Experimental tests of linear and nonlinear three-dimensional equilibrium models in DIII-D

DOE PAGES

King, Josh D.; Strait, Edward J.; Lazerson, Samuel A.; ...

2015-07-01

DIII-D experiments using new detailed magnetic diagnostics show that linear, ideal magnetohydrodynamics (MHD) theory quantitatively describes the magnetic structure (as measured externally) of three-dimensional (3D) equilibria resulting from applied fields with toroidal mode number n = 1, while a nonlinear solution to ideal MHD force balance, using the VMEC code, requires the inclusion of n ≥ 1 to achieve similar agreement. Moreover, these tests are carried out near ITER baseline parameters, providing a validated basis on which to exploit 3D fields for plasma control development. We determine scans of the applied poloidal spectrum and edge safety factors which confirm thatmore » low-pressure, n = 1 non-axisymmetric tokamak equilibria are a single, dominant, stable eigenmode. But, at higher beta, near the ideal kink mode stability limit in the absence of a conducting wall, the qualitative features of the 3D structure are observed to vary in a way that is not captured by ideal MHD.« less

An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta

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

Allanson, O., E-mail: oliver.allanson@st-andrews.ac.uk; Neukirch, T., E-mail: tn3@st-andrews.ac.uk; Wilson, F., E-mail: fw237@st-andrews.ac.uk

We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution functionmore » in two of the velocity directions to a Maxwellian distribution.« less

Constraints on stable equilibria with fluctuation-induced (Casimir) forces.

PubMed

Rahi, Sahand Jamal; Kardar, Mehran; Emig, Thorsten

2010-08-13

We examine whether fluctuation-induced forces can lead to stable levitation. First, we analyze a collection of classical objects at finite temperature that contain fixed and mobile charges and show that any arrangement in space is unstable to small perturbations in position. This extends Earnshaw's theorem for electrostatics by including thermal fluctuations of internal charges. Quantum fluctuations of the electromagnetic field are responsible for Casimir or van der Waals interactions. Neglecting permeabilities, we find that any equilibrium position of items subject to such forces is also unstable if the permittivities of all objects are higher or lower than that of the enveloping medium, the former being the generic case for ordinary materials in vacuum.

Thermodynamic properties for applications in chemical industry via classical force fields.

PubMed

Guevara-Carrion, Gabriela; Hasse, Hans; Vrabec, Jadran

2012-01-01

Thermodynamic properties of fluids are of key importance for the chemical industry. Presently, the fluid property models used in process design and optimization are mostly equations of state or G (E) models, which are parameterized using experimental data. Molecular modeling and simulation based on classical force fields is a promising alternative route, which in many cases reasonably complements the well established methods. This chapter gives an introduction to the state-of-the-art in this field regarding molecular models, simulation methods, and tools. Attention is given to the way modeling and simulation on the scale of molecular force fields interact with other scales, which is mainly by parameter inheritance. Parameters for molecular force fields are determined both bottom-up from quantum chemistry and top-down from experimental data. Commonly used functional forms for describing the intra- and intermolecular interactions are presented. Several approaches for ab initio to empirical force field parameterization are discussed. Some transferable force field families, which are frequently used in chemical engineering applications, are described. Furthermore, some examples of force fields that were parameterized for specific molecules are given. Molecular dynamics and Monte Carlo methods for the calculation of transport properties and vapor-liquid equilibria are introduced. Two case studies are presented. First, using liquid ammonia as an example, the capabilities of semi-empirical force fields, parameterized on the basis of quantum chemical information and experimental data, are discussed with respect to thermodynamic properties that are relevant for the chemical industry. Second, the ability of molecular simulation methods to describe accurately vapor-liquid equilibrium properties of binary mixtures containing CO(2) is shown.

MHD Studies of Advanced Tokamak Equilibria

NASA Astrophysics Data System (ADS)

Strumberger, E.

2005-10-01

Advanced tokamak scenarios are often characterized by an extremely reversed profile of the safety factor, q, and a fast toroidal rotation. ASDEX Upgrade type equilibria with toroidal flow are computed up to a toroidal Mach number of Mta= 0.5, and compared with the static solution. Using these equilibria, the stabilizing effect of differential toroidal rotation on double tearing modes (DTMs) is investigated. These studies show that the computation of equilibria with flow is necessary for toroidally rotating plasma with Mta>=0.2. The use of ρtor instead of ρpol as radial coordinate enables us also to investigate the stability of equilibria with current holes. For numerical reasons, the rotational transform, = 1/q, has to be unequal zero in the CASTOR$FLOW code, but values of a>=0.001 (qa<=1000) can be easily handled. Stability studies of DTMs in the presence of a current hole are presented. Tokamak equilibria are only approximately axisymmetric. The finite number of toroidal field coils destroys the perfect axisymmetry of the device, and the coils produce a short wavelength ripple in the magnetic field strength. This toroidal field ripple plays a crucial role for the loss of high energy particles. Therefore, three-dimensional tokamak equilibria with and without current holes are computed for various plasma beta values. In addition the influence of the plasma beta on the toroidal field ripple is investigated.

Static axisymmetric equilibria in general relativistic magnetohydrodynamics

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

Nunez, Manuel

2008-01-15

While the definition of static equilibria is not clear in a general relativistic context, in many cases of astrophysical interest a natural 3+1 split exists which allows us to define physically meaningful spatial and temporal coordinates. We study the possibility of axisymmetric magnetohydrodynamic equilibria in this setting. The presence of a nontrivial shift velocity provides a constraint not present in the Newtonian case, while the momentum equation may be set in a Grad-Shafranov-like form with the presence of additional terms involving the space-time metric coefficients. It is found that whenever the magnetic field or the shift velocity possesses poloidal component,more » the existence of even local static equilibria demands that the metric parameters satisfy such strong conditions that these equilibria are extremely unlikely. Only very particular cases such as purely toroidal fields and shifts yield existence of equilibria, provided we are able to choose arbitrarily the plasma pressure and density.« less

Applying the new HIT results to tokamak and solar plasmas

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Classification of singularities in the problem of motion of the Kovalevskaya top in a double force field

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

Ryabov, Pavel E; Kharlamov, Mikhail P

2012-02-28

The problem of motion of the Kovalevskaya top in a double force field is investigated (the integrable case of A.G. Reyman and M.A. Semenov-Tian-Shansky without a gyrostatic momentum). It is a completely integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems with two degrees of freedom. The critical set of the integral map is studied. The critical subsystems and bifurcation diagrams are described. The classification of all nondegenerate critical points is given. The set of these points consists of equilibria (nondegenerate singularities of rank 0), of singular periodic motions (nondegenerate singularities of rank 1),more » and also of critical two-frequency motions (nondegenerate singularities of rank 2). Bibliography: 32 titles.« less

Effect of resonant magnetic perturbations on three dimensional equilibria in the Madison Symmetric Torus reversed-field pinch

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

Munaretto, S., E-mail: smunaretto@wisc.edu; Chapman, B. E.; Nornberg, M. D.

2016-05-15

The orientation of 3D equilibria in the Madison Symmetric Torus (MST) [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field pinch can now be controlled with a resonant magnetic perturbation (RMP). Absent the RMP, the orientation of the stationary 3D equilibrium varies from shot to shot in a semi-random manner, making its diagnosis difficult. Produced with a poloidal array of saddle coils at the vertical insulated cut in MST's thick conducting shell, an m = 1 RMP with an amplitude b{sub r}/B ∼ 10% forces the 3D structure into any desired orientation relative to MST's diagnostics. This control has led to improvedmore » diagnosis, revealing enhancements in both the central electron temperature and density. With sufficient amplitude, the RMP also inhibits the generation of high-energy (>20 keV) electrons, which otherwise emerge due to a reduction in magnetic stochasticity in the core. Field line tracing reveals that the RMP reintroduces stochasticity to the core. A m = 3 RMP of similar amplitude has little effect on the magnetic topology or the high-energy electrons.« less

Quantification of in-contact probe-sample electrostatic forces with dynamic atomic force microscopy.

PubMed

Balke, Nina; Jesse, Stephen; Carmichael, Ben; Okatan, M Baris; Kravchenko, Ivan I; Kalinin, Sergei V; Tselev, Alexander

2017-01-04

Atomic force microscopy (AFM) methods utilizing resonant mechanical vibrations of cantilevers in contact with a sample surface have shown sensitivities as high as few picometers for detecting surface displacements. Such a high sensitivity is harnessed in several AFM imaging modes. Here, we demonstrate a cantilever-resonance-based method to quantify electrostatic forces on a probe in the probe-sample junction in the presence of a surface potential or when a bias voltage is applied to the AFM probe. We find that the electrostatic forces acting on the probe tip apex can produce signals equivalent to a few pm of surface displacement. In combination with modeling, the measurements of the force were used to access the strength of the electrical field at the probe tip apex in contact with a sample. We find an evidence that the electric field strength in the junction can reach ca. 1 V nm -1 at a bias voltage of a few volts and is limited by non-ideality of the tip-sample contact. This field is sufficiently strong to significantly influence material states and kinetic processes through charge injection, Maxwell stress, shifts of phase equilibria, and reduction of energy barriers for activated processes. Besides, the results provide a baseline for accounting for the effects of local electrostatic forces in electromechanical AFM measurements as well as offer additional means to probe ionic mobility and field-induced phenomena in solids.

Catenaries in Drag

NASA Astrophysics Data System (ADS)

Chakrabarti, Brato; Hanna, James

2014-11-01

Dynamical equilibria of towed cables and sedimenting filaments have been the targets of much numerical work; here, we provide analytical expressions for the configurations of a translating and axially moving string subjected to a uniform body force and local, linear, anisotropic drag forces. Generically, these configurations comprise a five-parameter family of planar shapes determined by the ratio of tangential (axial) and normal drag coefficients, the angle between the translational velocity and the body force, the relative magnitudes of translational and axial drag forces with respect to the body force, and a scaling parameter. This five-parameter family of shapes is, in fact, a degenerate six-parameter family of equilibria in which inertial forces rescale the tension in the string without affecting its shape. Each configuration is represented by a first order dynamical system for the tangential angle of the body. Limiting cases include the dynamic catenaries with or without drag, and purely sedimenting or towed strings.

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.

Magnetospheric Reconnection in Modified Current-Sheet Equilibria

NASA Astrophysics Data System (ADS)

Newman, D. L.; Goldman, M. V.; Lapenta, G.; Markidis, S.

2012-10-01

Particle simulations of magnetic reconnection in Earth's magnetosphere are frequently initialized with a current-carrying Harris equilibrium superposed on a current-free uniform background plasma. The Harris equilibrium satisfies local charge neutrality, but requires that the sheet current be dominated by the hotter species -- often the ions in Earth's magnetosphere. This constraint is not necessarily consistent with observations. A modified kinetic equilibrium that relaxes this constraint on the currents was proposed by Yamada et al. [Phys. Plasmas., 7, 1781 (2000)] with no background population. These modified equilibria were characterized by an asymptotic converging or diverging electrostatic field normal to the current sheet. By reintroducing the background plasma, we have developed new families of equilibria where the asymptotic fields are suppressed by Debye shielding. Because the electrostatic potential profiles of these new equilibria contain wells and/or barriers capable of spatially isolating different populations of electrons and/or ions, these solutions can be further generalized to include classes of asymmetric kinetic equilibria. Examples of both symmetric and asymmetric equilibria will be presented. The dynamical evolution of these equilibria, when perturbed, will be further explored by means of implicit 2D PIC reconnection simulations, including comparisons with simulations employing standard Harris-equilibrium initializations.

Quantification of in-contact probe-sample electrostatic forces with dynamic atomic force microscopy

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

Balke, Nina Wisinger; Jesse, Stephen; Carmichael, Ben D.

Here, atomic force microscopy (AFM) methods utilizing resonant mechanical vibrations of cantilevers in contact with a sample surface have shown sensitivities as high as few picometers for detecting surface displacements. Such a high sensitivity is harnessed in several AFM imaging modes. Here, we demonstrate a cantilever-resonance-based method to quantify electrostatic forces on a probe in the probe-sample junction in the presence of a surface potential or when a bias voltage is applied to the AFM probe. We find that the electrostatic forces acting on the probe tip apex can produce signals equivalent to a few pm of surface displacement. Inmore » combination with modeling, the measurements of the force were used to access the strength of the electrical field at the probe tip apex in contact with a sample. We find an evidence that the electric field strength in the junction can reach ca. 1 V nm –1 at a bias voltage of a few volts and is limited by non-ideality of the tip-sample contact. This field is sufficiently strong to significantly influence material states and kinetic processes through charge injection, Maxwell stress, shifts of phase equilibria, and reduction of energy barriers for activated processes. Besides, the results provide a baseline for accounting for the effects of local electrostatic forces in electromechanical AFM measurements as well as offer additional means to probe ionic mobility and field-induced phenomena in solids.« less

Quantification of In-Contact Probe-Sample Electrostatic Forces with Dynamic Atomic Force Microscopy.

PubMed

Balke, Nina; Jesse, Stephen; Carmichael, Ben; Okatan, M; Kravchenko, Ivan; Kalinin, Sergei; Tselev, Alexander

2016-12-13

Atomic Force Microscopy (AFM) methods utilizing resonant mechanical vibrations of cantilevers in contact with a sample surface have shown sensitivities as high as few picometers for detecting surface displacements. Such a high sensitivity is harnessed in several AFM imaging modes. Here, we demonstrate a cantilever-resonance-based method to quantify electrostatic forces on a probe in the probe-sample junction in the presence of a surface potential or when a bias voltage is applied to the AFM probe. We find that the electrostatic forces acting on the probe tip apex can produce signals equivalent to a few pm of surface displacement. In combination with modeling, the measurements of the force were used to access the strength of the electrical field at the probe tip apex in contact with a sample. We find an evidence that the electric field strength in the junction can reach ca. 1 V/nm at a bias voltage of a few volts and is limited by non-ideality of the tip-sample contact. This field is sufficiently strong to significantly influence material states and kinetic processes through charge injection, Maxwell stress, shifts of phase equilibria, and reduction of energy barriers for activated processes. Besides, the results provide a baseline for accounting for the effects of local electrostatic forces in electromechanical AFM measurements as well as offer additional means to probe ionic mobility and field-induced phenomena in solids. Copyright 2016 IOP Publishing Ltd.

Quantification of in-contact probe-sample electrostatic forces with dynamic atomic force microscopy

DOE PAGES

Balke, Nina Wisinger; Jesse, Stephen; Carmichael, Ben D.; ...

2017-01-04

Here, atomic force microscopy (AFM) methods utilizing resonant mechanical vibrations of cantilevers in contact with a sample surface have shown sensitivities as high as few picometers for detecting surface displacements. Such a high sensitivity is harnessed in several AFM imaging modes. Here, we demonstrate a cantilever-resonance-based method to quantify electrostatic forces on a probe in the probe-sample junction in the presence of a surface potential or when a bias voltage is applied to the AFM probe. We find that the electrostatic forces acting on the probe tip apex can produce signals equivalent to a few pm of surface displacement. Inmore » combination with modeling, the measurements of the force were used to access the strength of the electrical field at the probe tip apex in contact with a sample. We find an evidence that the electric field strength in the junction can reach ca. 1 V nm –1 at a bias voltage of a few volts and is limited by non-ideality of the tip-sample contact. This field is sufficiently strong to significantly influence material states and kinetic processes through charge injection, Maxwell stress, shifts of phase equilibria, and reduction of energy barriers for activated processes. Besides, the results provide a baseline for accounting for the effects of local electrostatic forces in electromechanical AFM measurements as well as offer additional means to probe ionic mobility and field-induced phenomena in solids.« less

Influence of Casimir-Lifshitz forces on actuation dynamics of MEMS

NASA Astrophysics Data System (ADS)

Broer, Wijnand; Palasantzas, George; Knoester, Jasper; Svetovoy, Vitaly

2013-03-01

Electromagnetic fluctuations generate forces between neutral bodies known as Casimir-Lifshitz forces, of which van der Waals forces are special cases, and which can become important in micromechanical systems (MEMS). For surface areas big enough but gaps small enough, the Casimir force can possibly draw and lock MEMS components together, an effect called stiction, causing device malfunction. Alternatively, stiction can also be exploited to add new functionalities to MEMS architecture. Here, using as inputs the measured frequency dependent dielectric response and surface roughness statistics from Atomic Force Microscopy (AFM) images, we perform the first realistic calculation of MEMS actuation. For our analysis the Casimir force is combined with the electrostatic force between rough surfaces to counterbalance the elastic restoring force. It is found that, even though surface roughness has an adverse effect on the availability of (stable) equilibria, it ensures that those stable equilibria can be reached more easily than in the case of flat surfaces. Hence our results can have significant implications on how to design MEM surfaces. The author would like this abstract to appear in a Casimir related session.

Slow rise and partial eruption of a double-decker filament. II. A double flux rope model

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

Kliem, Bernhard; Török, Tibor; Titov, Viacheslav S.

2014-09-10

Force-free equilibria containing two vertically arranged magnetic flux ropes of like chirality and current direction are considered as a model for split filaments/prominences and filament-sigmoid systems. Such equilibria are constructed analytically through an extension of the methods developed in Titov and Démoulin and numerically through an evolutionary sequence including shear flows, flux emergence, and flux cancellation in the photospheric boundary. It is demonstrated that the analytical equilibria are stable if an external toroidal (shear) field component exceeding a threshold value is included. If this component decreases sufficiently, then both flux ropes turn unstable for conditions typical of solar active regions,more » with the lower rope typically becoming unstable first. Either both flux ropes erupt upward, or only the upper rope erupts while the lower rope reconnects with the ambient flux low in the corona and is destroyed. However, for shear field strengths staying somewhat above the threshold value, the configuration also admits evolutions which lead to partial eruptions with only the upper flux rope becoming unstable and the lower one remaining in place. This can be triggered by a transfer of flux and current from the lower to the upper rope, as suggested by the observations of a split filament in Paper I. It can also result from tether-cutting reconnection with the ambient flux at the X-type structure between the flux ropes, which similarly influences their stability properties in opposite ways. This is demonstrated for the numerically constructed equilibrium.« less

Coil Design for Low Aspect Ratio Stellarators

NASA Astrophysics Data System (ADS)

Miner, W. H., Jr.; Valanju, P. M.; Wiley, J. C.; Hirshman, S. P.; Whitson, J. C.

1998-11-01

Two compact stellarator designs have recently been under investigation because of their potential as a reactor featuring steady-state, disruption-free operation, low recirculating power and good confinement and beta. Both quasi-axisymmetric (QA) equilibria and quasi-omnigenous (QO) equilibria have been obtained by using the 3-D MHD equilibrium code VMEC. In order to build an experiment, coil sets must be obtained that are compatable with these equilibria. We have been using both the NESCOIL(Merkel, P., Nucl. Fus. 27, 5 (1987) 867.) code and the COILOPT code to find coilsets for both of these types of equilibria. We are considering three types of coil configurations. The first is a combination of modular coils and vertical field coils. The second configuration is a combination of toroidal field coils, vertical field coils and saddle coils. A third configuration is a combination of modular coils and a single helical winding. The quality of each coil set will be evaluated by computing its magnetic field and using that as input to VMEC in free boundary mode to see how accurately the original equilibrium can be reconstructed.

Collisionless current sheet equilibria

NASA Astrophysics Data System (ADS)

Neukirch, T.; Wilson, F.; Allanson, O.

2018-01-01

Current sheets are important for the structure and dynamics of many plasma systems. In space and astrophysical plasmas they play a crucial role in activity processes, for example by facilitating the release of magnetic energy via processes such as magnetic reconnection. In this contribution we will focus on collisionless plasma systems. A sensible first step in any investigation of physical processes involving current sheets is to find appropriate equilibrium solutions. The theory of collisionless plasma equilibria is well established, but over the past few years there has been a renewed interest in finding equilibrium distribution functions for collisionless current sheets with particular properties, for example for cases where the current density is parallel to the magnetic field (force-free current sheets). This interest is due to a combination of scientific curiosity and potential applications to space and astrophysical plasmas. In this paper we will give an overview of some of the recent developments, discuss their potential applications and address a number of open questions.

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.

Theoretical study on the vibrational spectra of methoxy- and formyl-dihydroxy- trans-stilbenes and their hydrolytic equilibria

NASA Astrophysics Data System (ADS)

Molnár, Viktor; Billes, Ferenc; Tyihák, Ernő; Mikosch, Hans

2008-02-01

Compounds formed by exchanging one of the resveratrol hydroxy groups to methoxy or formyl groups are biologically important. Quantum chemical DFT calculations were applied for the simulation of some of their properties. Their optimized structures and charge distributions were computed. Based on the calculated vibrational force constants and optimized molecular structure infrared and Raman spectra were calculated. The characteristics of the vibrational modes were determined by normal coordinate analysis. Applying the calculated thermodynamic functions also for resveratrol, methanol, formaldehyde and water, thermodynamic equilibria were calculated for the equilibria between resveratrol and its methyl and formyl substituted derivatives, respectively.

Self-consistent current sheet structures in the quiet-time magnetotail

NASA Technical Reports Server (NTRS)

Holland, Daniel L.; Chen, James

1993-01-01

The structure of the quiet-time magnetotail is studied using a test particle simulation. Vlasov equilibria are obtained in the regime where v(D) = E(y) c/B(z) is much less than the ion thermal velocity and are self-consistent in that the current and magnetic field satisfy Ampere's law. Force balance between the plasma and magnetic field is satisfied everywhere. The global structure of the current sheet is found to be critically dependent on the source distribution function. The pressure tensor is nondiagonal in the current sheet with anisotropic temperature. A kinetic mechanism is proposed whereby changes in the source distribution results in a thinning of the current sheet.

Equilibria of the symmetric collinear restricted four-body problem with radiation pressure

NASA Astrophysics Data System (ADS)

Arribas, M.; Abad, A.; Elipe, A.; Palacios, M.

2016-02-01

In this paper, a restricted four-body problem with radiation pressure is considered. The three primaries are supposed in a collinear central configuration where both masses and both radiation forces of peripheral bodies are equal. After an adequate formulation, the problem is reduced to a tri-parametric one. A complete analysis of the position of equilibria and their stability in the space of parameters is performed.

Novel Hamiltonian method for collective dynamics analysis of an intense charged particle beam propagating through a periodic focusing quadrupole lattice a)

NASA Astrophysics Data System (ADS)

Startsev, Edward A.; Davidson, Ronald C.

2011-05-01

Identifying regimes for quiescent propagation of intense beams over long distances has been a major challenge in accelerator research. In particular, the development of systematic theoretical approaches that are able to treat self-consistently the applied oscillating force and the nonlinear self-field force of the beam particles simultaneously has been a major challenge of modern beam physics. In this paper, the recently developed Hamiltonian averaging technique [E. A. Startsev, R. C. Davidson, and M. Dorf, Phys. Rev. ST Accel. Beams 13, 064402 (2010)] which incorporates both the applied periodic focusing force and the self-field force of the beam particles, is generalized to the case of time-dependent beam distributions. The new formulation allows not only a determination of quasi-equilibrium solutions of the non-linear Vlasov-Poison system of equations but also a detailed study of their stability properties. The corrections to the well-known "smooth-focusing" approximation are derived, and the results are applied to a matched beam with thermal equilibrium distribution function. It is shown that the corrections remain small even for moderate values of the vacuum phase advance συ. Nonetheless, because the corrections to the average self-field potential are non-axisymmetric, the stability properties of the different beam quasi-equilibria can change significantly.

An integral equation-based numerical solver for Taylor states in toroidal geometries

NASA Astrophysics Data System (ADS)

O'Neil, Michael; Cerfon, Antoine J.

2018-04-01

We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.

Multiple Equilibria Associated with Response of the ITCZ to Seasonal SST Forcing

NASA Technical Reports Server (NTRS)

Chao, Winston C.

1998-01-01

Supported by numerical experiment results, the abrupt change of the location of the intertropical convergence zone (ITCZ), from the equatorial trough flow regime to the monsoon trough flow regime is interpreted as a subcritical instability. The existence of these multiple quasi-equilibria is due to the balance of two "forces" on the ITCZ: one toward the equator, due to the earth's rotation, has a nonlinear latitudinal dependence; and the other toward the latitude of the sea surface (or ground) temperature peak has a relatively linear latitudinal dependence. This work pivots on the finding that the ITCZ and Hadley circulation can still exist without the pole-to-equator gradient of radiative-convective equilibrium temperature.

Theory and computation of general force balance in non-axisymmetric tokamak equilibria

NASA Astrophysics Data System (ADS)

Park, Jong-Kyu; Logan, Nikolas; Wang, Zhirui; Kim, Kimin; Boozer, Allen; Liu, Yueqiang; Menard, Jonathan

2014-10-01

Non-axisymmetric equilibria in tokamaks can be effectively described by linearized force balance. In addition to the conventional isotropic pressure force, there are three important components that can strongly contribute to the force balance; rotational, anisotropic tensor pressure, and externally given forces, i.e. ∇ --> p + ρv-> . ∇ --> v-> + ∇ --> . <-->Π + f-> = j-> × B-> , especially in, but not limited to, high β and rotating plasmas. Within the assumption of nested flux surfaces, Maxwell equations and energy minimization lead to the modified-generalized Newcomb equation for radial displacements with simple algebraic relations for perpendicular and parallel displacements, including an inhomogeneous term if any of the forces are not explicitly dependent on displacements. The general perturbed equilibrium code (GPEC) solves this force balance consistent with energy and torque given by external perturbations. Local and global behaviors of solutions will be discussed when ∇ --> . <-->Π is solved by the semi-analytic code PENT and will be compared with MARS-K. Any first-principle transport code calculating ∇ --> . <-->Π or f-> , e.g. POCA, can also be incorporated without demanding iterations. This work was supported by DOE Contract DE-AC02-09CH11466.

Stability of Inhomogeneous Equilibria of Hamiltonian Continuous Media Field Theories

NASA Astrophysics Data System (ADS)

Hagstrom, George

2013-10-01

There are a wide variety of 1 + 1 Hamiltonian continuous media field theories that exhibit phase space pattern formation. In plasma physics, the most famous of these is the Vlasov-Poisson equation, but other examples include the incompressible Euler equation in two-dimensions and the Hamiltonian Mean Field (or XY) model. One of the characteristic phenomenon that occurs in systems described by these equations is the formation of cat's eye patterns in phase space as a result of the nonlinear saturation of instabilities. Corresponding to each of these cat's eyes is a spatially inhomogeneous equilibrium solution of the underlying model, in plasma physics these are called BGK modes, but analogous solutions exist in all of the above systems. Here we analyze the stability of inhomogeneous equilibria in the Hamiltonian Mean Field model and in the Single Wave model, which is an equation that was derived to provide a model of the formation of electron holes in plasmas. We use action angle variables and the properties of elliptic functions to analyze the resulting dispersion relation construct linearly stable inhomogeneous equilibria for in the limit of small numbers of particles and study the behavior of solutions near these equilibria. Work supported by USDOE grant no. DE-FG02-ER53223.

Surface currents on the plasma-vacuum interface in MHD equilibria

NASA Astrophysics Data System (ADS)

Hanson, James

2017-10-01

The VMEC non-axisymmetric MHD equilibrium code can compute free-boundary equilibria. Since VMEC assumes that magnetic fields within the plasma form closed and nested flux surfaces, the plasma-vacuum interface is a flux surface, and the total magnetic field there has no normal component. VMEC imposes this condition of zero normal field using the potential formulation of Merkel, and solves a Neumann problem for the magnetic potential in the exterior region. This boundary condition necessarily admits the possibility of a surface current on the interface. While this surface current may be small in MHD equilibrium, it is readily computed in terms of the magnetic potentials in both the interior and exterior regions, evaluated on the surface. If only the external magnetic potential is known (as in VMEC), then the surface current can be computed from the discontinuity of the tangential field across the interface. Examples of the surface current for VMEC equilibria will be shown for a zero-pressure stellarator equilibrium. Field-line following of the vacuum magnetic field shows magnetic islands within the plasma region.

Plasma Equilibria With Stochastic Magnetic Fields

NASA Astrophysics Data System (ADS)

Krommes, J. A.; Reiman, A. H.

2009-05-01

Plasma equilibria that include regions of stochastic magnetic fields are of interest in a variety of applications, including tokamaks with ergodic limiters and high-pressure stellarators. Such equilibria are examined theoretically, and a numerical algorithm for their construction is described.^2,3 % The balance between stochastic diffusion of magnetic lines and small effects^2 omitted from the simplest MHD description can support pressure and current profiles that need not be flattened in stochastic regions. The diffusion can be described analytically by renormalizing stochastic Langevin equations for pressure and parallel current j, with particular attention being paid to the satisfaction of the periodicity constraints in toroidal configurations with sheared magnetic fields. The equilibrium field configuration can then be constructed by coupling the prediction for j to Amp'ere's law, which is solved numerically. A. Reiman et al., Pressure-induced breaking of equilibrium flux surfaces in the W7AS stellarator, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes and A. H. Reiman, Plasma equilibrium in a magnetic field with stochastic regions, submitted to Phys. Plasmas. J. A. Krommes, Fundamental statistical theories of plasma turbulence in magnetic fields, Phys. Reports 360, 1--351.

The stability analysis of magnetohydrodynamic equilibria - Comparing the thermodynamic approach with the energy principle

NASA Technical Reports Server (NTRS)

Brinkmann, R. P.

1989-01-01

This paper is a contribution to the stability analysis of current-carrying plasmas, i.e., plasma systems that are forced by external mchanisms to carry a nonrelaxing electrical current. Under restriction to translationally invariant configurations, the thermodynamic stability criterion for a multicomponent plasma is rederived within the framework of nonideal MHD. The chosen dynamics neglects scalar resistivity, but allows for other types of dissipation effects both in Ohm's law and in the equation of motion. In the second section of the paper, the thermodynamic stability criterion is compared with the ideal MHD based energy principle of Bernstein et al. With the help of Schwarz's inequality, it is shown that the former criterion is always more 'pessimistic' than the latter, i.e., that thermodynamic stability implies stability according to the MHD principle, but not vice versa. This reuslt confirms the physical plausible idea that dissipational effects tend to weaken the stability properties of current-carrying plasma equilibria by breaking the constraints of ideal MHD and allowing for possibly destabilizing effects such as magnetic field line reconfiguration.

Protonation linked equilibria and apparent affinity constants: the thermodynamic profile of the alpha-chymotrypsin-proflavin interaction.

PubMed

Bruylants, Gilles; Wintjens, René; Looze, Yvan; Redfield, Christina; Bartik, Kristin

2007-12-01

Protonation/deprotonation equilibria are frequently linked to binding processes involving proteins. The presence of these thermodynamically linked equilibria affects the observable thermodynamic parameters of the interaction (K(obs), DeltaH(obs)(0) ). In order to try and elucidate the energetic factors that govern these binding processes, a complete thermodynamic characterisation of each intrinsic equilibrium linked to the complexation event is needed and should furthermore be correlated to structural information. We present here a detailed study, using NMR and ITC, of the interaction between alpha-chymotrypsin and one of its competitive inhibitors, proflavin. By performing proflavin titrations of the enzyme, at different pH values, we were able to highlight by NMR the effect of the complexation of the inhibitor on the ionisable residues of the catalytic triad of the enzyme. Using ITC we determined the intrinsic thermodynamic parameters of the different equilibria linked to the binding process. The possible driving forces of the interaction between alpha-chymotrypsin and proflavin are discussed in the light of the experimental data and on the basis of a model of the complex. This study emphasises the complementarities between ITC and NMR for the study of binding processes involving protonation/deprotonation equilibria.

MHD Stability of Axisymmetric Plasmas In Closed Line Magnetic Fields

NASA Astrophysics Data System (ADS)

Simakov, Andrei N.; Catto, Peter J.; Ramos, Jesus J.; Hastie, R. J.

2003-04-01

The stability of axisymmetric plasmas confined by closed poloidal magnetic field lines is considered. The results are relevant to plasmas in the dipolar fields of stars and planets, as well as the Levitated Dipole Experiment, multipoles, Z pinches and field reversed configurations. The ideal MHD energy principle is employed to study stability of pressure driven Alfvén modes. A point dipole is considered in detail to demonstrate that equilibria exist, which are MHD stable for arbitrary beta. Effects of sound waves and plasma resistivity are investigated next for point dipole equilibria by means of resistive MHD theory.

Ideal-Magnetohydrodynamic-Stable Tilting in Field-Reversed Configurations

NASA Astrophysics Data System (ADS)

Kanno, Ryutaro; Ishida, Akio; Steinhauer, Loren

1995-02-01

The tilting mode in field-reversed configurations (FRC) is examined using ideal-magnetohydrodynamic stability theory. Tilting, a global mode, is the greatest threat for disruption of FRC confinement. Previous studies uniformly found tilting to be unstable in ideal theory: the objective here is to ascertain if stable equilibria were overlooked in past work. Solving the variational problem with the Rayleigh-Ritz technique, tilting-stable equilibria are found for sufficiently hollow current profile and sufficient racetrackness of the separatrix shape. Although these equilibria were not examined previously, the present conclusion is quite surprising. Consequently checks of the method are offered. Even so it cannot yet be claimed with complete certainty that stability has been proved: absolute confirmation of ideal-stable tilting awaits the application of more complete methods.

Fractionation of Magnetic Microspheres in a Microfluidic Spiral: Interplay between Magnetic and Hydrodynamic Forces

PubMed Central

Hayden, M. E.; Häfeli, U. O.

2017-01-01

Magnetic forces and curvature-induced hydrodynamic drag have both been studied and employed in continuous microfluidic particle separation and enrichment schemes. Here we combine the two. We investigate consequences of applying an outwardly directed magnetic force to a dilute suspension of magnetic microspheres circulating in a spiral microfluidic channel. This force is realized with an array of permanent magnets arranged to produce a magnetic field with octupolar symmetry about the spiral axis. At low flow rates particles cluster around an apparent streamline of the flow near the outer wall of the turn. At high flow rates this equilibrium is disrupted by the induced secondary (Dean) flow and a new equilibrium is established near the inner wall of the turn. A model incorporating key forces involved in establishing these equilibria is described, and is used to extract quantitative information about the magnitude of local Dean drag forces from experimental data. Steady-state fractionation of suspensions by particle size under the combined influence of magnetic and hydrodynamic forces is demonstrated. Extensions of this work could lead to new continuous microscale particle sorting and enrichment processes with improved fidelity and specificity. PMID:28107472

Relativistic thermal plasmas - Effects of magnetic fields

NASA Technical Reports Server (NTRS)

Araki, S.; Lightman, A. P.

1983-01-01

Processes and equilibria in finite, relativistic, thermal plasmas are investigated, taking into account electron-positron creation and annihilation, photon production by internal processes, and photon production by a magnetic field. Inclusion of the latter extends previous work on such plasmas. The basic relations for thermal, Comptonized synchrotron emission are analyzed, including emission and absorption without Comptonization, Comptonized thermal synchrotron emission, and the Comptonized synchrotron and bremsstrahlung luminosities. Pair equilibria are calculated, including approximations and dimensionless parameters, the pair balance equation, maximum temperatures and field strengths, and individual models and cooling curves.

Double Current Sheet Instabilities and the Transition to Turbulence.

NASA Astrophysics Data System (ADS)

Pucci, F.; Velli, M.; Biferale, L.; Sahoo, G.

2016-12-01

The double tearing instability has often been studied as a proxy for the m=1 kink mode in cylindrical plasma. In this paper we describe the results of 3D simulations of an initially periodic double current sheet described by Harris equilibria with a guide field in two cases: 1) zero net helicity and an average magnetic field and 2) a well defined helicity (force free but non constant alpha). We study and contrast the de-stabilization and transition to turbulence for these two cases: we describe spectra, cascades, and possible application to heliospheric phenomena, in particular CME evolution and relaxation. The research leading to these results has received fund- ing from the European Union's Seventh Framework Pro- gramme (FP7/2007-2013) under grant agreement No. 339032

On the stability of a class of isothermal, magnetostatic atmospheres. [in sun

NASA Technical Reports Server (NTRS)

Webb, G. M.; Ko, C. M.

1989-01-01

The stability of a class of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is explored. Special attention is given to the stability of nonpotential equilibria that have the same magnetic field geometry as the potential equilibrium of the solution family. It is found that equilibria in which the source currents for the potential field are buried at large distances below the photospheric base are stable. Also considered is the stability of configurations in which the source currents for the potential field are located at a finite depth below the base.

Idealized modeling of convective organization with changing sea surface temperatures using multiple equilibria in weak temperature gradient simulations

NASA Astrophysics Data System (ADS)

Sentić, Stipo; Sessions, Sharon L.

2017-06-01

The weak temperature gradient (WTG) approximation is a method of parameterizing the influences of the large scale on local convection in limited domain simulations. WTG simulations exhibit multiple equilibria in precipitation; depending on the initial moisture content, simulations can precipitate or remain dry for otherwise identical boundary conditions. We use a hypothesized analogy between multiple equilibria in precipitation in WTG simulations, and dry and moist regions of organized convection to study tropical convective organization. We find that the range of wind speeds that support multiple equilibria depends on sea surface temperature (SST). Compared to the present SST, low SSTs support a narrower range of multiple equilibria at higher wind speeds. In contrast, high SSTs exhibit a narrower range of multiple equilibria at low wind speeds. This suggests that at high SSTs, organized convection might occur with lower surface forcing. To characterize convection at different SSTs, we analyze the change in relationships between precipitation rate, atmospheric stability, moisture content, and the large-scale transport of moist entropy and moisture with increasing SSTs. We find an increase in large-scale export of moisture and moist entropy from dry simulations with increasing SST, which is consistent with a strengthening of the up-gradient transport of moisture from dry regions to moist regions in organized convection. Furthermore, the changes in diagnostic relationships with SST are consistent with more intense convection in precipitating regions of organized convection for higher SSTs.

Surface currents on the plasma-vacuum interface in MHD equilibria

NASA Astrophysics Data System (ADS)

Hanson, James D.

2016-10-01

The VMEC non-axisymmetric MHD equilibrium code can compute free-boundary equilibria. Since VMEC assumes that magnetic fields within the plasma form closed and nested flux surfaces, the plasma-vacuum interface is a flux surface, and the total magnetic field there has no normal component. VMEC imposes this condition of zero normal field using the potential formulation of Merkel, and solves a Neumann problem for the magnetic potential in the exterior region. This boundary condition necessarily admits the possibility of a surface current on the plasma-vacuum interface. While this current may be small in MHD equilibrium, this current may be readily computed in terms of a magnetic potential in both the interior and exterior regions. Examples of the surface current for VMEC equilibria will be shown. This material is based upon work supported by Auburn University and the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences under Award Number DE-FG02-03ER54692.

Twisted magnetosphere with quadrupolar fields in the exterior of a neutron star

NASA Astrophysics Data System (ADS)

Kojima, Yasufumi

2018-04-01

The magnetar magnetosphere is gradually twisted by shearing from footpoint motion, and stored magnetic energy also increases at the same time. When a state exceeds a threshold, flares/outbursts manifest themselves as a result of a catastrophic transition. Axisymmetric static solutions for a relativistic force-free magnetosphere with dipole-quadrupole mixed fields at the surface have been calculated. The quadrupole component represents a kind of magnetic-field irregularity at a small scale. Locally twisted models are constructed by limiting current flow regions, where the small part originates from a dipole-quadrupole mixture. The energy along a sequence of equilibria increases and becomes sufficient to open the magnetic field in some models. In energetically metastable states, a magnetic flux rope is formed in the vicinity of the star. The excess energy may be ejected as a magnetar flare/outburst. The general relativistic gravity is sufficient to confine the flux rope and to store huge magnetic energy, and the mechanism is also discussed.

Twisted magnetosphere with quadrupolar fields in the exterior of a neutron star

NASA Astrophysics Data System (ADS)

Kojima, Yasufumi

2018-07-01

The magnetar magnetosphere is gradually twisted by shearing from footpoint motion, and stored magnetic energy also increases at the same time. When a state exceeds a threshold, flares/outbursts manifest themselves as a result of a catastrophic transition. Axisymmetric static solutions for a relativistic force-free magnetosphere with dipole-quadrupole mixed fields at the surface have been calculated. The quadrupole component represents a kind of magnetic-field irregularity at a small scale. Locally twisted models are constructed by limiting current flow regions, where the small part originates from a dipole-quadrupole mixture. The energy along a sequence of equilibria increases and becomes sufficient to open the magnetic field in some models. In energetically metastable states, a magnetic flux rope is formed in the vicinity of the star. The excess energy may be ejected as a magnetar flare/outburst. The general relativistic gravity is sufficient to confine the flux rope and to store huge magnetic energy, and the mechanism is also discussed.

Instability of signaling resolution models of parent–offspring conflict

PubMed Central

Rodríguez-Gironés, Miguel A.; Enquist, Magnus; Cotton, Peter A.

1998-01-01

Recent signaling resolution models of parent–offspring conflict have provided an important framework for theoretical and empirical studies of communication and parental care. According to these models, signaling of need is stabilized by its cost. However, our computer simulations of the evolutionary dynamics of chick begging and parental investment show that in Godfray’s model the signaling equilibrium is evolutionarily unstable: populations that start at the signaling equilibrium quickly depart from it. Furthermore, the signaling and nonsignaling equilibria are linked by a continuum of equilibria where chicks above a certain condition do not signal and we show that, contrary to intuition, fitness increases monotonically as the proportion of young that signal decreases. This result forces us to reconsider much of the current literature on signaling of need and highlights the need to investigate the evolutionary stability of signaling equilibria based on the handicap principle. PMID:9539758

Multiple Quasi-Equilibria of the ITCZ and the Origin of Monsoon Onset. Part 2; Rotational ITCZ Attractors

NASA Technical Reports Server (NTRS)

Chao, Winston C.; Chen, Baode; Einaudi, Franco (Technical Monitor)

2000-01-01

Chao's numerical and theoretical work on multiple quasi-equilibria of the intertropical convergence zone (ITCZ) and the origin of monsoon onset is extended to solve two additional puzzles. One is the highly nonlinear dependence on latitude of the "force" acting on the ITCZ due to earth's rotation, which makes the multiple quasi-equilibria of the ITCZ and monsoon onset possible. The other is the dramatic difference in such dependence when different cumulus parameterization schemes are used in a model. Such a difference can lead to a switch between a single ITCZ at the equator and a double ITCZ, when a different cumulus parameterization scheme is used. Sometimes one of the double ITCZ can diminish and only the other remain, but still this can mean different latitudinal locations for the single ITCZ. A single idea based on two off-equator attractors for the ITCZ, due to earth's rotation and symmetric with respect to the equator, and the dependence of the strength and size of these attractors on the cumulus parameterization scheme solves both puzzles. The origin of these rotational attractors, explained in Part I, is further discussed. The "force" acting on the ITCZ due to earth's rotation is the sum of the "forces" of the two attractors. Each attractor exerts on the ITCZ a "force" of simple shape in latitude; but the sum gives a shape highly varying in latitude. Also the strength and the domain of influence of each attractor vary, when change is made in the cumulus parameterization. This gives rise to the high sensitivity of the "force" shape to cumulus parameterization. Numerical results, of experiments using Goddard's GEOS general circulation model, supporting this idea are presented. It is also found that the model results are sensitive to changes outside of the cumulus parameterization. The significance of this study to El Nino forecast and to tropical forecast in general is discussed.

Spontaneous decay of periodic magnetostatic equilibria

DOE PAGES

East, William E.; Zrake, Jonathan; Yuan, Yajie; ...

