Statistical approach to partial equilibrium analysis

NASA Astrophysics Data System (ADS)

Wang, Yougui; Stanley, H. E.

2009-04-01

A statistical approach to market equilibrium and efficiency analysis is proposed in this paper. One factor that governs the exchange decisions of traders in a market, named willingness price, is highlighted and constitutes the whole theory. The supply and demand functions are formulated as the distributions of corresponding willing exchange over the willingness price. The laws of supply and demand can be derived directly from these distributions. The characteristics of excess demand function are analyzed and the necessary conditions for the existence and uniqueness of equilibrium point of the market are specified. The rationing rates of buyers and sellers are introduced to describe the ratio of realized exchange to willing exchange, and their dependence on the market price is studied in the cases of shortage and surplus. The realized market surplus, which is the criterion of market efficiency, can be written as a function of the distributions of willing exchange and the rationing rates. With this approach we can strictly prove that a market is efficient in the state of equilibrium.

Bus-based park-and-ride system: a stochastic model on multimodal network with congestion pricing schemes

NASA Astrophysics Data System (ADS)

Liu, Zhiyuan; Meng, Qiang

2014-05-01

This paper focuses on modelling the network flow equilibrium problem on a multimodal transport network with bus-based park-and-ride (P&R) system and congestion pricing charges. The multimodal network has three travel modes: auto mode, transit mode and P&R mode. A continuously distributed value-of-time is assumed to convert toll charges and transit fares to time unit, and the users' route choice behaviour is assumed to follow the probit-based stochastic user equilibrium principle with elastic demand. These two assumptions have caused randomness to the users' generalised travel times on the multimodal network. A comprehensive network framework is first defined for the flow equilibrium problem with consideration of interactions between auto flows and transit (bus) flows. Then, a fixed-point model with unique solution is proposed for the equilibrium flows, which can be solved by a convergent cost averaging method. Finally, the proposed methodology is tested by a network example.

Unique equilibrium states for Bonatti–Viana diffeomorphisms

NASA Astrophysics Data System (ADS)

Climenhaga, Vaughn; Fisher, Todd; Thompson, Daniel J.

2018-06-01

We show that the robustly transitive diffeomorphisms constructed by Bonatti and Viana have unique equilibrium states for natural classes of potentials. In particular, we characterize the SRB measure as the unique equilibrium state for a suitable geometric potential. The techniques developed are applicable to a wide class of DA diffeomorphisms, and persist under C 1 perturbations of the map. These results are an application of general machinery developed by the first and last named authors.

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.

Robustness analysis of uncertain dynamical neural networks with multiple time delays.

PubMed

Senan, Sibel

2015-10-01

This paper studies the problem of global robust asymptotic stability of the equilibrium point for the class of dynamical neural networks with multiple time delays with respect to the class of slope-bounded activation functions and in the presence of the uncertainties of system parameters of the considered neural network model. By using an appropriate Lyapunov functional and exploiting the properties of the homeomorphism mapping theorem, we derive a new sufficient condition for the existence, uniqueness and global robust asymptotic stability of the equilibrium point for the class of neural networks with multiple time delays. The obtained stability condition basically relies on testing some relationships imposed on the interconnection matrices of the neural system, which can be easily verified by using some certain properties of matrices. An instructive numerical example is also given to illustrate the applicability of our result and show the advantages of this new condition over the previously reported corresponding results. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

Global asymptotic stability of hybrid bidirectional associative memory neural networks with time delays

NASA Astrophysics Data System (ADS)

Arik, Sabri

2006-02-01

This Letter presents a sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for bidirectional associative memory (BAM) neural networks with distributed time delays. The results impose constraint conditions on the network parameters of neural system independently of the delay parameter, and they are applicable to all bounded continuous non-monotonic neuron activation functions. The results are also compared with the previous results derived in the literature.

Global robust stability of bidirectional associative memory neural networks with multiple time delays.

PubMed

Senan, Sibel; Arik, Sabri

2007-10-01

This correspondence presents a sufficient condition for the existence, uniqueness, and global robust asymptotic stability of the equilibrium point for bidirectional associative memory neural networks with discrete time delays. The results impose constraint conditions on the network parameters of the neural system independently of the delay parameter, and they are applicable to all bounded continuous nonmonotonic neuron activation functions. Some numerical examples are given to compare our results with the previous robust stability results derived in the literature.

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.

Integral Equation for the Equilibrium State of Colliding Electron Beams

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

Warnock, Robert L.

2002-11-11

We study a nonlinear integral equation for the equilibrium phase distribution of stored colliding electron beams. It is analogous to the Haissinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. We prove existence of a unique solution, thus the existence of a unique equilibrium state, for sufficiently small current. This is done for the Chao-Ruth model of the beam-beam interaction in one degree of freedom. We expect no difficulty in generalizing the argument to more realistic models.

Uniqueness of Nash equilibrium in vaccination games.

PubMed

Bai, Fan

2016-12-01

One crucial condition for the uniqueness of Nash equilibrium set in vaccination games is that the attack ratio monotonically decreases as the vaccine coverage level increasing. We consider several deterministic vaccination models in homogeneous mixing population and in heterogeneous mixing population. Based on the final size relations obtained from the deterministic epidemic models, we prove that the attack ratios can be expressed in terms of the vaccine coverage levels, and also prove that the attack ratios are decreasing functions of vaccine coverage levels. Some thresholds are presented, which depend on the vaccine efficacy. It is proved that for vaccination games in homogeneous mixing population, there is a unique Nash equilibrium for each game.

Demonstration of the Kibble-Zurek mechanism in a non-equilibrium phase transition

NASA Astrophysics Data System (ADS)

Patil, Yogesh S.; Cheung, Hil F. H.; Date, Aditya G.; Vengalattore, Mukund

2017-04-01

We describe the experimental realization of a driven-dissipative phase transition (DPT) in a mechanical parametric amplifier and demonstrate key signatures of a critical point in the system, where the susceptibilities and relaxation time scales diverge and coincide with the spontaneous breaking of symmetry and the emergence of macroscopic order. While these observations are reminiscent of equilibrium phase transitions, it is presently an open question whether such DPTs are amenable to the conventional Landau-Ginsburg-Wilson paradigm that relies on concepts of scale invariance and universality - Indeed, recent theoretical work has predicted that DPTs can exhibit phenomenology that departs from these conventional paradigms. By quenching the system past the critical point, we measure the dynamics of the emergent ordered phase and its departure from adiabaticity, and find that our measurements are in excellent agreement with the Kibble-Zurek hypothesis. In addition to validating the KZ mechanism in a DPT for the first time, we also uniquely show that the measured critical exponents accurately reflect the interplay between the intrinsic coherent dynamics and the environmental correlations, with a clear departure from mean field exponents in the case of non-Markovian system-bath interactions. We also discuss how the techniques of reservoir engineering and the imposition of artificial environmental correlations can result in the stabilization of novel many-body quantum phases and exotic non-equilibrium states of matter.

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.

Narayanaswamy's 1971 aging theory and material time

NASA Astrophysics Data System (ADS)

Dyre, Jeppe C.

2015-09-01

The Bochkov-Kuzovlev nonlinear fluctuation-dissipation theorem is used to derive Narayanaswamy's phenomenological theory of physical aging, in which this highly nonlinear phenomenon is described by a linear material-time convolution integral. A characteristic property of the Narayanaswamy aging description is material-time translational invariance, which is here taken as the basic assumption of the derivation. It is shown that only one possible definition of the material time obeys this invariance, namely, the square of the distance travelled from a configuration of the system far back in time. The paper concludes with suggestions for computer simulations that test for consequences of material-time translational invariance. One of these is the "unique-triangles property" according to which any three points on the system's path form a triangle such that two side lengths determine the third; this is equivalent to the well-known triangular relation for time-autocorrelation functions of aging spin glasses [L. F. Cugliandolo and J. Kurchan, J. Phys. A: Math. Gen. 27, 5749 (1994)]. The unique-triangles property implies a simple geometric interpretation of out-of-equilibrium time-autocorrelation functions, which extends to aging a previously proposed framework for such functions in equilibrium [J. C. Dyre, e-print arXiv:cond-mat/9712222 (1997)].

Discrete-time bidirectional associative memory neural networks with variable delays

NASA Astrophysics Data System (ADS)

Liang, variable delays [rapid communication] J.; Cao, J.; Ho, D. W. C.

2005-02-01

Based on the linear matrix inequality (LMI), some sufficient conditions are presented in this Letter for the existence, uniqueness and global exponential stability of the equilibrium point of discrete-time bidirectional associative memory (BAM) neural networks with variable delays. Some of the stability criteria obtained in this Letter are delay-dependent, and some of them are delay-independent, they are less conservative than the ones reported so far in the literature. Furthermore, the results provide one more set of easily verified criteria for determining the exponential stability of discrete-time BAM neural networks.

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.

Solving nonlinear equilibrium equations of deformable systems by method of embedded polygons

NASA Astrophysics Data System (ADS)

Razdolsky, A. G.

2017-09-01

Solving of nonlinear algebraic equations is an obligatory stage of studying the equilibrium paths of nonlinear deformable systems. The iterative method for solving a system of nonlinear algebraic equations stated in an explicit or implicit form is developed in the present work. The method consists of constructing a sequence of polygons in Euclidean space that converge into a single point that displays the solution of the system. Polygon vertices are determined on the assumption that individual equations of the system are independent from each other and each of them is a function of only one variable. Initial positions of vertices for each subsequent polygon are specified at the midpoints of certain straight segments determined at the previous iteration. The present algorithm is applied for analytical investigation of the behavior of biaxially compressed nonlinear-elastic beam-column with an open thin-walled cross-section. Numerical examples are made for the I-beam-column on the assumption that its material follows a bilinear stress-strain diagram. A computer program based on the shooting method is developed for solving the problem. The method is reduced to numerical integration of a system of differential equations and to the solution of a system of nonlinear algebraic equations between the boundary values of displacements at the ends of the beam-column. A stress distribution at the beam-column cross-sections is determined by subdividing the cross-section area into many small cells. The equilibrium path for the twisting angle and the lateral displacements tend to the stationary point when the load is increased. Configuration of the path curves reveals that the ultimate load is reached shortly once the maximal normal stresses at the beam-column fall outside the limit of the elastic region. The beam-column has a unique equilibrium state for each value of the load, that is, there are no equilibrium states once the maximum load is reached.

Stochastic driven systems far from equilibrium

NASA Astrophysics Data System (ADS)

Kim, Kyung Hyuk

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

Equilibrium theory of island biogeography: A review

Treesearch

Angela D. Yu; Simon A. Lei

2001-01-01

The topography, climatic pattern, location, and origin of islands generate unique patterns of species distribution. The equilibrium theory of island biogeography creates a general framework in which the study of taxon distribution and broad island trends may be conducted. Critical components of the equilibrium theory include the species-area relationship, island-...

Narayanaswamy’s 1971 aging theory and material time

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

Dyre, Jeppe C., E-mail: dyre@ruc.dk

2015-09-21

The Bochkov-Kuzovlev nonlinear fluctuation-dissipation theorem is used to derive Narayanaswamy’s phenomenological theory of physical aging, in which this highly nonlinear phenomenon is described by a linear material-time convolution integral. A characteristic property of the Narayanaswamy aging description is material-time translational invariance, which is here taken as the basic assumption of the derivation. It is shown that only one possible definition of the material time obeys this invariance, namely, the square of the distance travelled from a configuration of the system far back in time. The paper concludes with suggestions for computer simulations that test for consequences of material-time translational invariance.more » One of these is the “unique-triangles property” according to which any three points on the system’s path form a triangle such that two side lengths determine the third; this is equivalent to the well-known triangular relation for time-autocorrelation functions of aging spin glasses [L. F. Cugliandolo and J. Kurchan, J. Phys. A: Math. Gen. 27, 5749 (1994)]. The unique-triangles property implies a simple geometric interpretation of out-of-equilibrium time-autocorrelation functions, which extends to aging a previously proposed framework for such functions in equilibrium [J. C. Dyre, e-print arXiv:cond-mat/9712222 (1997)].« less

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.

Global exponential stability analysis on impulsive BAM neural networks with distributed delays

NASA Astrophysics Data System (ADS)

Li, Yao-Tang; Yang, Chang-Bo

2006-12-01

Using M-matrix and topological degree tool, sufficient conditions are obtained for the existence, uniqueness and global exponential stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with distributed delays and subjected to impulsive state displacements at fixed instants of time by constructing a suitable Lyapunov functional. The results remove the usual assumptions that the boundedness, monotonicity, and differentiability of the activation functions. It is shown that in some cases, the stability criteria can be easily checked. Finally, an illustrative example is given to show the effectiveness of the presented criteria.

Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays.

PubMed

Arik, Sabri

2005-05-01

This paper presents a sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for bidirectional associative memory (BAM) neural networks with distributed time delays. The results impose constraint conditions on the network parameters of neural system independently of the delay parameter, and they are applicable to all continuous nonmonotonic neuron activation functions. It is shown that in some special cases of the results, the stability criteria can be easily checked. Some examples are also given to compare the results with the previous results derived in the literature.

Dynamic stability analysis of fractional order leaky integrator echo state neural networks

NASA Astrophysics Data System (ADS)

Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Tenreiro Machado, J. A.

2017-06-01

The Leaky integrator echo state neural network (Leaky-ESN) is an improved model of the recurrent neural network (RNN) and adopts an interconnected recurrent grid of processing neurons. This paper presents a new proof for the convergence of a Lyapunov candidate function to zero when time tends to infinity by means of the Caputo fractional derivative with order lying in the range (0, 1). The stability of Fractional-Order Leaky-ESN (FO Leaky-ESN) is then analyzed, and the existence, uniqueness and stability of the equilibrium point are provided. A numerical example demonstrates the feasibility of the proposed method.

Kidnapping model: an extension of Selten's game.

PubMed

Iqbal, Azhar; Masson, Virginie; Abbott, Derek

2017-12-01

Selten's game is a kidnapping model where the probability of capturing the kidnapper is independent of whether the hostage has been released or executed. Most often, in view of the elevated sensitivities involved, authorities put greater effort and resources into capturing the kidnapper if the hostage has been executed, in contrast with the case when a ransom is paid to secure the hostage's release. In this paper, we study the asymmetric game when the probability of capturing the kidnapper depends on whether the hostage has been executed or not and find a new uniquely determined perfect equilibrium point in Selten's game.

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

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

Zhou, Xinyang; Tian, Jie; Chen, Lijun

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

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

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

Zhou, Xinyang; Tian, Jie; Chen, Lijun

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

Reversible shear-induced crystallization above equilibrium freezing temperature in a lyotropic surfactant system

PubMed Central

Rathee, Vikram; Krishnaswamy, Rema; Pal, Antara; Raghunathan, V. A.; Impéror-Clerc, Marianne; Pansu, Brigitte; Sood, A. K.

2013-01-01

We demonstrate a unique shear-induced crystallization phenomenon above the equilibrium freezing temperature in weakly swollen isotropic and lamellar mesophases with bilayers formed in a cationic-anionic mixed surfactant system. Synchrotron rheological X-ray diffraction study reveals the crystallization transition to be reversible under shear (i.e., on stopping the shear, the nonequilibrium crystalline phase melts back to the equilibrium mesophase). This is different from the shear-driven crystallization below , which is irreversible. Rheological optical observations show that the growth of the crystalline phase occurs through a preordering of the phase to an phase induced by shear flow, before the nucleation of the phase. Shear diagram of the phase constructed in the parameter space of shear rate vs. temperature exhibits and transitions above the equilibrium crystallization temperature , in addition to the irreversible shear-driven nucleation of in the phase below . In addition to revealing a unique class of nonequilibrium phase transition, the present study urges a unique approach toward understanding shear-induced phenomena in concentrated mesophases of mixed amphiphilic systems. PMID:23986497

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.

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

Models of supply function equilibrium with applications to the electricity industry

NASA Astrophysics Data System (ADS)

Aromi, J. Daniel

Electricity market design requires tools that result in a better understanding of incentives of generators and consumers. Chapter 1 and 2 provide tools and applications of these tools to analyze incentive problems in electricity markets. In chapter 1, models of supply function equilibrium (SFE) with asymmetric bidders are studied. I prove the existence and uniqueness of equilibrium in an asymmetric SFE model. In addition, I propose a simple algorithm to calculate numerically the unique equilibrium. As an application, a model of investment decisions is considered that uses the asymmetric SFE as an input. In this model, firms can invest in different technologies, each characterized by distinct variable and fixed costs. In chapter 2, option contracts are introduced to a supply function equilibrium (SFE) model. The uniqueness of the equilibrium in the spot market is established. Comparative statics results on the effect of option contracts on the equilibrium price are presented. A multi-stage game where option contracts are traded before the spot market stage is considered. When contracts are optimally procured by a central authority, the selected profile of option contracts is such that the spot market price equals marginal cost for any load level resulting in a significant reduction in cost. If load serving entities (LSEs) are price takers, in equilibrium, there is no trade of option contracts. Even when LSEs have market power, the central authority's solution cannot be implemented in equilibrium. In chapter 3, we consider a game in which a buyer must repeatedly procure an input from a set of firms. In our model, the buyer is able to sign long term contracts that establish the likelihood with which the next period contract is awarded to an entrant or the incumbent. We find that the buyer finds it optimal to favor the incumbent, this generates more intense competition between suppliers. In a two period model we are able to completely characterize the optimal mechanism.

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.

Mathematical analysis of tuberculosis transmission model with delay

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

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

Bifurcation analysis in SIR epidemic model with treatment

NASA Astrophysics Data System (ADS)

Balamuralitharan, S.; Radha, M.

2018-04-01

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

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

NASA Technical Reports Server (NTRS)

Raiszadeh, Ben

2003-01-01

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

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

PubMed

Kang, K; Dhont, J K G

2009-11-01

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

Backward Bifurcation in a Cholera Model: A Case Study of Outbreak in Zimbabwe and Haiti

NASA Astrophysics Data System (ADS)

Sharma, Sandeep; Kumari, Nitu

In this paper, a nonlinear deterministic model is proposed with a saturated treatment function. The expression of the basic reproduction number for the proposed model was obtained. The global dynamics of the proposed model was studied using the basic reproduction number and theory of dynamical systems. It is observed that proposed model exhibits backward bifurcation as multiple endemic equilibrium points exist when R0 < 1. The existence of backward bifurcation implies that making R0 < 1 is not enough for disease eradication. This, in turn, makes it difficult to control the spread of cholera in the community. We also obtain a unique endemic equilibria when R0 > 1. The global stability of unique endemic equilibria is performed using the geometric approach. An extensive numerical study is performed to support our analytical results. Finally, we investigate two major cholera outbreaks, Zimbabwe (2008-09) and Haiti (2010), with the help of the present study.

Auction-based Security Game for Multiuser Cooperative Networks

NASA Astrophysics Data System (ADS)

Wang, An; Cai, Yueming; Yang, Wendong; Cheng, Yunpeng

2013-04-01

In this paper, we develop an auction-based algorithm to allocate the relay power efficiently to improve the system secrecy rate in a cooperative network, where several source-destination pairs and one cooperative relay are involved. On the one hand, the cooperative relay assists these pairs to transmit under a peak power constraint. On the other hand, the relay is untrusty and is also a passive eavesdropper. The whole auction process is completely distributed and no instantaneous channel state information exchange is needed. We also prove the existence and uniqueness of the Nash Equilibrium (NE) for the proposed power auction game. Moreover, the Pareto optimality is also validated. Simulation results show that our proposed auction-based algorithm can effectively improve the system secrecy rate. Besides, the proposed auction-based algorithm can converge to the unique NE point within a finite number of iterations. More interestingly, we also find that the proposed power auction mechanism is cheat-proof.

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

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

Malaria and global change: Insights, uncertainties and possible surprises

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

Martin, P.H.; Steel, A.

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

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

PubMed

Latash, M L; Gutman, S R

1994-01-01

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

Power-efficient distributed resource allocation under goodput QoS constraints for heterogeneous networks

NASA Astrophysics Data System (ADS)

Andreotti, Riccardo; Del Fiorentino, Paolo; Giannetti, Filippo; Lottici, Vincenzo

2016-12-01

This work proposes a distributed resource allocation (RA) algorithm for packet bit-interleaved coded OFDM transmissions in the uplink of heterogeneous networks (HetNets), characterized by small cells deployed over a macrocell area and sharing the same band. Every user allocates its transmission resources, i.e., bits per active subcarrier, coding rate, and power per subcarrier, to minimize the power consumption while both guaranteeing a target quality of service (QoS) and accounting for the interference inflicted by other users transmitting over the same band. The QoS consists of the number of information bits delivered in error-free packets per unit of time, or goodput (GP), estimated at the transmitter by resorting to an efficient effective SNR mapping technique. First, the RA problem is solved in the point-to-point case, thus deriving an approximate yet accurate closed-form expression for the power allocation (PA). Then, the interference-limited HetNet case is examined, where the RA problem is described as a non-cooperative game, providing a solution in terms of generalized Nash equilibrium. Thanks to the closed-form of the PA, the solution analysis is based on the best response concept. Hence, sufficient conditions for existence and uniqueness of the solution are analytically derived, along with a distributed algorithm capable of reaching the game equilibrium.

Global Mittag-Leffler stability analysis of fractional-order impulsive neural networks with one-side Lipschitz condition.

PubMed

Zhang, Xinxin; Niu, Peifeng; Ma, Yunpeng; Wei, Yanqiao; Li, Guoqiang

2017-10-01

This paper is concerned with the stability analysis issue of fractional-order impulsive neural networks. Under the one-side Lipschitz condition or the linear growth condition of activation function, the existence of solution is analyzed respectively. In addition, the existence, uniqueness and global Mittag-Leffler stability of equilibrium point of the fractional-order impulsive neural networks with one-side Lipschitz condition are investigated by the means of contraction mapping principle and Lyapunov direct method. Finally, an example with numerical simulation is given to illustrate the validity and feasibility of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

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

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

2015-09-30

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

The tropical precipitation pickup threshold and clouds in a radiative convective equilibrium model: 2. Two-layer moisture

NASA Astrophysics Data System (ADS)

Igel, Matthew R.

2017-06-01

This paper complements Part 1 in which cloud processes of aggregated convection are examined in a large-domain radiative convective equilibrium simulation in order to uncover those responsible for a consistently observed, abrupt increase in mean precipitation at a column relative humidity value of approximately 77%. In Part 2, the focus is on how the transition is affected independently by total moisture above and below the base of the melting layer. When mean precipitation rates are examined as simultaneous functions of these two moisture layers, four distinct behaviors are observed. These four behaviors suggest unique, yet familiar, physical regimes in which (i) little rain is produced by infrequent clouds, (ii) shallow convection produces increasing warm rain with increasing low-level moisture, (iii) deep convection produces progressively heavier rain above the transition point with increasing total moisture, and (iv) deep stratiform cloud produces increasingly intense precipitation from melting for increasing upper level moisture. The independent thresholds separating regimes in upper and lower layer humidity are shown to result in the value of total column humidity at which a transition between clear air and deep convection, and therefore a pickup in precipitation, is possible. All four regimes force atmospheric columns toward the pickup value at 77% column humidity, but each does so through a unique set of physical processes. Layer moisture and microphysical budgets are analyzed and contrasted with column budgets.

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.

Mittag-Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments.

PubMed

Wu, Ailong; Liu, Ling; Huang, Tingwen; Zeng, Zhigang

2017-01-01

Neurodynamic system is an emerging research field. To understand the essential motivational representations of neural activity, neurodynamics is an important question in cognitive system research. This paper is to investigate Mittag-Leffler stability of a class of fractional-order neural networks in the presence of generalized piecewise constant arguments. To identify neural types of computational principles in mathematical and computational analysis, the existence and uniqueness of the solution of neurodynamic system is the first prerequisite. We prove that the existence and uniqueness of the solution of the network holds when some conditions are satisfied. In addition, self-active neurodynamic system demands stable internal dynamical states (equilibria). The main emphasis will be then on several sufficient conditions to guarantee a unique equilibrium point. Furthermore, to provide deeper explanations of neurodynamic process, Mittag-Leffler stability is studied in detail. The established results are based on the theories of fractional differential equation and differential equation with generalized piecewise constant arguments. The derived criteria improve and extend the existing related results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Closed set of the uniqueness conditions and bifurcation criteria in generalized coupled thermoplasticity for small deformations

NASA Astrophysics Data System (ADS)

Śloderbach, Zdzisław

2016-05-01

This paper reports the results of a study into global and local conditions of uniqueness and the criteria excluding the possibility of bifurcation of the equilibrium state for small strains. The conditions and criteria are derived on the basis of an analysis of the problem of uniqueness of a solution involving the basic incremental boundary problem of coupled generalized thermo-elasto-plasticity. This work forms a follow-up of previous research (Śloderbach in Bifurcations criteria for equilibrium states in generalized thermoplasticity, IFTR Reports, 1980, Arch Mech 3(35):337-349, 351-367, 1983), but contains a new derivation of global and local criteria excluding a possibility of bifurcation of an equilibrium state regarding a comparison body dependent on the admissible fields of stress rate. The thermal elasto-plastic coupling effects, non-associated laws of plastic flow and influence of plastic strains on thermoplastic properties of a body were taken into account in this work. Thus, the mathematical problem considered here is not a self-conjugated problem.

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.

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

PubMed

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

2015-11-01

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

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.

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)

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.

Game Design and Analysis for Price-Based Demand Response: An Aggregate Game Approach.

PubMed

Ye, Maojiao; Hu, Guoqiang

2016-02-18

In this paper, an aggregate game is adopted for the modeling and analysis of energy consumption control in smart grid. Since the electricity users' cost functions depend on the aggregate energy consumption, which is unknown to the end users, an average consensus protocol is employed to estimate it. By neighboring communication among the users about their estimations on the aggregate energy consumption, Nash seeking strategies are developed. Convergence properties are explored for the proposed Nash seeking strategies. For energy consumption game that may have multiple isolated Nash equilibria, a local convergence result is derived. The convergence is established by utilizing singular perturbation analysis and Lyapunov stability analysis. Energy consumption control for a network of heating, ventilation, and air conditioning systems is investigated. Based on the uniqueness of the Nash equilibrium, it is shown that the players' actions converge to a neighborhood of the unique Nash equilibrium nonlocally. More specially, if the unique Nash equilibrium is an inner Nash equilibrium, an exponential convergence result is obtained. Energy consumption game with stubborn players is studied. In this case, the actions of the rational players can be driven to a neighborhood of their best response strategies by using the proposed method. Numerical examples are presented to verify the effectiveness of the proposed methods.

Influence of point defects on the thermal conductivity in FeSi

NASA Astrophysics Data System (ADS)

Stern, Robin; Wang, Tao; Carrete, Jesús; Mingo, Natalio; Madsen, Georg K. H.

2018-05-01

The unique transport properties of B20 FeSi have been investigated for decades. The progress in theoretical calculations allows the explanation and prediction of more and more of such properties. In this paper we investigate the lattice thermal conductivity of FeSi. Calculation for pristine FeSi severely overestimates the lattice thermal conductivity compared to experiment. We point out that the defect concentration can be considerably larger than indicated by the Hall coefficient. The defect formation energies are calculated and it is found that a substantial amount of iron vacancies can form at thermal equilibrium. These will lead to an increased phonon scattering. To explain the thermal conductivity of FeSi, we consider phonon-phonon, isotope, and phonon-defect scattering to assess possible scattering mechanisms. The calculated thermal conductivities indicate that phonon-defect scattering is important in order to explain the reported experimental values.

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.

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

NASA Astrophysics Data System (ADS)

Toaha, S.; Azis, M. I.

2018-03-01

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

Stability in Cohen Grossberg-type bidirectional associative memory neural networks with time-varying delays

NASA Astrophysics Data System (ADS)

Cao, Jinde; Song, Qiankun

2006-07-01

In this paper, the exponential stability problem is investigated for a class of Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays. By using the analysis method, inequality technique and the properties of an M-matrix, several novel sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are derived. Moreover, the exponential convergence rate is estimated. The obtained results are less restrictive than those given in the earlier literature, and the boundedness and differentiability of the activation functions and differentiability of the time-varying delays are removed. Two examples with their simulations are given to show the effectiveness of the obtained results.

Impulsive effect on global exponential stability of BAM fuzzy cellular neural networks with time-varying delays

NASA Astrophysics Data System (ADS)

Li, Kelin

2010-02-01

In this article, a class of impulsive bidirectional associative memory (BAM) fuzzy cellular neural networks (FCNNs) with time-varying delays is formulated and investigated. By employing delay differential inequality and M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM FCNNs with time-varying delays are obtained. In particular, a precise estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive perturbation intention. It is believed that these results are significant and useful for the design and applications of BAM FCNNs. An example is given to show the effectiveness of the results obtained here.

Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties.

PubMed

Song, Qiankun; Yu, Qinqin; Zhao, Zhenjiang; Liu, Yurong; Alsaadi, Fuad E

2018-07-01

In this paper, the boundedness and robust stability for a class of delayed complex-valued neural networks with interval parameter uncertainties are investigated. By using Homomorphic mapping theorem, Lyapunov method and inequality techniques, sufficient condition to guarantee the boundedness of networks and the existence, uniqueness and global robust stability of equilibrium point is derived for the considered uncertain neural networks. The obtained robust stability criterion is expressed in complex-valued LMI, which can be calculated numerically using YALMIP with solver of SDPT3 in MATLAB. An example with simulations is supplied to show the applicability and advantages of the acquired result. Copyright © 2018 Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Singh, Jagadish; Leke, Oni

2014-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

NASA Astrophysics Data System (ADS)

Savitri, D.

2018-01-01

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

Non-equilibrium thermodynamics, maximum entropy production and Earth-system evolution.

PubMed

Kleidon, Axel

2010-01-13

The present-day atmosphere is in a unique state far from thermodynamic equilibrium. This uniqueness is for instance reflected in the high concentration of molecular oxygen and the low relative humidity in the atmosphere. Given that the concentration of atmospheric oxygen has likely increased throughout Earth-system history, we can ask whether this trend can be generalized to a trend of Earth-system evolution that is directed away from thermodynamic equilibrium, why we would expect such a trend to take place and what it would imply for Earth-system evolution as a whole. The justification for such a trend could be found in the proposed general principle of maximum entropy production (MEP), which states that non-equilibrium thermodynamic systems maintain steady states at which entropy production is maximized. Here, I justify and demonstrate this application of MEP to the Earth at the planetary scale. I first describe the non-equilibrium thermodynamic nature of Earth-system processes and distinguish processes that drive the system's state away from equilibrium from those that are directed towards equilibrium. I formulate the interactions among these processes from a thermodynamic perspective and then connect them to a holistic view of the planetary thermodynamic state of the Earth system. In conclusion, non-equilibrium thermodynamics and MEP have the potential to provide a simple and holistic theory of Earth-system functioning. This theory can be used to derive overall evolutionary trends of the Earth's past, identify the role that life plays in driving thermodynamic states far from equilibrium, identify habitability in other planetary environments and evaluate human impacts on Earth-system functioning. This journal is © 2010 The Royal Society

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.

