antipredator effectiveness increases. Under the complementary scenario (not considering the highest foraging costs), the equilibria are either stable when both costs are low, or unstable when both costs are higher, independent of antipredator effectiveness. No evidence of stabilizing effects of antipredator behavior was found. Copyright 2002 Elsevier Science (USA).

Report of 1,000 Hour Catalyst Longevity Evaluation

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

Daniel M. Ginosar

2009-06-01

This report presents the results of a 1,000 hour, high-pressure, catalyst longevity test for the decomposition of concentrated sulfuric acid. The reaction is used for both the sulfur-iodine (S-I) cycle and hybrid sulfur cycle. By the time of the delivery date of April 17, 2009, for project milestone no. 2NIN07TC050114, the 1% Pt/TiO2 catalyst had been in the reaction environment for 658 hours. During the first 480 hours of testing, the catalyst activity provided stable, near-equilibrium yields of 46.8% SO2 and 22.8% O2. However, product yields declined at sample exposure times >480 hours. At 658 hours of operation, catalyst activitymore » (based on oxygen yield) declined to 57% relative to the stable period of catalyst activity. Thus, as of April 17, this catalyst did not provide the desired stability level of <10% degradation per 1,000 hours. The experiment was terminated on April 27, after 792 hours, when a fitting failed and the catalyst was displaced from the reactor such that the sample could not be recovered. Oxygen conversion at the end of the experiment was 12.5% and declining, suggesting that at that point, catalyst activity had decreased to 54% of the initial level.« less

Neuronal networks with NMDARs and lateral inhibition implement winner-takes-all

PubMed Central

Shoemaker, Patrick A.

2015-01-01

A neural circuit that relies on the electrical properties of NMDA synaptic receptors is shown by numerical and theoretical analysis to be capable of realizing the winner-takes-all function, a powerful computational primitive that is often attributed to biological nervous systems. This biophysically-plausible model employs global lateral inhibition in a simple feedback arrangement. As its inputs increase, high-gain and then bi- or multi-stable equilibrium states may be assumed in which there is significant depolarization of a single neuron and hyperpolarization or very weak depolarization of other neurons in the network. The state of the winning neuron conveys analog information about its input. The winner-takes-all characteristic depends on the nonmonotonic current-voltage relation of NMDA receptor ion channels, as well as neural thresholding, and the gain and nature of the inhibitory feedback. Dynamical regimes vary with input strength. Fixed points may become unstable as the network enters a winner-takes-all regime, which can lead to entrained oscillations. Under some conditions, oscillatory behavior can be interpreted as winner-takes-all in nature. Stable winner-takes-all behavior is typically recovered as inputs increase further, but with still larger inputs, the winner-takes-all characteristic is ultimately lost. Network stability may be enhanced by biologically plausible mechanisms. PMID:25741276

New measurement technology for 'Critical Dynamics in Microgravity'

NASA Astrophysics Data System (ADS)

Duncan, Robert

2000-03-01

When driven away from equilibrium by a heat flux Q, the superfluid transition in ^4He evolves from a simple critical point into a fascinating and complex nonlinear region, where the onset of macroscopic quantum order is masked by Earth's gravity. Prior measurements of heat transport within this nonlinear region on Earth (and scheduled measurements on the International Space Station) require temperature resolution to 0.1 nK at 2.2 K in an exceptionally stable thermometer, with all heat flow stable to 3 fW/s. These measurements of the liquid helium temperature must be localized along the side of the experimental cell with a spatial resolution of 5 microns, and systematic offsets of the measured temperature from the true helium temperature must be controlled to within 0.3 nK. Such measurement technology has recently been developed, out-performing these demanding requirements by a comfortable margin. A new class of fundamental physics experiments may be facilitated by these recent advances in metrology. This work has been supported by the Microgravity Science Division of NASA, conducted in cooperation with JPL, and in collaboration with Mary Jayne Adriaans, Alex Babkin, S.T.P. Boyd, Peter Day, David Elliott, Beverly Klemme, T.D. McCarson, Ray Nelson, and Dmitri Sergatskov.

Order and chaos in the one-dimensional ϕ4 model: N-dependence and the Second Law of Thermodynamics

NASA Astrophysics Data System (ADS)

Hoover, William Graham; Aoki, Kenichiro

2017-08-01

We revisit the equilibrium one-dimensional ϕ4 model from the dynamical systems point of view. We find an infinite number of periodic orbits which are computationally stable. At the same time some of the orbits are found to exhibit positive Lyapunov exponents! The periodic orbits confine every particle in a periodic chain to trace out either the same or a mirror-image trajectory in its two-dimensional phase space. These ;computationally stable; sets of pairs of single-particle orbits are either symmetric or antisymmetric to the very last computational bit. In such a periodic chain the odd-numbered and even-numbered particles' coordinates and momenta are either identical or differ only in sign. ;Positive Lyapunov exponents; can and do result if an infinitesimal perturbation breaking a perfect two-dimensional antisymmetry is introduced so that the motion expands into a four-dimensional phase space. In that extended space a positive exponent results. We formulate a standard initial condition for the investigation of the microcanonical chaotic number dependence of the model. We speculate on the uniqueness of the model's chaotic sea and on the connection of such collections of deterministic and time-reversible states to the Second Law of Thermodynamics.

Elevated nonlinearity as an indicator of shifts in the dynamics of populations under stress.

PubMed

Dakos, Vasilis; Glaser, Sarah M; Hsieh, Chih-Hao; Sugihara, George

2017-03-01

Populations occasionally experience abrupt changes, such as local extinctions, strong declines in abundance or transitions from stable dynamics to strongly irregular fluctuations. Although most of these changes have important ecological and at times economic implications, they remain notoriously difficult to detect in advance. Here, we study changes in the stability of populations under stress across a variety of transitions. Using a Ricker-type model, we simulate shifts from stable point equilibrium dynamics to cyclic and irregular boom-bust oscillations as well as abrupt shifts between alternative attractors. Our aim is to infer the loss of population stability before such shifts based on changes in nonlinearity of population dynamics. We measure nonlinearity by comparing forecast performance between linear and nonlinear models fitted on reconstructed attractors directly from observed time series. We compare nonlinearity to other suggested leading indicators of instability (variance and autocorrelation). We find that nonlinearity and variance increase in a similar way prior to the shifts. By contrast, autocorrelation is strongly affected by oscillations. Finally, we test these theoretical patterns in datasets of fisheries populations. Our results suggest that elevated nonlinearity could be used as an additional indicator to infer changes in the dynamics of populations under stress. © 2017 The Author(s).

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

Price game and chaos control among three oligarchs with different rationalities in property insurance market.

PubMed

Ma, Junhai; Zhang, Junling

2012-12-01

Combining with the actual competition in Chinese property insurance market and assuming that the property insurance companies take the marginal utility maximization as the basis of decision-making when they play price games, we first established the price game model with three oligarchs who have different rationalities. Then, we discussed the existence and stability of equilibrium points. Third, we studied the theoretical value of Lyapunov exponent at Nash equilibrium point and its change process with the main parameters' changes though having numerical simulation for the system such as the bifurcation, chaos attractors, and so on. Finally, we analyzed the influences which the changes of different parameters have on the profits and utilities of oligarchs and their corresponding competition advantage. Based on this, we used the variable feedback control method to control the chaos of the system and stabilized the chaos state to Nash equilibrium point again. The results have significant theoretical and practical application value.

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.

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.

Price game and chaos control among three oligarchs with different rationalities in property insurance market

NASA Astrophysics Data System (ADS)

Ma, Junhai; Zhang, Junling

2012-12-01

Combining with the actual competition in Chinese property insurance market and assuming that the property insurance companies take the marginal utility maximization as the basis of decision-making when they play price games, we first established the price game model with three oligarchs who have different rationalities. Then, we discussed the existence and stability of equilibrium points. Third, we studied the theoretical value of Lyapunov exponent at Nash equilibrium point and its change process with the main parameters' changes though having numerical simulation for the system such as the bifurcation, chaos attractors, and so on. Finally, we analyzed the influences which the changes of different parameters have on the profits and utilities of oligarchs and their corresponding competition advantage. Based on this, we used the variable feedback control method to control the chaos of the system and stabilized the chaos state to Nash equilibrium point again. The results have significant theoretical and practical application value.

Surface thermodynamic analysis of fluid confined in a cone and comparison with the sphere-plate and plate-plate geometries.

PubMed

Zargarzadeh, Leila; Elliott, Janet A W

2013-10-22

The behavior of pure fluid confined in a cone is investigated using thermodynamic stability analysis. Four situations are explained on the basis of the initial confined phase (liquid/vapor) and its pressure (above/below the saturation pressure). Thermodynamic stability analysis (a plot of the free energy of the system versus the size of the new potential phase) reveals whether the phase transition is possible and, if so, the number and type (unstable/metastable/stable) of equilibrium states in each of these situations. Moreover we investigated the effect of the equilibrium contact angle and the cone angle (equivalent to the confinement's surface separation distance) on the free energy (potential equilibrium states). The results are then compared to our previous study of pure fluid confined in the gap between a sphere and a flat plate and the gap between two flat plates.1 Confined fluid behavior of the four possible situations (for these three geometries) can be explained in a unified framework under two categories based on only the meniscus shape (concave/convex). For systems with bulk-phase pressure imposed by a reservoir, the stable coexistence of pure liquid and vapor is possible only when the meniscus is concave.

Spin Polarization Transfer from a Photogenerated Radical Ion Pair to a Stable Radical Controlled by Charge Recombination.