2015-08-28

In order to understand the conditions which lead a highly magnetized, relativistic plasma to become unstable, and in such cases how the plasma evolves, we study a prototypical class of magnetostatic equilibria where the magnetic field satisfies ∇ x B = αB , where \\alpha is spatially uniform, on a periodic domain. Using numerical solutions we show that generic examples of such equilibria are unstable to ideal modes (including incompressible ones) which are marked by exponential growth in the linear phase. We characterize the unstable mode, showing how it can be understood in terms of merging magnetic and current structures,more » and explicitly demonstrate its instability using the energy principle. Following the nonlinear evolution of these solutions, we find that they rapidly develop regions with relativistic velocities and electric fields of comparable magnitude to the magnetic field, liberating magnetic energy on dynamical timescales and eventually settling into a configuration with the largest allowable wavelength. Furthermore, these properties make such solutions a promising setting for exploring the mechanisms behind extreme cosmic sources of gamma rays.« less

DOWNWARD CATASTROPHE OF SOLAR MAGNETIC FLUX ROPES

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

Zhang, Quanhao; Wang, Yuming; Hu, Youqiu

2016-07-10

2.5-dimensional time-dependent ideal magnetohydrodynamic (MHD) models in Cartesian coordinates were used in previous studies to seek MHD equilibria involving a magnetic flux rope embedded in a bipolar, partially open background field. As demonstrated by these studies, the equilibrium solutions of the system are separated into two branches: the flux rope sticks to the photosphere for solutions at the lower branch but is suspended in the corona for those at the upper branch. Moreover, a solution originally at the lower branch jumps to the upper, as the related control parameter increases and reaches a critical value, and the associated jump ismore » here referred to as an upward catastrophe. The present paper advances these studies in three aspects. First, the magnetic field is changed to be force-free; the system still experiences an upward catastrophe with an increase in each control parameter. Second, under the force-free approximation, there also exists a downward catastrophe, characterized by the jump of a solution from the upper branch to the lower. Both catastrophes are irreversible processes connecting the two branches of equilibrium solutions so as to form a cycle. Finally, the magnetic energy in the numerical domain is calculated. It is found that there exists a magnetic energy release for both catastrophes. The Ampère's force, which vanishes everywhere for force-free fields, appears only during the catastrophes and does positive work, which serves as a major mechanism for the energy release. The implications of the downward catastrophe and its relevance to solar activities are briefly discussed.« less

Non-equilibrium statistical mechanics theory for the large scales of geophysical flows

NASA Astrophysics Data System (ADS)

Eric, S.; Bouchet, F.

2010-12-01

The aim of any theory of turbulence is to understand the statistical properties of the velocity field. As a huge number of degrees of freedom is involved, statistical mechanics is a natural approach. The self-organization of two-dimensional and geophysical turbulent flows is addressed based on statistical mechanics methods. We discuss classical and recent works on this subject; from the statistical mechanics basis of the theory up to applications to Jupiter’s troposphere and ocean vortices and jets. The equilibrium microcanonical measure is built from the Liouville theorem. Important statistical mechanics concepts (large deviations, mean field approach) and thermodynamic concepts (ensemble inequivalence, negative heat capacity) are briefly explained and used to predict statistical equilibria for turbulent flows. This is applied to make quantitative models of two-dimensional turbulence, the Great Red Spot and other Jovian vortices, ocean jets like the Gulf-Stream, and ocean vortices. A detailed comparison between these statistical equilibria and real flow observations will be discussed. We also present recent results for non-equilibrium situations, for which forces and dissipation are in a statistical balance. As an example, the concept of phase transition allows us to describe drastic changes of the whole system when a few external parameters are changed. F. Bouchet and E. Simonnet, Random Changes of Flow Topology in Two-Dimensional and Geophysical Turbulence, Physical Review Letters 102 (2009), no. 9, 094504-+. F. Bouchet and J. Sommeria, Emergence of intense jets and Jupiter's Great Red Spot as maximum-entropy structures, Journal of Fluid Mechanics 464 (2002), 165-207. A. Venaille and F. Bouchet, Ocean rings and jets as statistical equilibrium states, submitted to JPO F. Bouchet and A. Venaille, Statistical mechanics of two-dimensional and geophysical flows, submitted to Physics Reports Non-equilibrium phase transitions for the 2D Navier-Stokes equations with stochastic forces (time series and probability density functions (PDFs) of the modulus of the largest scale Fourrier component, showing bistability between dipole and unidirectional flows). This bistability is predicted by statistical mechanics.

On the Malthusian theory of long swings.

PubMed

Waterman, A M

1987-05-01

"In the Essay on Population economic growth consists of alternating surges of population (during which real wages fall and the rate of profit rises) and capital (during which the reverse occurs). A series of temporary equilibria exists at which wages are maximal, the rate of profit minimal, and fully employed work-force in technically determined relation to fixed capital stock. Between these equilibria occur episodes of excess labour, below-maximum wages, above minimum profit-rate and capital accumulation. Malthus's 'ratios' presuppose a logarithmic production function that implies first, that the full-employment real wage will fall to subsistence; secondly, that the full-employment 'wages fund' is constant." (SUMMARY IN FRE) excerpt

Laboratory study of low-β forces in arched, line-tied magnetic flux ropes

NASA Astrophysics Data System (ADS)

Myers, C. E.; Yamada, M.; Ji, H.; Yoo, J.; Jara-Almonte, J.; Fox, W.

2016-11-01

The loss-of-equilibrium is a solar eruption mechanism whereby a sudden breakdown of the magnetohydrodynamic force balance in the Sun's corona ejects a massive burst of particles and energy into the heliosphere. Predicting a loss-of-equilibrium, which has more recently been formulated as the torus instability, relies on a detailed understanding of the various forces that hold the pre-eruption magnetic flux rope in equilibrium. Traditionally, idealized analytical force expressions are used to derive simplified eruption criteria that can be compared to solar observations and modeling. What is missing, however, is a validation that these idealized analytical force expressions can be applied to the line-tied, low-aspect-ratio conditions of the corona. In this paper, we address this shortcoming by using a laboratory experiment to study the forces that act on long-lived, arched, line-tied magnetic flux ropes. Three key force terms are evaluated over a wide range of experimental conditions: (1) the upward hoop force; (2) the downward strapping force; and (3) the downward toroidal field tension force. First, the laboratory force measurements show that, on average, the three aforementioned force terms cancel to produce a balanced line-tied equilibrium. This finding validates the laboratory force measurement techniques developed here, which were recently used to identify a dynamic toroidal field tension force that can prevent flux rope eruptions [Myers et al., Nature 528, 526 (2015)]. The verification of magnetic force balance also confirms the low-β assumption that the plasma thermal pressure is negligible in these experiments. Next, the measured force terms are directly compared to corresponding analytical expressions. While the measured and analytical forces are found to be well correlated, the low-aspect-ratio, line-tied conditions in the experiment are found to both reduce the measured hoop force and increase the measured tension force with respect to analytical expectations. These two co-directed effects combine to generate laboratory flux rope equilibria at lower altitudes than are predicted analytically. Such considerations are expected to modify the loss-of-equilibrium eruption criteria for analogous flux ropes in the solar corona.

Laboratory study of low- β forces in arched, line-tied magnetic flux ropes

DOE PAGES

Myers, C. E.; Yamada, M.; Ji, H.; ...

2016-11-04

Here, the loss-of-equilibrium is a solar eruption mechanism whereby a sudden breakdown of the magnetohydrodynamic force balance in the Sun's corona ejects a massive burst of particles and energy into the heliosphere. Predicting a loss-of-equilibrium, which has more recently been formulated as the torus instability, relies on a detailed understanding of the various forces that hold the pre-eruption magnetic flux rope in equilibrium. Traditionally, idealized analytical force expressions are used to derive simplified eruption criteria that can be compared to solar observations and modeling. What is missing, however, is a validation that these idealized analytical force expressions can be appliedmore » to the line-tied, low-aspect-ratio conditions of the corona. In this paper, we address this shortcoming by using a laboratory experiment to study the forces that act on long-lived, arched, line-tied magnetic flux ropes. Three key force terms are evaluated over a wide range of experimental conditions: (1) the upward hoop force; (2) the downward strapping force; and (3) the downward toroidal field tension force. First, the laboratory force measurements show that, on average, the three aforementioned force terms cancel to produce a balanced line-tied equilibrium. This finding validates the laboratory force measurement techniques developed here, which were recently used to identify a dynamic toroidal field tension force that can prevent flux rope eruption. The verification of magnetic force balance also confirms the low-beta assumption that the plasma thermal pressure is negligible in these experiments. Next, the measured force terms are directly compared to corresponding analytical expressions. While the measured and analytical forces are found to be well correlated, the low-aspect-ratio, line-tied conditions in the experiment are found to both reduce the measured hoop force and increase the measured tension force with respect to analytical expectations. These two co-directed effects combine to generate laboratory flux rope equilibria at lower altitudes than are predicted analytically. Such considerations are expected to modify the loss-of-equilibrium eruption criteria for analogous flux ropes in the solar corona.« less

Laboratory study of low- β forces in arched, line-tied magnetic flux ropes

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

Myers, C. E.; Yamada, M.; Ji, H.

Here, the loss-of-equilibrium is a solar eruption mechanism whereby a sudden breakdown of the magnetohydrodynamic force balance in the Sun's corona ejects a massive burst of particles and energy into the heliosphere. Predicting a loss-of-equilibrium, which has more recently been formulated as the torus instability, relies on a detailed understanding of the various forces that hold the pre-eruption magnetic flux rope in equilibrium. Traditionally, idealized analytical force expressions are used to derive simplified eruption criteria that can be compared to solar observations and modeling. What is missing, however, is a validation that these idealized analytical force expressions can be appliedmore » to the line-tied, low-aspect-ratio conditions of the corona. In this paper, we address this shortcoming by using a laboratory experiment to study the forces that act on long-lived, arched, line-tied magnetic flux ropes. Three key force terms are evaluated over a wide range of experimental conditions: (1) the upward hoop force; (2) the downward strapping force; and (3) the downward toroidal field tension force. First, the laboratory force measurements show that, on average, the three aforementioned force terms cancel to produce a balanced line-tied equilibrium. This finding validates the laboratory force measurement techniques developed here, which were recently used to identify a dynamic toroidal field tension force that can prevent flux rope eruption. The verification of magnetic force balance also confirms the low-beta assumption that the plasma thermal pressure is negligible in these experiments. Next, the measured force terms are directly compared to corresponding analytical expressions. While the measured and analytical forces are found to be well correlated, the low-aspect-ratio, line-tied conditions in the experiment are found to both reduce the measured hoop force and increase the measured tension force with respect to analytical expectations. These two co-directed effects combine to generate laboratory flux rope equilibria at lower altitudes than are predicted analytically. Such considerations are expected to modify the loss-of-equilibrium eruption criteria for analogous flux ropes in the solar corona.« less

Theoretical features of MHD equilibria with flow

NASA Astrophysics Data System (ADS)

Beklemishev, Alexei; Tessarotto, Massimo

2002-11-01

The effect produced on plasma dynamics by plasma flows, especially those produced by strong E× B-drifts represent an important theoretical issue in magnetic confinement. These include in particular Stellarator equilibria in the presence of weak flows, with velocity much smaller in magnitude than the ion thermal velocity [1]. Strong flows, however, more generally can be produced locally in a variety of physical situations (for example due to strong radial electric fields, neutral beams, RF heating, etc.). These flows can be important in establishing advanced operational regimes, such as the recently discovered HDH mode in the W7-AS Stellarator [2]. Goal of this work is to investigate theoretical features of the MHD equilibria in the presence of strong flows, with particular reference to conditions of existence of kinetic equilibria, particle adiabatic and/or bounce-averaged invariants. References 1 - M. Tessarotto, J.L. Johnson, R.B. White and L.J. Zheng, Phys. Plasmas 3, 2653 (1996); 2 - K. McCormick et al., Phys. Rev. Lett. 89, 15001 (2002).

The Spectral Web of stationary plasma equilibria. II. Internal modes

NASA Astrophysics Data System (ADS)

Goedbloed, J. P.

2018-03-01

The new method of the Spectral Web to calculate the spectrum of waves and instabilities of plasma equilibria with sizeable flows, developed in the preceding Paper I [Goedbloed, Phys. Plasmas 25, 032109 (2018)], is applied to a collection of classical magnetohydrodynamic instabilities operating in cylindrical plasmas with shear flow or rotation. After a review of the basic concepts of the complementary energy giving the solution path and the conjugate path, which together constitute the Spectral Web, the cylindrical model is presented and the spectral equations are derived. The first example concerns the internal kink instabilities of a cylindrical force-free magnetic field of constant α subjected to a parabolic shear flow profile. The old stability diagram and the associated growth rate calculations for static equilibria are replaced by a new intricate stability diagram and associated complex growth rates for the stationary model. The power of the Spectral Web method is demonstrated by showing that the two associated paths in the complex ω-plane nearly automatically guide to the new class of global Alfvén instabilities of the force-free configuration that would have been very hard to predict by other methods. The second example concerns the Rayleigh-Taylor instability of a rotating theta-pinch. The old literature is revisited and shown to suffer from inconsistencies that are remedied. The most global n = 1 instability and a cluster sequence of more local but much more unstable n =2 ,3 ,…∞ modes are located on separate solution paths in the hydrodynamic (HD) version of the instability, whereas they merge in the MHD version. The Spectral Web offers visual demonstration of the central position the HD flow continuum and of the MHD Alfvén and slow magneto-sonic continua in the respective spectra by connecting the discrete modes in the complex plane by physically meaningful curves towards the continua. The third example concerns the magneto-rotational instability (MRI) thought to be operating in accretion disks about black holes. The sequence n =1 ,2 ,… of unstable MRIs is located on one continuous solution path, but also on infinitely many separate loops ("pancakes") of the conjugate path with just one MRI on each of them. For narrow accretion disks, those sequences are connected with the slow magneto-sonic continuum, which is far away though from the marginal stability transition. In this case, the Spectral Web method is the first to effectively incorporate the MRIs into the general MHD spectral theory of equilibria with background flows. Together, the three examples provide compelling evidence of the computational power of the Spectral Web Method.

Two-fluid flowing equilibria of spherical torus sustained by coaxial helicity injection

NASA Astrophysics Data System (ADS)

Kanki, Takashi; Steinhauer, Loren; Nagata, Masayoshi

2007-11-01

Two-dimensional equilibria in helicity-driven systems using two-fluid model were previously computed, showing the existence of an ultra-low-q spherical torus (ST) configuration with diamagnetism and higher beta. However, this computation assumed purely toroidal ion flow and uniform density. The purpose of the present study is to apply the two-fluid model to the two-dimensional equilibria of helicity-driven ST with non-uniform density and both toroidal and poloidal flows for each species by means of the nearby-fluids procedure, and to explore their properties. We focus our attention on the equilibria relevant to the HIST device, which are characterized by either driven or decaying λ profiles. The equilibrium for the driven λ profile has a diamagnetic toroidal field, high-β (βt = 32%), and centrally broad density. By contrast, the decaying equilibrium has a paramagnetic toroidal field, low-β (βt = 10%), and centrally peaked density with a steep gradient in the outer edge region. In the driven case, the toroidal ion and electron flows are in the same direction, and two-fluid effects are less important since the ExB drift is dominant. In the decaying case, the toroidal ion and electron flows are opposite in the outer edge region, and two-fluid effects are significant locally in the edge due to the ion diamagnetic drift.

Effects of density gradient caused by multi-pulsing CHI on two-fluid flowing equilibria of spherical torus plasmas

NASA Astrophysics Data System (ADS)

Kanki, T.; Nagata, M.

2014-10-01

Two-fluid dynamo relaxation is examined to understand sustainment mechanism of spherical torus (ST) plasmas by multi-pulsing CHI (M-CHI) in the HIST device. The steeper density gradient between the central open flux column (OFC) and closed flux regions by applying the second CHI pulse is observed to cause not only the E × B drift but also the ion diamagnetic drift, leading the two-fluid dynamo. The purpose of this study is to investigate the effects of the steep change in the density gradient on the ST equilibria by using the two-fluid equilibrium calculations. The toroidal magnetic field becomes from a diamagnetic to a paramagnetic profile in the closed flux region while it remains a diamagnetic profile in the OFC region. The toroidal ion flow velocity is increased from negative to positive values in the closed flux region. Here, the negative ion flow velocity is the opposite direction to the toroidal current. The poloidal ion flow velocity between the OFC and closed flux regions is increased, because the ion diamagnetic drift velocity is changed in the same direction as the E × B drift velocity through the steeper ion pressure gradient. As a result, the strong shear flow and the paramagnetic toroidal field are generated in the closed flux region. Here, the ion flow velocity is the same direction as the poloidal current. The radial electric field shear between the OFC and closed flux regions is enhanced due to the strong dependence on the magnetic force through the interaction of toroidal ion flow velocity and axial magnetic field. The two-fluid effect is significant there due to the ion diamagnetic effect.

On the Support of Solar Prominence Material by the Dips of a Coronal Flux Tube

NASA Astrophysics Data System (ADS)

Hillier, Andrew; van Ballegooijen, Adriaan

2013-04-01

The dense prominence material is believed to be supported against gravity through the magnetic tension of dipped coronal magnetic field. For quiescent prominences, which exhibit many gravity-driven flows, hydrodynamic forces are likely to play an important role in the determination of both the large- and small-scale magnetic field distributions. In this study, we present the first steps toward creating a three-dimensional magneto-hydrostatic prominence model where the prominence is formed in the dips of a coronal flux tube. Here 2.5D equilibria are created by adding mass to an initially force-free magnetic field, then performing a secondary magnetohydrodynamic relaxation. Two inverse polarity magnetic field configurations are studied in detail, a simple o-point configuration with a ratio of the horizontal field (Bx ) to the axial field (By ) of 1:2 and a more complex model that also has an x-point with a ratio of 1:11. The models show that support against gravity is either by total pressure or tension, with only tension support resembling observed quiescent prominences. The o-point of the coronal flux tube was pulled down by the prominence material, leading to compression of the magnetic field at the base of the prominence. Therefore, tension support comes from the small curvature of the compressed magnetic field at the bottom and the larger curvature of the stretched magnetic field at the top of the prominence. It was found that this method does not guarantee convergence to a prominence-like equilibrium in the case where an x-point exists below the prominence flux tube. The results imply that a plasma β of ~0.1 is necessary to support prominences through magnetic tension.

Monodomain dynamics for rigid rod and platelet suspensions in strongly coupled coplanar linear flow and magnetic fields. II. Kinetic theory

NASA Astrophysics Data System (ADS)

Forest, M. Gregory; Sircar, Sarthok; Wang, Qi; Zhou, Ruhai

2006-10-01

We establish reciprocity relations of the Doi-Hess kinetic theory for rigid rod macromolecular suspensions governed by the strong coupling among an excluded volume potential, linear flow, and a magnetic field. The relation provides a reduction of the flow and field driven Smoluchowski equation: from five parameters for coplanar linear flows and magnetic field, to two field parameters. The reduced model distinguishes flows with a rotational component, which map to simple shear (with rate parameter) subject to a transverse magnetic field (with strength parameter), and irrotational flows, for which the reduced model consists of a triaxial extensional flow (with two extensional rate parameters). We solve the Smoluchowski equation of the reduced model to explore: (i) the effect of introducing a coplanar magnetic field on each sheared monodomain attractor of the Doi-Hess kinetic theory and (ii) the coupling of coplanar extensional flow and magnetic fields. For (i), we show each sheared attractor (steady and unsteady, with peak axis in and out of the shearing plane, periodic and chaotic orbits) undergoes its own transition sequence versus magnetic field strength. Nonetheless, robust predictions emerge: out-of-plane degrees of freedom are arrested with increasing field strength, and a unique flow-aligning or tumbling/wagging limit cycle emerges above a threshold magnetic field strength or modified geometry parameter value. For (ii), irrotational flows coupled with a coplanar magnetic field yield only steady states. We characterize all (generically biaxial) equilibria in terms of an explicit Boltzmann distribution, providing a natural generalization of analytical results on pure nematic equilibria [P. Constantin, I. Kevrekidis, and E. S. Titi, Arch. Rat. Mech. Anal. 174, 365 (2004); P. Constantin, I. Kevrekidis, and E. S. Titi, Discrete and Continuous Dynamical Systems 11, 101 (2004); P. Constantin and J. Vukadinovic, Nonlinearity 18, 441 (2005); H. Liu, H. Zhang, and P. Zhang, Comm. Math. Sci. 3, 201 (2005); C. Luo, H. Zhang, and P. Zhang, Nonlinearity 18, 379 (2005); I. Fatkullin and V. Slastikov, Nonlinearity 18, 2565 (2005); H. Zhou, H. Wang, Q. Wang, and M. G. Forest, Nonlinearity 18, 2815 (2005)] and extensional flow-induced equilibria [Q. Wang, S. Sircar, and H. Zhou, Comm. Math. Sci. 4, 605 (2005)]. We predict large parameter regions of bi-stable equilibria; the lowest energy state always has principal axis aligned in the flow plane, while another minimum energy state often exists, with primary alignment transverse to the coplanar field.

Anisotropic magnetotail equilibrium and convection

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

Hau, L.N.

This paper reports on self-consistent two-dimensional equilibria with anisotropic plasma pressure for the Earth's magnetotail. These configurations are obtained by numerically solving the generalized Grad-Shafranov equation, describing anisotropic plasmas with p[parallel] [ne] p[perpendicular], including the Earth's dipolar field. Consistency between these new equilibria and the assumption of steady-state, sunward convection, described by the double-adiabatic laws, is examined. As for the case of isotropic pressure [Erickson and Wolf, 1980], there exists a discrepancy between typical quite-time magnetic field models and the assumption of steady-state double-adiabatic lossless plasma sheet convection. However, unlike that case, this inconsistency cannot be removed by the presencemore » of a weak equatorial normal magnetic field strength in the near tail region: magnetic field configurations of this type produce unreasonably large pressure anisotropies, p[parallel] > p[perpendicular], in the plasma sheet. 16 refs., 5 figs.« less

a Theoretical Study of Coherent Structures in Nonneutral Plasma Columns

NASA Astrophysics Data System (ADS)

Lund, Steven M.

A ubiquitous feature of experimental and computer simulation studies of magnetically confined pure electron plasmas in cylindrical confinement devices is the formation of nonaxisymmetric (partial/partial theta ne 0) rotating equilibria. In this dissertation, nonaxisymmetric rotating equilibria are investigated theoretically for strongly magnetized, low-density (omega_sp{pe} {2}/omega_sp{ce}{2 } << 1) pure electron plasmas confined in a two-dimensional cylindrical geometry. These dynamic equilibria are also called rotating coherent structures, and are stationary (time-independent) in a frame of reference rotating with angular velocity omega_ {r} = const. about the cylinder axis (r = 0). Radial confinement of the pure electron plasma is provided by a uniform axial magnetic field B_0 {bf e}_{z}, and a grounded, perfectly conducting, cylindrical wall is located at radius r = r_{w}. The analysis is based on a nonrelativistic, guiding-center model in the cold-fluid limit (the continuity and Poisson equations) that treats the electrons as a massless fluid (m_{e} to 0) with E times B flow velocity V _{e} = -(c/B_0)nablaphi times {bf e}_{z}. Within this model, general rotating equilibria with electron density (n_{e} equiv n_{R}(r,theta-omega _{r}t) and electrostatic potential phi equiv phi_{R }(r,theta-omega_{r}t) have the property that the electron density is functionally related to the streamfunction psi _{R} = -ephi_{R} + omega_{r}(eB_0/2c)r^2 by n_{R} = n_{R }(psi_{R}). The streamfunction psi_{R} satisfies the nonlinear equilibrium equation nabla ^2psi_{R} = -4pi e^2n _{R}(psi_{R}) + 2omega_{r}eB_0/c with psi_{R} = omega _{r}(eB_0/2c)r_sp{w }{2} equiv psi_{w } = const. on the cylindrical wall at r = r_{w}. A general methodology for the solution of this equilibrium system is presented and several properties of rotating equilibria are analyzed. Following this analysis, two classes of nonaxisymmetric equilibria are investigated. These two classes of equilibria can have large amplitude (strongly nonaxisymmetric). First, a class of vortex-like rotating equilibria is analyzed that is characterized by a structured density profile that fills a confinement geometry with an inner conducting cylinder at radius r = r_{I} < r_ {w}. The streamfunction describing these vortex-like equilibria is derived exactly and analyzed in several relevant limits. Next, a physically motivated class of rotating equilibria with "waterbag" (step-function) density profiles and free plasma-vacuum interfaces is investigated. An integral equation formulation of the nonlinear equilibrium equation that describes general waterbag equilibria is developed. Then a numerical method that can be used to construct diverse varieties of solutions for highly nonlinear waterbag equilibria is formulated. This method is employed to examine two classes of nonaxisymmetric equilibria that are nonlinear extrapolations of well-known small-amplitude equilibria. These two classes of rotating equilibria bear strong similarities to coherent structures observed experimentally by Driscoll and Fine (Phys. Fluid B 2, 1359 (1990)). (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).

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

Wiegelmann, T.; Solanki, S. K.; Barthol, P.

Magneto-static models may overcome some of the issues facing force-free magnetic field extrapolations. So far they have seen limited use and have faced problems when applied to quiet-Sun data. Here we present a first application to an active region. We use solar vector magnetic field measurements gathered by the IMaX polarimeter during the flight of the Sunrise balloon-borne solar observatory in 2013 June as boundary conditions for a magneto-static model of the higher solar atmosphere above an active region. The IMaX data are embedded in active region vector magnetograms observed with SDO /HMI. This work continues our magneto-static extrapolation approach,more » which was applied earlier to a quiet-Sun region observed with Sunrise I. In an active region the signal-to-noise-ratio in the measured Stokes parameters is considerably higher than in the quiet-Sun and consequently the IMaX measurements of the horizontal photospheric magnetic field allow us to specify the free parameters of the model in a special class of linear magneto-static equilibria. The high spatial resolution of IMaX (110–130 km, pixel size 40 km) enables us to model the non-force-free layer between the photosphere and the mid-chromosphere vertically by about 50 grid points. In our approach we can incorporate some aspects of the mixed beta layer of photosphere and chromosphere, e.g., taking a finite Lorentz force into account, which was not possible with lower-resolution photospheric measurements in the past. The linear model does not, however, permit us to model intrinsic nonlinear structures like strongly localized electric currents.« less

Finding Bounded Rational Equilibria. Part 1; Iterative Focusing

NASA Technical Reports Server (NTRS)

Wolpert, David H.

2004-01-01

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality characterizing all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. It has recently been shown that the same information theoretic mathematical structure, known as Probability Collectives (PC) underlies both issues. This relationship between statistical physics and game theory allows techniques and insights from the one field to be applied to the other. In particular, PC provides a formal model-independent definition of the degree of rationality of a player and of bounded rationality equilibria. This pair of papers extends previous work on PC by introducing new computational approaches to effectively find bounded rationality equilibria of common-interest (team) games.

Role of a continuous MHD dynamo in the formation of 3D equilibria in fusion plasmas

NASA Astrophysics Data System (ADS)

Piovesan, P.; Bonfiglio, D.; Cianciosa, M.; Luce, T. C.; Taylor, N. Z.; Terranova, D.; Turco, F.; Wilcox, R. S.; Wingen, A.; Cappello, S.; Chrystal, C.; Escande, D. F.; Holcomb, C. T.; Marrelli, L.; Paz-Soldan, C.; Piron, L.; Predebon, I.; Zaniol, B.; DIII-D, The; RFX-Mod Teams

2017-07-01

Stationary 3D equilibria can form in fusion plasmas via saturation of magnetohydrodynamic (MHD) instabilities or stimulated by external 3D fields. In these cases the current profile is anomalously broad due to magnetic flux pumping produced by the MHD modes. Flux pumping plays an important role in hybrid tokamak plasmas, maintaining the minimum safety factor above unity and thus removing sawteeth. It also enables steady-state hybrid operation, by redistributing non-inductive current driven near the center by electron cyclotron waves. A validated flux pumping model is not yet available, but it would be necessary to extrapolate hybrid operation to future devices. In this work flux pumping physics is investigated for helical core equilibria stimulated by external 3D fields in DIII-D hybrid plasmas. We show that flux pumping can be produced in a continuous way by an MHD dynamo emf. The same effect maintains helical equilibria in reversed-field pinch (RFP) plasmas. The effective MHD dynamo loop voltage is calculated for experimental 3D equilibrium reconstructions, by balancing Ohm’s law over helical flux surfaces, and is consistent with the expected current redistribution. Similar results are also obtained with more sophisticated nonlinear MHD simulations. The same modelling approach is applied to helical RFP states forming spontaneously in RFX-mod as the plasma current is raised above 0.8-1 MA. This comparison allows to identify the underlying physics common to tokamak and RFP: a helical core displacement modulates parallel current density along flux tubes, which requires a helical electrostatic potential to build up, giving rise to a helical MHD dynamo flow.

Role of a continuous MHD dynamo in the formation of 3D equilibria in fusion plasmas

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

Piovesan, P.; Bonfiglio, D.; Cianciosa, M.

Stationary 3D equilibria can form in fusion plasmas via saturation of magnetohydrodynamic (MHD) instabilities or stimulated by external 3D fields. In these cases the current profile is anomalously broad due to magnetic flux pumping produced by the MHD modes. Flux pumping plays an important role in hybrid tokamak plasmas, maintaining the minimum safety factor above unity and thus removing sawteeth. It also enables steady-state hybrid operation, by redistributing non-inductive current driven near the center by electron cyclotron waves. A validated flux pumping model is not yet available, but it would be necessary to extrapolate hybrid operation to future devices. Inmore » this work flux pumping physics is investigated for helical core equilibria stimulated by external 3D fields in DIII-D hybrid plasmas. We show that flux pumping can be produced in a continuous way by an MHD dynamo emf. The same effect maintains helical equilibria in reversed-field pinch (RFP) plasmas. The effective MHD dynamo loop voltage is calculated for experimental 3D equilibrium reconstructions, by balancing Ohm’s law over helical flux surfaces, and is consistent with the expected current redistribution. Similar results are also obtained with more sophisticated nonlinear MHD simulations. The same modelling approach is applied to helical RFP states forming spontaneously in RFX-mod as the plasma current is raised above 0.8–1 MA. This comparison allows to identify the underlying physics common to tokamak and RFP: a helical core displacement modulates parallel current density along flux tubes, which requires a helical electrostatic potential to build up, giving rise to a helical MHD dynamo flow.« less

Role of a continuous MHD dynamo in the formation of 3D equilibria in fusion plasmas

DOE PAGES

Piovesan, P.; Bonfiglio, D.; Cianciosa, M.; ...

2017-04-28

Stationary 3D equilibria can form in fusion plasmas via saturation of magnetohydrodynamic (MHD) instabilities or stimulated by external 3D fields. In these cases the current profile is anomalously broad due to magnetic flux pumping produced by the MHD modes. Flux pumping plays an important role in hybrid tokamak plasmas, maintaining the minimum safety factor above unity and thus removing sawteeth. It also enables steady-state hybrid operation, by redistributing non-inductive current driven near the center by electron cyclotron waves. A validated flux pumping model is not yet available, but it would be necessary to extrapolate hybrid operation to future devices. Inmore » this work flux pumping physics is investigated for helical core equilibria stimulated by external 3D fields in DIII-D hybrid plasmas. We show that flux pumping can be produced in a continuous way by an MHD dynamo emf. The same effect maintains helical equilibria in reversed-field pinch (RFP) plasmas. The effective MHD dynamo loop voltage is calculated for experimental 3D equilibrium reconstructions, by balancing Ohm’s law over helical flux surfaces, and is consistent with the expected current redistribution. Similar results are also obtained with more sophisticated nonlinear MHD simulations. The same modelling approach is applied to helical RFP states forming spontaneously in RFX-mod as the plasma current is raised above 0.8–1 MA. This comparison allows to identify the underlying physics common to tokamak and RFP: a helical core displacement modulates parallel current density along flux tubes, which requires a helical electrostatic potential to build up, giving rise to a helical MHD dynamo flow.« less

Inclusion of pressure and flow in a new 3D MHD equilibrium code

NASA Astrophysics Data System (ADS)

Raburn, Daniel; Fukuyama, Atsushi

2012-10-01

Flow and nonsymmetric effects can play a large role in plasma equilibria and energy confinement. A concept for such a 3D equilibrium code was developed and presented in 2011. The code is called the Kyoto ITerative Equilibrium Solver (KITES) [1], and the concept is based largely on the PIES code [2]. More recently, the work-in-progress KITES code was used to calculate force-free equilibria. Here, progress and results on the inclusion of pressure and flow in the code are presented. [4pt] [1] Daniel Raburn and Atsushi Fukuyama, Plasma and Fusion Research: Regular Articles, 7:240381 (2012).[0pt] [2] H. S. Greenside, A. H. Reiman, and A. Salas, J. Comput. Phys, 81(1):102-136 (1989).

Integrated Modeling of Time Evolving 3D Kinetic MHD Equilibria and NTV Torque

NASA Astrophysics Data System (ADS)

Logan, N. C.; Park, J.-K.; Grierson, B. A.; Haskey, S. R.; Nazikian, R.; Cui, L.; Smith, S. P.; Meneghini, O.

2016-10-01

New analysis tools and integrated modeling of plasma dynamics developed in the OMFIT framework are used to study kinetic MHD equilibria evolution on the transport time scale. The experimentally observed profile dynamics following the application of 3D error fields are described using a new OMFITprofiles workflow that directly addresses the need for rapid and comprehensive analysis of dynamic equilibria for next-step theory validation. The workflow treats all diagnostic data as fundamentally time dependent, provides physics-based manipulations such as ELM phase data selection, and is consistent across multiple machines - including DIII-D and NSTX-U. The seamless integration of tokamak data and simulation is demonstrated by using the self-consistent kinetic EFIT equilibria and profiles as input into 2D particle, momentum and energy transport calculations using TRANSP as well as 3D kinetic MHD equilibrium stability and neoclassical transport modeling using General Perturbed Equilibrium Code (GPEC). The result is a smooth kinetic stability and NTV torque evolution over transport time scales. Work supported by DE-AC02-09CH11466.

3D Equilibrium Effects Due to RMP Application on DIII-D

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

S. Lazerson, E. Lazarus, S. Hudson, N. Pablant and D. Gates

2012-06-20

The mitigation and suppression of edge localized modes (ELMs) through application of resonant magnetic perturbations (RMPs) in Tokamak plasmas is a well documented phenomenon [1]. Vacuum calculations suggest the formation of edge islands and stochastic regions when RMPs are applied to the axisymmetric equilibria. Self-consistent calculations of the plasma equilibrium with the VMEC [2] and SPEC [3] codes have been performed for an up-down symmetric shot (142603) in DIII-D. In these codes, a self-consistent calculation of the plasma response due to the RMP coils is calculated. The VMEC code globally enforces the constraints of ideal MHD; consequently, a continuously nestedmore » family of flux surfaces is enforced throughout the plasma domain. This approach necessarily precludes the observation of islands or field-line chaos. The SPEC code relaxes the constraints of ideal MHD locally, and allows for islands and field line chaos at or near the rational surfaces. Equilibria with finite pressure gradients are approximated by a set of discrete "ideal-interfaces" at the most irrational flux surfaces and where the strongest pressure gradients are observed. Both the VMEC and SPEC calculations are initialized from EFIT reconstructions of the plasma that are consistent with the experimental pressure and current profiles. A 3D reconstruction using the STELLOPT code, which fits VMEC equilibria to experimental measurements, has also been performed. Comparisons between the equilibria generated by the 3D codes and between STELLOPT and EFIT are presented.« less

3D Equilibrium Effects Due to RMP Application on DIII-D

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

Lazerson, S.; Lazarus, E.; Hudson, S.

2012-06-20

The mitigation and suppression of edge localized modes (ELMs) through application of resonant magnetic perturbations (RMPs) in Tokamak plasmas is a well documented phenomenon. Vacuum calculations suggest the formation of edge islands and stochastic regions when RMPs are applied to the axisymmetric equilibria. Self-consistent calculations of the plasma equilibrium with the VMEC and SPEC codes have been performed for an up-down symmetric shot in DIII-D. In these codes, a self-consistent calculation of the plasma response due to the RMP coils is calculated. The VMEC code globally enforces the constraints of ideal MHD; consequently, a continuously nested family of flux surfacesmore » is enforced throughout the plasma domain. This approach necessarily precludes the observation of islands or field-line chaos. The SPEC code relaxes the constraints of ideal MHD locally, and allows for islands and field line chaos at or near the rational surfaces. Equilibria with finite pressure gradients are approximated by a set of discrete "ideal-interfaces" at the most irrational flux surfaces and where the strongest pressure gradients are observed. Both the VMEC and SPEC calculations are initialized from EFIT reconstructions of the plasma that are consistent with the experimental pressure and current profiles. A 3D reconstruction using the STELLOPT code, which fits VMEC equilibria to experimental measurements, has also been performed. Comparisons between the equilibria generated by the 3D codes and between STELLOPT and EFIT are presented.« less

All substituted nickel porphyrins are highly nonplanar

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

Shelnutt, J.A.; Song, X.Z.; Jentzen, W.

1996-12-31

X-ray crystallographic and resonance Raman studies show that only un-substituted Ni porphine is planar in solution; all substituted Ni porphyrin derivatives either are nonplanar or exist as a mixture of planar and nonplanar conformers in solution. Recent modifications in a molecular mechanics force field improve the ability the MM calculations to predict the X-ray structures of porphyrins and also the planar-nonplanar conformational equilibria in many cases. Calculations using the new force field suggests that all geoporphyrins will be highly nonplanar, especially those having meso substituents. The nonplanarity is expected to influence properties such as solubility and metallation/dematallation reactions. Further, amore » method of quantifying these nonplanar structures has been devised; any porphyrin structure can be decomposed into displacements along the out-of-plane normal coordinates. However, usually distortions along only the lowest-frequency normal modes of each symmetry type are required to adequately describe the structure. The lowest-frequency normal coordinates of b{sub lu}, a{sub 2u}, b{sub 2u}, and e{sub g} symmetries correspond to commonly observed symmetric distortions called ruffling (ruf), doming(dom), saddling (sad), and waving (wav(x), wav(y)). The application of this structural decomposition method to several problems including the influences of steric crowding and protein folding on porphyrin conformation will be described.« less

Finding Bounded Rational Equilibria. Part 2; Alternative Lagrangians and Uncountable Move Spaces

NASA Technical Reports Server (NTRS)

Wolpert, David H.

2004-01-01

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality characterizing all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. It has recently been shown that the same information theoretic mathematical structure, known as Probability Collectives (PC) underlies both issues. This relationship between statistical physics and game theory allows techniques and insights &om the one field to be applied to the other. In particular, PC provides a formal model-independent definition of the degree of rationality of a player and of bounded rationality equilibria. This pair of papers extends previous work on PC by introducing new computational approaches to effectively find bounded rationality equilibria of common-interest (team) games.

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

NASA Astrophysics Data System (ADS)

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

2015-08-01

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

Ideal relaxation of the Hopf fibration

NASA Astrophysics Data System (ADS)

Smiet, Christopher Berg; Candelaresi, Simon; Bouwmeester, Dirk

2017-07-01

Ideal magnetohydrodynamics relaxation is the topology-conserving reconfiguration of a magnetic field into a lower energy state where the net force is zero. This is achieved by modeling the plasma as perfectly conducting viscous fluid. It is an important tool for investigating plasma equilibria and is often used to study the magnetic configurations in fusion devices and astrophysical plasmas. We study the equilibrium reached by a localized magnetic field through the topology conserving relaxation of a magnetic field based on the Hopf fibration in which magnetic field lines are closed circles that are all linked with one another. Magnetic fields with this topology have recently been shown to occur in non-ideal numerical simulations. Our results show that any localized field can only attain equilibrium if there is a finite external pressure, and that for such a field a Taylor state is unattainable. We find an equilibrium plasma configuration that is characterized by a lowered pressure in a toroidal region, with field lines lying on surfaces of constant pressure. Therefore, the field is in a Grad-Shafranov equilibrium. Localized helical magnetic fields are found when plasma is ejected from astrophysical bodies and subsequently relaxes against the background plasma, as well as on earth in plasmoids generated by, e.g., a Marshall gun. This work shows under which conditions an equilibrium can be reached and identifies a toroidal depression as the characteristic feature of such a configuration.

Meyer-Overton reforged: The origins of alcohol and anesthetic potency in membranes as determined by a new NMR partitioning probe, benzyl alcohol

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

Janes, N.; Ma, L.; Hsu, J.W.

1992-01-01

The Meyer-Overton hypothesis--that anesthesia arises from the nonspecific action of solutes on membrane lipids--is reformulated using colligative thermodynamics. Configurational entropy, the randomness imparted by the solute through the partitioning process, is implicated as the energetic driving force that pertubs cooperative membrane equilibria. A proton NMR partitioning approach based on the anesthetic benzyl alcohol is developed to assess the reformulation. Ring resonances from the partitioned drug are shielded by 0.2 ppm and resolved from the free, aqueous drug. Free alcohol is quantitated in dilute lipid dispersions using an acetate internal standard. Cooperative equilibria in model dipalmitoyl lecithin membranes are examined withmore » changes in temperature and alcohol concentration. The L[sub [beta][prime

Boundary modelling of the stellarator Wendelstein 7-X

NASA Astrophysics Data System (ADS)

Renner, H.; Strumberger, E.; Kisslinger, J.; Nührenberg, J.; Wobig, H.

1997-02-01

To justify the design of the divertor plates in W7-X the magnetic fields of finite-β HELIAS equilibria for the so-called high-mirror case have been computed for various average β-values up to < β > = 0.04 with the NEMEC free-boundary equilibrium code [S.P. Hirshman, W.I. van Rij and W.I. Merkel, Comput. Phys. Commun. 43 (1986) 143] in combination with the newly developed MFBE (magnetic field solver for finite-beta equilibria) code. In a second study the unloading of the target plates by radiation was investigated. The B2 code [B.J. Braams, Ph.D. Thesis, Rijksuniversiteit Utrecht (1986)] was applied for the first time to stellarators to provide of a self-consistent modelling of the SOL including effects of neutrals and impurities.

Catenaries in viscous fluid

NASA Astrophysics Data System (ADS)

Hanna, James; Chakrabarti, Brato

2015-11-01

Slender structures live in fluid flows across many scales, from towed instruments to plant blades to microfluidic valves. The present work details a simple model of a flexible structure in a uniform flow. We present analytical solutions for the translating, axially flowing equilibria of strings subjected to a uniform body force and linear drag forces. This is an extension of the classical catenaries to a five-parameter family of solutions, represented as trajectories in angle-curvature ``phase space.'' Limiting cases include neutrally buoyant towed cables and freely sedimenting flexible filaments. Now at University of California, San Diego.

Constructing Integrable Full-pressure Full-current Free-boundary Stellarator Magnetohydrodynamic Equilibria

NASA Astrophysics Data System (ADS)

Hudson, S. R.; Monticello, D. A.; Reiman, A. H.; Strickler, D. J.; Hirshman, S. P.

2003-06-01

For the (non-axisymmetric) stellarator class of plasma confinement devices to be feasible candidates for fusion power stations it is essential that, to a good approximation, the magnetic field lines lie on nested flux surfaces; however, the inherent lack of a continuous symmetry implies that magnetic islands are guaranteed to exist. Magnetic islands break the smooth topology of nested flux surfaces and chaotic field lines result when magnetic islands overlap. An analogous case occurs with 11/2-dimension Hamiltonian systems where resonant perturbations cause singularities in the transformation to action-angle coordinates and destroy integrability. The suppression of magnetic islands is a critical issue for stellarator design, particularly for small aspect ratio devices. Techniques for `healing' vacuum fields and fixed-boundary plasma equilibria have been developed, but what is ultimately required is a procedure for designing stellarators such that the self-consistent plasma equilibrium currents and the coil currents combine to produce an integrable magnetic field, and such a procedure is presented here for the first time. Magnetic islands in free-boundary full-pressure full-current stellarator magnetohydrodynamic equilibria are suppressed using a procedure based on the Princeton Iterative Equilibrium Solver [A.H.Reiman & H.S.Greenside, Comp. Phys. Comm., 43:157, 1986.] which iterates the equilibrium equations to obtain the plasma equilibrium. At each iteration, changes to a Fourier representation of the coil geometry are made to cancel resonant fields produced by the plasma. As the iterations continue, the coil geometry and the plasma simultaneously converge to an equilibrium in which the island content is negligible. The method is applied to a candidate plasma and coil design for the National Compact Stellarator eXperiment [G.H.Neilson et.al., Phys. Plas., 7:1911, 2000.].