Slope-Velocity-Equilibrium and evolution of surface roughness on a stony hillslope

USDA-ARS?s Scientific Manuscript database

Slope-velocity equilibrium is hypothesized as a state that evolves naturally over time due to the interaction between overland flow and bed morphology, wherein steeper areas develop a relative increase in physical and hydraulic roughness such that flow velocity is a unique function of overland flow ...

Realization of atomistic transitions with colloidal nanoparticles using an ultrafast laser

NASA Astrophysics Data System (ADS)

Akguc, Gursoy; Ilday, Serim; Ilday, Omer; Gulseren, Oguz; Makey, Ghaith; Yavuz, Koray

We report on realization of rapid atomistic transitions with colloidal nanoparticles in a setting that constitutes a dissipative far-from-equilibrium system subject to stochastic forces. Large colloidal crystals (comprising hundreds of particles) can be formed and transitions between solid-liquid-gas phases can be observed effortlessly and within seconds. Furthermore, this system allows us to form and dynamically arrest metastable phases such as glassy structures and to controllably transform a crystal pattern from square to hexagonal lattices and vice versa as well as to observe formation and propagation of crystal defects (i.e. line defects, point defects, planar defects). The mechanism largely relies on an interplay between convective forces induced by femtosecond pulses and strong Brownian motion; the former drags the colloids to form and reinforce the crystal and the latter is analogous to lattice vibrations, which makes it possible to observe phase transitions, defect formation and propagation and lattice transformation. This unique system can help us get insight into the mechanisms underlying various solid state phenomena that were previously studied under slowly evolving (within hours/days), near-equilibrium colloidal systems.

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

NASA Astrophysics Data System (ADS)

Novi W, Cascarilla; Lestari, Dwi

2016-02-01

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

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.

Social Interactions under Incomplete Information: Games, Equilibria, and Expectations

NASA Astrophysics Data System (ADS)

Yang, Chao

My dissertation research investigates interactions of agents' behaviors through social networks when some information is not shared publicly, focusing on solutions to a series of challenging problems in empirical research, including heterogeneous expectations and multiple equilibria. The first chapter, "Social Interactions under Incomplete Information with Heterogeneous Expectations", extends the current literature in social interactions by devising econometric models and estimation tools with private information in not only the idiosyncratic shocks but also some exogenous covariates. For example, when analyzing peer effects in class performances, it was previously assumed that all control variables, including individual IQ and SAT scores, are known to the whole class, which is unrealistic. This chapter allows such exogenous variables to be private information and models agents' behaviors as outcomes of a Bayesian Nash Equilibrium in an incomplete information game. The distribution of equilibrium outcomes can be described by the equilibrium conditional expectations, which is unique when the parameters are within a reasonable range according to the contraction mapping theorem in function spaces. The equilibrium conditional expectations are heterogeneous in both exogenous characteristics and the private information, which makes estimation in this model more demanding than in previous ones. This problem is solved in a computationally efficient way by combining the quadrature method and the nested fixed point maximum likelihood estimation. In Monte Carlo experiments, if some exogenous characteristics are private information and the model is estimated under the mis-specified hypothesis that they are known to the public, estimates will be biased. Applying this model to municipal public spending in North Carolina, significant negative correlations between contiguous municipalities are found, showing free-riding effects. The Second chapter "A Tobit Model with Social Interactions under Incomplete Information", is an application of the first chapter to censored outcomes, corresponding to the situation when agents" behaviors are subjected to some binding restrictions. In an interesting empirical analysis for property tax rates set by North Carolina municipal governments, it is found that there is a significant positive correlation among near-by municipalities. Additionally, some private information about its own residents is used by a municipal government to predict others' tax rates, which enriches current empirical work about tax competition. The third chapter, "Social Interactions under Incomplete Information with Multiple Equilibria", extends the first chapter by investigating effective estimation methods when the condition for a unique equilibrium may not be satisfied. With multiple equilibria, the previous model is incomplete due to the unobservable equilibrium selection. Neither conventional likelihoods nor moment conditions can be used to estimate parameters without further specifications. Although there are some solutions to this issue in the current literature, they are based on strong assumptions such as agents with the same observable characteristics play the same strategy. This paper relaxes those assumptions and extends the all-solution method used to estimate discrete choice games to a setting with both discrete and continuous choices, bounded and unbounded outcomes, and a general form of incomplete information, where the existence of a pure strategy equilibrium has been an open question for a long time. By the use of differential topology and functional analysis, it is found that when all exogenous characteristics are public information, there are a finite number of equilibria. With privately known exogenous characteristics, the equilbria can be represented by a compact set in a Banach space and be approximated by a finite set. As a result, a finite-state probability mass function can be used to specify a probability measure for equilibrium selection, which completes the model. From Monte Carlo experiments about two types of binary choice models, it is found that assuming equilibrium uniqueness can bring in estimation biases when the true value of interaction intensity is large and there are multiple equilibria in the data generating process.

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.

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.

Equilibrium and Stability of a Pendulum in an Orbiting Spaceship.

ERIC Educational Resources Information Center

Blitzer, Leon

1979-01-01

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

Frozen Orbits-Near Constant or Beneficially Varying Orbital Parameters.

DTIC Science & Technology

1986-05-15

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

Connecting Solubility, Equilibrium, and Periodicity in a Green, Inquiry Experiment for the General Chemistry Laboratory

ERIC Educational Resources Information Center

Cacciatore, Kristen L.; Amado, Jose; Evans, Jason J.; Sevian, Hannah

2008-01-01

We present a novel first-year chemistry laboratory experiment that connects solubility, equilibrium, and chemical periodicity concepts. It employs a unique format that asks students to replicate experiments described in different sample lab reports, each lacking some essential information, rather than follow a scripted procedure. This structure is…

Influence of phase connectivity on the relationship among capillary pressure, fluid saturation, and interfacial area in two-fluid-phase porous medium systems

DOE PAGES

McClure, James E.; Berrill, Mark A.; Gray, William G.; ...

2016-09-02

Here, multiphase flow in porous medium systems is typically modeled using continuum mechanical representations at the macroscale in terms of averaged quantities. These models require closure relations to produce solvable forms. One of these required closure relations is an expression relating fluid pressures, fluid saturations, and, in some cases, the interfacial area between the fluid phases, and the Euler characteristic. An unresolved question is whether the inclusion of these additional morphological and topological measures can lead to a non-hysteretic closure relation compared to the hysteretic forms that are used in traditional models, which typically do not include interfacial areas, ormore » the Euler characteristic. We develop a lattice-Boltzmann (LB) simulation approach to investigate the equilibrium states of a two-fluid-phase porous medium system, which include disconnected now- wetting phase features. The proposed approach is applied to a synthetic medium consisting of 1,964 spheres arranged in a random, non-overlapping, close-packed manner, yielding a total of 42,908 different equilibrium points. This information is evaluated using a generalized additive modeling approach to determine if a unique function from this family exists, which can explain the data. The variance of various model estimates is computed, and we conclude that, except for the limiting behavior close to a single fluid regime, capillary pressure can be expressed as a deterministic and non-hysteretic function of fluid saturation, interfacial area between the fluid phases, and the Euler characteristic. This work is unique in the methods employed, the size of the data set, the resolution in space and time, the true equilibrium nature of the data, the parameterizations investigated, and the broad set of functions examined. The conclusion of essentially non-hysteretic behavior provides support for an evolving class of two-fluid-phase flow in porous medium systems models.« less

Influence of phase connectivity on the relationship among capillary pressure, fluid saturation, and interfacial area in two-fluid-phase porous medium systems

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

McClure, James E.; Berrill, Mark A.; Gray, William G.

Here, multiphase flow in porous medium systems is typically modeled using continuum mechanical representations at the macroscale in terms of averaged quantities. These models require closure relations to produce solvable forms. One of these required closure relations is an expression relating fluid pressures, fluid saturations, and, in some cases, the interfacial area between the fluid phases, and the Euler characteristic. An unresolved question is whether the inclusion of these additional morphological and topological measures can lead to a non-hysteretic closure relation compared to the hysteretic forms that are used in traditional models, which typically do not include interfacial areas, ormore » the Euler characteristic. We develop a lattice-Boltzmann (LB) simulation approach to investigate the equilibrium states of a two-fluid-phase porous medium system, which include disconnected now- wetting phase features. The proposed approach is applied to a synthetic medium consisting of 1,964 spheres arranged in a random, non-overlapping, close-packed manner, yielding a total of 42,908 different equilibrium points. This information is evaluated using a generalized additive modeling approach to determine if a unique function from this family exists, which can explain the data. The variance of various model estimates is computed, and we conclude that, except for the limiting behavior close to a single fluid regime, capillary pressure can be expressed as a deterministic and non-hysteretic function of fluid saturation, interfacial area between the fluid phases, and the Euler characteristic. This work is unique in the methods employed, the size of the data set, the resolution in space and time, the true equilibrium nature of the data, the parameterizations investigated, and the broad set of functions examined. The conclusion of essentially non-hysteretic behavior provides support for an evolving class of two-fluid-phase flow in porous medium systems models.« less

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

NASA Astrophysics Data System (ADS)

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

2014-02-01

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

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.

Bright solitons in non-equilibrium coherent quantum matter

PubMed Central

Pinsker, F.; Flayac, H.

2016-01-01

We theoretically demonstrate a mechanism for bright soliton generation in spinor non-equilibrium Bose–Einstein condensates made of atoms or quasi-particles such as polaritons in semiconductor microcavities. We give analytical expressions for bright (half) solitons as minimizing functions of a generalized non-conservative Lagrangian elucidating the unique features of inter and intra-competition in non-equilibrium systems. The analytical results are supported by a detailed numerical analysis that further shows the rich soliton dynamics inferred by their instability and mutual cross-interactions. PMID:26997892

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.

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.

Global exponential stability of bidirectional associative memory neural networks with distributed delays

NASA Astrophysics Data System (ADS)

Song, Qiankun; Cao, Jinde

2007-05-01

A bidirectional associative memory neural network model with distributed delays is considered. By constructing a new Lyapunov functional, employing the homeomorphism theory, M-matrix theory and the inequality (a[greater-or-equal, slanted]0,bk[greater-or-equal, slanted]0,qk>0 with , and r>1), a sufficient condition is obtained to ensure the existence, uniqueness and global exponential stability of the equilibrium point for the model. Moreover, the exponential converging velocity index is estimated, which depends on the delay kernel functions and the system parameters. The results generalize and improve the earlier publications, and remove the usual assumption that the activation functions are bounded . Two numerical examples are given to show the effectiveness of the obtained results.

New exponential stability criteria for stochastic BAM neural networks with impulses

NASA Astrophysics Data System (ADS)

Sakthivel, R.; Samidurai, R.; Anthoni, S. M.

2010-10-01

In this paper, we study the global exponential stability of time-delayed stochastic bidirectional associative memory neural networks with impulses and Markovian jumping parameters. A generalized activation function is considered, and traditional assumptions on the boundedness, monotony and differentiability of activation functions are removed. We obtain a new set of sufficient conditions in terms of linear matrix inequalities, which ensures the global exponential stability of the unique equilibrium point for stochastic BAM neural networks with impulses. The Lyapunov function method with the Itô differential rule is employed for achieving the required result. Moreover, a numerical example is provided to show that the proposed result improves the allowable upper bound of delays over some existing results in the literature.

A new delay-independent condition for global robust stability of neural networks with time delays.

PubMed

Samli, Ruya

2015-06-01

This paper studies the problem of robust stability of dynamical neural networks with discrete time delays under the assumptions that the network parameters of the neural system are uncertain and norm-bounded, and the activation functions are slope-bounded. By employing the results of Lyapunov stability theory and matrix theory, new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for delayed neural networks are presented. The results reported in this paper can be easily tested by checking some special properties of symmetric matrices associated with the parameter uncertainties of neural networks. We also present a numerical example to show the effectiveness of the proposed theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Global exponential stability and lag synchronization for delayed memristive fuzzy Cohen-Grossberg BAM neural networks with impulses.

PubMed

Yang, Wengui; Yu, Wenwu; Cao, Jinde; Alsaadi, Fuad E; Hayat, Tasawar

2018-02-01

This paper investigates the stability and lag synchronization for memristor-based fuzzy Cohen-Grossberg bidirectional associative memory (BAM) neural networks with mixed delays (asynchronous time delays and continuously distributed delays) and impulses. By applying the inequality analysis technique, homeomorphism theory and some suitable Lyapunov-Krasovskii functionals, some new sufficient conditions for the uniqueness and global exponential stability of equilibrium point are established. Furthermore, we obtain several sufficient criteria concerning globally exponential lag synchronization for the proposed system based on the framework of Filippov solution, differential inclusion theory and control theory. In addition, some examples with numerical simulations are given to illustrate the feasibility and validity of obtained results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Stability of Poisson Equilibria and Hamiltonian Relative Equilibria by Energy Methods

NASA Astrophysics Data System (ADS)

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

2004-12-01

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

Remarks on Hierarchic Control for a Linearized Micropolar Fluids System in Moving Domains

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

Jesus, Isaías Pereira de, E-mail: isaias@ufpi.edu.br

We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations in domains with moving boundaries, considering a Nash multi-objective equilibrium (non necessarily cooperative) for the “follower players” (as is called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following main results: the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability of the linearized micropolar system with respect to the leader control and the existence and uniqueness of the Stackelberg–Nash problem, where the optimality system for the leader is given.

Inverse design of an isotropic suspended Kirchhoff rod: theoretical and numerical results on the uniqueness of the natural shape.

PubMed

Bertails-Descoubes, Florence; Derouet-Jourdan, Alexandre; Romero, Victor; Lazarus, Arnaud

2018-04-01

Solving the equations for Kirchhoff elastic rods has been widely explored for decades in mathematics, physics and computer science, with significant applications in the modelling of thin flexible structures such as DNA, hair or climbing plants. As demonstrated in previous experimental and theoretical studies, the natural curvature plays an important role in the equilibrium shape of a Kirchhoff rod, even in the simple case where the rod is isotropic and suspended under gravity. In this paper, we investigate the reverse problem: can we characterize the natural curvature of a suspended isotropic rod, given an equilibrium curve? We prove that although there exists an infinite number of natural curvatures that are compatible with the prescribed equilibrium, they are all equivalent in the sense that they correspond to a unique natural shape for the rod. This natural shape can be computed efficiently by solving in sequence three linear initial value problems, starting from any framing of the input curve. We provide several numerical experiments to illustrate this uniqueness result, and finally discuss its potential impact on non-invasive parameter estimation and inverse design of thin elastic rods.

Slope-velocity equilibrium and evolution of surface roughness on a stony hillslope

NASA Astrophysics Data System (ADS)

Nearing, Mark A.; Polyakov, Viktor O.; Nichols, Mary H.; Hernandez, Mariano; Li, Li; Zhao, Ying; Armendariz, Gerardo

2017-06-01

Slope-velocity equilibrium is hypothesized as a state that evolves naturally over time due to the interaction between overland flow and surface morphology, wherein steeper areas develop a relative increase in physical and hydraulic roughness such that flow velocity is a unique function of overland flow rate independent of slope gradient. This study tests this hypothesis under controlled conditions. Artificial rainfall was applied to 2 m by 6 m plots at 5, 12, and 20 % slope gradients. A series of simulations were made with two replications for each treatment with measurements of runoff rate, velocity, rock cover, and surface roughness. Velocities measured at the end of each experiment were a unique function of discharge rates, independent of slope gradient or rainfall intensity. Physical surface roughness was greater at steeper slopes. The data clearly showed that there was no unique hydraulic coefficient for a given slope, surface condition, or rainfall rate, with hydraulic roughness greater at steeper slopes and lower intensities. This study supports the hypothesis of slope-velocity equilibrium, implying that use of hydraulic equations, such as Chezy and Manning, in hillslope-scale runoff models is problematic because the coefficients vary with both slope and rainfall intensity.

Inverse design of an isotropic suspended Kirchhoff rod: theoretical and numerical results on the uniqueness of the natural shape

NASA Astrophysics Data System (ADS)

Bertails-Descoubes, Florence; Derouet-Jourdan, Alexandre; Romero, Victor; Lazarus, Arnaud

2018-04-01

Solving the equations for Kirchhoff elastic rods has been widely explored for decades in mathematics, physics and computer science, with significant applications in the modelling of thin flexible structures such as DNA, hair or climbing plants. As demonstrated in previous experimental and theoretical studies, the natural curvature plays an important role in the equilibrium shape of a Kirchhoff rod, even in the simple case where the rod is isotropic and suspended under gravity. In this paper, we investigate the reverse problem: can we characterize the natural curvature of a suspended isotropic rod, given an equilibrium curve? We prove that although there exists an infinite number of natural curvatures that are compatible with the prescribed equilibrium, they are all equivalent in the sense that they correspond to a unique natural shape for the rod. This natural shape can be computed efficiently by solving in sequence three linear initial value problems, starting from any framing of the input curve. We provide several numerical experiments to illustrate this uniqueness result, and finally discuss its potential impact on non-invasive parameter estimation and inverse design of thin elastic rods.

On the Uniqueness Conditions and Bifurcation Criteria in Coupled Thermo-Elasto-Plasticity

NASA Astrophysics Data System (ADS)

Śloderbach, Z.

2017-02-01

The global and local conditions of uniqueness and the criteria excluding a possibility of bifurcation of the equilibrium state for small strains are derived. The conditions and criteria are derived analyzing the problem of uniqueness of solution of the basic incremental boundary problem of coupled generalized thermo-elasto-plasticity. This paper is a continuation of some previous works by the author, but contains new derivation of the global and local criteria excluding a possibility of bifurcation of the equilibrium state for a comparison body dependent on statically admissible fields of stress velocity. All the thermal elastoplastic coupling effects, non-associated laws of plastic flow and influence of plastic strains on thermoplastic properties of a body were taken into account in this work. Thus, the mathematical problem considered here is not a self-conjugated problem. The paper contains four Appendices A, B, C and D where the local necessery and sufficient conditions of uniqueness have been derived.

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

NASA Astrophysics Data System (ADS)

Yong, Benny; Samat, Nor Azah

2016-02-01

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

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

NASA Astrophysics Data System (ADS)

Chakraborty, A.; Narayan, A.

2018-03-01

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

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.

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.

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.

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

PubMed

Liu, Peng; Zeng, Zhigang; Wang, Jun

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

Mandal, Partha Sarathi

2018-04-01

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

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.

Soil Moisture Flow and Nitrate Movement Simulation through Deep and Heterogeneous Vadose Zone using Dual-porosity Approach

NASA Astrophysics Data System (ADS)

Yadav, B. K.; Tomar, J.; Harter, T.

2014-12-01

We investigate nitrate movement from non-point sources in deep, heterogeneous vadose zones, using multi-dimensional variably saturated flow and transport simulations. We hypothesize that porous media heterogeneity causes saturation variability that leads to preferential flow systems such that a significant portion of the vadose zone does not significantly contribute to flow. We solve Richards' equation and the advection-dispersion equation to simulate soil moisture and nitrate transport regimes in plot-scale experiments conducted in the San Joaquin Valley, California. We compare equilibrium against non-equilibrium (dual-porosity) approaches. In the equilibrium approach we consider each soil layer to have unique hydraulic properties as a whole, while in the dual-porosity approach we assume that large fractions of the porous flow domain are immobile. However we consider exchange of water and solute between mobile and immobile zone using the appropriate mass transfer terms. The results indicate that flow and transport in a nearly 16 m deep stratified vadose zone comprised of eight layers of unconsolidated alluvium experiences highly non-uniform, localized preferential flow and transport patterns leading to accelerated nitrate transfer. The equilibrium approach largely under-predicted the leaching of nitrate to groundwater while the dual-porosity approach showed higher rates of nitrate leaching, consistent with field observations. The dual-porosity approach slightly over-predicted nitrogen storage in the vadose zone, which may be the result of limited matrix flow or denitrification not accounted for in the model. Results of this study may be helpful to better predict fertilizer and pesticide retention times in deep vadose zone, prior to recharge into the groundwater flow system. Keywords: Nitrate, Preferential flow, Heterogeneous vadose zone, Dual-porosity approach

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.

Interpreting equilibrium-conductivity and conductivity-relaxation measurements to establish thermodynamic and transport properties for multiple charged defect conducting ceramics.

PubMed

Zhu, Huayang; Ricote, Sandrine; Coors, W Grover; Kee, Robert J

2015-01-01

A model-based interpretation of measured equilibrium conductivity and conductivity relaxation is developed to establish thermodynamic, transport, and kinetics parameters for multiple charged defect conducting (MCDC) ceramic materials. The present study focuses on 10% yttrium-doped barium zirconate (BZY10). In principle, using the Nernst-Einstein relationship, equilibrium conductivity measurements are sufficient to establish thermodynamic and transport properties. However, in practice it is difficult to establish unique sets of properties using equilibrium conductivity alone. Combining equilibrium and conductivity-relaxation measurements serves to significantly improve the quantitative fidelity of the derived material properties. The models are developed using a Nernst-Planck-Poisson (NPP) formulation, which enables the quantitative representation of conductivity relaxations caused by very large changes in oxygen partial pressure.

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

PubMed

Nie, Xiaobing; Cao, Jinde

2011-11-01

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

Equilibrium Strategy and Population-Size Effects in Lowest Unique Bid Auctions

NASA Astrophysics Data System (ADS)

Pigolotti, Simone; Bernhardsson, Sebastian; Juul, Jeppe; Galster, Gorm; Vivo, Pierpaolo

2012-02-01

In lowest unique bid auctions, N players bid for an item. The winner is whoever places the lowest bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies. We then study the properties of the solution as a function of the mean number of players, and compare them with a large data set of internet auctions. The theory agrees with the data with striking accuracy for small population-size N, while for larger N a qualitatively different distribution is observed. We interpret this result as the emergence of two different regimes, one in which adaptation is feasible and one in which it is not. Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.

Auxiliary principle technique and iterative algorithm for a perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems.

PubMed

Rahaman, Mijanur; Pang, Chin-Tzong; Ishtyak, Mohd; Ahmad, Rais

2017-01-01

In this article, we introduce a perturbed system of generalized mixed quasi-equilibrium-like problems involving multi-valued mappings in Hilbert spaces. To calculate the approximate solutions of the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems, firstly we develop a perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems, and then by using the celebrated Fan-KKM technique, we establish the existence and uniqueness of solutions of the perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems. By deploying an auxiliary principle technique and an existence result, we formulate an iterative algorithm for solving the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems. Lastly, we study the strong convergence analysis of the proposed iterative sequences under monotonicity and some mild conditions. These results are new and generalize some known results in this field.

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.

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.

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.

Towards Automated Bargaining in Electronic Markets: A Partially Two-Sided Competition Model

NASA Astrophysics Data System (ADS)

Gatti, Nicola; Lazaric, Alessandro; Restelli, Marcello

This paper focuses on the prominent issue of automating bargaining agents within electronic markets. Models of bargaining in literature deal with settings wherein there are only two agents and no model satisfactorily captures settings in which there is competition among buyers, being they more than one, and analogously among sellers. In this paper, we extend the principal bargaining protocol, i.e. the alternating-offers protocol, to capture bargaining in markets. The model we propose is such that, in presence of a unique buyer and a unique seller, agents' equilibrium strategies are those in the original protocol. Moreover, we game theoretically study the considered game providing the following results: in presence of one-sided competition (more buyers and one seller or vice versa) we provide agents' equilibrium strategies for all the values of the parameters, in presence of two-sided competition (more buyers and more sellers) we provide an algorithm that produce agents' equilibrium strategies for a large set of the parameters and we experimentally evaluate its effectiveness.

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.

A stochastic chemostat model with an inhibitor and noise independent of population sizes

NASA Astrophysics Data System (ADS)

Sun, Shulin; Zhang, Xiaolu

2018-02-01

In this paper, a stochastic chemostat model with an inhibitor is considered, here the inhibitor is input from an external source and two organisms in chemostat compete for a nutrient. Firstly, we show that the system has a unique global positive solution. Secondly, by constructing some suitable Lyapunov functions, we investigate that the average in time of the second moment of the solutions of the stochastic model is bounded for a relatively small noise. That is, the asymptotic behaviors of the stochastic system around the equilibrium points of the deterministic system are studied. However, the sufficient large noise can make the microorganisms become extinct with probability one, although the solutions to the original deterministic model may be persistent. Finally, the obtained analytical results are illustrated by computer simulations.

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

Reconstruction of equilibrium trajectories during whole-body movements.

PubMed

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

1999-03-01

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

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

PubMed

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

2016-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

SOL Thermal Instability due to Radial Blob Convection

NASA Astrophysics Data System (ADS)

D'Ippolito, D. A.

2005-10-01

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

Dynamic Analysis of a Reaction-Diffusion Rumor Propagation Model

NASA Astrophysics Data System (ADS)

Zhao, Hongyong; Zhu, Linhe

2016-06-01

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

A hyperjerk memristive system with infinite equilibrium points

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Equilibrium points of the tilted perfect fluid Bianchi VIh state space

NASA Astrophysics Data System (ADS)

Apostolopoulos, Pantelis S.

2005-05-01

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

Optical-cell evidence for superheated ice under gas-hydrate-forming conditions

USGS Publications Warehouse

Stern, L.A.; Hogenboom, D.L.; Durham, W.B.; Kirby, S.H.; Chou, I.-Ming

1998-01-01

We previously reported indirect but compelling evidence that fine-grained H2O ice under elevated CH4 gas pressure can persist to temperatures well above its ordinary melting point while slowly reacting to form methane clathrate hydrate. This phenomenon has now been visually verified by duplicating these experiments in an optical cell while observing the very slow hydrate-forming process as the reactants were warmed from 250 to 290 K at methane pressures of 23 to 30 MPa. Limited hydrate growth occurred rapidly after initial exposure of the methane gas to the ice grains at temperatures well within the ice subsolidus region. No evidence for continued growth of the hydrate phase was observed until samples were warmed above the equilibrium H2O melting curve. With continued heating, no bulk melting of the ice grains or free liquid water was detected anywhere within the optical cell until hydrate dissociation conditions were reached (292 K at 30 MPa), even though full conversion of the ice grains to hydrate requires 6-8 h at temperatures approaching 290 K. In a separate experimental sequence, unreacted portions of H2O ice grains that had persisted to temperatures above their ordinary melting point were successfully induced to melt, without dissociating the coexisting hydrate in the sample tube, by reducing the pressure overstep of the equilibrium phase boundary and thereby reducing the rate of hydrate growth at the ice-hydrate interface. Results from similar tests using CO2 as the hydrate-forming species demonstrated that this superheating effect is not unique to the CH4-H2O system.

Foundations of atmospheric pressure non-equilibrium plasmas

NASA Astrophysics Data System (ADS)

Bruggeman, Peter J.; Iza, Felipe; Brandenburg, Ronny

2017-12-01

Non-equilibrium plasmas have been intensively studied over the past century in the context of material processing, environmental remediation, ozone generation, excimer lamps and plasma display panels. Research on atmospheric pressure non-equilibrium plasmas intensified over the last two decades leading to a large variety of plasma sources that have been developed for an extended application range including chemical conversion, medicine, chemical analysis and disinfection. The fundamental understanding of these discharges is emerging but there remain a lot of unexplained phenomena in these intrinsically complex plasmas. The properties of non-equilibrium plasmas at atmospheric pressure span over a huge range of electron densities as well as heavy particle and electron temperatures. This paper provides an overview of the key underlying processes that are important for the generation and stabilization of atmospheric pressure non-equilibrium plasmas. The unique physical and chemical properties of theses discharges are also summarized.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

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

NASA Astrophysics Data System (ADS)

Ma, C. K.

1995-08-01

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

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

NASA Astrophysics Data System (ADS)

Tan, James P. L.

2018-01-01

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

Symmetric and Asymmetric Tendencies in Stable Complex Systems

PubMed Central

Tan, James P. L.

2016-01-01

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

Symmetric and Asymmetric Tendencies in Stable Complex Systems.

PubMed

Tan, James P L

2016-08-22

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

An Impact Triggered Runaway Greenhouse on Mars

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

Implementation Of Fuzzy Automated Brake Controller Using TSK Algorithm

NASA Astrophysics Data System (ADS)

Mittal, Ruchi; Kaur, Magandeep

2010-11-01

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

Stability of differential susceptibility and infectivity epidemic models

PubMed Central

Bonzi, B.; Fall, A. A.; Iggidr, Abderrahman; Sallet, Gauthier

2011-01-01

We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio ≤ 1 and the existence and uniqueness of an endemic equilibrium when > 1. We also prove the global asymptotic stability of the endemic equilibrium for a differential susceptibility and staged progression infectivity model, when > 1. Our results encompass and generalize those of [18, 22]. AMS Subject Classification : 34A34,34D23,34D40,92D30 PMID:20148330

The sensitivity of tokamak magnetohydrodynamics stability on the edge equilibrium

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

PubMed

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

2017-10-12

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

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.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

PubMed

Nie, Xiaobing; Zheng, Wei Xing

2015-05-01

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

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

PubMed

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

2010-10-01

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

Individual welfare maximization in electricity markets including consumer and full transmission system modeling

NASA Astrophysics Data System (ADS)

Weber, James Daniel

1999-11-01

This dissertation presents a new algorithm that allows a market participant to maximize its individual welfare in the electricity spot market. The use of such an algorithm in determining market equilibrium points, called Nash equilibria, is also demonstrated. The start of the algorithm is a spot market model that uses the optimal power flow (OPF), with a full representation of the transmission system. The OPF is also extended to model consumer behavior, and a thorough mathematical justification for the inclusion of the consumer model in the OPF is presented. The algorithm utilizes price and dispatch sensitivities, available from the Hessian matrix of the OPF, to help determine an optimal change in an individual's bid. The algorithm is shown to be successful in determining local welfare maxima, and the prospects for scaling the algorithm up to realistically sized systems are very good. Assuming a market in which all participants maximize their individual welfare, economic equilibrium points, called Nash equilibria, are investigated. This is done by iteratively solving the individual welfare maximization algorithm for each participant until a point is reached where all individuals stop modifying their bids. It is shown that these Nash equilibria can be located in this manner. However, it is also demonstrated that equilibria do not always exist, and are not always unique when they do exist. It is also shown that individual welfare is a highly nonconcave function resulting in many local maxima. As a result, a more global optimization technique, using a genetic algorithm (GA), is investigated. The genetic algorithm is successfully demonstrated on several systems. It is also shown that a GA can be developed using special niche methods, which allow a GA to converge to several local optima at once. Finally, the last chapter of this dissertation covers the development of a new computer visualization routine for power system analysis: contouring. The contouring algorithm is demonstrated to be useful in visualizing bus-based and transmission line-based quantities.

Structure of the thermodynamic arrow of time in classical and quantum theories

NASA Astrophysics Data System (ADS)

Korzekwa, Kamil

2017-05-01

In this work we analyze the structure of the thermodynamic arrow of time, defined by transformations that leave the thermal equilibrium state unchanged, in classical (incoherent) and quantum (coherent) regimes. We note that in the infinite-temperature limit, the thermodynamic ordering of states in both regimes exhibits a lattice structure. This means that when energy does not matter and the only thermodynamic resource is given by information, the thermodynamic arrow of time has a very specific structure. Namely, for any two states at present there exists a unique state in the past consistent with them and with all possible joint pasts. Similarly, there also exists a unique state in the future consistent with those states and with all possible joint futures. We also show that the lattice structure in the classical regime is broken at finite temperatures, i.e., when energy is a relevant thermodynamic resource. Surprisingly, however, we prove that in the simplest quantum scenario of a two-dimensional system, this structure is preserved at finite temperatures. We provide the physical interpretation of these results by introducing and analyzing the history erasure process, and point out that quantum coherence may be a necessary resource for the existence of an optimal erasure process.