PubMed

Horwitz, Noah E; Phelan, Brian T; Nelson, Jordan N; Mauck, Catherine M; Krzyaniak, Matthew D; Wasielewski, Michael R

2017-06-15

Photoexcitation of electron donor-acceptor molecules frequently produces radical ion pairs with well-defined initial spin-polarized states that have attracted significant interest for spintronics. Transfer of this initial spin polarization to a stable radical is predicted to depend on the rates of the radical ion pair recombination reactions, but this prediction has not been tested experimentally. In this study, a stable radical/electron donor/chromophore/electron acceptor molecule, BDPA • -mPD-ANI-NDI, where BDPA • is α,γ-bisdiphenylene-β-phenylallyl, mPD is m-phenylenediamine, ANI is 4-aminonaphthalene-1,8-dicarboximide, and NDI is naphthalene-1,4:5,8-bis(dicarboximide), was synthesized. Photoexcitation of ANI produces the triradical BDPA • -mPD +• -ANI-NDI -• in which the mPD +• -ANI-NDI -• radical ion pair is spin coupled to the BDPA • stable radical. BDPA • -mPD +• -ANI-NDI -• and its counterpart lacking the stable radical are found to exhibit spin-selective charge recombination in which the triplet radical ion pair 3 (mPD +• -ANI-NDI -• ) is in equilibrium with the 3 *NDI charge recombination product. Time-resolved EPR measurements show that this process is associated with an inversion of the sign of the polarization transferred to BDPA • over time. The polarization transfer rates are found to be strongly solvent dependent, as shifts in this equilibrium affect the spin dynamics. These results demonstrate that even small changes in electron transfer dynamics can have a large effect on the spin dynamics of photogenerated multispin systems.

Detecting animal by-product intake using stable isotope ratio mass spectrometry (IRMS).

PubMed

da Silva, D A F; Biscola, N P; Dos Santos, L D; Sartori, M M P; Denadai, J C; da Silva, E T; Ducatti, C; Bicudo, S D; Barraviera, B; Ferreira, R S

2016-11-01

Sheep are used in many countries as food and for manufacturing bioproducts. However, when these animals consume animal by-products (ABP), which is widely prohibited, there is a risk of transmitting scrapie - a fatal prion disease in human beings. Therefore, it is essential to develop sensitive methods to detect previous ABP intake to select safe animals for producing biopharmaceuticals. We used stable isotope ratio mass spectrometry (IRMS) for 13 C and 15 N to trace animal proteins in the serum of three groups of sheep: 1 - received only vegetable protein (VP) for 89 days; 2 - received animal and vegetable protein (AVP); and 3 - received animal and vegetable protein with animal protein subsequently removed (AVPR). Groups 2 and 3 received diets with 30% bovine meat and bone meal (MBM) added to a vegetable diet (from days 16-89 in the AVP group and until day 49 in the AVPR group, when MBM was removed). The AVPR group showed 15 N equilibrium 5 days after MBM removal (54th day). Conversely, 15 N equilibrium in the AVP group occurred 22 days later (76th day). The half-life differed between these groups by 3.55 days. In the AVPR group, 15 N elimination required 53 days, which was similar to this isotope's incorporation time. Turnover was determined based on natural 15 N signatures. IRMS followed by turnover calculations was used to evaluate the time period for the incorporation and elimination of animal protein in sheep serum. The δ 13 C and δ 15 N values were used to track animal protein in the diet. This method is biologically and economically relevant for the veterinary field because it can track protein over time or make a point assessment of animal feed with high sensitivity and resolution, providing a low-cost analysis coupled with fast detection. Isotopic profiles could be measured throughout the experimental period, demonstrating the potential to use the method for traceability and certification assessments. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

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.

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.

Dynamic analysis of a hepatitis B model with three-age-classes

NASA Astrophysics Data System (ADS)

Zhang, Suxia; Zhou, Yicang

2014-07-01

Based on the fact that the likelihood of becoming chronically infected is dependent on age at primary infection Kane (1995) [2], Edmunds et al. (1993) [3], Medley et al. (2001) [4], and Ganem and Prince (2004) [6], we formulate a hepatitis B transmission model with three age classes. The reproduction number, R0 is defined and the dynamical behavior of the model is analyzed. It is proved that the disease-free equilibrium is globally stable if R0<1, and there exists at least one endemic equilibrium and that the disease is uniformly persistent if R0>1. The unique endemic equilibrium and its global stability is obtained in a special case. Simulations are also conducted to compare the dynamical behavior of the model with and without age classes.

The stability of lawsonite and zoisite at high pressures: Experiments in CASH to 92 kbar and implications for the presence of hydrous phases in subducted lithosphere

NASA Astrophysics Data System (ADS)

Schmidt, Max W.; Poli, Stefano

1994-06-01

The breakdown reactions of lawsonite in SiO2 + H2O- and in Al2O3 + H2O-saturated synthetic CASH systems were examined between 17 and 92 kbar in both forward and reversed experiments. Lawsonite is stable to 565 C at 20 kbar, 760 C at 40 kbar, and 980 C at 65 kbar. In this pressure range lawsonite breaks down to zoisite + kyanite + quartz/ coesite + H2O. An invariant point occurs at 1000 C, 67 kbar. At higher pressures lawsonite breaks down to the assemblage grossular + kyanite + coesite + H20. The steep positive dP/dT slope of this higher pressure breakdown reaction becomes steeply negative when coesite transforms to stishovite. At 92 kbar, the highest pressure investigated, lawsonite is stable to 1040 C. The invariant point marks also the pressure stability limit of zoisite since zoisite reacts to lawsonite + grossular + kyanite + coesite (at temperatures below 1000 C), to grossular + kyanite + coesite + H2O (1000-1040 C) and to grossular + kyanite + melt + H20 (above 1040C). These three reactions have a flat Clapeyron slope, and they locate the maximum pressure stability of zoisite between 65 and 68 kbar (between 800 and 1200 C). Eutectic melting in the SiO2 + H2O-saturated CASH system occurs for the assemblage zoisite + kyanite + coesite + H2O at temperatures approximately 100 C (at 40 kbar) to 40 C (at 65 kbar) higher than the lawsonite breakdown reaction. In the Al2O3+H2O-saturated system the reaction lawsonite + diaspore/corundum = zoisite + kyanite + H2O limits the stability of lawsonite. The diaspore = corundum + H2O equilibrium is found to be located about 50 C lower than predicted by previous studies. The equilibrium boundaries of the reactions between 17 and 38 kbar from both SiO2+H2O- and Al2O3 + H2O-saturated chemical systems were used to improve the thermochemical data on lawsonite. Two sets of thermodynamic properties internally consistent with the databases of both Berman and Holland and Powell, and also consistent with most previous experimental studies, were calculated employing the technique of linear programming (for Berman's data) and a least-squares fit procedure (for Holland and Powell's data). Because lawsonite is stable to 1040 C at 92 kbar, a temperature far higher than predicted by thermal modelling of subduction zones, it is expected to be stable in metabasalts and intermediate compositions (e.g., andesites and greywackes) subducted to depths exceeding 300 km. Lawsonite contains 11 wt% water in its structure, and is thus capable of transporting water deep into the mantle. Its breakdown would contribute significantly to the fluid budget of the slab and overlying mantle wedge. The experimental data in combination with thermal modelling studies indicate that a complete dehydration of the descending oceanic crust is unlikely to occur at shallow levels.

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).

Information dynamics in living systems: prokaryotes, eukaryotes, and cancer.

PubMed

Frieden, B Roy; Gatenby, Robert A

2011-01-01

Living systems use information and energy to maintain stable entropy while far from thermodynamic equilibrium. The underlying first principles have not been established. We propose that stable entropy in living systems, in the absence of thermodynamic equilibrium, requires an information extremum (maximum or minimum), which is invariant to first order perturbations. Proliferation and death represent key feedback mechanisms that promote stability even in a non-equilibrium state. A system moves to low or high information depending on its energy status, as the benefit of information in maintaining and increasing order is balanced against its energy cost. Prokaryotes, which lack specialized energy-producing organelles (mitochondria), are energy-limited and constrained to an information minimum. Acquisition of mitochondria is viewed as a critical evolutionary step that, by allowing eukaryotes to achieve a sufficiently high energy state, permitted a phase transition to an information maximum. This state, in contrast to the prokaryote minima, allowed evolution of complex, multicellular organisms. A special case is a malignant cell, which is modeled as a phase transition from a maximum to minimum information state. The minimum leads to a predicted power-law governing the in situ growth that is confirmed by studies measuring growth of small breast cancers. We find living systems achieve a stable entropic state by maintaining an extreme level of information. The evolutionary divergence of prokaryotes and eukaryotes resulted from acquisition of specialized energy organelles that allowed transition from information minima to maxima, respectively. Carcinogenesis represents a reverse transition: of an information maximum to minimum. The progressive information loss is evident in accumulating mutations, disordered morphology, and functional decline characteristics of human cancers. The findings suggest energy restriction is a critical first step that triggers the genetic mutations that drive somatic evolution of the malignant phenotype.

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.

Twin tubular pinch effect in curving confined flows

PubMed Central

Clime, Liviu; Morton, Keith J.; Hoa, Xuyen D.; Veres, Teodor

2015-01-01

Colloidal suspensions of buoyancy neutral particles flowing in circular pipes focus into narrow distributions near the wall due to lateral migration effects associated with fluid inertia. In curving flows, these distributions are altered by Dean currents and the interplay between Reynolds and Dean numbers is used to predict equilibrium positions. Here, we propose a new description of inertial lateral migration in curving flows that expands current understanding of both focusing dynamics and equilibrium distributions. We find that at low Reynolds numbers, the ratio δ between lateral inertial migration and Dean forces scales simply with the particle radius, coil curvature and pipe radius as . A critical value δc = 0.148 of this parameter is identified along with two related inertial focusing mechanisms. In the regime below δc, coined subcritical, Dean forces generate permanently circulating, twinned annuli, each with intricate equilibrium particle distributions including eyes and trailing arms. At δ > δc (supercritical regime) inertial lateral migration forces are dominant and particles focus to a single stable equilibrium position. PMID:25927878

Evolution of recombination rates in a multi-locus, haploid-selection, symmetric-viability model.