Spreading dynamics of a SIQRS epidemic model on scale-free networks

NASA Astrophysics Data System (ADS)

Li, Tao; Wang, Yuanmei; Guan, Zhi-Hong

2014-03-01

In order to investigate the influence of heterogeneity of the underlying networks and quarantine strategy on epidemic spreading, a SIQRS epidemic model on the scale-free networks is presented. Using the mean field theory the spreading dynamics of the virus is analyzed. The spreading critical threshold and equilibria are derived. Theoretical results indicate that the critical threshold value is significantly dependent on the topology of the underlying networks and quarantine rate. The existence of equilibria is determined by threshold value. The stability of disease-free equilibrium and the permanence of the disease are proved. Numerical simulations confirmed the analytical results.

Scaling-law equilibria for calcium in canopy-type models of the solar chromosphere

NASA Technical Reports Server (NTRS)

Jones, H. P.

1982-01-01

Scaling laws for resonance line formation are used to obtain approximate excitation and ionization equilibria for a three-level model of singly ionized calcium. The method has been developed for and is applied to the study of magnetograph response in the 8542 A infrared triplet line to magnetostatic canopies which schematically model diffuse, nearly horizontal fields in the low solar chromosphere. For this application, the method is shown to be efficient and semi-quantitative, and the results indicate the type and range of effects on calcium-line radiation which result from reduced gas pressure inside the magnetic regions.

Analysis of SI models with multiple interacting populations using subpopulations.

PubMed

Thomas, Evelyn K; Gurski, Katharine F; Hoffman, Kathleen A

2015-02-01

Computing endemic equilibria and basic reproductive numbers for systems of differential equations describing epidemiological systems with multiple connections between subpopulations is often algebraically intractable. We present an alternative method which deconstructs the larger system into smaller subsystems and captures the interactions between the smaller systems as external forces using an approximate model. We bound the basic reproductive numbers of the full system in terms of the basic reproductive numbers of the smaller systems and use the alternate model to provide approximations for the endemic equilibrium. In addition to creating algebraically tractable reproductive numbers and endemic equilibria, we can demonstrate the influence of the interactions between subpopulations on the basic reproductive number of the full system. The focus of this paper is to provide analytical tools to help guide public health decisions with limited intervention resources.

Study of Three-dimensional Magnetic Structure and the Successive Eruptive Nature of Active Region 12371

NASA Astrophysics Data System (ADS)

Vemareddy, P.; Demóulin, P.

2018-04-01

We study the magnetic structure of a successively erupting sigmoid in active region 12371 by modeling the quasi-static coronal field evolution with nonlinear force-free field (NLFFF) equilibria. Helioseismic and Magnetic Imager/Solar Dynamic Observatory vector magnetograms are used as input to the NLFFF model. In all eruption events, the modeled structure resembles the observed pre-eruptive coronal sigmoid and the NLFFF core field is a combination of double inverse-J-shaped and inverse-S field lines with dips touching the photosphere. Such field lines are formed by the flux cancellation reconnection of opposite-J field lines at bald-patch locations, which in turn implies the formation of a weakly twisted flux-rope (FR) from large-scale sheared arcade field lines. Later on, this FR undergoes coronal tether-cutting reconnection until a coronal mass ejection is triggered. The modeled structure captured these major features of sigmoid-to-arcade-to-sigmoid transformation, which is reoccuring under continuous photospheric flux motions. Calculations of the field line twist reveal a fractional increase followed by a decrease of the number of pixels having a range of twist. This traces the buildup process of a twisted core field by slow photospheric motions and the relaxation after eruption, respectively. Our study infers that the large eruptivity of this AR is due to a steep decrease of the background coronal field meeting the torus instability criteria at a low height (≈40 Mm) in contrast to noneruptive ARs.

The effects of magnetic B(y) component on geomagnetic tail equilibria

NASA Technical Reports Server (NTRS)

Hilmer, Robert V.; Voigt, Gerd-Hannes

1987-01-01

A two-dimensional linear magnetohydrostatic model of the magnetotail is developed here in order to investigate the effects of a significant B(y) component on the configuration of magnetotail equilibria. It is concluded that the enhanced B(y) values must be an essential part of the quiet magnetotail and do not result from a simple intrusion of the IMF. The B(y) field consists of a constant background component plus a nonuniform field existing only in the plasma sheet, where it is dependent on the plasma paramater beta and the strength of the magnetic B(z) component. B(y) is strongest at the neutral sheet and decreases monotonically in the + or - z direction, reaching a constant tail lobe value at the plasma sheet boundaries. The presence of a significant positive B(y) component produces currents, including field-aligned currents, that flow through the equatorial plane and toward and away from earth in the northern and southern halves of the plasma sheet, respectively.

Kinetic Simulations of Current-Sheet Formation and Reconnection at a Magnetic X Line

NASA Technical Reports Server (NTRS)

Black, C.; Antiochos, S. K.; Hesse, M.; Karpen, J. T.; DeVore, C. R.; Kuznetsova, M. M.; Zenitani, S.

2011-01-01

The integration of kinetic effects into macroscopic numerical models is currently of great interest to the plasma physics community, particularly in the context of magnetic reconnection. We are examining the formation and reconnection of current sheets in a simple, two-dimensional X-line configuration using high resolution particle-in-cell (PIC) simulations. The initial potential magnetic field is perturbed by thermal pressure introduced into the particle distribution far from the X line. The relaxation of this added stress leads to the development of a current sheet, which reconnects for imposed stress of sufficient strength. We compare the evolution and final state of our PIC simulations with magnetohydrodynamic simulations assuming both uniform and localized resistivities, and with force-free magnetic-field equilibria in which the amount of reconnect ion across the X line can be constrained to be zero (ideal evolution) or optimal (minimum final magnetic energy). We will discuss implications of our results for reconnection onset and cessation at kinetic scales in dynamically formed current sheets, such as those occurring in the terrestrial magnetotail and solar corona.

Hybrid reconstruction of field-reversed configurations

NASA Astrophysics Data System (ADS)

Steinhauer, Loren; TAE Team

2016-10-01

Field-reversed configurations (FRC) are poorly represented by fluid-based models and require instead an ion-distribution function. Two such populations are needed since ``core'' ions are roughly restricted to the region inside the separatrix, whereas ``periphery'' ions can escape along open field lines. The Vlasov equation governs the distribution, the general solution to which is an arbitrary function of the constants of motion (Hamiltonian, canonical angular momentum). Only a small subset of such distributions are realistic in view of collisions, which smooth the distribution, and instabilities, which reorganize the field structure. Collisions and end loss are included if the distribution is a solution to the Fokker-Planck (FP) equation. Vlasov and FP solutions are nearly identical in weakly-collisional plasmas. Numerical construction of such equilibria requires solving both Ampere's law for the magnetic flux variable and the ponderous task of a full velocity-space integration at each point. The latter can be done analytically by expressing the distribution as the superposition of simple basis elements. This procedure allows rapid reconstruction of evolving equilibria based on limited diagnostic observables in FRC experiments.

Dynamical analysis of an orbiting three-rigid-body system

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

Pagnozzi, Daniele, E-mail: daniele.pagnozzi@strath.ac.uk, E-mail: james.biggs@strath.ac.uk; Biggs, James D., E-mail: daniele.pagnozzi@strath.ac.uk, E-mail: james.biggs@strath.ac.uk

2014-12-10

The development of multi-joint-spacecraft mission concepts calls for a deeper understanding of their nonlinear dynamics to inform and enhance system design. This paper presents a study of a three-finite-shape rigid-body system under the action of an ideal central gravitational field. The aim of this paper is to gain an insight into the natural dynamics of this system. The Hamiltonian dynamics is derived and used to identify relative attitude equilibria of the system with respect to the orbital reference frame. Then a numerical investigation of the behaviour far from the equilibria is provided using tools from modern dynamical systems theory suchmore » as energy methods, phase portraits and Poincarè maps. Results reveal a complex structure of the dynamics as well as the existence of connections between some of the equilibria. Stable equilibrium configurations appear to be surrounded by very narrow regions of regular and quasi-regular motions. Trajectories evolve on chaotic motions in the rest of the domain.« less

Adaptive Topographies and Equilibrium Selection in an Evolutionary Game

PubMed Central

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

2015-01-01

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

Toroidal equilibrium states with reversed magnetic shear and parallel flow in connection with the formation of Internal Transport Barriers

NASA Astrophysics Data System (ADS)

Kuiroukidis, Ap.; Throumoulopoulos, G. N.

2015-08-01

We construct nonlinear toroidal equilibria of fixed diverted boundary shaping with reversed magnetic shear and flows parallel to the magnetic field. The equilibria have hole-like current density and the reversed magnetic shear increases as the equilibrium nonlinearity becomes stronger. Also, application of a sufficient condition for linear stability implies that the stability is improved as the equilibrium nonlinearity correlated to the reversed magnetic shear gets stronger with a weaker stabilizing contribution from the flow. These results indicate synergetic stabilizing effects of reversed magnetic shear, equilibrium nonlinearity and flow in the establishment of Internal Transport Barriers (ITBs).

Magnetic islands and singular currents at rational surfaces in three-dimensional magnetohydrodynamic equilibria

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

Loizu, J., E-mail: joaquim.loizu@ipp.mpg.de; Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton New Jersey 08543; Hudson, S.

2015-02-15

Using the recently developed multiregion, relaxed MHD (MRxMHD) theory, which bridges the gap between Taylor's relaxation theory and ideal MHD, we provide a thorough analytical and numerical proof of the formation of singular currents at rational surfaces in non-axisymmetric ideal MHD equilibria. These include the force-free singular current density represented by a Dirac δ-function, which presumably prevents the formation of islands, and the Pfirsch-Schlüter 1/x singular current, which arises as a result of finite pressure gradient. An analytical model based on linearized MRxMHD is derived that can accurately (1) describe the formation of magnetic islands at resonant rational surfaces, (2)more » retrieve the ideal MHD limit where magnetic islands are shielded, and (3) compute the subsequent formation of singular currents. The analytical results are benchmarked against numerical simulations carried out with a fully nonlinear implementation of MRxMHD.« less

A coronal magnetic field model with horizontal volume and sheet currents

NASA Technical Reports Server (NTRS)

Zhao, Xuepu; Hoeksema, J. Todd

1994-01-01

When globally mapping the observed photospheric magnetic field into the corona, the interaction of the solar wind and magnetic field has been treated either by imposing source surface boundary conditions that tacitly require volume currents outside the source surface or by limiting the interaction to thin current sheets between oppositely directed field regions. Yet observations and numerical Magnetohydrodynamic (MHD) calculations suggest the presence of non-force-free volume currents throughout the corona as well as thin current sheets in the neighborhoods of the interfaces between closed and open field lines or between oppositely directed open field lines surrounding coronal helmet-streamer structures. This work presents a model including both horizontal volume currents and streamer sheet currents. The present model builds on the magnetostatic equilibria developed by Bogdan and Low and the current-sheet modeling technique developed by Schatten. The calculation uses synoptic charts of the line-of-sight component of the photospheric magnetic field measured at the Wilcox Solar Observatory. Comparison of an MHD model with the calculated model results for the case of a dipole field and comparison of eclipse observations with calculations for CR 1647 (near solar minimum) show that this horizontal current-current-sheet model reproduces polar plumes and axes of corona streamers better than the source-surface model and reproduces polar plumes and axes of corona streamers better than the source-surface model and reproduces coro nal helmet structures better than the current-sheet model.

Dynamics of confined reactive water in smectite clay-zeolite composites.

PubMed

Pitman, Michael C; van Duin, Adri C T

2012-02-15

The dynamics of water confined to mesoporous regions in minerals such as swelling clays and zeolites is fundamental to a wide range of resource management issues impacting many processes on a global scale, including radioactive waste containment, desalination, and enhanced oil recovery. Large-scale atomic models of freely diffusing multilayer smectite particles at low hydration confined in a silicalite cage are used to investigate water dynamics in the composite environment with the ReaxFF reactive force field over a temperature range of 300-647 K. The reactive capability of the force field enabled a range of relevant surface chemistry to emerge, including acid/base equilibria in the interlayer calcium hydrates and silanol formation on the edges of the clay and inner surface of the zeolite housing. After annealing, the resulting clay models exhibit both mono- and bilayer hydration structures. Clay surface hydration redistributed markedly and yielded to silicalite water loading. We find that the absolute rates and temperature dependence of water dynamics compare well to neutron scattering data and pulse field gradient measures from relevant samples of Ca-montmorillonite and silicalite, respectively. Within an atomistic, reactive context, our results distinguish water dynamics in the interlayer Ca(OH)(2)·nH(2)O environment from water flowing over the clay surface, and from water diffusing within silicalite. We find that the diffusion of water when complexed to Ca hydrates is considerably slower than freely diffusing water over the clay surface, and the reduced mobility is well described by a difference in the Arrhenius pre-exponential factor rather than a change in activation energy.

PIES free boundary stellarator equilibria with improved initial conditions

NASA Astrophysics Data System (ADS)

Drevlak, M.; Monticello, D.; Reiman, A.

2005-07-01

The MFBE procedure developed by Strumberger (1997 Nucl. Fusion 37 19) is used to provide an improved starting point for free boundary equilibrium computations in the case of W7-X (Nührenberg and Zille 1986 Phys. Lett. A 114 129) using the Princeton iterative equilibrium solver (PIES) code (Reiman and Greenside 1986 Comput. Phys. Commun. 43 157). Transferring the consistent field found by the variational moments equilibrium code (VMEC) (Hirshmann and Whitson 1983 Phys. Fluids 26 3553) to an extended coordinate system using the VMORPH code, a safe margin between plasma boundary and PIES domain is established. The new EXTENDER_P code implements a generalization of the virtual casing principle, which allows field extension both for VMEC and PIES equilibria. This facilitates analysis of the 5/5 islands of the W7-X standard case without including them in the original PIES computation.

Planar attitude motion of a satellite with a variable mass distribution in field of gravity of attracting center

NASA Astrophysics Data System (ADS)

Burov, Alexander; Kosenko, Ivan

2018-05-01

Dynamics of a spacecraft with a variable mass distribution in a central field of Newtonian attraction is considered. Using another viewpoint one can regard sufficiently compact formation instead of a spacecraft. This formation can vary distances between its particular spacecrafts thus implementing pulsing motions of the system as a whole. Within the so-called "satellite approximation" the equations of spatial attitude motion are obtained. Rules of the mass redistribution providing prescribed in advance attitude motions are indicated. For classes of relative equilibria previously found and existing under appropriate rules of the mass redistribution, stability study is performed. The investigation splits into two topics: (a) general dynamical consideration for the planar attitude satellite motion with use of the KAM theory; (b) constructing the families of periodic solutions represented by means of convergent series in powers of eccentricity and describing satellite motions emanating from its relative equilibria.

EXTENDING THE REALM OF OPTIMIZATION FOR COMPLEX SYSTEMS: UNCERTAINTY, COMPETITION, AND DYNAMICS

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

Shanbhag, Uday V; Basar, Tamer; Meyn, Sean

Research reported addressed these topics: the development of analytical and algorithmic tools for distributed computation of Nash equilibria; synchronization in mean-field oscillator games, with an emphasis on learning and efficiency analysis; questions that combine learning and computation; questions including stochastic and mean-field games; modeling and control in the context of power markets.

Hyper-resistivity and electron thermal conductivity due to destroyed magnetic surfaces in axisymmetric plasma equilibria

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

Weening, R. H.

2012-06-15

In order to model the effects of small-scale current-driven magnetic fluctuations in a mean-field theoretical description of a large-scale plasma magnetic field B(x,t), a space and time dependent hyper-resistivity {Lambda}(x,t) can be incorporated into the Ohm's law for the parallel electric field E Dot-Operator B. Using Boozer coordinates, a theoretical method is presented that allows for a determination of the hyper-resistivity {Lambda}({psi}) functional dependence on the toroidal magnetic flux {psi} for arbitrary experimental steady-state Grad-Shafranov axisymmetric plasma equilibria, if values are given for the parallel plasma resistivity {eta}({psi}) and the local distribution of any auxiliary plasma current. Heat transport inmore » regions of plasma magnetic surfaces destroyed by resistive tearing modes can then be modeled by an electron thermal conductivity k{sub e}({psi})=({epsilon}{sub 0}{sup 2}m{sub e}/e{sup 2}){Lambda}({psi}), where e and m{sub e} are the electron charge and mass, respectively, while {epsilon}{sub 0} is the permittivity of free space. An important result obtained for axisymmetric plasma equilibria is that the {psi}{psi}-component of the metric tensor of Boozer coordinates is given by the relation g{sup {psi}{psi}}({psi}){identical_to}{nabla}{psi} Dot-Operator {nabla}{psi}=[{mu}{sub 0}G({psi})][{mu}{sub 0}I({psi})]/{iota}({psi}), with {mu}{sub 0} the permeability of free space, G({psi}) the poloidal current outside a magnetic surface, I({psi}) the toroidal current inside a magnetic surface, and {iota}({psi}) the rotational transform.« less

Free-Boundary 3D Equilibria and Resistive Wall Instabilities with Extended-MHD

NASA Astrophysics Data System (ADS)

Ferraro, N. M.

2015-11-01

The interaction of the plasma with external currents, either imposed or induced, is a critical element of a wide range of important tokamak phenomena, including resistive wall mode (RWM) stability and feedback control, island penetration and locking, and disruptions. A model of these currents may be included within the domain of extended-MHD codes in a way that preserves the self-consistency, scalability, and implicitness of their numerical methods. Such a model of the resistive wall and non-axisymmetric coils is demonstrated using the M3D-C1 code for a variety of applications, including RWMs, perturbed non-axisymmetric equilibria, and a vertical displacement event (VDE) disruption. The calculated free-boundary equilibria, which include Spitzer resistivity, rotation, and two-fluid effects, are compared to external magnetic and internal thermal measurements for several DIII-D discharges. In calculations of the perturbed equilibria in ELM suppressed discharges, the tearing response at the top of the pedestal is found to correlate with the onset of ELM suppression. Nonlinear VDE calculations, initialized using a vertically unstable DIII-D equilibrium, resolve in both space and time the currents induced in the wall and on the plasma surface, and also the currents flowing between the plasma and the wall. The relative magnitude of these contributions and the total impulse to the wall depend on the resistive wall time, although the maximum axisymmetric force on the wall over the course of the VDE is found to be essentially independent of the wall conductivity. This research was supported by US DOE contracts DE-FG02-95ER54309, DE-FC02-04ER54698 and DE-AC52-07NA27344.

Nonlinear Magnetic Dynamics and The Switching Phase Diagrams in Spintronic Devices

NASA Astrophysics Data System (ADS)

Yan, Shu

Spin-transfer torque induced magnetic switching, by which the spin-polarized current transfers its magnetic moment to the ferromagnetic layer and changes its magnetization, holds great promise towards faster and smaller magnetic bits in data-storage applications due to the lower power consumption and better scalability. We propose an analytic approach which can be used to calculate the switching phase diagram of a nanomagnetic system in the presence of both magnetic field and spin-transfer torque in an exact fashion. This method is applied to the study of switching conditions for the uniaxial, single domain magnetic layers in different spin-transfer devices. In a spin valve with spin polarization collinear with the easy axis, we get a modified Stoner-Wohlfarth astroid which represents many of the features that have been found in experiment. It also shows a self-crossing boundary and demonstrates a region with three stable equilibria. We demonstrate that the region of stable equilibria with energy near the maximum can be reached only through a narrow bottleneck in the field space, which sets a stringent requirement for magnetic field alignment in the experiments. Switching diagrams are then calculated for the setups with magnetic field not perfectly aligned with the easy axis. In a ferromagnet-heavy-metal bilayer device with strong spin Hall effect, the in plane current becomes spin-polarized and transfers its magnetic moment to the ferromagnetic layer by diffusion. The three-dimensional asymmetric phase diagram is calculated. In the case that the external field is confined in the vertical plane defined by the direction of the current and the easy axis, the spin-transfer torque shifts the conventional in-plane (IP) equilibria within the same plane, and also creates two out-of-plane (OOP) equilibria, one of which can be stable. The threshold switching currents for IP switching and OOP switching are discussed. We also address the magnetic switching processes. Damping switching and precessional switching are two different switching types that are typically considered in recent studies. In the damping mode the switching is slow and heavily depends on the initial deviation, while in the precessional mode the accurate manipulation of the field or current pulse is required. We propose a switching scenario for a fast and reliable switching by taking advantage of the out-of-plane stable equilibrium in the SHE induced magnetic switching. The magnetization is first driven by a pulse of field and current towards the OOP equilibrium without precession. Since it is in the lower half of the unit sphere, no backwards pulse is required for a complete switching. This indicates a potentially feasible method of reliable ultra-fast magnetic control.

Quantum Nash Equilibria and Quantum Computing

NASA Astrophysics Data System (ADS)

Fellman, Philip Vos; Post, Jonathan Vos

In 2004, At the Fifth International Conference on Complex Systems, we drew attention to some remarkable findings by researchers at the Santa Fe Institute (Sato, Farmer and Akiyama, 2001) about hitherto unsuspected complexity in the Nash Equilibrium. As we progressed from these findings about heteroclinic Hamiltonians and chaotic transients hidden within the learning patterns of the simple rock-paper-scissors game to some related findings on the theory of quantum computing, one of the arguments we put forward was just as in the late 1990's a number of new Nash equilibria were discovered in simple bi-matrix games (Shubik and Quint, 1996; Von Stengel, 1997, 2000; and McLennan and Park, 1999) we would begin to see new Nash equilibria discovered as the result of quantum computation. While actual quantum computers remain rather primitive (Toibman, 2004), and the theory of quantum computation seems to be advancing perhaps a bit more slowly than originally expected, there have, nonetheless, been a number of advances in computation and some more radical advances in an allied field, quantum game theory (Huberman and Hogg, 2004) which are quite significant. In the course of this paper we will review a few of these discoveries and illustrate some of the characteristics of these new "Quantum Nash Equilibria". The full text of this research can be found at http://necsi.org/events/iccs6/viewpaper.php?id-234

Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles

NASA Astrophysics Data System (ADS)

Kraus, B. F.; Hudson, S. R.

2017-09-01

In three-dimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotational-transform and pressure gradients, as these features together produce unphysical, infinite currents. A proposed set of equilibria nullifies these currents by flattening the pressure on sufficiently wide intervals around each rational surface. Such rational surfaces exist at every scale, which characterizes the pressure profile as self-similar and thus fractal. The pressure profile is approximated numerically by considering a finite number of rational regions and analyzed mathematically by classifying the irrational numbers that support gradients into subsets. Applying these results to a given rotational-transform profile in cylindrical geometry, we find magnetic field and current density profiles compatible with the fractal pressure.

Current Issues in Evolutionary Paleontology.

ERIC Educational Resources Information Center

Scully, Erik Paul

1987-01-01

Describes some of the contributions made by the field of paleontology to theories in geology and biology. Suggests that the two best examples of modern evolutionary paleontology relate to the theory of punctuated equilibria, and the possibility that mass extinctions may be cyclic. (TW)

Recovery of time evolution of Grad-Shafranov equilibria from single-spacecraft data: Benchmarking and application to a flux transfer event

NASA Astrophysics Data System (ADS)

Hasegawa, Hiroshi; Sonnerup, Bengt U. Ã.-.; Nakamura, Takuma K. M.

2010-11-01

First results are presented of a method, developed by Sonnerup and Hasegawa (2010), for analyzing time evolution of magnetohydrostatic Grad-Shafranov (GS) equilibria, using data recorded by an observing probe as it traverses a quasi-static, two-dimensional (2D), magnetic-field/plasma structure. The method recovers spatial initial values used in the classical GS reconstruction for an interval before and after the time of actual measurements, by advancing them backward and forward in time based on a set of equations for an incompressible plasma; the consequence is generation of multiple GS maps or a movie of the 2D field structure. The method is successfully benchmarked by use of a 2D magnetohydrodynamic simulation of time-dependent magnetic reconnection, and then is applied to a flux transfer event (FTE) seen by the Cluster spacecraft at the dayside high-latitude magnetopause. The application shows that the field lines constituting the FTE flux rope were contracting toward its center as a result of modest convective flow in the region around the core of the flux rope.

A generalized energy principle for a magnetorotational instability model

NASA Astrophysics Data System (ADS)

Tassi, Emanuele; Morrison, Phil; Tronko, Natalia

2012-03-01

We study the equilibria of the Magnetorotational Instability system by using the noncanonical Hamiltonian approach [1], since it provides variational principles for equilibria that can be used to assess stability. We show that a reduced system of equations derived in [2] is an infinite-dimensional noncanonical Hamiltonian system. The noncanonical Poisson bracket is identified and shown to obey the Jacobi identity, and families of Casimir invariants are obtained. Explicit sufficient conditions for the energy stability of two classes of equilibria are identified by means of the Energy-Casimir method. Comparison between the stability conditions obtained in the two cases indicates that the presence of an equilibirum magnetic field along the direction of the ignorable coordinate does not introduce destabilizing effects. An analogy is found and physically interpreted between terms of the MRI perturbation energy and terms appearing in the energy principle stability analysis of CRMHD for tokamaks [3].[4pt] [1] P. J. Morrison, Rev. Mod. Phys., 70, 467 (1998).[0pt] [2] K. Julien and E. Knobloch, Phil. Trans. Roy. Soc., 386A,1607 (2010).[0pt] [3] R.D. Hazeltine, et. al, Phys. Fluids 28, 2466 (1985).

Kinetic study of radiation-reaction-limited particle acceleration during the relaxation of unstable force-free equilibria

DOE PAGES

Yuan, Yajie; Nalewajko, Krzysztof; Zrake, Jonathan; ...

2016-09-07

Many powerful and variable gamma-ray sources, including pulsar wind nebulae, active galactic nuclei and gamma-ray bursts, seem capable of accelerating particles to gamma-ray emitting energies efficiently over very short timescales. These are likely due to the rapid dissipation of electromagnetic energy in a highly magnetized, relativistic plasma. In order to understand the generic features of such processes, we have investigated simple models based on the relaxation of unstable force-free magnetostatic equilibria. In this work, we make the connection between the corresponding plasma dynamics and the expected radiation signal, using 2D particle-in-cell simulations that self-consistently include synchrotron radiation reactions. We focusmore » on the lowest order unstable force-free equilibrium in a 2D periodic box. We find that rapid variability, with modest apparent radiation efficiency as perceived by a fixed observer, can be produced during the evolution of the instability. The "flares" are accompanied by an increased polarization degree in the high energy band, with rapid variation in the polarization angle. Furthermore, the separation between the acceleration sites and the synchrotron radiation sites for the highest energy particles facilitates acceleration beyond the synchrotron radiation reaction limit. We also discuss the dynamical consequences of the radiation reaction, and some astrophysical applications of this model. Our current simulations with numerically tractable parameters are not yet able to reproduce the most dramatic gamma-ray flares, e.g., from the Crab Nebula. As a result, higher magnetization studies are promising and will be carried out in the future.« less

The utilization of satellite data and dynamics in understanding and predicting global weather phenomena

NASA Technical Reports Server (NTRS)

Shirer, H. N. (Editor); Dutton, J. A. (Editor)

1985-01-01

A two layer spectral quasi-geostrophic model is used to simulate the effects of topography on the equilibria, the stability, and the long term evaluation of incipient unstable waves. The flow is forced by latitudinally dependent radiational heating. The nature of the form drag instability of high index equilibria is investigated. The proximity of the equilibrium shear to a resonant value is essential for the instability, provided the equilibrium occurs at a slightly stronger shear than resonance. The properties of the steady Hadley and Rossby required for a thermally forced rotating fluid on a sphere are further explained. An objective parameterization technique is developed for general nonlinear hydrodynamical systems. The typical structure is one in which the rates of change of the dependent variables depend on homogeneous quadratic and linear forms, as well as on inhomogeneous forcing terms. Also documented is a steady, axisymmetric model of the general circulation developed as a basis for climate stability studies. The model includes the effects of heating, rotation, and internal friction, but neglects topography. Included is further research on cloud street phenomena. Orientation angles and horizontal wavelengths of boundary layer rolls and cloud streets are determined from an analysis of a truncated spectral model of three dimensional shallow moist Boussinesq convection in a shearing environment is further explained. Relatively broadly spaced roll clouds have orientations for which the Fourier component of the roll perpendicular shear is nearly zero, but the second corresponds to narrowly spaced rolls having orientations for which the Fourier coefficients of both the perpendicular and the parallel components of the shear are nearly equal.

KINETIC STUDY OF RADIATION-REACTION-LIMITED PARTICLE ACCELERATION DURING THE RELAXATION OF UNSTABLE FORCE-FREE EQUILIBRIA

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

Yuan, Yajie; Nalewajko, Krzysztof; Zrake, Jonathan

2016-09-10

Many powerful and variable gamma-ray sources, including pulsar wind nebulae, active galactic nuclei and gamma-ray bursts, seem capable of accelerating particles to gamma-ray emitting energies efficiently over very short timescales. These are likely due to the rapid dissipation of electromagnetic energy in a highly magnetized, relativistic plasma. In order to understand the generic features of such processes, we have investigated simple models based on the relaxation of unstable force-free magnetostatic equilibria. In this work, we make the connection between the corresponding plasma dynamics and the expected radiation signal, using 2D particle-in-cell simulations that self-consistently include synchrotron radiation reactions. We focusmore » on the lowest order unstable force-free equilibrium in a 2D periodic box. We find that rapid variability, with modest apparent radiation efficiency as perceived by a fixed observer, can be produced during the evolution of the instability. The “flares” are accompanied by an increased polarization degree in the high energy band, with rapid variation in the polarization angle. Furthermore, the separation between the acceleration sites and the synchrotron radiation sites for the highest energy particles facilitates acceleration beyond the synchrotron radiation reaction limit. We also discuss the dynamical consequences of the radiation reaction, and some astrophysical applications of this model. Our current simulations with numerically tractable parameters are not yet able to reproduce the most dramatic gamma-ray flares, e.g., from the Crab Nebula. Higher magnetization studies are promising and will be carried out in the future.« less

Phase transformations and phase equilibria in the Co–Sn–Ti system in the crystallization interval

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

Fartushna, Iu.; Bulanova, M.; National Technical University of Ukraine, Kiev Polytechnical Institute, Kiev

2016-12-15

The Co–Sn–Ti system was studied in the crystallization interval (below ~50 at% Sn) by the methods of Scanning Electron Microscopy, microprobe analysis, Differential Thermal Analysis, X-ray diffraction. The liquidus and solidus projections and the melting diagram were constructed. Only Co{sub 2}TiSn(τ1) ternary compound (Heusler phase-L1{sub 2}) was found in equilibria with the liquid in the concentration interval studied. Taking into account our recent data, the liquidus projection is characterized by the fields of primary crystallization of (βTi), (Co), binary-based phases Ti{sub 3}Sn, Ti{sub 2}Sn, Ti{sub 5}Sn{sub 3}, Ti{sub 6}Sn{sub 5}, Ti{sub 2}Co, TiCo, TiCo{sub 2} (c), TiCo{sub 2} (h), TiCo{submore » 3}, βCo{sub 3}Sn{sub 2}, CoSn and ternary τ1. The solidus projection is characterized by thirteen three-phase fields, which result from invariant four-phase equilibria, five are of eutectic type (E) and eight of transition type (U) and the existence of one more region Ti{sub 2}Sn{sub 3}+βCoSn{sub 3}+(Sn) in the solidus projection is discussed. - Graphical abstract: Liquidus projection of the Ti–РЎРѕ –Sn system. Fields of crystallization, isotherms and monovariant lines. - Highlights: • The Ti–Co–Sn system is first studied in the composition range up to 50% of Sn. • Liquidus and solidus projections, melting diagram and reaction scheme are constructed. • One ternary compound form in the studied temperature interval: (Co{sub 2}TiSn(τ1)).« less

SUNSPOT ROTATION AS A DRIVER OF MAJOR SOLAR ERUPTIONS IN THE NOAA ACTIVE REGION 12158

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

Vemareddy, P.; Ravindra, B.; Cheng, X., E-mail: vemareddy@iiap.res.in

We studied the development conditions of sigmoid structure under the influence of the magnetic non-potential characteristics of a rotating sunspot in the active region (AR) 12158. Vector magnetic field measurements from the Helioseismic Magnetic Imager and coronal EUV observations from the Atmospheric Imaging Assembly reveal that the erupting inverse-S sigmoid had roots at the location of the rotating sunspot. The sunspot rotates at a rate of 0°–5° h{sup −1} with increasing trend in the first half followed by a decrease. The time evolution of many non-potential parameters had a good correspondence with the sunspot rotation. The evolution of the ARmore » magnetic structure is approximated by a time series of force-free equilibria. The non-linear force-free field magnetic structure around the sunspot manifests the observed sigmoid structure. Field lines from the sunspot periphery constitute the body of the sigmoid and those from the interior overlie the sigmoid, similar to a flux rope structure. While the sunspot was rotating, two major coronal mass ejection eruptions occurred in the AR. During the first (second) event, the coronal current concentrations were enhanced (degraded), consistent with the photospheric net vertical current; however, magnetic energy was released during both cases. The analysis results suggest that the magnetic connections of the sigmoid are driven by the slow motion of sunspot rotation, which transforms to a highly twisted flux rope structure in a dynamical scenario. Exceeding the critical twist in the flux rope probably leads to the loss of equilibrium, thus triggering the onset of the two eruptions.« less

A stepped pressure profile model for internal transport barriers

NASA Astrophysics Data System (ADS)

Hole, Matthew; Hudson, Stuart; Dewar, Robert

2007-11-01

B ∇x et al We develop a multiple interface variational model, comprising multiple Taylor-relaxed plasma regions separated by ideal MHD barriers. The magnetic field in each region is Beltrami, = μ, and the pressure constant. Between these regions the pressure, field strength, and rotational transform may have step changes at the ideal barrier. A principle motivation is the development of a mathematically rigorous ideal MHD model to describe intrinsically 3D equilibria, with nonzero internal pressure, using robust KAM surfaces as the barriers. As each region is locally relaxed however, such a model may also yield reasons for existence of internal transport barriers (ITBs). Focusing on the latter, we build on Hole Nuc. Fus. 47, pp746-753, 2007, which recently studied the stability of a two-interface periodic-cylinder configuration. In this work, we perform a stability scan over pressure and for a two-interface configuration with no jump in , and compare the characteristics of stable equilibria to those of ITB's.

Untangling the Diverse Interior and Multiple Exterior Guest Interactions of a Supramolecular Host by the Simultaneous Analysis of Complementary Observables.

PubMed

Sgarlata, Carmelo; Raymond, Kenneth N

2016-07-05

The entropic and enthalpic driving forces for encapsulation versus sequential exterior guest binding to the [Ga4L6](12-) supramolecular host in solution are very different, which significantly complicates the determination of these thermodynamic parameters. The simultaneous use of complementary techniques, such as NMR, UV-vis, and isothermal titration calorimetry, enables the disentanglement of such multiple host-guest interactions. Indeed, data collected by each technique measure different components of the host-guest equilibria and together provide a complete picture of the solution thermodynamics. Unfortunately, commercially available programs do not allow for global analysis of different physical observables. We thus resorted to a novel procedure for the simultaneous refinement of multiple parameters (ΔG°, ΔH°, and ΔS°) by treating different observables through a weighted nonlinear least-squares analysis of a constrained model. The refinement procedure is discussed for the multiple binding of the Et4N(+) guest, but it is broadly applicable to the deconvolution of other intricate host-guest equilibria.

The effect of topography on the evolution of unstable disturbances in a baroclinic atmosphere

NASA Technical Reports Server (NTRS)

Clark, J. H. E.

1985-01-01

A two layer spectral quasi-geostrophic model is used to simulate the effects of topography on the equilibria, their stability, and the long term evolution of incipient unstable waves. The flow is forced by latitudinally dependent radiative heating. Dissipation is in the form of Rayleigh friction. An analytical solution is found for the propagating finite amplitude waves which result from baroclinic instability of the zonal winds when topography is absent. The appearance of this solution for wavelengths just longer than the Rossby radius of deformation and disappearance of ultra-long wavelengths is interpreted in terms of the Hopf bifurcation theory. Simple dynamic and thermodynamic criteria for the existence of periodic Rossby solutions are presented. A Floquet stability analysis shows that the waves are neutral. The nature of the form drag instability of high index equilibria is investigated. The proximity of the equilibrium shear to a resonant value is essential for the instability, provided the equilibrium occurs at a slightly stronger shear than resonance.

Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles

DOE PAGES

Kraus, B. F.; Hudson, S. R.

2017-09-29

In three-dimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotational-transform and pressure gradients, as these features together produce unphysical, infinite currents. A proposed set of equilibria nullifies these currents by flattening the pressure on sufficiently wide intervals around each rational surface. Such rational surfaces exist at every scale, which characterizes the pressure profile as self-similar and thus fractal. The pressure profile is approximated numerically by considering a finite number of rational regions and analyzed mathematically by classifying the irrational numbers that support gradients into subsets. As a result, applying these results to a given rotational-transform profile in cylindricalmore » geometry, we find magnetic field and current density profiles compatible with the fractal pressure.« less

Experimental confirmation of stable, small-debye-length, pure-electron-plasma equilibria in a stellarator.

PubMed

Kremer, J P; Pedersen, T Sunn; Lefrancois, R G; Marksteiner, Q

2006-09-01

The creation of the first small-Debye length, low temperature pure electron plasmas in a stellarator is reported. A confinement time of 20 ms has been measured. The long confinement time implies the existence of macroscopically stable equilibria and that the single particle orbits are well confined despite the lack of quasisymmetry in the device, the Columbia non-neutral torus. This confirms the beneficial confinement effects of strong electric fields and the resulting rapid E x B rotation of the electrons. The particle confinement time is presently limited by the presence of bulk insulating materials in the plasma, rather than any intrinsic plasma transport processes. A nearly flat temperature profile is seen in the inner part of the plasma.

Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles

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

Kraus, B. F.; Hudson, S. R.

In three-dimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotational-transform and pressure gradients, as these features together produce unphysical, infinite currents. A proposed set of equilibria nullifies these currents by flattening the pressure on sufficiently wide intervals around each rational surface. Such rational surfaces exist at every scale, which characterizes the pressure profile as self-similar and thus fractal. The pressure profile is approximated numerically by considering a finite number of rational regions and analyzed mathematically by classifying the irrational numbers that support gradients into subsets. As a result, applying these results to a given rotational-transform profile in cylindricalmore » geometry, we find magnetic field and current density profiles compatible with the fractal pressure.« less

Use of reconstructed 3D VMEC equilibria to match effects of toroidally rotating discharges in DIII-D

DOE PAGES

Wingen, Andreas; Wilcox, Robert S.; Cianciosa, Mark R.; ...

2016-10-13

Here, a technique for tokamak equilibrium reconstructions is used for multiple DIII-D discharges, including L-mode and H-mode cases when weakly 3D fieldsmore » $$\\left(\\delta B/B\\sim {{10}^{-3}}\\right)$$ are applied. The technique couples diagnostics to the non-linear, ideal MHD equilibrium solver VMEC, using the V3FIT code, to find the most likely 3D equilibrium based on a suite of measurements. It is demonstrated that V3FIT can be used to find non-linear 3D equilibria that are consistent with experimental measurements of the plasma response to very weak 3D perturbations, as well as with 2D profile measurements. Observations at DIII-D show that plasma rotation larger than 20 krad s –1 changes the relative phase between the applied 3D fields and the measured plasma response. Discharges with low averaged rotation (10 krad s –1) and peaked rotation profiles (40 krad s –1) are reconstructed. Similarities and differences to forward modeled VMEC equilibria, which do not include rotational effects, are shown. Toroidal phase shifts of up to $${{30}^{\\circ}}$$ are found between the measured and forward modeled plasma responses at the highest values of rotation. The plasma response phases of reconstructed equilibra on the other hand match the measured ones. This is the first time V3FIT has been used to reconstruct weakly 3D tokamak equilibria.« less

Equilibria of a charged artificial satellite subject to gravitational and Lorentz torques

NASA Astrophysics Data System (ADS)

Abdel-Aziz, Yehia A.; Shoaib, Muhammad

2014-07-01

The attitude dynamics of a rigid artificial satellite subject to a gravity gradient and Lorentz torques in a circular orbit are considered. Lorentz torque is developed on the basis of the electrodynamic effects of the Lorentz force acting on the charged satellite's surface. We assume that the satellite is moving in a Low Earth Orbit in the geomagnetic field, which is considered to be a dipole. Our model of torque due to the Lorentz force is developed for an artificial satellite with a general shape, and the nonlinear differential equations of Euler are used to describe its attitude orientation. All equilibrium positions are determined and conditions for their existence are obtained. The numerical results show that the charge q and radius ρ0 of the center of charge for the satellite provide a certain type of semi-passive control for the attitude of the satellite. The technique for this kind of control would be to increase or decrease the electrostatic screening on the satellite. The results obtained confirm that the change in charge can affect the magnitude of the Lorentz torque, which can also affect control of the satellite. Moreover, the relationship between magnitude of the Lorentz torque and inclination of the orbit is investigated.

Modeling the growth and branching of plants: A simple rod-based model

NASA Astrophysics Data System (ADS)

Faruk Senan, Nur Adila; O'Reilly, Oliver M.; Tresierras, Timothy N.

A rod-based model for plant growth and branching is developed in this paper. Specifically, Euler's theory of the elastica is modified to accommodate growth and remodeling. In addition, branching is characterized using a configuration force and evolution equations are postulated for the flexural stiffness and intrinsic curvature. The theory is illustrated with examples of multiple static equilibria of a branched plant and the remodeling and tip growth of a plant stem under gravitational loading.

Stability of a Tethered Satellite Formation about the Likins-Pringle Equilibria

DTIC Science & Technology

2002-03-01

research advisor Steven G. Tragesser . I also would like to thank him for his creative ideas, great patience and a great deal of excellent advice. I am...orbital mean motion, so the spin axis maintains a nearly inertially fixed direction. Tragesser [4] has focused on a satellite ring as DeCou. Tethers...Air Force News Release, 4 July 2000. 4. Tragesser , Steven G. “Formation Flying With Tethered Spacecraft.” AIAA/AAS Astrodynamics

End-State Relative Equilibria in the Sphere-Restricted Full Three-Body Problem

NASA Astrophysics Data System (ADS)

Gabriel, Travis; Scheeres, Daniel J.

2015-05-01

The Sphere-Restricted Full Three-Body Problem studies the motion of three finite density spheres as they interact under surface and gravitational forces. When accounting for the dissipation of energy, full-body systems may achieve minimum energy states that are unatainable in the classic treatment of the N-Body Problem. This serves as a simple model for the mechanics of rubble pile asteroids, interacting grains in a protoplanetary disk, and potentially the interactions of planetary ring particles. Previous studies of this problem have been performed in the case where the three spheres are of equal size and mass, with all possible relative equilibria and their stability having been identified as a function of the total angular momentum of the system. These studies uncovered that at certain levels of angular momentum there exists more than one stable relative equilibrium state. Thus a question of interest is which of these states a dissipative system would preferentially settle in provided some domain of initial conditions, and whether this would be a function of the dissipation parameters. Using perfectly-rigid dynamics, three-equal-sphere systems are simulated in a purpose-written C-based code to uncover these details. Results from this study are relevant to the mechanics and dynamics in small solar system bodies where relative forces are not great enough to compromise the rigidity of the constituents.