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.

Dynamics of eco-epidemiological model with harvesting

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Chemical equilibrium of ablation materials including condensed species

NASA Technical Reports Server (NTRS)

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

1975-01-01

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

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

DOE PAGES

Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi

2016-11-23

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

Competitive Cyber-Insurance and Internet Security

NASA Astrophysics Data System (ADS)

Shetty, Nikhil; Schwartz, Galina; Felegyhazi, Mark; Walrand, Jean

This paper investigates how competitive cyber-insurers affect network security and welfare of the networked society. In our model, a user's probability to incur damage (from being attacked) depends on both his security and the network security, with the latter taken by individual users as given. First, we consider cyberinsurers who cannot observe (and thus, affect) individual user security. This asymmetric information causes moral hazard. Then, for most parameters, no equilibrium exists: the insurance market is missing. Even if an equilibrium exists, the insurance contract covers only a minor fraction of the damage; network security worsens relative to the no-insurance equilibrium. Second, we consider insurers with perfect information about their users' security. Here, user security is perfectly enforceable (zero cost); each insurance contract stipulates the required user security. The unique equilibrium contract covers the entire user damage. Still, for most parameters, network security worsens relative to the no-insurance equilibrium. Although cyber-insurance improves user welfare, in general, competitive cyber-insurers fail to improve network security.

Phase equilibrium of methane and nitrogen at low temperatures - Application to Titan

NASA Technical Reports Server (NTRS)

Kouvaris, Louis C.; Flasar, F. M.

1991-01-01

Since the vapor phase composition of Titan's methane-nitrogen lower atmosphere is uniquely determined as a function of the Gibbs phase rule, these data are presently computed via integration of the Gibbs-Duhem equation. The thermodynamic consistency of published measurements and calculations of the vapor phase composition is then examined, and the saturated mole fraction of gaseous methane is computed as a function of altitude up to the 700-mbar level. The mole fraction is found to lie approximately halfway between that computed from Raoult's law, for a gas in equilibrium with an ideal solution of liquid nitrogen and methane, and that for a gas in equilibrium with pure liquid methane.

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.

Metastable Eutectic Equilibrium in Natural Environments: Recent Developments and Research Opportunities

NASA Technical Reports Server (NTRS)

Rietmeijer, Fans J. M.; Nuth, Joseph A., II; Jablonska, Mariola; Karner, James M.

2000-01-01

Chemical ordering at metastable eutectics was recognized in non-equilibrium gas-to- solid condensation experiments to constrain 'silicate' dust formation in O-rich circumstellar environments. The predictable metastable eutectic behavior successfully predicted the observed ferromagnesiosilica, compositions of circumstellar dust, presolar and solar nebula grains in the matrix of the collected aggregate IDPs. Many of the experimentally determined metastable eutectic solids match the fundamental building blocks of common rock-forming layer silicates: this could have implications for the origin of Life. The physical conditions conducive to metastable eutectic behavior, i.e. high temperature and (ultra)fast quenching, lead to unique amorphous, typically nano- to micrometer-sized, materials. The new paradigm of metastable eutectic behavior opens the door to new and exciting research opportunities in uncovering the many implications of these unique amorphous and typically nano- to micrometer-sized, metastable eutectic materials.

Efficient and robust relaxation procedures for multi-component mixtures including phase transition

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

Han, Ee, E-mail: eehan@math.uni-bremen.de; Hantke, Maren, E-mail: maren.hantke@ovgu.de; Müller, Siegfried, E-mail: mueller@igpm.rwth-aachen.de

We consider a thermodynamic consistent multi-component model in multi-dimensions that is a generalization of the classical two-phase flow model of Baer and Nunziato. The exchange of mass, momentum and energy between the phases is described by additional source terms. Typically these terms are handled by relaxation procedures. Available relaxation procedures suffer from efficiency and robustness resulting in very costly computations that in general only allow for one-dimensional computations. Therefore we focus on the development of new efficient and robust numerical methods for relaxation processes. We derive exact procedures to determine mechanical and thermal equilibrium states. Further we introduce a novelmore » iterative method to treat the mass transfer for a three component mixture. All new procedures can be extended to an arbitrary number of inert ideal gases. We prove existence, uniqueness and physical admissibility of the resulting states and convergence of our new procedures. Efficiency and robustness of the procedures are verified by means of numerical computations in one and two space dimensions. - Highlights: • We develop novel relaxation procedures for a generalized, thermodynamically consistent Baer–Nunziato type model. • Exact procedures for mechanical and thermal relaxation procedures avoid artificial parameters. • Existence, uniqueness and physical admissibility of the equilibrium states are proven for special mixtures. • A novel iterative method for mass transfer is introduced for a three component mixture providing a unique and admissible equilibrium state.« less

Exploring the Mass Balance and Sea Level Contribution of Global Glaciers During the Last Interglaciation and Mid-Holocene

NASA Astrophysics Data System (ADS)

Smith, S.; Ullman, D. J.; He, F.; Carlson, A. E.; Marzeion, B.; Maussion, F.

2017-12-01

Understanding the behavior of the world's glaciers during previous interglaciations is key to interpreting the sensitivity and behavior of the cryosphere under scenarios of future anthropogenic warming. Previous studies of the Last Interglaciation (LIG, 130 ka to 116 ka) indicate elevated global temperatures and higher sea levels than the Holocene, but most assessments of the impact on the cryosphere have focused on the mass balance and volume change of polar ice sheets. In assessing sea-level sources, most studies assume complete deglacation of global glaciers, but this has yet to be tested. In addition, the significant changes in orbital forcing during the LIG and the associated impacts on climate seasonality and variability may have led to unique glacier evolution.Here, we explore the effect of LIG climate on the global glacier budget. We employ the Open Global Glacier Model (OGGM), forced by simulated LIG equilibrium climate anomalies (127 ka) from the Community Climate System Model Version 3 (CCSM3). OGGM is a glacier mass balance and dynamics model, specifically designed to reconstruct global glacier volume change. Our simulations have been conducted in an equilibrium state to determine the effect of the prolonged climate forcing of the LIG. Due to unknown flow characteristics of glaciers during the LIG, we explore the parametric uncertainty in the mass balance and flow sensitivity parameters. As a point of comparison, we also conduct a series of simulations using forcing anomalies from the CCSM3 mid-Holocene (6 ka) experiment. Results from both experiments show that glacier mass balance is highly sensitive to these sensitivity parameters, pointing at the need for glacier margin calibration for OGGM in paleoclimate applications.

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.

Some properties of correlations of quantum lattice systems in thermal equilibrium

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

Fröhlich, Jürg, E-mail: juerg@phys.ethz.ch; Ueltschi, Daniel, E-mail: daniel@ueltschi.org

Simple proofs of uniqueness of the thermodynamic limit of KMS states and of the decay of equilibrium correlations are presented for a large class of quantum lattice systems at high temperatures. New quantum correlation inequalities for general Heisenberg models are described. Finally, a simplified derivation of a general result on power-law decay of correlations in 2D quantum lattice systems with continuous symmetries is given, extending results of McBryan and Spencer for the 2D classical XY model.

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.

On the Boltzmann-Grad Limit for Smooth Hard-Sphere Systems

NASA Astrophysics Data System (ADS)

Tessarotto, Massimo; Cremaschini, Claudio; Mond, Michael; Asci, Claudio; Soranzo, Alessandro; Tironi, Gino

2018-03-01

The problem is posed of the prescription of the so-called Boltzmann-Grad limit operator (L_{BG}) for the N-body system of smooth hard-spheres which undergo unary, binary as well as multiple elastic instantaneous collisions. It is proved, that, despite the non-commutative property of the operator L_{BG}, the Boltzmann equation can nevertheless be uniquely determined. In particular, consistent with the claim of Uffink and Valente (Found Phys 45:404, 2015) that there is "no time-asymmetric ingredient" in its derivation, the Boltzmann equation is shown to be time-reversal symmetric. The proof is couched on the "ab initio" axiomatic approach to the classical statistical mechanics recently developed (Tessarotto et al. in Eur Phys J Plus 128:32, 2013). Implications relevant for the physical interpretation of the Boltzmann H-theorem and the phenomenon of decay to kinetic equilibrium are pointed out.

Variable-Internal-Stores models of microbial growth and metabolism with dynamic allocation of cellular resources.

PubMed

Nev, Olga A; van den Berg, Hugo A

2017-01-01

Variable-Internal-Stores models of microbial metabolism and growth have proven to be invaluable in accounting for changes in cellular composition as microbial cells adapt to varying conditions of nutrient availability. Here, such a model is extended with explicit allocation of molecular building blocks among various types of catalytic machinery. Such an extension allows a reconstruction of the regulatory rules employed by the cell as it adapts its physiology to changing environmental conditions. Moreover, the extension proposed here creates a link between classic models of microbial growth and analyses based on detailed transcriptomics and proteomics data sets. We ascertain the compatibility between the extended Variable-Internal-Stores model and the classic models, demonstrate its behaviour by means of simulations, and provide a detailed treatment of the uniqueness and the stability of its equilibrium point as a function of the availabilities of the various nutrients.

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

NASA Astrophysics Data System (ADS)

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

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

Anomaly on Superspace of Time Series Data

NASA Astrophysics Data System (ADS)

Capozziello, Salvatore; Pincak, Richard; Kanjamapornkul, Kabin

2017-11-01

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

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

PubMed

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

2015-09-04

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

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.

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

NASA Astrophysics Data System (ADS)

Toaha, Syamsuddin; Rustam

2017-03-01

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

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

PubMed

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

1978-09-01

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

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

NASA Astrophysics Data System (ADS)

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

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

A Class of Solvable Stopping Games

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

Alvarez, Luis H. R.

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

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

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

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

Takeshita, Shunpei; Tanaka, Takahiro; Arakawa, Tomonori

2016-03-07

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Nakedly singular non-vacuum gravitating equilibrium states

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

How Stable Is Stable?

ERIC Educational Resources Information Center

Baehr, Marie

1994-01-01

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

Phase Transitions in Model Active Systems

NASA Astrophysics Data System (ADS)

Redner, Gabriel S.

The amazing collective behaviors of active systems such as bird flocks, schools of fish, and colonies of microorganisms have long amazed scientists and laypeople alike. Understanding the physics of such systems is challenging due to their far-from-equilibrium dynamics, as well as the extreme diversity in their ingredients, relevant time- and length-scales, and emergent phenomenology. To make progress, one can categorize active systems by the symmetries of their constituent particles, as well as how activity is expressed. In this work, we examine two categories of active systems, and explore their phase behavior in detail. First, we study systems of self-propelled spherical particles moving in two dimensions. Despite the absence of an aligning interaction, this system displays complex emergent dynamics, including phase separation into a dense active solid and dilute gas. Using simulations and analytic modeling, we quantify the phase diagram and separation kinetics. We show that this nonequilibrium phase transition is analogous to an equilibrium vapor-liquid system, with binodal and spinodal curves and a critical point. We also characterize the dense active solid phase, a unique material which exhibits the structural signatures of a crystalline solid near the crystal-hexatic transition point, as well as anomalous dynamics including superdiffusive motion on intermediate timescales. We also explore the role of interparticle attraction in this system. We demonstrate that attraction drastically changes the phase diagram, which contains two distinct phase-separated regions and is reentrant as a function of propulsion speed. We interpret this complex situation with a simple kinetic model, which builds from the observed microdynamics of individual particles to a full description of the macroscopic phase behavior. We also study active nematics, liquid crystals driven out of equilibrium by energy-dissipating active stresses. The equilibrium nematic state is unstable in these materials, leading to beautiful and surprising behaviors including the spontaneous generation of topological defect pairs which stream through the system and later annihilate, yielding a complex, seemingly chaotic dynamical steady-state. Here, we describe the emergence of order from this chaos in the form of previously unknown broken-symmetry phases in which the topological defects themselves undergo orientational ordering. We have identified these defect-ordered phases in two realizations of an active nematic: first, a suspension of extensile bundles of microtubules and molecular motor proteins, and second, a computational model of extending hard rods. We will describe the defect-stabilized phases that manifest in these systems, our current understanding of their origins, and discuss whether such phases may be a general feature of extensile active nematics.

(Magneto)caloric refrigeration: Is there light at the end of the tunnel?

DOE PAGES

Pecharsky, Vitalij K.; Cui, Jun; Johnson, Duane D.

2016-07-11

Here, caloric cooling and heat pumping rely on reversible thermal effects triggered in solids by magnetic, electric or stress fields. In the recent past, there have been several successful demonstrations of using first-order phase transition materials in laboratory cooling devices based on both the giant magnetocaloric and elastocaloric effects. All such materials exhibit non-equilibrium behaviours when driven through phase transformations by corresponding fields. Common wisdom is that non-equilibrium states should be avoided; yet, as we show using a model material exhibiting a giant magnetocaloric effect, non-equilibrium phase-separated states offer a unique opportunity to achieve uncommonly large caloric effects by verymore » small perturbations of the driving field(s).« less

(Magneto)caloric refrigeration: Is there light at the end of the tunnel?

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

Pecharsky, Vitalij K.; Cui, Jun; Johnson, Duane D.

Here, caloric cooling and heat pumping rely on reversible thermal effects triggered in solids by magnetic, electric or stress fields. In the recent past, there have been several successful demonstrations of using first-order phase transition materials in laboratory cooling devices based on both the giant magnetocaloric and elastocaloric effects. All such materials exhibit non-equilibrium behaviours when driven through phase transformations by corresponding fields. Common wisdom is that non-equilibrium states should be avoided; yet, as we show using a model material exhibiting a giant magnetocaloric effect, non-equilibrium phase-separated states offer a unique opportunity to achieve uncommonly large caloric effects by verymore » small perturbations of the driving field(s).« less

Lithium-ion Open Circuit Voltage (OCV) curve modelling and its ageing adjustment

NASA Astrophysics Data System (ADS)

Lavigne, L.; Sabatier, J.; Francisco, J. Mbala; Guillemard, F.; Noury, A.

2016-08-01

This paper is a contribution to lithium-ion batteries modelling taking into account aging effects. It first analyses the impact of aging on electrode stoichiometry and then on lithium-ion cell Open Circuit Voltage (OCV) curve. Through some hypotheses and an appropriate definition of the cell state of charge, it shows that each electrode equilibrium potential, but also the whole cell equilibrium potential can be modelled by a polynomial that requires only one adjustment parameter during aging. An adjustment algorithm, based on the idea that for two fixed OCVs, the state of charge between these two equilibrium states is unique for a given aging level, is then proposed. Its efficiency is evaluated on a battery pack constituted of four cells.

Metastable Eutectic Equilibrium in Natural Environments: Recent Development and Research Opportunities

NASA Technical Reports Server (NTRS)

Rietmeijer, Frans J. M.; Nuth, Joseph A., III; Jablonska, Mariola; Karner, James M.

2000-01-01

Chemical ordering at metastable eutectics was recognized in non-equilibrium gas-to- solid condensation experiments to constrain 'silicate' dust formation in O-rich circumstellar environments. The predictable metastable eutectic behavior successfully predicted the observed ferromagnesiosilica compositions of circumstellar dust presolar and solar nebula grains in the matrix of the collected aggregate IDPs (Interplanetary Dust Particles). Many of the experimentally determined metastable eutectic solids match the fundamental building blocks of common rock-forming layer silicates: this could have implications for the origin of Life. The physical conditions conducive to metastable eutectic behavior, i.e. high temperature and (ultra) fast quenching, lead to unique amorphous, typically nano- to micrometer-sized, materials. The new paradigm of metastable eutectic behavior opens the door to new and exciting research opportunities in uncovering the many implications of these unique amorphous, and typically nano-to micrometer-sized, metastable eutectic materials.

Non-equilibrium dissipative supramolecular materials with a tunable lifetime

NASA Astrophysics Data System (ADS)

Tena-Solsona, Marta; Rieß, Benedikt; Grötsch, Raphael K.; Löhrer, Franziska C.; Wanzke, Caren; Käsdorf, Benjamin; Bausch, Andreas R.; Müller-Buschbaum, Peter; Lieleg, Oliver; Boekhoven, Job

2017-07-01

Many biological materials exist in non-equilibrium states driven by the irreversible consumption of high-energy molecules like ATP or GTP. These energy-dissipating structures are governed by kinetics and are thus endowed with unique properties including spatiotemporal control over their presence. Here we show man-made equivalents of materials driven by the consumption of high-energy molecules and explore their unique properties. A chemical reaction network converts dicarboxylates into metastable anhydrides driven by the irreversible consumption of carbodiimide fuels. The anhydrides hydrolyse rapidly to the original dicarboxylates and are designed to assemble into hydrophobic colloids, hydrogels or inks. The spatiotemporal control over the formation and degradation of materials allows for the development of colloids that release hydrophobic contents in a predictable fashion, temporary self-erasing inks and transient hydrogels. Moreover, we show that each material can be re-used for several cycles.

Non-equilibrium dissipative supramolecular materials with a tunable lifetime

PubMed Central

Tena-Solsona, Marta; Rieß, Benedikt; Grötsch, Raphael K.; Löhrer, Franziska C.; Wanzke, Caren; Käsdorf, Benjamin; Bausch, Andreas R.; Müller-Buschbaum, Peter; Lieleg, Oliver; Boekhoven, Job

2017-01-01

Many biological materials exist in non-equilibrium states driven by the irreversible consumption of high-energy molecules like ATP or GTP. These energy-dissipating structures are governed by kinetics and are thus endowed with unique properties including spatiotemporal control over their presence. Here we show man-made equivalents of materials driven by the consumption of high-energy molecules and explore their unique properties. A chemical reaction network converts dicarboxylates into metastable anhydrides driven by the irreversible consumption of carbodiimide fuels. The anhydrides hydrolyse rapidly to the original dicarboxylates and are designed to assemble into hydrophobic colloids, hydrogels or inks. The spatiotemporal control over the formation and degradation of materials allows for the development of colloids that release hydrophobic contents in a predictable fashion, temporary self-erasing inks and transient hydrogels. Moreover, we show that each material can be re-used for several cycles. PMID:28719591

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.

Self-Coexistence among IEEE 802.22 Networks: Distributed Allocation of Power and Channel

PubMed Central

Sakin, Sayef Azad; Alamri, Atif; Tran, Nguyen H.

2017-01-01

Ensuring self-coexistence among IEEE 802.22 networks is a challenging problem owing to opportunistic access of incumbent-free radio resources by users in co-located networks. In this study, we propose a fully-distributed non-cooperative approach to ensure self-coexistence in downlink channels of IEEE 802.22 networks. We formulate the self-coexistence problem as a mixed-integer non-linear optimization problem for maximizing the network data rate, which is an NP-hard one. This work explores a sub-optimal solution by dividing the optimization problem into downlink channel allocation and power assignment sub-problems. Considering fairness, quality of service and minimum interference for customer-premises-equipment, we also develop a greedy algorithm for channel allocation and a non-cooperative game-theoretic framework for near-optimal power allocation. The base stations of networks are treated as players in a game, where they try to increase spectrum utilization by controlling power and reaching a Nash equilibrium point. We further develop a utility function for the game to increase the data rate by minimizing the transmission power and, subsequently, the interference from neighboring networks. A theoretical proof of the uniqueness and existence of the Nash equilibrium has been presented. Performance improvements in terms of data-rate with a degree of fairness compared to a cooperative branch-and-bound-based algorithm and a non-cooperative greedy approach have been shown through simulation studies. PMID:29215591

Self-Coexistence among IEEE 802.22 Networks: Distributed Allocation of Power and Channel.

PubMed

Sakin, Sayef Azad; Razzaque, Md Abdur; Hassan, Mohammad Mehedi; Alamri, Atif; Tran, Nguyen H; Fortino, Giancarlo

2017-12-07

Ensuring self-coexistence among IEEE 802.22 networks is a challenging problem owing to opportunistic access of incumbent-free radio resources by users in co-located networks. In this study, we propose a fully-distributed non-cooperative approach to ensure self-coexistence in downlink channels of IEEE 802.22 networks. We formulate the self-coexistence problem as a mixed-integer non-linear optimization problem for maximizing the network data rate, which is an NP-hard one. This work explores a sub-optimal solution by dividing the optimization problem into downlink channel allocation and power assignment sub-problems. Considering fairness, quality of service and minimum interference for customer-premises-equipment, we also develop a greedy algorithm for channel allocation and a non-cooperative game-theoretic framework for near-optimal power allocation. The base stations of networks are treated as players in a game, where they try to increase spectrum utilization by controlling power and reaching a Nash equilibrium point. We further develop a utility function for the game to increase the data rate by minimizing the transmission power and, subsequently, the interference from neighboring networks. A theoretical proof of the uniqueness and existence of the Nash equilibrium has been presented. Performance improvements in terms of data-rate with a degree of fairness compared to a cooperative branch-and-bound-based algorithm and a non-cooperative greedy approach have been shown through simulation studies.

Self-consistent elastic continuum theory of degenerate, equilibrium aperiodic solids.

PubMed

Bevzenko, Dmytro; Lubchenko, Vassiliy

2014-11-07

We show that the vibrational response of a glassy liquid at finite frequencies can be described by continuum mechanics despite the vast degeneracy of the vibrational ground state; standard continuum elasticity assumes a unique ground state. The effective elastic constants are determined by the bare elastic constants of individual free energy minima of the liquid, the magnitude of built-in stress, and temperature, analogously to how the dielectric response of a polar liquid is determined by the dipole moment of the constituent molecules and temperature. In contrast with the dielectric constant--which is enhanced by adding polar molecules to the system--the elastic constants are down-renormalized by the relaxation of the built-in stress. The renormalization flow of the elastic constants has three fixed points, two of which are trivial and correspond to the uniform liquid state and an infinitely compressible solid, respectively. There is also a nontrivial fixed point at the Poisson ratio equal to 1/5, which corresponds to an isospin-like degeneracy between shear and uniform deformation. The present description predicts a discontinuous jump in the (finite frequency) shear modulus at the crossover from collisional to activated transport, consistent with the random first order transition theory.

Clines in quantitative traits: The role of migration patterns and selection scenarios

PubMed Central

Geroldinger, Ludwig; Bürger, Reinhard

2015-01-01

The existence, uniqueness, and shape of clines in a quantitative trait under selection toward a spatially varying optimum is studied. The focus is on deterministic diploid two-locus n-deme models subject to various migration patterns and selection scenarios. Migration patterns may exhibit isolation by distance, as in the stepping-stone model, or random dispersal, as in the island model. The phenotypic optimum may change abruptly in a single environmental step, more gradually, or not at all. Symmetry assumptions are imposed on phenotypic optima and migration rates. We study clines in the mean, variance, and linkage disequilibrium (LD). Clines result from polymorphic equilibria. The possible equilibrium configurations are determined as functions of the migration rate. Whereas for weak migration, many polymorphic equilibria may be simultaneously stable, their number decreases with increasing migration rate. Also for intermediate migration rates polymorphic equilibria are in general not unique, however, for loci of equal effects the corresponding clines in the mean, variance, and LD are unique. For sufficiently strong migration, no polymorphism is maintained. Both migration pattern and selection scenario exert strong influence on the existence and shape of clines. The results for discrete demes are compared with those from models in which space varies continuously and dispersal is modeled by diffusion. Comparisons with previous studies, which investigated clines under neutrality or under linkage equilibrium, are performed. If there is no long-distance migration, the environment does not change abruptly, and linkage is not very tight, populations are almost everywhere close to linkage equilibrium. PMID:25446959

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.

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.

Risk neutral second best toll pricing.

DOT National Transportation Integrated Search

2011-08-01

We propose a risk-neutral second best toll pricing scheme to account for the possible no uniqueness : of user equilibrium solutions. The scheme is designed to optimize for the expected objective value : as the UE solution varies within the solution s...

Simple Chaotic Flow with Circle and Square Equilibrium

NASA Astrophysics Data System (ADS)

Gotthans, Tomas; Sprott, Julien Clinton; Petrzela, Jiri

Simple systems of third-order autonomous nonlinear differential equations can exhibit chaotic behavior. In this paper, we present a new class of chaotic flow with a square-shaped equilibrium. This unique property has apparently not yet been described. Such a system belongs to a newly introduced category of chaotic systems with hidden attractors that are interesting and important in engineering applications. The mathematical model is accompanied by an electrical circuit implementation, demonstrating structural stability of the strange attractor. The circuit is simulated with PSpice, constructed, and analyzed (measured).

Capacity choice in a large market.

PubMed

Godenhielm, Mats; Kultti, Klaus

2014-01-01

We analyze endogenous capacity formation in a large frictional market with perfectly divisible goods. Each seller posts a price and decides on a capacity. The buyers base their decision on which seller to visit on both characteristics. In this setting we determine the conditions for the existence and uniqueness of a symmetric equilibrium. When capacity is unobservable there exists a continuum of equilibria. We show that the "best" of these equilibria leads to the same seller capacities and the same number of trades as the symmetric equilibrium under observable capacity.

Effect of stirring on the safety of flammable liquid mixtures.

PubMed

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

2010-05-15

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

Late-time behaviour of the tilted Bianchi type VIh models

NASA Astrophysics Data System (ADS)

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

2007-08-01

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

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

PubMed

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

2003-08-29

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

Probability and surprisal in auditory comprehension of morphologically complex words.

PubMed

Balling, Laura Winther; Baayen, R Harald

2012-10-01

Two auditory lexical decision experiments document for morphologically complex words two points at which the probability of a target word given the evidence shifts dramatically. The first point is reached when morphologically unrelated competitors are no longer compatible with the evidence. Adapting terminology from Marslen-Wilson (1984), we refer to this as the word's initial uniqueness point (UP1). The second point is the complex uniqueness point (CUP) introduced by Balling and Baayen (2008), at which morphologically related competitors become incompatible with the input. Later initial as well as complex uniqueness points predict longer response latencies. We argue that the effects of these uniqueness points arise due to the large surprisal (Levy, 2008) carried by the phonemes at these uniqueness points, and provide independent evidence that how cumulative surprisal builds up in the course of the word co-determines response latencies. The presence of effects of surprisal, both at the initial uniqueness point of complex words, and cumulatively throughout the word, challenges the Shortlist B model of Norris and McQueen (2008), and suggests that a Bayesian approach to auditory comprehension requires complementation from information theory in order to do justice to the cognitive cost of updating probability distributions over lexical candidates. Copyright © 2012 Elsevier B.V. All rights reserved.

Modified NASA-Lewis chemical equilibrium code for MHD applications

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

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

PubMed

Wang, Zhen; Campbell, Sue Ann

2017-11-01

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

A Floating Cylinder on an Unbounded Bath

NASA Astrophysics Data System (ADS)

Chen, Hanzhe; Siegel, David

2018-03-01

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

Legendre submanifolds in contact manifolds as attractors and geometric nonequilibrium thermodynamics

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

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

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

Analysis of gene network robustness based on saturated fixed point attractors

PubMed Central

2014-01-01

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

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.

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.

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.

Local thermodynamic equilibrium in a laser-induced plasma evidenced by blackbody radiation

NASA Astrophysics Data System (ADS)

Hermann, Jörg; Grojo, David; Axente, Emanuel; Craciun, Valentin

2018-06-01

We show that the plasma produced by laser ablation of solid materials in specific conditions has an emission spectrum that is characterized by the saturation of the most intense spectral lines at the blackbody radiance. The blackbody temperature equals the excitation temperature of atoms and ions, proving directly and unambiguously a plasma in local thermodynamic equilibrium. The present investigations take benefit from the very rich and intense emission spectrum generated by ablation of a nickel-chromium-molybdenum alloy. This alternative and direct proof of the plasma equilibrium state re-opens the perspectives of quantitative material analyses via calibration-free laser-induced breakdown spectroscopy. Moreover, the unique properties of this laser-produced plasma promote its use as radiation standard for intensity calibration of spectroscopic instruments.

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.

Development of interactive graphic user interfaces for modeling reaction-based biogeochemical processes in batch systems with BIOGEOCHEM

NASA Astrophysics Data System (ADS)

Chang, C.; Li, M.; Yeh, G.

2010-12-01

The BIOGEOCHEM numerical model (Yeh and Fang, 2002; Fang et al., 2003) was developed with FORTRAN for simulating reaction-based geochemical and biochemical processes with mixed equilibrium and kinetic reactions in batch systems. A complete suite of reactions including aqueous complexation, adsorption/desorption, ion-exchange, redox, precipitation/dissolution, acid-base reactions, and microbial mediated reactions were embodied in this unique modeling tool. Any reaction can be treated as fast/equilibrium or slow/kinetic reaction. An equilibrium reaction is modeled with an implicit finite rate governed by a mass action equilibrium equation or by a user-specified algebraic equation. A kinetic reaction is modeled with an explicit finite rate with an elementary rate, microbial mediated enzymatic kinetics, or a user-specified rate equation. None of the existing models has encompassed this wide array of scopes. To ease the input/output learning curve using the unique feature of BIOGEOCHEM, an interactive graphic user interface was developed with the Microsoft Visual Studio and .Net tools. Several user-friendly features, such as pop-up help windows, typo warning messages, and on-screen input hints, were implemented, which are robust. All input data can be real-time viewed and automated to conform with the input file format of BIOGEOCHEM. A post-processor for graphic visualizations of simulated results was also embedded for immediate demonstrations. By following data input windows step by step, errorless BIOGEOCHEM input files can be created even if users have little prior experiences in FORTRAN. With this user-friendly interface, the time effort to conduct simulations with BIOGEOCHEM can be greatly reduced.

13-Moment System with Global Hyperbolicity for Quantum Gas

NASA Astrophysics Data System (ADS)

Di, Yana; Fan, Yuwei; Li, Ruo

2017-06-01

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

Equilibrium radiative heating tables for aerobraking in the Martian atmosphere

NASA Astrophysics Data System (ADS)

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

1990-05-01

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

Equilibrium radiative heating tables for aerobraking in the Martian atmosphere

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

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

PubMed Central

Zhuang, Qian; Di, Zengru; Wu, Jinshan

2014-01-01

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

Access point selection game with mobile users using correlated equilibrium.

PubMed

Sohn, Insoo

2015-01-01

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

Access Point Selection Game with Mobile Users Using Correlated Equilibrium

PubMed Central

Sohn, Insoo

2015-01-01

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

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.

The Equilibrium Allele Frequency Distribution for a Population with Reproductive Skew

PubMed Central

Der, Ricky; Plotkin, Joshua B.