PubMed

Chasnov, J R; Ye, Felix Xiaofeng

2013-02-01

A fast algorithm for computing multi-locus recombination is extended to include a recombination-modifier locus. This algorithm and a linear stability analysis is used to investigate the evolution of recombination rates in a multi-locus, haploid-selection, symmetric-viability model for which stable equilibria have recently been determined. When the starting equilibrium is symmetric with two selected loci, we show analytically that modifier alleles that reduce recombination always invade. When the starting equilibrium is monomorphic, and there is a fixed nonzero recombination rate between the modifier locus and the selected loci, we determine analytical conditions for which a modifier allele can invade. In particular, we show that a gap exists between the recombination rates of modifiers that can invade and the recombination rate that specifies the lower stability boundary of the monomorphic equilibrium. A numerical investigation shows that a similar gap exists in a weakened form when the starting equilibrium is fully polymorphic but asymmetric. Copyright © 2012 Elsevier Inc. All rights reserved.

A Computational Study of the Rheology and Structure of Surfactant Covered Droplets

NASA Astrophysics Data System (ADS)

Maia, Joao; Boromand, Arman; Jamali, Safa

2015-11-01

The use of different types of surface-active agents is ubiquitous practice in different industrial applications ranging from cosmetic and food industries to polymeric nano-composite and blends. This allows stable multiphasic systems like foams and emulsions to be produced. Stability and shelf-life of those products are directly determined by the efficiency of the surfactant molecules. Although the effect of molecular configuration of the surface-active molecules on the planar interfaces has been studied both experimentally and computationally, it remains challenging to track the efficiency and effectiveness of different surfactant molecules on curved interfaces. In this study we address this gap by using Dissipative Particle Dynamics, to study the effectiveness and efficiency of different surfactant molecules (linear vs. branched) on a curved interface in equilibrium and far from equilibrium. In particular, we are interested to relate interfacial properties of the surface covered droplets and its dynamics to the molecular configuration of the surface active molecules under equilibrium and far from equilibrium condition.

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.

Identifying apparent local stable isotope equilibrium in a complex non-equilibrium system.

PubMed

He, Yuyang; Cao, Xiaobin; Wang, Jianwei; Bao, Huiming

2018-02-28

Although being out of equilibrium, biomolecules in organisms have the potential to approach isotope equilibrium locally because enzymatic reactions are intrinsically reversible. A rigorous approach that can describe isotope distribution among biomolecules and their apparent deviation from equilibrium state is lacking, however. Applying the concept of distance matrix in graph theory, we propose that apparent local isotope equilibrium among a subset of biomolecules can be assessed using an apparent fractionation difference (|Δα|) matrix, in which the differences between the observed isotope composition (δ') and the calculated equilibrium fractionation factor (1000lnβ) can be more rigorously evaluated than by using a previous approach for multiple biomolecules. We tested our |Δα| matrix approach by re-analyzing published data of different amino acids (AAs) in potato and in green alga. Our re-analysis shows that biosynthesis pathways could be the reason for an apparently close-to-equilibrium relationship inside AA families in potato leaves. Different biosynthesis/degradation pathways in tubers may have led to the observed isotope distribution difference between potato leaves and tubers. The analysis of data from green algae does not support the conclusion that AAs are further from equilibrium in glucose-cultured green algae than in the autotrophic ones. Application of the |Δα| matrix can help us to locate potential reversible reactions or reaction networks in a complex system such as a metabolic system. The same approach can be broadly applied to all complex systems that have multiple components, e.g. geochemical or atmospheric systems of early Earth or other planets. Copyright © 2017 John Wiley & Sons, Ltd.

Kinetic Equation for an Unstable Plasma

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

Balescu, R.

1963-01-01

A kinetic equation is derived for the description of the evolution in time of the distribution of velocities in a spatially homogeneous ionized gas that, at the initial time, is able to sustain exponentially growing oscillations. This equation is expressed in terms of a functional of the distribution finction that obeys the same integral equation as in the stable case. Although the method of solution used in the stable case breaks down, the equation can still be solved in closed form under unstable conditions, and hence an explicit form of the kinetic equation is obtained. The latter contains the normalmore » collision term and a new additional term describing the stabilization of the plasma. The latter acts through friction and diffusion and brings the plasma into a state of neutral stability. From there on the system evolves toward thermal equilibrium under the action of the normal collision term as well as of an additional Fokker-Planck- like term with timedependent coefficients, which however becomes less and less efficient as the plasma approaches equilibrium.« less

Suppression of Ostwald Ripening by Chemical Reactions

NASA Astrophysics Data System (ADS)

Zwicker, David; Hyman, Anthony A.; Jülicher, Frank

2015-03-01

Emulsions consisting of droplets immersed in a fluid are typically unstable and coarsen over time. One important coarsening process is Ostwald ripening, which is driven by the surface tension of the droplets. Ostwald ripening must thus be suppressed to stabilize emulsions, e.g. to control the properties of pharmaceuticals, food, or cosmetics. Suppression of Ostwald ripening is also important in biological cells, which contain stable liquid-like compartments, e.g. germ granules, Cajal-bodies, and centrosomes. Such systems are often driven away from equilibrium by chemical reactions and can thus be called active emulsions. Here, we show that non-equilibrium chemical reactions can suppress Ostwald Ripening, leading to stable, monodisperse emulsions. We derive analytical approximations of the typical droplet size, droplet count, and time scale of the dynamics from a coarse-grained description of the droplet dynamics. We also compare these results to numerical simulations of the continuous concentration fields. Generally, we thus show how chemical reactions can be used to stabilize emulsions and to control their properties in technology and nature.

Global threshold dynamics of an SIVS model with waning vaccine-induced immunity and nonlinear incidence.

PubMed

Yang, Junyuan; Martcheva, Maia; Wang, Lin

2015-10-01

Vaccination is the most effective method of preventing the spread of infectious diseases. For many diseases, vaccine-induced immunity is not life long and the duration of immunity is not always fixed. In this paper, we propose an SIVS model taking the waning of vaccine-induced immunity and general nonlinear incidence into consideration. Our analysis shows that the model exhibits global threshold dynamics in the sense that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable implying the disease dies out; while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable indicating that the disease persists. This global threshold result indicates that if the vaccination coverage rate is below a critical value, then the disease always persists and only if the vaccination coverage rate is above the critical value, the disease can be eradicated. Copyright © 2015 Elsevier Inc. All rights reserved.

Nucleation via an unstable intermediate phase.

PubMed

Sear, Richard P

2009-08-21

The pathway for crystallization from dilute vapors and solutions is often observed to take a detour via a liquid or concentrated-solution phase. For example, in moist subzero air, droplets of liquid water form, which then freeze. In this example and in many others, an intermediate phase (here liquid water) is dramatically accelerating the kinetics of a phase transition between two other phases (water vapor and ice). Here we study this phenomenon via exact computer simulations of a simple lattice model. Surprisingly, we find that the rate of nucleation of the new equilibrium phase is actually fastest when the intermediate phase is slightly unstable in the bulk, i.e., has a slightly higher free energy than the phase we start in. Nucleation occurs at a concave part of the surface and microscopic amounts of the intermediate phase can form there even before the phase is stable in the bulk. As the nucleus of the equilibrium phase is microscopic, this allows nucleation to occur effectively in the intermediate phase before it is stable in the bulk.

The anhysteretic polarisation of ferroelectrics

NASA Astrophysics Data System (ADS)

Kaeswurm, B.; Segouin, V.; Daniel, L.; Webber, K. G.

2018-02-01

Measurement and calculation of anhysteretic curves is a well-established method in the field of magnetic materials and is applied to ferroelectric materials here. The anhysteretic curve is linked to a stable equilibrium state in the domain structure, and ignores dissipative effects related to mechanisms such as domain wall pinning. In this study, an experimental method for characterising the anhysteretic behaviour of ferroelectrics is presented, which is subsequently used to determine the anhysteretic polarisation response of polycrystalline barium titanate and a doped lead zirconate titanate composition at room temperature. Various external parameters, such as electric field, stress, and temperature, can significantly affect ferroelectric behaviour. Ferroelectric hysteresis curves can assess the importance of such effects but cannot distinguish their contribution on the different intrinsic and extrinsic mechanisms involved in ferroelectric behaviour. In this work, the influence of compressive stress on the anhysteretic polarisation is measured and discussed. The comparison of the polarization loop to the anhysteretic curve under compressive stress elucidates the effects on the stable equilibrium domain configuration and dynamic effects associated to dissipation.

Thermodynamics, stability and Hawking-Page transition of Kerr black holes from Rényi statistics

NASA Astrophysics Data System (ADS)

Czinner, Viktor G.; Iguchi, Hideo

2017-12-01

Thermodynamics of rotating black holes described by the Rényi formula as equilibrium and zeroth law compatible entropy function is investigated. We show that similarly to the standard Boltzmann approach, isolated Kerr black holes are stable with respect to axisymmetric perturbations in the Rényi model. On the other hand, when the black holes are surrounded by a bath of thermal radiation, slowly rotating black holes can also be in stable equilibrium with the heat bath at a fixed temperature, in contrast to the Boltzmann description. For the question of possible phase transitions in the system, we show that a Hawking-Page transition and a first order small black hole/large black hole transition occur, analogous to the picture of rotating black holes in AdS space. These results confirm the similarity between the Rényi-asymptotically flat and Boltzmann-AdS approaches to black hole thermodynamics in the rotating case as well. We derive the relations between the thermodynamic parameters based on this correspondence.