A coordinate free description of magnetohydrostatic equilibria

NASA Technical Reports Server (NTRS)

Martens, P. C. H.

1986-01-01

The question what geometrical restrictions are imposed on static magnetic fields by the magnetohydrostatic (MHS) equation is addressed. The general mathematical problem is therefore to determine the solutions of the MHS equations in the corona subject to an arbitrary normal component of the magnetic field at the boundary and arbitrary connectivity. What constraints the MHS equations impose on the geometry of the solutions, expressed in metric tensors, will be determined.

Equilibrium and Stability Properties of Low Aspect Ratio Mirror Systems: from Neutron Source Design to the Parker Spiral

NASA Astrophysics Data System (ADS)

Peterson, Ethan; Anderson, Jay; Clark, Mike; Egedal, Jan; Endrizzi, Douglass; Flanagan, Ken; Harvey, Robert; Lynn, Jacob; Milhone, Jason; Wallace, John; Waleffe, Roger; Mirnov, Vladimir; Forest, Cary

2017-10-01

Equilibrium reconstructions of rotating magnetospheres in the lab are computed using a user-friendly extended Grad-Shafranov solver written in Python and various magnetic and kinetic measurements. The stability of these equilibria are investigated using the NIMROD code with two goals: understand the onset of the classic ``wobble'' in the heliospheric current sheet and demonstrating proof-of-principle for a laboratory source of high- β turbulence. Using the same extended Grad-Shafranov solver, equilibria for an axisymmetric, non-paraxial magnetic mirror are used as a design foundation for a high-field magnetic mirror neutron source. These equilibria are numerically shown to be stable to the m=1 flute instability, with higher modes likely stabilized by FLR effects; this provides stability to gross MHD modes in an axisymmetric configuration. Numerical results of RF heating and neutral beam injection (NBI) from the GENRAY/CQL3D code suite show neutron fluxes promising for medical radioisotope production as well as materials testing. Synergistic effects between NBI and high-harmonic fast wave heating show large increases in neutron yield for a modest increase in RF power. work funded by DOE, NSF, NASA.

Interpretation of trace element and isotope features of basalts: relevance of field relations, petrology, major element data, phase equilibria, and magma chamber modeling in basalt petrogenesis

NASA Astrophysics Data System (ADS)

O'Hara, M. J.; Herzberg, C.

2002-06-01

The concentrations and ratios of the major elements determine the physical properties and the phase equilibria behavior of peridotites and basalts in response to the changing energy contents of the systems. The behavior of the trace elements and isotopic features are influenced in their turn by the phase equilibria, by the physical character of the partial melting and partial crystallization processes, and by the way in which a magma interacts with its wall rocks. Concentrating on the trace element and isotope contents of basalts to the exclusion of the field relations, petrology, major element data, and phase equilibria is as improvident as slaughtering the buffalo for the sake of its tongue. The crust is a cool boundary layer and a density filter, which impedes the upward transfer of hot, dense "primary" picritic and komatiitic liquids. Planetary crusts are sites of large-scale contamination and extensive partial crystallization of primitive melts striving to escape to the surface. Escape of truly unmodified primitive melts to the surface is a rare event, requiring the resolution of daunting problems in chemical and mechanical engineering. Primary status for volumetrically abundant basalts such as mid-ocean ridge basalt, ocean island basalt, and continental flood basalts is denied by their low-pressure cotectic character, first remarked upon on petrological grounds in 1928 and on experimental grounds in 1962. These basalt liquids are products of crystal-liquid separation at low pressure. Primary status for these common basalts is further denied by the phase equilibria of such compositions at elevated pressures, when the required residual mantle mineralogy (magnesian olivine and orthopyroxene) is not stable at the liquidus. It is also denied by the picritic or komatiitic nature of partial melts of candidate upper-mantle compositions at high pressures - a conclusion supported by calculation of the melt composition, which would need to be extracted in order to explain the chemical variation between fertile and residual peridotite in natural ultramafic rock suites. The subtleties of magma chamber partial crystallization processes can produce an astounding array of "pseudospidergrams," a small selection of which have been explored here. Major modification of the trace element geochemistry and trace element ratios, even those of the highly incompatible elements, must always be entertained whenever the evidence suggests the possibility of partial crystallization. At one extreme, periodically recharged, periodically tapped magma chambers might undergo partial crystallization by ˜95% consolidation of a succession of small packets of the magma. Refluxing of the 5% residual melts from such a process into the main body of melt would lead to eventual discrimination between highly incompatible elements in that residual liquid comparable with that otherwise achieved by 0.1 to 0.3% liquid extraction in equilibrium partial melting. Great caution needs to be exercised in attempting the reconstruction of more primitive compositions by addition of troctolite, gabbro, and olivine to apparently primitive lava compositions. Special attention is focussed on the phase equilibria involving olivine, plagioclase (i.e., troctolite), and liquid because a high proportion of erupted basalts carry these two phases as phenocrysts, yet the equilibria are restricted to crustal pressures and are only encountered by wide ranges of basaltic compositions at pressures less than 0.5 GPa. The mere presence of plagioclase phenocrysts may be sufficient to disqualify candidate primitive magmas. Determination of the actual contributions of crustal processes to petrogenesis requires a return to detailed field, experimental, and forensic petrologic studies of individual erupted basalt flows; of a multitude of cumulate gabbros and their contacts; and of upper-mantle outcrops.

Complex dynamics of a nonlinear voter model with contrarian agents

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

Tanabe, Shoma; Masuda, Naoki, E-mail: masuda@mist.i.u-tokyo.ac.jp

2013-12-15

We investigate mean-field dynamics of a nonlinear opinion formation model with congregator and contrarian agents. Each agent assumes one of the two possible states. Congregators imitate the state of other agents with a rate that increases with the number of other agents in the opposite state, as in the linear voter model and nonlinear majority voting models. Contrarians flip the state with a rate that increases with the number of other agents in the same state. The nonlinearity controls the strength of the majority voting and is used as a main bifurcation parameter. We show that the model undergoes amore » rich bifurcation scenario comprising the egalitarian equilibrium, two symmetric lopsided equilibria, limit cycle, and coexistence of different types of stable equilibria with intertwining attractive basins.« less

Evolutionary Thinking in Microeconomic Models: Prestige Bias and Market Bubbles

PubMed Central

Bell, Adrian Viliami

2013-01-01

Evolutionary models broadly support a number of social learning strategies likely important in economic behavior. Using a simple model of price dynamics, I show how prestige bias, or copying of famed (and likely successful) individuals, influences price equilibria and investor disposition in a way that exacerbates or creates market bubbles. I discuss how integrating the social learning and demographic forces important in cultural evolution with economic models provides a fruitful line of inquiry into real-world behavior. PMID:23544100

Current-Sheet Formation and Reconnection at a Magnetic X Line in Particle-in-Cell Simulations

NASA Technical Reports Server (NTRS)

Black, C.; Antiochos, S. K.; Hesse, M.; Karpen, J. T.; Kuznetsova, M. M.; Zenitani, S.

2011-01-01

The integration of kinetic effects into macroscopic numerical models is currently of great interest to the heliophysics community, particularly in the context of magnetic reconnection. Reconnection governs the large-scale energy release and topological rearrangement of magnetic fields in a wide variety of laboratory, heliophysical, and astrophysical systems. We are examining the formation and reconnection of current sheets in a simple, two-dimensional X-line configuration using high-resolution particle-in-cell (PIC) simulations. The initial minimum-energy, potential magnetic field is perturbed by excess thermal pressure introduced into the particle distribution function far from the X line. Subsequently, the relaxation of this added stress leads self-consistently to the development of a current sheet that reconnects for imposed stress of sufficient strength. We compare the time-dependent evolution and final state of our PIC simulations with macroscopic magnetohydrodynamic simulations assuming both uniform and localized electrical resistivities (C. R. DeVore et al., this meeting), as well as with force-free magnetic-field equilibria in which the amount of reconnection across the X line can be constrained to be zero (ideal evolution) or optimal (minimum final magnetic energy). We will discuss implications of our results for understanding magnetic-reconnection onset and cessation at kinetic scales in dynamically formed current sheets, such as those occurring in the solar corona and terrestrial magnetotail.

Liquidus Diagram of the Ba-Y-Cu-O System in the Vicinity of the Ba2YCu3O6+x Phase Field

PubMed Central

Wong-Ng, Winnie; Cook, Lawrence P.

1998-01-01

This paper describes the melting equilibria in the vicinity of the high Tc phase Ba2YCu3O6+x, including evidence for two Ba-Y-Cu-O immiscible liquids. Melting equilibria have been investigated in purified air using a combination of differential thermal analysis (DTA), thermogravimetric analysis (TGA), powder x-ray diffraction (XRD), MgO wick entrapment of liquid for analysis, scanning electron microscopy (SEM) coupled with energy dispersive x-ray analysis (EDS), and hydrogen reduction for determination of copper oxidation state. For relatively barium-rich compositions, it was necessary to prepare the starting materials under controlled atmosphere conditions using BaO. A liquidus diagram was derived from quantitative data for the melts involved in various melting reactions. In general the 1/2(Y2O3) contents of the melts participating in these equilibria were low (mole fraction <4 %). The primary phase field of Ba2YCu3O6+x occurs at a mole fraction of <2.0 % 1/2Y2O3 and lies very close along the BaO-CuOx edge, extending from a mole fraction of ≈43 % CuO to a mole fraction of ≈76 % CuO. It is divided by a liquid miscibility gap and extends on either side about this gap. The topological sequence of melting reactions associated with the liquidus is presented as a function of temperature. Implications for the growth of Ba2YCu3O6+x crystals are discussed. PMID:28009382

Adaptive Equilibrium Regulation: A Balancing Act in Two Timescales

PubMed Central

Boker, Steven M.

2015-01-01

An equilibrium involves a balancing of forces. Just as one maintains upright posture in standing or walking, many self-regulatory and interpersonal behaviors can be framed as a balancing act between an ever changing environment and within-person processes. The emerging balance between person and environment, the equilibria, are dynamic and adaptive in response to development and learning. A distinction is made between equilibrium achieved solely due to a short timescale balancing of forces and a longer timescale preferred equilibrium which we define as a state towards which the system slowly adapts. Together, these are developed into a framework that this article calls Adaptive Equilibrium Regulation (ÆR), which separates a regulatory process into two timescales: a faster regulation that automatically balances forces and a slower timescale adaptation process that reconfigures the fast regulation so as to move the system towards its preferred equilibrium when an environmental force persists over the longer timescale. This way of thinking leads to novel models for the interplay between multiple timescales of behavior, learning, and development. PMID:27066197

Properties of two-fluid flowing equilibria observed in double-pulsing coaxial helicity injection on HIST

NASA Astrophysics Data System (ADS)

Kanki, T.; Nagata, M.

2013-10-01

Multi-pulsing coaxial helicity injection (M-CHI) method which aims to achieve both quasi-steady sustainment and good confinement has been proposed as a refluxing scenario of the CHI. To explore the usefulness of the M-CHI for spherical torus (ST) configurations, the double-pulsing operations have been carried out in the HIST, verifying the flux amplification and the formation of the closed flux surfaces after the second CHI pulse. The purpose of this study is to investigate the properties of the magnetic field and plasma flow structures during the sustainment by comparing the results of plasma flow, density, and magnetic fields measurements with those of two-fluid equilibrium calculations. The two-fluid flowing equilibrium model which is described by a pair of generalized Grad-Shafranov equations for ion and electron surface variables and Bernoulli equations for density is applied to reconstruct the ST configuration with poloidal flow shear observed in the HIST. Due to the negative steep density gradient in high field side, the toroidal field has a diamagnetic profile (volume average beta, < β > = 68 %) in the central open flux column region. The ion flow velocity with strong flow shear from the separatrix in the inboard side to the core region is the opposite direction to the electron flow velocity due to the diamagentic drift through the density gradient. The electric field is relatively small in the whole region, and thus the Lorentz force nearly balances with the two-fluid effect which is particularly significant in a region with the steep density gradient due to the ion and electron diamagnetic drifts.

Magnetic barriers and their q95 dependence at DIII-D

NASA Astrophysics Data System (ADS)

Volpe, F. A.; Kessler, J.; Ali, H.; Evans, T. E.; Punjabi, A.

2012-05-01

It is well known that externally generated resonant magnetic perturbations (RMPs) can form islands in the plasma edge. In turn, large overlapping islands generate stochastic fields, which are believed to play a role in the avoidance and suppression of edge localized modes (ELMs) at DIII-D. However, large coalescing islands can also generate, in the middle of these stochastic regions, KAM surfaces effectively acting as ‘barriers’ against field-line dispersion and, indirectly, particle diffusion. It was predicted in Ali and Punjabi (2007 Plasma Phys. Control. Fusion 49 1565-82) that such magnetic barriers can form in piecewise analytic DIII-D plasma equilibria. In this work, the formation of magnetic barriers at DIII-D is corroborated by field-line tracing calculations using experimentally constrained EFIT (Lao et al 1985 Nucl. Fusion 25 1611) DIII-D equilibria perturbed to include the vacuum field from the internal coils utilized in the experiments. According to these calculations, the occurrence and location of magnetic barriers depend on the edge safety factor q95. It was thus suggested that magnetic barriers might contribute to narrowing the edge stochastic layer and play an indirect role in the RMPs failing to control ELMs for certain values of q95. The analysis of DIII-D discharges where q95 was varied, however, does not show anti-correlation between barrier formation and ELM suppression.

Asymmetric kinetic equilibria: Generalization of the BAS model for rotating magnetic profile and non-zero electric field

NASA Astrophysics Data System (ADS)

Dorville, Nicolas; Belmont, Gérard; Aunai, Nicolas; Dargent, Jérémy; Rezeau, Laurence

2015-09-01

Finding kinetic equilibria for non-collisional/collisionless tangential current layers is a key issue as well for their theoretical modeling as for our understanding of the processes that disturb them, such as tearing or Kelvin Helmholtz instabilities. The famous Harris equilibrium [E. Harris, Il Nuovo Cimento Ser. 10 23, 115-121 (1962)] assumes drifting Maxwellian distributions for ions and electrons, with constant temperatures and flow velocities; these assumptions lead to symmetric layers surrounded by vacuum. This strongly particular kind of layer is not suited for the general case: asymmetric boundaries between two media with different plasmas and different magnetic fields. The standard method for constructing more general kinetic equilibria consists in using Jeans theorem, which says that any function depending only on the Hamiltonian constants of motion is a solution to the steady Vlasov equation [P. J. Channell, Phys. Fluids (1958-1988) 19, 1541 (1976); M. Roth et al., Space Sci. Rev. 76, 251-317 (1996); and F. Mottez, Phys. Plasmas 10, 1541-1545 (2003)]. The inverse implication is however not true: when using the motion invariants as variables instead of the velocity components, the general stationary particle distributions keep on depending explicitly of the position, in addition to the implicit dependence introduced by these invariants. The standard approach therefore strongly restricts the class of solutions to the problem and probably does not select the most physically reasonable. The BAS (Belmont-Aunai-Smets) model [G. Belmont et al., Phys. Plasmas 19, 022108 (2012)] used for the first time the concept of particle accessibility to find new solutions: considering the case of a coplanar-antiparallel magnetic field configuration without electric field, asymmetric solutions could be found while the standard method can only lead to symmetric ones. These solutions were validated in a hybrid simulation [N. Aunai et al., Phys. Plasmas (1994-present) 20, 110702 (2013)], and more recently in a fully kinetic simulation as well [J. Dargent and N. Aunai, Phys. Plasmas (submitted)]. Nevertheless, in most asymmetric layers like the terrestrial magnetopause, one would indeed expect a magnetic field rotation from one direction to another without going through zero [J. Berchem and C. T. Russell, J. Geophys. Res. 87, 8139-8148 (1982)], and a non-zero normal electric field. In this paper, we propose the corresponding generalization: in the model presented, the profiles can be freely imposed for the magnetic field rotation (although restricted to a 180 rotation hitherto) and for the normal electric field. As it was done previously, the equilibrium is tested with a hybrid simulation.

An Improved Lattice Boltzmann Model for Non-Newtonian Flows with Applications to Solid-Fluid Interactions in External Flows

NASA Astrophysics Data System (ADS)

Adam, Saad; Premnath, Kannan

2016-11-01

Fluid mechanics of non-Newtonian fluids, which arise in numerous settings, are characterized by non-linear constitutive models that pose certain unique challenges for computational methods. Here, we consider the lattice Boltzmann method (LBM), which offers some computational advantages due to its kinetic basis and its simpler stream-and-collide procedure enabling efficient simulations. However, further improvements are necessary to improve its numerical stability and accuracy for computations involving broader parameter ranges. Hence, in this study, we extend the cascaded LBM formulation by modifying its moment equilibria and relaxation parameters to handle a variety of non-Newtonian constitutive equations, including power-law and Bingham fluids, with improved stability. In addition, we include corrections to the moment equilibria to obtain an inertial frame invariant scheme without cubic-velocity defects. After preforming its validation study for various benchmark flows, we study the physics of non-Newtonian flow over pairs of circular and square cylinders in a tandem arrangement, especially the wake structure interactions and their effects on resulting forces in each cylinder, and elucidate the effect of the various characteristic parameters.

Melt-gas phase equilibria and state diagrams of the selenium-tellurium system

NASA Astrophysics Data System (ADS)

Volodin, V. N.; Trebukhov, S. A.; Burabaeva, N. M.; Nitsenko, A. V.

2017-05-01

The partial pressures of saturated vapor of the components in the Se-Te system are determined and presented in the form of temperature-concentration dependences from which the boundaries of the melt-gas phase transition are calculated at atmospheric pressure and vacuums of 2000 and 100 Pa. The existence of azeotropic mixtures is revealed. It is found that the points of inseparably boiling melts correspond to 7.5 at % of Se and 995°C at 101325 Pa, 10.9 at % at 673°C and 19.5 at % at 522°C in vacuums of 2000 and 100 Pa, respectively. A complete state diagram is constructed, including the fields of gas-liquid equilibria at atmospheric and low pressures, the boundaries of which allow us to assess the behavior of selenium and tellurium upon distillation fractionation.

Phase equilibria and thermodynamic modeling of ethane and propane hydrates in porous silica gels.

PubMed

Seo, Yongwon; Lee, Seungmin; Cha, Inuk; Lee, Ju Dong; Lee, Huen

2009-04-23

In the present study, we examined the active role of porous silica gels when used as natural gas storage and transportation media. We adopted the dispersed water in silica gel pores to substantially enhance active surface for contacting and encaging gas molecules. We measured the three-phase hydrate (H)-water-rich liquid (L(W))-vapor (V) equilibria of C(2)H(6) and C(3)H(8) hydrates in 6.0, 15.0, 30.0, and 100.0 nm silica gel pores to investigate the effect of geometrical constraints on gas hydrate phase equilibria. At specified temperatures, the hydrate stability region is shifted to a higher pressure region depending on pore size when compared with those of bulk hydrates. Through application of the Gibbs-Thomson relationship to the experimental data, we determined the values for the C(2)H(6) hydrate-water and C(3)H(8) hydrate-water interfacial tensions to be 39 +/- 2 and 45 +/- 1 mJ/m(2), respectively. By using these values, the calculation values were in good agreement with the experimental ones. The overall results given in this study could also be quite useful in various fields, such as exploitation of natural gas hydrate in marine sediments and sequestration of carbon dioxide into the deep ocean.

First-Principles Monte Carlo Simulations of Reaction Equilibria in Compressed Vapors

PubMed Central

2016-01-01

Predictive modeling of reaction equilibria presents one of the grand challenges in the field of molecular simulation. Difficulties in the study of such systems arise from the need (i) to accurately model both strong, short-ranged interactions leading to the formation of chemical bonds and weak interactions arising from the environment, and (ii) to sample the range of time scales involving frequent molecular collisions, slow diffusion, and infrequent reactive events. Here we present a novel reactive first-principles Monte Carlo (RxFPMC) approach that allows for investigation of reaction equilibria without the need to prespecify a set of chemical reactions and their ideal-gas equilibrium constants. We apply RxFPMC to investigate a nitrogen/oxygen mixture at T = 3000 K and p = 30 GPa, i.e., conditions that are present in atmospheric lightning strikes and explosions. The RxFPMC simulations show that the solvation environment leads to a significantly enhanced NO concentration that reaches a maximum when oxygen is present in slight excess. In addition, the RxFPMC simulations indicate the formation of NO2 and N2O in mole fractions approaching 1%, whereas N3 and O3 are not observed. The equilibrium distributions obtained from the RxFPMC simulations agree well with those from a thermochemical computer code parametrized to experimental data. PMID:27413785

GPU.proton.DOCK: Genuine Protein Ultrafast proton equilibria consistent DOCKing.

PubMed

Kantardjiev, Alexander A

2011-07-01

GPU.proton.DOCK (Genuine Protein Ultrafast proton equilibria consistent DOCKing) is a state of the art service for in silico prediction of protein-protein interactions via rigorous and ultrafast docking code. It is unique in providing stringent account of electrostatic interactions self-consistency and proton equilibria mutual effects of docking partners. GPU.proton.DOCK is the first server offering such a crucial supplement to protein docking algorithms--a step toward more reliable and high accuracy docking results. The code (especially the Fast Fourier Transform bottleneck and electrostatic fields computation) is parallelized to run on a GPU supercomputer. The high performance will be of use for large-scale structural bioinformatics and systems biology projects, thus bridging physics of the interactions with analysis of molecular networks. We propose workflows for exploring in silico charge mutagenesis effects. Special emphasis is given to the interface-intuitive and user-friendly. The input is comprised of the atomic coordinate files in PDB format. The advanced user is provided with a special input section for addition of non-polypeptide charges, extra ionogenic groups with intrinsic pK(a) values or fixed ions. The output is comprised of docked complexes in PDB format as well as interactive visualization in a molecular viewer. GPU.proton.DOCK server can be accessed at http://gpudock.orgchm.bas.bg/.

The Price of Anarchy in Network Creation Games Is (Mostly) Constant

NASA Astrophysics Data System (ADS)

Mihalák, Matúš; Schlegel, Jan Christoph

We study the price of anarchy and the structure of equilibria in network creation games. A network creation game (first defined and studied by Fabrikant et al. [4]) is played by n players {1,2,...,n}, each identified with a vertex of a graph (network), where the strategy of player i, i = 1,...,n, is to build some edges adjacent to i. The cost of building an edge is α> 0, a fixed parameter of the game. The goal of every player is to minimize its creation cost plus its usage cost. The creation cost of player i is α times the number of built edges. In the SumGame (the original variant of Fabrikant et al. [4]) the usage cost of player i is the sum of distances from i to every node of the resulting graph. In the MaxGame (variant defined and studied by Demaine et al. [3]) the usage cost is the eccentricity of i in the resulting graph of the game. In this paper we improve previously known bounds on the price of anarchy of the game (of both variants) for various ranges of α, and give new insights into the structure of equilibria for various values of α. The two main results of the paper show that for α > 273·n all equilibria in SumGame are trees and thus the price of anarchy is constant, and that for α> 129 all equilibria in MaxGame are trees and the price of anarchy is constant. For SumGame this (almost) answers one of the basic open problems in the field - is price of anarchy of the network creation game constant for all values of α? - in an affirmative way, up to a tiny range of α.

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.

A Dynamical Analysis of a Piecewise Smooth Pest Control SI Model

NASA Astrophysics Data System (ADS)

Liu, Bing; Liu, Wanbo; Tao, Fennmei; Kang, Baolin; Cong, Jiguang

In this paper, we propose a piecewise smooth SI pest control system to model the process of spraying pesticides and releasing infectious pests. We assume that the pest population consists of susceptible pests and infectious pests, and that the disease spreads horizontally between pests. We take the susceptible pest as the control index on whether to implement chemical control and biological control strategies. Based on the theory of Filippov system, the sliding-mode domain and conditions for the existence of real equilibria, virtual equilibria, pseudo-equilibrium and boundary equilibria are given. Further, we show the global stability of real equilibria (or boundary equilibria) and pseudo-equilibrium. Our results can provide theoretical guidance for the problem of pest control.

Detection beyond Debye's length with an electrolyte-gated organic field-effect transistor.

PubMed

Palazzo, Gerardo; De Tullio, Donato; Magliulo, Maria; Mallardi, Antonia; Intranuovo, Francesca; Mulla, Mohammad Yusuf; Favia, Pietro; Vikholm-Lundin, Inger; Torsi, Luisa

2015-02-04

Electrolyte-gated organic field-effect transistors are successfully used as biosensors to detect binding events occurring at distances from the transistor electronic channel that are much larger than the Debye length in highly concentrated solutions. The sensing mechanism is mainly capacitive and is due to the formation of Donnan's equilibria within the protein layer, leading to an extra capacitance (CDON) in series to the gating system. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Tearing relaxation and the globalization of transport in field-reversed configurations

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

Steinhauer, Loren; Barnes, D. C.

2009-09-15

Tearing instability of field-reversed configurations (FRC) is investigated using the method of neighboring equilibria. It is shown that the conducting wall position in experiment lies very close to the location needed for tearing stability. This strongly suggests that vigorous but benign tearing modes, acting globally, are the engine of continual self-organization in FRCs, i.e., tearing relaxation. It also explains the ''profile consistency'' and anomalous loss rate of magnetic flux. In effect, tearing globalizes the effect of edge-driven transport.

MTDATA and the Prediction of Phase Equilibria in Oxide Systems: 30 Years of Industrial Collaboration

NASA Astrophysics Data System (ADS)

Gisby, John; Taskinen, Pekka; Pihlasalo, Jouni; Li, Zushu; Tyrer, Mark; Pearce, Jonathan; Avarmaa, Katri; Björklund, Peter; Davies, Hugh; Korpi, Mikko; Martin, Susan; Pesonen, Lauri; Robinson, Jim

2017-02-01

This paper gives an introduction to MTDATA, Phase Equilibrium Software from the National Physical Laboratory (NPL), and describes the latest advances in the development of a comprehensive database of thermodynamic parameters to underpin calculations of phase equilibria in large oxide, sulfide, and fluoride systems of industrial interest. The database, MTOX, has been developed over a period of thirty years based upon modeling work at NPL and funded by industrial partners in a project co-ordinated by Mineral Industry Research Organisation. Applications drawn from the fields of modern copper scrap smelting, high-temperature behavior of basic oxygen steelmaking slags, flash smelting of nickel, electric furnace smelting of ilmenite, and production of pure TiO2 via a low-temperature molten salt route are discussed along with calculations to assess the impact of impurities on the uncertainty of fixed points used to realize the SI unit of temperature, the kelvin.

Eutectic equilibria in the quaternary system Fe-Cr-Mn-C

NASA Technical Reports Server (NTRS)

Nowotny, H.; Wayne, S.; Schuster, J. C.

1982-01-01

The constitution of the quaternary system, Fe-Cr-Mn-C and to a lesser extent of the quinary system, Fe-Cr-Mn-Al-C were examined for in situ composite alloy candidates. Multivariant eutectic compositions were determined from phase equilibria studies wherein M7C3 carbides (approximately 30% by volume) formed from the melt within gamma iron. An extended field of the hexagonal carbide, (Cr, Fe, Mn)7 C3, was found without undergoing transformation to the orthorhombic structure. Increasing stability for this carbide was found for higher ratios of Cr/Fe(+) Cr + Mn. Aluminum additions promoted a ferritic matrix while manganese favored the desired gamma austenitic matrix. In coexistence with the matrix phase, chromium enters preferentially the carbide phase while manganese distributes equally between the gamma matrix and the M7C3 carbide. The composition and lattice parameters of the carbide and matrix phases were determined to establish their respective stabilities.

Rotation and neoclassical ripple transport in ITER

DOE PAGES

Paul, Elizabeth Joy; Landreman, Matt; Poli, Francesca M.; ...

2017-07-13

Neoclassical transport in the presence of non-axisymmetric magnetic fields causes a toroidal torque known as neoclassical toroidal viscosity (NTV). The toroidal symmetry of ITER will be broken by the finite number of toroidal field coils and by test blanket modules (TBMs). The addition of ferritic inserts (FIs) will decrease the magnitude of the toroidal field ripple. 3D magnetic equilibria in the presence of toroidal field ripple and ferromagnetic structures are calculated for an ITER steady-state scenario using the Variational Moments Equilibrium Code (VMEC). Furthermore, neoclassical transport quantities in the presence of these error fields are calculated using the Stellarator Fokker-Planckmore » Iterative Neoclassical Conservative Solver (SFINCS).« less

Rotation and neoclassical ripple transport in ITER

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

Paul, Elizabeth Joy; Landreman, Matt; Poli, Francesca M.

Neoclassical transport in the presence of non-axisymmetric magnetic fields causes a toroidal torque known as neoclassical toroidal viscosity (NTV). The toroidal symmetry of ITER will be broken by the finite number of toroidal field coils and by test blanket modules (TBMs). The addition of ferritic inserts (FIs) will decrease the magnitude of the toroidal field ripple. 3D magnetic equilibria in the presence of toroidal field ripple and ferromagnetic structures are calculated for an ITER steady-state scenario using the Variational Moments Equilibrium Code (VMEC). Furthermore, neoclassical transport quantities in the presence of these error fields are calculated using the Stellarator Fokker-Planckmore » Iterative Neoclassical Conservative Solver (SFINCS).« less

Local support against gravity in magnetoturbulent fluids

NASA Astrophysics Data System (ADS)

Schmidt, W.; Collins, D. C.; Kritsuk, A. G.

2013-06-01

Comparisons of the integrated thermal pressure support of gas against its gravitational potential energy lead to critical mass scales for gravitational instability such as the Jeans and the Bonnor-Ebert masses, which play an important role in the analysis of many physical systems, including the heuristics of numerical simulations. In a strict theoretical sense, however, neither the Jeans nor the Bonnor-Ebert mass is meaningful when applied locally to substructure in a self-gravitating turbulent medium. For this reason, we investigate the local support by thermal pressure, turbulence and magnetic fields against gravitational compression through an approach that is independent of these concepts. At the centre of our approach is the dynamical equation for the divergence of the velocity field. We carry out a statistical analysis of the source terms of the local compression rate (the negative time derivative of the divergence) for simulations of forced self-gravitating turbulence in periodic boxes with zero, weak and moderately strong mean magnetic fields (measured by the averages of the magnetic and thermal pressures). We also consider the amplification of the magnetic field energy by shear and by compression. Thereby, we are able to demonstrate that the support against gravity is dominated by thermal pressure fluctuations, although magnetic pressure also yields a significant contribution. The net effect of turbulence in the highly supersonic regime, however, is to enhance compression rather than supporting overdense gas even if the vorticity is very high. This is incommensurate with the support of the highly dynamical substructures in magnetoturbulent fluids being determined by local virial equilibria of volume energies without surface stresses.

Magnetosonic solitons in space plasmas: dark or bright solitons?

NASA Astrophysics Data System (ADS)

Pokhotelov, O. A.; Onishchenko, O. G.; Balikhin, M. A.; Stenflo, L.; Shukla, P. K.

2007-12-01

The nonlinear theory of large-amplitude magnetosonic (MS) waves in highβ space plasmas is revisited. It is shown that solitary waves can exist in the form of `bright' or `dark' solitons in which the magnetic field is increased or decreased relative to the background magnetic field. This depends on the shape of the equilibrium ion distribution function. The basic parameter that controls the nonlinear structure is the wave dispersion, which can be either positive or negative. A general dispersion relation for MS waves propagating perpendicularly to the external magnetic field in a plasma with an arbitrary velocity distribution function is derived.It takes into account general plasma equilibria, such as the Dory-Guest-Harris (DGH) or Kennel-Ashour-Abdalla (KA) loss-cone equilibria, as well as distributions with a power-law velocity dependence that can be modelled by κdistributions. It is shown that in a bi-Maxwellian plasma the dispersion is negative, i.e. the phase velocity decreases with an increase of the wavenumber. This means that the solitary solution in this case has the form of a `bright' soliton with the magnetic field increased. On the contrary, in some non-Maxwellian plasmas, such as those with ring-type ion distributions or DGH plasmas, the solitary solution may have the form of a magnetic hole. The results of similar investigations based on nonlinear Hall-MHD equations are reviewed. The relevance of our theoretical results to existing satellite wave observations is outlined.

Magnetosonic Solitons in Non-Maxwellian Space Plasmas

NASA Astrophysics Data System (ADS)

Pokhotelov, O. A.; Balikhin, M.; Onishchenko, O. G.

2006-12-01

The nonlinear theory of large-amplitude magnetosonic (MS) waves in high-beta space plasmas is developed. It is shown that solitary waves can exist in the form of magnetic humps and holes in which the magnetic field is increased or decreased relative to the background magnetic field. This depends on the shape of the equilibrium ion velocity distribution function. The basic parameter that controls the nonlinear structure is the wave dispersion which can be either positive or negative. A general dispersion relation for MS waves propagating perpendicularly to the external magnetic field in a plasma with an arbitrary velocity distribution function is derived. It takes into account general plasma equilibria such as the Dory-Guest-Harris or Kennel- Ashour-Abdalla loss cone equilibria, as well as distributions with a power law velocity dependence that can be modelled by kappa-distributions. It is shown that in Maxwellian and bi-Maxwellian plasmas the dispersion is negative, i.e. the phase velocity decreases with an increase of the wave number. This means that the solitary solution in this case has the form of a magnetic hump with the magnetic field increased. On the contrary, in some non-Maxwellian plasmas such as those with ring-type ion distributions or DGH plasmas, the solitary solution may have the form of a magnetic hole. The results of similar investigations based on nonlinear Hall-MHD equations are reviewed. The relevance of our theoretical results to experimental observations is outlined

Two-dimensional interpreter for field-reversed configurations

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

Steinhauer, Loren, E-mail: lstein@uw.edu

2014-08-15

An interpretive method is developed for extracting details of the fully two-dimensional (2D) “internal” structure of field-reversed configurations (FRC) from common diagnostics. The challenge is that only external and “gross” diagnostics are routinely available in FRC experiments. Inferring such critical quantities as the poloidal flux and the particle inventory has commonly relied on a theoretical construct based on a quasi-one-dimensional approximation. Such inferences sometimes differ markedly from the more accurate, fully 2D reconstructions of equilibria. An interpreter based on a fully 2D reconstruction is needed to enable realistic within-the-shot tracking of evolving equilibrium properties. Presented here is a flexible equilibriummore » reconstruction with which an extensive data base of equilibria was constructed. An automated interpreter then uses this data base as a look-up table to extract evolving properties. This tool is applied to data from the FRC facility at Tri Alpha Energy. It yields surprising results at several points, such as the inferences that the local β (plasma pressure/external magnetic pressure) of the plasma climbs well above unity and the poloidal flux loss time is somewhat longer than previously thought, both of which arise from full two-dimensionality of FRCs.« less

Phase Equilibria Diagrams Database

National Institute of Standards and Technology Data Gateway

SRD 31 NIST/ACerS Phase Equilibria Diagrams Database (PC database for purchase)   The Phase Equilibria Diagrams Database contains commentaries and more than 21,000 diagrams for non-organic systems, including those published in all 21 hard-copy volumes produced as part of the ACerS-NIST Phase Equilibria Diagrams Program (formerly titled Phase Diagrams for Ceramists): Volumes I through XIV (blue books); Annuals 91, 92, 93; High Tc Superconductors I & II; Zirconium & Zirconia Systems; and Electronic Ceramics I. Materials covered include oxides as well as non-oxide systems such as chalcogenides and pnictides, phosphates, salt systems, and mixed systems of these classes.

Computing Nash equilibria through computational intelligence methods

NASA Astrophysics Data System (ADS)

Pavlidis, N. G.; Parsopoulos, K. E.; Vrahatis, M. N.

2005-03-01

Nash equilibrium constitutes a central solution concept in game theory. The task of detecting the Nash equilibria of a finite strategic game remains a challenging problem up-to-date. This paper investigates the effectiveness of three computational intelligence techniques, namely, covariance matrix adaptation evolution strategies, particle swarm optimization, as well as, differential evolution, to compute Nash equilibria of finite strategic games, as global minima of a real-valued, nonnegative function. An issue of particular interest is to detect more than one Nash equilibria of a game. The performance of the considered computational intelligence methods on this problem is investigated using multistart and deflection.

Asymmetric kinetic equilibria: Generalization of the BAS model for rotating magnetic profile and non-zero electric field

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

Dorville, Nicolas, E-mail: nicolas.dorville@lpp.polytechnique.fr; Belmont, Gérard; Aunai, Nicolas

Finding kinetic equilibria for non-collisional/collisionless tangential current layers is a key issue as well for their theoretical modeling as for our understanding of the processes that disturb them, such as tearing or Kelvin Helmholtz instabilities. The famous Harris equilibrium [E. Harris, Il Nuovo Cimento Ser. 10 23, 115–121 (1962)] assumes drifting Maxwellian distributions for ions and electrons, with constant temperatures and flow velocities; these assumptions lead to symmetric layers surrounded by vacuum. This strongly particular kind of layer is not suited for the general case: asymmetric boundaries between two media with different plasmas and different magnetic fields. The standard methodmore » for constructing more general kinetic equilibria consists in using Jeans theorem, which says that any function depending only on the Hamiltonian constants of motion is a solution to the steady Vlasov equation [P. J. Channell, Phys. Fluids (1958–1988) 19, 1541 (1976); M. Roth et al., Space Sci. Rev. 76, 251–317 (1996); and F. Mottez, Phys. Plasmas 10, 1541–1545 (2003)]. The inverse implication is however not true: when using the motion invariants as variables instead of the velocity components, the general stationary particle distributions keep on depending explicitly of the position, in addition to the implicit dependence introduced by these invariants. The standard approach therefore strongly restricts the class of solutions to the problem and probably does not select the most physically reasonable. The BAS (Belmont-Aunai-Smets) model [G. Belmont et al., Phys. Plasmas 19, 022108 (2012)] used for the first time the concept of particle accessibility to find new solutions: considering the case of a coplanar-antiparallel magnetic field configuration without electric field, asymmetric solutions could be found while the standard method can only lead to symmetric ones. These solutions were validated in a hybrid simulation [N. Aunai et al., Phys. Plasmas (1994-present) 20, 110702 (2013)], and more recently in a fully kinetic simulation as well [J. Dargent and N. Aunai, Phys. Plasmas (submitted)]. Nevertheless, in most asymmetric layers like the terrestrial magnetopause, one would indeed expect a magnetic field rotation from one direction to another without going through zero [J. Berchem and C. T. Russell, J. Geophys. Res. 87, 8139–8148 (1982)], and a non-zero normal electric field. In this paper, we propose the corresponding generalization: in the model presented, the profiles can be freely imposed for the magnetic field rotation (although restricted to a 180 rotation hitherto) and for the normal electric field. As it was done previously, the equilibrium is tested with a hybrid simulation.« less

Recovery of evolution of Grad-Shafranov equilibria from single-spacecraft data: Benchmarking and application to a flux transfer event

NASA Astrophysics Data System (ADS)

Sonnerup, B. U.; Hasegawa, H.; Nakamura, T.

2010-12-01

Even after the advent of multi-spacecraft missions such as Cluster and THEMIS, it has been difficult to distinguish between time evolution of, and spatial variation within, a space plasma structure on the basis of in situ measurements. We present a method for analyzing time evolution of two-dimensional (2D) and magnetohydrostatic, namely Grad-Shafranov equilibria, using data recorded by an observing probe as it traverses a quasi-static, 2D magnetic-field/plasma structure. The method recovers spatial initial values used in the classical Grad-Shafranov (GS) reconstruction [Sonnerup et al., JGR, 2006] for an interval before and after the time of actual measurements, by advancing them backward and forward in time based on a set of equation for an incompressible plasma; the consequence is generation of multiple GS maps or a movie of the 2D field structure. The method is successfully benchmarked by use of a 2D magnetohydrodynamic simulation of time-dependent magnetic reconnection, and then is applied to a magnetic flux transfer event (FTE) seen by Cluster at the dayside high-latitude magnetopause, which has been analyzed with the GS method [Hasegawa et al., Ann. Geophys., 2006]. The application shows that the field lines constituting the FTE flux rope were contracting toward its center as a result of modest convective flow in the region around the core of the flux rope.

Casimir forces from conductive silicon carbide surfaces

NASA Astrophysics Data System (ADS)

Sedighi, M.; Svetovoy, V. B.; Broer, W. H.; Palasantzas, G.

2014-05-01

Samples of conductive silicon carbide (SiC), which is a promising material due to its excellent properties for devices operating in severe environments, were characterized with the atomic force microscope for roughness, and the optical properties were measured with ellipsometry in a wide range of frequencies. The samples show significant far-infrared absorption due to concentration of charge carriers and a sharp surface phonon-polariton peak. The Casimir interaction of SiC with different materials is calculated and discussed. As a result of the infrared structure and beyond to low frequencies, the Casimir force for SiC-SiC and SiC-Au approaches very slowly the limit of ideal metals, while it saturates significantly below this limit if interaction with insulators takes place (SiC-SiO2). At short separations (<10 nm) analysis of the van der Waals force yielded Hamaker constants for SiC-SiC interactions lower but comparable to those of metals, which is of significance to adhesion and surface assembly processes. Finally, bifurcation analysis of microelectromechanical system actuation indicated that SiC can enhance the regime of stable equilibria against stiction.

Relative equilibria in quasi-homogeneous planar three body problems

NASA Astrophysics Data System (ADS)

Arredondo, John A.

2018-01-01

In this paper we find the families of relative equilibria for the three body problem in the plane, when the interaction between the bodies is given by a quasi-homogeneous potential. The number of the relative equilibria depends on the values of the masses and on the size of the system, measured by the moment of inertia.

Discovering the Thermodynamics of Simultaneous Equilibria: An Entropy Analysis Activity Involving Consecutive Equilibria

ERIC Educational Resources Information Center

Bindel, Thomas H.

2007-01-01

An activity is presented in which the thermodynamics of simultaneous, consecutive equilibria are explored. The activity is appropriate for second-year high school or AP chemistry. Students discover that a reactant-favored (entropy-diminishing or endergonic) reaction can be caused to happen if it is coupled with a product-favored reaction of…

First-principles Monte Carlo simulations of reaction equilibria in compressed vapors

DOE PAGES

Fetisov, Evgenii O.; Kuo, I-Feng William; Knight, Chris; ...