2014-01-01

We study the population genetics of two neutral alleles under reversible mutation in a model that features a skewed offspring distribution, called the Λ-Fleming–Viot process. We describe the shape of the equilibrium allele frequency distribution as a function of the model parameters. We show that the mutation rates can be uniquely identified from this equilibrium distribution, but the form of the offspring distribution cannot itself always be so identified. We introduce an estimator for the mutation rate that is consistent, independent of the form of reproductive skew. We also introduce a two-allele infinite-sites version of the Λ-Fleming–Viot process, and we use it to study how reproductive skew influences standing genetic diversity in a population. We derive asymptotic formulas for the expected number of segregating sites as a function of sample size and offspring distribution. We find that the Wright–Fisher model minimizes the equilibrium genetic diversity, for a given mutation rate and variance effective population size, compared to all other Λ-processes. PMID:24473932

Reactive solute transport in streams: 1. Development of an equilibrium- based model

USGS Publications Warehouse

Runkel, Robert L.; Bencala, Kenneth E.; Broshears, Robert E.; Chapra, Steven C.

1996-01-01

An equilibrium-based solute transport model is developed for the simulation of trace metal fate and transport in streams. The model is formed by coupling a solute transport model with a chemical equilibrium submodel based on MINTEQ. The solute transport model considers the physical processes of advection, dispersion, lateral inflow, and transient storage, while the equilibrium submodel considers the speciation and complexation of aqueous species, precipitation/dissolution and sorption. Within the model, reactions in the water column may result in the formation of solid phases (precipitates and sorbed species) that are subject to downstream transport and settling processes. Solid phases on the streambed may also interact with the water column through dissolution and sorption/desorption reactions. Consideration of both mobile (water-borne) and immobile (streambed) solid phases requires a unique set of governing differential equations and solution techniques that are developed herein. The partial differential equations describing physical transport and the algebraic equations describing chemical equilibria are coupled using the sequential iteration approach.

A Unique Supernova Graphite: Contemporaneous Condensation of All Things Carbonaceous

NASA Astrophysics Data System (ADS)

Croat, T. K.; Jadhav, M.; Lebsack, E.; Bernatowicz, T. J.

2011-03-01

We report a supernova graphite that contains internal subgrains of TiC, SiC, Fe and Ni silicides, and iron metal. These phases comprise a complete list of the phases predicted by equilibrium calculations to condense from C-rich supernova zones.

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

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

Averboukh, Yurii V

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

Quantum gambling based on Nash-equilibrium

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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

NASA Technical Reports Server (NTRS)

Palmer, Grant

1987-01-01

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

Excito-oscillatory dynamics as a mechanism of ventricular fibrillation.

PubMed

Gray, Richard A; Huelsing, Delilah J

2008-04-01

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

On The Dynamics And Kinematics Of Two Fluid Phase Flow In Porous Media

DTIC Science & Technology

2015-06-16

fluid-fluid interfacial area density in a two-fluid-system. This dynamic equation set is unique to this work, and the importance of the modeled...saturation data intended to denote an equilibrium state is likely a sampling from a dynamic system undergoing changes of interfacial curvatures that are not... interfacial area density in a two-fluid-system. This dynamic equation set is unique to this work, and the importance of the modeled physics is shown

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

NASA Astrophysics Data System (ADS)

Feng, Jinglang; Hou, Xiyun

2017-07-01

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

Quantum oligopoly

NASA Astrophysics Data System (ADS)

Lo, C. F.; Kiang, D.

2003-12-01

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

TIME-DEPENDENT COROTATION RESONANCE IN BARRED GALAXIES

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

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

2016-10-20

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

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.

On the use of two-time correlation functions for X-ray photon correlation spectroscopy data analysis.

PubMed

Bikondoa, Oier

2017-04-01

Multi-time correlation functions are especially well suited to study non-equilibrium processes. In particular, two-time correlation functions are widely used in X-ray photon correlation experiments on systems out of equilibrium. One-time correlations are often extracted from two-time correlation functions at different sample ages. However, this way of analysing two-time correlation functions is not unique. Here, two methods to analyse two-time correlation functions are scrutinized, and three illustrative examples are used to discuss the implications for the evaluation of the correlation times and functional shape of the correlations.

A Game Theoretical Model for Location of Terror Response Facilities under Capacitated Resources

PubMed Central

Kang, Qi; Xu, Weisheng; Wu, Qidi

2013-01-01

This paper is concerned with the effect of capacity constraints on the locations of terror response facilities. We assume that the state has limited resources, and multiple facilities may be involved in the response until the demand is satisfied consequently. We formulate a leader-follower game model between the state and the terrorist and prove the existence and uniqueness of the Nash equilibrium. An integer linear programming is proposed to obtain the equilibrium results when the facility number is fixed. The problem is demonstrated by a case study of the 19 districts of Shanghai, China. PMID:24459446

Quantum Approach to Cournot-type Competition

NASA Astrophysics Data System (ADS)

Frąckiewicz, Piotr

2018-02-01

The aim of this paper is to investigate Cournot-type competition in the quantum domain with the use of the Li-Du-Massar scheme for continuous-variable quantum games. We derive a formula which, in a simple way, determines a unique Nash equilibrium. The result concerns a large class of Cournot duopoly problems including the competition, where the demand and cost functions are not necessary linear. Further, we show that the Nash equilibrium converges to a Pareto-optimal strategy profile as the quantum correlation increases. In addition to illustrating how the formula works, we provide the readers with two examples.

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

PubMed

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

2017-12-15

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

Gaussian random bridges and a geometric model for information equilibrium

NASA Astrophysics Data System (ADS)

Mengütürk, Levent Ali

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

Adams, Fred C.

2018-04-01

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

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

PubMed

Ispolatov, Iaroslav; Madhok, Vaibhav; Doebeli, Michael

2016-02-07

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

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

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

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

2013-07-10

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

Global dynamics of a network-based SIQRS epidemic model with demographics and vaccination

NASA Astrophysics Data System (ADS)

Huang, Shouying; Chen, Fengde; Chen, Lijuan

2017-02-01

This paper investigates a new SIQRS epidemic model with demographics and vaccination on complex heterogeneous networks. We analytically derive the basic reproduction number R0, which determines not only the existence of endemic equilibrium but also the global dynamics of the model. The permanence of the disease and the globally asymptotical stability of disease-free equilibrium are proved in detail. By using a monotone iterative technique, we show that the unique endemic equilibrium is globally attractive under certain conditions. Our results really improve and enrich the results in Li et al (2014) [14]. Interestingly, the basic reproduction number R0 bears no relation to the degree-dependent birth, but our simulations indicate that the degree-dependent birth does affect the epidemic dynamics. Furthermore, we find that quarantine plays a more active role than vaccination in controlling the disease.

The Equilibrium State of Colliding Electron Beams

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

Warnock, R

2003-12-12

We study a nonlinear integral equation that is a necessary condition on the equilibrium phase space distribution function of stored, colliding electron beams. It is analogous to the Haissinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. The equation is analyzed for the case of the Chao-Ruth model of the beam-beam interaction in one degree of freedom, a so-called strong-strong model with nonlinear beam-beam force. We prove existence of a unique solution, for sufficiently small beam current, by an application of the implicit function theorem. We have not yet proved that this solution is positive, asmore » would be required to establish existence of an equilibrium. There is, however, numerical evidence of a positive solution. We expect that our analysis can be extended to more realistic models.« less

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

PubMed

Fronczak, Agata; Fronczak, Piotr

2016-07-01

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

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

PubMed Central

Latash, Mark L.

2009-01-01

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

Laser fusion neutron source employing compression with short pulse lasers

DOEpatents

Sefcik, Joseph A; Wilks, Scott C

2013-11-05

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

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

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

The effects of practice on movement distance and final position reproduction: implications for the equilibrium-point control of movements.

PubMed

Jaric, S; Corcos, D M; Gottlieb, G L; Ilic, D B; Latash, M L

1994-01-01

Predictions of two views on single-joint motor control, namely programming of muscle force patterns and equilibrium-point control, were compared with the results of experiments with reproduction of movement distance and final location during fast unidirectional elbow flexions. Two groups of subjects were tested. The first group practiced movements over a fixed distance (36 degrees), starting from seven different initial positions (distance group, DG). The second group practiced movements from the same seven initial positions to a fixed final location (location group, LG). Later, all the subjects were tested at the practiced task with their eyes closed, and then, unexpectedly for the subjects, they were tested at the other, unpracticed task. In both groups, the task to reproduce final position had lower indices of final position variability than the task to reproduce movement distance. Analysis of the linear regression lines between initial position and final position (or movement distance) also demonstrated a better (more accurate) performance during final position reproduction than during distance reproduction. The data are in a good correspondence with the predictions of the equilibrium-point hypothesis, but not with the predictions of the force-pattern control approach.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

PubMed

Niu, Yuanling; Wang, Yue; Zhou, Da

2015-12-07

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

Creation and protection of entanglement in systems out of thermal equilibrium

NASA Astrophysics Data System (ADS)

Bellomo, Bruno; Antezza, Mauro

2013-11-01

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

The Painting-Sponging Analogy for Chemical Equilibrium

NASA Astrophysics Data System (ADS)

Gamitz, Adoni

1997-05-01

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

Gas-liquid chromatography with a volatile "stationary" liquid phase.

PubMed

Wells, P S; Zhou, S; Parcher, J F

2002-05-01

A unique type of gas-liquid chromatography is described in which both mobile and "stationary" phases are composed of synthetic mixtures of helium and carbon dioxide. At temperatures below the critical point of the binary mixture and pressures above the vapor pressure of pure liquid carbon dioxide, helium and carbon dioxide can form two immiscible phases over extended composition ranges. A binary vapor phase enriched in helium can act as the mobile phase for chromatographic separations, whereas a CO2-rich liquid in equilibrium with the vapor phase, but condensed on the column wall, can act as a pseudostationary phase. Several examples of chromatographic separations obtained in "empty" capillary columns with no ordinary stationary liquid phase illustrate the range of conditions that produce such separations. In addition, several experiments are reported that confirm the proposed two-phase hypothesis. The possible consequences of the observed chromatographic phenomenon in the field of supercritical fluid chromatography with helium headspace carbon dioxide are discussed.

Family matters: sibling rivalry and bonding between p53 and p63 in cancer.

PubMed

Romano, Rose-Anne; Sinha, Satrajit

2014-04-01

The p53 family (p53, p63 and p73) is intimately linked with an overwhelming number of cellular processes during normal physiological as well as pathological conditions including cancer. The fact that these proteins are expressed in myriad isoforms, each with unique biochemical properties and distinct effects on tumorigenesis, complicates their study. A case in point is Squamous Cell Carcinoma (SCC) where p53 is often mutated and the ΔNp63 isoform is overexpressed. Given that p53 and p63 can hetero-dimerize, bind to quite similar DNA elements and share common co-factors, any alterations in their individual expression levels, activity and/or mutation can severely disrupt the family equilibrium. The burgeoning genomics data sets and new additions to the experimental toolbox are offering crucial insights into the complex role of the p53 family in SCC, but more mechanistic studies are needed. © 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Global analysis of an impulsive delayed Lotka-Volterra competition system

NASA Astrophysics Data System (ADS)

Xia, Yonghui

2011-03-01

In this paper, a retarded impulsive n-species Lotka-Volterra competition system with feedback controls is studied. Some sufficient conditions are obtained to guarantee the global exponential stability and global asymptotic stability of a unique equilibrium for such a high-dimensional biological system. The problem considered in this paper is in many aspects more general and incorporates as special cases various problems which have been extensively studied in the literature. Moreover, applying the obtained results to some special cases, I derive some new criteria which generalize and greatly improve some well known results. A method is proposed to investigate biological systems subjected to the effect of both impulses and delays. The method is based on Banach fixed point theory and matrix's spectral theory as well as Lyapunov function. Moreover, some novel analytic techniques are employed to study GAS and GES. It is believed that the method can be extended to other high-dimensional biological systems and complex neural networks. Finally, two examples show the feasibility of the results.

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

PubMed Central

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

2015-01-01

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

Equilibrium-point control of human elbow-joint movement under isometric environment by using multichannel functional electrical stimulation

PubMed Central

Matsui, Kazuhiro; Hishii, Yasuo; Maegaki, Kazuya; Yamashita, Yuto; Uemura, Mitsunori; Hirai, Hiroaki; Miyazaki, Fumio

2014-01-01

Functional electrical stimulation (FES) is considered an effective technique for aiding quadriplegic persons. However, the human musculoskeletal system has highly non-linearity and redundancy. It is thus difficult to stably and accurately control limbs using FES. In this paper, we propose a simple FES method that is consistent with the motion-control mechanism observed in humans. We focus on joint motion by a pair of agonist-antagonist muscles of the musculoskeletal system, and define the “electrical agonist-antagonist muscle ratio (EAA ratio)” and “electrical agonist-antagonist muscle activity (EAA activity)” in light of the agonist-antagonist muscle ratio and agonist-antagonist muscle activity, respectively, to extract the equilibrium point and joint stiffness from electromyography (EMG) signals. These notions, the agonist-antagonist muscle ratio and agonist-antagonist muscle activity, are based on the hypothesis that the equilibrium point and stiffness of the agonist-antagonist motion system are controlled by the central nervous system. We derived the transfer function between the input EAA ratio and force output of the end-point. We performed some experiments in an isometric environment using six subjects. This transfer-function model is expressed as a cascade-coupled dead time element and a second-order system. High-speed, high-precision, smooth control of the hand force were achieved through the agonist-antagonist muscle stimulation pattern determined by this transfer function model. PMID:24987326

Equilibrium-point control of human elbow-joint movement under isometric environment by using multichannel functional electrical stimulation.

PubMed

Matsui, Kazuhiro; Hishii, Yasuo; Maegaki, Kazuya; Yamashita, Yuto; Uemura, Mitsunori; Hirai, Hiroaki; Miyazaki, Fumio

2014-01-01

Functional electrical stimulation (FES) is considered an effective technique for aiding quadriplegic persons. However, the human musculoskeletal system has highly non-linearity and redundancy. It is thus difficult to stably and accurately control limbs using FES. In this paper, we propose a simple FES method that is consistent with the motion-control mechanism observed in humans. We focus on joint motion by a pair of agonist-antagonist muscles of the musculoskeletal system, and define the "electrical agonist-antagonist muscle ratio (EAA ratio)" and "electrical agonist-antagonist muscle activity (EAA activity)" in light of the agonist-antagonist muscle ratio and agonist-antagonist muscle activity, respectively, to extract the equilibrium point and joint stiffness from electromyography (EMG) signals. These notions, the agonist-antagonist muscle ratio and agonist-antagonist muscle activity, are based on the hypothesis that the equilibrium point and stiffness of the agonist-antagonist motion system are controlled by the central nervous system. We derived the transfer function between the input EAA ratio and force output of the end-point. We performed some experiments in an isometric environment using six subjects. This transfer-function model is expressed as a cascade-coupled dead time element and a second-order system. High-speed, high-precision, smooth control of the hand force were achieved through the agonist-antagonist muscle stimulation pattern determined by this transfer function model.

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

NASA Astrophysics Data System (ADS)

Coley, Alan; Hervik, Sigbjørn

2005-02-01

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

Phase Transitions and Scaling in Systems Far from Equilibrium

NASA Astrophysics Data System (ADS)

Täuber, Uwe C.

2017-03-01

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

Revealing missing charges with generalised quantum fluctuation relations.

PubMed

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

2018-05-22

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

Hysteresis of Contact Angle of Sessile Droplets on Smooth Homogeneous Solid Substrates via Disjoining/Conjoining Pressure.

PubMed

Kuchin, I; Starov, V

2015-05-19

A theory of contact angle hysteresis of liquid droplets on smooth, homogeneous solid substrates is developed in terms of the shape of the disjoining/conjoining pressure isotherm and quasi-equilibrium phenomena. It is shown that all contact angles, θ, in the range θr < θ < θa, which are different from the unique equilibrium contact angle θ ≠ θe, correspond to the state of slow "microscopic" advancing or receding motion of the liquid if θe < θ < θa or θr < θ < θe, respectively. This "microscopic" motion almost abruptly becomes fast "macroscopic" advancing or receding motion after the contact angle reaches the critical values θa or θr, correspondingly. The values of the static receding, θr, and static advancing, θa, contact angles in cylindrical capillaries were calculated earlier, based on the shape of disjoining/conjoining pressure isotherm. It is shown now that (i) both advancing and receding contact angles of a droplet on a on smooth, homogeneous solid substrate can be calculated based on shape of disjoining/conjoining pressure isotherm, and (ii) both advancing and receding contact angles depend on the drop volume and are not unique characteristics of the liquid-solid system. The latter is different from advancing/receding contact angles in thin capillaries. It is shown also that the receding contact angle is much closer to the equilibrium contact angle than the advancing contact angle. The latter conclusion is unexpected and is in a contradiction with the commonly accepted view that the advancing contact angle can be taken as the first approximation for the equilibrium contact angle. The dependency of hysteresis contact angles on the drop volume has a direct experimental confirmation.

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

ERIC Educational Resources Information Center

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

2017-01-01

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

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

ERIC Educational Resources Information Center

Flores, Alfinio; Park, Jungeun

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

BINARY CORRELATIONS IN IONIZED GASES

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

Balescu, R.; Taylor, H.S.

1961-01-01

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

Equilibrium and nonequilibrium models on Solomon networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2016-05-01

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

Algorithm For Hypersonic Flow In Chemical Equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

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

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

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

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

2017-07-01

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

Dynamical System Analysis of Reynolds Stress Closure Equations

NASA Technical Reports Server (NTRS)

Girimaji, Sharath S.

1997-01-01

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

Equilibrium shape of 4He crystal under zero gravity below 200 mK

PubMed Central

Takahashi, Takuya; Ohuchi, Haruka; Nomura, Ryuji; Okuda, Yuichi

2015-01-01

Equilibrium crystal shape is the lowest energy crystal shape that is hardly realized in ordinary crystals because of their slow relaxation. 4He quantum crystals in a superfluid have been expected as unique exceptions that grow extremely fast at very low temperatures. However, on the ground, gravity considerably deforms the crystals and conceals the equilibrium crystal shape, and thus, gravity-free environment is needed to observe the equilibrium shape of 4He. We report the relaxation processes of macroscopic 4He crystals in a superfluid below 200 mK under zero gravity using a parabolic flight of a jet plane. When gravity was removed from a gravity-flattened 4He crystal, the crystal rapidly transformed into a shape with flat surfaces. Although the relaxation processes were highly dependent on the initial condition, the crystals relaxed to a nearly homothetic shape in the end, indicating that they were truly in an equilibrium shape minimizing the interfacial free energy. Thanks to the equilibrium shape, we were able to determine the Wulff’s origin and the size of the c-facet together with the vicinal surface profile next to the c-facet. The c-facet size was extremely small in the quantum crystals, and the facet-like flat surfaces were found to be the vicinal surfaces. At the same time, the interfacial free energy of the a-facet and s-facet was also obtained. PMID:26601315

Equilibrium shape of (4)He crystal under zero gravity below 200 mK.

PubMed

Takahashi, Takuya; Ohuchi, Haruka; Nomura, Ryuji; Okuda, Yuichi

2015-10-01

Equilibrium crystal shape is the lowest energy crystal shape that is hardly realized in ordinary crystals because of their slow relaxation. (4)He quantum crystals in a superfluid have been expected as unique exceptions that grow extremely fast at very low temperatures. However, on the ground, gravity considerably deforms the crystals and conceals the equilibrium crystal shape, and thus, gravity-free environment is needed to observe the equilibrium shape of (4)He. We report the relaxation processes of macroscopic (4)He crystals in a superfluid below 200 mK under zero gravity using a parabolic flight of a jet plane. When gravity was removed from a gravity-flattened (4)He crystal, the crystal rapidly transformed into a shape with flat surfaces. Although the relaxation processes were highly dependent on the initial condition, the crystals relaxed to a nearly homothetic shape in the end, indicating that they were truly in an equilibrium shape minimizing the interfacial free energy. Thanks to the equilibrium shape, we were able to determine the Wulff's origin and the size of the c-facet together with the vicinal surface profile next to the c-facet. The c-facet size was extremely small in the quantum crystals, and the facet-like flat surfaces were found to be the vicinal surfaces. At the same time, the interfacial free energy of the a-facet and s-facet was also obtained.

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

NASA Technical Reports Server (NTRS)

Wilkinson, R. Allen

1992-01-01

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

Building a Foundation for Bioenergetics

ERIC Educational Resources Information Center

Hamori, Eugene

2002-01-01

To give students a lasting comprehension of bioenergetics, first such basics as heat, work, equilibrium, entropy, free energy, closed "versus" open systems, steady state, and reversibility should be explained to them in a meticulous manner, albeit with a minimal use of mathematical formulae. The unique feature of thermodynamics, that it does not…

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

NASA Astrophysics Data System (ADS)

Lei, Hanlun; Xu, Bo; Circi, Christian

2018-05-01

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

Prediction of boiling points of organic compounds by QSPR tools.

PubMed

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

2013-07-01

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

The modeling and analysis of the word-of-mouth marketing

NASA Astrophysics Data System (ADS)

Li, Pengdeng; Yang, Xiaofan; Yang, Lu-Xing; Xiong, Qingyu; Wu, Yingbo; Tang, Yuan Yan

2018-03-01

As compared to the traditional advertising, word-of-mouth (WOM) communications have striking advantages such as significantly lower cost and much faster propagation, and this is especially the case with the popularity of online social networks. This paper focuses on the modeling and analysis of the WOM marketing. A dynamic model, known as the SIPNS model, capturing the WOM marketing processes with both positive and negative comments is established. On this basis, a measure of the overall profit of a WOM marketing campaign is proposed. The SIPNS model is shown to admit a unique equilibrium, and the equilibrium is determined. The impact of different factors on the equilibrium of the SIPNS model is illuminated through theoretical analysis. Extensive experimental results suggest that the equilibrium is much likely to be globally attracting. Finally, the influence of different factors on the expected overall profit of a WOM marketing campaign is ascertained both theoretically and experimentally. Thereby, some promotion strategies are recommended. To our knowledge, this is the first time the WOM marketing is treated in this way.

General framework for fluctuating dynamic density functional theory

NASA Astrophysics Data System (ADS)

Durán-Olivencia, Miguel A.; Yatsyshin, Peter; Goddard, Benjamin D.; Kalliadasis, Serafim

2017-12-01

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig’s projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium.

Conformational Equilibria in Monomeric α-Synuclein at the Single-Molecule Level

PubMed Central

Tessari, Isabella; Mammi, Stefano; Bergantino, Elisabetta; Musiani, Francesco; Brucale, Marco; Bubacco, Luigi; Samorì, Bruno

2008-01-01

Human α-Synuclein (αSyn) is a natively unfolded protein whose aggregation into amyloid fibrils is involved in the pathology of Parkinson disease. A full comprehension of the structure and dynamics of early intermediates leading to the aggregated states is an unsolved problem of essential importance to researchers attempting to decipher the molecular mechanisms of αSyn aggregation and formation of fibrils. Traditional bulk techniques used so far to solve this problem point to a direct correlation between αSyn's unique conformational properties and its propensity to aggregate, but these techniques can only provide ensemble-averaged information for monomers and oligomers alike. They therefore cannot characterize the full complexity of the conformational equilibria that trigger the aggregation process. We applied atomic force microscopy–based single-molecule mechanical unfolding methodology to study the conformational equilibrium of human wild-type and mutant αSyn. The conformational heterogeneity of monomeric αSyn was characterized at the single-molecule level. Three main classes of conformations, including disordered and “β-like” structures, were directly observed and quantified without any interference from oligomeric soluble forms. The relative abundance of the “β-like” structures significantly increased in different conditions promoting the aggregation of αSyn: the presence of Cu2+, the pathogenic A30P mutation, and high ionic strength. This methodology can explore the full conformational space of a protein at the single-molecule level, detecting even poorly populated conformers and measuring their distribution in a variety of biologically important conditions. To the best of our knowledge, we present for the first time evidence of a conformational equilibrium that controls the population of a specific class of monomeric αSyn conformers, positively correlated with conditions known to promote the formation of aggregates. A new tool is thus made available to test directly the influence of mutations and pharmacological strategies on the conformational equilibrium of monomeric αSyn. PMID:18198943

Stationary Black Holes: Uniqueness and Beyond.

PubMed

Heusler, Markus

1998-01-01

The spectrum of known black hole solutions to the stationary Einstein equations has increased in an unexpected way during the last decade. In particular, it has turned out that not all black hole equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black hole space-times ceases to exist in self-gravitating non-linear field theories. This text aims to review some of the recent developments and to discuss them in the light of the uniqueness theorem for the Einstein-Maxwell system.

Stationary Black Holes: Uniqueness and Beyond.

PubMed

Chruściel, Piotr T; Costa, João Lopes; Heusler, Markus

2012-01-01

The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black-hole spacetimes ceases to exist in self-gravitating non-linear field theories. This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.

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

PubMed

Su, Nan-Yao; Lee, Sang-Hee

2008-04-01

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

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.

Disk in a groove with friction: An analysis of static equilibrium and indeterminacy

NASA Astrophysics Data System (ADS)

Donolato, Cesare

2018-05-01

This note studies the statics of a rigid disk placed in a V-shaped groove with frictional walls and subjected to gravity and a torque. The two-dimensional equilibrium problem is formulated in terms of the angles that contact forces form with the normal to the walls. This approach leads to a single trigonometric equation in two variables whose domain is determined by Coulomb's law of friction. The properties of solutions (existence, uniqueness, or indeterminacy) as functions of groove angle, friction coefficient and applied torque are derived by a simple geometric representation. The results modify some of the conclusions by other authors on the same problem.

Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects

PubMed Central

Baumann, Hendrik; Sandmann, Werner

2016-01-01

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity. PMID:27010993

Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects.

PubMed

Baumann, Hendrik; Sandmann, Werner

2016-01-01

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity.

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

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

NASA Astrophysics Data System (ADS)

Moawad, S. M.; Moawad

2013-10-01

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

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

PubMed

Spruijt, E; Biesheuvel, P M

2014-02-19

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

A note on AB INITIO semiconductor band structures

NASA Astrophysics Data System (ADS)

Fiorentini, Vincenzo

1992-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

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

PubMed

Wang, Lili; Chen, Tianping

2014-05-01

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

Rambling and trembling in response to body loading.

PubMed

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

2012-04-01

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

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

NASA Astrophysics Data System (ADS)

Wang, Shoucheng; Huang, Guoqing; Wu, Xin

2018-02-01

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

Statistical investigation of simulated fed intestinal media composition on the equilibrium solubility of oral drugs.

PubMed

Zhou, Zhou; Dunn, Claire; Khadra, Ibrahim; Wilson, Clive G; Halbert, Gavin W

2017-03-01

Gastrointestinal fluid is a complex milieu and it is recognised that gut drug solubility is different to that observed in simple aqueous buffers. Simulated gastrointestinal media have been developed covering fasted and fed states to facilitate in vitro prediction of gut solubility and product dissolution. However, the combination of bile salts, phospholipids, fatty acids and proteins in an aqueous buffered system creates multiple phases and drug solubility is therefore a complex interaction between these components, which may create unique environments for each API. The impact on solubility can be assessed through a statistical design of experiment (DoE) approach, to determine the influence and relationships between factors. In this paper DoE has been applied to fed simulated gastrointestinal media consisting of eight components (pH, bile salt, lecithin, sodium oleate, monoglyceride, buffer, salt and pancreatin) using a two level D-optimal design with forty-four duplicate measurements and four centre points. The equilibrium solubility of a range of poorly soluble acidic (indomethacin, ibuprofen, phenytoin, valsartan, zafirlukast), basic (aprepitant, carvedilol, tadalafil, bromocriptine) and neutral (fenofibrate, felodipine, probucol, itraconazole) drugs was investigated. Results indicate that the DoE provides equilibrium solubility values that are comparable to literature results for other simulated fed gastrointestinal media systems or human intestinal fluid samples. For acidic drugs the influence of pH predominates but other significant factors related to oleate and bile salt or interactions between them are present. For basic drugs pH, oleate and bile salt have equal significance along with interactions between pH and oleate and lecithin and oleate. Neutral drugs show diverse effects of the media components particularly with regard to oleate, bile salt, pH and lecithin but the presence of monoglyceride, pancreatin and buffer have significant but smaller effects on solubility. There are fourteen significant interactions between factors mainly related to the surfactant components and pH, indicating that the solubility of neutral drugs in fed simulated media is complex. The results also indicate that the equilibrium solubility of each drug can exhibit individualistic behaviour associated with the drug's chemical structure, physicochemical properties and interaction with media components. The utility of DoE for fed simulated media has been demonstrated providing equilibrium solubility values comparable with similar in vitro systems whilst also providing greater information on the influence of media factors and their interactions. The determination of a drug's gastrointestinal solubility envelope provides useful limits that can potentially be applied to in silico modelling and in vivo experiments. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.

Examples of equilibrium and non-equilibrium behavior in evolutionary systems

NASA Astrophysics Data System (ADS)

Soulier, Arne

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

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

PubMed

Forti, Mauro; Nistri, Paolo; Quincampoix, Marc

2006-11-01

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

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

NASA Astrophysics Data System (ADS)

Romero, Pilar; Barderas, Gonzalo; Mejuto, Javier

2018-05-01

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

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

PubMed

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

2014-01-01

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

Blurring out hydrogen: The dynamical structure of teflic acid

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

DOT National Transportation Integrated Search

1978-04-01

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

Granular flow: Dry and wet

NASA Astrophysics Data System (ADS)

Mitarai, N.; Nakanishi, H.

2012-04-01

Granular material is a collection of macroscopic particles that are visible with naked eyes. The non-equilibrium nature of the granular materials makes their rheology quite different from that of molecular systems. In this minireview, we present the unique features of granular materials focusing on the shear flow of dry granular materials and granule-liquid mixture.

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.

Nonequilibrium Tricritical Point in a System with Long-Range Interactions

NASA Astrophysics Data System (ADS)

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

2007-07-01

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

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

PubMed

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

1998-07-01

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

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

PubMed

Latash, M; Gottleib, G

1990-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Study of chaos in chaotic satellite systems

NASA Astrophysics Data System (ADS)

Khan, Ayub; Kumar, Sanjay

2018-01-01

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

Space and time renormalization in phase transition dynamics

DOE PAGES

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

2016-02-18

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

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

NASA Astrophysics Data System (ADS)

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

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

Kinetics of NO and O2 binding to a maleimide poly(ethylene glycol)-conjugated human haemoglobin

PubMed Central

2004-01-01

The hypertensive effect observed with most cell-free haemoglobins has been proposed to result from NO scavenging. However, a newly developed PEG [poly(ethylene glycol)]-conjugated haemoglobin, MalPEG-Hb [maleimide-activated PEG-conjugated haemoglobin], is non-hypertensive with unique physicochemical properties: high O2 affinity, low co-operativity and large molecular radius. It is therefore of interest to compare the ligand-binding properties of MalPEG-Hb with unmodified cell-free HbA (stroma-free human haemoglobin). NO association rates for deoxy and oxyMalPEG-Hb and HbA were found to be identical. These results confirm the lack of correlation between hypertension and NO for a similar modified haemoglobin with high molecular radius and low p50 (pO2 at which haemoglobin is half-saturated with O2) [Rohlfs, Bruner, Chiu, Gonzales, Gonzales, Magde, Magde, Vandegriff and Winslow (1998) J. Biol. Chem. 273, 12128–12134]. The R-state O2 association kinetic constants were also the same for the two haemoglobins. However, even though the p50 of MalPEG-Hb is approx. half of that of HbA, the biphasic O2 dissociation rates measured at relatively high pO2 (150 Torr) were 2-fold higher, giving rise to a 2-fold lower R-state equilibrium association constant for MalPEG-Hb compared with HbA. Thus the O2 affinity of MalPEG-Hb is higher only at pO2 values lower than the intersection point of the O2 equilibrium curves for MalPEG-Hb and HbA. In summary, the present studies found similar rates of NO binding to HbA and MalPEG-Hb, eliminating the possibility that the lack of vasoactivity of MalPEG-Hb is simply the result of reduced molecular reactivity with NO. Alternatively, the unique O2-binding characteristics with low p50 and co-operativity suggest that the ‘R-state’ conformation of MalPEG-Hb is in a more T-state configuration and restricted from conformational change. PMID:15175010

The specific entropy of elliptical galaxies: an explanation for profile-shape distance indicators?