Localization and Symmetry Breaking in the Quantum Quasiperiodic Ising Glass

NASA Astrophysics Data System (ADS)

Chandran, A.; Laumann, C. R.

2017-07-01

Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. In this article, we show that such systems can exhibit dynamically stable long-range orders forbidden in equilibrium. Specifically, we show that the interplay of symmetry breaking and localization in the quasiperiodic quantum Ising chain produces a quasiperiodic Ising glass stable at all energy densities. The glass order parameter vanishes with an essential singularity at the melting transition with no signatures in the equilibrium properties. The zero-temperature phase diagram is also surprisingly rich, consisting of paramagnetic, ferromagnetic, and quasiperiodically alternating ground-state phases with extended, localized, and critically delocalized low-energy excitations. The system exhibits an unusual quantum Ising transition whose properties are intermediate between those of the clean and infinite randomness Ising transitions. Many of these results follow from a geometric generalization of the Aubry-André duality that we develop. The quasiperiodic Ising glass may be realized in near-term quantum optical experiments.

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

PubMed

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

2001-02-01

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

Once more on the equilibrium-point hypothesis (lambda model) for motor control.

PubMed

Feldman, A G

1986-03-01

The equilibrium control hypothesis (lambda model) is considered with special reference to the following concepts: (a) the length-force invariant characteristic (IC) of the muscle together with central and reflex systems subserving its activity; (b) the tonic stretch reflex threshold (lambda) as an independent measure of central commands descending to alpha and gamma motoneurons; (c) the equilibrium point, defined in terms of lambda, IC and static load characteristics, which is associated with the notion that posture and movement are controlled by a single mechanism; and (d) the muscle activation area (a reformulation of the "size principle")--the area of kinematic and command variables in which a rank-ordered recruitment of motor units takes place. The model is used for the interpretation of various motor phenomena, particularly electromyographic patterns. The stretch reflex in the lambda model has no mechanism to follow-up a certain muscle length prescribed by central commands. Rather, its task is to bring the system to an equilibrium, load-dependent position. Another currently popular version defines the equilibrium point concept in terms of alpha motoneuron activity alone (the alpha model). Although the model imitates (as does the lambda model) spring-like properties of motor performance, it nevertheless is inconsistent with a substantial data base on intact motor control. An analysis of alpha models, including their treatment of motor performance in deafferented animals, reveals that they suffer from grave shortcomings. It is concluded that parameterization of the stretch reflex is a basis for intact motor control. Muscle deafferentation impairs this graceful mechanism though it does not remove the possibility of movement.

Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks

DOE PAGES

Kostova, Tanya

2010-07-09

We present and analyze a discrete-time susceptible-infected epidemic network model which represents each host as a separate entity and allows heterogeneous hosts and contacts. We establish a necessary and sufficient condition for global stability of the disease-free equilibrium of the system (defined as epidemic controllability) which defines the epidemic reproduction number of the network. When this condition is not fulfilled, we show that the system has a unique, locally stable equilibrium. As a result, we further derive sufficient conditions for epidemic controllability in terms of the epidemic rates and the network topology.

Bifurcation analysis of dengue transmission model in Baguio City, Philippines

NASA Astrophysics Data System (ADS)

Libatique, Criselda P.; Pajimola, Aprimelle Kris J.; Addawe, Joel M.

2017-11-01

In this study, we formulate a deterministic model for the transmission dynamics of dengue fever in Baguio City, Philippines. We analyzed the existence of the equilibria of the dengue model. We computed and obtained conditions for the existence of the equilibrium states. Stability analysis for the system is carried out for disease free equilibrium. We showed that the system becomes stable under certain conditions of the parameters. A particular parameter is taken and with the use of the Theory of Centre Manifold, the proposed model demonstrates a bifurcation phenomenon. We performed numerical simulation to verify the analytical results.

Equilibriumizing all food chain chaos through reproductive efficiency.

PubMed

Deng, Bo

2006-12-01

The intraspecific interference of a top-predator is incorporated into a classical mathematical model for three-trophic food chains. All chaos types known to the classical model are shown to exist for this comprehensive model. It is further demonstrated that if the top-predator reproduces at high efficiency, then all chaotic dynamics will change to a stable coexisting equilibrium, a novel property not found in the classical model. This finding gives a mechanistic explanation to the question of why food chain chaos is rare in the field. It also suggests that high reproductive efficiency of top-predators tends to stabilize food chains.

Analysis of current-driven oscillatory dynamics of single-layer homoepitaxial islands on crystalline conducting substrates

NASA Astrophysics Data System (ADS)

Dasgupta, Dwaipayan; Kumar, Ashish; Maroudas, Dimitrios

2018-03-01

We report results of a systematic study on the complex oscillatory current-driven dynamics of single-layer homoepitaxial islands on crystalline substrate surfaces and the dependence of this driven dynamical behavior on important physical parameters, including island size, substrate surface orientation, and direction of externally applied electric field. The analysis is based on a nonlinear model of driven island edge morphological evolution that accounts for curvature-driven edge diffusion, edge electromigration, and edge diffusional anisotropy. Using a linear theory of island edge morphological stability, we calculate a critical island size at which the island's equilibrium edge shape becomes unstable, which sets a lower bound for the onset of time-periodic oscillatory dynamical response. Using direct dynamical simulations, we study the edge morphological dynamics of current-driven single-layer islands at larger-than-critical size, and determine the actual island size at which the migrating islands undergo a transition from steady to time-periodic asymptotic states through a subcritical Hopf bifurcation. At the highest symmetry of diffusional anisotropy examined, on {111} surfaces of face-centered cubic crystalline substrates, we find that more complex stable oscillatory states can be reached through period-doubling bifurcation at island sizes larger than those at the Hopf points. We characterize in detail the island morphology and dynamical response at the stable time-periodic asymptotic states, determine the range of stability of these oscillatory states terminated by island breakup, and explain the morphological features of the stable oscillating islands on the basis of linear stability theory.

Aero-thermo-dynamic analysis of a low ballistic coefficient deployable capsule in Earth re-entry

NASA Astrophysics Data System (ADS)

Zuppardi, G.; Savino, R.; Mongelluzzo, G.

2016-10-01

The paper deals with a microsatellite and the related deployable recovery capsule. The aero-brake is folded at launch and deployed in space and is able to perform a de-orbiting controlled re-entry. This kind of capsule, with a flexible, high temperature resistant fabric, thanks to its lightness and modulating capability, can be an alternative to the current ;conventional; recovery capsules. The present authors already analyzed the trajectory and the aerodynamic behavior of low ballistic coefficient capsules during Earth re-entry and Mars entry. In previous studies, aerodynamic longitudinal stability analysis and evaluation of thermal and aerodynamic loads for a possible suborbital re-entry demonstrator were carried out in both continuum and rarefied regimes. The present study is aimed at providing preliminary information about thermal and aerodynamic loads and longitudinal stability for a similar deployable capsule, as well as information about the electronic composition of the plasma sheet and its possible influence on radio communications at the altitudes where GPS black-out could occur. Since the computer tests were carried out at high altitudes, therefore in rarefied flow fields, use of Direct Simulation Monte Carlo codes was mandatory. The computations involved both global aerodynamic quantities (drag and longitudinal moment coefficients) and local aerodynamic quantities (heat flux and pressure distributions along the capsule surface). The results verified that the capsule at high altitude (150 km) is self-stabilizing; it is stable around the nominal attitude or at zero angle of attack and unstable around the reverse attitude or at 180° angle of attack. The analysis also pointed out the presence of extra statically stable equilibrium trim points.

Collective Modes of Dust Helical Clusters

NASA Astrophysics Data System (ADS)

Tsytovich, V. N.; Gousein-Zade, N. G.; Morfill, G. E.

2005-10-01

The helical structures are the simplest 3D crystal-like cylindrical structures with radius R being a system of 2D clusters equally separated along the cylindrical axis with a relative rotation on constant angle φ0. For mean free path for grain charging much larger than the separation of the grains, the total energy of grain interaction is a sum of all pair grain interactions. The helical structures have been found experimentally for ions in laser traps in cylindrical gas discharges at very low temperatures (in both case as ``warms''). The equilibrium criterion and the criteria of stability including the absence of saddle points show that in the plane ρ, φ the bifurcation points are often present with new branches appearing (stable and unstable). Numerical MD simulations show that for cylindrical symmetry any random distributions of grains is developing into helical structures. The theory of collective modes of helical structures is developed for arbitrary grain interactions. The dispersion relation for frequencies of the collective modes for different branches of helical structures is derived and solved numerically for interaction including different type of screened grain potentials including the grain attraction. The dispersion relation in the first Brillouin zone for the square of the frequency ω2 is shown to be a be-cubic equation and gives the square of frequency ω2 > 0 for stable modes and the square of the growth rates for the unstable modes ω2 < 0. Modes for helical structures in parabolic external confining potential well perpendicular to cylindrical axis are found. Stabile self-confined structures without external confinement are discovered in presence of both non-collective and collective grain attractions.