2016-06-13

Predictive modeling of reaction equilibria presents one of the grand challenges in the field of molecular simulation. Difficulties in the study of such systems arise from the need (i) to accurately model both strong, short-ranged interactions leading to the formation of chemical bonds and weak interactions arising from the environment, and (ii) to sample the range of time scales involving frequent molecular collisions, slow diffusion, and infrequent reactive events. Here we present a novel reactive first-principles Monte Carlo (RxFPMC) approach that allows for investigation of reaction equilibria without the need to prespecify a set of chemical reactions and their ideal-gasmore » equilibrium constants. We apply RxFPMC to investigate a nitrogen/oxygen mixture at T = 3000 K and p = 30 GPa, i.e., conditions that are present in atmospheric lightning strikes and explosions. The RxFPMC simulations show that the solvation environment leads to a significantly enhanced NO concentration that reaches a maximum when oxygen is present in slight excess. In addition, the RxFPMC simulations indicate the formation of NO 2 and N 2O in mole fractions approaching 1%, whereas N 3 and O 3 are not observed. Lastly, the equilibrium distributions obtained from the RxFPMC simulations agree well with those from a thermochemical computer code parametrized to experimental data.« less

First-principles Monte Carlo simulations of reaction equilibria in compressed vapors

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

Fetisov, Evgenii O.; Kuo, I-Feng William; Knight, Chris

Predictive modeling of reaction equilibria presents one of the grand challenges in the field of molecular simulation. Difficulties in the study of such systems arise from the need (i) to accurately model both strong, short-ranged interactions leading to the formation of chemical bonds and weak interactions arising from the environment, and (ii) to sample the range of time scales involving frequent molecular collisions, slow diffusion, and infrequent reactive events. Here we present a novel reactive first-principles Monte Carlo (RxFPMC) approach that allows for investigation of reaction equilibria without the need to prespecify a set of chemical reactions and their ideal-gasmore » equilibrium constants. We apply RxFPMC to investigate a nitrogen/oxygen mixture at T = 3000 K and p = 30 GPa, i.e., conditions that are present in atmospheric lightning strikes and explosions. The RxFPMC simulations show that the solvation environment leads to a significantly enhanced NO concentration that reaches a maximum when oxygen is present in slight excess. In addition, the RxFPMC simulations indicate the formation of NO 2 and N 2O in mole fractions approaching 1%, whereas N 3 and O 3 are not observed. Lastly, the equilibrium distributions obtained from the RxFPMC simulations agree well with those from a thermochemical computer code parametrized to experimental data.« less

Analysis of the interaction among rice, weeds, inorganic fertilizer, and a herbivore in a composite farming paddy ecosystem.

PubMed

Wu, Zhaohua; Wang, Yi; Zhou, Xiaoli; Zhou, Tiejun

2018-06-01

As one of the Globally Important Agricultural Heritage Systems (GIAHS), rice field composite farming is an ecological measure in rice production, which can reduce the amount of chemical fertilizers, pesticides and herbicides. This research studies the interaction among rice, weed, inorganic fertilizer and herbivore in a composite farming paddy ecosystem. We develop a differential equation model to analyze the relations and interactions among those components. Results show the existence of an equilibrium for paddy and weed extinction, one or two equilibria for rice extinction, an equilibrium for weed extinction, and an equilibrium for rice and weed coexistence. Based on the obtained stability conditions of these equilibria, measures are proposed to avoid the existence or the stability of equilibria for rice extinction. Other measures are proposed to lead to a stable equilibrium for weed extinction, which is the most desirable result in rice production. Conditions for maximizing the yield of rice are also obtained by taking the relative mortality of rice as variable. In addition, we discover the existence of Hopf bifurcation phenomenon in the system, and develop the critical value of Hopf bifurcation by taking the artificial fertilizer rate as the bifurcation parameter. Our findings provide effective guidance and insights for rice production in a composite farming paddy ecosystem. Copyright © 2018 Elsevier Inc. All rights reserved.

The Gibbs free energy of nukundamite (Cu3.38Fe0.62S4): A correction and implications for phase equilibria

USGS Publications Warehouse

Seal, R.R.; Inan, E.E.; Hemingway, B.S.

2001-01-01

The Gibbs free energy of formation of nukundamite (Cu3.38Fe0.62S4) was calculated from published experimental studies of the reaction 3.25 Cu3.38Fe0.62S4 + S2 = 11 CuS + 2 FeS2 in order to correct an erroneous expression in the published record. The correct expression describing the Gibbs free energy of formation (kJ???mol-1) of nukundamite relative to the elements and ideal S2 gas is ??fG?? nukundamite T(K) = -549.75 + 0.23242 T + 3.1284 T0.5, with an uncertainty of 0.6%. An evaluation of the phase equilibria of nukundamite with associated phases in the system Cu-Fe-S as a function of temperature and sulfur fugacity indicates that nukundamite is stable from 224 to 501??C at high sulfidation states. At its greatest extent, at 434??C, the stability field of nukundamite is only 0.4 log f(S2) units wide, which explains its rarity. Equilibria between nukundamite and bornite, which limit the stability of both phases, involve bornite compositions that deviate significantly from stoichiometric Cu5FeS4. Under equilibrium conditions in the system Cu-Fe-S, nukundamite + chalcopyrite is not a stable assemblage at any temperature.

Goldilocks and the three inorganic equilibria: how Earth's chemistry and life coevolve to be nearly in tune.

PubMed

Rickaby, R E M

2015-03-13

Life and the chemical environment are united in an inescapable feedback cycle. The periodic table of the elements essential for life has transformed over Earth's history, but, as today, evolved in tune with the elements available in abundance in the environment. The most revolutionary time in life's history was the advent and proliferation of oxygenic photosynthesis which forced the environment towards a greater degree of oxidation. Consideration of three inorganic chemical equilibria throughout this gradual oxygenation prescribes a phased release of trace metals to the environment, which appear to have coevolved with employment of these new chemicals by life. Evolution towards complexity was chemically constrained, and changes in availability of notably Fe, Zn and Cu paced the systematic development of complex organisms. Evolving life repeatedly catalysed its own chemical challenges via the unwitting release of new and initially toxic chemicals. Ultimately, the harnessing of these allowed life to advance to greater complexity, though the mechanism responsible for translating novel chemistry to heritable use remains elusive. Whether a chemical acts as a poison or a nutrient lies both in the dose and in its environmental history. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Jump conditions in transonic equilibria

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

Guazzotto, L.; Betti, R.; Jardin, S. C.

2013-04-15

In the present paper, the numerical calculation of transonic equilibria, first introduced with the FLOW code in Guazzotto et al.[Phys. Plasmas 11, 604 (2004)], is critically reviewed. In particular, the necessity and effect of imposing explicit jump conditions at the transonic discontinuity are investigated. It is found that 'standard' (low-{beta}, large aspect ratio) transonic equilibria satisfy the correct jump condition with very good approximation even if the jump condition is not explicitly imposed. On the other hand, it is also found that high-{beta}, low aspect ratio equilibria require the correct jump condition to be explicitly imposed. Various numerical approaches aremore » described to modify FLOW to include the jump condition. It is proved that the new methods converge to the correct solution even in extreme cases of very large {beta}, while they agree with the results obtained with the old implementation of FLOW in lower-{beta} equilibria.« less

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

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

Dynamics of unforced and vertically forced rocking elliptical and semi-elliptical disks

NASA Astrophysics Data System (ADS)

Wang, Xue-She; Mazzoleni, Michael J.; Mann, Brian P.

2018-03-01

This paper presents the results of an investigation on the dynamics of unforced and vertically forced rocking elliptical and semi-elliptical disks. The full equation of motion for both rocking disks is derived from first principles. For unforced behavior, Lamb's method is used to derive the linear natural frequency of both disks, and harmonic balance is used to determine their amplitude-dependent rocking frequencies. A stability analysis then reveals that the equilibria and stability of the two disks are considerably different, as the semi-elliptical disk has a super-critical pitchfork bifurcation that enables it to exhibit bistable rocking behavior. Experimental studies were conducted to verify the trends. For vertically forced behavior, numerical investigations show the disk's responses to forward and reverse frequency sweeps. Three modes of periodicity were observed for the steady state behavior. Experiments were performed to verify the frequency responses and the presence of the three rocking modes. Comparisons between the experiments and numerical investigations show good agreement.

Impurity screening behavior of the high-field side scrape-off layer in near-double-null configurations: prospect for mitigating plasma-material interactions on RF actuators and first-wall components

NASA Astrophysics Data System (ADS)

LaBombard, B.; Kuang, A. Q.; Brunner, D.; Faust, I.; Mumgaard, R.; Reinke, M. L.; Terry, J. L.; Howard, N.; Hughes, J. W.; Chilenski, M.; Lin, Y.; Marmar, E.; Rice, J. E.; Rodriguez-Fernandez, P.; Wallace, G.; Whyte, D. G.; Wolfe, S.; Wukitch, S.

2017-07-01

The impurity screening response of the high-field side (HFS) scrape-off layer (SOL) to localized nitrogen injection is investigated on Alcator C-Mod for magnetic equilibria spanning lower-single-null, double-null and upper-single-null configurations under otherwise identical plasma conditions. L-mode, EDA H-mode and I-mode discharges are investigated. HFS impurity screening is found to depend on magnetic flux balance and the direction of B  ×  \

Predominance Diagrams, a Useful Tool for the Correlation of the Precipitation-Solubility Equilibrium with Other Ionic Equilibria

ERIC Educational Resources Information Center

Pereira, Constantino Fernandez; Alcalde, Manuel; Villegas, Rosario; Vale, Jose

2007-01-01

The four types of ionic equilibria--acid-base, redox, precipitation, and complexation--have certain similarities, which has led some authors to develop a unified treatment of them. These authors have highlighted the common aspects and tried to find a systemization of the equilibria that would facilitate learning them. In this unified treatment,…

Tautomerism, Hammett σ, and QSAR

NASA Astrophysics Data System (ADS)

Martin, Yvonne Connolly

2010-06-01

A consideration of equilibrium model-based equations suggests that tautomeric equilibria do not markedly affect observed potency if the tautomer bound represents at least 50% of the compound in solution. Tautomeric equilibria can enhance or attenuate the correlation of potency with Hammett σ. Additionally, tautomeric equilibria can lead to a correlation of potency with σ even in the absence of a correlation of binding with σ.

Morse Theory and Relative Equilibria in the Planar n-Vortex Problem

NASA Astrophysics Data System (ADS)

Roberts, Gareth E.

2018-04-01

Morse theoretical ideas are applied to the study of relative equilibria in the planar n-vortex problem. For the case of positive circulations, we prove that the Morse index of a critical point of the Hamiltonian restricted to a level surface of the angular impulse is equal to the number of pairs of real eigenvalues of the corresponding relative equilibrium periodic solution. The Morse inequalities are then used to prove the instability of some families of relative equilibria in the four-vortex problem with two pairs of equal vorticities. We also show that, for positive circulations, relative equilibria cannot accumulate on the collision set.

A Parametric Study of Erupting Flux Rope Rotation: Modeling the 'Cartwheel CME' on 9 April 2008

NASA Technical Reports Server (NTRS)

Kliem, B.; Toeroek, T.; Thompson, W. T.

2012-01-01

The rotation of erupting filaments in the solar corona is addressed through a parametric simulation study of unstable, rotating flux ropes in bipolar force-free initial equilibrium. The Lorentz force due to the external shear-field component and the relaxation of tension in the twisted field are the major contributors to the rotation in this model, while reconnection with the ambient field is of minor importance, due to the field's simple structure. In the low-beta corona, the rotation is not guided by the changing orientation of the vertical field component's polarity inversion line with height. The model yields strong initial rotations which saturate in the corona and differ qualitatively from the profile of rotation vs. height obtained in a recent simulation of an eruption without preexisting flux rope. Both major mechanisms writhe the flux rope axis, converting part of the initial twist helicity, and produce rotation profiles which, to a large part, are very similar within a range of shear-twist combinations. A difference lies in the tendency of twist-driven rotation to saturate at lower heights than shear-driven rotation. For parameters characteristic of the source regions of erupting filaments and coronal mass ejections, the shear field is found to be the dominant origin of rotations in the corona and to be required if the rotation reaches angles of order 90 degrees and higher; it dominates even if the twist exceeds the threshold of the helical kink instability. The contributions by shear and twist to the total rotation can be disentangled in the analysis of observations if the rotation and rise profiles are simultaneously compared with model calculations. The resulting twist estimate allows one to judge whether the helical kink instability occurred. This is demonstrated for the erupting prominence in the "Cartwheel CME" on 9 April 2008, which has shown a rotation of approximately 115 deg. up to a height of 1.5 Solar R above the photosphere. Out of a range of initial equilibria which include strongly kink-unstable (Phi = 5 pi), weakly kink-unstable (Phi = 3.5 pi), and kink-stable (Phi = 2.5 pi) configurations, only the evolution of the weakly kink-unstable flux rope matches the observations in their entirety.

ICPP: Beltrami fields in plasmas -- H-mode boundary layers and high beta equilibria

NASA Astrophysics Data System (ADS)

Yoshida, Zensho

2000-10-01

The Beltrami fields, eigenfunctions of the curl operator, represent essential characteristics of twisted, spiral, chiral or helical structures in various vector fields. Amongst diverse applications of the theory of Beltrami fields, the present paper focuses on the self-organized states of plasmas. The Taylor relaxed state is the principal example of self-organized Beltrami fields. Suppose that a plasma is produced in an external magnetic field (harmonic field). If we do not apply any drive, the plasma will disappear and the system will relax into the harmonic magnetic field. When we drive a current and sustain the total helicity, the plasma relaxes into the Taylor state and achieves the Beltrami magnetic field. When a strong flow is implemented to a plasma, self-organized states becomes qualitatively different from the conventional relaxed stats. The two-fluid effect induces a coupling among the flow, magnetic field, electric field and the pressure, resulting in a "singular perturbation" to the MHD system. To invoke this effect, one must supply a driving force to sustain a strong flow. It is equivalent to giving an internal electric field or applying a steep gradient in pressure, because these fields are tightly coupled. In the two-fluid model, the Beltrami condition demands that the vorticity parallels the flow in both electron and ion fluids. We find that a superposition of two Beltrami magnetic fields (and also two Beltrami flows) solves the simultaneous two-fluid Beltrami conditions [1]. Despite this simple mathematical structure, the set of solutions contains field configurations that are far richer than the conventional theory. The hydrodynamic pressure of a shear flow yields a diamagnetic state that is suitable for confining a high-beta plasma. The H-mode boundary layer is an example, which is spontaneously generated by the core plasma pressure [2]. Active control of shear flow will significantly extend the scope of such self-organized states [3]. [1] S. M. Mahajan and Z. Yoshida, Phys. Rev. Lett. 81, 4863 (1998). [2] S. M. Mahajan and Z. Yoshida, Phys. Plasmas 7, 635 (2000). [3] Z. Yoshida et al., in Non-Neutral Plasma Physics III (ed. J.J. Bollinger, AIP, 1999), 397.

Phase Equilibria in the ZnO-"FeO"-SiO2 System in Reducing Atmosphere and in the ZnO-"FeO"-SiO2-"Cu2O" System in Equilibrium with Liquid Copper Metal at 1250 °C (1523 K)

NASA Astrophysics Data System (ADS)

Hidayat, Taufiq; Hayes, Peter C.; Jak, Evgueni

2018-05-01

Recent experimental studies in the ZnO-"FeO"-SiO2 system in reducing atmosphere demonstrated significant discrepancies with the current FactSage thermodynamic model developed using previous experimental data in this system in equilibrium with metallic iron and air. The present experimental study on phase equilibria in the ZnO-"FeO"-SiO2-"Cu2O" system in equilibrium with liquid copper at 1250 °C (1523 K) at low copper oxide concentrations in slag was initiated and undertaken to resolve these discrepancies. A high-temperature equilibration-rapid quenching-electron-probe X-ray microanalysis (EPMA) technique using a primary phase substrate support and closed system approach with Cu metal introduced to determine effective equilibrium oxygen partial pressure from the Cumetal/Cu2Oslag equilibria was applied to provide accurate information on the liquidus and corresponding solid compositions in the spinel, willemite, and tridymite primary phase fields. The present results confirmed the accuracy of the FactSage model, resolved discrepancies, and demonstrated significant uncertainties in the recent studies by other authors on the system in the open reducing atmosphere. The present study shows how this closed system approach can be used to obtain key thermodynamic data on phase equilibria in systems containing volatile metal species, overcoming the limitations and uncertainties encountered in conventional open gas/condensed phase equilibration with these systems. The study highlights the importance of the focus on obtaining accurate experimental data and the risks of misleading information from inadequate experimental control and analysis. The study also demonstrates that continuing in-depth critical review and analysis of the elemental reactions taking place in complex systems is an essential step in phase equilibrium research.

Evaluation of mineral-aqueous chemical equilibria of felsic reservoirs with low-medium temperature: A comparative study in Yangbajing geothermal field and Guangdong geothermal fields

NASA Astrophysics Data System (ADS)

Li, Jiexiang; Sagoe, Gideon; Yang, Guang; Lu, Guoping

2018-02-01

Classical geothermometers are useful tools for estimating reservoir temperatures of geothermal systems. However, their application to low-medium temperature reservoirs is limited because large variations of temperatures calculated by different classical geothermometers are usually observed. In order to help choose the most appropriate classical geothermometer for calculating the temperatures of low-medium temperature reservoirs, this study evaluated the mineral-aqueous equilibria of typical low-medium temperature felsic reservoirs in the Yangbajing geothermal field and Guangdong geothermal fields. The findings of this study support that reservoirs in the Guangdong geothermal fields have no direct magma influence. Also, natural reservoirs may represent the intermediate steady state before reaching full equilibrium, which rarely occurs. For the low-medium temperature geothermal systems without the influence of magma, even with seawater intrusion, the process of minerals reaching mineral-aqueous equilibrium is sequential: chlorite and chalcedony are the first, then followed by K-feldspar, kaolinite and K-mica. Chlorite may reach equilibrium at varying activity values, and the equilibrium between K-feldspar and kaolinite or K-feldspar and K-mica can fix the contents of K and Al in the solutions. Although the SiO2 and Al attain equilibrium state, albite and laumontite remain unsaturated and thus may affect low-medium temperature calculations. In this study, the chalcedony geothermometer was found to be the most suitable geothermometer for low-medium temperature reservoirs. The results of K-Mg geothermometer may be useful to complement that of the chalcedony geothermometer in low-medium temperature reservoir systems. Na-K geothermometer will give unreliable results at low-medium temperatures; and Na-K-Ca will also be unsuitable to calculate reservoir temperatures lower than 180 °C, probably caused by the chemical imbalance of laumontite.

Thermodynamic characteristics of protolytic equilibria in aqueous solutions of glycyl peptides

NASA Astrophysics Data System (ADS)

Gridchin, S. N.

2016-11-01

Protolytic equilibria in aqueous solutions of glycyl-DL-serine, glycyl-DL-threonine, and glycyl-DL-valine are investigated by means of potentiometry and calorimetry. Dissociation constants and heat effects of the above dipeptides are determined. Standard thermodynamic characteristics (p K°, Δdis G°, Δdis H°, Δdis S°) of the investigated equilibria are calculated. The obtained results are compared to corresponding data on relative compounds.

Dip coating of sol-gels

NASA Astrophysics Data System (ADS)

Schunk, P. R.; Hurd, A. J.; Brinker, C. J.

Dip coating is the primary means of depositing sol-gel films for precision optical coatings. Sols are typically multicomponent systems consisting of an inorganic phase dispersed in a solvent mixture, with each component differing in volatility and surface tension. This, together with slow coating speeds (less than 1cm/s), makes analysis of the coating process complicated; unlike most high-speed coating methods, solvent evaporation, evolving rheology, and surface tension gradients alter significantly the fluid mechanics of the deposition stage. These phenomena were studied with computer-aided predictions of the flow and species transport fields. The underlying theory involves mass, momentum, and species transport on a domain of unknown shape, with models and constitutive equations for vapor-liquid equilibria and surface tension. Due accounting is made for the unknown position of the free surface, which locates according to the capillary hydrodynamic forces and solvent loss by evaporation. Predictions of the effects of mass transfer, hydrodynamics, and surface tension gradients on final film thickness are compared with ellipsometry measurements of film thickness on a laboratory pilot coater. Although quantitative agreement is still lacking, both experiment and theory reveal that the film profile near the drying line takes on a parabolic shape.

An improved molecular dynamics algorithm to study thermodiffusion in binary hydrocarbon mixtures

NASA Astrophysics Data System (ADS)

Antoun, Sylvie; Saghir, M. Ziad; Srinivasan, Seshasai

2018-03-01

In multicomponent liquid mixtures, the diffusion flow of chemical species can be induced by temperature gradients, which leads to a separation of the constituent components. This cross effect between temperature and concentration is known as thermodiffusion or the Ludwig-Soret effect. The performance of boundary driven non-equilibrium molecular dynamics along with the enhanced heat exchange (eHEX) algorithm was studied by assessing the thermodiffusion process in n-pentane/n-decane (nC5-nC10) binary mixtures. The eHEX algorithm consists of an extended version of the HEX algorithm with an improved energy conservation property. In addition to this, the transferable potentials for phase equilibria-united atom force field were employed in all molecular dynamics (MD) simulations to precisely model the molecular interactions in the fluid. The Soret coefficients of the n-pentane/n-decane (nC5-nC10) mixture for three different compositions (at 300.15 K and 0.1 MPa) were calculated and compared with the experimental data and other MD results available in the literature. Results of our newly employed MD algorithm showed great agreement with experimental data and a better accuracy compared to other MD procedures.

Toward a Reasoned Classification of Diseases Using Physico-Chemical Based Phenotypes

PubMed Central

Schwartz, Laurent; Lafitte, Olivier; da Veiga Moreira, Jorgelindo

2018-01-01

Background: Diseases and health conditions have been classified according to anatomical site, etiological, and clinical criteria. Physico-chemical mechanisms underlying the biology of diseases, such as the flow of energy through cells and tissues, have been often overlooked in classification systems. Objective: We propose a conceptual framework toward the development of an energy-oriented classification of diseases, based on the principles of physical chemistry. Methods: A review of literature on the physical chemistry of biological interactions in a number of diseases is traced from the point of view of the fluid and solid mechanics, electricity, and chemistry. Results: We found consistent evidence in literature of decreased and/or increased physical and chemical forces intertwined with biological processes of numerous diseases, which allowed the identification of mechanical, electric and chemical phenotypes of diseases. Discussion: Biological mechanisms of diseases need to be evaluated and integrated into more comprehensive theories that should account with principles of physics and chemistry. A hypothetical model is proposed relating the natural history of diseases to mechanical stress, electric field, and chemical equilibria (ATP) changes. The present perspective toward an innovative disease classification may improve drug-repurposing strategies in the future. PMID:29541031

Simulating the Coronal Evolution of AR 11437 Using SDO/HMI Magnetograms

NASA Astrophysics Data System (ADS)

Yardley, Stephanie L.; Mackay, Duncan H.; Green, Lucie M.

2018-01-01

The coronal magnetic field evolution of AR 11437 is simulated by applying the magnetofrictional relaxation technique of Mackay et al. A sequence of photospheric line-of-sight magnetograms produced by the Solar Dynamics Observatory (SDO)/Helioseismic Magnetic Imager (HMI) is used to drive the simulation and continuously evolve the coronal magnetic field of the active region through a series of nonlinear force-free equilibria. The simulation is started during the first stages of the active region emergence so that its full evolution from emergence to decay can be simulated. A comparison of the simulation results with SDO/Atmospheric Imaging Assembly (AIA) observations show that many aspects of the active region’s observed coronal evolution are reproduced. In particular, it shows the presence of a flux rope, which forms at the same location as sheared coronal loops in the observations. The observations show that eruptions occurred on 2012 March 17 at 05:09 UT and 10:45 UT and on 2012 March 20 at 14:31 UT. The simulation reproduces the first and third eruption, with the simulated flux rope erupting roughly 1 and 10 hr before the observed ejections, respectively. A parameter study is conducted where the boundary and initial conditions are varied along with the physical effects of Ohmic diffusion, hyperdiffusion, and an additional injection of helicity. When comparing the simulations, the evolution of the magnetic field, free magnetic energy, relative helicity and flux rope eruption timings do not change significantly. This indicates that the key element in reproducing the coronal evolution of AR 11437 is the use of line-of-sight magnetograms to drive the evolution of the coronal magnetic field.

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

PubMed

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

2016-12-21

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

Chapter A6. Section 6.1. Temperature

USGS Publications Warehouse

Revised by Wilde, Franceska D.

2006-01-01

Accurate temperature measurements are required for accurate determinations of important environmental parameters such as pH, specific electrical conductance, and dissolved oxygen, and to the determination of chemical reaction rates and equilibria, biological activity, and physical fluid properties. This section of the National Field Manual (NFM) describes U.S. Geological Survey (USGS) guidance and protocols for measurement of temperature in air, ground water, and surface water and calibration of the equipment used.

Effects of the current boundary conditions at the plasma-gun gap on density in SSPX

NASA Astrophysics Data System (ADS)

Kolesnikov, Roman; Lodestro, L. L.; Meyer, W. H.

2012-10-01

The Sustained Spheromak Physics Experiment (SSPX) was a toroidal magnetic-confinement device without toroidal magnetic-field coils or a central transformer but which generated core-plasma currents by dynamo processes driven by coaxial plasma-gun injection into a flux-conserving vessel. Record electron temperatures in a spheromak (Te˜500eV) were achieved, and final results of the SSPX program were reported in [1]. Plasma density, which depended strongly on wall conditions, was an important parameter in SSPX. It was observed that density rises with Igun and that confinement improved as the density was lowered. Shortly after the last experiments, a new feature was added to the Corsica code's solver used to reconstruct SSPX equilibria. Motivated by n=0 fields observed in NIMROD simulations of SSPX, an insulating boundary condition was implemented at the plasma-gun gap. Using this option we will perform new reconstructions of SSPX equilibria and look for correlations between the location of the separatrix (which moves up the gun wall and onto the insulating gap as Igun increases) and plasma density and magnetic-flux amplification [2].[4pt] [1] H. S. McLean, APS, DPP, Dallas, TX, 2008.[0pt] [2] E. B. Hooper et al., Nucl. Fusion 47, 1064 (2007).

Optimal Equilibria and Plasma Parameter Evolutions for the Ignitor Experiment*

NASA Astrophysics Data System (ADS)

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

2011-10-01

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

Molecular equilibria and condensation sequences in carbon rich gases

NASA Technical Reports Server (NTRS)

Sharp, C. M.; Wasserburg, G. J.

1993-01-01

Chemical equilibria in stellar atmospheres have been investigated by many authors. Lattimer, Schramm, and Grossman presented calculations in both O rich and C rich environments and predicted possible presolar condensates. A recent paper by Cherchneff and Barker considered a C rich composition with PAH's included in the calculations. However, the condensation sequences of C bearing species have not been investigated in detail. In a carbon rich gas surrounding an AGB star, it is often assumed that graphite (or diamond) condenses out before TiC and SiC. However, Lattimer et al. found some conditions under which TiC condenses before graphite. We have performed molecular equilibrium calculations to establish the stability fields of C(s), TiC(s), and SiC(s) and other high temperature phases under conditions of different pressures and C/O. The preserved presolar interstellar dust grains so far discovered in meteorites are graphite, diamond, SiC, TiC, and possibly Al2O3.

High order finite volume WENO schemes for the Euler equations under gravitational fields

NASA Astrophysics Data System (ADS)

Li, Gang; Xing, Yulong

2016-07-01

Euler equations with gravitational source terms are used to model many astrophysical and atmospheric phenomena. This system admits hydrostatic balance where the flux produced by the pressure is exactly canceled by the gravitational source term, and two commonly seen equilibria are the isothermal and polytropic hydrostatic solutions. Exact preservation of these equilibria is desirable as many practical problems are small perturbations of such balance. High order finite difference weighted essentially non-oscillatory (WENO) schemes have been proposed in [22], but only for the isothermal equilibrium state. In this paper, we design high order well-balanced finite volume WENO schemes, which can preserve not only the isothermal equilibrium but also the polytropic hydrostatic balance state exactly, and maintain genuine high order accuracy for general solutions. The well-balanced property is obtained by novel source term reformulation and discretization, combined with well-balanced numerical fluxes. Extensive one- and two-dimensional simulations are performed to verify well-balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.

Design of snowflake-diverted equilibria of CFETR

NASA Astrophysics Data System (ADS)

Hang, LI; Xiang, GAO; Guoqiang, LI; Zhengping, LUO; Damao, YAO; Yong, GUO

2018-03-01

The Chinese Fusion Engineering Test Reactor (CFETR) represents the next generation of full superconducting fusion reactors in China. Recently, CFETR was redesigned with a larger size and will be operated in two phases. To reduce the heat flux on the target plate, a snowflake (SF) divertor configuration is proposed. In this paper we show that by adding two dedicated poloidal field (PF) coils, the SF configuration can be achieved in both phases. The equilibria were calculated by TEQ code for a range of self-inductances l i3. The coil currents were calculated at some fiducial points in the flattop phase. The results indicate that the PF coil system has the ability to maintain a long flattop phase in 7.5 and 10 MA inductive scenarios for the single null divertor (SND) and SF divertor configurations. The properties of the SF configuration were also analyzed. The connection length and flux expansion of the SF divertor were both increased significantly over the SND.

Theory of plasma confinement in non-axisymmetric magnetic fields.

PubMed

Helander, Per

2014-08-01

The theory of plasma confinement by non-axisymmetric magnetic fields is reviewed. Such fields are used to confine fusion plasmas in stellarators, where in contrast to tokamaks and reversed-field pinches the magnetic field generally does not possess any continuous symmetry. The discussion is focussed on magnetohydrodynamic equilibrium conditions, collisionless particle orbits, and the kinetic theory of equilbrium and transport. Each of these topics is fundamentally affected by the absence of symmetry in the magnetic field: the field lines need not trace out nested flux surfaces, the particle orbits may not be confined, and the cross-field transport can be very large. Nevertheless, by tailoring the magnetic field appropriately, well-behaved equilibria with good confinement can be constructed, potentially offering an attractive route to magnetic fusion. In this article, the mathematical apparatus to describe stellarator plasmas is developed from first principles and basic elements underlying confinement optimization are introduced.

Determination of 3D Equilibria from Flux Surface Knowledge Only

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

H.E. Mynick; N. Pomphrey

We show that the method of Christiansen and Taylor, from which complete tokamak equilibria can be determined given only knowledge of the shape of the flux surfaces, can be extended to 3-dimensional equilibria, such as those of stellarators. As for the tokamak case, the given geometric knowledge has a high degree of redundancy, so that the full equilibrium can be obtained using only a small portion of that information.

Biparametric equilibria bifurcations of the Pierce diode: A one-dimensional plasma-filled device

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

Terra, Maisa O.

2011-03-15

The equilibria bifurcations of the biparametric version of the classical Pierce diode, a one-dimensional plasma-filled device, are analyzed in detail. Our investigation reveals that this spatiotemporal model is not structurally stable in relation to a second control parameter, the ratio of the plasma ion density to the injected electron beam density. For the first time, we relate the existence of one-fluid chaotic regions with specific biparametric equilibria bifurcations, identifying the restricted regions in the parametric plane where they occur. We show that the system presents several biparametric scenarios involving codimension-two transcritical bifurcations. Finally, we provide the spatial profile of themore » stable and unstable one-fluid equilibria in order to describe their metamorphoses.« less

Corruption and economic growth with non constant labor force growth

NASA Astrophysics Data System (ADS)

Brianzoni, Serena; Campisi, Giovanni; Russo, Alberto

2018-05-01

Based on Brianzoni et al. [1] in the present work we propose an economic model regarding the relationship between corruption in public procurement and economic growth. We extend the benchmark model by introducing endogenous labor force growth, described by the logistic equation. The results of previous studies, as Del Monte and Papagni [2] and Mauro [3], show that countries are stuck in one of the two equilibria (high corruption and low economic growth or low corruption and high economic growth). Brianzoni et al. [1] prove the existence of a further steady state characterized by intermediate levels of capital per capita and corruption. Our aim is to investigate the effects of the endogenous growth around such equilibrium. Moreover, due to the high number of parameters of the model, specific attention is given to the numerical simulations which highlight new policy measures that can be adopted by the government to fight corruption.

Phase Equilibria Modeling of Coesite Eclogite from the Sulu Belt, Eastern China

NASA Astrophysics Data System (ADS)

Xia, B.; Brown, M.; Wang, L.; Wang, S.; Piccoli, P. M.

2016-12-01

Modeling of phase equilibria and tectonic processes are essential components to understand controls on P-T paths of UHPM rocks. However, diffusion at higher temperatures (> 700 °C), and issues with determination of Fe3+ in minerals and estimating H2O contents limit our ability to determine prograde, peak P and retrograde P-T data. Also, the lack of an appropriate activity-composition model for melt in basic rocks has limited the application of phase equilibria modeling to understand partial melting associated with exhumation. Here we apply phase equilibria modeling to coesite eclogite from Yangkou to assess the influence of Fe3+ and fluid during metamorphism, monitor reactions and phase relations in eclogite during deep subduction and exhumation and investigate partial melting at HP conditions. The modeling used the THERMOCALC software and the new internally consistent thermodynamic dataset for basic rocks (http://www.metamorph.geo.uni-mainz.de/thermocalc/dataset6/index.html). Here we investigate bimineralic (gt+omp+coe/qz+ru/ilm), phengite-bearing (gt+omp+phen (2 samples, <5 vol% and >5 vol%) +coe/qz+ru/ilm) and kyanite-bearing (gt+omp+phen+ky+coe/qz+ru/ilm) eclogites. Coesite in the matrix is the hallmark of the Yangkou eclogite. For each sample, we use an iterative process to estimate the H2O and O content in the bulk composition, and then calculate a P-T pseudosection. The results suggest that some prograde information (670-770 °C, > 3.0 GPa) is retained in large garnet cores in bimineralic and phengite-bearing eclogite. The peak P-T conditions are a challenge because in the field of gt+omp+coe/qz±phen+H2O at T > 750 °C and P > 3.5 GPa mode and compositional changes are small. However, isopleths of Si in phengite suggest that the peak P could have been > 5-6 GPa. Re-equilibration of garnet and omphacite compositions occurred during exhumation, yielding P-T conditions of 700-790 °C at 3.1-2.0 GPa. Amphibolite facies metamorphism occurred at 630-710 °C, 1.3-1.2 GPa. The retrograde P-T path passes through the suprasolidus field; however, the melt produced is very low (< 5 mol%). Our work provides new quantitative P-T data for UHP eclogite in the Sulu belt and contributes to further understanding of the processes that affect deeply subducted continental crust.

Mixed Nash equilibria in Eisert-Lewenstein-Wilkens (ELW) games

NASA Astrophysics Data System (ADS)

Bolonek-Lasoń, Katarzyna; Kosiński, Piotr

2017-01-01

The classification of all mixed Nash equilibria for the original ELW game is presented. It is based on the quaternionic form of the game proposed by Landsburg (Proc. Am. Math. Soc. 139 (2011), 4423; Rochester Working Paper No 524 (2006); Wiley Encyclopedia of Operations Research and Management Science (Wiley and Sons, New York, (2011)). This approach allows to reduce the problem of finding the Nash equilibria to relatively simple analysis of the extrema of certain quadratic forms.

Theory of equilibria of elastic braids with applications to DNA supercoiling

NASA Astrophysics Data System (ADS)

van der Heijden, Gert; Starostin, Eugene

2014-03-01

Motivated by supercoiling of DNA and other filamentous structures, we formulate a new theory for equilibria of 2-braids, i.e., structures formed by two elastic rods winding around each other in continuous contact and subject to a local interstrand interaction. Unlike in previous work no assumption is made on the shape of the contact curve. Rather, this shape is solved for. The theory is developed in terms of a moving frame of directors attached to one of the strands with one of the directors pointing to the position of the other strand. The constant-distance constraint is automatically satisfied by the introduction of what we call braid strains. The price we pay is that the potential energy involves arclength derivatives of these strains, thus giving rise to a second-order variational problem. The Euler-Lagrange equations for this problem give balance equations for the overall braid force and moment referred to the moving frame as well as differential equations that can be interpreted as effective constitutive relations encoding the effect that the second strand has on the first as the braid deforms under the action of end loads. Both open braid and closed braid solutions (links and knots) are computed and current applications to DNA supercoiling are discussed. Research supported by EPSRC and HFSP.

Chaos Versus Noisy Periodicity: Alternative Hypotheses for Childhood Epidemics

NASA Astrophysics Data System (ADS)

Olsen, L. F.; Schaffer, W. M.

1990-08-01

Whereas case rates for some childhood diseases (chickenpox) often vary according to an almost regular annual cycle, the incidence of more efficiently transmitted infections such as measles is more variable. Three hypotheses have been proposed to account for such fluctuations. (i) Irregular dynamics result from random shocks to systems with stable equilibria. (ii) The intrinsic dynamics correspond to biennial cycles that are subject to stochastic forcing. (iii) Aperiodic fluctuations are intrinsic to the epidemiology. Comparison of real world data and epidemiological models suggests that measles epidemics are inherently chaotic. Conversely, the extent to which chickenpox outbreaks approximate a yearly cycle depends inversely on the population size.

Generalized thermodynamics of phase equilibria in scalar active matter

NASA Astrophysics Data System (ADS)

Solon, Alexandre P.; Stenhammar, Joakim; Cates, Michael E.; Kafri, Yariv; Tailleur, Julien

2018-02-01

Motility-induced phase separation (MIPS) arises generically in fluids of self-propelled particles when interactions lead to a kinetic slowdown at high densities. Starting from a continuum description of scalar active matter akin to a generalized Cahn-Hilliard equation, we give a general prescription for the mean densities of coexisting phases in flux-free steady states that amounts, at a hydrodynamics scale, to extremizing an effective free energy. We illustrate our approach on two well-known models: self-propelled particles interacting either through a density-dependent propulsion speed or via direct pairwise forces. Our theory accounts quantitatively for their phase diagrams, providing a unified description of MIPS.

Phase equilibria of H2SO4, HNO3, and HCl hydrates and the composition of polar stratospheric clouds

NASA Technical Reports Server (NTRS)

Wooldridge, Paul J.; Zhang, Renyi; Molina, Mario J.

1995-01-01

Thermodynamic properties and phase equilibria behavior for the hydrates and coexisting pairs of hydrates of common acids which exist in the stratosphere are assembled from new laboratory measurements and standard literature data. The analysis focuses upon solid-vapor and solid-solid-vapor equilibria at temperatures around 200 K and includes new calorimetric and vapor pressure data. Calculated partial pressures versus 1/T slopes for the hydrates and coexisting hydrates agree well with experimental data where available.

Phase Equilibria of H2SO4, HNO3, and HCl Hydrates and the Composition of Polar Stratospheric Clouds

NASA Technical Reports Server (NTRS)

Wooldridge, Paul J.; Zhang, Renyi; Molina, Mario J.

1995-01-01

Thermodynamic properties and phase equilibria behavior for the hydrates and coexisting pairs of hydrates of common acids which exist in the stratosphere are assembled from new laboratory measurements and standard literature data. The analysis focuses upon solid-vapor and solid-solid-vapor equilibria at temperatures around 200 K and includes new calorimetric and vapor pressure data. Calculated partial pressures versus 1/T slopes for the hydrates and coexisting hydrates agree well with experimental data where available.

Rotating and binary relativistic stars with magnetic field

NASA Astrophysics Data System (ADS)

Markakis, Charalampos

We develop a geometrical treatment of general relativistic magnetohydrodynamics for perfectly conducting fluids in Einstein--Maxwell--Euler spacetimes. The theory is applied to describe a neutron star that is rotating or is orbiting a black hole or another neutron star. Under the hypotheses of stationarity and axisymmetry, we obtain the equations governing magnetohydrodynamic equilibria of rotating neutron stars with poloidal, toroidal or mixed magnetic fields. Under the hypothesis of an approximate helical symmetry, we obtain the first law of thermodynamics governing magnetized equilibria of double neutron star or black hole - neutron star systems in close circular orbits. The first law is written as a relation between the change in the asymptotic Noether charge deltaQ and the changes in the area and electric charge of black holes, and in the vorticity, baryon rest mass, entropy, charge and magnetic flux of the magnetofluid. In an attempt to provide a better theoretical understanding of the methods used to construct models of isolated rotating stars and corotating or irrotational binaries and their unexplained convergence properties, we analytically examine the behavior of different iterative schemes near a static solution. We find the spectrum of the linearized iteration operator and show for self-consistent field methods that iterative instability corresponds to unstable modes of this operator. On the other hand, we show that the success of iteratively stable methods is due to (quasi-)nilpotency of this operator. Finally, we examine the integrability of motion of test particles in a stationary axisymmetric gravitational field. We use a direct approach to seek nontrivial constants of motion polynomial in the momenta---in addition to energy and angular momentum about the symmetry axis. We establish the existence and uniqueness of quadratic constants and the nonexistence of quartic constants for stationary axisymmetric Newtonian potentials with equatorial symmetry and elucidate their relativistic analogues.

Overview of the SAMPL5 host–guest challenge: Are we doing better?

PubMed Central

Yin, Jian; Henriksen, Niel M.; Slochower, David R.; Shirts, Michael R.; Chiu, Michael W.; Mobley, David L.; Gilson, Michael K.

2016-01-01

The ability to computationally predict protein-small molecule binding affinities with high accuracy would accelerate drug discovery and reduce its cost by eliminating rounds of trial-and-error synthesis and experimental evaluation of candidate ligands. As academic and industrial groups work toward this capability, there is an ongoing need for datasets that can be used to rigorously test new computational methods. Although protein–ligand data are clearly important for this purpose, their size and complexity make it difficult to obtain well-converged results and to troubleshoot computational methods. Host–guest systems offer a valuable alternative class of test cases, as they exemplify noncovalent molecular recognition but are far smaller and simpler. As a consequence, host–guest systems have been part of the prior two rounds of SAMPL prediction exercises, and they also figure in the present SAMPL5 round. In addition to being blinded, and thus avoiding biases that may arise in retrospective studies, the SAMPL challenges have the merit of focusing multiple researchers on a common set of molecular systems, so that methods may be compared and ideas exchanged. The present paper provides an overview of the host–guest component of SAMPL5, which centers on three different hosts, two octa-acids and a glycoluril-based molecular clip, and two different sets of guest molecules, in aqueous solution. A range of methods were applied, including electronic structure calculations with implicit solvent models; methods that combine empirical force fields with implicit solvent models; and explicit solvent free energy simulations. The most reliable methods tend to fall in the latter class, consistent with results in prior SAMPL rounds, but the level of accuracy is still below that sought for reliable computer-aided drug design. Advances in force field accuracy, modeling of protonation equilibria, electronic structure methods, and solvent models, hold promise for future improvements. PMID:27658802

Overview of the SAMPL5 host-guest challenge: Are we doing better?

PubMed

Yin, Jian; Henriksen, Niel M; Slochower, David R; Shirts, Michael R; Chiu, Michael W; Mobley, David L; Gilson, Michael K

2017-01-01

The ability to computationally predict protein-small molecule binding affinities with high accuracy would accelerate drug discovery and reduce its cost by eliminating rounds of trial-and-error synthesis and experimental evaluation of candidate ligands. As academic and industrial groups work toward this capability, there is an ongoing need for datasets that can be used to rigorously test new computational methods. Although protein-ligand data are clearly important for this purpose, their size and complexity make it difficult to obtain well-converged results and to troubleshoot computational methods. Host-guest systems offer a valuable alternative class of test cases, as they exemplify noncovalent molecular recognition but are far smaller and simpler. As a consequence, host-guest systems have been part of the prior two rounds of SAMPL prediction exercises, and they also figure in the present SAMPL5 round. In addition to being blinded, and thus avoiding biases that may arise in retrospective studies, the SAMPL challenges have the merit of focusing multiple researchers on a common set of molecular systems, so that methods may be compared and ideas exchanged. The present paper provides an overview of the host-guest component of SAMPL5, which centers on three different hosts, two octa-acids and a glycoluril-based molecular clip, and two different sets of guest molecules, in aqueous solution. A range of methods were applied, including electronic structure calculations with implicit solvent models; methods that combine empirical force fields with implicit solvent models; and explicit solvent free energy simulations. The most reliable methods tend to fall in the latter class, consistent with results in prior SAMPL rounds, but the level of accuracy is still below that sought for reliable computer-aided drug design. Advances in force field accuracy, modeling of protonation equilibria, electronic structure methods, and solvent models, hold promise for future improvements.