NASA Astrophysics Data System (ADS)

Lima Neto, G. B.; Gerbal, D.; Márquez, I.

1999-10-01

Dynamical systems in equilibrium have a stationary entropy; we suggest that elliptical galaxies, as stellar systems in a stage of quasi-equilibrium, may have in principle a unique specific entropy. This uniqueness, a priori unknown, should be reflected in correlations between the fundamental parameters describing the mass (light) distribution in galaxies. Following recent photometrical work on elliptical galaxies by Caon et al., Graham & Colless and Prugniel & Simien, we use the Sérsic law to describe the light profile and an analytical approximation to its three-dimensional deprojection. The specific entropy is then calculated, supposing that the galaxy behaves as a spherical, isotropic, one-component system in hydrostatic equilibrium, obeying the ideal-gas equations of state. We predict a relation between the three parameters of the Sérsic law linked to the specific entropy, defining a surface in the parameter space, an `Entropic Plane', by analogy with the well-known Fundamental Plane. We have analysed elliptical galaxies in two rich clusters of galaxies (Coma and ABCG 85) and a group of galaxies (associated with NGC 4839, near Coma). We show that, for a given cluster, the galaxies follow closely a relation predicted by the constant specific entropy hypothesis with a typical dispersion (one standard deviation) of 9.5per cent around the mean value of the specific entropy. Moreover, assuming that the specific entropy is also the same for galaxies of different clusters, we are able to derive relative distances between Coma, ABGC 85, and the group of NGC 4839. If the errors are due only to the determination of the specific entropy (about 10per cent), then the error in the relative distance determination should be less than 20per cent for rich clusters. We suggest that the unique specific entropy may provide a physical explanation for the distance indicators based on the Sérsic profile put forward by Young & Currie and recently discussed by Binggeli & Jerjen.

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

PubMed

Wilhelmsen, Øivind; Trinh, Thuat T; Lervik, Anders

2018-01-01

Density gradient theory for fluids has played a key role in the study of interfacial phenomena for a century. In this work, we revisit its fundamentals by examining the vapor-liquid interface of argon, represented by the cut and shifted Lennard-Jones fluid. The starting point has traditionally been a Helmholtz energy functional using mass densities as arguments. By using rather the internal energy as starting point and including the entropy density as an additional argument, following thereby the phenomenological approach from classical thermodynamics, the extended theory suggests that the configurational part of the temperature has different contributions from the parallel and perpendicular directions at the interface, even at equilibrium. We find a similar anisotropy by examining the configurational temperature in molecular dynamics simulations and obtain a qualitative agreement between theory and simulations. The extended theory shows that the temperature anisotropy originates in nonlocal entropic contributions, which are currently missing from the classical theory. The nonlocal entropic contributions discussed in this work are likely to play a role in the description of both equilibrium and nonequilibrium properties of interfaces. At equilibrium, they influence the temperature- and curvature-dependence of the surface tension. Across the vapor-liquid interface of the Lennard Jones fluid, we find that the maximum in the temperature anisotropy coincides precisely with the maximum in the thermal resistivity relative to the equimolar surface, where the integral of the thermal resistivity gives the Kapitza resistance. This links the temperature anisotropy at equilibrium to the Kapitza resistance of the vapor-liquid interface at nonequilibrium.

Temperature anisotropy at equilibrium reveals nonlocal entropic contributions to interfacial properties

NASA Astrophysics Data System (ADS)

Wilhelmsen, Øivind; Trinh, Thuat T.; Lervik, Anders

2018-01-01

Density gradient theory for fluids has played a key role in the study of interfacial phenomena for a century. In this work, we revisit its fundamentals by examining the vapor-liquid interface of argon, represented by the cut and shifted Lennard-Jones fluid. The starting point has traditionally been a Helmholtz energy functional using mass densities as arguments. By using rather the internal energy as starting point and including the entropy density as an additional argument, following thereby the phenomenological approach from classical thermodynamics, the extended theory suggests that the configurational part of the temperature has different contributions from the parallel and perpendicular directions at the interface, even at equilibrium. We find a similar anisotropy by examining the configurational temperature in molecular dynamics simulations and obtain a qualitative agreement between theory and simulations. The extended theory shows that the temperature anisotropy originates in nonlocal entropic contributions, which are currently missing from the classical theory. The nonlocal entropic contributions discussed in this work are likely to play a role in the description of both equilibrium and nonequilibrium properties of interfaces. At equilibrium, they influence the temperature- and curvature-dependence of the surface tension. Across the vapor-liquid interface of the Lennard Jones fluid, we find that the maximum in the temperature anisotropy coincides precisely with the maximum in the thermal resistivity relative to the equimolar surface, where the integral of the thermal resistivity gives the Kapitza resistance. This links the temperature anisotropy at equilibrium to the Kapitza resistance of the vapor-liquid interface at nonequilibrium.

Isometric torque-angle relationship and movement-related activity of human elbow flexors: implications for the equilibrium-point hypothesis.

PubMed

Hasan, Z; Enoka, R M

1985-01-01

Since the moment arms for the elbow-flexor muscles are longest at intermediate positions of the elbow and shorter at the extremes of the range of motion, it was expected that the elbow torque would also show a peak at an intermediate angle provided the activity of the flexor muscles remained constant. We measured the isometric elbow torque at different elbow angles while the subject attempted to keep constant the electromyographic activity (EMG) of the brachioradialis muscle. The torque-angle relationship thus obtained exhibited a peak, as expected, but the shape of the relationship varied widely among subjects. This was due in part to differences in the variation of the biceps brachii EMG with elbow angle among the different subjects. The implications of these observations for the equilibrium-point hypothesis of movement were investigated as follows. The subject performed elbow movements in the presence of an external torque (which tended to extend the elbow joint) provided by a weight-and-pulley arrangement. We found in the case of flexion movements that invariably there was a transient increase in flexor EMG, as would seem necessary for initiating the movement. However, the steady-state EMG after the movement could be greater or less than the pre-movement EMG. Specifically, the least flexor EMG was required for equilibrium in the intermediate range of elbow angles, compared to the extremes of the range of motion. The EMG-angle relationship, however, varied with the muscle and the subject. The observation that the directions of change in the transient and the steady-state EMG are independent of each other militates against the generality of the equilibrium-point hypothesis. However, a form of the hypothesis which includes the effects of the stretch reflex is not contradicted by this observation.

Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir

2017-11-01

In this paper, a stochastic delayed HIV-1 infection model with nonlinear incidence is proposed and investigated. First of all, we prove that there is a unique global positive solution as desired in any population dynamics. Then by constructing some suitable Lyapunov functions, we show that if the basic reproduction number R0 ≤ 1, then the solution of the stochastic system oscillates around the infection-free equilibrium E0, while if R0 > 1, then the solution of the stochastic system fluctuates around the infective equilibrium E∗. Sufficient conditions of these results are established. Finally, we give some examples and a series of numerical simulations to illustrate the analytical results.

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

PubMed

Gribble, P L; Ostry, D J

2000-12-01

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

Perspectives: Black Holes

NASA Technical Reports Server (NTRS)

Dolan, Joseph F.; Fisher, Richard R. (Technical Monitor)

2001-01-01

When asked to discuss Cyg XR-1, E. E. Salpeter once concluded, 'A black hole in Cyg X(R)-1 is the most conservative hypothesis.' Recent observations now make it likely that a black hole in Cyg XR-1 is the only hypothesis tenable. Chandrasekhar first showed that compact stars - those with the inward force of gravity on their outer layers balanced by the pressure generated by the Pauli exclusion principle acting on its electrons (in white dwarfs) or nucleons (in neutron stars) - have a maximum mass. Equilibrium is achieved at a minimum of the total energy of the star, which is the sum of the positive Fermi energy and the negative gravitational energy. The maximum mass attainable in equilibrium is found by setting E = 0: M(max) = 1.5 M(Sun). If the mass of the star is larger than this, then E can be decreased without bound by decreasing the star's radius and increasing its (negative) gravitational energy. No equilibrium value of the radius exist, and general relativity predicts that gravitational collapse to a point occurs. This point singularity is a black hole.

Equation of state of detonation products based on statistical mechanical theory

NASA Astrophysics Data System (ADS)

Zhao, Yanhong; Liu, Haifeng; Zhang, Gongmu; Song, Haifeng

2015-06-01

The equation of state (EOS) of gaseous detonation products is calculated using Ross's modification of hard-sphere variation theory and the improved one-fluid van der Waals mixture model. The condensed phase of carbon is a mixture of graphite, diamond, graphite-like liquid and diamond-like liquid. For a mixed system of detonation products, the free energy minimization principle is used to calculate the equilibrium compositions of detonation products by solving chemical equilibrium equations. Meanwhile, a chemical equilibrium code is developed base on the theory proposed in this article, and then it is used in the three typical calculations as follow: (i) Calculation for detonation parameters of explosive, the calculated values of detonation velocity, the detonation pressure and the detonation temperature are in good agreement with experimental ones. (ii) Calculation for isentropic unloading line of RDX explosive, whose starting points is the CJ point. Comparison with the results of JWL EOS it is found that the calculated value of gamma is monotonically decreasing using the presented theory in this paper, while double peaks phenomenon appears using JWL EOS.

Equation of state of detonation products based on statistical mechanical theory

NASA Astrophysics Data System (ADS)

Zhao, Yanhong; Liu, Haifeng; Zhang, Gongmu; Song, Haifeng; Iapcm Team

2013-06-01

The equation of state (EOS) of gaseous detonation products is calculated using Ross's modification of hard-sphere variation theory and the improved one-fluid van der Waals mixture model. The condensed phase of carbon is a mixture of graphite, diamond, graphite-like liquid and diamond-like liquid. For a mixed system of detonation products, the free energy minimization principle is used to calculate the equilibrium compositions of detonation products by solving chemical equilibrium equations. Meanwhile, a chemical equilibrium code is developed base on the theory proposed in this article, and then it is used in the three typical calculations as follow: (i) Calculation for detonation parameters of explosive, the calculated values of detonation velocity, the detonation pressure and the detonation temperature are in good agreement with experimental ones. (ii) Calculation for isentropic unloading line of RDX explosive, whose starting points is the CJ point. Comparison with the results of JWL EOS it is found that the calculated value of gamma is monotonically decreasing using the presented theory in this paper, while double peaks phenomenon appears using JWL EOS.

Punishment in a complementarity game

NASA Astrophysics Data System (ADS)

Li, W.; Cai, X.; Wang, Q. A.

2006-05-01

We study the effects arisen from the punishment in an evolutionary complementarity game. Each round one member of population “buyers” deals with a randomly chosen member of population “sellers”. When the buyer's offer is greater than the seller's, a deal is done and both players are rewarded by gaining some points. Otherwise the transaction is not successful and both will lose certain points as punishment. Our simulations indicate that the resulting equilibrium of the game with punishment embedded is remarkably time-delayed compared to the counterpart of the non-punishment game. However, the median fee and the success rate of deals at the equilibrium remain nearly unchanged in various cases of games with different degrees of punishment, whether severe or not. Symmetry, between the two populations, and the equilibrium value can still be maintained when the members of both of them are punished fairly in any failed transaction. If they are done in a different manner, namely, the members of one population are subject to very severe punishment whereas their opponents receive less or no punishment at all, the latter in most cases will be better off.

Exploration of RNA Sequence Space in the Absence of a Replicase.

PubMed

Tirumalai, Madhan R; Tran, Quyen; Paci, Maxim; Chavan, Dimple; Marathe, Anuradha; Fox, George E

2018-05-11

It is generally considered that if an RNA World ever existed that it would be driven by an RNA capable of RNA replication. Whether such a catalytic RNA could emerge in an RNA World or not, there would need to be prior routes to increasing complexity in order to produce it. It is hypothesized here that increasing sequence variety, if not complexity, can in fact readily emerge in response to a dynamic equilibrium between synthesis and degradation. A model system in which T4 RNA ligase catalyzes synthesis and Benzonase catalyzes degradation was constructed. An initial 20-mer served as a seed and was subjected to 180 min of simultaneous ligation and degradation. The seed RNA rapidly disappeared and was replaced by an increasing number and variety of both larger and smaller variants. Variants of 40-80 residues were consistently seen, typically representing 2-4% of the unique sequences. In a second experiment with four individual 9-mers, numerous variants were again produced. These included variants of the individual 9-mers as well as sequences that contained sequence segments from two or more 9-mers. In both cases, the RNA products lack large numbers of point mutations but instead incorporate additions and subtractions of fragments of the original RNAs. The system demonstrates that if such equilibrium were established in a prebiotic world it would result in significant exploration of RNA sequence space and likely increased complexity. It remains to be seen if the variety of products produced is affected by the presence of small peptide oligomers.

Soil-moisture constants and their variation

Treesearch

Walter M. Broadfoot; Hubert D. Burke

1958-01-01

"Constants" like field capacity, liquid limit, moisture equivalent, and wilting point are used by most students and workers in soil moisture. These constants may be equilibrium points or other values that describe soil moisture. Their values under specific soil and cover conditions have been discussed at length in the literature, but few general analyses and...

Artificial equilibrium points in binary asteroid systems with continuous low-thrust

NASA Astrophysics Data System (ADS)

Bu, Shichao; Li, Shuang; Yang, Hongwei

2017-08-01

The positions and dynamical characteristics of artificial equilibrium points (AEPs) in the vicinity of a binary asteroid with continuous low-thrust are studied. The restricted ellipsoid-ellipsoid model of binary system is employed for the binary asteroid system. The positions of AEPs are obtained by this model. It is found that the set of the point L1 or L2 forms a shape of an ellipsoid while the set of the point L3 forms a shape like a "banana". The effect of the continuous low-thrust on the feasible region of motion is analyzed by zero velocity curves. Because of using the low-thrust, the unreachable region can become reachable. The linearized equations of motion are derived for stability's analysis. Based on the characteristic equation of the linearized equations, the stability conditions are derived. The stable regions of AEPs are investigated by a parametric analysis. The effect of the mass ratio and ellipsoid parameters on stable region is also discussed. The results show that the influence of the mass ratio on the stable regions is more significant than the parameters of ellipsoid.

Energy flow in non-equilibrium conformal field theory

NASA Astrophysics Data System (ADS)

Bernard, Denis; Doyon, Benjamin

2012-09-01

We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.

Minimal energy configurations of gravitationally interacting rigid bodies

NASA Astrophysics Data System (ADS)

Moeckel, Richard

2017-05-01

Consider a collection of n rigid, massive bodies interacting according to their mutual gravitational attraction. A relative equilibrium motion is one where the entire configuration rotates rigidly and uniformly about a fixed axis in R^3. Such a motion is possible only for special positions and orientations of the bodies. A minimal energy motion is one which has the minimum possible energy in its fixed angular momentum level. While every minimal energy motion is a relative equilibrium motion, the main result here is that a relative equilibrium motion of n≥3 disjoint rigid bodies is never an energy minimizer. This generalizes a known result about point masses to the case of rigid bodies.

A General Method for Automatic Computation of Equilibrium Compositions and Theoretical Rocket Performance of Propellants

NASA Technical Reports Server (NTRS)

Gordon, Sanford; Zeleznik, Frank J.; Huff, Vearl N.

1959-01-01

A general computer program for chemical equilibrium and rocket performance calculations was written for the IBM 650 computer with 2000 words of drum storage, 60 words of high-speed core storage, indexing registers, and floating point attachments. The program is capable of carrying out combustion and isentropic expansion calculations on a chemical system that may include as many as 10 different chemical elements, 30 reaction products, and 25 pressure ratios. In addition to the equilibrium composition, temperature, and pressure, the program calculates specific impulse, specific impulse in vacuum, characteristic velocity, thrust coefficient, area ratio, molecular weight, Mach number, specific heat, isentropic exponent, enthalpy, entropy, and several thermodynamic first derivatives.

Equilibrium and nonequilibrium models on solomon networks with two square lattices

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios γ/ν, β/ν, and 1/ν. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

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

Heavy ion beam probe operation in time varying equilibria of improved confinement reversed field pinch discharges.

PubMed

Demers, D R; Chen, X; Schoch, P M; Fimognari, P J

2010-10-01

Operation of a heavy ion beam probe (HIBP) on a reversed field pinch is unique from other toroidal applications because the magnetic field is more temporal and largely produced by plasma current. Improved confinement, produced through the transient application of a poloidal electric field which leads to a reduction of dynamo activity, exhibits gradual changes in equilibrium plasma quantities. A consequence of this is sweeping of the HIBP trajectories by the dynamic magnetic field, resulting in motion of the sample volume. In addition, the plasma potential evolves with the magnetic equilibrium. Measurement of the potential as a function of time is thus a combination of temporal changes of the equilibrium and motion of the sample volume. A frequent additional complication is a nonideal balance of ion current on the detectors resulting from changes in the beam trajectory (magnetic field) and energy (plasma potential). This necessitates use of data selection criteria. Nevertheless, the HIBP on the Madison Symmetric Torus has acquired measurements as a function of time throughout improved confinement. A technique developed to infer the potential in the improved confinement reversed field pinch from HIBP data in light of the time varying plasma equilibrium will be discussed.

Physics of Magnetospheric Variability

NASA Astrophysics Data System (ADS)

Vasyliūnas, Vytenis M.

2011-01-01

Many widely used methods for describing and understanding the magnetosphere are based on balance conditions for quasi-static equilibrium (this is particularly true of the classical theory of magnetosphere/ionosphere coupling, which in addition presupposes the equilibrium to be stable); they may therefore be of limited applicability for dealing with time-variable phenomena as well as for determining cause-effect relations. The large-scale variability of the magnetosphere can be produced both by changing external (solar-wind) conditions and by non-equilibrium internal dynamics. Its developments are governed by the basic equations of physics, especially Maxwell's equations combined with the unique constraints of large-scale plasma; the requirement of charge quasi-neutrality constrains the electric field to be determined by plasma dynamics (generalized Ohm's law) and the electric current to match the existing curl of the magnetic field. The structure and dynamics of the ionosphere/magnetosphere/solar-wind system can then be described in terms of three interrelated processes: (1) stress equilibrium and disequilibrium, (2) magnetic flux transport, (3) energy conversion and dissipation. This provides a framework for a unified formulation of settled as well as of controversial issues concerning, e.g., magnetospheric substorms and magnetic storms.

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

NASA Astrophysics Data System (ADS)

Inampudi, Ravi Kishore

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

Lunar Navigation with Libration Point Orbiters and GPS

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2004-01-01

NASA is currently studying a Vision for Space Exploration based on spiral development of robotic and piloted missions to the moon and Mars, but research into how to perform such missions has continued ever since the first era of lunar exploration. One area of study that a number of researchers have pursued is libration point navigation and communication relay concepts. These concepts would appear to support many of NASA's current requirements for navigation and communications coverage for human and robotic spacecraft operating in lunar space and beyond. In trading libration point concepts against other options, designers must consider issues such as the number of spacecraft, required to provide coverage, insertion and stationkeeping costs, power and data rate requirements, frequency allocations, and many others. The libration points, along with a typical cis-lunar trajectory, are equilibrium locations for an infinitesimal mass in the rotating coordinate system that follows the motion of two massive bodies in circular orbits with respect to their common barycenter. There are three co-linear points along the line connecting the massive bodies: between the bodies, beyond the secondary body, and beyond the primary body. The relative distances of these points along the line connecting the bodies depend on the mass ratios. There are also two points that form equilateral triangles with the massive bodies. Ideally, motion in the neighborhood of the co-linear points is unstable, while motion near the equilibrium points is stable. However, in the real world, the motions are highly perturbed so that a satellite will require stationkeeping maneuvers.

Basic and Applied Studies of the RAM Accelerator as a Hypervelocity Projectile Launcher

DTIC Science & Technology

1993-12-10

The quasi-steady, one-dimensional "blackbox" model of thermally choked ram accelerator performance 18 that has been widely used by the authors and...the thermal choke point is assumed to be in equilibrium, the conditions can be determined by an equilibrium chemistry combustion routine. This model ...to operation, the details of the flow field must be examined. I The simplest model of the thermally choked ram accelerator flow field treats the flow

Integrable structure in discrete shell membrane theory

PubMed Central

Schief, W. K.

2014-01-01

We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory. PMID:24808755

Integrable structure in discrete shell membrane theory.

PubMed

Schief, W K

2014-05-08

We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory.

Nonlinear Dynamics and Nucleation Kinetics in Near-Critical Liquids

NASA Technical Reports Server (NTRS)

Patashinski, Alexander Z.; Ratner, Mark A.; Pines, Vladimir

1996-01-01

The objective of our study is to model the nonlinear behavior of a near-critical liquid following a rapid change of the temperature and/or other thermodynamic parameters (pressure, external electric or gravitational field). The thermodynamic critical point is manifested by large, strongly correlated fluctuations of the order parameter (particle density in liquid-gas systems, concentration in binary solutions) in the critical range of scales. The largest critical length scale is the correlation radius r(sub c). According to the scaling theory, r(sub c) increases as r(sub c) = r(sub 0)epsilon(exp -alpha) when the nondimensional distance epsilon = (T - T(sub c))/T(sub c) to the critical point decreases. The normal gravity alters the nature of correlated long-range fluctuations when one reaches epsilon approximately equal to 10(exp -5), and correspondingly the relaxation time, tau(r(sub c)), is approximately equal to 10(exp -3) seconds; this time is short when compared to the typical experimental time. Close to the critical point, a rapid, relatively small temperature change may perturb the thermodynamic equilibrium on many scales. The critical fluctuations have a hierarchical structure, and the relaxation involves many length and time scales. Above the critical point, in the one-phase region, we consider the relaxation of the liquid following a sudden temperature change that simultaneously violates the equilibrium on many scales. Below T(sub c), a non-equilibrium state may include a distribution of small scale phase droplets; we consider the relaxation of such a droplet following a temperature change that has made the phase of the matrix stable.

Global exponential stability of BAM neural networks with time-varying delays and diffusion terms

NASA Astrophysics Data System (ADS)

Wan, Li; Zhou, Qinghua

2007-11-01

The stability property of bidirectional associate memory (BAM) neural networks with time-varying delays and diffusion terms are considered. By using the method of variation parameter and inequality technique, the delay-independent sufficient conditions to guarantee the uniqueness and global exponential stability of the equilibrium solution of such networks are established.

Dating Preferences and Meeting Opportunities in Mate Choice Decisions

ERIC Educational Resources Information Center

Belot, Michele; Francesconi, Marco

2013-01-01

Much empirical evidence shows that female and male partners look alike along a variety of attributes. It is, however, unclear how this positive sorting comes about because marriage is an equilibrium outcome arising from a process that entails searching, meeting, and choosing one another. This study takes advantage of unique data to shed light on…

Robert Curl, Jr. and the Discovery of Fullerenes

Science.gov Websites

produced thousands of variations of the buckyball, including carbon sheets one atom thick and microscopic equilibrium in the carbon vapor that allowed the group to identify a unique, 60-atom configuration of carbon Interview with Robert F. Curl, Jr., nobelprize.org (video) Interview with Robert Curl (video) Buckyballs

Dynamical behaviour of a discrete selection-migration model with arbitrary dominance

Treesearch

James F. Selgrade; Jordan West Bostic; James H. Roberds

2009-01-01

To study the effects of immigration of genes (possibly transgenic) into a natural population, a one-island selection-migration model with density-dependent regulation is used to track allele frequency and population size. The existence and uniqueness of a polymorphic genetic equilibrium is proved under a general assumption about dominance in fitnesses. Also, conditions...

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

PubMed

Latash, M L

1992-01-01

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

Bifurcation Analysis Using Rigorous Branch and Bound Methods

NASA Technical Reports Server (NTRS)

Smith, Andrew P.; Crespo, Luis G.; Munoz, Cesar A.; Lowenberg, Mark H.

2014-01-01

For the study of nonlinear dynamic systems, it is important to locate the equilibria and bifurcations occurring within a specified computational domain. This paper proposes a new approach for solving these problems and compares it to the numerical continuation method. The new approach is based upon branch and bound and utilizes rigorous enclosure techniques to yield outer bounding sets of both the equilibrium and local bifurcation manifolds. These sets, which comprise the union of hyper-rectangles, can be made to be as tight as desired. Sufficient conditions for the existence of equilibrium and bifurcation points taking the form of algebraic inequality constraints in the state-parameter space are used to calculate their enclosures directly. The enclosures for the bifurcation sets can be computed independently of the equilibrium manifold, and are guaranteed to contain all solutions within the computational domain. A further advantage of this method is the ability to compute a near-maximally sized hyper-rectangle of high dimension centered at a fixed parameter-state point whose elements are guaranteed to exclude all bifurcation points. This hyper-rectangle, which requires a global description of the bifurcation manifold within the computational domain, cannot be obtained otherwise. A test case, based on the dynamics of a UAV subject to uncertain center of gravity location, is used to illustrate the efficacy of the method by comparing it with numerical continuation and to evaluate its computational complexity.

Non-equilibrium freezing behaviour of aqueous systems.

PubMed

MacKenzie, A P

1977-03-29

The tendencies to non-equilibrium freezing behaviour commonly noted in representative aqueous systems derive from bulk and surface properties according to the circumstances. Supercooling and supersaturation are limited by heterogeneous nucleation in the presence of solid impurities. Homogeneous nucleation has been observed in aqueous systems freed from interfering solids. Once initiated, crystal growth is ofter slowed and, very frequently, terminated with increasing viscosity. Nor does ice first formed always succeed in assuming its most stable crystalline form. Many of the more significant measurements on a given systeatter permitting the simultaneous representation of thermodynamic and non-equilibrium properties. The diagram incorporated equilibrium melting points, heterogeneous nucleation temperatures, homogeneous nucleation temperatures, glass transition and devitrification temperatures, recrystallization temperatures, and, where appropriate, solute solubilities and eutectic temperatures. Taken together, the findings on modle systems aid the identification of the kinetic and thermodynamic factors responsible for the freezing-thawing survival of living cells.

Phylogenies support out-of-equilibrium models of biodiversity.

PubMed

Manceau, Marc; Lambert, Amaury; Morlon, Hélène

2015-04-01

There is a long tradition in ecology of studying models of biodiversity at equilibrium. These models, including the influential Neutral Theory of Biodiversity, have been successful at predicting major macroecological patterns, such as species abundance distributions. But they have failed to predict macroevolutionary patterns, such as those captured in phylogenetic trees. Here, we develop a model of biodiversity in which all individuals have identical demographic rates, metacommunity size is allowed to vary stochastically according to population dynamics, and speciation arises naturally from the accumulation of point mutations. We show that this model generates phylogenies matching those observed in nature if the metacommunity is out of equilibrium. We develop a likelihood inference framework that allows fitting our model to empirical phylogenies, and apply this framework to various mammalian families. Our results corroborate the hypothesis that biodiversity dynamics are out of equilibrium. © 2015 John Wiley & Sons Ltd/CNRS.

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

NASA Technical Reports Server (NTRS)

Glass, Christopher E.

1990-01-01

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

NASA Astrophysics Data System (ADS)

Glass, Christopher E.

1990-08-01

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

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

PubMed

Armao, Joseph J; Lehn, Jean-Marie

2016-10-17

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

Mathematical model for HIV spreads control program with ART treatment

NASA Astrophysics Data System (ADS)

Maimunah; Aldila, Dipo

2018-03-01

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

A comparative study of the adsorption equilibrium of progesterone by a carbon black and a commercial activated carbon

NASA Astrophysics Data System (ADS)

Valenzuela-Calahorro, Cristóbal; Navarrete-Guijosa, Antonio; Stitou, Mostafa; Cuerda-Correa, Eduardo M.

2007-04-01

In this paper the adsorption process of a natural steroid hormone (progesterone) by a carbon black and a commercial activated carbon has been studied. The corresponding equilibrium isotherms have been analyzed according to a previously proposed model which establishes a kinetic law satisfactorily fitting the C versus t isotherms. The analysis of the experimental data points out the existence of two well-defined sections in the equilibrium isotherms. A general equation including these two processes has been proposed, the global adsorption process being fitted to such equation. From the values of the kinetic equilibrium constant so obtained, values of standard average adsorption enthalpy ( ΔH°) and entropy ( ΔS°) have been calculated. Finally, information related to variations of differential adsorption enthalpy ( ΔH) and entropy ( ΔS) with the surface coverage fraction ( θ) was obtained by using the corresponding Clausius-Clapeyron equations.

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.

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.

The 3'-end region of the human PDGFR-β core promoter nuclease hypersensitive element forms a mixture of two unique end-insertion G-quadruplexes.

PubMed

Onel, Buket; Carver, Megan; Agrawal, Prashansa; Hurley, Laurence H; Yang, Danzhou

2018-04-01

While the most stable G-quadruplex formed in the human PDGFR-β promoter nuclease hypersensitive element (NHE) is the 5'-mid G-quadruplex, the 3'-end sequence that contains a 3'-GGA run forms a less stable G-quadruplex. Recently, the 3'-end G-quadruplex was found to be a transcriptional repressor and can be selectively targeted by a small molecule for PDGFR-β downregulation. We use 1D and 2D high-field NMR, in combination with Dimethylsulfate Footprinting, Circular Dichroism Spectroscopy, and Electrophoretic Mobility Shift Assay. We determine that the PDGFR-β extended 3'-end NHE sequence forms two novel end-insertion intramolecular G-quadruplexes that co-exist in equilibrium under physiological salt conditions. One G-quadruplex has a 3'-non-adjacent flanking guanine inserted into the 3'-external tetrad (3'-insertion-G4), and another has a 5'-non-adjacent flanking guanine inserted into the 5'-external tetrad (5'-insertion-G4). The two guanines in the GGA-run move up or down within the G-quadruplex to accommodate the inserted guanine. Each end-insertion G-quadruplex has a low thermal stability as compared to the 5'-mid G-quadruplex, but the selective stabilization of GSA1129 shifts the equilibrium toward the 3'-end G-quadruplex in the PDGFR-β NHE. An equilibrium mixture of two unique end-insertion intramolecular G-quadruplexes forms in the PDGFR-β NHE 3'-end sequence that contains a GGA-run and non-adjacent guanines in both the 3'- and 5'- flanking segments; the novel end-insertion structures of the 3'-end G-quadruplex are selectively stabilized by GSA1129. We show for the first time that an equilibrium mixture of two unusual end-insertion G-quadruplexes forms in a native promoter sequence and appears to be the molecular recognition for PDGFR-β downregulation. Copyright © 2017 Elsevier B.V. All rights reserved.