Stability and Hopf bifurcation of a delayed ratio-dependent predator-prey system

NASA Astrophysics Data System (ADS)

Wang, Wan-Yong; Pei, Li-Jun

2011-04-01

Since the ratio-dependent theory reflects the fact that predators must share and compete for food, it is suitable for describing the relationship between predators and their preys and has recently become a very important theory put forward by biologists. In order to investigate the dynamical relationship between predators and their preys, a so-called Michaelis-Menten ratio-dependent predator-prey model is studied in this paper with gestation time delays of predators and preys taken into consideration. The stability of the positive equilibrium is investigated by the Nyquist criteria, and the existence of the local Hopf bifurcation is analyzed by employing the theory of Hopf bifurcation. By means of the center manifold and the normal form theories, explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. The above theoretical results are validated by numerical simulations with the help of dynamical software WinPP. The results show that if both the gestation delays are small enough, their sizes will keep stable in the long run, but if the gestation delays of predators are big enough, their sizes will periodically fluctuate in the long term. In order to reveal the effects of time delays on the ratio-dependent predator-prey model, a ratio-dependent predator-prey model without time delays is considered. By Hurwitz criteria, the local stability of positive equilibrium of this model is investigated. The conditions under which the positive equilibrium is locally asymptotically stable are obtained. By comparing the results with those of the model with time delays, it shows that the dynamical behaviors of ratio-dependent predator-prey model with time delays are more complicated. Under the same conditions, namely, with the same parameters, the stability of positive equilibrium of ratio-dependent predator-prey model would change due to the introduction of gestation time delays for predators and preys. Moreover, with the variation of time delays, the positive equilibrium of the ratio-dependent predator-prey model subjects to Hopf bifurcation.

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.

Half-Heusler Alloys as Promising Thermoelectric Materials

NASA Astrophysics Data System (ADS)

Page, Alexander A.

This thesis describes Ph.D. research on the half-Heusler class of thermoelectric materials. Half-Heusler alloys are a versatile class of materials that have been studied for use in photovoltaics, phase change memory, and thermoelectric power generation. With respect to thermoelectric power generation, new approaches were recently developed in order to improve the thermoelectric figure of merit, ZT, of half-Heusler alloys. Two of the strategies discussed in this work are adding excess Ni within MNiSn (M = Ti, Zr, or Hf) compounds to form full-Heusler nanostructures and using isoelectronic substitution of Ti, Zr, and Hf in MNiSn compounds to create microscale grain boundaries. This work uses computational simulations based on density functional theory, combined with the cluster expansion method, to predict the stable phases of pseudo-binary and pseudo-ternary composition systems. Statistical mechanics methods were used to calculate temperature-composition phase diagrams that relate the equilibrium phases. It is shown that full-Heusler nanostructures are predicted to remain stable even at high temperatures, and the microscale grain boundaries observed in (Ti,Zr,Hf)NiSn materials are found to be thermodynamically unstable at equilibrium. A new strategy of combining MNiSn materials with ZrNiPb has also recently emerged, and theoretical and experimental work show that a solid solution of the two materials is stable.

The feasibility and stability of large complex biological networks: a random matrix approach.

PubMed

Stone, Lewi

2018-05-29

In the 70's, Robert May demonstrated that complexity creates instability in generic models of ecological networks having random interaction matrices A. Similar random matrix models have since been applied in many disciplines. Central to assessing stability is the "circular law" since it describes the eigenvalue distribution for an important class of random matrices A. However, despite widespread adoption, the "circular law" does not apply for ecological systems in which density-dependence operates (i.e., where a species growth is determined by its density). Instead one needs to study the far more complicated eigenvalue distribution of the community matrix S = DA, where D is a diagonal matrix of population equilibrium values. Here we obtain this eigenvalue distribution. We show that if the random matrix A is locally stable, the community matrix S = DA will also be locally stable, providing the system is feasible (i.e., all species have positive equilibria D > 0). This helps explain why, unusually, nearly all feasible systems studied here are locally stable. Large complex systems may thus be even more fragile than May predicted, given the difficulty of assembling a feasible system. It was also found that the degree of stability, or resilience of a system, depended on the minimum equilibrium population.

Model for capping of membrane receptors based on boundary surface effects

PubMed Central

Gershon, N. D.

1978-01-01

Crosslinking of membrane surface receptors may lead to their segregation into patches and then into a single large aggregate at one pole of the cell. This process is called capping. Here, a novel explanation of such a process is presented in which the membrane is viewed as a supersaturated solution of receptors in the lipid bilayer and the adjacent two aqueous layers. Without a crosslinking agent, a patch of receptors that is less than a certain size cannot stay in equilibrium with the solution and thus should dissolve. Patches greater than a certain size are stable and can, in principle, grow by the precipitation of the remaining dissolved receptors from the supersaturated solution. The task of the crosslinking molecules is to form such stable patches. These considerations are based on a qualitative thermodynamic calculation that takes into account the existence of a boundary tension in a patch (in analogy to the surface tension of a droplet). Thermodynamically, these systems should cap spontaneously after the patches have reached a certain size. But, in practice, such a process can be very slow. A suspension of patches may stay practically stable. The ways in which a cell may abolish this metastable equilibrium and thus achieve capping are considered and possible effects of capping inhibitors are discussed. PMID:274724

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.

Analysis of Island Formation Due to RMPs in D3D Plasmas Using SIESTA

NASA Astrophysics Data System (ADS)

Hirshman, Steven; Shafer, Morgan; Seal, Sudip; Canik, John

2015-11-01

By varying the initial helical perturbation amplitude of Resonant Magnetic Perturbations (RMPs) applied to a Doublet III-D (DIII-D) plasma, a variety of meta-stable equilibrium are scanned using the SIESTA MHD equilibrium code. It is found that increasing the perturbation strength at the dominant m =2 resonant surface leads to lower MHD energies and significant increases in the equilibrium island widths at the m =2 (and sidebands) surfaces. Island overlap eventually leads to stochastic magnetic fields which correlate well with the experimentally inferred field line structure. The magnitude and spatial phase (around associated rational surfaces) of resonant (shielding) components of the parallel current is shown to be correlated with the magnetic island topology. Work supported by U.S. DOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

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.

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.

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

Nonlinear ballooning modes in tokamaks: stability and saturation

NASA Astrophysics Data System (ADS)

Ham, C. J.; Cowley, S. C.; Brochard, G.; Wilson, H. R.

2018-07-01

The nonlinear dynamics of magneto-hydrodynamic ballooning mode perturbations is conjectured to be characterised by the motion of isolated elliptical flux tubes. The theory of stability, dynamics and saturation of such tubes in tokamaks is developed using a generalised Archimedes’ principle. The equation of motion for a tube moving against a drag force in a general axisymmetric equilibrium is derived and then applied to a simplified ‘s–α’ equilibrium. The perturbed nonlinear tube equilibrium (saturated) states are investigated in an ‘s–α’ equilibrium with specific pressure and magnetic shear profiles. The energy of these nonlinear (ballooning) saturated states is calculated. In some cases, particularly at low magnetic shear, these finitely displaced states can have a lower energy than the equilibrium state even if the profile is linearly stable to ballooning modes (infinitesimal tube displacements) at all radii. Thus nonlinear ballooning modes can be metastable. The amplitude of the saturated tube displacement in such cases can be as large as the pressure gradient scale length. We conjecture that triggering a transition into these filamentary states can lead to hard instability limits. A short survey of different pressure profiles is presented to illustrate the variety of behaviour of perturbed elliptical flux tubes.

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.

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

Inertial migrations of cylindrical particles in rectangular microchannels: Variations of equilibrium positions and equivalent diameters

NASA Astrophysics Data System (ADS)

Su, Jinghong; Chen, Xiaodong; Hu, Guoqing

2018-03-01

Inertial migration has emerged as an efficient tool for manipulating both biological and engineered particles that commonly exist with non-spherical shapes in microfluidic devices. There have been numerous studies on the inertial migration of spherical particles, whereas the non-spherical particles are still largely unexplored. Here, we conduct three-dimensional direct numerical simulations to study the inertial migration of rigid cylindrical particles in rectangular microchannels with different width/height ratios under the channel Reynolds numbers (Re) varying from 50 to 400. Cylindrical particles with different length/diameter ratios and blockage ratios are also concerned. Distributions of surface force with the change of rotation angle show that surface stresses acting on the particle end near the wall are the major contributors to the particle rotation. We obtain lift forces experienced by cylindrical particles at different lateral positions on cross sections of two types of microchannels at various Re. It is found that there are always four stable equilibrium positions on the cross section of a square channel, while the stable positions are two or four in a rectangular channel, depending on Re. By comparing the equilibrium positions of cylindrical particles and spherical particles, we demonstrate that the equivalent diameter of cylindrical particles monotonously increases with Re. Our work indicates the influence of a non-spherical shape on the inertial migration and can be useful for the precise manipulation of non-spherical particles.

Weak interactions, omnivory and emergent food-web properties.

PubMed

Emmerson, Mark; Yearsley, Jon M

2004-02-22

Empirical studies have shown that, in real ecosystems, species-interaction strengths are generally skewed in their distribution towards weak interactions. Some theoretical work also suggests that weak interactions, especially in omnivorous links, are important for the local stability of a community at equilibrium. However, the majority of theoretical studies use uniform distributions of interaction strengths to generate artificial communities for study. We investigate the effects of the underlying interaction-strength distribution upon the return time, permanence and feasibility of simple Lotka-Volterra equilibrium communities. We show that a skew towards weak interactions promotes local and global stability only when omnivory is present. It is found that skewed interaction strengths are an emergent property of stable omnivorous communities, and that this skew towards weak interactions creates a dynamic constraint maintaining omnivory. Omnivory is more likely to occur when omnivorous interactions are skewed towards weak interactions. However, a skew towards weak interactions increases the return time to equilibrium, delays the recovery of ecosystems and hence decreases the stability of a community. When no skew is imposed, the set of stable omnivorous communities shows an emergent distribution of skewed interaction strengths. Our results apply to both local and global concepts of stability and are robust to the definition of a feasible community. These results are discussed in the light of empirical data and other theoretical studies, in conjunction with their broader implications for community assembly.