Non-solenoidal Plasma Startup in the Pegasus Toroidal Experiment

NASA Astrophysics Data System (ADS)

Sontag, Aaron

2008-11-01

Non-solenoidal (NS) startup will simplify the design of future tokamaks by eliminating need for a central solenoid and is required for an ST based CTF. In Pegasus, washer-stack current sources (plasma guns) are used to initiate NS discharges via point-source DC helicity injection. Current injected parallel to the helical vacuum field can relax into a tokamak-like configuration with toroidally-averaged closed flux and tokamak-like confinement. This requires no modification of the vacuum vessel and is scalable to fusion grade systems with proper geometry. Guns in the divertor region create discharges with Ip up to 50 kA, 3 times the vacuum windup. Nonlinear 3D simulation with NIMROD shows excitation of a line-tied kink, producing poloidal flux amplification. Evidence of flux amplification includes: reversal of edge poloidal magnetic flux; Ip increase over vacuum geometric windup; plasma position subject to radial force balance; and persistence of Ip after gun shut-off. Equilibria show high edge current (li = 0.2) and elevated q (qmin> 6), allowing access to high IN (IN> 12). Guns at the outboard midplane produce Ip up to 7 times the vacuum windup with large n=1 activity when edge q passes through rational surfaces. Line averaged density up to 2x10^19 m-3 after relaxation shows an increase in particle confinement over non-relaxed cases. Maximum Ip is determined by helicity and radial force balance, tokamak stability, and Taylor relaxation. Coupling midplane gun discharges to other CD is straightforward due to Ip decay times >3 ms. Poloidal field induction has been used to create NS discharges up to 80 kA and gun plasmas with Ip of 60 kA have been ramped to over 100 kA by including OH drive. Present research is aimed at understanding the physics of this technique in order to form NS targets in excess of 200 kA and design NS startup systems for larger devices.

Magnetic field generation from shear flow in flux ropes

NASA Astrophysics Data System (ADS)

Intrator, T. P.; Sears, J.; Gao, K.; Klarenbeek, J.; Yoo, C.

2012-10-01

In the Reconnection Scaling Experiment (RSX) we have measured out of plane quadrupole magnetic field structure in situations where magnetic reconnection was minimal. This quadrupole out of plane magnetic signature has historically been presumed to be the smoking gun harbinger of reconnection. On the other hand, we showed that when flux ropes bounced instead of merging and reconnecting, this signature could evolve. This can follow from sheared fluid flows in the context of a generalized Ohms Law. We reconstruct a shear flow model from experimental data for flux ropes that have been experimentally well characterized in RSX as screw pinch equilibria, including plasma ion and electron flow, with self consistent profiles for magnetic field, pressure, and current density. The data can account for the quadrupole field structure.

A Multistep Equilibria-Redox-Complexation Demonstration to Illustrate Le Chatelier's Principle.

ERIC Educational Resources Information Center

Berger, Tomas G.; Mellon, Edward K.

1996-01-01

Describes a process that can be used to illustrate a number of chemical principles including Le Chatelier's principle, redox chemistry, equilibria versus steady state situations, and solubility of species. (JRH)

On Nash-Equilibria of Approximation-Stable Games

NASA Astrophysics Data System (ADS)

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

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

Experimental technique for studying high-temperature phase equilibria in reactive molten metal based systems

NASA Astrophysics Data System (ADS)

Ermoline, Alexandre

The general objective of this work is to develop an experimental technique for studying the high-temperature phase compositions and phase equilibria in molten metal-based binary and ternary systems, such as Zr-O-N, B-N-O, Al-O, and others. A specific material system of Zr-O-N was selected for studying and testing this technique. The information about the high-temperature phase equilibria in reactive metal-based systems is scarce and their studying is difficult because of chemical reactions occurring between samples and essentially any container materials, and causing contamination of the system. Containerless microgravity experiments for studying equilibria in molten metal-gas systems were designed to be conducted onboard of a NASA KC-135 aircraft flying parabolic trajectories. A uniaxial apparatus suitable for acoustic levitation, laser heating, and splat quenching of small samples was developed and equipped with computer-based controller and optical diagnostics. Normal-gravity tests were conducted to determine the most suitable operating parameters of the levitator by direct observations of the levitated samples, as opposed to more traditional pressure mapping of the acoustic field. The size range of samples that could be reliably heated and quenched in this setup was determined to be on the order of 1--3 mm. In microgravity experiments, small spherical specimens (1--2 mm diameter), prepared as pressed, premixed solid components, ZrO2, ZrN, and Zr powders, were acoustically levitated inside an argon-filled chamber at one atmosphere and heated by a CO2 laser. The levitating samples could be continuously laser heated for about 1 sec, resulting in local sample melting. The sample stability in the vertical direction was undisturbed by simultaneous laser heating. Oscillations of the levitating sample in the horizontal direction increased while it was heated, which eventually resulted in the movement of the sample away from its stable levitation position and the laser beam. The follow-up on-ground experiments were conducted to study phase relations in the Zr-O-N system at high-temperatures. Samples with specific compositions were laser-heated above the melt formation and naturally cooled. Recovered samples were characterized using electron microscopy, energy-dispersive spectroscopy, and x-ray diffraction. Results of these analyses combined with the interpretations of the binary Zr-O and Zr-N phase diagrams enabled us to outline the liquidus and the subsolidus equilibria for the ternary Zr-ZrO2-ZrN phase diagrams. Further research is suggested to develop the microgravity techniques for detailed characterization of high-temperature relations in the reactive, metal based systems.

An Experimental Investigation on the Static Equilibria and Dynamics of Liquid Bridges. Degree Awarded by the University of Alabama, 1997

NASA Technical Reports Server (NTRS)

Resnick, Andrew Howard

1997-01-01

A liquid bridge is a volume of liquid held between two or more solid supports. In the case of small disk supports with a sharp edge, the contact line between the bridge and the support disk will be anchored along the edge of the disk. For these cases the solid presents a geometrical singularity and the contact angle is indeterminate within a given range. This dissertation presents research conducted on liquid bridges with anchored contact lines. The three major topics covered are: determining the role of support geometry on static equilibria, liquid bridge dynamical behavior, and forces exerted by a liquid bridge on a support structure. The work was primarily experimental and conducted in a "Plateau tank" that allowed for the simulation of equivalent low-gravity conditions. The main thrust of the experimental work involved the use of a high resolution optical measurement system for imaging the dynamic zone shape, measurement of the static and dynamic contact angles and non-invasive analysis of excited surface modes. The liquid bridge was manipulated by computer controlled linear actuators which allowed precise control over the physical characteristics of the bridge. Experiments have been carried out to locate a bifurcation point along the maximum volume axisymmetric stability margin. Below the critical slenderness the bifurcation from an axisymmetric to a stable nonaxisymmetric configuration is supercritical. However, above this critical slenderness, the bifurcation is subcritical. A series of experiments analyzed the effect on axisymmetric bridge stability by using support disks of different radii, The shape behavior as transition points were approached, as well as the limiting case of a vanishing support radius was investigated. Experiments were performed to determine the resonant frequencies of axisymmetric bridges subject to lateral vibrations. Anomolous results led to a series of experiments to characterize nonlinearities present in the dynamic bridge shape. Finally, an attempt was made to experimentally measure the force exerted by the bridge on the lower support disk. This was done through use of a force balance apparatus. Particular attention was paid to the behavior of the bridge as the minimum volume stability limit was approached.

Nonlinear stability and control of gliding vehicles

NASA Astrophysics Data System (ADS)

Bhatta, Pradeep

In this thesis we use nonlinear systems analysis to study dynamics and design control solutions for vehicles subject to hydrodynamic or aerodynamic forcing. Application of energy-based methods for such vehicles is challenging due to the presence of energy-conserving lift and side forces. We study how the lift force determines the geometric structure of vehicle dynamics. A Hamiltonian formulation of the integrable phugoid-mode equations provides a Lyapunov function candidate, which is used throughout the thesis for deriving equilibrium stability results and designing stabilizing control laws. A strong motivation for our work is the emergence of underwater gliders as an important observation platform for oceanography. Underwater gliders rely on buoyancy regulation and internal mass redistribution for motion control. These vehicles are attractive because they are designed to operate autonomously and continuously for several weeks. The results presented in this thesis contribute toward the development of systematic control design procedures for extending the range of provably stable maneuvers of the underwater glider. As the first major contribution we derive conditions for nonlinear stability of longitudinal steady gliding motions using singular perturbation theory. Stability is proved using a composite Lyapunov function, composed of individual Lyapunov functions that prove stability of rotational and translational subsystem equilibria. We use the composite Lyapunov function to design control laws for stabilizing desired relative equilibria in different actuation configurations for the underwater glider. We propose an approximate trajectory tracking method for an aircraft model. Our method uses exponential stability results of controllable steady gliding motions, derived by interpreting the aircraft dynamics as an interconnected system of rotational and translational subsystems. We prove bounded position error for tracking prescribed, straight-line trajectories, and demonstrate good performance in tracking unsteady trajectories in the longitudinal plane. We present all possible relative equilibrium motions for a rigid body moving in a fluid. Motion along a circular helix is a practical relative equilibrium for an underwater glider. We present a study of how internal mass distribution and buoyancy of the underwater glider influence the size of the steady circular helix, and the effect of a vehicle bottom-heaviness parameter on its stability.

Recovery of an evolving magnetic flux rope in the solar wind: Decomposing spatial and temporal variations from single-spacecraft data

NASA Astrophysics Data System (ADS)

Hasegawa, H.; Sonnerup, B.; Hu, Q.; Nakamura, T.

2013-12-01

We present a novel single-spacecraft data analysis method for decomposing spatial and temporal variations of physical quantities at points along the path of a spacecraft in spacetime. The method is designed for use in the reconstruction of slowly evolving two-dimensional, magneto-hydrostatic structures (Grad-Shafranov equilibria) in a space plasma. It is an extension of the one developed by Sonnerup and Hasegawa [2010] and Hasegawa et al. [2010], in which it was assumed that variations in the time series of data, recorded as the structures move past the spacecraft, are all due to spatial effects. In reality, some of the observed variations are usually caused by temporal evolution of the structure during the time it moves past the observing spacecraft; the information in the data about the spatial structure is aliased by temporal effects. The purpose here is to remove this time aliasing from the reconstructed maps of field and plasma properties. Benchmark tests are performed by use of synthetic data taken by a virtual spacecraft as it traverses, at a constant velocity, a slowly growing magnetic flux rope in a two-dimensional magnetohydrodynamic simulation of magnetic reconnection. These tests show that the new method can better recover the spacetime behavior of the flux rope than does the original version, in which time aliasing effects had not been removed. An application of the new method to a solar wind flux rope, observed by the ACE spacecraft, suggests that it was evolving in a significant way during the ~17 hour interval of the traversal. References Hasegawa, H., B. U. Ö. Sonnerup, and T. K. M. Nakamura (2010), Recovery of time evolution of Grad-Shafranov equilibria from single-spacecraft data: Benchmarking and application to a flux transfer event, J. Geophys. Res., 115, A11219, doi:10.1029/2010JA015679. Sonnerup, B. U. Ö., and H. Hasegawa (2010), On slowly evolving Grad-Shafranov equilibria, J. Geophys. Res., 115, A11218, doi:10.1029/2010JA015678. Magnetic field maps recovered from (a) the aliased (original) and (b) de-aliased (new) versions of the time evolution method. Colors show the out-of-plane (z) magnetic field component, and white arrows at points along y = 0 show the transverse velocities obtained from the reconstruction. The blue diamonds in panels (b) mark the location of the ACE spacecraft.

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

Collective states in social systems with interacting learning agents

NASA Astrophysics Data System (ADS)

Semeshenko, Viktoriya; Gordon, Mirta B.; Nadal, Jean-Pierre

2008-08-01

We study the implications of social interactions and individual learning features on consumer demand in a simple market model. We consider a social system of interacting heterogeneous agents with learning abilities. Given a fixed price, agents repeatedly decide whether or not to buy a unit of a good, so as to maximize their expected utilities. This model is close to Random Field Ising Models, where the random field corresponds to the idiosyncratic willingness to pay. We show that the equilibrium reached depends on the nature of the information agents use to estimate their expected utilities. It may be different from the systems’ Nash equilibria.

Phase Equilibria of the Brine Systems Containing Strontium and Calcium Ions

NASA Astrophysics Data System (ADS)

Wang, Xia; Zhao, Kaiyu; Li, Long; Guo, Yafei; Meng, Lingzong; Deng, Tianlong

2017-12-01

It is well known that the comprehensive utilization of the Salt Lake resources successfully must be guided corresponding to the aqueous phase equilibria and phase diagrams. Researches on the phase relationships of brine systems containing calcium and strontium ions are essential to promote the development for the relative resources discovered in China at recent years. In this paper, the phase equilibria of calcium-containing systems, strontium-containing systems and calcium-strontium coexisted brine systems around the world were reviewed. The problems existed recently and new trends in future were point out.

LEPER: Library of Experimental PhasE Relations

NASA Astrophysics Data System (ADS)

Davis, F.; Gordon, S.; Mukherjee, S.; Hirschmann, M.; Ghiorso, M.

2006-12-01

The Library of Experimental PhasE Relations (LEPER) seeks to compile published experimental determinations of magmatic phase equilibria and provide those data on the web with a searchable and downloadable interface. Compiled experimental data include the conditions and durations of experiments, the bulk compositions of experimental charges, and the identity, compositions and proportions of phases observed, and, where available, estimates of experimental and analytical uncertainties. Also included are metadata such as the type of experimental device, capsule material, and method(s) of quantitative analysis. The database may be of use to practicing experimentalists as well as the wider Earth science community. Experimentalists may find the data useful for planning new experiments and will easily be able to compare their results to the full body of previous experimentnal data. Geologists may use LEPER to compare rocks sampled in the field with experiments performed on similar bulk composition or with experiments that produced similar-composition product phases. Modelers may use LEPER to parameterize partial melting of various lithologies. One motivation for compiling LEPER is for calibration of updated and revised versions of MELTS, however, it is hoped that the availability of LEPER will facilitate formulation and calibration of additional thermodynamic or empirical models of magmatic phase relations and phase equilibria, geothermometers and more. Data entry for LEPER is occuring presently: As of August, 2006, >6200 experiments have been entered, chiefly from work published between 1997 and 2005. A prototype web interface has been written and beta release on the web is anticipated in Fall, 2006. Eventually, experimentalists will be able to submit their new experimental data to the database via the web. At present, the database contains only data pertaining to the phase equilibria of silicate melts, but extension to other experimental data involving other fluids or sub-solidus phase equilibria may be contemplated. Also, the data are at present limited to natural or near-natural systems, but in the future, extension to synthetic (i.e., CMAS, etc.) systems is also possible. Each would depend in part on whether there is community demand for such databases. A trace element adjunct to LEPER is presently in planning stages.

Hermite Polynomials and the Inverse Problem for Collisionless Equilibria

NASA Astrophysics Data System (ADS)

Allanson, O.; Neukirch, T.; Troscheit, S.; Wilson, F.

2017-12-01

It is long established that Hermite polynomial expansions in either velocity or momentum space can elegantly encode the non-Maxwellian velocity-space structure of a collisionless plasma distribution function (DF). In particular, Hermite polynomials in the canonical momenta naturally arise in the consideration of the 'inverse problem in collisionless equilibria' (IPCE): "for a given macroscopic/fluid equilibrium, what are the self-consistent Vlasov-Maxwell equilibrium DFs?". This question is of particular interest for the equilibrium and stability properties of a given macroscopic configuration, e.g. a current sheet. It can be relatively straightforward to construct a formal solution to IPCE by a Hermite expansion method, but several important questions remain regarding the use of this method. We present recent work that considers the necessary conditions of non-negativity, convergence, and the existence of all moments of an equilibrium DF solution found for IPCE. We also establish meaningful analogies between the equations that link the microscopic and macrosopic descriptions of the Vlasov-Maxwell equilibrium, and those that solve the initial value problem for the heat equation. In the language of the heat equation, IPCE poses the pressure tensor as the 'present' heat distribution over an infinite domain, and the non-Maxwellian features of the DF as the 'past' distribution. We find sufficient conditions for the convergence of the Hermite series representation of the DF, and prove that the non-negativity of the DF can be dependent on the magnetisation of the plasma. For DFs that decay at least as quickly as exp(-v^2/4), we show non-negativity is guaranteed for at least a finite range of magnetisation values, as parameterised by the ratio of the Larmor radius to the gradient length scale. 1. O. Allanson, T. Neukirch, S. Troscheit & F. Wilson: From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials, Journal of Plasma Physics, 82, 905820306, 2016 2. O. Allanson, S. Troscheit & T. Neukirch: The inverse problem for collisionless plasma equilibria (invited paper for IMA Journal of Applied Mathematics, under review)

Hydrostatic Equilibria of Rotating Stars with Realistic Equation of State

NASA Astrophysics Data System (ADS)

Yasutake, Nobutoshi; Fujisawa, Kotaro; Okawa, Hirotada; Yamada, Shoichi

Stars rotate generally, but it is a non-trivial issue to obtain hydrostatic equilibria for rapidly rotating stars theoretically, especially for baroclinic cases, in which the pressure depends not only on the density, but also on the temperature and compositions. It is clear that the stellar structures with realistic equation of state are the baroclinic cases, but there are not so many studies for such equilibria. In this study, we propose two methods to obtain hydrostatic equilibria considering rotation and baroclinicity, namely the weak-solution method and the strong-solution method. The former method is based on the variational principle, which is also applied to the calculation of the inhomogeneous phases, known as the pasta structures, in crust of neutron stars. We found this method might break the balance equation locally, then introduce the strong-solution method. Note that our method is formulated in the mass coordinate, and it is hence appropriated for the stellar evolution calculations.

Multi-objective Optimization Strategies Using Adjoint Method and Game Theory in Aerodynamics

NASA Astrophysics Data System (ADS)

Tang, Zhili

2006-08-01

There are currently three different game strategies originated in economics: (1) Cooperative games (Pareto front), (2) Competitive games (Nash game) and (3) Hierarchical games (Stackelberg game). Each game achieves different equilibria with different performance, and their players play different roles in the games. Here, we introduced game concept into aerodynamic design, and combined it with adjoint method to solve multi-criteria aerodynamic optimization problems. The performance distinction of the equilibria of these three game strategies was investigated by numerical experiments. We computed Pareto front, Nash and Stackelberg equilibria of the same optimization problem with two conflicting and hierarchical targets under different parameterizations by using the deterministic optimization method. The numerical results show clearly that all the equilibria solutions are inferior to the Pareto front. Non-dominated Pareto front solutions are obtained, however the CPU cost to capture a set of solutions makes the Pareto front an expensive tool to the designer.

Dynamics of Perturbed Relative Equilibria of Point Vortices on the Sphere or Plane

NASA Astrophysics Data System (ADS)

Patrick, G. W.

2000-06-01

, and there are stable relative equilibria of four point vortices, where three identical point vortices form an equilateral triangle circling a central vortex. These relative equilibria have zero (nongeneric) momentum and form a family that extends to arbitrarily small diameters. Using the energy-momentum method, I show their shape is stable while their location on the sphere is unstable, and they move, after perturbation to nonzero momentum, on the sphere as point particles move under the influence of a magnetic monopole. In the analysis the internal and external degrees of freedom are separated and the mass of these point particles determined. In addition, two identical such relative equilibria attract one another, while opposites repel, and in energetic collisions, opposites disintegrate to vortex pairs while identicals interact by exchanging a vortex. An analogous situation also occurs for the planar system with its noncompact SE(2) symmetry.

Comparison of united-atom potentials for the simulation of vapor-liquid equilibria and interfacial properties of long-chain n-alkanes up to n-C100.

PubMed

Müller, Erich A; Mejía, Andrés

2011-11-10

Canonical ensemble molecular dynamics (MD) simulations are reported which compute both the vapor-liquid equilibrium properties (vapor pressure and liquid and vapor densities) and the interfacial properties (density profiles, interfacial tensions, entropy and enthalpy of surface formation) of four long-chained n-alkanes: n-decane (n-C(10)), n-eicosane (n-C(20)), n-hexacontane (n-C(60)), and n-decacontane (n-C(100)). Three of the most commonly employed united-atom (UA) force fields for alkanes (SKS: Smit, B.; Karaborni, S.; Siepmann, J. I. J. Chem. Phys. 1995,102, 2126-2140; J. Chem. Phys. 1998,109, 352; NERD: Nath, S. K.; Escobedo, F. A.; de Pablo, J. J. J. Chem. Phys. 1998, 108, 9905-9911; and TraPPE: Martin M. G.; Siepmann, J. I. J. Phys. Chem. B1998, 102, 2569-2577.) are critically appraised. The computed results have been compared to the available experimental data and those fitted using the square gradient theory (SGT). In the latter approach, the Lennard-Jones chain equation of state (EoS), appropriately parametrized for long hydrocarbons, is used to model the homogeneous bulk phase Helmholtz energy. The MD results for phase equilibria of n-decane and n-eicosane exhibit sensible agreement both to the experimental data and EoS correlation for all potentials tested, with the TraPPE potential showing the lowest deviations. However, as the molecular chain increases to n-hexacontane and n-decacontane, the reliability of the UA potentials decreases, showing notorious subpredictions of both saturated liquid density and vapor pressure. Based on the recommended data and EoS results for the heaviest hydrocarbons, it is possible to attest, that in this extreme, the TraPPE potential shows the lowest liquid density deviations. The low absolute values of the vapor pressure preclude the discrimination among the three UA potentials studied. On the other hand, interfacial properties are very sensitive to the type of UA potential thus allowing a differentiation of the potentials. Comparing the interfacial tension MD results to the available experimental data and SGT results, the TraPPE model exhibits the lowest deviations for all hydrocarbons.

Optimizing stellarator coil winding surfaces with Regcoil

NASA Astrophysics Data System (ADS)

Bader, Aaron; Landreman, Matt; Anderson, David; Hegna, Chris

2017-10-01

We show initial attempts at optimizing a coil winding surface using the Regcoil code [1] for selected quasi helically symmetric equilibria. We implement a generic optimization scheme which allows for variation of the winding surface to allow for improved diagnostic access and allow for flexible divertor solutions. Regcoil and similar coil-solving algorithms require a user-input winding surface, on which the coils lie. Simple winding surfaces created by uniformly expanding the plasma boundary may not be ideal. Engineering constraints on reactor design require a coil-plasma separation sufficient for the introduction of neutron shielding and a tritium generating blanket. This distance can be the limiting factor in determining reactor size. Furthermore, expanding coils in other regions, where possible, can be useful for diagnostic and maintenance access along with providing sufficient room for a divertor. We minimize a target function that includes as constraints, the minimum coil-plasma distance, the winding surface volume, and the normal magnetic field on the plasma boundary. Results are presented for two quasi-symmetric equilibria at different aspect ratios. Work supported by the US DOE under Grant DE-FG02-93ER54222.

Binary Solid-Liquid Phase Equilibria

ERIC Educational Resources Information Center

Ellison, Herbert R.

1978-01-01

Indicates some of the information that may be obtained from a binary solid-liquid phase equilibria experiment and a method to write a computer program that will plot an ideal phase diagram to which the experimental results may be compared. (Author/CP)

Phase Equilibria in the System "FeO"-CaO-SiO2-Al2O3-MgO at Different CaO/SiO2 Ratios

NASA Astrophysics Data System (ADS)

Jang, Kyoung-oh; Ma, Xiaodong; Zhu, Jinming; Xu, Haifa; Wang, Geoff; Zhao, Baojun

2017-06-01

The "FeO"-containing slags play an important role in the operation of an ironmaking blast furnace (BF), in particular the primary slags such as the system "FeO"-CaO-SiO2-Al2O3-2 mass pct MgO with CaO/SiO2 weight ratios of 1.3, 1.5, and 1.8 saturated with metallic iron. To investigate the characteristics of such a slag system and its behavior in BF, the phase equilibria and liquidus temperatures in the slag system have been experimentally determined using the high-temperature equilibration and quenching technique followed by an electron probe X-ray microanalysis (EPMA). Isotherms between 1553 K and 1603 K (1280 °C and 1330 °C) were determined in the primary phase fields of dicalcium silicate, melilite, spinel, and monoxide [(Mg,Fe2+)O]. Pseudo-ternary phase diagrams of (CaO + SiO2)-Al2O3-"FeO" with a fixed MgO concentration at 2 mass pct and at CaO/SiO2 ratios of 1.3, 1.5, and 1.8 have been discussed, respectively, simplifying the complexity of the slag system for easy understanding and applying in BF operation. It was found that the liquidus temperatures increase in melilite and spinel primary phase fields, but decrease in dicalcium silicate and monoxide primary phase fields with increasing Al2O3/(CaO + SiO2) ratio. In addition, the liquidus temperatures decrease with increasing "FeO" concentration in dicalcium silicate and melilite primary phase fields, while showing an increasing trend in the spinel and monoxide primary phase fields. The data resulted from this study can be used to improve and optimize currently available database of thermodynamic models used in FactSage.

On axisymmetric resistive magnetohydrodynamic equilibria with flow free of Pfirsch-Schlüter diffusion

NASA Astrophysics Data System (ADS)

Throumoulopoulos, G. N.; Tasso, H.

2003-06-01

The equilibrium of an axisymmetric magnetically confined plasma with anisotropic resistivity and incompressible flows parallel to the magnetic field is investigated within the framework of the magnetohydrodynamic (MHD) theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order elliptic partial differential equation for the poloidal magnetic flux function ψ along with a decoupled Bernoulli equation for the pressure identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the resistivities η∥ and η⊥ parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic resistivity and parallel flows [G. N. Throumoulopoulos and H. Tasso, J. Plasma Phys. 64, 601 (2000)] the equilibrium is compatible with nonvanishing poloidal current densities. Also, although exactly Spitzer resistivities either η∥(ψ) or η⊥(ψ) are not allowed, exact solutions with vanishing poloidal electric fields can be constructed with η∥ and η⊥ profiles compatible with roughly collisional resistivity profiles, i.e., profiles having a minimum close to the magnetic axis, taking very large values on the boundary and such that η⊥>η∥. For equilibria with vanishing flows satisfying the relation (dP/dψ)(dI2/dψ)>0, where P and I are the pressure and the poloidal current functions, the difference η⊥-η∥ for the reversed-field pinch scaling, Bp≈Bt, is nearly two times larger than that for the tokamak scaling, Bp≈0.1Bt (Bp and Bt are the poloidal and toroidal magnetic-field components). The particular resistive equilibrium solutions obtained in the present work, inherently free of—but not inconsistent with—Pfirsch-Schlüter diffusion, indicate that parallel flows might result in a reduction of the diffusion observed in magnetically confined plasmas.

A general equilibrium model of a production economy with asset markets

NASA Astrophysics Data System (ADS)

Raberto, Marco; Teglio, Andrea; Cincotti, Silvano

2006-10-01

In this paper, a general equilibrium model of a monetary production economy is presented. The model is characterized by three classes of agents: a representative firm, heterogeneous households, and the government. Two markets (i.e., a labour market and a goods market, are considered) and two assets are traded in exchange of money, namely, government bonds and equities. Households provide the labour force and decide on consumption and savings, whereas the firm provides consumption goods and demands labour. The government receives taxes from households and pays interests on debt. The Walrasian equilibrium is derived analytically. The dynamics through quantity constrained equilibria out from the Walrasian equilibrium is also studied by means of computer simulations.

Thermodynamic curvature for attractive and repulsive intermolecular forces

NASA Astrophysics Data System (ADS)

May, Helge-Otmar; Mausbach, Peter; Ruppeiner, George

2013-09-01

The thermodynamic curvature scalar R for the Lennard-Jones system is evaluated in phase space, including vapor, liquid, and solid state. We paid special attention to the investigation of R along vapor-liquid, liquid-solid, and vapor-solid equilibria. Because R is a measure of interaction strength, we traced out the line R=0 dividing the phase space into regions with effectively attractive (R<0) or repulsive (R>0) interactions. Furthermore, we analyzed the dependence of R on the strength of attraction applying a perturbation ansatz proposed by Weeks-Chandler-Anderson. Our results show clearly a transition from R>0 (for poorly repulsive interaction) to R<0 when loading attraction in the intermolecular potential.

Experiments and simulations of flux rope dynamics in a plasma

NASA Astrophysics Data System (ADS)

Intrator, Thomas; Abbate, Sara; Ryutov, Dmitri

2005-10-01

The behavior of flux ropes is a key issue in solar, space and astrophysics. For instance, magnetic fields and currents on the Sun are sheared and twisted as they store energy, experience an as yet unidentified instability, open into interplanetary space, eject the plasma trapped in them, and cause a flare. The Reconnection Scaling Experiment (RSX) provides a simple means to systematically characterize the linear and non-linear evolution of driven, dissipative, unstable plasma-current filaments. Topology evolves in three dimensions, supports multiple modes, and can bifurcate to quasi-helical equilibria. The ultimate saturation to a nonlinear force and energy balance is the link to a spectrum of relaxation processes. RSX has adjustable energy density β1 to β 1, non-negligible equilibrium plasma flows, driven steady-state scenarios, and adjustable line tying at boundaries. We will show magnetic structure of a kinking, rotating single line tied column, magnetic reconnection between two flux ropes, and pictures of three braided flux ropes. We use computed simulation movies to bridge the gap between the solar physics scales and experimental data with computational modeling. In collaboration with Ivo Furno, Tsitsi Madziwa-Nussinovm Giovanni Lapenta, Adam Light, Los Alamos National Laboratory; Sara Abbate, Torino Polytecnico; and Dmitri Ryutov, Lawrence Livermore National Laboratory.

Pedestal-to-Wall 3D Fluid Transport Simulations on DIII-D

DOE PAGES

Lore, Jeremy D.; Wolfmeister, Alexis Briesemeister; Ferraro, Nathaniel M.; ...

2017-03-30

The 3D fluid-plasma edge transport code EMC3-EIRENE is used to test several magnetic field models with and without plasma response against DIII-D experimental data for even and odd-parity n=3 magnetic field perturbations. The field models include ideal and extended MHD equilibria, and the vacuum approximation. Plasma response is required to reduce the stochasticity in the pedestal region for even-parity fields, however too much screening suppresses the measured splitting of the downstream T e profile. Odd-parity perturbations result in weak tearing and only small additional peaks in the downstream measurements. In this case plasma response is required to increase the sizemore » of the lobe structure. Finally, no single model is able to simultaneously reproduce the upstream and downstream characteristics for both odd and even-parity perturbations.« less

The Pitfalls of Precipitation Reactions.

ERIC Educational Resources Information Center

Slade, Peter W.; Rayner-Canham, Geoffrey W.

1990-01-01

Described are some of the difficulties presented in these reactions by competing equilibria that are usually ignored. Situations involving acid-base equilibria, solubility product calculations, the use of ammonia as a complexing agent, and semiquantitative comparisons of solubility product values are discussed. (CW)

Liquid-vapor phase equilibria and the thermodynamic properties of 2-methylpropanol- n-alkyl propanoate solutions

NASA Astrophysics Data System (ADS)

Suntsov, Yu. K.; Goryunov, V. A.; Chuikov, A. M.; Meshcheryakov, A. V.

2016-08-01

The boiling points of solutions of five binary systems are measured via ebulliometry in the pressure range of 2.05-103.3 kPa. Equilibrium vapor phase compositions, the values of the excess Gibbs energies, enthalpies, and entropies of solution of these systems are calculated. Patterns in the changes of phase equilibria and thermodynamic properties of solutions are established, depending on the compositions and temperatures of the systems. Liquid-vapor equilibria in the systems are described using the equations of Wilson and the NRTL (Non-Random Two-Liquid Model).

Experimental investigation of the phase equilibria in the carbon dioxide-propane-3 M MDEA system

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

Jou, F.Y.; Mather, A.E.; Otto, F.D.

1995-07-01

The treating of liquefied petroleum gas (LPG) to remove carbon dioxide and hydrogen sulfide using aqueous alkanolamine solutions is an important aspect of gas processing. One of the amines used in the natural gas industry is methyldiethanolamine (MDEA). Measurements of the phase equilibria in the carbon dioxide-propane-3 M MDEA system have been made at 25 and 40 C at pressures up to 15.5 MPa. Vapor-liquid, liquid-liquid, and vapor-liquid-liquid equilibria were determined. The vapor-liquid equilibrium data were compared with the model of Deshmukh and Mather.

Multiple Equilibria and Endogenous Cycles in a Non-Linear Harrodian Growth Model

NASA Astrophysics Data System (ADS)

Commendatore, Pasquale; Michetti, Elisabetta; Pinto, Antonio

The standard result of Harrod's growth model is that, because investors react more strongly than savers to a change in income, the long run equilibrium of the economy is unstable. We re-interpret the Harrodian instability puzzle as a local instability problem and integrate his model with a nonlinear investment function. Multiple equilibria and different types of complex behaviour emerge. Moreover, even in the presence of locally unstable equilibria, for a large set of initial conditions the time path of the economy is not diverging, providing a solution to the instability puzzle.

Emergence of scale-free characteristics in socio-ecological systems with bounded rationality

PubMed Central

Kasthurirathna, Dharshana; Piraveenan, Mahendra

2015-01-01

Socio–ecological systems are increasingly modelled by games played on complex networks. While the concept of Nash equilibrium assumes perfect rationality, in reality players display heterogeneous bounded rationality. Here we present a topological model of bounded rationality in socio-ecological systems, using the rationality parameter of the Quantal Response Equilibrium. We argue that system rationality could be measured by the average Kullback–-Leibler divergence between Nash and Quantal Response Equilibria, and that the convergence towards Nash equilibria on average corresponds to increased system rationality. Using this model, we show that when a randomly connected socio-ecological system is topologically optimised to converge towards Nash equilibria, scale-free and small world features emerge. Therefore, optimising system rationality is an evolutionary reason for the emergence of scale-free and small-world features in socio-ecological systems. Further, we show that in games where multiple equilibria are possible, the correlation between the scale-freeness of the system and the fraction of links with multiple equilibria goes through a rapid transition when the average system rationality increases. Our results explain the influence of the topological structure of socio–ecological systems in shaping their collective cognitive behaviour, and provide an explanation for the prevalence of scale-free and small-world characteristics in such systems. PMID:26065713

Emergence of scale-free characteristics in socio-ecological systems with bounded rationality.

PubMed

Kasthurirathna, Dharshana; Piraveenan, Mahendra

2015-06-11

Socio-ecological systems are increasingly modelled by games played on complex networks. While the concept of Nash equilibrium assumes perfect rationality, in reality players display heterogeneous bounded rationality. Here we present a topological model of bounded rationality in socio-ecological systems, using the rationality parameter of the Quantal Response Equilibrium. We argue that system rationality could be measured by the average Kullback--Leibler divergence between Nash and Quantal Response Equilibria, and that the convergence towards Nash equilibria on average corresponds to increased system rationality. Using this model, we show that when a randomly connected socio-ecological system is topologically optimised to converge towards Nash equilibria, scale-free and small world features emerge. Therefore, optimising system rationality is an evolutionary reason for the emergence of scale-free and small-world features in socio-ecological systems. Further, we show that in games where multiple equilibria are possible, the correlation between the scale-freeness of the system and the fraction of links with multiple equilibria goes through a rapid transition when the average system rationality increases. Our results explain the influence of the topological structure of socio-ecological systems in shaping their collective cognitive behaviour, and provide an explanation for the prevalence of scale-free and small-world characteristics in such systems.

The nucleation rate surfaces design over diagram of phase equilibria and their applications for computational chemistry

NASA Astrophysics Data System (ADS)

Anisimov, M. P.

2016-12-01

One can find in scientific literature a pretty fresh idea of the nucleation rate surfaces design over the diagrams of phase equilibria. That idea looks like profitable for the nucleation theory development and for various practical applications where predictions of theory have no high enough accuracy for today. The common thermodynamics has no real ability to predict parameters of the first order phase transition. Nucleation experiment can be provided in very local nucleation conditions even the nucleation takes place from the critical line (in two-component case) down to the absolute zero temperature limit and from zero nucleation rates at phase equilibria up to the spinodal conditions. Theory predictions have low reliability as a rule. The computational chemistry has chance to make solution of that problem easier when a set of the used axiomatic statements will adapt enough progressive assumptions [1]. Semiempirical design of the nucleation rate surfaces over diagrams of phase equilibria have a potential ability to provide a reasonable quality information on nucleation rate for each channel of nucleation. Consideration and using of the nucleation rate surface topologies to optimize synthesis of a given phase of the target material can be available when data base on nucleation rates over diagrams of phase equilibria will be created.

Phase Equilibria and Crystallography of Ceramic Oxides

PubMed Central

Wong-Ng, W.; Roth, R. S.; Vanderah, T. A.; McMurdie, H. F.

2001-01-01

Research in phase equilibria and crystallography has been a tradition in the Ceramics Division at National Bureau of Standards/National Institute of Standatrds and Technology (NBS/NIST) since the early thirties. In the early years, effort was concentrated in areas of Portland cement, ceramic glazes and glasses, instrument bearings, and battery materials. In the past 40 years, a large portion of the work was related to electronic materials, including ferroelectrics, piezoelectrics, ionic conductors, dielectrics, microwave dielectrics, and high-temperature superconductors. As a result of the phase equilibria studies, many new compounds have been discovered. Some of these discoveries have had a significant impact on US industry. Structure determinations of these new phases have often been carried out as a joint effort among NBS/NIST colleagues and also with outside collaborators using both single crystal and neutron and x-ray powder diffraction techniques. All phase equilibria diagrams were included in Phase Diagrams for Ceramists, which are collaborative publications between The American Ceramic Society (ACerS) and NBS/NIST. All x-ray powder diffraction patterns have been included in the Powder Diffraction File (PDF). This article gives a brief account of the history of the development of the phase equilibria and crystallographic research on ceramic oxides in the Ceramics Division. Represented systems, particularly electronic materials, are highlighted. PMID:27500068

Calculation of prompt loss and toroidal field ripple loss under neutral beam injection on EAST

NASA Astrophysics Data System (ADS)

Wu, Bin; Hao, Baolong; White, Roscoe; Wang, Jinfang; Zang, Qing; Han, Xiaofeng; Hu, Chundong

2017-02-01

Neutral beam injection is a major auxiliary heating method in the EAST experimental campaign. This paper gives detailed calculations of beam loss with different plasma equilibria using the guiding center code ORBIT and NUBEAM/TRANSP. Increasing plasma current can dramatically lower the beam ion prompt loss and ripple loss. Countercurrent beam injection gives a much larger prompt loss fraction than co-injection, and ripple-induced collisionless stochastic diffusion is the dominant loss channel.

Calculation of prompt loss and toroidal field ripple loss under neutral beam injection on EAST

DOE PAGES

Wu, Bin; Hao, Baolong; White, Roscoe; ...

2016-12-09

Here, neutral beam injection is a major auxiliary heating method in the EAST experimental campaign. This paper gives detailed calculations of beam loss with different plasma equilibria using the guiding center code ORBIT and NUBEAM/TRANSP. Increasing plasma current can dramatically lower the beam ion prompt loss and ripple loss. Countercurrent beam injection gives a much larger prompt loss fraction than co-injection, and ripple-induced collisionless stochastic diffusion is the dominant loss channel.

Calculation of prompt loss and toroidal field ripple loss under neutral beam injection on EAST

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

Wu, Bin; Hao, Baolong; White, Roscoe

Here, neutral beam injection is a major auxiliary heating method in the EAST experimental campaign. This paper gives detailed calculations of beam loss with different plasma equilibria using the guiding center code ORBIT and NUBEAM/TRANSP. Increasing plasma current can dramatically lower the beam ion prompt loss and ripple loss. Countercurrent beam injection gives a much larger prompt loss fraction than co-injection, and ripple-induced collisionless stochastic diffusion is the dominant loss channel.

Simulating Donnan equilibria based on the Nernst-Planck equation

NASA Astrophysics Data System (ADS)

Gimmi, Thomas; Alt-Epping, Peter

2018-07-01

Understanding ion transport through clays and clay membranes is important for many geochemical and environmental applications. Ion transport is affected by electrostatic forces exerted by charged clay surfaces. Anions are partly excluded from pore water near these surfaces, whereas cations are enriched. Such effects can be modeled by the Donnan approach. Here we introduce a new, comparatively simple way to represent Donnan equilibria in transport simulations. We include charged surfaces as immobile ions in the balance equation and calculate coupled transport of all components, including the immobile charges, with the Nernst-Planck equation. This results in an additional diffusion potential that influences ion transport, leading to Donnan ion distributions while maintaining local charge balance. The validity of our new approach was demonstrated by comparing Nernst-Planck simulations using the reactive transport code Flotran with analytical solutions available for simple Donnan systems. Attention has to be paid to the numerical evaluation of the electrochemical migration term in the Nernst-Planck equation to obtain correct results for asymmetric electrolytes. Sensitivity simulations demonstrate the influence of various Donnan model parameters on simulated anion accessible porosities. It is furthermore shown that the salt diffusion coefficient in a Donnan pore depends on local concentrations, in contrast to the aqueous salt diffusion coefficient. Our approach can be easily implemented into other transport codes. It is versatile and facilitates, for instance, assessing the implications of different activity models for the Donnan porosity.

Structural instability, multiple stable states, and hysteresis in periphyton driven by phosphorus enrichment in the Everglades

USGS Publications Warehouse

Dong, Quan; McCormick, Paul V.; Sklar, Fred H.; DeAngelis, Donald L.

2002-01-01

Periphyton is a key component of the Everglades ecosystems. It is a major primary producer, providing food and habitat for a variety of organisms, contributing material to the surface soil, and regulating water chemistry. Periphyton is sensitive to the phosphorus (P) supply and P enrichment has caused dramatic changes in the native Everglades periphyton assemblages. Periphyton also affects P availability by removing P from the water column and depositing a refractory portion into sediment. A quantitative understanding of the response of periphyton assemblages to P supply and its effects on P cycling could provide critical supports to decision making in the conservation and restoration of the Everglades. We constructed a model to examine the interaction between periphyton and P dynamics. The model contains two differential equations: P uptake and periphyton growth are assumed to follow the Monod equation and are limited by a modified logistic equation. Equilibrium and stability analyses suggest that P loading is the driving force and determines the system behavior. The position and number of steady states and the stability also depend upon the rate of sloughing, through which periphyton deposits refractory P into sediment. Multiple equilibria may exist, with two stable equilibria separated by an unstable equilibrium. Due to nonlinear interplay of periphyton and P in this model, catastrophe and hysteresis are likely to occur.

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

NASA Astrophysics Data System (ADS)

Vedartham, Padmaja B.

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

Seasonal multiphase equilibria in the atmospheres of Titan and Pluto

NASA Astrophysics Data System (ADS)

Tan, S. P.; Kargel, J. S.

2017-12-01

At the extremely low temperatures in Titan's upper troposphere and on Pluto's surface, the atmospheres as a whole are subject to freeze into solid solutions, not pure ices. The presence of the solid phases introduces conditions with rich phase equilibria upon seasonal changes, even if the temperature undergoes only small changes. For the first time, the profile of atmospheric methane in Titan's troposphere will be reproduced complete with the solid solutions. This means that the freezing point, i.e. the altitude where the first solid phase appears, is determined. The seasonal change will also be evaluated both at the equator and the northern polar region. For Pluto, also for the first time, the seasonal solid-vapor equilibria will be evaluated. The fate of the two solid phases, the methane-rich and carbon-monoxide-rich solid solutions, will be analyzed upon temperature and pressure changes. Such investigations are enabled by the development of a molecular-based thermodynamic model for cryogenic chemical systems, referred to as CRYOCHEM, which includes solid solutions in its phase-equilibria calculations. The atmospheres of Titan and Pluto are modeled as ternary gas mixtures: nitrogen-methane-ethane and nitrogen-methane-carbon monoxide, respectively. Calculations using CRYOCHEM can provide us with compositions not only in two-phase equilibria, but also that in three-phase equilibria. Densities of all phases involved will also be calculated. For Titan, density inversion between liquid and solid phases will be identified and presented. In the inversion, the density of solid phase is less than that in the liquid phase. The method and results of this work will be useful for further investigations and modeling on the atmospheres of Titan, Pluto, and other bodies with similar conditions in the Solar System and beyond.