A basic introduction to the thermodynamics of the Earth system far from equilibrium and maximum entropy production

PubMed Central

Kleidon, A.

2010-01-01

The Earth system is remarkably different from its planetary neighbours in that it shows pronounced, strong global cycling of matter. These global cycles result in the maintenance of a unique thermodynamic state of the Earth's atmosphere which is far from thermodynamic equilibrium (TE). Here, I provide a simple introduction of the thermodynamic basis to understand why Earth system processes operate so far away from TE. I use a simple toy model to illustrate the application of non-equilibrium thermodynamics and to classify applications of the proposed principle of maximum entropy production (MEP) to such processes into three different cases of contrasting flexibility in the boundary conditions. I then provide a brief overview of the different processes within the Earth system that produce entropy, review actual examples of MEP in environmental and ecological systems, and discuss the role of interactions among dissipative processes in making boundary conditions more flexible. I close with a brief summary and conclusion. PMID:20368248

A basic introduction to the thermodynamics of the Earth system far from equilibrium and maximum entropy production.

PubMed

Kleidon, A

2010-05-12

The Earth system is remarkably different from its planetary neighbours in that it shows pronounced, strong global cycling of matter. These global cycles result in the maintenance of a unique thermodynamic state of the Earth's atmosphere which is far from thermodynamic equilibrium (TE). Here, I provide a simple introduction of the thermodynamic basis to understand why Earth system processes operate so far away from TE. I use a simple toy model to illustrate the application of non-equilibrium thermodynamics and to classify applications of the proposed principle of maximum entropy production (MEP) to such processes into three different cases of contrasting flexibility in the boundary conditions. I then provide a brief overview of the different processes within the Earth system that produce entropy, review actual examples of MEP in environmental and ecological systems, and discuss the role of interactions among dissipative processes in making boundary conditions more flexible. I close with a brief summary and conclusion.

Floquet Symmetry-Protected Topological Phases in Cold-Atom Systems

NASA Astrophysics Data System (ADS)

Potirniche, I.-D.; Potter, A. C.; Schleier-Smith, M.; Vishwanath, A.; Yao, N. Y.

2017-09-01

We propose and analyze two distinct routes toward realizing interacting symmetry-protected topological (SPT) phases via periodic driving. First, we demonstrate that a driven transverse-field Ising model can be used to engineer complex interactions which enable the emulation of an equilibrium SPT phase. This phase remains stable only within a parametric time scale controlled by the driving frequency, beyond which its topological features break down. To overcome this issue, we consider an alternate route based upon realizing an intrinsically Floquet SPT phase that does not have any equilibrium analog. In both cases, we show that disorder, leading to many-body localization, prevents runaway heating and enables the observation of coherent quantum dynamics at high energy densities. Furthermore, we clarify the distinction between the equilibrium and Floquet SPT phases by identifying a unique micromotion-based entanglement spectrum signature of the latter. Finally, we propose a unifying implementation in a one-dimensional chain of Rydberg-dressed atoms and show that protected edge modes are observable on realistic experimental time scales.

Haze heats Pluto's atmosphere yet explains its cold temperature.

PubMed

Zhang, Xi; Strobel, Darrell F; Imanaka, Hiroshi

2017-11-15

Pluto's atmosphere is cold and hazy. Recent observations have shown it to be much colder than predicted theoretically, suggesting an unknown cooling mechanism. Atmospheric gas molecules, particularly water vapour, have been proposed as a coolant; however, because Pluto's thermal structure is expected to be in radiative-conductive equilibrium, the required water vapour would need to be supersaturated by many orders of magnitude under thermodynamic equilibrium conditions. Here we report that atmospheric hazes, rather than gases, can explain Pluto's temperature profile. We find that haze particles have substantially larger solar heating and thermal cooling rates than gas molecules, dominating the atmospheric radiative balance from the ground to an altitude of 700 kilometres, above which heat conduction maintains an isothermal atmosphere. We conclude that Pluto's atmosphere is unique among Solar System planetary atmospheres, as its radiative energy equilibrium is controlled primarily by haze particles instead of gas molecules. We predict that Pluto is therefore several orders of magnitude brighter at mid-infrared wavelengths than previously thought-a brightness that could be detected by future telescopes.

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.

Polynomials for crystal frameworks and the rigid unit mode spectrum

PubMed Central

Power, S. C.

2014-01-01

To each discrete translationally periodic bar-joint framework in , we associate a matrix-valued function defined on the d-torus. The rigid unit mode (RUM) spectrum of is defined in terms of the multi-phases of phase-periodic infinitesimal flexes and is shown to correspond to the singular points of the function and also to the set of wavevectors of harmonic excitations which have vanishing energy in the long wavelength limit. To a crystal framework in Maxwell counting equilibrium, which corresponds to being square, the determinant of gives rise to a unique multi-variable polynomial . For ideal zeolites, the algebraic variety of zeros of on the d-torus coincides with the RUM spectrum. The matrix function is related to other aspects of idealized framework rigidity and flexibility, and in particular leads to an explicit formula for the number of supercell-periodic floppy modes. In the case of certain zeolite frameworks in dimensions two and three, direct proofs are given to show the maximal floppy mode property (order N). In particular, this is the case for the cubic symmetry sodalite framework and some other idealized zeolites. PMID:24379422

Spectroscopic evidence for negative electronic compressibility in a quasi-three-dimensional spin–orbit correlated metal

DOE PAGES

He, Junfeng; Hogan, T.; Mion, Thomas R.; ...

2015-04-27

Negative compressibility is a sign of thermodynamic instability of open1,2,3 or non-equilibrium4,5 systems. In quantum materials consisting of multiple mutually coupled subsystems, the compressibility of one subsystem can be negative if it is countered by positive compressibility of the others. Manifestations of this effect have so far been limited to low-dimensional dilute electron systems6,7,8,9,10,11. Here, we present evidence from angle-resolved photoemission spectroscopy (ARPES) for negative electronic compressibility (NEC) in the quasi-three-dimensional (3D) spin–orbit correlated metal (Sr1-xLax)3Ir2O7. Increased electron filling accompanies an anomalous decrease of the chemical potential, as indicated by the overall movement of the deep valence bands. Such anomaly,more » suggestive of NEC, is shown to be primarily driven by the lowering in energy of the conduction band as the correlated bandgap reduces. Our finding points to a distinct pathway towards an uncharted territory of NEC featuring bulk correlated metals with unique potential for applications in low-power nanoelectronics and novel metamaterials.« less

Surfactant-enhanced remediation of a trichloroethene-contaminated aquifer. 1. Transport of triton X-100

USGS Publications Warehouse

Smith, J.A.; Sahoo, D.; Mclellan, H.M.; Imbrigiotta, T.E.

1997-01-01

Transport of a nonionic surfactant (Triton X-100) at aqueous concentrations less than 400 mg/L through a trichloroethene-contaminated sand-and-gravel aquifer at Picatinny Arsenal, NJ, has been studied through a series of laboratory and field experiments. In the laboratory, batch and column experiments were conducted to quantify the rate and amount of Triton X-100 sorption to the aquifer sediments. In the field, a 400 mg/L aqueous Triton X-100 solution was injected into the aquifer at a rate of 26.5 L/min for a 35-d period. The transport of Triton X-100 was monitored by sampling and analysis of groundwater at six locations surrounding the injection well. Equilibrium batch sorption experiments showed that Triton X-100 sorbs strongly and nonlinearly to the field soil with the sharpest inflection point of the isotherm occurring at an equilibrium aqueous Triton X-100 concentration close to critical micelle concentration. Batch, soil column, and field experimental data were analyzed with zero-, one-, and two- dimensional (respectively) transient solute transport models with either equilibrium or rate-limited sorption. These analyses reveal that Triton X- 100 sorption to the aquifer solids is slow relative to advective and dispersive transport and that an equilibrium sorption model cannot simulate accurately the observed soil column and field data. Comparison of kinetic sorption parameters from batch, column, and field transport data indicate that both physical heterogeneities and Triton X-100 mass transfer between water and soil contribute to the kinetic transport effects.Transport of a nonionic surfactant (Triton X-100) at aqueous concentrations less than 400 mg/L through a trichloroethene-contaminated sand-and-gravel aquifer was studied. Equilibrium batch sorption experiments showed that Triton X-100 sorbs strongly and nonlinearly to the field soil with the sharpest inflection point of the isotherm occurring at an equilibrium aqueous Triton X-100 concentration close to critical micelle concentration. Batch, soil column, and field experimental data were analyzed with zero-, one-, and two-dimensional transient solute transport models with either equilibrium or rate-limited sorption. These analyses revealed that Triton X-100 sorption to the aquifer solids was slow relative to advective and dispersive transport.

Universal relations for differentially rotating relativistic stars at the threshold to collapse

NASA Astrophysics Data System (ADS)

Bozzola, Gabriele; Stergioulas, Nikolaos; Bauswein, Andreas

2018-03-01

A binary neutron star merger produces a rapidly and differentially rotating compact remnant whose lifespan heavily affects the electromagnetic and gravitational emissions. Its stability depends on both the equation of state (EOS) and the rotation law and it is usually investigated through numerical simulations. Nevertheless, by means of a sufficient criterion for secular instability, equilibrium sequences can be used as a computational inexpensive way to estimate the onset of dynamical instability, which, in general, is close to the secular one. This method works well for uniform rotation and relies on the location of turning points: stellar models that are stationary points in a sequence of equilibrium solutions with constant rest mass or angular momentum. Here, we investigate differentially rotating models (using a large number of EOSs and different rotation laws) and find that several universal relations between properly scaled gravitational mass, rest mass and angular momentum of the turning-point models that are valid for uniform rotation are insensitive to the degree of differential rotation, to high accuracy.

Response of South American Ecosystems to Precipitation Variability

NASA Astrophysics Data System (ADS)

Knox, R. G.; Kim, Y.; Longo, M.; Medvigy, D.; Wang, J.; Moorcroft, P. R.; Bras, R. L.

2009-12-01

The Ecosystem Demography Model 2 is a dynamic ecosystem model and land surface energy balance model. ED2 discretizes landscapes of particular terrain and meteorology into fractional areas of unique disturbance history. Each fraction, defined by a shared vertical soil column and canopy air space, contains a stratum of plant groups unique in functional type, size and number density. The result is a vertically distributed representation of energy transfer and plant dynamics (mortality, productivity, recruitment, disturbance, resource competition, etc) that successfully approximates the behaviour of individual-based vegetation models. In previous exercises simulating Amazonian land surface dynamics with ED 2, it was observed that when using grid averaged precipitation as an external forcing the resulting water balance typically over-estimated leaf interception and leaf evaporation while under estimating through-fall and transpiration. To investigate this result, two scenario were conducted in which land surface biophysics and ecosystem demography over the Northern portion of South America are simulated over ~200 years: (1) ED2 is forced with grid averaged values taken from the ERA40 reanalysis meteorological dataset; (2) ED2 is forced with ERA40 reanalysis, but with its precipitation re-sampled to reflect statistical qualities of point precipitation found at rain gauge stations in the region. The findings in this study suggest that the equilibrium moisture states and vegetation demography are co-dependent and show sensitivity to temporal variability in precipitation. These sensitivities will need to be accounted for in future projections of coupled climate-ecosystem changes in South America.

New phenomena in non-equilibrium quantum physics

NASA Astrophysics Data System (ADS)

Kitagawa, Takuya

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

Tidal evolution of close binary stars. I - Revisiting the theory of the equilibrium tide

NASA Technical Reports Server (NTRS)

Zahn, J.-P.

1989-01-01

The theory of the equilibrium tide in stars that possess a convective envelope is reexamined critically, taking recent developments into account and treating thermal convection in the most consistent way within the mixing-length approach. The weak points are identified and discussed, in particular, the reduction of the turbulent viscosity when the tidal period becomes shorter than the convective turnover time. An improved version is derived for the secular equations governing the dynamical evolution of close binaries of such type.

Condensation of helium in aerogel and athermal dynamics of the random-field Ising model.

PubMed

Aubry, Geoffroy J; Bonnet, Fabien; Melich, Mathieu; Guyon, Laurent; Spathis, Panayotis; Despetis, Florence; Wolf, Pierre-Etienne

2014-08-22

High resolution measurements reveal that condensation isotherms of (4)He in high porosity silica aerogel become discontinuous below a critical temperature. We show that this behavior does not correspond to an equilibrium phase transition modified by the disorder induced by the aerogel structure, but to the disorder-driven critical point predicted for the athermal out-of-equilibrium dynamics of the random-field Ising model. Our results evidence the key role of nonequilibrium effects in the phase transitions of disordered systems.

Equilibrium econophysics: A unified formalism for neoclassical economics and equilibrium thermodynamics

NASA Astrophysics Data System (ADS)

Sousa, Tânia; Domingos, Tiago

2006-11-01

We develop a unified conceptual and mathematical structure for equilibrium econophysics, i.e., the use of concepts and tools of equilibrium thermodynamics in neoclassical microeconomics and vice versa. Within this conceptual structure the results obtained in microeconomic theory are: (1) the definition of irreversibility in economic behavior; (2) the clarification that the Engel curve and the offer curve are not descriptions of real processes dictated by the maximization of utility at constant endowment; (3) the derivation of a relation between elasticities proving that economic elasticities are not all independent; (4) the proof that Giffen goods do not exist in a stable equilibrium; (5) the derivation that ‘economic integrability’ is equivalent to the generalized Le Chatelier principle and (6) the definition of a first order phase transition, i.e., a transition between separate points in the utility function. In thermodynamics the results obtained are: (1) a relation between the non-dimensional isothermal and adiabatic compressibilities and the increase or decrease in the thermodynamic potentials; (2) the distinction between mathematical integrability and optimization behavior and (3) the generalization of the Clapeyron equation.

A new PIC noise reduction technique

NASA Astrophysics Data System (ADS)

Barnes, D. C.

2014-10-01

Numerical solution of the Vlasov equation is considered in a general situation in which there is an underlying static solution (equilibrium). There are no further assumptions about dimensionality, smallenss of orbits, or disparate time scales. The semi-characteristic (SC) method for Vlasov solution is described. The usual characteristics of the equation, which are the single particle orbits, are modified in such a way that the equilibrium phase-space flow is removed. In this way, the shot noise introduced by the usual discrete particle representation of the equilibrium is static in time and can be removed completely by subtraction. An almost exact algorithm for this is based on the observation that a (infinitesimal or) discrete time step of any equilibrium MC realization is again a realization of the equilibrium, building up strings of associated simulation particles. In this way, the only added discretization error arises from the need to extrapolate backward in time the chain end points one dt using a canonical transformation. Previously developed energy-conserving time-implicit methods are applied without modification. 1D ES examples of Landau damping and velocity-space instability are given to illustrate the method.

Universal ideal behavior and macroscopic work relation of linear irreversible stochastic thermodynamics

NASA Astrophysics Data System (ADS)

Ma, Yi-An; Qian, Hong

2015-06-01

We revisit the Ornstein-Uhlenbeck (OU) process as the fundamental mathematical description of linear irreversible phenomena, with fluctuations, near an equilibrium. By identifying the underlying circulating dynamics in a stationary process as the natural generalization of classical conservative mechanics, a bridge between a family of OU processes with equilibrium fluctuations and thermodynamics is established through the celebrated Helmholtz theorem. The Helmholtz theorem provides an emergent macroscopic ‘equation of state’ of the entire system, which exhibits a universal ideal thermodynamic behavior. Fluctuating macroscopic quantities are studied from the stochastic thermodynamic point of view and a non-equilibrium work relation is obtained in the macroscopic picture, which may facilitate experimental study and application of the equalities due to Jarzynski, Crooks, and Hatano and Sasa.

Physical analysis of the process of cavitation in xylem sap.

PubMed

Shen, Fanyi; Gao, Rongfu; Liu, Wenji; Zhang, Wenjie

2002-06-01

Recent studies have confirmed that cavitation in xylem is caused by air bubbles. We analyzed expansion of a preexistent bubble adhering to a crack in a conduit wall and a bubble formed by the passage of air through a pore of a pit membrane, a process known as air seeding. We consider that there are two equilibrium states for a very small air bubble in the xylem: one is temporarily stable with a bubble radius r1 at point s1 on the curve P(r) relating pressure within the bubble (P) with bubble radius (r); the other is unstable with a bubble radius r2 at point s2 on Pr (where r1 < r2). In each equilibrium state, the bubble collapse pressure (2sigma/r, where sigma is surface tension of water) is balanced by the pressure difference across its surface. In the case of a bubble from a crack in a conduit wall, which is initially at point s1, expansion will occur steadily as water potential decreases. The bubble will burst only if the xylem pressure drops below a threshold value. A formula giving the threshold pressure for bubble bursting is proposed. In the case of an air seed entering a xylem conduit through a pore in a pit membrane, its initial radius may be r2 (i.e., the radius of the pore by which the air seed entered the vessel) at point s2 on Pr. Because the bubble is in an unstable equilibrium when entering the conduit, it can either expand or contract to point s1. As water vaporizes into the air bubble at s2, P rises until it exceeds the gas pressure that keeps the bubble in equilibrium, at which point the bubble will burst and induce a cavitation event in accordance with the air-seeding hypothesis. However, other possible perturbations could make the air-seeded bubble contract to s1, in which case the bubble will burst at a threshold pressure proposed for a bubble expanding from a crack in a conduit wall. For this reason some cavitation events may take place at a xylem threshold pressure (Pl'*) other than that determined by the formula, Plp'* = -2sigma/rp, proposed by Sperry and Tyree (1988), which is applicable only to air-seeded bubbles at s2. The more general formula we propose for calculating the threshold pressure for bubble breaking is consistent with the results of published experiments.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Rational and Empirical Play in the Simple Hot Potato Game

ERIC Educational Resources Information Center

Butts, Carter T.; Rode, David C.

2007-01-01

We define a "hot potato" to be a good that may be traded a finite number of times, but which becomes a bad if and when it can no longer be exchanged. We describe a game involving such goods, and show that non-acceptance is a unique subgame perfect Nash equilibrium for rational egoists. Contrastingly, experiments with human subjects show…

Calculating phase diagrams using PANDAT and panengine

NASA Astrophysics Data System (ADS)

Chen, S.-L.; Zhang, F.; Xie, F.-Y.; Daniel, S.; Yan, X.-Y.; Chang, Y. A.; Schmid-Fetzer, R.; Oates, W. A.

2003-12-01

Knowledge of phase equilibria or phase diagrams and thermodynamic properties is important in alloy design and materials-processing simulation. In principle, stable phase equilibrium is uniquely determined by the thermodynamic properties of the system, such as the Gibbs energy functions of the phases. PANDAT, a new computer software package for multicomponent phase-diagram calculation, was developed under the guidance of this principle.

One-dimensional models of quasi-neutral parallel electric fields

NASA Technical Reports Server (NTRS)

Stern, D. P.

1981-01-01

Parallel electric fields can exist in the magnetic mirror geometry of auroral field lines if they conform to the quasineutral equilibrium solutions. Results on quasi-neutral equilibria and on double layer discontinuities were reviewed and the effects on such equilibria due to non-unique solutions, potential barriers and field aligned current flows using as inputs monoenergetic isotropic distribution functions were examined.

Geoid Anomalies and the Near-Surface Dipole Distribution of Mass

NASA Technical Reports Server (NTRS)

Turcotte, D. L.; Ockendon, J. R.

1978-01-01

Although geoid or surface gravity anomalies cannot be uniquely related to an interior distribution of mass, they can be related to a surface mass distribution. However, over horizontal distances greater than about 100 km, the condition of isostatic equilibrium above the asthenosphere is a good approximation and the total mass per unit column is zero. Thus the surface distribution of mass is also zero. For this case we show that the surface gravitational potential anomaly can be uniquely related to a surface dipole distribution of mass. Variations in the thickness of the crust and lithosphere can be expected to produce undulations in the geoid.

Motion of the angular momentum vector in body coordinates for torque-free dual-spin spacecraft

NASA Technical Reports Server (NTRS)

Fedor, J. V.

1981-01-01

The motion of the angular momentum vector in body coordinates for torque free, asymmetric dual spin spacecraft without and, for a special case, with energy dissipation on the main spacecraft is investigated. Without energy dissipation, two integrals can be obtained from the Euler equations of motion. Using the classical method of elimination of variable, the motion about the equilibrium points (six for the general case) are derived with these integrals. For small nutation angle, theta, the trajectories about the theta = 0 deg and theta = 180 deg points readily show the requirements for stable motion about these points. Also the conditions needed to eliminate stable motion about the theta = 180 deg point as well as the other undesireable equilibrium points follow directly from these equations. For the special case where the angular momentum vector moves about the principal axis which contains the momentum wheel, the notion of 'free variable' azimuth angle is used. Physically this angle must vary from 0 to 2 pi in a circular periodic fashion. Expressions are thus obtained for the nutation angle in terms of the free variable and other spacecraft parameters. Results show that in general there are two separate trajectory expressions that govern the motion of the angular momentum vector in body coordinates.

Electric-Field Instrument With Ac-Biased Corona Point

NASA Technical Reports Server (NTRS)

Markson, R.; Anderson, B.; Govaert, J.

1993-01-01

Measurements indicative of incipient lightning yield additional information. New instrument gives reliable readings. High-voltage ac bias applied to needle point through high-resistance capacitance network provides corona discharge at all times, enabling more-slowly-varying component of electrostatic potential of needle to come to equilibrium with surrounding air. High resistance of high-voltage coupling makes instrument insensitive to wind. Improved corona-point instrument expected to yield additional information assisting in safety-oriented forecasting of lighting.

A Course of Lectures on Statistical Mechanics

DTIC Science & Technology

2010-06-01

of mathematics goes a long way to making it tractable. In particular for doing problems in thermodynamics , we’ll stress the following point . For any...disentangle temperature from k. This is done by setting T = 273.16 K at the triple point of water (’ 0.01◦C). Note that the SI unit of the Kelvin...energy, 11 of harmonic oscillator, 66 thermal equilibrium, 19 thermal resistance, 27 triple point of water, 19 ultraviolet catastrophe, 71 validity

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

PubMed

Hinder, Mark R; Milner, Theodore E

2003-06-15

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

Influence of Two-Phase Thermocapillary Flow on Cryogenic Liquid Retention in Microscopic Pores

NASA Technical Reports Server (NTRS)

Schmidt, G. R.; Nadarajah, A.; Chung, T. J.; Karr, G. R.

1994-01-01

Previous experiments indicate that the bubble point pressure of spacecraft liquid hydrogen acquisition devices is reduced substantially when the ullage is pressurized with heated hydrogen vapor. The objective is to determine whether the two-phase thermocapillary convection arising from thermodynamic non-equilibrium along the porous surfaces of such devices could lead to this observed degradation in retention performance. We also examine why retention capability appears to be unaffected by pressurization with heated helium or direct heating through the porous structure. Computational assessments based on coupled solution of the flowfield and liquid free surface indicate that for highly wetting fluids in small pores, dynamic pressure and vapor recoil dictate surface morphology and drive meniscus deformation. With superheating, the two terms exert the same influence on curvature and promote mechanical equilibrium, but with subcooling, the pressure distribution produces a suction about the pore center-line that degrades retention. This result points to thermocapillary-induced deformation arising from condensation as the cause for retention loss. It also indicates that increasing the level of non-equilibrium by reducing accommodation coefficient restricts deformation and explains why retention failure does not occur with direct screen heating or helium pressurization.

Ergodic Theory, Interpretations of Probability and the Foundations of Statistical Mechanics

NASA Astrophysics Data System (ADS)

van Lith, Janneke

The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of these two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well known that this account is problematic. This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented.

Global stability analysis of two-strain epidemic model with bilinear and non-monotone incidence rates

NASA Astrophysics Data System (ADS)

Baba, Isa Abdullahi; Hincal, Evren

2017-05-01

In this article we studied an epidemic model consisting of two strains with different types of incidence rates; bilinear and non-monotone. The model consists of four equilibrium points: disease-free equilibrium, endemic with respect to strain 1, endemic with respect to strain 2, and endemic with respect to both strains. The global stability analysis of the equilibrium points was carried out through the use of Lyapunov functions. Two basic reproduction ratios R 1 0 and R 2 0 are found, and we have shown that if both are less than one, the disease dies out, and if both are greater than one epidemic occurs. Furthermore, epidemics occur with respect to any strain with a basic reproduction ratio greater than one and disease dies out with respect to any strain with a basic reproduction ratio less than one. It was also shown that any strain with highest basic reproduction ratio will automatically outperform the other strain, thereby eliminating it. Numerical simulations were carried out to support the analytic result and to show the effect of the parameter k in the non-monotone incidence rate, which describes the psychological effect of general public towards infection.

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

PubMed

Gomi, H; Kawato, M

1997-03-01

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

Local Equilibrium and Retardation Revisited.

PubMed

Hansen, Scott K; Vesselinov, Velimir V

2018-01-01

In modeling solute transport with mobile-immobile mass transfer (MIMT), it is common to use an advection-dispersion equation (ADE) with a retardation factor, or retarded ADE. This is commonly referred to as making the local equilibrium assumption (LEA). Assuming local equilibrium, Eulerian textbook treatments derive the retarded ADE, ostensibly exactly. However, other authors have presented rigorous mathematical derivations of the dispersive effect of MIMT, applicable even in the case of arbitrarily fast mass transfer. We resolve the apparent contradiction between these seemingly exact derivations by adopting a Lagrangian point of view. We show that local equilibrium constrains the expected time immobile, whereas the retarded ADE actually embeds a stronger, nonphysical, constraint: that all particles spend the same amount of every time increment immobile. Eulerian derivations of the retarded ADE thus silently commit the gambler's fallacy, leading them to ignore dispersion due to mass transfer that is correctly modeled by other approaches. We then present a particle tracking simulation illustrating how poor an approximation the retarded ADE may be, even when mobile and immobile plumes are continually near local equilibrium. We note that classic "LEA" (actually, retarded ADE validity) criteria test for insignificance of MIMT-driven dispersion relative to hydrodynamic dispersion, rather than for local equilibrium. Published 2017. This article is a U.S. Government work and is in the public domain in the USA.

Adsorption of saturated fatty acid in urea complexation: Kinetics and equilibrium studies

NASA Astrophysics Data System (ADS)

Setyawardhani, Dwi Ardiana; Sulistyo, Hary; Sediawan, Wahyudi Budi; Fahrurrozi, Mohammad

2018-02-01

Urea complexation is fractionation process for concentrating poly-unsaturated fatty acids (PUFAs) from vegetable oil or animal fats. For process design and optimization in commercial industries, it is necessary to provide kinetics and equilibrium data. Urea inclusion compounds (UICs) as the product is a unique complex form which one molecule (guest) is enclosed within another molecule (host). In urea complexation, the guest-host bonding exists between saturated fatty acids (SFAs) and crystalline urea. This research studied the complexation is analogous to an adsorption process. The Batch adsorption process was developed to obtain the experimental data. The ethanolic urea solution was mixed with SFA in certain compositions and adsorption times. The mixture was heated until it formed homogenous and clear solution, then it cooled very slowly until the first numerous crystal appeared. Adsorption times for the kinetic data were determined since the crystal formed. The temperature was maintained constant at room temperature. Experimental sets of data were observed with adsorption kinetics and equilibrium models. High concentration of saturated fatty acid (SFA) was used to represent adsorption kinetics and equilibrium parameters. Kinetic data were examined with pseudo first-order, pseudo second-order and intra particle diffusion models. Linier, Freundlich and Langmuir isotherm were used to study the equilibrium model of this adsorption. The experimental data showed that SFA adsorption in urea crystal followed pseudo second-order model. The compatibility of the data with Langmuir isotherm showed that urea complexation was a monolayer adsorption.

Synthesis and amphiphilic properties of decanoyl esters of tri- and tetraethylene glycol.

PubMed

Zhu, Ying; Molinier, Valérie; Queste, Sébastien; Aubry, Jean-Marie

2007-08-15

Well-defined decanoyl triethylene glycol ester and decanoyl tetraethylene glycol ester were synthesized and compared to their ether counterparts (C(10)E(4) and C(10)E(3)). Their physicochemical properties i.e. critical micelle concentrations (CMC), cloud points, and equilibrium surface tensions were determined. Binary water-surfactant phase behavior was also studied by polarized optical microscopy. The stability of the ester bond was determined by investigating alkaline hydrolysis of the compounds. It was found that CMC, cloud point and equilibrium surface tension are roughly the same for corresponding ethers and esters. In the binary diagram, the esters form only lamellar phases, the area of which is smaller than that of the ether counterparts. These different behaviors can be related to the modification of the molecular conformation induced by the replacement of the ether group by the ester group.

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.

Upwind MacCormack Euler solver with non-equilibrium chemistry

NASA Technical Reports Server (NTRS)

Sherer, Scott E.; Scott, James N.

1993-01-01

A computer code, designated UMPIRE, is currently under development to solve the Euler equations in two dimensions with non-equilibrium chemistry. UMPIRE employs an explicit MacCormack algorithm with dissipation introduced via Roe's flux-difference split upwind method. The code also has the capability to employ a point-implicit methodology for flows where stiffness is introduced through the chemical source term. A technique consisting of diagonal sweeps across the computational domain from each corner is presented, which is used to reduce storage and execution requirements. Results depicting one dimensional shock tube flow for both calorically perfect gas and thermally perfect, dissociating nitrogen are presented to verify current capabilities of the program. Also, computational results from a chemical reactor vessel with no fluid dynamic effects are presented to check the chemistry capability and to verify the point implicit strategy.

Design and implementation of grid multi-scroll fractional-order chaotic attractors

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

Chen, Liping, E-mail: lip-chenhut@126.com; Pan, Wei; Wu, Ranchao

2016-08-15

This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most.more » Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.« less

Dynamic analysis of trapping and escaping in dual beam optical trap

NASA Astrophysics Data System (ADS)

Li, Wenqiang; Hu, Huizhu; Su, Heming; Li, Zhenggang; Shen, Yu

2016-10-01

In this paper, we simulate the dynamic movement of a dielectric sphere in optical trap. This dynamic analysis can be used to calibrate optical forces, increase trapping efficiency and measure viscous coefficient of surrounding medium. Since an accurate dynamic analysis is based on a detailed force calculation, we calculate all forces a sphere receives. We get the forces of dual-beam gradient radiation pressure on a micron-sized dielectric sphere in the ray optics regime and utilize Einstein-Ornstein-Uhlenbeck to deal with its Brownian motion forces. Hydrodynamic viscous force also exists when the sphere moves in liquid. Forces from buoyance and gravity are also taken into consideration. Then we simulate trajectory of a sphere when it is subject to all these forces in a dual optical trap. From our dynamic analysis, the sphere can be trapped at an equilibrium point in static water, although it permanently fluctuates around the equilibrium point due to thermal effects. We go a step further to analyze the effects of misalignment of two optical traps. Trapping and escaping phenomena of the sphere in flowing water are also simulated. In flowing water, the sphere is dragged away from the equilibrium point. This dragging distance increases with the decrease of optical power, which results in escaping of the sphere with optical power below a threshold. In both trapping and escaping process we calculate the forces and position of the sphere. Finally, we analyze a trapping region in dual optical tweezers.