Equilibrium shapes and surface selection of nanostructures in 6H-SiC

DOE PAGES

Kondo, Sosuke; Parish, Chad M.; Koyanagi, Takaaki; ...

2017-04-03

Here, the equilibrium shape of 6H-SiC nanostructures and their surfaces were studied by analyzing nano-void (~10 nm) shapes, which were introduced in monocrystalline 6H-SiC by high-temperature neutron irradiation, using transmission electron microscopy. The nano-voids were determined to be irregular icosahedrons truncated with six {1¯100}, twelve {1¯103}, one smaller top-basal, and one larger bottom-basal planes, which suggests that {1¯100} and {1¯103} are the next stable surface class after the basal planes. The relatively frequent absence of the {1¯100} surface in the nano-voids indicated that the (1¯103¯) surface type is energetically rather stable. These non-basal surfaces were found not to be atomicallymore » flat due to the creation of nanofacets with half unit-cell height in the c-axis. The {1¯100} and {1¯103} surfaces were classified as two and four face types according to their possible nanofacets and surface termination, respectively. We also discuss the surface energy difference between the (1¯103¯) and (1¯103) face types in relation to the energy balance within the equilibrium, but irregular, polyhedron, in which the (1¯103) surface had double the surface energy of the (1¯103¯) surface (~3900 erg/cm 2).« less

Efficient ECH-assisted plasma start-up using trapped particle configuration in the versatile experiment spherical torus

NASA Astrophysics Data System (ADS)

An, YoungHwa; Lee, Jeongwon; Jo, JongGab; Jung, Bong-Ki; Lee, HyunYeong; Chung, Kyoung-Jae; Na, Yong-Su; Hahm, T. S.; Hwang, Y. S.

2017-01-01

An efficient and robust ECH (electron cyclotron heating)-assisted plasma start-up scheme with a low loop voltage and low volt-second consumption utilizing the trapped particle configuration (TPC) has been developed in the versatile experiment spherical torus (VEST). The TPC is a mirror-like magnetic field configuration providing a vertical magnetic field in the same direction as the equilibrium field. It significantly enhances ECH pre-ionization with enhanced particle confinement due to its mirror effect, and intrinsically provides an equilibrium field with a stable decay index enabling prompt plasma current initiation. Consequently, the formation of TPC before the onset of the loop voltage allows the plasma to start up with a lower loop voltage and lower volt-second consumption as well as a wider operation range in terms of ECH pre-ionization power and H2 filling pressure. The TPC can improve the widely-used field null configuration significantly for more efficient start-up when ECH pre-ionization is used. This can then be utilized in superconducting tokamaks requiring a low loop voltage start-up, such as ITER, or in spherical tori with limited volt-seconds. The TPC can be particularly useful in superconducting tokamaks with a limited current slew-rate of superconducting PF coils, as it can save volt-second consumption before plasma current initiation by providing prompt initiation with an intrinsic stable equilibrium field.

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.

Equilibrium modeling of 5-HT(2A) receptors with [18F]deuteroaltanserin and PET: feasibility of a constant infusion paradigm.

PubMed

van Dyck, C H; Soares, J C; Tan, P Z; Staley, J K; Baldwin, R M; Amici, L A; Fu, X; Garg, P K; Seibyl, J P; Charney, D S; Innis, R B

2000-11-01

[(18)F]Altanserin has emerged as a promising positron emission tomography (PET) ligand for serotonin-2A (5-HT(2A)) receptors. The deuterium substitution of both of the 2'-hydrogens of altanserin ([(18)F]deuteroaltanserin) yields a metabolically more stable radiotracer with higher ratios of parent tracer to radiometabolites and increased specific brain uptake than [(18)F]altanserin. The slower metabolism of the deuterated analog might preclude the possibility of achieving stable plasma and brain activities with a bolus plus constant infusion within a reasonable time frame for an (18)F-labeled tracer (T(1/2) 110 min). Thus, the purpose of this study was to test the feasibility in human subjects of a constant infusion paradigm for equilibrium modeling of [(18)F]deuteroaltanserin with PET. Seven healthy male subjects were injected with [(18)F]deuteroaltanserin as a bolus plus constant infusion lasting 10 h postinjection. PET acquisitions and venous blood sampling were performed throughout the infusion period. Linear regression analysis revealed that time-activity curves for both specific brain uptake and plasma [(18)F]deuteroaltanserin concentration stabilized after about 5 h. This permitted equilibrium modeling and estimation of V(')(3) (ratio of specific uptake to total plasma parent concentration) and the binding potential V(3) (ratio of specific uptake to free plasma parent concentration). Cortical/cerebellar ratios were increased by 26% relative to those we previously observed with [(18)F]altanserin using similar methodology in a somewhat older subject sample. These results demonstrate feasibility of equilibrium imaging with [(18)F]deuteroaltanserin and suggest that it may be superior to [(18)F]altanserin as a PET radioligand.

Are Equilibrium Multichannel Networks Predictable? the Case of the Indus River, Pakistan

NASA Astrophysics Data System (ADS)

Darby, S. E.; Carling, P. A.

2017-12-01

Focusing on the specific case of the Indus River, we argue that the equilibrium planform network structure of large, multi-channel, rivers is predictable. Between Chashma and Taunsa, Pakistan, the Indus is a 264 km long multiple-channel reach. Remote sensing imagery, including a period of time that encompasses the occurrence of major floods in 2007 and 2010, shows that Indus has a minimum of two and a maximum of nine channels, with on average four active channels during the dry season and five during the monsoon. We show that the network structure, if not detailed planform, remains stable, even for the record 2010 flood (27,100 m3s-1; recurrence interval > 100 years). Bankline recession is negligible for discharges less than a peak annual discharge of 6,000 m3s-1 ( 80% of mean annual flow). Maximum Flow Efficiency (MFE) principle demonstrates the channel network is insensitive to the monsoon floods, which typically peak at 13,200 m3s-1. Rather, the network is in near-equilibrium with the mean annual flood (7,530 m3s-1). MFE principle indicates stable networks have three to four channels, thus the observed stability in the number of active channels accords with the presence of a near-equilibrium reach-scale channel network. Insensitivity to the annual hydrological cycle demonstrates that the time-scale for network adjustment is much longer than the time-scale of the monsoon hydrograph, with the annual excess water being stored on floodplains, rather than being conveyed in an enlarged channel network. The analysis explains the lack of significant channel adjustment following the largest flood in 40 years and the extensive Indus flooding experienced on an annual basis, with its substantial impacts on the populace and agricultural production.

Stability of Kinesthetic Perception in Efferent-Afferent Spaces: The Concept of Iso-perceptual Manifold.

PubMed

Latash, Mark L

2018-02-21

The main goal of this paper is to introduce the concept of iso-perceptual manifold for perception of body configuration and related variables (kinesthetic perception) and to discuss its relation to the equilibrium-point hypothesis and the concepts of reference coordinate and uncontrolled manifold. Hierarchical control of action is postulated with abundant transformations between sets of spatial reference coordinates for salient effectors at different levels. Iso-perceptual manifold is defined in the combined space of afferent and efferent variables as the subspace corresponding to a stable percept. Examples of motion along an iso-perceptual manifold (perceptually equivalent motion) are considered during various natural actions. Some combinations of afferent and efferent signals, in particular those implying a violation of body's integrity, give rise to variable percepts by artificial projection onto iso-perceptual manifolds. This framework is used to interpret unusual features of vibration-induced kinesthetic illusions and to predict new illusions not yet reported in the literature. Copyright © 2017 IBRO. Published by Elsevier Ltd. All rights reserved.

Two novel bursting patterns in the Duffing system with multiple-frequency slow parametric excitations

NASA Astrophysics Data System (ADS)

Han, Xiujing; Zhang, Yi; Bi, Qinsheng; Kurths, Jürgen

2018-04-01

This paper aims to report two novel bursting patterns, the turnover-of-pitchfork-hysteresis-induced bursting and the compound pitchfork-hysteresis bursting, demonstrated for the Duffing system with multiple-frequency parametric excitations. Typically, a hysteresis behavior between the origin and non-zero equilibria of the fast subsystem can be observed due to delayed pitchfork bifurcation. Based on numerical analysis, we show that the stable equilibrium branches, related to the non-zero equilibria resulted from the pitchfork bifurcation, may become the ones with twists and turns. Then, the novel bursting pattern turnover-of-pitchfork-hysteresis-induced bursting is revealed accordingly. In particular, we show that additional pitchfork bifurcation points may appear in the fast subsystem under certain parameter conditions. This creates multiple delay-induced hysteresis behavior and helps us to reveal the other novel bursting pattern, the compound pitchfork-hysteresis bursting. Besides, effects of parameters on the bursting patterns are studied to explore the relation of these two novel bursting patterns.