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

Cary, J.R.

During the most recent funding period the authors obtained results important for helical confinement systems and in the use of modern computational methods for modeling of fusion systems. The most recent results include showing that the set of magnetic field functions that are omnigenous (i.e., the bounce-average drift lies within the flux surface) and, therefore, have good transport properties, is much larger than the set of quasihelical systems. This is important as quasihelical systems exist only for large aspect ratio. The authors have also carried out extensive earlier work on developing integrable three-dimensional magnetic fields, on trajectories in three-dimensional configurations,more » and on the existence of three-dimensional MHD equilibria close to vacuum integrable fields. At the same time they have been investigating the use of object oriented methods for scientific computing.« less

Correct Representation of Conformational Equilibria.

ERIC Educational Resources Information Center

Fulop, F.; And Others

1983-01-01

In representing conformational equilibria of compounds having only one chiral center, erroneous formulas showing different antipodes on the two sides of the equilibrium are rare. In contrast, with compounds having two or more chiral centers especially with saturated heterocycles, this erroneous representation occurs frequently in the chemical…

Multiple Reaction Equilibria--With Pencil and Paper: A Class Problem on Coal Methanation.

ERIC Educational Resources Information Center

Helfferich, Friedrich G.

1989-01-01

Points out a different and much simpler approach for the study of equilibria of multiple and heterogeneous chemical reactions. A simulation on coal methanation is used to teach the technique. An example and the methodology used are provided. (MVL)

Acid-Base and Precipitation Equilibria in Wine

ERIC Educational Resources Information Center

Palma, Miguel; Barroso, Carmelo G.

2004-01-01

Experiments are performed to establish the changes of pH during the precipitation of potassium hydrogen tartrate, with its unfavorable impact on the stability of wine. Students, thus, obtain a clearer understanding of the interplay between a variety of chemical equilibria within a single medium.

On the manifestation of coexisting nontrivial equilibria leading to potential well escapes in an inhomogeneous floating body

NASA Astrophysics Data System (ADS)

Sequeira, Dane; Wang, Xue-She; Mann, B. P.

2018-02-01

This paper examines the bifurcation and stability behavior of inhomogeneous floating bodies, specifically a rectangular prism with asymmetric mass distribution. A nonlinear model is developed to determine the stability of the upright and tilted equilibrium positions as a function of the vertical position of the center of mass within the prism. These equilibria positions are defined by an angle of rotation and a vertical position where rotational motion is restricted to a two dimensional plane. Numerical investigations are conducted using path-following continuation methods to determine equilibria solutions and evaluate stability. Bifurcation diagrams and basins of attraction that illustrate the stability of the equilibrium positions as a function of the vertical position of the center of mass within the prism are generated. These results reveal complex stability behavior with many coexisting solutions. Static experiments are conducted to validate equilibria orientations against numerical predictions with results showing good agreement. Dynamic experiments that examine potential well hopping behavior in a waveflume for various wave conditions are also conducted.

Dynamical analysis of a cubic Liénard system with global parameters (II)

NASA Astrophysics Data System (ADS)

Chen, Hebai; Chen, Xingwu

2016-06-01

In this paper, we continue to study the global dynamics of a cubic Liénard system for global parameters in the case of three equilibria to follow (2015 Nonlinearity 28 3535-62), which deals with the case of two equilibria. We first analyse qualitative properties of all equilibria and judge the existences of limit cycles and homoclinic loops and their numbers. Then we obtain the bifurcation diagram and all phase portraits as our main results. Based on these results, in the case of three equilibria a positive answer to conjecture 3.2 of (1998 Nonlinearity 11 1505-19), which is about the existence of some function whose graph is exactly the surface of double limit cycles, is obtained. Moreover, a parameter region for the nonexistence of figure-eight loops is given theoretically to compensate for previous numerical results and is illustrated numerically. Supported by NSFC 11471228, 11572263, the Fundamental Research Funds for the Central Universities and Cultivation Foundation of Excellent Doctoral Dissertation of Southwest Jiaotong University (2015).

Phase equilibria in fullerene-containing systems as a basis for development of manufacture and application processes for nanocarbon materials

NASA Astrophysics Data System (ADS)

Semenov, K. N.; Charykov, N. A.; Postnov, V. N.; Sharoyko, V. V.; Murin, I. V.

2016-01-01

This review is the first attempt to integrate the available data on all types of phase equilibria (solubility, extraction and sorption) in systems containing light fullerenes (C60 and C70). In the case of solubility diagrams, the following types of phase equilibria are considered: individual fullerene (C60 or C70)-solvent under polythermal and polybaric conditions; C60-C70-solvent, individual fullerene-solvent(1)-solvent(2), as well as multicomponent systems comprising a single fullerene or an industrial mixture of fullerenes and vegetable oils, animal fats or essential oils under polythermal conditions. All published experimental data on the extraction equilibria in C60-C70-liquid phase(1)-liquid phase(2) systems are described systematically and the sorption characteristics of various materials towards light fullerenes are estimated. The possibility of application of these experimental data for development of pre-chromatographic and chromatographic methods for separation of fullerene mixtures and application of fullerenes as nanomodifiers are described. The bibliography includes 87 references.

Roto-orbital dynamics of a triaxial rigid body around a sphere. Relative equilibria and stability

NASA Astrophysics Data System (ADS)

Crespo, F.; Ferrer, S.

2018-06-01

We study the roto-orbital motion of a triaxial rigid body around a sphere, which is assumed to be much more massive than the triaxial body. The associated dynamics of this system, which consists of a normalized Hamiltonian with respect to the fast angles (partial averaging), is investigated making use of variables referred to the total angular momentum. The first order approximation of this model is integrable. We carry out the analysis of the relative equilibria, which hinges principally in the dihedral angle between the orbital and rotational planes and the ratio among the moments of inertia ρ = (B - A) / (2 C - B - A) . In particular, the dynamics of the body frame, though formally given by the classical Euler equations, experiences changes of stability in the principal directions related to the roto-orbital coupling. When ρ = 1 / 3 , we find a family of relative equilibria connected to the unstable equilibria of the free rigid body.

Rethinking pattern formation in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Halatek, J.; Frey, E.

2018-05-01

The present theoretical framework for the analysis of pattern formation in complex systems is mostly limited to the vicinity of fixed (global) equilibria. Here we present a new theoretical approach to characterize dynamical states arbitrarily far from (global) equilibrium. We show that reaction-diffusion systems that are driven by locally mass-conserving interactions can be understood in terms of local equilibria of diffusively coupled compartments. Diffusive coupling generically induces lateral redistribution of the globally conserved quantities, and the variable local amounts of these quantities determine the local equilibria in each compartment. We find that, even far from global equilibrium, the system is well characterized by its moving local equilibria. We apply this framework to in vitro Min protein pattern formation, a paradigmatic model for biological pattern formation. Within our framework we can predict and explain transitions between chemical turbulence and order arbitrarily far from global equilibrium. Our results reveal conceptually new principles of self-organized pattern formation that may well govern diverse dynamical systems.

Statics and Dynamics of Selfish Interactions in Distributed Service Systems

PubMed Central

Altarelli, Fabrizio; Braunstein, Alfredo; Dall’Asta, Luca

2015-01-01

We study a class of games which models the competition among agents to access some service provided by distributed service units and which exhibits congestion and frustration phenomena when service units have limited capacity. We propose a technique, based on the cavity method of statistical physics, to characterize the full spectrum of Nash equilibria of the game. The analysis reveals a large variety of equilibria, with very different statistical properties. Natural selfish dynamics, such as best-response, usually tend to large-utility equilibria, even though those of smaller utility are exponentially more numerous. Interestingly, the latter actually can be reached by selecting the initial conditions of the best-response dynamics close to the saturation limit of the service unit capacities. We also study a more realistic stochastic variant of the game by means of a simple and effective approximation of the average over the random parameters, showing that the properties of the average-case Nash equilibria are qualitatively similar to the deterministic ones. PMID:26177449

Magnetospheric equilibrium configurations and slow adiabatic convection

NASA Technical Reports Server (NTRS)

Voigt, Gerd-Hannes

1986-01-01

This review paper demonstrates how the magnetohydrostatic equilibrium (MHE) theory can be used to describe the large-scale magnetic field configuration of the magnetosphere and its time evolution under the influence of magnetospheric convection. The equilibrium problem is reviewed, and levels of B-field modelling are examined for vacuum models, quasi-static equilibrium models, and MHD models. Results from two-dimensional MHE theory as they apply to the Grad-Shafranov equation, linear equilibria, the asymptotic theory, magnetospheric convection and the substorm mechanism, and plasma anisotropies are addressed. Results from three-dimensional MHE theory are considered as they apply to an intermediate analytical magnetospheric model, magnetotail configurations, and magnetopause boundary conditions and the influence of the IMF.

A new 4D chaotic system with hidden attractor and its engineering applications: Analog circuit design and field programmable gate array implementation

NASA Astrophysics Data System (ADS)

Abdolmohammadi, Hamid Reza; Khalaf, Abdul Jalil M.; Panahi, Shirin; Rajagopal, Karthikeyan; Pham, Viet-Thanh; Jafari, Sajad

2018-06-01

Nowadays, designing chaotic systems with hidden attractor is one of the most interesting topics in nonlinear dynamics and chaos. In this paper, a new 4D chaotic system is proposed. This new chaotic system has no equilibria, and so it belongs to the category of systems with hidden attractors. Dynamical features of this system are investigated with the help of its state-space portraits, bifurcation diagram, Lyapunov exponents diagram, and basin of attraction. Also a hardware realisation of this system is proposed by using field programmable gate arrays (FPGA). In addition, an electronic circuit design for the chaotic system is introduced.

Simplest bifurcation diagrams for monotone families of vector fields on a torus

NASA Astrophysics Data System (ADS)

Baesens, C.; MacKay, R. S.

2018-06-01

In part 1, we prove that the bifurcation diagram for a monotone two-parameter family of vector fields on a torus has to be at least as complicated as the conjectured simplest one proposed in Baesens et al (1991 Physica D 49 387–475). To achieve this, we define ‘simplest’ by sequentially minimising the numbers of equilibria, Bogdanov–Takens points, closed curves of centre and of neutral saddle, intersections of curves of centre and neutral saddle, Reeb components, other invariant annuli, arcs of rotational homoclinic bifurcation of horizontal homotopy type, necklace points, contractible periodic orbits, points of neutral horizontal homoclinic bifurcation and half-plane fan points. We obtain two types of simplest case, including that initially proposed. In part 2, we analyse the bifurcation diagram for an explicit monotone family of vector fields on a torus and prove that it has at most two equilibria, precisely four Bogdanov–Takens points, no closed curves of centre nor closed curves of neutral saddle, at most two Reeb components, precisely four arcs of rotational homoclinic connection of ‘horizontal’ homotopy type, eight horizontal saddle-node loop points, two necklace points, four points of neutral horizontal homoclinic connection, and two half-plane fan points, and there is no simultaneous existence of centre and neutral saddle, nor contractible homoclinic connection to a neutral saddle. Furthermore, we prove that all saddle-nodes, Bogdanov–Takens points, non-neutral and neutral horizontal homoclinic bifurcations are non-degenerate and the Hopf condition is satisfied for all centres. We also find it has four points of degenerate Hopf bifurcation. It thus provides an example of a family satisfying all the assumptions of part 1 except the one of at most one contractible periodic orbit.

Photon mass drag and the momentum of light in a medium

NASA Astrophysics Data System (ADS)

Partanen, Mikko; Häyrynen, Teppo; Oksanen, Jani; Tulkki, Jukka

2017-06-01

Conventional theories of electromagnetic waves in a medium assume that the energy propagating with the light pulse in the medium is entirely carried by the field. Thus, the possibility that the optical force field of the light pulse would drive forward an atomic mass density wave (MDW) and the related kinetic and elastic energies is neglected. In this work, we present foundations of a covariant theory of light propagation in a medium by considering a light wave simultaneously with the dynamics of the medium atoms driven by optoelastic forces between the induced dipoles and the electromagnetic field. We show that a light pulse having a total electromagnetic energy ℏ ω propagating in a nondispersive medium transfers a mass equal to δ m =(n2-1 ) ℏ ω /c2 , where n is the refractive index. MDW, which carries this mass, consists of atoms, which are more densely spaced inside the light pulse as a result of the field-dipole interaction. We also prove that the transfer of mass with the light pulse, the photon mass drag effect, gives an essential contribution to the total momentum of the light pulse, which becomes equal to the Minkowski momentum pM=n ℏ ω /c . The field's share of the momentum is the Abraham momentum pA=ℏ ω /(n c ) , while the difference pM-pA is carried by MDW. Due to the coupling of the field and matter, only the total momentum of the light pulse and the transferred mass δ m can be directly measured. Thus, our theory gives an unambiguous physical meaning to the Abraham and Minkowski momenta. We also show that to solve the centenary Abraham-Minkowski controversy of the momentum of light in a nondispersive medium in a way that is consistent with Newton's first law, one must account for the mass transfer effect. We derive the photon mass drag effect using two independent but complementary covariant models. In the mass-polariton (MP) quasiparticle approach, we consider the light pulse as a coupled state between the photon and matter, isolated from the rest of the medium. The momentum and the transferred mass of MP follow unambiguously from the Lorentz invariance and the fundamental conservation laws of nature. To enable the calculation of the mass and momentum distribution of a light pulse, we have also generalized the electrodynamics of continuous media to account for the space- and time-dependent optoelastic dynamics of the medium driven by the field-dipole forces. In this optoelastic continuum dynamics (OCD) approach, we obtain with an appropriate space-time discretization a numerically accurate solution of the Newtonian continuum dynamics of the medium when the light pulse is propagating in it. The OCD simulations of a Gaussian light pulse propagating in a diamond crystal give the same momentum pM and the transferred mass δ m for the light pulse as the MP quasiparticle approach. Our simulations also show that, after photon transmission, some nonequilibrium of the mass distribution is left in the medium. Since the elastic forces are included in our simulations on equal footing with the optical forces, our simulations also depict how the mass and thermal equilibria are reestablished by elastic waves. In the relaxation process, a small amount of photon energy is dissipated into lattice heat. We finally discuss a possibility of an optical waveguide setup for experimental measurement of the transferred mass of the light pulse. Our main result that a light pulse is inevitably associated with an experimentally measurable mass is a fundamental change in our understanding of light propagation in a medium.

Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization

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

Canale, Eduardo A., E-mail: ecanale@pol.una.py; Monzón, Pablo, E-mail: monzon@fing.edu.uy

2015-02-15

This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1–15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree–order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.

A decentralized process for finding equilibria given by linear equations.

PubMed Central

Reiter, S

1994-01-01

I present a decentralized process for finding the equilibria of an economy characterized by a finite number of linear equilibrium conditions. The process finds all equilibria or, if there are none, reports that, in a finite number of steps at most equal to the number of equations. The communication and computational complexity compare favorably with other decentralized processes. The process may also be interpreted as an algorithm for solving a distributed system of linear equations. Comparisons with the Linpack program for LU (lower and upper triangular decomposition of the matrix of the equation system, a version of Gaussian elimination) are presented. PMID:11607486

Two Different Approaches to Nonzero-Sum Stochastic Differential Games

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

Rainer, Catherine

2007-06-15

We make the link between two approaches to Nash equilibria for nonzero-sum stochastic differential games: the first one using backward stochastic differential equations and the second one using strategies with delay. We prove that, when both exist, the two notions of Nash equilibria coincide.

Kinetic Simulations of the Lowest-order Unstable Mode of Relativistic Magnetostatic Equilibria

NASA Astrophysics Data System (ADS)

Nalewajko, Krzysztof; Zrake, Jonathan; Yuan, Yajie; East, William E.; Blandford, Roger D.

2016-08-01

We present the results of particle-in-cell numerical pair plasma simulations of relativistic two-dimensional magnetostatic equilibria known as the “Arnold-Beltrami-Childress” fields. In particular, we focus on the lowest-order unstable configuration consisting of two minima and two maxima of the magnetic vector potential. Breaking of the initial symmetry leads to exponential growth of the electric energy and to the formation of two current layers, which is consistent with the picture of “X-point collapse” first described by Syrovatskii. Magnetic reconnection within the layers heats a fraction of particles to very high energies. After the saturation of the linear instability, the current layers are disrupted and the system evolves chaotically, diffusing the particle energies in a stochastic second-order Fermi process, leading to the formation of power-law energy distributions. The power-law slopes harden with the increasing mean magnetization, but they are significantly softer than those produced in simulations initiated from Harris-type layers. The maximum particle energy is proportional to the mean magnetization, which is attributed partly to the increase of the effective electric field and partly to the increase of the acceleration timescale. We describe in detail the evolving structure of the dynamical current layers and report on the conservation of magnetic helicity. These results can be applied to highly magnetized astrophysical environments, where ideal plasma instabilities trigger rapid magnetic dissipation with efficient particle acceleration and flares of high-energy radiation.

KINETIC SIMULATIONS OF THE LOWEST-ORDER UNSTABLE MODE OF RELATIVISTIC MAGNETOSTATIC EQUILIBRIA

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

Nalewajko, Krzysztof; Zrake, Jonathan; Yuan, Yajie

2016-08-01

We present the results of particle-in-cell numerical pair plasma simulations of relativistic two-dimensional magnetostatic equilibria known as the “Arnold–Beltrami–Childress” fields. In particular, we focus on the lowest-order unstable configuration consisting of two minima and two maxima of the magnetic vector potential. Breaking of the initial symmetry leads to exponential growth of the electric energy and to the formation of two current layers, which is consistent with the picture of “X-point collapse” first described by Syrovatskii. Magnetic reconnection within the layers heats a fraction of particles to very high energies. After the saturation of the linear instability, the current layers aremore » disrupted and the system evolves chaotically, diffusing the particle energies in a stochastic second-order Fermi process, leading to the formation of power-law energy distributions. The power-law slopes harden with the increasing mean magnetization, but they are significantly softer than those produced in simulations initiated from Harris-type layers. The maximum particle energy is proportional to the mean magnetization, which is attributed partly to the increase of the effective electric field and partly to the increase of the acceleration timescale. We describe in detail the evolving structure of the dynamical current layers and report on the conservation of magnetic helicity. These results can be applied to highly magnetized astrophysical environments, where ideal plasma instabilities trigger rapid magnetic dissipation with efficient particle acceleration and flares of high-energy radiation.« less

Geostrophic tripolar vortices in a two-layer fluid: Linear stability and nonlinear evolution of equilibria

NASA Astrophysics Data System (ADS)

Reinaud, J. N.; Sokolovskiy, M. A.; Carton, X.

2017-03-01

We investigate equilibrium solutions for tripolar vortices in a two-layer quasi-geostrophic flow. Two of the vortices are like-signed and lie in one layer. An opposite-signed vortex lies in the other layer. The families of equilibria can be spanned by the distance (called separation) between the two like-signed vortices. Two equilibrium configurations are possible when the opposite-signed vortex lies between the two other vortices. In the first configuration (called ordinary roundabout), the opposite signed vortex is equidistant to the two other vortices. In the second configuration (eccentric roundabouts), the distances are unequal. We determine the equilibria numerically and describe their characteristics for various internal deformation radii. The two branches of equilibria can co-exist and intersect for small deformation radii. Then, the eccentric roundabouts are stable while unstable ordinary roundabouts can be found. Indeed, ordinary roundabouts exist at smaller separations than eccentric roundabouts do, thus inducing stronger vortex interactions. However, for larger deformation radii, eccentric roundabouts can also be unstable. Then, the two branches of equilibria do not cross. The branch of eccentric roundabouts only exists for large separations. Near the end of the branch of eccentric roundabouts (at the smallest separation), one of the like-signed vortices exhibits a sharp inner corner where instabilities can be triggered. Finally, we investigate the nonlinear evolution of a few selected cases of tripoles.

Sigmoidal equilibria and eruptive instabilities in laboratory magnetic flux ropes

NASA Astrophysics Data System (ADS)

Myers, C. E.; Yamada, M.; Belova, E.; Ji, H.; Yoo, J.

2013-12-01

The Magnetic Reconnection Experiment (MRX) has recently been modified to study quasi-statically driven line-tied magnetic flux ropes in the context of storage-and-release eruptions in the corona. Detailed in situ magnetic measurements and supporting MHD simulations permit quantitative analysis of the plasma behavior. We find that the behavior of these flux ropes depends strongly on the properties of the applied potential magnetic field arcade. For example, when the arcade is aligned parallel to the flux rope footpoints, force free currents induced in the expanding rope modify the pressure and tension in the arcade, resulting in a confined, quiescent discharge with a saturated kink instability. When the arcade is obliquely aligned to the footpoints, on the other hand, a highly sigmoidal equilibrium forms that can dynamically erupt (see Fig. 1 and Fig. 2). To our knowledge, these storage-and-release eruptions are the first of their kind to be produced in the laboratory. A new 2D magnetic probe array is used to map out the internal structure of the flux ropes during both the storage and the release phases of the discharge. The kink instability and the torus instability are studied as candidate eruptive mechanisms--the latter by varying the vertical gradient of the potential field arcade. We also investigate magnetic reconnection events that accompany the eruptions. The long-term objective of this work is to use internal magnetic measurements of the flux rope structure to better understand the evolution and eruption of comparable structures in the corona. This research is supported by DoE Contract Number DE-AC02-09CH11466 and by the Center for Magnetic Self-Organization (CMSO). Qualitative sketches of flux ropes formed in (1) a parallel potential field arcade; and (2) an oblique potential field arcade. One-dimensional magnetic measurements from (1) a parallel arcade discharge that is confined; and (2) an oblique arcade discharge that erupts.

Extension of laboratory-measured soil spectra to field conditions

NASA Technical Reports Server (NTRS)

Stoner, E. R.; Baumgardner, M. F.; Weismiller, R. A.; Biehl, L. L.; Robinson, B. F.

1982-01-01

Spectral responses of two glaciated soils, Chalmers silty clay loam and Fincastle silt loam, formed under prairie grass and forest vegetation, respectively, were measured in the laboratory under controlled moisture equilibria using an Exotech Model 20C spectroradiometer to obtain spectral data in the laboratory under artificial illumination. The same spectroradiometer was used outdoors under solar illumination to obtain spectral response from dry and moistened field plots with and without corn residue cover, representing the two different soils. Results indicate that laboratory-measured spectra of moist soil are directly proportional to the spectral response of that same field-measured moist bare soil over the 0.52 micrometer to 1.75 micrometer wavelength range. The magnitudes of difference in spectral response between identically treated Chalmers and Fincastle soils are greatest in the 0.6 micrometers to 0.8 micrometer transition region between the visible and near infrared, regardless of field condition or laboratory preparation studied.

Numerical optimization of three-dimensional coils for NSTX-U

DOE PAGES

Lazerson, S. A.; Park, J. -K.; Logan, N.; ...

2015-09-03

A tool for the calculation of optimal three-dimensional (3D) perturbative magnetic fields in tokamaks has been developed. The IPECOPT code builds upon the stellarator optimization code STELLOPT to allow for optimization of linear ideal magnetohydrodynamic perturbed equilibrium (IPEC). This tool has been applied to NSTX-U equilibria, addressing which fields are the most effective at driving NTV torques. The NTV torque calculation is performed by the PENT code. Optimization of the normal field spectrum shows that fields with n = 1 character can drive a large core torque. It is also shown that fields with n = 3 features are capablemore » of driving edge torque and some core torque. Coil current optimization (using the planned in-vessel and existing RWM coils) on NSTX-U suggest the planned coils set is adequate for core and edge torque control. In conclusion, comparison between error field correction experiments on DIII-D and the optimizer show good agreement.« less

Graphic Representation of Carbon Dioxide Equilibria in Biological Systems.

ERIC Educational Resources Information Center

Kindig, Neal B.; Filley, Giles F.

1983-01-01

The log C-pH diagram is a useful means of displaying quantitatively the many variables (including temperature) that determine acid-base equilibria in biological systems. Presents the diagram as extended to open/closed biological systems and derives a new water-ion balance method for determining equilibrium pH. (JN)

On Endogenous Competitive Business Cycles

DTIC Science & Technology

1984-01-01

Equilibria Part II. Properties of Bequest Equilibria" by Debraj Ray and Douglas Bernheim. Reports in this Series . • . ■ 1J20. "On the Existence...or equivalently by the map W. It ray be worthwhile to end up this section with a simple graphical illustration of the backward dynamics associated to

Dissipative particle dynamics: Systematic parametrization using water-octanol partition coefficients

NASA Astrophysics Data System (ADS)

Anderson, Richard L.; Bray, David J.; Ferrante, Andrea S.; Noro, Massimo G.; Stott, Ian P.; Warren, Patrick B.

2017-09-01

We present a systematic, top-down, thermodynamic parametrization scheme for dissipative particle dynamics (DPD) using water-octanol partition coefficients, supplemented by water-octanol phase equilibria and pure liquid phase density data. We demonstrate the feasibility of computing the required partition coefficients in DPD using brute-force simulation, within an adaptive semi-automatic staged optimization scheme. We test the methodology by fitting to experimental partition coefficient data for twenty one small molecules in five classes comprising alcohols and poly-alcohols, amines, ethers and simple aromatics, and alkanes (i.e., hexane). Finally, we illustrate the transferability of a subset of the determined parameters by calculating the critical micelle concentrations and mean aggregation numbers of selected alkyl ethoxylate surfactants, in good agreement with reported experimental values.

On application of asymmetric Kan-like exact equilibria to the Earth magnetotail modeling

NASA Astrophysics Data System (ADS)

Korovinskiy, Daniil B.; Kubyshkina, Darya I.; Semenov, Vladimir S.; Kubyshkina, Marina V.; Erkaev, Nikolai V.; Kiehas, Stefan A.

2018-04-01

A specific class of solutions of the Vlasov-Maxwell equations, developed by means of generalization of the well-known Harris-Fadeev-Kan-Manankova family of exact two-dimensional equilibria, is studied. The examined model reproduces the current sheet bending and shifting in the vertical plane, arising from the Earth dipole tilting and the solar wind nonradial propagation. The generalized model allows magnetic configurations with equatorial magnetic fields decreasing in a tailward direction as slow as 1/x, contrary to the original Kan model (1/x3); magnetic configurations with a single X point are also available. The analytical solution is compared with the empirical T96 model in terms of the magnetic flux tube volume. It is found that parameters of the analytical model may be adjusted to fit a wide range of averaged magnetotail configurations. The best agreement between analytical and empirical models is obtained for the midtail at distances beyond 10-15 RE at high levels of magnetospheric activity. The essential model parameters (current sheet scale, current density) are compared to Cluster data of magnetotail crossings. The best match of parameters is found for single-peaked current sheets with medium values of number density, proton temperature and drift velocity.

Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets

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

Loizu, J.; Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543; Hudson, S. R.

2015-09-15

We consider the linear and nonlinear ideal plasma response to a boundary perturbation in a screw pinch. We demonstrate that three-dimensional, ideal-MHD equilibria with continuously nested flux-surfaces and with discontinuous rotational-transform across the resonant rational-surfaces are well defined and can be computed both perturbatively and using fully nonlinear equilibrium calculations. This rescues the possibility of constructing MHD equilibria with current sheets and continuous, smooth pressure profiles. The results predict that, even if the plasma acts as a perfectly conducting fluid, a resonant magnetic perturbation can penetrate all the way into the center of a tokamak without being shielded at themore » resonant surface.« less

Efficiency reduction and pseudo-convergence in replica exchange sampling of peptide folding unfolding equilibria

NASA Astrophysics Data System (ADS)

Denschlag, Robert; Lingenheil, Martin; Tavan, Paul

2008-06-01

Replica exchange (RE) molecular dynamics (MD) simulations are frequently applied to sample the folding-unfolding equilibria of β-hairpin peptides in solution, because efficiency gains are expected from this technique. Using a three-state Markov model featuring key aspects of β-hairpin folding we show that RE simulations can be less efficient than conventional techniques. Furthermore we demonstrate that one is easily seduced to erroneously assign convergence to the RE sampling, because RE ensembles can rapidly reach long-lived stationary states. We conclude that typical REMD simulations covering a few tens of nanoseconds are by far too short for sufficient sampling of β-hairpin folding-unfolding equilibria.

Reconfiguration of a smart surface using heteroclinic connections

PubMed Central

McInnes, Colin R.; Xu, Ming

2017-01-01

A reconfigurable smart surface with multiple equilibria is presented, modelled using discrete point masses and linear springs with geometric nonlinearity. An energy-efficient reconfiguration scheme is then investigated to connect equal-energy unstable (but actively controlled) equilibria. In principle, zero net energy input is required to transition the surface between these unstable states, compared to transitions between stable equilibria across a potential barrier. These transitions between equal-energy unstable states, therefore, form heteroclinic connections in the phase space of the problem. Moreover, the smart surface model developed can be considered as a unit module for a range of applications, including modules which can aggregate together to form larger distributed smart surface systems. PMID:28265191

Potentials of mean force for biomolecular simulations: Theory and test on alanine dipeptide

NASA Astrophysics Data System (ADS)

Pellegrini, Matteo; Grønbech-Jensen, Niels; Doniach, Sebastian

1996-06-01

We describe a technique for generating potentials of mean force (PMF) between solutes in an aqueous solution. We first generate solute-solvent correlation functions (CF) using Monte Carlo (MC) simulations in which we place a single atom solute in a periodic boundary box containing a few hundred water molecules. We then make use of the Kirkwood superposition approximation, where the 3-body correlation function is approximated as the product of 2-body CFs, to describe the mean water density around two solutes. Computing the force generated on the solutes by this average water density allows us to compute potentials of mean force between the two solutes. For charged solutes an additional approximation involving dielectric screening is made, by setting the dielectric constant of water to ɛ=80. These potentials account, in an approximate manner, for the average effect of water on the atoms. Following the work of Pettitt and Karplus [Chem. Phys. Lett. 121, 194 (1985)], we approximate the n-body potential of mean force as a sum of the pairwise potentials of mean force. This allows us to run simulations of biomolecules without introducing explicit water, hence gaining several orders of magnitude in efficiency with respect to standard molecular dynamics techniques. We demonstrate the validity of this technique by first comparing the PMFs for methane-methane and sodium-chloride generated with this procedure, with those calculated with a standard Monte Carlo simulation with explicit water. We then compare the results of the free energy profiles between the equilibria of alanine dipeptide generated by the two methods.

Plasma Equilibrium in a Magnetic Field with Stochastic Regions

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

J.A. Krommes and Allan H. Reiman

The nature of plasma equilibrium in a magnetic field with stochastic regions is examined. It is shown that the magnetic differential equation that determines the equilibrium Pfirsch-Schluter currents can be cast in a form similar to various nonlinear equations for a turbulent plasma, allowing application of the mathematical methods of statistical turbulence theory. An analytically tractable model, previously studied in the context of resonance-broadening theory, is applied with particular attention paid to the periodicity constraints required in toroidal configurations. It is shown that even a very weak radial diffusion of the magnetic field lines can have a significant effect onmore » the equilibrium in the neighborhood of the rational surfaces, strongly modifying the near-resonant Pfirsch-Schluter currents. Implications for the numerical calculation of 3D equilibria are discussed« less

A quantum extension to inspection game

NASA Astrophysics Data System (ADS)

Deng, Xinyang; Deng, Yong; Liu, Qi; Chang, Shuhua; Wang, Zhen

2016-06-01

Quantum game theory is a new interdisciplinary field between game theory and system engineering research. In this paper, we extend the classical inspection game into a quantum game version by quantizing the strategy space and importing entanglement between players. Our results show that the quantum inspection game has various Nash equilibria depending on the initial quantum state of the game. It is also shown that quantization can respectively help each player to increase his own payoff, yet fails to bring Pareto improvement for the collective payoff in the quantum inspection game.

Competing edge networks

NASA Astrophysics Data System (ADS)

Parsons, Mark; Grindrod, Peter

2012-06-01

We introduce a model for a pair of nonlinear evolving networks, defined over a common set of vertices, subject to edgewise competition. Each network may grow new edges spontaneously or through triad closure. Both networks inhibit the other's growth and encourage the other's demise. These nonlinear stochastic competition equations yield to a mean field analysis resulting in a nonlinear deterministic system. There may be multiple equilibria; and bifurcations of different types are shown to occur within a reduced parameter space. This situation models competitive communication networks such as BlackBerry Messenger displacing SMS; or instant messaging displacing emails.

An evaluation of the deep reservoir conditions of the Bacon-Manito geothermal field, Philippines using well gas chemistry

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

D'Amore, Franco; Maniquis-Buenviaje, Marinela; Solis, Ramonito P.

1993-01-28

Gas chemistry from 28 wells complement water chemistry and physical data in developing a reservoir model for the Bacon-Manito geothermal project (BMGP), Philippines. Reservoir temperature, T HSH, and steam fraction, y, are calculated or extrapolated from the grid defined by the Fischer-Tropsch (FT) and H 2-H 2S (HSH) gas equilibria reactions. A correction is made for H 2 that is lost due to preferential partitioning into the vapor phase and the reequilibration of H 2S after steam loss.

Substituent Effects on Keto-Enol Equilibria Using NMR Spectroscopy

ERIC Educational Resources Information Center

Manbeck, Kimberly A.; Boaz, Nicholas C.; Bair, Nathaniel C.; Sanders, Allix M. S.; Marsh, Anderson L.

2011-01-01

In this extension to a classic physical chemistry experiment, students record the proton nuclear magnetic resonance spectra of the [beta]-diketones 2,4-pentanedione, 3-methyl-2,4-pentanedione, and 3-chloro-2,4-pentanedione to investigate the effect of substituents on keto-enol tautomerization equilibria. From the integrated intensities of keto and…

Vapor-Liquid Equilibria Using the Gibbs Energy and the Common Tangent Plane Criterion

ERIC Educational Resources Information Center

Olaya, Maria del Mar; Reyes-Labarta, Juan A.; Serrano, Maria Dolores; Marcilla, Antonio

2010-01-01

Phase thermodynamics is often perceived as a difficult subject with which many students never become fully comfortable. The Gibbsian geometrical framework can help students to gain a better understanding of phase equilibria. An exercise to interpret the vapor-liquid equilibrium of a binary azeotropic mixture, using the equilibrium condition based…

Using Computer-Based "Experiments" in the Analysis of Chemical Reaction Equilibria

ERIC Educational Resources Information Center

Li, Zhao; Corti, David S.

2018-01-01

The application of the Reaction Monte Carlo (RxMC) algorithm to standard textbook problems in chemical reaction equilibria is discussed. The RxMC method is a molecular simulation algorithm for studying the equilibrium properties of reactive systems, and therefore provides the opportunity to develop computer-based "experiments" for the…

Equilibrator: Modeling Chemical Equilibria with Excel

ERIC Educational Resources Information Center

Vander Griend, Douglas A.

2011-01-01

Equilibrator is a Microsoft Excel program for learning about chemical equilibria through modeling, similar in function to EQS4WIN, which is no longer supported and does not work well with newer Windows operating systems. Similar to EQS4WIN, Equilibrator allows the user to define a system with temperature, initial moles, and then either total…

A Computer Algebra Approach to Solving Chemical Equilibria in General Chemistry

ERIC Educational Resources Information Center

Kalainoff, Melinda; Lachance, Russ; Riegner, Dawn; Biaglow, Andrew

2012-01-01

In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…

Predicting vapor-liquid phase equilibria with augmented ab initio interatomic potentials

NASA Astrophysics Data System (ADS)

Vlasiuk, Maryna; Sadus, Richard J.

2017-06-01

The ability of ab initio interatomic potentials to accurately predict vapor-liquid phase equilibria is investigated. Monte Carlo simulations are reported for the vapor-liquid equilibria of argon and krypton using recently developed accurate ab initio interatomic potentials. Seventeen interatomic potentials are studied, formulated from different combinations of two-body plus three-body terms. The simulation results are compared to either experimental or reference data for conditions ranging from the triple point to the critical point. It is demonstrated that the use of ab initio potentials enables systematic improvements to the accuracy of predictions via the addition of theoretically based terms. The contribution of three-body interactions is accounted for using the Axilrod-Teller-Muto plus other multipole contributions and the effective Marcelli-Wang-Sadus potentials. The results indicate that the predictive ability of recent interatomic potentials, obtained from quantum chemical calculations, is comparable to that of accurate empirical models. It is demonstrated that the Marcelli-Wang-Sadus potential can be used in combination with accurate two-body ab initio models for the computationally inexpensive and accurate estimation of vapor-liquid phase equilibria.

Predicting vapor-liquid phase equilibria with augmented ab initio interatomic potentials.

PubMed

Vlasiuk, Maryna; Sadus, Richard J

2017-06-28

The ability of ab initio interatomic potentials to accurately predict vapor-liquid phase equilibria is investigated. Monte Carlo simulations are reported for the vapor-liquid equilibria of argon and krypton using recently developed accurate ab initio interatomic potentials. Seventeen interatomic potentials are studied, formulated from different combinations of two-body plus three-body terms. The simulation results are compared to either experimental or reference data for conditions ranging from the triple point to the critical point. It is demonstrated that the use of ab initio potentials enables systematic improvements to the accuracy of predictions via the addition of theoretically based terms. The contribution of three-body interactions is accounted for using the Axilrod-Teller-Muto plus other multipole contributions and the effective Marcelli-Wang-Sadus potentials. The results indicate that the predictive ability of recent interatomic potentials, obtained from quantum chemical calculations, is comparable to that of accurate empirical models. It is demonstrated that the Marcelli-Wang-Sadus potential can be used in combination with accurate two-body ab initio models for the computationally inexpensive and accurate estimation of vapor-liquid phase equilibria.

Solution influence on biomolecular equilibria - Nucleic acid base associations

NASA Technical Reports Server (NTRS)

Pohorille, A.; Pratt, L. R.; Burt, S. K.; Macelroy, R. D.

1984-01-01

Various attempts to construct an understanding of the influence of solution environment on biomolecular equilibria at the molecular level using computer simulation are discussed. First, the application of the formal statistical thermodynamic program for investigating biomolecular equilibria in solution is presented, addressing modeling and conceptual simplications such as perturbative methods, long-range interaction approximations, surface thermodynamics, and hydration shell. Then, Monte Carlo calculations on the associations of nucleic acid bases in both polar and nonpolar solvents such as water and carbon tetrachloride are carried out. The solvent contribution to the enthalpy of base association is positive (destabilizing) in both polar and nonpolar solvents while negative enthalpies for stacked complexes are obtained only when the solute-solute in vacuo energy is added to the total energy. The release upon association of solvent molecules from the first hydration layer around a solute to the bulk is accompanied by an increase in solute-solvent energy and decrease in solvent-solvent energy. The techniques presented are expectd to displace less molecular and more heuristic modeling of biomolecular equilibria in solution.

Density-functional study on the equilibria in the ThDP activation.

PubMed

Delgado, Eduardo J; Alderete, Joel B; Jaña, Gonzalo A

2011-11-01

The equilibria among the various ionization and tautomeric states involved in the activation of ThDP is addressed using high level density functional theory calculations, X3LYP/6-311++G(d,p)//X3LYP(PB)/6-31++G(d,p). This study provides the first theoretically derived thermodynamic data for the internal equilibria in the activation of ThDP. The role of the medium polarity on the geometry and thermodynamics of the diverse equilibria of ThDP is addressed. The media chosen are cyclohexane and water, as paradigms of apolar and polar media. The results suggest that all ionization and tautomeric states are accessible during the catalytic cycle, even in the absence of substrate, being APH(+) the form required to interconvert the AP and IP tautomers; and the generation of the ylide proceeds via the formation of the IP form. Additionally, the calculated ΔG° values allow to calculate all the equilibrium constants, including the pK(C2) for the thiazolium C2 atom whose ionization is believed to initiate the catalytic cycle.

Predict-first experimental analysis using automated and integrated magnetohydrodynamic modeling

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

Lyons, B. C.; Paz-Soldan, C.; Meneghini, O.

An integrated-modeling workflow has been developed in this paper for the purpose of performing predict-first analysis of transient-stability experiments. Starting from an existing equilibrium reconstruction from a past experiment, the workflow couples together the EFIT Grad-Shafranov solver [L. Lao et al., Fusion Sci. Technol. 48, 968 (2005)], the EPED model for the pedestal structure [P. B. Snyder et al., Phys. Plasmas 16, 056118 (2009)], and the NEO drift-kinetic-equation solver [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)] (for bootstrap current calculations) in order to generate equilibria with self-consistent pedestal structures as the plasma shape andmore » various scalar parameters (e.g., normalized β, pedestal density, and edge safety factor [q 95]) are changed. These equilibria are then analyzed using automated M3D-C1 extended-magnetohydrodynamic modeling [S. C. Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)] to compute the plasma response to three-dimensional magnetic perturbations. This workflow was created in conjunction with a DIII-D experiment examining the effect of triangularity on the 3D plasma response. Several versions of the workflow were developed, and the initial ones were used to help guide experimental planning (e.g., determining the plasma current necessary to maintain the constant edge safety factor in various shapes). Subsequent validation with the experimental results was then used to revise the workflow, ultimately resulting in the complete model presented here. We show that quantitative agreement was achieved between the M3D-C1 plasma response calculated for equilibria generated by the final workflow and equilibria reconstructed from experimental data. A comparison of results from earlier workflows is used to show the importance of properly matching certain experimental parameters in the generated equilibria, including the normalized β, pedestal density, and q 95. On the other hand, the details of the pedestal current did not significantly impact the plasma response in these equilibria. A comparison to the experimentally measured plasma response shows mixed agreement, indicating that while the equilibria are predicted well, additional analysis tools may be needed. In conclusion, we note the implications that these results have for the success of future predict-first studies, particularly the need for scans of uncertain parameters and for close collaboration between experimentalists and theorists.« less

Predict-first experimental analysis using automated and integrated magnetohydrodynamic modeling

DOE PAGES

Lyons, B. C.; Paz-Soldan, C.; Meneghini, O.; ...

2018-05-07

An integrated-modeling workflow has been developed in this paper for the purpose of performing predict-first analysis of transient-stability experiments. Starting from an existing equilibrium reconstruction from a past experiment, the workflow couples together the EFIT Grad-Shafranov solver [L. Lao et al., Fusion Sci. Technol. 48, 968 (2005)], the EPED model for the pedestal structure [P. B. Snyder et al., Phys. Plasmas 16, 056118 (2009)], and the NEO drift-kinetic-equation solver [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)] (for bootstrap current calculations) in order to generate equilibria with self-consistent pedestal structures as the plasma shape andmore » various scalar parameters (e.g., normalized β, pedestal density, and edge safety factor [q 95]) are changed. These equilibria are then analyzed using automated M3D-C1 extended-magnetohydrodynamic modeling [S. C. Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)] to compute the plasma response to three-dimensional magnetic perturbations. This workflow was created in conjunction with a DIII-D experiment examining the effect of triangularity on the 3D plasma response. Several versions of the workflow were developed, and the initial ones were used to help guide experimental planning (e.g., determining the plasma current necessary to maintain the constant edge safety factor in various shapes). Subsequent validation with the experimental results was then used to revise the workflow, ultimately resulting in the complete model presented here. We show that quantitative agreement was achieved between the M3D-C1 plasma response calculated for equilibria generated by the final workflow and equilibria reconstructed from experimental data. A comparison of results from earlier workflows is used to show the importance of properly matching certain experimental parameters in the generated equilibria, including the normalized β, pedestal density, and q 95. On the other hand, the details of the pedestal current did not significantly impact the plasma response in these equilibria. A comparison to the experimentally measured plasma response shows mixed agreement, indicating that while the equilibria are predicted well, additional analysis tools may be needed. In conclusion, we note the implications that these results have for the success of future predict-first studies, particularly the need for scans of uncertain parameters and for close collaboration between experimentalists and theorists.« less

Predict-first experimental analysis using automated and integrated magnetohydrodynamic modeling

NASA Astrophysics Data System (ADS)

Lyons, B. C.; Paz-Soldan, C.; Meneghini, O.; Lao, L. L.; Weisberg, D. B.; Belli, E. A.; Evans, T. E.; Ferraro, N. M.; Snyder, P. B.