Self-assembled materials and supramolecular chemistry within microfluidic environments: from common thermodynamic states to non-equilibrium structures.

PubMed

Sevim, S; Sorrenti, A; Franco, C; Furukawa, S; Pané, S; deMello, A J; Puigmartí-Luis, J

2018-05-01

Self-assembly is a crucial component in the bottom-up fabrication of hierarchical supramolecular structures and advanced functional materials. Control has traditionally relied on the use of encoded building blocks bearing suitable moieties for recognition and interaction, with targeting of the thermodynamic equilibrium state. On the other hand, nature leverages the control of reaction-diffusion processes to create hierarchically organized materials with surprisingly complex biological functions. Indeed, under non-equilibrium conditions (kinetic control), the spatio-temporal command of chemical gradients and reactant mixing during self-assembly (the creation of non-uniform chemical environments for example) can strongly affect the outcome of the self-assembly process. This directly enables a precise control over material properties and functions. In this tutorial review, we show how the unique physical conditions offered by microfluidic technologies can be advantageously used to control the self-assembly of materials and of supramolecular aggregates in solution, making possible the isolation of intermediate states and unprecedented non-equilibrium structures, as well as the emergence of novel functions. Selected examples from the literature will be used to confirm that microfluidic devices are an invaluable toolbox technology for unveiling, understanding and steering self-assembly pathways to desired structures, properties and functions, as well as advanced processing tools for device fabrication and integration.

Theories and applications of second-order correlation of longitudinal velocity increments at three points in isotropic turbulence

NASA Astrophysics Data System (ADS)

Wu, J. Z.; Fang, L.; Shao, L.; Lu, L. P.

2018-06-01

In order to introduce new physics to traditional two-point correlations, we define the second-order correlation of longitudinal velocity increments at three points and obtain the analytical expressions in isotropic turbulence. By introducing the Kolmogorov 4/5 law, this three-point correlation explicitly contains velocity second- and third-order moments, which correspond to energy and energy transfer respectively. The combination of them then shows additional information of non-equilibrium turbulence by comparing to two-point correlations. Moreover, this three-point correlation shows the underlying inconsistency between numerical interpolation and three-point scaling law in numerical calculations, and inspires a preliminary model to correct this problem in isotropic turbulence.

Laser-induced breakdown spectroscopy (LIBS), part I: review of basic diagnostics and plasma-particle interactions: still-challenging issues within the analytical plasma community.

PubMed

Hahn, David W; Omenetto, Nicoló

2010-12-01

Laser-induced breakdown spectroscopy (LIBS) has become a very popular analytical method in the last decade in view of some of its unique features such as applicability to any type of sample, practically no sample preparation, remote sensing capability, and speed of analysis. The technique has a remarkably wide applicability in many fields, and the number of applications is still growing. From an analytical point of view, the quantitative aspects of LIBS may be considered its Achilles' heel, first due to the complex nature of the laser-sample interaction processes, which depend upon both the laser characteristics and the sample material properties, and second due to the plasma-particle interaction processes, which are space and time dependent. Together, these may cause undesirable matrix effects. Ways of alleviating these problems rely upon the description of the plasma excitation-ionization processes through the use of classical equilibrium relations and therefore on the assumption that the laser-induced plasma is in local thermodynamic equilibrium (LTE). Even in this case, the transient nature of the plasma and its spatial inhomogeneity need to be considered and overcome in order to justify the theoretical assumptions made. This first article focuses on the basic diagnostics aspects and presents a review of the past and recent LIBS literature pertinent to this topic. Previous research on non-laser-based plasma literature, and the resulting knowledge, is also emphasized. The aim is, on one hand, to make the readers aware of such knowledge and on the other hand to trigger the interest of the LIBS community, as well as the larger analytical plasma community, in attempting some diagnostic approaches that have not yet been fully exploited in LIBS.

Equilibrium charge distribution on a finite straight one-dimensional wire

NASA Astrophysics Data System (ADS)

Batle, Josep; Ciftja, Orion; Abdalla, Soliman; Elhoseny, Mohamed; Alkhambashi, Majid; Farouk, Ahmed

2017-09-01

The electrostatic properties of uniformly charged regular bodies are prominently discussed on college-level electromagnetism courses. However, one of the most basic problems of electrostatics that deals with how a continuous charge distribution reaches equilibrium is rarely mentioned at this level. In this work we revisit the problem of equilibrium charge distribution on a straight one-dimensional (1D) wire with finite length. The majority of existing treatments in the literature deal with the 1D wire as a limiting case of a higher-dimensional structure that can be treated analytically for a Coulomb interaction potential between point charges. Surprisingly, different models (for instance, an ellipsoid or a cylinder model) may lead to different results, thus there is even some ambiguity on whether the problem is well-posed. In this work we adopt a different approach where we do not start with any higher-dimensional body that reduces to a 1D wire in the appropriate limit. Instead, our starting point is the obvious one, a finite straight 1D wire that contains charge. However, the new tweak in the model is the assumption that point charges interact with each other via a non-Coulomb power-law interaction potential. This potential is well-behaved, allows exact analytical results and approaches the standard Coulomb interaction potential as a limit. The results originating from this approach suggest that the equilibrium charge distribution for a finite straight 1D wire is a uniform charge density when the power-law interaction potential approaches the Coulomb interaction potential as a suitable limit. We contrast such a finding to results obtained using a different regularised logarithmic interaction potential which allows exact treatment in 1D. The present self-contained material may be of interest to instructors teaching electromagnetism as well as students who will discover that simple-looking problems may sometimes pose important scientific challenges.

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.

Linear dynamics of classical spin as Mobius transformation

DOE PAGES

Galda, Alexey; Vinokur, Valerii М.

2017-04-26

Though the overwhelming majority of natural processes occur far from the equilibrium, general theoretical approaches to non-equilibrium phase transitions remain scarce. Recent breakthroughs introduced a description of open dissipative systems in terms of non-Hermitian quantum mechanics enabling the identification of a class of non-equilibrium phase transitions associated with the loss of combined parity (reflection) and time-reversal symmetries. Here we report that the time evolution of a single classical spin (e.g. monodomain ferromagnet) governed by the Landau-Lifshitz-Gilbert-Slonczewski equation in the absence of magnetic anisotropy terms is described by a Mobius transformation in complex stereographic coordinates. We identify the parity-time symmetry-breaking phasemore » transition occurring in spin-transfer torque-driven linear spin systems as a transition between hyperbolic and loxodromic classes of Mobius transformations, with the critical point of the transition corresponding to the parabolic transformation. However, this establishes the understanding of non-equilibrium phase transitions as topological transitions in configuration space.« less

Does shaking increase the pressure inside a bottle of champagne?

PubMed

Vreme, A; Pouligny, B; Nadal, F; Liger-Belair, G

2015-02-01

Colas, beers and sparkling wines are all concentrated solutions of carbon dioxide in aqueous solvents. Any such carbonated liquid is ordinarily conditioned inside a closed bottle or a metal can as a liquid-gas 2-phase system. At thermodynamic equilibrium, the partial pressure of carbon-dioxide in the gas phase and its concentration in the liquid are proportional (Henry's law). In practical conditions and use (transport, opening of the container, exterior temperature change, etc.), Henry's equilibrium can be perturbed. The goal of this paper is to describe and understand how the system responds to such perturbations and evolves towards a new equilibrium state. Formally, we investigate the dynamics around Henry's equilibrium of a closed system, through dedicated experiments and modeling. We focus on the response to a sudden pressure change and to mechanical shaking (the latter point inspired the article's title). Observations are rationalized through basic considerations including molecular diffusion, bubble dynamics (based on Epstein-Plesset theory) and chemi-convective hydrodynamic instabilities. Copyright © 2014 Elsevier Inc. All rights reserved.

Viscous-shock-layer solutions with coupled radiation and ablation injection for earth entry

NASA Technical Reports Server (NTRS)

Gupta, Roop N.; Lee, Kam-Pui; Moos, James N.; Sutton, Kenneth

1990-01-01

Results are obtained for the forebody of a planetary exploration vehicle entering the earth's atmosphere. A viscous-shock-layer analysis is used assuming the flow to be laminar and in chemical equilibrium. Presented results include coupled radiation and ablation injection. This study further includes the effect of different transport and thermodynamic properties and radiation models. A Lewis number of 1.4 appears adequate for the radiation-dominated flows. Five velocities corresponding to different possible trajectory points at an altitude of 70 km have been further analyzed in detail. Sublimation and radiative equilibrium wall temperatures are employed for cases with and without coupled injection, respectively. For the cases analyzed here, the mass injection rates are small. However, the rates could become large if a lower altitude is used for aerobraking and/or the body size is increased. A comparison of the equilibrium results with finite-rate chemistry calculation shows the flowfield to be in chemical equilibrium.

Analysis of Steady, Two-Dimensional Chemically Reacting Nonequilibrium Flow by an Unsteady, Asymptotically Consistent Technique. Volume I. Theoretical Development.

DTIC Science & Technology

1982-09-01

wall, and exit points are know,, collectively as boundary points. In the following discussion, thi numerical treatment used for each type of mesh point...and fiozen solutions and that it matches the ODK solution 6 [Reference (10)] quite well. Also note that in this case, there is only a small departure...shows the results of the H-F system analysis. The mass-averaged temperature profile falls between the equilibrium and frozen solutions and matches the ODK

An Investigation of Spinup Dynamics of Axial Gyrostats Using Elliptic Integrals and the Method of Averaging

DTIC Science & Technology

1991-01-01

is a gyrostat near one of the five libration points . She identified the equilibria and determined their stability regions. Also, Mavraga- nis [71] has...defines a family of periodic orbits , depending on how close the all-spun motion is to an equilibrium point of the equations of motion for a single...determined by the relationship between the mission orbit and the object the platform is supposed to track. As a limiting case, one might wish to point

Uniqueness of the joint measurement and the structure of the set of compatible quantum measurements

NASA Astrophysics Data System (ADS)

Guerini, Leonardo; Terra Cunha, Marcelo

2018-04-01

We address the problem of characterising the compatible tuples of measurements that admit a unique joint measurement. We derive a uniqueness criterion based on the method of perturbations and apply it to show that extremal points of the set of compatible tuples admit a unique joint measurement, while all tuples that admit a unique joint measurement lie in the boundary of such a set. We also provide counter-examples showing that none of these properties are both necessary and sufficient, thus completely describing the relation between the joint measurement uniqueness and the structure of the compatible set. As a by-product of our investigations, we completely characterise the extremal and boundary points of the set of general tuples of measurements and of the subset of compatible tuples.

Linearized theory of inhomogeneous multiple 'water-bag' plasmas

NASA Technical Reports Server (NTRS)

Bloomberg, H. W.; Berk, H. L.

1973-01-01

Equations are derived for describing the inhomogeneous equilibrium and small deviations from the equilibrium, giving particular attention to systems with trapped particles. An investigation is conducted of periodic systems with a single trapped-particle water bag, taking into account the behavior of the perturbation equations at the turning points. An outline is provided concerning a procedure for obtaining the eigenvalues. The results of stability calculations connected with the sideband effects are considered along with questions regarding the general applicability of the multiple water-bag approach in stability calculations.

Extrapolation to Nonequilibrium from Coarse-Grained Response Theory

NASA Astrophysics Data System (ADS)

Basu, Urna; Helden, Laurent; Krüger, Matthias

2018-05-01

Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many-body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse-grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far-from-equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many-body systems. It is illustrated in a four-state model and in the near critical Ising model.

Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

NASA Astrophysics Data System (ADS)

Zheng, Da-Chuan; Tong, Ning-Hua

2017-06-01

Using the bosonic numerical renormalization group method, we studied the equilibrium dynamical correlation function C(ω) of the spin operator σ z for the biased sub-Ohmic spin-boson model. The small-ω behavior C(ω )\\propto {ω }s is found to be universal and independent of the bias ɛ and the coupling strength α (except at the quantum critical point α ={α }{{c}} and ɛ = 0). Our NRG data also show C(ω )\\propto {χ }2{ω }s for a wide range of parameters, including the biased strong coupling regime (\\varepsilon \

Stable Spheromaks with Profile Control

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

Fowler, T K; Jayakumar, R

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

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 Thermal Equilibrium Solution of a Generic Bipolar Quantum Hydrodynamic Model

NASA Astrophysics Data System (ADS)

Unterreiter, Andreas

The thermal equilibrium state of a bipolar, isothermic quantum fluid confined to a bounded domain ,d = 1,2 or d = 3 is entirely described by the particle densities n, p, minimizing the energy where G1,2 are strictly convex real valued functions, . It is shown that this variational problem has a unique minimizer in and some regularity results are proven. The semi-classical limit is carried out recovering the minimizer of the limiting functional. The subsequent zero space charge limit leads to extensions of the classical boundary conditions. Due to the lack of regularity the asymptotics can not be settled on Sobolev embedding arguments. The limit is carried out by means of a compactness-by-convexity principle.

Bifurcation and Stability in a Delayed Predator-Prey Model with Mixed Functional Responses

NASA Astrophysics Data System (ADS)

Yafia, R.; Aziz-Alaoui, M. A.; Merdan, H.; Tewa, J. J.

2015-06-01

The model analyzed in this paper is based on the model set forth by Aziz Alaoui et al. [Aziz Alaoui & Daher Okiye, 2003; Nindjin et al., 2006] with time delay, which describes the competition between the predator and prey. This model incorporates a modified version of the Leslie-Gower functional response as well as that of Beddington-DeAngelis. In this paper, we consider the model with one delay consisting of a unique nontrivial equilibrium E* and three others which are trivial. Their dynamics are studied in terms of local and global stabilities and of the description of Hopf bifurcation at E*. At the third trivial equilibrium, the existence of the Hopf bifurcation is proven as the delay (taken as a parameter of bifurcation) that crosses some critical values.

Vaccination strategies for SIR vector-transmitted diseases.

PubMed

Cruz-Pacheco, Gustavo; Esteva, Lourdes; Vargas, Cristobal

2014-08-01

Vector-borne diseases are one of the major public health problems in the world with the fastest spreading rate. Control measures have been focused on vector control, with poor results in most cases. Vaccines should help to reduce the diseases incidence, but vaccination strategies should also be defined. In this work, we propose a vector-transmitted SIR disease model with age-structured population subject to a vaccination program. We find an expression for the age-dependent basic reproductive number R(0), and we show that the disease-free equilibrium is locally stable for R(0) ≤ 1, and a unique endemic equilibrium exists for R(0) > 1. We apply the theoretical results to public data to evaluate vaccination strategies, immunization levels, and optimal age of vaccination for dengue disease.

Nanostructure control: Nucleation and diffusion studies for predictable ultra thin film morphologies

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

Hershberger, Matthew

This thesis covers PhD research on two systems with unique and interesting physics. The first system is lead (Pb) deposited on the silicon (111) surface with the 7x7 reconstruction. Pb and Si are mutually bulk insoluble resulting in this system being an ideal case for studying metal and semiconductor interactions. Initial Pb deposition causes an amorphous wetting layer to form across to surface. Continued deposition results in Pb(111) island growth. Classic literature has classified this system as the Stranski-Krastanov growth mode although the system is not near equilibrium conditions. Our research shows a growth mode distinctly different than classical expectationsmore » and begins a discussion of reclassifying diffusion and nucleation for systems far away from the well-studied equilibrium cases.« less

Disease Extinction Versus Persistence in Discrete-Time Epidemic Models.

PubMed

van den Driessche, P; Yakubu, Abdul-Aziz

2018-04-12

We focus on discrete-time infectious disease models in populations that are governed by constant, geometric, Beverton-Holt or Ricker demographic equations, and give a method for computing the basic reproduction number, [Formula: see text]. When [Formula: see text] and the demographic population dynamics are asymptotically constant or under geometric growth (non-oscillatory), we prove global asymptotic stability of the disease-free equilibrium of the disease models. Under the same demographic assumption, when [Formula: see text], we prove uniform persistence of the disease. We apply our theoretical results to specific discrete-time epidemic models that are formulated for SEIR infections, cholera in humans and anthrax in animals. Our simulations show that a unique endemic equilibrium of each of the three specific disease models is asymptotically stable whenever [Formula: see text].

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

PubMed

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

2012-01-01

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

Communication: A method to compute the transport coefficient of pure fluids diffusing through planar interfaces from equilibrium molecular dynamics simulations.

PubMed

Vermorel, Romain; Oulebsir, Fouad; Galliero, Guillaume

2017-09-14

The computation of diffusion coefficients in molecular systems ranks among the most useful applications of equilibrium molecular dynamics simulations. However, when dealing with the problem of fluid diffusion through vanishingly thin interfaces, classical techniques are not applicable. This is because the volume of space in which molecules diffuse is ill-defined. In such conditions, non-equilibrium techniques allow for the computation of transport coefficients per unit interface width, but their weak point lies in their inability to isolate the contribution of the different physical mechanisms prone to impact the flux of permeating molecules. In this work, we propose a simple and accurate method to compute the diffusional transport coefficient of a pure fluid through a planar interface from equilibrium molecular dynamics simulations, in the form of a diffusion coefficient per unit interface width. In order to demonstrate its validity and accuracy, we apply our method to the case study of a dilute gas diffusing through a smoothly repulsive single-layer porous solid. We believe this complementary technique can benefit to the interpretation of the results obtained on single-layer membranes by means of complex non-equilibrium methods.

Conformal field theory out of equilibrium: a review

NASA Astrophysics Data System (ADS)

Bernard, Denis; Doyon, Benjamin

2016-06-01

We provide a pedagogical review of the main ideas and results in non-equilibrium conformal field theory and connected subjects. These concern the understanding of quantum transport and its statistics at and near critical points. Starting with phenomenological considerations, we explain the general framework, illustrated by the example of the Heisenberg quantum chain. We then introduce the main concepts underlying conformal field theory (CFT), the emergence of critical ballistic transport, and the CFT scattering construction of non-equilibrium steady states. Using this we review the theory for energy transport in homogeneous one-dimensional critical systems, including the complete description of its large deviations and the resulting (extended) fluctuation relations. We generalize some of these ideas to one-dimensional critical charge transport and to the presence of defects, as well as beyond one-dimensional criticality. We describe non-equilibrium transport in free-particle models, where connections are made with generalized Gibbs ensembles, and in higher-dimensional and non-integrable quantum field theories, where the use of the powerful hydrodynamic ideas for non-equilibrium steady states is explained. We finish with a list of open questions. The review does not assume any advanced prior knowledge of conformal field theory, large-deviation theory or hydrodynamics.

Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality.

PubMed

Alba, Vincenzo

2017-06-01

In recent years entanglement measures, such as the von Neumann and the Rényi entropies, provided a unique opportunity to access elusive features of quantum many-body systems. However, extracting entanglement properties analytically, experimentally, or in numerical simulations can be a formidable task. Here, by combining the replica trick and the Jarzynski equality we devise an alternative effective out-of-equilibrium protocol for measuring the equilibrium Rényi entropies. The key idea is to perform a quench in the geometry of the replicas. The Rényi entropies are obtained as the exponential average of the work performed during the quench. We illustrate an application of the method in classical Monte Carlo simulations, although it could be useful in different contexts, such as in quantum Monte Carlo, or experimentally in cold-atom systems. The method is most effective in the quasistatic regime, i.e., for a slow quench. As a benchmark, we compute the Rényi entropies in the Ising universality class in 1+1 dimensions. We find perfect agreement with the well-known conformal field theory predictions.

Nash Equilibrium of Social-Learning Agents in a Restless Multiarmed Bandit Game.

PubMed

Nakayama, Kazuaki; Hisakado, Masato; Mori, Shintaro

2017-05-16

We study a simple model for social-learning agents in a restless multiarmed bandit (rMAB). The bandit has one good arm that changes to a bad one with a certain probability. Each agent stochastically selects one of the two methods, random search (individual learning) or copying information from other agents (social learning), using which he/she seeks the good arm. Fitness of an agent is the probability to know the good arm in the steady state of the agent system. In this model, we explicitly construct the unique Nash equilibrium state and show that the corresponding strategy for each agent is an evolutionarily stable strategy (ESS) in the sense of Thomas. It is shown that the fitness of an agent with ESS is superior to that of an asocial learner when the success probability of social learning is greater than a threshold determined from the probability of success of individual learning, the probability of change of state of the rMAB, and the number of agents. The ESS Nash equilibrium is a solution to Rogers' paradox.

Acoustic equations of state for simple lattice Boltzmann velocity sets.

PubMed

Viggen, Erlend Magnus

2014-07-01

The lattice Boltzmann (LB) method typically uses an isothermal equation of state. This is not sufficient to simulate a number of acoustic phenomena where the equation of state cannot be approximated as linear and constant. However, it is possible to implement variable equations of state by altering the LB equilibrium distribution. For simple velocity sets with velocity components ξ(iα)∈(-1,0,1) for all i, these equilibria necessarily cause error terms in the momentum equation. These error terms are shown to be either correctable or negligible at the cost of further weakening the compressibility. For the D1Q3 velocity set, such an equilibrium distribution is found and shown to be unique. Its sound propagation properties are found for both forced and free waves, with some generality beyond D1Q3. Finally, this equilibrium distribution is applied to a nonlinear acoustics simulation where both mechanisms of nonlinearity are simulated with good results. This represents an improvement on previous such simulations and proves that the compressibility of the method is still sufficiently strong even for nonlinear acoustics.

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.

Mathematical analysis of a power-law form time dependent vector-borne disease transmission model.

PubMed

Sardar, Tridip; Saha, Bapi

2017-06-01

In the last few years, fractional order derivatives have been used in epidemiology to capture the memory phenomena. However, these models do not have proper biological justification in most of the cases and lack a derivation from a stochastic process. In this present manuscript, using theory of a stochastic process, we derived a general time dependent single strain vector borne disease model. It is shown that under certain choice of time dependent transmission kernel this model can be converted into the classical integer order system. When the time-dependent transmission follows a power law form, we showed that the model converted into a vector borne disease model with fractional order transmission. We explicitly derived the disease-free and endemic equilibrium of this new fractional order vector borne disease model. Using mathematical properties of nonlinear Volterra type integral equation it is shown that the unique disease-free state is globally asymptotically stable under certain condition. We define a threshold quantity which is epidemiologically known as the basic reproduction number (R 0 ). It is shown that if R 0 > 1, then the derived fractional order model has a unique endemic equilibrium. We analytically derived the condition for the local stability of the endemic equilibrium. To test the model capability to capture real epidemic, we calibrated our newly proposed model to weekly dengue incidence data of San Juan, Puerto Rico for the time period 30th April 1994 to 23rd April 1995. We estimated several parameters, including the order of the fractional derivative of the proposed model using aforesaid data. It is shown that our proposed fractional order model can nicely capture real epidemic. Copyright © 2017 Elsevier Inc. All rights reserved.

Multi-period equilibrium/near-equilibrium in electricity markets based on locational marginal prices

NASA Astrophysics Data System (ADS)

Garcia Bertrand, Raquel

In this dissertation we propose an equilibrium procedure that coordinates the point of view of every market agent resulting in an equilibrium that simultaneously maximizes the independent objective of every market agent and satisfies network constraints. Therefore, the activities of the generating companies, consumers and an independent system operator are modeled: (1) The generating companies seek to maximize profits by specifying hourly step functions of productions and minimum selling prices, and bounds on productions. (2) The goals of the consumers are to maximize their economic utilities by specifying hourly step functions of demands and maximum buying prices, and bounds on demands. (3) The independent system operator then clears the market taking into account consistency conditions as well as capacity and line losses so as to achieve maximum social welfare. Then, we approach this equilibrium problem using complementarity theory in order to have the capability of imposing constraints on dual variables, i.e., on prices, such as minimum profit conditions for the generating units or maximum cost conditions for the consumers. In this way, given the form of the individual optimization problems, the Karush-Kuhn-Tucker conditions for the generating companies, the consumers and the independent system operator are both necessary and sufficient. The simultaneous solution to all these conditions constitutes a mixed linear complementarity problem. We include minimum profit constraints imposed by the units in the market equilibrium model. These constraints are added as additional constraints to the equivalent quadratic programming problem of the mixed linear complementarity problem previously described. For the sake of clarity, the proposed equilibrium or near-equilibrium is first developed for the particular case considering only one time period. Afterwards, we consider an equilibrium or near-equilibrium applied to a multi-period framework. This model embodies binary decisions, i.e., on/off status for the units, and therefore optimality conditions cannot be directly applied. To avoid limitations provoked by binary variables, while retaining the advantages of using optimality conditions, we define the multi-period market equilibrium using Benders decomposition, which allows computing binary variables through the master problem and continuous variables through the subproblem. Finally, we illustrate these market equilibrium concepts through several case studies.

Existence and uniqueness theorems for impulsive fractional differential equations with the two-point and integral boundary conditions.

PubMed

Mardanov, M J; Mahmudov, N I; Sharifov, Y A

2014-01-01

We study a boundary value problem for the system of nonlinear impulsive fractional differential equations of order α (0 < α ≤ 1) involving the two-point and integral boundary conditions. Some new results on existence and uniqueness of a solution are established by using fixed point theorems. Some illustrative examples are also presented. We extend previous results even in the integer case α = 1.

Statistical prescission point model of fission fragment angular distributions

NASA Astrophysics Data System (ADS)

John, Bency; Kataria, S. K.

1998-03-01

In light of recent developments in fission studies such as slow saddle to scission motion and spin equilibration near the scission point, the theory of fission fragment angular distribution is examined and a new statistical prescission point model is developed. The conditional equilibrium of the collective angular bearing modes at the prescission point, which is guided mainly by their relaxation times and population probabilities, is taken into account in the present model. The present model gives a consistent description of the fragment angular and spin distributions for a wide variety of heavy and light ion induced fission reactions.

Analysis of Thermal Track Buckling in the Lateral Plane

DOT National Transportation Integrated Search

1976-09-01

The post-buckling equilibrium states are determined analytically. To obtain a consistent formulation of the problem, use is made of the principle of virtual displacements and the variational calculus for variable matching points. The obtained formula...

Games with fuzzy parameters

NASA Astrophysics Data System (ADS)

Messaoud, Deghdak

2010-11-01

In this paper, we study the existence of equilibrium in non-cooperative game with fuzzy parameters. We generalize te results of Larbani and Kacher(2008, 2009) in infinite dimentional spaces. The proof is based on the Browder-Fan fixed point theorem.

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

NASA Astrophysics Data System (ADS)

Akahane, Kenji; Russo, John; Tanaka, Hajime

2016-08-01

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

An equilibrium-point model for fast, single-joint movement: I. Emergence of strategy-dependent EMG patterns.

PubMed

Latash, M L; Gottlieb, G L

1991-09-01

We describe a model for the regulation of fast, single-joint movements, based on the equilibrium-point hypothesis. Limb movement follows constant rate shifts of independently regulated neuromuscular variables. The independently regulated variables are tentatively identified as thresholds of a length sensitive reflex for each of the participating muscles. We use the model to predict EMG patterns associated with changes in the conditions of movement execution, specifically, changes in movement times, velocities, amplitudes, and moments of limb inertia. The approach provides a theoretical neural framework for the dual-strategy hypothesis, which considers certain movements to be results of one of two basic, speed-sensitive or speed-insensitive strategies. This model is advanced as an alternative to pattern-imposing models based on explicit regulation of timing and amplitudes of signals that are explicitly manifest in the EMG patterns.

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.

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

NASA Astrophysics Data System (ADS)

Maiti, Atasi Patra; Dubey, B.

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

Stability of Contact Lines in Fluids: 2D Stokes Flow

NASA Astrophysics Data System (ADS)

Guo, Yan; Tice, Ian

2018-02-01

In an effort to study the stability of contact lines in fluids, we consider the dynamics of an incompressible viscous Stokes fluid evolving in a two-dimensional open-top vessel under the influence of gravity. This is a free boundary problem: the interface between the fluid in the vessel and the air above (modeled by a trivial fluid) is free to move and experiences capillary forces. The three-phase interface where the fluid, air, and solid vessel wall meet is known as a contact point, and the angle formed between the free interface and the vessel is called the contact angle. We consider a model of this problem that allows for fully dynamic contact points and angles. We develop a scheme of a priori estimates for the model, which then allow us to show that for initial data sufficiently close to equilibrium, the model admits global solutions that decay to equilibrium exponentially quickly.

Numerical study of the geometry of the phase space of the Augmented Hill Three-Body problem

NASA Astrophysics Data System (ADS)

Farrés, Ariadna; Jorba, Àngel; Mondelo, Josep-Maria

2017-09-01

The Augmented Hill Three-Body problem is an extension of the classical Hill problem that, among other applications, has been used to model the motion of a solar sail around an asteroid. This model is a 3 degrees of freedom (3DoF) Hamiltonian system that depends on four parameters. This paper describes the bounded motions (periodic orbits and invariant tori) in an extended neighbourhood of some of the equilibrium points of the model. An interesting feature is the existence of equilibrium points with a 1:1 resonance, whose neighbourhood we also describe. The main tools used are the computation of periodic orbits (including their stability and bifurcations), the reduction of the Hamiltonian to centre manifolds at equilibria, and the numerical approximation of invariant tori. It is remarkable how the combination of these techniques allows the description of the dynamics of a 3DoF Hamiltonian system.

Dynamics of Entropy in Quantum-like Model of Decision Making

NASA Astrophysics Data System (ADS)

Basieva, Irina; Khrennikov, Andrei; Asano, Masanari; Ohya, Masanori; Tanaka, Yoshiharu

2011-03-01

We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices. By using this equilibrium point Alice determines her mixed (i.e., probabilistic) strategy with respect to Bob. Thus our model is a model of thinking through decoherence of initially pure mental state. Decoherence is induced by interaction with memory and external environment. In this paper we study (numerically) dynamics of quantum entropy of Alice's state in the process of decision making. Our analysis demonstrates that this dynamics depends nontrivially on the initial state of Alice's mind on her own actions and her prediction state (for possible actions of Bob.)

Application of constrained equilibrium thermodynamics to irradiated alloy systems

NASA Astrophysics Data System (ADS)

Holloway, James Paul; Stubbins, James F.

1984-05-01

Equilibrium thermodynamics are applied to systems with an excess of point defects to calculate the relative stability of phases. It is possible to model systems with supersaturation levels of vacancies and interstitials, such as those found under irradiation. The calculations reveal the extent to which phase compositional boundaries could shift when one phase or both in a two phase system contain an excess of point defects. Phase boundary shifts in the Ni-Si, Fe-Ni, Ni-Cr, and Fe-Cr systems are examined as a function of the number of excess defects in each phase. It is also found that the critical temperature of the sigma phase in the Fe-Cr system and the fcc-bcc transition in the Fe-Ni are sensitive to excess defect concentrations. These results may apply to local irradiation-induced phase transformations in the presence of solute segregation.

Nonequilibrium Second-Order Phase Transition in a Cooper-Pair Insulator.