Political model of social evolution

PubMed Central

Acemoglu, Daron; Egorov, Georgy; Sonin, Konstantin

2011-01-01

Almost all democratic societies evolved socially and politically out of authoritarian and nondemocratic regimes. These changes not only altered the allocation of economic resources in society but also the structure of political power. In this paper, we develop a framework for studying the dynamics of political and social change. The society consists of agents that care about current and future social arrangements and economic allocations; allocation of political power determines who has the capacity to implement changes in economic allocations and future allocations of power. The set of available social rules and allocations at any point in time is stochastic. We show that political and social change may happen without any stochastic shocks or as a result of a shock destabilizing an otherwise stable social arrangement. Crucially, the process of social change is contingent (and history-dependent): the timing and sequence of stochastic events determine the long-run equilibrium social arrangements. For example, the extent of democratization may depend on how early uncertainty about the set of feasible reforms in the future is resolved. PMID:22198760

NASA ER-2 Doppler radar reflectivity calibration for the CAMEX project

NASA Technical Reports Server (NTRS)

Caylor, I. J.; Heymsfield, G. M.; Bidwell, S. W.; Ameen, S.

1994-01-01

The NASA ER-2 Doppler radar (EDOP) was flown aboard the ER-2 high-altitude aircraft in September and October 1993 for the Convection and Moisture Experiment. During these flights, the first reliable reflectivity observations were performed with the EDOP instrument. This report details the procedure used to convert real-time engineering data into calibrated radar reflectivity. Application of the calibration results produces good agreement between the EDOP nadir pointing reflectivity and ground truth provided by a National Weather Service WSR-88D radar. The rms deviation between WSR-88D and EDOP is 6.9 dB, while measurements of the ocean surface backscatter coefficient are less than 3 dB from reported scatterometer coefficients. After an initial 30-minute period required for the instrument to reach thermal equilibrium, the radar is stable to better than 0.25 dB during flight. The range performance of EDOP shows excellent agreement with aircraft altimeter and meteorological sounding data.

The anomalously high melting temperature of bilayer ice.

PubMed

Kastelowitz, Noah; Johnston, Jessica C; Molinero, Valeria

2010-03-28

Confinement of water usually depresses its melting temperature. Here we use molecular dynamics simulations to determine the liquid-crystal equilibrium temperature for water confined between parallel hydrophobic or mildly hydrophilic plates as a function of the distance between the surfaces. We find that bilayer ice, an ice polymorph in which the local environment of each water molecule strongly departs from the most stable tetrahedral structure, has the highest melting temperature (T(m)) of the series of l-layer ices. The melting temperature of bilayer ice is not only unusually high compared to the other confined ices, but also above the melting point of bulk hexagonal ice. Recent force microscopy experiments of water confined between graphite and a tungsten tip reveal the formation of ice at room temperature [K. B. Jinesh and J. W. M. Frenken, Phys. Rev. Lett. 101, 036101 (2008)]. Our results suggest that bilayer ice, for which we compute a T(m) as high as 310 K in hydrophobic confinement, is the crystal formed in those experiments.

Political model of social evolution.

PubMed

Acemoglu, Daron; Egorov, Georgy; Sonin, Konstantin

2011-12-27

Almost all democratic societies evolved socially and politically out of authoritarian and nondemocratic regimes. These changes not only altered the allocation of economic resources in society but also the structure of political power. In this paper, we develop a framework for studying the dynamics of political and social change. The society consists of agents that care about current and future social arrangements and economic allocations; allocation of political power determines who has the capacity to implement changes in economic allocations and future allocations of power. The set of available social rules and allocations at any point in time is stochastic. We show that political and social change may happen without any stochastic shocks or as a result of a shock destabilizing an otherwise stable social arrangement. Crucially, the process of social change is contingent (and history-dependent): the timing and sequence of stochastic events determine the long-run equilibrium social arrangements. For example, the extent of democratization may depend on how early uncertainty about the set of feasible reforms in the future is resolved.

Dynamical mechanism of circadian singularity behavior in Neurospora

NASA Astrophysics Data System (ADS)

Sun, Maorong; Wang, Yi; Xu, Xin; Yang, Ling

2016-09-01

Many organisms have oscillators with a period of about 24 hours, called "circadian clocks". They employ negative biochemical feedback loops that are self-contained within a single cell (requiring no cell-to-cell interaction). Circadian singularity behavior is a phenomenon of the abolishment of circadian rhythmicities by a critical stimulus. These behaviors have been found experimentally in Neurospora, human and hamster, by temperature step-up or light pulse. Two alternative models have been proposed to explain this phenomenon: desynchronization of cell populations, and loss of oscillations in all cells by resetting each cell close to a steady state. In this work, we use a mathematical model to investigate the dynamical mechanism of circadian singularity behavior in Neurospora. Our findings suggest that the arrhythmic behavior after the critical stimulus is caused by the collaboration of the desynchronization and the loss of oscillation amplitude. More importantly, we found that the stable manifold of the unstable equilibrium point, instead of the steady state itself, plays a crucial role in circadian singularity behavior.

Energetics and solvation structure of a dihalogen dopant (I2) in (4)He clusters.

PubMed

Pérez de Tudela, Ricardo; Barragán, Patricia; Valdés, Álvaro; Prosmiti, Rita

2014-08-21

The energetics and structure of small HeNI2 clusters are analyzed as the size of the system changes, with N up to 38. The full interaction between the I2 molecule and the He atoms is based on analytical ab initio He-I2 potentials plus the He-He interaction, obtained from first-principle calculations. The most stable structures, as a function of the number of solvent He atoms, are obtained by employing an evolutionary algorithm and compared with CCSD(T) and MP2 ab initio computations. Further, the classical description is completed by explicitly including thermal corrections and quantum features, such as zero-point-energy values and spatial delocalization. From quantum PIMC calculations, the binding energies and radial/angular probability density distributions of the thermal equilibrium state for selected-size clusters are computed at a low temperature. The sequential formation of regular shell structures is analyzed and discussed for both classical and quantum treatments.

Monitoring solar irradiance from L2 with Gaia

NASA Astrophysics Data System (ADS)

Serpell, E.

2017-09-01

Gaia is the European Space Agency's cornerstone astrometry mission to measure the positions of a billion stars in the Milky Way with unprecedented accuracy. Since early 2014 Gaia has been operating in a halo orbit around the second Sun-Earth Lagrange point that provides the stable thermal environment, without Earth eclipses, needed for the payload to function accurately. The spacecraft is equipped with a number of thermally isolated, sun-facing thermistors that provide a continuous measurement of the local equilibrium temperature. As a consequence of the spacecraft design and operational conditions these temperature measurements have been used to infer the solar output over a broad wavelength range. In this paper we present an analysis of temperature measurements made of the Gaia solar panels at frequencies of up to 1 Hz for the first 35 months of routine operations. We show that the Gaia solar panel temperature measurements are capable of precisely determining short term changes to the solar output at a level of better than 0.04% with time constants of a few minutes.

Catastrophic Regime Shift in Water Reservoirs and São Paulo Water Supply Crisis.

PubMed

Coutinho, Renato M; Kraenkel, Roberto A; Prado, Paulo I

2015-01-01

The relation between rainfall and water accumulated in reservoirs comprises nonlinear feedbacks. Here we show that they may generate alternative equilibrium regimes, one of high water-volume, the other of low water-volume. Reservoirs can be seen as socio-environmental systems at risk of regime shifts, characteristic of tipping point transitions. We analyze data from stored water, rainfall, and water inflow and outflow in the main reservoir serving the metropolitan area of São Paulo, Brazil, by means of indicators of critical regime shifts, and find a strong signal of a transition. We furthermore build a mathematical model that gives a mechanistic view of the dynamics and demonstrates that alternative stable states are an expected property of water reservoirs. We also build a stochastic version of this model that fits well to the data. These results highlight the broader aspect that reservoir management must account for their intrinsic bistability, and should benefit from dynamical systems theory. Our case study illustrates the catastrophic consequences of failing to do so.

The application of thermally induced multistable composites to morphing aircraft structures

NASA Astrophysics Data System (ADS)

Mattioni, Filippo; Weaver, Paul M.; Potter, Kevin D.; Friswell, Michael I.

2008-03-01

One approach to morphing aircraft is to use bistable or multistable structures that have two or more stable equilibrium configurations to define a discrete set of shapes for the morphing structure. Moving between these stable states may be achieved using an actuation system or by aerodynamic loads. This paper considers three concepts for morphing aircraft based on multistable structures, namely a variable sweep wing, bistable blended winglets and a variable camber trailing edge. The philosophy behind these concepts is outlined, and simulated and experimental results are given.

Discovery of a meta-stable Al-Sm phase with unknown stoichiometry using a genetic algorithm

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

Zhang, Feng; McBrearty, Ian; Ott, R. T.

Unknown crystalline phases observed during the devitrification process of glassy metal alloys significantly limit our ability to understand and control phase selection in these systems driven far from equilibrium. Here, we report a new meta-stable Al 5Sm phase identified by simultaneously searching Al-rich compositions of the Al–Sm system, using an efficient genetic algorithm. The excellent match between calculated and experimental X-ray diffraction patterns confirms that this new phase appeared in the crystallization of melt-spun Al 90Sm 10 alloys.

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.

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.

Does the nervous system use equilibrium-point control to guide single and multiple joint movements?

PubMed

Bizzi, E; Hogan, N; Mussa-Ivaldi, F A; Giszter, S

1992-12-01

The hypothesis that the central nervous system (CNS) generates movement as a shift of the limb's equilibrium posture has been corroborated experimentally in studies involving single- and multijoint motions. Posture may be controlled through the choice of muscle length-tension curve that set agonist-antagonist torque-angle curves determining an equilibrium position for the limb and the stiffness about the joints. Arm trajectories seem to be generated through a control signal defining a series of equilibrium postures. The equilibrium-point hypothesis drastically simplifies the requisite computations for multijoint movements and mechanical interactions with complex dynamic objects in the environment. Because the neuromuscular system is springlike, the instantaneous difference between the arm's actual position and the equilibrium position specified by the neural activity can generate the requisite torques, avoiding the complex "inverse dynamic" problem of computing the torques at the joints. The hypothesis provides a simple, unified description of posture and movement as well as contact control task performance, in which the limb must exert force stably and do work on objects in the environment. The latter is a surprisingly difficult problem, as robotic experience has shown. The prior evidence for the hypothesis came mainly from psychophysical and behavioral experiments. Our recent work has shown that microstimulation of the frog spinal cord's premotoneural network produces leg movements to various positions in the frog's motor space. The hypothesis can now be investigated in the neurophysiological machinery of the spinal cord.