PubMed

Doron, A; Tamir, I; Mitra, S; Zeltzer, G; Ovadia, M; Shahar, D

2016-02-05

In certain disordered superconductors, upon increasing the magnetic field, superconductivity terminates with a direct transition into an insulating phase. This phase is comprised of localized Cooper pairs and is termed a Cooper-pair insulator. The current-voltage characteristics measured in this insulating phase are highly nonlinear and, at low temperatures, exhibit abrupt current jumps. Increasing the temperature diminishes the jumps until the current-voltage characteristics become continuous. We show that a direct correspondence exists between our system and systems that undergo an equilibrium, second-order, phase transition. We illustrate this correspondence by comparing our results to the van der Waals equation of state for the liquid-gas mixture. We use the similarities to identify a critical point where an out of equilibrium second-order-like phase transition occurs in our system. Approaching the critical point, we find a power-law behavior with critical exponents that characterizes the transition.

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

PubMed Central

Akahane, Kenji; Russo, John; Tanaka, Hajime

2016-01-01

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

Unique Spectroscopy and Imaging of Mars with the James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Villanueva, Geronimo L.; Altieri, Francesca; Clancy, R. Todd; Encrenaz, Therese; Fouchet, Thierry; Hartogh, Paul; Lellouch, Emmanuel; Lopez-Valverde, Miguel A.; Mumma, Michael J.; Novak, Robert E.;

Extensive Evaluation of the Conductor-like Screening Model for Real Solvents Method in Predicting Liquid-Liquid Equilibria in Ternary Systems of Ionic Liquids with Molecular Compounds.

PubMed

Paduszyński, Kamil

2018-04-12

A conductor-like screening model for real solvents (COSMO-RS) is nowadays one of the most popular and commonly applied tools for the estimation of thermodynamic properties of complex fluids. The goal of this work is to provide a comprehensive review and analysis of the performance of this approach in calculating liquid-liquid equilibrium (LLE) phase diagrams in ternary systems composed of ionic liquid and two molecular compounds belonging to diverse families of chemicals (alkanes, aromatics, S/N-compounds, alcohols, ketones, ethers, carboxylic acid, esters, and water). The predictions are presented for extensive experimental database, including 930 LLE data sets and more than 9000 data points (LLE tie lines) reported for 779 unique ternary mixtures. An impact of the type of molecular binary subsystem on the accuracy of predictions is demonstrated and discussed on the basis of representative examples. The model's capability of capturing qualitative trends in the LLE distribution ratio and selectivity is also checked for a number of structural effects. Comparative analysis of two levels of quantum chemical theory (BP-TZVP-COSMO vs BP-TZVPD-FINE) for the input molecular data for COSMO-RS is presented. Finally, some general recommendations for the applicability of the model are indicated based on the analysis of the global performance as well as on the results obtained for systems relevant from the point of view of important separation problems.

Reversible hydration and aqueous exfoliation of the acetate-intercalated layered double hydroxide of Ni and Al: Observation of an ordered interstratified phase

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

Manohara, G.V.; Vishnu Kamath, P., E-mail: vishnukamath8@hotmail.com; Milius, Wolfgang

2012-12-15

Acetate-intercalated layered double hydroxides (LDHs) of Ni and Al undergo reversible hydration in the solid state in response to the ambient humidity. The LDH with a high layer charge (0.33/formula unit) undergoes facile hydration in a single step, whereas the LDH with a lower layer charge (0.24/formula unit) exhibits an ordered interstratified intermediate, comprising the hydrated and dehydrated layers stacked alternatively. This phase, also known as the staged S-2 phase, coexists with the end members suggesting the existence of a solution-type equilibrium between the S-2 phase and the end members of the hydration cycle. These LDHs also undergo facile aqueousmore » exfoliation into 2-5 nm-thick tactoids with a radial dimension of 0.2-0.5 {mu}m. - Graphical abstract: Schematic of the hydrated, dehydrated and interstratified phases observed during the hydration-dehydration of Ni/Al-CH{sub 3}COO LDH. Highlights: Black-Right-Pointing-Pointer Ni/Al-acetate LDHs were synthesized by HPFS method by hydrolysis of acetamide. Black-Right-Pointing-Pointer Intercalated acetate ion shows reversible hydration with variation in humidity. Black-Right-Pointing-Pointer An ordered interstratified phase was observed during hydration/dehydration cycle. Black-Right-Pointing-Pointer A solution type equilibrium is observed between hydration-dehydration phases. Black-Right-Pointing-Pointer These LDHs undergo facile aqueous exfoliation.« less

Simplified Thermo-Chemical Modelling For Hypersonic Flow

NASA Astrophysics Data System (ADS)

Sancho, Jorge; Alvarez, Paula; Gonzalez, Ezequiel; Rodriguez, Manuel

2011-05-01

Hypersonic flows are connected with high temperatures, generally associated with strong shock waves that appear in such flows. At high temperatures vibrational degrees of freedom of the molecules may become excited, the molecules may dissociate into atoms, the molecules or free atoms may ionize, and molecular or ionic species, unimportant at lower temperatures, may be formed. In order to take into account these effects, a chemical model is needed, but this model should be simplified in order to be handled by a CFD code, but with a sufficient precision to take into account the physics more important. This work is related to a chemical non-equilibrium model validation, implemented into a commercial CFD code, in order to obtain the flow field around bodies in hypersonic flow. The selected non-equilibrium model is composed of seven species and six direct reactions together with their inverse. The commercial CFD code where the non- equilibrium model has been implemented is FLUENT. For the validation, the X38/Sphynx Mach 20 case is rebuilt on a reduced geometry, including the 1/3 Lref forebody. This case has been run in laminar regime, non catalytic wall and with radiative equilibrium wall temperature. The validated non-equilibrium model is applied to the EXPERT (European Experimental Re-entry Test-bed) vehicle at a specified trajectory point (Mach number 14). This case has been run also in laminar regime, non catalytic wall and with radiative equilibrium wall temperature.

The Voronoi volume and molecular representation of molar volume: equilibrium simple fluids.

PubMed

Hunjan, Jagtar Singh; Eu, Byung Chan

2010-04-07

The Voronoi volume of simple fluids was previously made use of in connection with volume transport phenomena in nonequilibrium simple fluids. To investigate volume transport phenomena, it is important to develop a method to compute the Voronoi volume of fluids in nonequilibrium. In this work, as a first step to this goal, we investigate the equilibrium limit of the nonequilibrium Voronoi volume together with its attendant related molar (molal) and specific volumes. It is proved that the equilibrium Voronoi volume is equivalent to the molar (molal) volume. The latter, in turn, is proved equivalent to the specific volume. This chain of equivalences provides an alternative procedure of computing the equilibrium Voronoi volume from the molar volume/specific volume. We also show approximate methods of computing the Voronoi and molar volumes from the information on the pair correlation function. These methods may be employed for their quick estimation, but also provide some aspects of the fluid structure and its relation to the Voronoi volume. The Voronoi volume obtained from computer simulations is fitted to a function of temperature and pressure in the region above the triple point but below the critical point. Since the fitting function is given in terms of reduced variables for the Lennard-Jones (LJ) model and the kindred volumes (i.e., specific and molar volumes) are in essence equivalent to the equation of state, the formula obtained is a reduced equation state for simple fluids obeying the LJ model potential in the range of temperature and pressure examined and hence can be used for other simple fluids.

Spontaneous evolution of microstructure in materials

NASA Astrophysics Data System (ADS)

Kirkaldy, J. S.

1993-08-01

Microstructures which evolve spontaneously from random solutions in near isolation often exhibit patterns of remarkable symmetry which can only in part be explained by boundary and crystallographic effects. With reference to the detailed experimental record, we seek the source of causality in this natural tendency to constructive autonomy, usually designated as a principle of pattern or wavenumber selection in a free boundary problem. The phase field approach which incorporates detailed boundary structure and global rate equations has enjoyed some currency in removing internal degrees of freedom, and this will be examined critically in reference to the migration of phase-antiphase boundaries produced in an order-disorder transformation. Analogous problems for singular interfaces including solute trapping are explored. The microscopic solvability hypothesis has received much attention, particularly in relation to dendrite morphology and the Saffman-Taylor fingering problem in hydrodynamics. A weak form of this will be illustrated in relation to local equilibrium binary solidification cells which renders the free boundary problem unique. However, the main thrust of this article concerns dynamic configurations at anisotropic singular interfaces and the related patterns of eutectoid(ic)s, nonequilibrium cells, cellular dendrites, and Liesegang figures where there is a recognizable macroscopic phase space of pattern fluctuations and/or solitons. These possess a weakly defective stability point and thereby submit to a statistical principle of maximum path probability and to a variety of corollary dissipation principles in the determination of a unique average patterning behavior. A theoretical development of the principle based on Hamilton's principle for frictional systems is presented in an Appendix. Elements of the principles of scaling, universality, and deterministic chaos are illustrated.

Motor control theories and their applications.

PubMed

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

2010-01-01

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

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.

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.

Nash equilibrium and evolutionary dynamics in semifinalists' dilemma.

PubMed

Baek, Seung Ki; Son, Seung-Woo; Jeong, Hyeong-Chai

2015-04-01

We consider a tournament among four equally strong semifinalists. The players have to decide how much stamina to use in the semifinals, provided that the rest is available in the final and the third-place playoff. We investigate optimal strategies for allocating stamina to the successive matches when players' prizes (payoffs) are given according to the tournament results. From the basic assumption that the probability to win a match follows a nondecreasing function of stamina difference, we present symmetric Nash equilibria for general payoff structures. We find three different phases of the Nash equilibria in the payoff space. First, when the champion wins a much bigger payoff than the others, any pure strategy can constitute a Nash equilibrium as long as all four players adopt it in common. Second, when the first two places are much more valuable than the other two, the only Nash equilibrium is such that everyone uses a pure strategy investing all stamina in the semifinal. Third, when the payoff for last place is much smaller than the others, a Nash equilibrium is formed when every player adopts a mixed strategy of using all or none of its stamina in the semifinals. In a limiting case that only last place pays the penalty, this mixed-strategy profile can be proved to be a unique symmetric Nash equilibrium, at least when the winning probability follows a Heaviside step function. Moreover, by using this Heaviside step function, we study the tournament by using evolutionary replicator dynamics to obtain analytic solutions, which reproduces the corresponding Nash equilibria on the population level and gives information on dynamic aspects.

Nash equilibrium and evolutionary dynamics in semifinalists' dilemma

NASA Astrophysics Data System (ADS)

Baek, Seung Ki; Son, Seung-Woo; Jeong, Hyeong-Chai

2015-04-01

We consider a tournament among four equally strong semifinalists. The players have to decide how much stamina to use in the semifinals, provided that the rest is available in the final and the third-place playoff. We investigate optimal strategies for allocating stamina to the successive matches when players' prizes (payoffs) are given according to the tournament results. From the basic assumption that the probability to win a match follows a nondecreasing function of stamina difference, we present symmetric Nash equilibria for general payoff structures. We find three different phases of the Nash equilibria in the payoff space. First, when the champion wins a much bigger payoff than the others, any pure strategy can constitute a Nash equilibrium as long as all four players adopt it in common. Second, when the first two places are much more valuable than the other two, the only Nash equilibrium is such that everyone uses a pure strategy investing all stamina in the semifinal. Third, when the payoff for last place is much smaller than the others, a Nash equilibrium is formed when every player adopts a mixed strategy of using all or none of its stamina in the semifinals. In a limiting case that only last place pays the penalty, this mixed-strategy profile can be proved to be a unique symmetric Nash equilibrium, at least when the winning probability follows a Heaviside step function. Moreover, by using this Heaviside step function, we study the tournament by using evolutionary replicator dynamics to obtain analytic solutions, which reproduces the corresponding Nash equilibria on the population level and gives information on dynamic aspects.

High vacuum measurements and calibrations, molecular flow fluid transient effects

DOE PAGES

Leishear, Robert A.; Gavalas, Nickolas A.

2015-04-29

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

Classical evolution of fractal measures on the lattice

NASA Astrophysics Data System (ADS)

Antoniou, N. G.; Diakonos, F. K.; Saridakis, E. N.; Tsolias, G. A.

2007-04-01

We consider the classical evolution of a lattice of nonlinear coupled oscillators for a special case of initial conditions resembling the equilibrium state of a macroscopic thermal system at the critical point. The displacements of the oscillators define initially a fractal measure on the lattice associated with the scaling properties of the order parameter fluctuations in the corresponding critical system. Assuming a sudden symmetry breaking (quench), leading to a change in the equilibrium position of each oscillator, we investigate in some detail the deformation of the initial fractal geometry as time evolves. In particular, we show that traces of the critical fractal measure can be sustained for large times, and we extract the properties of the chain that determine the associated time scales. Our analysis applies generally to critical systems for which, after a slow developing phase where equilibrium conditions are justified, a rapid evolution, induced by a sudden symmetry breaking, emerges on time scales much shorter than the corresponding relaxation or observation time. In particular, it can be used in the fireball evolution in a heavy-ion collision experiment, where the QCD critical point emerges, or in the study of evolving fractals of astrophysical and cosmological scales, and may lead to determination of the initial critical properties of the Universe through observations in the symmetry-broken phase.

The Kibble-Zurek mechanism in phase transitions of non-equilibrium systems

NASA Astrophysics Data System (ADS)

Cheung, Hil F. H.; Patil, Yogesh S.; Date, Aditya G.; Vengalattore, Mukund

2017-04-01

We experimentally realize a driven-dissipative phase transition using a mechanical parametric amplifier to demonstrate key signatures of a second order phase transition, including a point where the susceptibilities and relaxation time scales diverge, and where the system exhibits a spontaneous breaking of symmetry. Though reminiscent of conventional equilibrium phase transitions, it is unclear if such driven-dissipative phase transitions are amenable to the conventional Landau-Ginsburg-Wilson paradigm, which relies on concepts of scale invariance and universality, and recent work has shown that such phase transitions can indeed lie beyond such conventional universality classes. By quenching the system past the critical point, we investigate the dynamics of the emergent ordered phase and find that our measurements are in excellent agreement with the Kibble-Zurek mechanism. In addition to verifying the Kibble-Zurek hypothesis in driven-dissipative phase transitions for the first time, we also demonstrate that the measured critical exponents accurately reflect the interplay between intrinsic coherent dynamics and environmental correlations, showing a clear departure from mean field exponents in the case of non-Markovian system-bath interactions. We further discuss how reservoir engineering and the imposition of artificial environmental correlations can result in the stabilization of novel many-body quantum phases and aid in the creation of exotic non-equilibrium states of matter.

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.

Direct Numerical Simulations of Dynamic Drainage and Imbibition to Investigate Capillary Pressure-Saturation-Interfacial Area Relation

NASA Astrophysics Data System (ADS)

Konangi, S.; Palakurthi, N. K.; Karadimitriou, N.; Comer, K.; Ghia, U.

2017-12-01

We present results of pore-scale direct numerical simulations (DNS) of drainage and imbibition in a quasi-two-dimensional (40µm thickness) porous medium with a randomly distributed packing of cylindrical obstructions. The Navier-Stokes (NS) equations are solved in the pore space on an Eulerian mesh using the open-source finite-volume computational fluid dynamics (CFD) code, OpenFOAM. The Volume-of-Fluid (VOF) method is employed to track the evolution of the fluid-fluid interface; a static contact angle is used to account for wall adhesion. From the DNS data, we focus on the macroscopic capillary pressure-saturation (Pc-Sw) relation, which is known to be hysteretic, i.e., this relation is flow process (such as drainage, imbibition and scanning curves) and history dependent. In order to overcome the problem of hysteresis, extended theories of multiphase flow hypothesized that the inclusion of specific interfacial area as a state variable will result in a unique relation between capillary pressure, saturation and interfacial area (Pc-Sw-awn). We study the role of specific interfacial area on hysteresis in the macroscopic Pc-Sw relation under non-equilibrium (dynamic) conditions. Under dynamic conditions, capillary pressure depends on the rate of change of the wetting phase saturation, and the dynamic Pc-Sw relation includes the changes caused by viscous effects. Simulations of drainage and imbibition are performed for two capillary numbers by controlling the flow rate of the non-wetting (polydimenthlysiloxane oil) and wetting (water) fluids. From these simulations, the Pc-Sw curves will be estimated; the Pc-S-awn surface will be constructed to determine whether the data points from drainage and imbibition processes fall on a unique surface under transient conditions. Different macroscopic capillary pressure definitions based on phase-averaged pressures and interfacial area will be evaluated. Understanding macroscopic capillary pressure definitions and the uniqueness of the Pc-S- awn relation is step towards complete description of two-phase flow at the Darcy scale.

Interactive Mechanisms of Sliding-Surface Bearings.

DTIC Science & Technology

1983-08-01

lower, upper) bearing surface V Three-dimensional gradient operator ix Two-dimensional surface gradient operator ( ),. Pertaining to the bearing surface...thermal gradients . The tilt-pad feature required the pad inclination to be determined by the condition of moment equilibrium about the pivot point. This...into the computation of pressure and shear in a fluid film. Incipience Point of Film Rupture On page 93 of Appendix A, pressure gradient and pressure of

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Three-Phase Melting Curves in the Binary System of Carbon Dioxide and Water

NASA Astrophysics Data System (ADS)

Abramson, E. H.

2017-10-01

Invariant, three-phase melting curves, of ice VI in equilibrium with solid CO2, of ice VII in equilibrium with solid CO2, and of solid CO2 in simultaneous equilibrium with a majority aqueous and a majority CO2 fluid, were explored in the binary system of carbon dioxide and water. Diamond-anvil cells were used to develop pressures of 5 GPa. Water exhibits a large melting temperature depression (73°C less than its pure melting temperature of 253°C at 5 GPa) indicative of large concentrations of CO2 in the aqueous solution. The melting point of water-saturated CO2 does not show a measureable departure from that of the pure system at temperatures lower than ∼200°C and only 10°C at 5 GPa (from 327°C).

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.

On the LHC sensitivity for non-thermalised hidden sectors

NASA Astrophysics Data System (ADS)

Kahlhoefer, Felix

2018-04-01

We show under rather general assumptions that hidden sectors that never reach thermal equilibrium in the early Universe are also inaccessible for the LHC. In other words, any particle that can be produced at the LHC must either have been in thermal equilibrium with the Standard Model at some point or must be produced via the decays of another hidden sector particle that has been in thermal equilibrium. To reach this conclusion, we parametrise the cross section connecting the Standard Model to the hidden sector in a very general way and use methods from linear programming to calculate the largest possible number of LHC events compatible with the requirement of non-thermalisation. We find that even the HL-LHC cannot possibly produce more than a few events with energy above 10 GeV involving states from a non-thermalised hidden sector.

Using NMR to Determine the Boiling Point Diagram for a Non-Ideal Solution

ERIC Educational Resources Information Center

Allen, Fritz S.; And Others

1975-01-01

Describes an experiment that enables the student to concentrate on the fundamentals of the non-ideal liquid-vapor equilibrium. Presents typical student data and suggests features which might be added to the experiment. (GS)

Invariants for models of interacting populations

NASA Astrophysics Data System (ADS)

Cairó, L.; Feix, M. R.; Goedert, J.

1989-10-01

The generalised Lotka-Volterra system is studied. We use a modification of the Carleman embedding method. The position of the equilibrium point, the possibility of obtaining invariants, the asymptotic cyclic motions and the connection to the Volterra model are discussed.

Using Nonlinear Stochastic Evolutionary Game Strategy to Model an Evolutionary Biological Network of Organ Carcinogenesis Under a Natural Selection Scheme

PubMed Central

Chen, Bor-Sen; Tsai, Kun-Wei; Li, Cheng-Wei

2015-01-01

Molecular biologists have long recognized carcinogenesis as an evolutionary process that involves natural selection. Cancer is driven by the somatic evolution of cell lineages. In this study, the evolution of somatic cancer cell lineages during carcinogenesis was modeled as an equilibrium point (ie, phenotype of attractor) shifting, the process of a nonlinear stochastic evolutionary biological network. This process is subject to intrinsic random fluctuations because of somatic genetic and epigenetic variations, as well as extrinsic disturbances because of carcinogens and stressors. In order to maintain the normal function (ie, phenotype) of an evolutionary biological network subjected to random intrinsic fluctuations and extrinsic disturbances, a network robustness scheme that incorporates natural selection needs to be developed. This can be accomplished by selecting certain genetic and epigenetic variations to modify the network structure to attenuate intrinsic fluctuations efficiently and to resist extrinsic disturbances in order to maintain the phenotype of the evolutionary biological network at an equilibrium point (attractor). However, during carcinogenesis, the remaining (or neutral) genetic and epigenetic variations accumulate, and the extrinsic disturbances become too large to maintain the normal phenotype at the desired equilibrium point for the nonlinear evolutionary biological network. Thus, the network is shifted to a cancer phenotype at a new equilibrium point that begins a new evolutionary process. In this study, the natural selection scheme of an evolutionary biological network of carcinogenesis was derived from a robust negative feedback scheme based on the nonlinear stochastic Nash game strategy. The evolvability and phenotypic robustness criteria of the evolutionary cancer network were also estimated by solving a Hamilton–Jacobi inequality – constrained optimization problem. The simulation revealed that the phenotypic shift of the lung cancer-associated cell network takes 54.5 years from a normal state to stage I cancer, 1.5 years from stage I to stage II cancer, and 2.5 years from stage II to stage III cancer, with a reasonable match for the statistical result of the average age of lung cancer. These results suggest that a robust negative feedback scheme, based on a stochastic evolutionary game strategy, plays a critical role in an evolutionary biological network of carcinogenesis under a natural selection scheme. PMID:26244004

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.

Non-equilibrium character of resistive switching and negative differential resistance in Ga-doped Cr2O3 system

NASA Astrophysics Data System (ADS)

Bhowmik, R. N.; Siva, K. Venkata

2018-07-01

The samples of Ga-doped Cr2O3 system in rhombohedral crystal structure with space group R 3 bar C were prepared by chemical co-precipitation route and annealing at 800 °C. The current-voltage (I-V) curves exhibited many unique non-linear properties, e.g., hysteresis loop, resistive switching, and negative differential resistance (NDR). In this work, we report non-equilibrium properties of resistive switching and NDR phenomena. The non-equilibrium I-V characteristics were confirmed by repetiting measurement and time relaxation of current. The charge conduction process was understood by analysing the I-V curves using electrode-limited and bulk-limited charge conduction mechanisms, which were proposed for metal electrode/metal oxide/metal electrode structure. The I-V curves in the NDR regime and at higher bias voltage regime in our samples did not obey Fowler-Nordheim equation, which was proposed for charge tunneling mechanism in many thin film junctions. The non-equilibrium I-V phenomena were explained by considering the competitions between the injection of charge carriers from metal electrode to metal oxide, the charge flow through bulk material mediated by trapping/de-trapping and recombination of charge carriers at the defect sites of ions, the space charge effects at the junctions of electrodes and metal oxides, and finally, the out flow of electrons from metal oxide to metal electrode.

Multiscale model within-host and between-host for viral infectious diseases.

PubMed

Almocera, Alexis Erich S; Nguyen, Van Kinh; Hernandez-Vargas, Esteban A

2018-05-08

Multiscale models possess the potential to uncover new insights into infectious diseases. Here, a rigorous stability analysis of a multiscale model within-host and between-host is presented. The within-host model describes viral replication and the respective immune response while disease transmission is represented by a susceptible-infected model. The bridging of scales from within- to between-host considered transmission as a function of the viral load. Consequently, stability and bifurcation analyses were developed coupling the two basic reproduction numbers [Formula: see text] and [Formula: see text] for the within- and the between-host subsystems, respectively. Local stability results for each subsystem, including a unique stable equilibrium point, recapitulate classical approaches to infection and epidemic control. Using a Lyapunov function, global stability of the between-host system was obtained. Our main result was the derivation of the [Formula: see text] as an increasing function of [Formula: see text]. Numerical analyses reveal that a Michaelis-Menten form based on the virus is more likely to recapitulate the behavior between the scales than a form directly proportional to the virus. Our work contributes basic understandings of the two models and casts light on the potential effects of the coupling function on linking the two scales.

Multispectral study of CO production from C/1995 O1 (Hale-Bopp)

NASA Astrophysics Data System (ADS)

Harris, W. M.; Nordsieck, K. H.; Scherb, F.; Mierkiwicz, E. J.; Morgenthaler, J. P.; Oliversen, R. J.

1998-09-01

A series of unique observartions of CO and its daughter products that were obtained simultaneously as part of the University of Wisconsin/Goddard Space Flight Center Hale-Bopp campaign are presented. CO is the second most abundant volatile species in the coma of comets, one that actually dominates production at large heliocentric distances, however its photchemical evolution is poorly understood due to the lack of good emission line tracers in the visible. On 8 April, 1997, we obtained wide field simultaneous observations of CI (1657 Angstroms) intensity and polarization from a sounding rocket, OI (6300 Angstroms) emission using the Wisconsin Hα Mapper (WHaM) facility, and measurements using the McMath-Pierce Solar telescope of CI (9850 Angstroms) emission at different points in the inner coma. Combined, these data contain information on the radial distribution, source function, equilibrium structure, photochemical lifetime of CO, and the outflow speed of its C and O daughter products. Combined, these results suggest rapid dissociation of CO in the collisionally thick inner coma of Hale-Bopp, followed by a high velocity outflow of the daughter products. Both results suggest some discrepancies with expectations, and we discuss their implications.

Nonconvergence to Saddle Boundary Points under Perturbed Reinforcement Learning

DTIC Science & Technology

2012-12-07

of the ODE (12). Note that for some games not all stationary points of the ODE (12) are Nash equilibria. For example, if you consider the Typewriter ...B A 4, 4 2, 2 B 2, 2 3, 3 Table 1: The Typewriter Game. On the other hand, any stationary point in the interior of the probability simplex will... Typewriter Game of Table 1. We observe that it is possible for the process to converge to a pure strategy profile which is not a Nash equilibrium when Ri(α

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

Shafer, Morgan W; Battaglia, D. J.; Unterberg, Ezekial A

A new tangential 2D Soft X-Ray Imaging System (SXRIS) is being designed to examine the edge magnetic island structure in the lower X-point region of DIII-D. A synthetic diagnostic calculation coupled to 3D emissivity estimates is used to generate phantom images. Phillips-Tikhonov regularization is used to invert the phantom images for comparison to the original emissivity model. Noise level, island size, and equilibrium accuracy are scanned to assess the feasibility of detecting edge island structures. Models of typical DIII-D discharges indicate integration times > 1 ms with accurate equilibrium reconstruction are needed for small island (< 3 cm) detection.

Double simple-harmonic-oscillator formulation of the thermal equilibrium of a fluid interacting with a coherent source of phonons

NASA Technical Reports Server (NTRS)

Defacio, B.; Vannevel, Alan; Brander, O.

1993-01-01

A formulation is given for a collection of phonons (sound) in a fluid at a non-zero temperature which uses the simple harmonic oscillator twice; one to give a stochastic thermal 'noise' process and the other which generates a coherent Glauber state of phonons. Simple thermodynamic observables are calculated and the acoustic two point function, 'contrast' is presented. The role of 'coherence' in an equilibrium system is clarified by these results and the simple harmonic oscillator is a key structure in both the formulation and the calculations.

The gallium melting-point standard: a determination of the liquid-solid equilibrium temperature of pure gallium on the International Practical Temperature Scale of 1968.

PubMed

Thornton, D D

1977-01-01

The sharpness and reproducibility of the gallium melting point were studied and the melting temperature of gallium in terms of IPTS-68 was determined. Small melting-point cells designed for use with thermistors are described. Nine gallium cells including three levels of purity were used in 68 separate determinations fo the melting point. The melting point of 99.99999% pure gallium in terms of IPTS-68 is found to be 29.771(4) +/- 0.001(4) degree C; the melting range is less than 0.0005 degree C and is reproducible to +/- 0.0004 degree C.

Development of tough, moisture resistant laminating resins

NASA Technical Reports Server (NTRS)

Brand, R. A.; Harrison, E. S.

1982-01-01

Tough, moisture resistant laminating resins for employment with graphite fibers were developed. The new laminating resins exhibited cost, handleability and processing characteristics equivalent to 394K (250 F) curing epoxies. The laminating resins were based on bisphenol A dicyanate and monofunctional cyanates with hydrophobic substituents. These resins sorb only small quantities of moisture at equilibrium (0.5% or less) with minimal glass transition temperature depression and represent an improvement over epoxies which sorb around 2% moisture at equilibrium. Toughening was accomplished by the precipitation of small diameter particles of butadiene nitrile rubber throughout the resin matrix. The rubber domains act as microcrack termini and energy dissipation sites, allowing increased stress accommodation prior to catastrophic failure. A unique blend of amine terminated butadiene nitrile elastomer (MW 2,000) and a high nitrile content butadiene nitrile rubber yielded the desired resin morphology.

Strong lattice correlation of non-equilibrium quasiparticles in a pseudospin-1/2 Mott insulator Sr 2IrO 4

DOE PAGES

Li, Yuelin; Schaller, Richard D.; Zhu, Mengze; ...

2016-01-20

In correlated oxides the coupling of quasiparticles to other degrees of freedom such as spin and lattice plays critical roles in the emergence of symmetry-breaking quantum ordered states such as high temperature superconductivity. We report a strong lattice coupling of photon-induced quasiparticles in spin-orbital coupling Mott insulator Sr 2IrO 4 probed via optical excitation. Combining time-resolved x-ray diffraction and optical spectroscopy techniques, we reconstruct a spatiotemporal map of the diffusion of these quasiparticles. Lastly, due to the unique electronic configuration of the quasiparticles, the strong lattice correlation is unexpected but extends the similarity between Sr 2IrO 4 and cuprates tomore » a new dimension of electron-phonon coupling which persists under highly non-equilibrium conditions.« less

Calcium influx through TRP channels induced by short-lived reactive species in plasma-irradiated solution

NASA Astrophysics Data System (ADS)

Sasaki, Shota; Kanzaki, Makoto; Kaneko, Toshiro

2016-05-01

Non-equilibrium helium atmospheric-pressure plasma (He-APP), which allows for a strong non-equilibrium chemical reaction of O2 and N2 in ambient air, uniquely produces multiple extremely reactive products, such as reactive oxygen species (ROS), in plasma-irradiated solution. We herein show that relatively short-lived unclassified reactive species (i.e., deactivated within approximately 10 min) generated by the He-APP irradiation can trigger physiologically relevant Ca2+ influx through ruthenium red- and SKF 96365-sensitive Ca2+-permeable channel(s), possibly transient receptor potential channel family member(s). Our results provide novel insight into understanding of the interactions between cells and plasmas and the mechanism by which cells detect plasma-induced chemically reactive species, in addition to facilitating development of plasma applications in medicine.

Simulation of continuous variable quantum games without entanglement

NASA Astrophysics Data System (ADS)

Li, Shang-Bin

2011-07-01

A simulation scheme of quantum version of Cournot's duopoly is proposed, in which there is a new Nash equilibrium that may also be Pareto optimal without any entanglement involved. The unique property of this simulation scheme is decoherence-free against the symmetric photon loss. Furthermore, we analyze the effects of the asymmetric information on this simulation scheme and investigate the case of asymmetric game caused by asymmetric photon loss. A second-order phase transition-like behavior of the average profits of firms 1 and 2 in a Nash equilibrium can be observed with the change of the degree of asymmetry of the information or the degree of 'virtual cooperation'. It is also found that asymmetric photon loss in this simulation scheme plays a similar role as that with the asymmetric entangled states in the quantum game.