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.

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.

Assessment of Stable Isotope Distribution in Complex Systems

NASA Astrophysics Data System (ADS)

He, Y.; Cao, X.; Wang, J.; Bao, H.

2017-12-01

Biomolecules in living organisms have the potential to approach chemical steady state and even apparent isotope equilibrium because enzymatic reactions are intrinsically reversible. If an apparent local equilibrium can be identified, enzymatic reversibility and its controlling factors may be quantified, which helps to understand complex biochemical processes. Earlier research on isotope fractionation tends to focus on specific process and compare mostly two different chemical species. Using linear regression, "Thermodynamic order", which refers to correlated δ13C and 13β values, has been proposed to be present among many biomolecules by Galimov et al. However, the concept "thermodynamic order" they proposed and the approach they used has been questioned. Here, we propose that the deviation of a complex system from its equilibrium state can be rigorously described as a graph problem as is applied in discrete mathematics. The deviation of isotope distribution from equilibrium state and apparent local isotope equilibrium among a subset of biomolecules can be assessed using an apparent fractionation difference matrix (|Δα|). Applying the |Δα| matrix analysis to earlier published data of amino acids, we show the existence of apparent local equilibrium among different amino acids in potato and a kind of green alga. The existence of apparent local equilibrium is in turn consistent with the notion that enzymatic reactions can be reversible even in living systems. The result also implies that previous emphasis on external carbon source intake may be misplaced when studying isotope distribution in physiology. In addition to the identification of local equilibrium among biomolecules, the difference matrix approach has the potential to explore chemical or isotope equilibrium state in extraterrestrial bodies, to distinguish living from non-living systems, and to classify living species. This approach will benefit from large numbers of systematic data and advanced pattern recognition techniques.

Effect of organic matters on CO2 hydrate phase equilibrium conditions in Na-montmorillonite clay

NASA Astrophysics Data System (ADS)

Park, T.; Kyung, D.; Lee, W.

2013-12-01

Formation of gas hydrates provides an attractive idea for storing greenhouse gases in a long-term stable geological formation. Since the phase equilibrium conditions of gas hydrates indicate the stability of hydrates, estimation of the phase equilibrium conditions of gas hydrates in marine geological conditions is necessary. In this study, we have identified the effects of organic matters (glycine, glucose, and urea) and solid surface (montmorillonite (MMT)) on the three-phase (liquid-hydrate-vapor) equilibrium conditions of CO2 hydrate. CO2 phase equilibrium experiments were conducted using 0.5mol% organic matter solutions with and without 10g soil mineral were experimentally conducted. Addition of organic matters shifted the phase equilibrium conditions of CO2 hydrate to the higher pressure or lower pressure region because of higher competition of water molecules due to the dissolved organic matters. Presence of MMT also leaded to the higher equilibrium pressure due to the interaction of cations with water molecules. By addition of organic matters to the clay suspension, the hydrate phase equilibrium conditions were less inhibited compared to those of MMT and organic matters independently. The diminished magnitudes by addition of organic matters to the clay suspension (MMT > MMT+urea > MMT+glycine > MMT+glucose > DIW) were different to the order of inhibition degree without MMT (Glucose > glycine > urea > DIW). X-ray diffraction (XRD), scanning electron microscope (SEM), and ion chromatography (IC) analysis were conducted to support the hypothesis that the organic matters interact with cations in MMT interlayer space, and leads to the less inhibition of phase equilibrium conditions. The present study provides basic information for the formation and dissociation of CO2 hydrates in the geological formation when sequestering CO2 as a form of CO2 hydrate.

Potential-pH Diagrams.

ERIC Educational Resources Information Center

Barnum, Dennis W.

1982-01-01

Potential-pH diagrams show the domains of redoxpotential and pH in which major species are most stable. Constructing such diagrams provides students with opportunities to decide what species must be considered, search literature for equilibrium constants and free energies of formation, and practice in using the Nernst equation. (Author/JN)

Effect of gravitational and aerodynamic torques on a rigid Skylab-type satellite

NASA Technical Reports Server (NTRS)

Sperling, H. J.

1974-01-01

A theoretical investigation of the influence of the aerodynamic torque on a Skylab-type satellite is presented. Only the case of free flow of uniform velocity and completely diffuse reflection is considered. It is found by linear stability analysis that the satellite has no stable equilibrium.

NUMERICAL TECHNIQUES TO SOLVE CONDENSATIONAL AND DISSOLUTIONAL GROWTH EQUATIONS WHEN GROWTH IS COUPLED TO REVERSIBLE REACTIONS (R823186)

EPA Science Inventory

Noniterative, unconditionally stable numerical techniques for solving condensational and
dissolutional growth equations are given. Growth solutions are compared to Gear-code solutions for
three cases when growth is coupled to reversible equilibrium chemistry. In all cases, ...

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.

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

Equilibrium-based movement endpoints elicited from primary motor cortex using repetitive microstimulation.

PubMed

Van Acker, Gustaf M; Amundsen, Sommer L; Messamore, William G; Zhang, Hongyu Y; Luchies, Carl W; Cheney, Paul D

2014-11-19

High-frequency, long-duration intracortical microstimulation (HFLD-ICMS) is increasingly being used to deduce how the brain encodes coordinated muscle activity and movement. However, the full movement repertoire that can be elicited from the forelimb representation of primary motor cortex (M1) using this method has not been systematically determined. Our goal was to acquire a comprehensive M1 forelimb representational map of movement endpoints elicited with HFLD-ICMS, using stimulus parameters optimal for evoking stable forelimb spatial endpoints. The data reveal a 3D forelimb movement endpoint workspace that is represented in a patchwork fashion on the 2D M1 cortical surface. Although cortical maps of movement endpoints appear quite disorderly with respect to movement space, we show that the endpoint locations in the workspace evoked with HFLD-ICMS of two adjacent cortical points are closer together than would be expected if the organization were random. Although there were few obvious consistencies in the endpoint maps across the two monkeys tested, one notable exception was endpoints bringing the hand to the mouth, which was located at the boundary between the hand and face representation. Endpoints at the extremes of the monkey's workspace and locations above the head were largely absent. Our movement endpoints are best explained as resulting from coactivation of agonist and antagonist muscles driving the joints toward equilibrium positions determined by the length-tension relationships of the muscles. Copyright © 2014 the authors 0270-6474/14/3415722-13$15.00/0.

Assessment of the accuracy of plasma shape reconstruction by the Cauchy condition surface method in JT-60SA

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

Miyata, Y.; Suzuki, T.; Takechi, M.

2015-07-15

For the purpose of stable plasma equilibrium control and detailed analysis, it is essential to reconstruct an accurate plasma boundary on the poloidal cross section in tokamak devices. The Cauchy condition surface (CCS) method is a numerical approach for calculating the spatial distribution of the magnetic flux outside a hypothetical surface and reconstructing the plasma boundary from the magnetic measurements located outside the plasma. The accuracy of the plasma shape reconstruction has been assessed by comparing the CCS method and an equilibrium calculation in JT-60SA with a high elongation and triangularity of plasma shape. The CCS, on which both Dirichletmore » and Neumann conditions are unknown, is defined as a hypothetical surface located inside the real plasma region. The accuracy of the plasma shape reconstruction is sensitive to the CCS free parameters such as the number of unknown parameters and the shape in JT-60SA. It is found that the optimum number of unknown parameters and the size of the CCS that minimizes errors in the reconstructed plasma shape are in proportion to the plasma size. Furthermore, it is shown that the accuracy of the plasma shape reconstruction is greatly improved using the optimum number of unknown parameters and shape of the CCS, and the reachable reconstruction errors in plasma shape and locations of strike points are within the target ranges in JT-60SA.« less

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.

Stability of a rigid rotor supported on oil-film journal bearings under dynamic load

NASA Technical Reports Server (NTRS)

Majumdar, B. C.; Brewe, D. E.

1987-01-01

Most published work relating to dynamically loaded journal bearings are directed to determining the minimum film thickness from the predicted journal trajectories. These do not give any information about the subsynchronous whirl stability of journal bearing systems since they do not consider the equations of motion. It is, however, necessary to know whether the bearing system operation is stable or not under such an operating condition. The stability characteristics of the system are analyzed. A linearized perturbation theory about the equilibrium point can predict the threshold of stability; however it does not indicate postwhirl orbit detail. The linearized method may indicate that a bearing is unstable for a given operating condition whereas the nonlinear analysis may indicate that it forms a stable limit cycle. For this reason, a nonlinear transient analysis of a rigid rotor supported on oil journal bearings under: (1) a unidirectional constant load, (2) a unidirectional periodic load, and (3) variable rotating load are performed. The hydrodynamic forces are calculated after solving the time-dependent Reynolds equation by a finite difference method with a successive overrelaxation scheme. Using these forces, equations of motion are solved by the fourth-order Runge-Kutta method to predict the transient behavior of the rotor. With the aid of a high-speed digital computer and graphics, the journal trajectories are obtained for several different operating conditions.