2018-05-01

An integrated-modeling workflow has been developed for the purpose of performing predict-first analysis of transient-stability experiments. Starting from an existing equilibrium reconstruction from a past experiment, the workflow couples together the EFIT Grad-Shafranov solver [L. Lao et al., Fusion Sci. Technol. 48, 968 (2005)], the EPED model for the pedestal structure [P. B. Snyder et al., Phys. Plasmas 16, 056118 (2009)], and the NEO drift-kinetic-equation solver [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)] (for bootstrap current calculations) in order to generate equilibria with self-consistent pedestal structures as the plasma shape and various scalar parameters (e.g., normalized β, pedestal density, and edge safety factor [q95]) are changed. These equilibria are then analyzed using automated M3D-C1 extended-magnetohydrodynamic modeling [S. C. Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)] to compute the plasma response to three-dimensional magnetic perturbations. This workflow was created in conjunction with a DIII-D experiment examining the effect of triangularity on the 3D plasma response. Several versions of the workflow were developed, and the initial ones were used to help guide experimental planning (e.g., determining the plasma current necessary to maintain the constant edge safety factor in various shapes). Subsequent validation with the experimental results was then used to revise the workflow, ultimately resulting in the complete model presented here. We show that quantitative agreement was achieved between the M3D-C1 plasma response calculated for equilibria generated by the final workflow and equilibria reconstructed from experimental data. A comparison of results from earlier workflows is used to show the importance of properly matching certain experimental parameters in the generated equilibria, including the normalized β, pedestal density, and q95. On the other hand, the details of the pedestal current did not significantly impact the plasma response in these equilibria. A comparison to the experimentally measured plasma response shows mixed agreement, indicating that while the equilibria are predicted well, additional analysis tools may be needed. Finally, we note the implications that these results have for the success of future predict-first studies, particularly the need for scans of uncertain parameters and for close collaboration between experimentalists and theorists.

Theory of equilibria of elastic 2-braids with interstrand interaction

NASA Astrophysics Data System (ADS)

Starostin, E. L.; van der Heijden, G. H. M.

2014-03-01

Motivated by continuum models for DNA supercoiling we formulate a theory for equilibria of 2-braids, i.e., structures formed by two elastic rods winding around each other in continuous contact and subject to a local interstrand interaction. No assumption is made on the shape of the contact curve. The theory is developed in terms of a moving frame of directors attached to one of the strands. The other strand is tracked by including in this frame the normalised closest-approach chord connecting the two strands. The kinematic constant-distance constraint is formulated at strain level through the introduction of what we call braid strains. As a result the total potential energy involves arclength derivatives of these strains, thus giving rise to a second-order variational problem. The Euler-Lagrange equations for this problem give balance equations for the overall braid force and moment referred to the moving frame as well as differential equations that can be interpreted as effective constitutive relations encoding the effect that the second strand has on the first as the braid deforms under the action of end loads. Hard contact models are used to obtain the normal contact pressure between strands that has to be non-negative for a physically realisable solution without the need for external devices such as clamps or glue to keep the strands together. The theory is first illustrated by a number of problems that can be solved analytically and then applied to several new problems that have not hitherto been treated.

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

Textbook Forum: Equilibrium Constants of Chemical Reactions Involving Condensed Phases: Pressure Dependence and Choice of Standard State.

ERIC Educational Resources Information Center

Perlmutter-Hayman, Berta

1984-01-01

Problems of equilibria in condensed phases (particularly those involving solutes in dilute solutions) are encountered by students in their laboratory work; the thermodynamics of these equilibria is neglected in many textbooks. Therefore, several aspects of this topic are explored, focusing on pressure dependence and choice of standard state. (JN)

Predicting phase equilibria in one-component systems

NASA Astrophysics Data System (ADS)

Korchuganova, M. R.; Esina, Z. N.

2015-07-01

It is shown that Simon equation coefficients for n-alkanes and n-alcohols can be modeled using critical and triple point parameters. Predictions of the phase liquid-vapor, solid-vapor, and liquid-solid equilibria in one-component systems are based on the Clausius-Clapeyron relation, Van der Waals and Simon equations, and the principle of thermodynamic similarity.

Using a Differential Scanning Calorimeter to Teach Phase Equilibria to Students of Igneous and Metamorphic Petrology

ERIC Educational Resources Information Center

Maria, Anton H.; Millam, Evan L.; Wright, Carrie L.

2011-01-01

As an aid for teaching phase equilibria to undergraduate students of igneous and metamorphic petrology, we have designed a laboratory exercise that allows them to create a phase diagram from data produced by differential scanning calorimetry. By preparing and analyzing samples of naphthalene and phenanthrene, students acquire hands-on insight into…

Tethered spacecraft in asteroid gravitational environment

NASA Astrophysics Data System (ADS)

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

2018-02-01

Relative equilibria of a pendulum attached to the surface of a uniformly rotating celestial body are considered. The locations of the tether anchor that correspond to a given spacecraft position are defined. The domains, where the spacecraft can be held with the help of such a pendulum, are also described. Stability of the found relative equilibria is studied.

Semistable extremal ground states for nonlinear evolution equations in unbounded domains

NASA Astrophysics Data System (ADS)

Rodríguez-Bernal, Aníbal; Vidal-López, Alejandro

2008-02-01

In this paper we show that dissipative reaction-diffusion equations in unbounded domains posses extremal semistable ground states equilibria, which bound asymptotically the global dynamics. Uniqueness of such positive ground state and their approximation by extremal equilibria in bounded domains is also studied. The results are then applied to the important case of logistic equations.

An Introduction to Multivariate Curve Resolution-Alternating Least Squares: Spectrophotometric Study of the Acid-Base Equilibria of 8-Hydroxyquinoline-5-Sulfonic Acid

ERIC Educational Resources Information Center

Rodriguez-Rodriguez, Cristina; Amigo, Jose Manuel; Coello, Jordi; Maspoch, Santiago

2007-01-01

A spectrophotometric study of the acid-base equilibria of 8-hydroxyquinoline-5-sulfonic acid to describe the multivariate curve resolution-alternating least squares algorithm (MCR-ALS) is described. The algorithm provides a lot of information and hence is of great importance for the chemometrics research.

Stability of short-axial-wavelength internal kink modes of an anisotropic plasma

NASA Astrophysics Data System (ADS)

Faghihi, M.; Scheffel, J.

1987-12-01

The double adiabatic equations are used to study the stability of a cylindrical Z-pinch with respect to small axial wavelength, internal kink (m ≥ 1) modes. It is found that marginally (ideally) unstable, isotropic equilibria are stabilized. Also, constant-current-density equilibria can be stabilized for P > P and large β

An intrinsic approach in the curved n-body problem: The negative curvature case

NASA Astrophysics Data System (ADS)

Diacu, Florin; Pérez-Chavela, Ernesto; Reyes Victoria, J. Guadalupe

We consider the motion of n point particles of positive masses that interact gravitationally on the 2-dimensional hyperbolic sphere, which has negative constant Gaussian curvature. Using the stereographic projection, we derive the equations of motion of this curved n-body problem in the Poincaré disk, where we study the elliptic relative equilibria. Then we obtain the equations of motion in the Poincaré upper half plane in order to analyze the hyperbolic and parabolic relative equilibria. Using techniques of Riemannian geometry, we characterize each of the above classes of periodic orbits. For n=2 and n=3 we recover some previously known results and find new qualitative results about relative equilibria that were not apparent in an extrinsic setting.

Electromagnetic Torque in Tokamaks with Toroidal Asymmetries

NASA Astrophysics Data System (ADS)

Logan, Nikolas Christopher

Toroidal rotation and rotation shear strongly influences stability and confinement in tokamaks. Breaking of the toroidal symmetry by fields orders of magnitude smaller than the axisymmetric field can, however, produce electromagnetic torques that significantly affect the plasma rotation, stability and confinement. These electromagnetic torques are the study of this thesis. There are two typical types of electromagnetic torques in tokamaks: 1) "resonant torques" for which a plasma current defined by a single toroidal and single poloidal harmonic interact with external currents and 2) "nonresonant torques" for which the global plasma response to nonaxisymmetric fields is phase shifted by kinetic effects that drive the rotation towards a neoclassical offset. This work describes the diagnostics and analysis necessary to evaluate the torque by measuring the rate of momentum transfer per unit area in the vacuum region between the plasma and external currents using localized magnetic sensors to measure the Maxwell stress. These measurements provide model independent quantification of both the resonant and nonresonant electromagnetic torques, enabling direct verification of theoretical models. Measured values of the nonresonant torque are shown to agree well with the perturbed equilibrium nonambipolar transport (PENT) code calculation of torque from cross field transport in nonaxisymmetric equilibria. A combined neoclassical toroidal viscosity (NTV) theory, valid across a wide range of kinetic regimes, is fully implemented for the first time in general aspect ratio and shaped plasmas. The code captures pitch angle resonances, reproducing previously inaccessible collisionality limits in the model. The complete treatment of the model enables benchmarking to the hybrid kinetic MHD stability codes MARS-K and MISK, confirming the energy-torque equivalency principle in perturbed equilibria. Experimental validations of PENT results confirm the torque applied by nonaxisymmetric coils is often proportional to the energy put into the dominant ideal MHD kink mode. This reduces the control of nonresonant torque to a single mode model, enabling efficient feed forward optimization of applied fields. Initial results including the anisotropic kinetic pressure tensor directly in the plasma eigenmode calculations are presented here, and may eventually provide accurate metrics for multimodal coupling similar to the established single mode metrics.

Effect of Fluorine on Near-Liquidus Phase Equilibria of Basalts

NASA Technical Reports Server (NTRS)

Filiberto, Justin; Wood, Justin; Loan, Le; Dasgupta, Rajdeep; Shimizu, Nobumichi; Treiman, Allan H.

2010-01-01

Volatile species such as H2O, CO2, F, and Cl have significant impact in generation and differentiation of basaltic melts. Thus far experimental work has primarily focused on the effect of water and carbon dioxide on basalt crystallization, liquid-line of descent, and mantle melting [e.g., 1, 2] and the effects of halogens have received far less attention [3-4]. However, melts in the planetary interiors can have non-negligible chlorine and fluorine concentrations. Here, we explore the effects of fluorine on near-liquidus phase equilibria of basalt. We have conducted nominally anhydrous piston cylinder experiments using graphite capsules at 0.6 - 1.5 GPa on an Fe-rich model basalt composition. 1.75 wt% fluorine was added to the starting mix in the form of AgF2. Fluorine in the experimental glass was measured by SIMS and major elements of glass and minerals were analyzed by EPMA. Nominally volatile free experiments yield a liquidus temperature from 1330 C at 0.8GPa to 1400 at 1.6GPa and an olivine(Fo72)-pyroxene(En68)-liquid multiple saturation point at 1.25 GPa and 1375 C. The F-bearing experiments yield a liquiudus temperature from 1260 C at 0.6GPa to 1305 at 1.5GPa and an ol(Fo66)-pyx(En64)-MSP at 1 GPa and 1260 C. This shows that F depresses the basalt liquidus, extends the pyroxene stability field to lower pressure, and forces the liquidus phases to be more Fe-rich. KD(Fe-Mg/mineral-melt) calculated for both pyroxenes and olivines show an increase with increasing F content of the melt. Therefore, we infer that F complexes with Mg in the melt and thus increases the melt s silica activity, depressing the liquidus and changing the composition of the crystallizing minerals. Our study demonstrates that on a weight percent basis, the effect of fluorine is similar to the effect of H2O [1] and Cl [3] on freezing point depression of basalts. But on an atomic fraction basis, the effect of F on liquidus depression of basalts is xxxx compared to the effect of H. Future studies on kimberlitic and subduction zone magmas, which could have significant amount of fluorine, will need to consider the combined effects of F, Cl, and H on their stability and chemical evolution.

Dynamical Analysis of Density-dependent Selection in a Discrete one-island Migration Model

Treesearch

James H. Roberds; James F. Selgrade

2000-01-01

A system of non-linear difference equations is used to model the effects of density-dependent selection and migration in a population characterized by two alleles at a single gene locus. Results for the existence and stability of polymorphic equilibria are established. Properties for a genetically important class of equilibria associated with complete dominance in...

Vapor Pressure Plus: An Experiment for Studying Phase Equilibria in Water, with Observation of Supercooling, Spontaneous Freezing, and the Triple Point

ERIC Educational Resources Information Center

Tellinghuisen, Joel

2010-01-01

Liquid-vapor, solid-vapor, and solid-liquid-vapor equilibria are studied for the pure substance water, using modern equipment that includes specially fabricated glass cells. Samples are evaporatively frozen initially, during which they typically supercool to -5 to -10 [degrees]C before spontaneously freezing. Vacuum pumping lowers the temperature…

Imitation dynamics of vaccine decision-making behaviours based on the game theory.

PubMed

Yang, Junyuan; Martcheva, Maia; Chen, Yuming

2016-01-01

Based on game theory, we propose an age-structured model to investigate the imitation dynamics of vaccine uptake. We first obtain the existence and local stability of equilibria. We show that Hopf bifurcation can occur. We also establish the global stability of the boundary equilibria and persistence of the disease. The theoretical results are supported by numerical simulations.

Energetics of photosynthetic glow peaks

PubMed Central

DeVault, Don; Govindjee; Arnold, William

1983-01-01

By postulating temperature-dependent equilibria between two or more electron carriers acting as traps for electrons or holes, it is possible to modify the Randall-Wilkins theory of thermoluminescence so as to explain the abnormally large apparent activation energies and apparent frequency factors observed in photosynthetic glow curves when fitted by unmodified Randall-Wilkins theory. The equilibria serve to inhibit the formation of the light-emitting excited state by withholding the needed precursor state. When the inhibition is released at higher temperature by shift of equilibrium with temperature, the rise of the glow peak can be much faster than would result from Arrhenius behavior based on the true activation energy and so appears to correspond to a higher activation energy accompanied by a larger frequency factor. From another viewpoint, the enthalpy changes, ΔH, of the equilibria tend to add to the activation energy. Similarly the entropy changes, ΔS, of the equilibria tend to add to the entropy of activation, giving the large apparent frequency factors. The positive values of ΔS needed would correspond to entropy decreases in the forward early electron transport. A comparison of the glow peaks obtained by different workers is also presented. PMID:16593283

A stochastic cellular automata model of tautomer equilibria

NASA Astrophysics Data System (ADS)

Bowers, Gregory A.; Seybold, Paul G.

2018-03-01

Many chemical substances, including drugs and biomolecules, exist in solution not as a single species, but as a collection of tautomers and related species. Importantly, each of these species is an independent compoundwith its own specific biochemical and physicochemical properties. The species interconvert in a dynamic and often complicated manner, making modelling the overall species composition difficult. Agent-based cellular automata models are uniquely suited to meet this challenge, allowing the equilibria to be simulated using simple rulesand at the same time capturing the inherent stochasticity of the natural phenomenon. In the present example a stochastic cellular automata model is employed to simulate the tautomer equilibria of 9-anthrone and 9-anthrol in the presence of their common anion. The observed KE of the 9-anthrone ⇌ 9-anthrol tautomerisation along with the measured tautomer pKa values were used to model the equilibria at pH values 4, 7 and 10. At pH 4 and 7, the anthrone comprises >99% of the total species population, while at pH 10the anthrone and the anion each represent just under half of the total population. The advantages of the cellular automata approach over the customary coupled differential equation approach are discussed.

Modeling Complex Equilibria in ITC Experiments: Thermodynamic Parameters Estimation for a Three Binding Site Model

PubMed Central

Le, Vu H.; Buscaglia, Robert; Chaires, Jonathan B.; Lewis, Edwin A.

2013-01-01

Isothermal Titration Calorimetry, ITC, is a powerful technique that can be used to estimate a complete set of thermodynamic parameters (e.g. Keq (or ΔG), ΔH, ΔS, and n) for a ligand binding interaction described by a thermodynamic model. Thermodynamic models are constructed by combination of equilibrium constant, mass balance, and charge balance equations for the system under study. Commercial ITC instruments are supplied with software that includes a number of simple interaction models, for example one binding site, two binding sites, sequential sites, and n-independent binding sites. More complex models for example, three or more binding sites, one site with multiple binding mechanisms, linked equilibria, or equilibria involving macromolecular conformational selection through ligand binding need to be developed on a case by case basis by the ITC user. In this paper we provide an algorithm (and a link to our MATLAB program) for the non-linear regression analysis of a multiple binding site model with up to four overlapping binding equilibria. Error analysis demonstrates that fitting ITC data for multiple parameters (e.g. up to nine parameters in the three binding site model) yields thermodynamic parameters with acceptable accuracy. PMID:23262283

Maintenance of Genetic Variability under Strong Stabilizing Selection: A Two-Locus Model

PubMed Central

Gavrilets, S.; Hastings, A.

1993-01-01

We study a two locus model with additive contributions to the phenotype to explore the relationship between stabilizing selection and recombination. We show that if the double heterozygote has the optimum phenotype and the contributions of the loci to the trait are different, then any symmetric stabilizing selection fitness function can maintain genetic variability provided selection is sufficiently strong relative to linkage. We present results of a detailed analysis of the quadratic fitness function which show that selection need not be extremely strong relative to recombination for the polymorphic equilibria to be stable. At these polymorphic equilibria the mean value of the trait, in general, is not equal to the optimum phenotype, there exists a large level of negative linkage disequilibrium which ``hides'' additive genetic variance, and different equilibria can be stable simultaneously. We analyze dependence of different characteristics of these equilibria on the location of optimum phenotype, on the difference in allelic effect, and on the strength of selection relative to recombination. Our overall result that stabilizing selection does not necessarily eliminate genetic variability is compatible with some experimental results where the lines subject to strong stabilizing selection did not have significant reductions in genetic variability. PMID:8514145

Analysis of the statistical thermodynamic model for nonlinear binary protein adsorption equilibria.

PubMed

Zhou, Xiao-Peng; Su, Xue-Li; Sun, Yan

2007-01-01

The statistical thermodynamic (ST) model was used to study nonlinear binary protein adsorption equilibria on an anion exchanger. Single-component and binary protein adsorption isotherms of bovine hemoglobin (Hb) and bovine serum albumin (BSA) on DEAE Spherodex M were determined by batch adsorption experiments in 10 mM Tris-HCl buffer containing a specific NaCl concentration (0.05, 0.10, and 0.15 M) at pH 7.40. The ST model was found to depict the effect of ionic strength on the single-component equilibria well, with model parameters depending on ionic strength. Moreover, the ST model gave acceptable fitting to the binary adsorption data with the fitted single-component model parameters, leading to the estimation of the binary ST model parameter. The effects of ionic strength on the model parameters are reasonably interpreted by the electrostatic and thermodynamic theories. The effective charge of protein in adsorption phase can be separately calculated from the two categories of the model parameters, and the values obtained from the two methods are consistent. The results demonstrate the utility of the ST model for describing nonlinear binary protein adsorption equilibria.

The coordination chemistry of group 15 element ligand complexes--a developing area.

PubMed

Scheer, Manfred

2008-09-07

A survey of the contemporary challenges of the field of unsubstituted group 15 element ligand complexes (excluding N) is given. The focus of the article is on the coordination chemistry behaviour of such E(n) ligand complexes. This field is subdivided into two areas of reactivity: E(n) ligand complexes with (i) noncoordinated Lewis-acidic cations and (ii) Lewis-acidic coordination compounds containing at least one permanently coordinating ligand. In the latter case, insoluble 1D and 2D polymers respectively are obtained; however, under special conditions soluble, spherical, fullerene-like giant molecules are formed. These nano-sized molecules are up to 2.4 nm in diameter and are able to encapsulate small molecules in their holes. In contrast, the first-mentioned field uses weakly coordinating anions to obtain readily soluble di- and polycationic products. These show depolymerisation tendencies in solution under the formation of oligomer-monomer equilibria and thus reveal dynamic supramolecular aggregation processes.

Species-Specific Thiol-Disulfide Equilibrium Constant: A Tool To Characterize Redox Transitions of Biological Importance.

PubMed

Mirzahosseini, Arash; Somlyay, Máté; Noszál, Béla

2015-08-13

Microscopic redox equilibrium constants, a new species-specific type of physicochemical parameters, were introduced and determined to quantify thiol-disulfide equilibria of biological significance. The thiol-disulfide redox equilibria of glutathione with cysteamine, cysteine, and homocysteine were approached from both sides, and the equilibrium mixtures were analyzed by quantitative NMR methods to characterize the highly composite, co-dependent acid-base and redox equilibria. The directly obtained, pH-dependent, conditional constants were then decomposed by a new evaluation method, resulting in pH-independent, microscopic redox equilibrium constants for the first time. The 80 different, microscopic redox equilibrium constant values show close correlation with the respective thiolate basicities and provide sound means for the development of potent agents against oxidative stress.

Microbial control of mineral–groundwater equilibria:Macroscale to microscale

USGS Publications Warehouse

Bennett, Philip C.; Hiebert, Franz K.; Roger, Jennifer Roberts

2000-01-01

macroscaleprocesses that perturb general groundwater chemistry and therefore mineral–water equilibria; and microscale interactions, where attached organisms locally perturb mineral–water equilibria, potentially releasing limiting trace nutrients from the dissolving mineral.In the contaminated unconfined glacio-fluvial aquifer near Bemidji, Minnesota, USA, carbonate chemistry is influenced primarily at the macroscale. Under oxic conditions, respiration by native aerobic heterotrophs produces excess carbon dioxide that promotes calcite and dolomite dissolution. Aerobic microorganisms do not colonize dolomite surfaces and few occur on calcite. Within the anoxic groundwater, calcite overgrowths form on uncolonized calcite cleavage surfaces, possibly due to the consumption of acidity by dissimilatory iron-reducing bacteria. As molecular oxygen concentration increases downgradient of the oil pool, aerobes again dominate and residual hydrocarbons and ferrous iron are oxidized, resulting in macroscale carbonate-mineral dissolution and iron precipitation.

Current Status of Protein Force Fields for Molecular Dynamics

PubMed Central

Lopes, Pedro E.M.; Guvench, Olgun

2015-01-01

Summary The current status of classical force fields for proteins is reviewed. These include additive force fields as well as the latest developments in the Drude and AMOEBA polarizable force fields. Parametrization strategies developed specifically for the Drude force field are described and compared with the additive CHARMM36 force field. Results from molecular simulations of proteins and small peptides are summarized to illustrate the performance of the Drude and AMOEBA force fields. PMID:25330958

Capillary Flow of Liquid Metals in Brazing

NASA Astrophysics Data System (ADS)

Dehsara, Mohammad

Capillary flow is driven or controlled by capillary forces, exerted at the triple line where the fluid phases meet the solid boundary. Phase field (PF) models naturally accommodate diffusive triple line motion with variable contact angle, thus allowing for the no-slip boundary condition without the stress singularities. Moreover, they are uniquely suited for modeling of topological discontinuities which often arise during capillary flows. In this study, we consider diffusive triple line motion within two PF models: the compositionally compressible (CC) and the incompressible (IC) models. We derive the IC model as a systematic approximation to the CC model, based on a suitable choice of continuum velocity field. The CC model, applied to the fluids of dissimilar mass densities, exhibits a computational instability at the triple line. The IC model perfectly represents the analytic equilibria. We develop the parameter identification procedure and show that the triple line kinetics can be well represented by the IC model's diffusive boundary condition. The IC model is first tested by benchmarking the phase-field and experimental kinetics of water, and silicone oil spreading over the glass plates in which two systems do not interact with the substrate. Then, two high-temperature physical settings involving spreading of the molten Al-Si alloy: one over a rough wetting substrate, the other over a non-wetting substrate are modeled in a T-joint structure which is a typical geometric configuration for many brazing and soldering applications. Surface roughness directly influences the spreading of the molten metal by causing break-ups of the liquid film and trapping the liquid away from the joint. In the early stages of capillary flow over non-wetting surface, the melting and flow are concurrent, so that the kinetics of wetting is strongly affected by the variations in effective viscosity of the partially molten metal. We define adequate time-dependent functions for the variations of Al-Si alloy viscosity and triple line mobility to describe the wetting kinetics.

Resistive wall modes in the EXTRAP T2R reversed-field pinch

NASA Astrophysics Data System (ADS)

Brunsell, P. R.; Malmberg, J.-A.; Yadikin, D.; Cecconello, M.

2003-10-01

Resistive wall modes (RWM) in the reversed field pinch are studied and a detailed comparison of experimental growth rates and linear magnetohydrodynamic (MHD) theory is made. RWM growth rates are experimentally measured in the thin shell device EXTRAP T2R [P. R. Brunsell et al., Plasma Phys. Controlled Fusion 43, 1 (2001)]. Linear MHD calculations of RWM growth rates are based on experimental equilibria. Experimental and linear MHD RWM growth rate dependency on the equilibrium profiles is investigated experimentally by varying the pinch parameter Θ=Bθ(a)/ in the range Θ=1.5-1.8. Quantitative agreement between experimental and linear MHD growth rates is seen. The dominating RWMs are the internal on-axis modes (having the same helicity as the central equilibrium field). At high Θ, external nonresonant modes are also observed. For internal modes experimental growth rates decrease with Θ while for external modes, growth rates increase with Θ. The effect of RWMs on the reversed-field pinch plasma performance is discussed.

Non-Maxwellian effects in magnetosonic solitons

NASA Astrophysics Data System (ADS)

Pokhotelov, O. A.; Balikhin, M. A.; Onishchenko, O. G.; Walker, S. N.

2007-12-01

The role of non-Maxwellian effects on magnetosonic (MS) solitons propagating perpendicular to the external magnetic field in high- β plasmas is analysed. It is shown that they can exist in the form of either humps or holes in the magnetic field in which the field is either increased or decreased relative to the background magnetic field. The shape of the solitary structure depends upon both the form of the ion velocity distribution function and the wave dispersion. A nonlinear equation describing the propagation of MS solitons in high- β plasmas with an arbitrary particle velocity distribution function is derived. It is shown that for Maxwellian and bi-Maxwellian plasmas MS solitons can only exist in the form of the magnetic humps. The same is true for plasmas possessing either a kappa distribution or Kennel-Ashour-Abdalla equilibria. However, plasmas with a ring type ion velocity distribution or a Dory-Guest-Harris distribution with large loss-cone index can support the formation of magnetic holes. The theoretical results obtained are then compared with recent satellite observations.

Hydrodynamic modeling of petroleum reservoirs using simulator MUFITS

NASA Astrophysics Data System (ADS)

Afanasyev, Andrey

2015-04-01

MUFITS is new noncommercial software for numerical modeling of subsurface processes in various applications (www.mufits.imec.msu.ru). To this point, the simulator was used for modeling nonisothermal flows in geothermal reservoirs and for modeling underground carbon dioxide storage. In this work, we present recent extension of the code to petroleum reservoirs. The simulator can be applied in conventional black oil modeling, but it also utilizes a more complicated models for volatile oil and gas condensate reservoirs as well as for oil rim fields. We give a brief overview of the code by providing the description of internal representation of reservoir models, which are constructed of grid blocks, interfaces, stock tanks as well as of pipe segments and pipe junctions for modeling wells and surface networks. For conventional black oil approach, we present the simulation results for SPE comparative tests. We propose an accelerated compositional modeling method for sub- and supercritical flows subjected to various phase equilibria, particularly to three-phase equilibria of vapour-liquid-liquid type. The method is based on the calculation of the thermodynamic potential of reservoir fluid as a function of pressure, total enthalpy and total composition and storing its values as a spline table, which is used in hydrodynamic simulation for accelerated PVT properties prediction. We provide the description of both the spline calculation procedure and the flashing algorithm. We evaluate the thermodynamic potential for a mixture of two pseudo-components modeling the heavy and light hydrocarbon fractions. We develop a technique for converting black oil PVT tables to the potential, which can be used for in-situ hydrocarbons multiphase equilibria prediction under sub- and supercritical conditions, particularly, in gas condensate and volatile oil reservoirs. We simulate recovery from a reservoir subject to near-critical initial conditions for hydrocarbon mixture. We acknowledge financial support by a Grant from the president of the Russian Federation (SP-2222.2012.5) and by Russian foundation for basic research (RFBR 15-31-20585).

Particle paths and phase plane for time-dependent similarity solutions of the one-dimensional Vlasov-Maxwell equations

NASA Technical Reports Server (NTRS)

Roberts, Dana Aaron; Abraham-Shrauner, Barbara

1987-01-01

The phase trajectories of particles in a plasma described by the one-dimensional Vlasov-Maxwell equations are determined qualitatively, analyzing exact general similarity solutions for the cases of temporally damped and growing (sinusoidal or localized) electric fields. The results of numerical integration in both untransformed and Lie-group point-transformed coordinates are presented in extensive graphs and characterized in detail. The implications of the present analysis for the stability of BGK equilibria are explored, and the existence of nonlinear solutions arbitrarily close to and significantly different from the BGK solutions is demonstrated.

Calculating Equilibrium Constants in the SnCl2-H2O-NaOH System According to Potentiometric Titration Data

NASA Astrophysics Data System (ADS)

Maskaeva, L. N.; Fedorova, E. A.; Yusupov, R. A.; Markov, V. F.

2018-05-01

The potentiometric titration of tin chloride SnCl2 is performed in the concentration range of 0.00009-1.1 mol/L with a solution of sodium hydroxide NaOH. According to potentiometric titration data based on modeling equilibria in the SnCl2-H2O-NaOH system, basic equations are generated for the main processes, and instability constants are calculated for the resulting hydroxo complexes and equilibrium constants of low-soluble tin(II) compounds. The data will be of interest for specialists in the field of theory of solutions.

Dynamics and Self-consistent Chaos in a Mean Field Hamiltonian Model

NASA Astrophysics Data System (ADS)

del-Castillo-Negrete, Diego

We study a mean field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas in the finite N and N-> infty kinetic limit (where N is the number of particles). The linear stability of equilibria in the kinetic model is studied as well as the initial value problem including Landau damping . Numerical simulations show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles and show that the N=2 limit has a family of rotating integrable solutions that provide an accurate description of the dynamics. We discuss the role of self-consistent Hamiltonian chaos in the formation of coherent structures, and discuss a mechanism of "violent" mixing caused by a self-consistent elliptic-hyperbolic bifurcation in phase space.

Thermodynamic characteristics of the acid-base equilibria of ethylenediamine- N, N'-diglutaric acid in aqueous solutions using calorimetric data

NASA Astrophysics Data System (ADS)

Gridchin, S. N.; Nikol'skii, V. M.

2017-10-01

The enthalpies of reaction of betaine group neutralization of ethylenediamine- N, N'-diglutaric acid (H4L) at 298.15 K and at different values of ionic strength of 0.1, 0.5, 1.0 (KNO3) is measured by direct calorimetry. The standard thermodynamic characteristics of the protolytic equilibria of H4L are calculated.

Surprising Impact of Remote Groups on the Folding-Unfolding and Dimer-Chain Equilibria of Bifunctionl H-Bonding Unimers

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

Liu, Rui; Cheng, Shuang; Baker, Erin Shammel

2016-01-28

Oligoamide 1, consisting of two H-bonding units linked by a trimethylene linker, was previously found to form a very stable, folded dimer. In this work, replacing the side chains and end groups of 1 led to derivatives that show the surprising impact of end groups on the folding and dimer-chain equilibria of the resultant molecules.

Free boundary skin current MHD (magnetohydrodynamic) equilibria

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

Reusch, M.F.

1988-02-01

Function theoretic methods in the complex plane are used to develop simple parametric hodograph formulae which generate sharp boundary equilibria of arbitrary shape. The related method of Gorenflo and Merkel is discussed. A numerical technique for the construction of solutions, based on one of the methods is presented. A study is made of the bifurcations of an equilibrium of general form. 28 refs., 9 figs.

Spacecraft Debris Avoidance Using Positively Invariant Constraint Admissible Sets

DTIC Science & Technology

2013-07-11

Search; Bounded Disturbances; Linear Time-Varying (LTV); Clohessy - Wiltshire -Hill (CWH) 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT...spacecraft equilibria in the Clohessy - Wiltshire -Hill (CWH) relative motion frame [2]. The collection of equilibria form a virtual net in the vicinity of...ABBREVIATIONS, AND ACRONYMS CWH Clohessy - Wiltshire -Hill LTV linear time-varying Distribution Statement A: Approved for public release; distribution is unlimited

Experimental investigation and application of the equilibrium rutile + orthopyroxene = quartz + ilmenite

USGS Publications Warehouse

Hayob, J.L.; Bohlen, S.R.; Essene, E.J.

1993-01-01

Equilibria in the Sirf (Silica-Ilmenite-Rutile-Ferrosilite) system: {Mathematical expression} have been calibrated in the range 800-1100?? C and 12-26 kbar using a piston-cylinder apparatus to assess the potential of the equilibria for geobarometry in granulite facies assemblages that lack garnet. Thermodynamic calculations indicate that the two end-member equilibria involving quartz + geikielite = rutile + enstatite, and quartz + ilmenite = rutile + ferrosilite, are metastable. We therefore reversed equilibria over the compositional range Fs40-70, using Ag80Pd20 capsules with {Mathematical expression} buffered at or near iron-wu??stite. Ilmenite compositions coexisting with orthopyroxene are {Mathematical expression} of 0.06 to 0.15 and {Mathematical expression} of 0.00 to 0.01, corresponding to KD values of 13.3, 10.2, 9.0 and 8.0 (??0.5) at 800, 900, 1000 and 1100?? C, respectively, where KD=(XMg/XFe)Opx/(XMg/XFe)Ilm. Pressures have been calculated using equilibria in the Sirf system for granulites from the Grenville Province of Ontario and for granulite facies xenoliths from central Mexico. Pressures are consistent with other well-calibrated geobarometers for orthopyroxeneilmenite pairs from two Mexican samples in which oxide textures appear to represent equilibrium. Geologically unreasonable pressures are obtained, however, where oxide textures are complex. Application of data from this study on the equilibrium distribution of iron and magnesium between ilmenite and orthopyroxene suggests that some ilmenite in deep crustal xenoliths is not equilibrated with coexisting pyroxene, while assemblages from exposed granulite terranes have reequilibrated during retrogression. The Sirf equilibria are sensitive to small changes in composition and may be used for determination of activity/composition (a/X) relations of orthopyroxene if an ilmenite model is specified. A symmetric regular solution model has been used for orthopyroxene in conjunction with activity models for ilmenite available from the literature to calculate a/X relations in orthopyroxene of intermediate composition. Data from this study indicate that FeSiO3-MgSiO3 orthopyroxene exhibits small, positive deviations from ideality over the range 800-1100??C. ?? 1993 Springer-Verlag.

An Asymptotic and Stochastic Theory for the Effects of Surface Gravity Waves on Currents and Infragravity Waves

NASA Astrophysics Data System (ADS)

McWilliams, J. C.; Lane, E.; Melville, K.; Restrepo, J.; Sullivan, P.

2004-12-01

Oceanic surface gravity waves are approximately irrotational, weakly nonlinear, and conservative, and they have a much shorter time scale than oceanic currents and longer waves (e.g., infragravity waves) --- except where the primary surface waves break. This provides a framework for an asymptotic theory, based on separation of time (and space) scales, of wave-averaged effects associated with the conservative primary wave dynamics combined with a stochastic representation of the momentum transfer and induced mixing associated with non-conservative wave breaking. Such a theory requires only modest information about the primary wave field from measurements or operational model forecasts and thus avoids the enormous burden of calculating the waves on their intrinsically small space and time scales. For the conservative effects, the result is a vortex force associated with the primary wave's Stokes drift; a wave-averaged Bernoulli head and sea-level set-up; and an incremental material advection by the Stokes drift. This can be compared to the "radiation stress" formalism of Longuet-Higgins, Stewart, and Hasselmann; it is shown to be a preferable representation since the radiation stress is trivial at its apparent leading order. For the non-conservative breaking effects, a population of stochastic impulses is added to the current and infragravity momentum equations with distribution functions taken from measurements. In offshore wind-wave equilibria, these impulses replace the conventional surface wind stress and cause significant differences in the surface boundary layer currents and entrainment rate, particularly when acting in combination with the conservative vortex force. In the surf zone, where breaking associated with shoaling removes nearly all of the primary wave momentum and energy, the stochastic forcing plays an analogous role as the widely used nearshore radiation stress parameterizations. This talk describes the theoretical framework and presents some preliminary solutions using it. McWilliams, J.C., J.M. Restrepo, & E.M. Lane, 2004: An asymptotic theory for the interaction of waves and currents in coastal waters. J. Fluid Mech. 511, 135-178. Sullivan, P.P., J.C. McWilliams, & W.K. Melville, 2004: The oceanic boundary layer driven by wave breaking with stochastic variability. J. Fluid Mech. 507, 143-174.

The effect of delays on filament oscillations and stability

NASA Astrophysics Data System (ADS)

van den Oord, G. H. J.; Schutgens, N. A. J.; Kuperus, M.

1998-11-01

We discuss the linear response of a filament to perturbations, taking the finite communication time between the filament and the photosphere into account. The finite communication time introduces delays in the system. Recently Schutgens (1997ab) investigated the solutions of the delay equation for vertical perturbations. In this paper we expand his analysis by considering also horizontal and coupled oscillations. The latter occur in asymmetric coronal fields. We also discuss the effect of Alfven wave emission on filament oscillations and show that wave emission is important for stabilizing filaments. We introduce a fairly straightforward method to study the solutions of delay equations as a function of the filament-photosphere communication time. A solution can be described by a linear combination of damped harmonic oscillations each characterized by a frequency, a damping/growth time and, accordingly, a quality factor. As a secondary result of our analysis we show that, within the context of line current models, Kippenhahn/Schlüter-type filament equilibria can never be stable in the horizontal and the vertical direction at the same time but we also demonstrate that Kuperus/Raadu-type equilibria can account for both an inverse or a normal polarity signature. The diagnostic value of our analysis for determining, e.g., the filament current from observations of oscillating filaments is discussed.

Relativistic Self-similar Equilibria and Non-axisymmetric Neutral Modes

NASA Astrophysics Data System (ADS)

Cai, Mike J.; Shu, F. H.

2002-05-01

We have constructed semi-analytic axisymmetric scale free solutions to Einstein field equations with perfect fluid matter source. These spacetimes are self-similar under the simultaneous transformation r'= ar and t'=a1-nt. We explored the two dimensional solution space parameterized by the rescaling index n and the isothermal sound speed γ 1/2. The isopycnic surfaces are in general toroids. As the equilibrium configuration rotates faster, an ergo region develops in the form of the exterior of a cone centered about the symmetry axis. The sequence of solution terminates when frame dragging becomes infinite and the ergo cone closes onto the axis. In the extreme flattening limit, we have also searched for non-axisymmetric neutral modes in a self-similar disk. Two separate sets of tracks are discovered in the solution space. One corresponds to the bifurcation points to non-axisymmetric equilibria, which is confined in the non-ergo solutions. The other track signals the onset of instability driven by gravitational radiation. These solutions are formally infinite in extent, and thus can not represent realistic astrophysical systems. However, if these properties do not alter qualitatively when the self-similar configurations are truncated, then these solutions may serve as initial data for dynamic collapse in super massive black hole formation.

Dynamics of an eco-epidemiological model with saturated incidence rate

NASA Astrophysics Data System (ADS)

Suryanto, Agus

2017-03-01

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

Packings of a charged line on a sphere.

PubMed

Alben, Silas

2008-12-01

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

The strongest magnetic barrier in the DIII-D tokamak and comparison with the ASDEX UG

NASA Astrophysics Data System (ADS)

Ali, Halima; Punjabi, Alkesh

2013-05-01

Magnetic perturbations in tokamaks lead to the formation of magnetic islands, chaotic field lines, and the destruction of flux surfaces. Controlling or reducing transport along chaotic field lines is a key challenge in magnetically confined fusion plasmas. A local control method was proposed by Chandre et al. [Nucl. Fusion 46, 33-45 (2006)] to build barriers to magnetic field line diffusion by addition of a small second-order control term localized in the phase space to the field line Hamiltonian. Formation and existence of such magnetic barriers in Ohmically heated tokamaks (OHT), ASDEX UG and piecewise analytic DIII-D [Luxon, J.L.; Davis, L.E., Fusion Technol. 8, 441 (1985)] plasma equilibria was predicted by the authors [Ali, H.; Punjabi, A., Plasma Phys. Control. Fusion 49, 1565-1582 (2007)]. Very recently, this prediction for the DIII-D has been corroborated [Volpe, F.A., et al., Nucl. Fusion 52, 054017 (2012)] by field-line tracing calculations, using experimentally constrained Equilibrium Fit (EFIT) [Lao, et al., Nucl. Fusion 25, 1611 (1985)] DIII-D equilibria perturbed to include the vacuum field from the internal coils utilized in the experiments. This second-order approach is applied to the DIII-D tokamak to build noble irrational magnetic barriers inside the chaos created by the locked resonant magnetic perturbations (RMPs) (m, n)=(3, 1)+(4, 1), with m and n the poloidal and toroidal mode numbers of the Fourier expansion of the magnetic perturbation with amplitude δ. A piecewise, analytic, accurate, axisymmetric generating function for the trajectories of magnetic field lines in the DIII-D is constructed in magnetic coordinates from the experimental EFIT Grad-Shafranov solver [Lao, L, et al., Fusion Sci. Technol. 48, 968 (2005)] for the shot 115,467 at 3000 ms in the DIII-D. A symplectic mathematical map is used to integrate field lines in the DIII-D. A numerical algorithm [Ali, H., et al., Radiat. Eff. Def. Solids Inc. Plasma Sc. Plasma Tech. 165, 83 (2010)] based on continued fraction decomposition of the rotational transform labeling the barriers for selecting and identifying the strongest noble irrational barrier is used. The results are compared and contrasted with our previous results on the ASDEX UG. About six times stronger a barrier can be built in the DIII-D than in the ASDEX UG. High magnetic shear near the separatrix in the DIII-D is inferred as the possible cause of this. Implications of this for the DIII-D and the International Thermonuclear Experimental Reactor (ITER) are discussed.

Levitation forces of a bulk YBCO superconductor in gradient varying magnetic fields

NASA Astrophysics Data System (ADS)

Jiang, J.; Gong, Y. M.; Wang, G.; Zhou, D. J.; Zhao, L. F.; Zhang, Y.; Zhao, Y.

2015-09-01

The levitation forces of a bulk YBCO superconductor in gradient varying high and low magnetic fields generated from a superconducting magnet were investigated. The magnetic field intensity of the superconducting magnet was measured when the exciting current was 90 A. The magnetic field gradient and magnetic force field were both calculated. The YBCO bulk was cooled by liquid nitrogen in field-cooling (FC) and zero-field-cooling (ZFC) condition. The results showed that the levitation forces increased with increasing the magnetic field intensity. Moreover, the levitation forces were more dependent on magnetic field gradient and magnetic force field than magnetic field intensity.

A Review and Evaluation of the Phase Equilibria, Liquid-Phase Heats of Mixing and Excess Volumes, and Gas-Phase PVT Measurements for Nitrogen+Methane

NASA Astrophysics Data System (ADS)

Kidnay, A. J.; Miller, R. C.; Sloan, E. D.; Hiza, M. J.

1985-07-01

The available experimental data for vapor-liquid equilibria, heat of mixing, change in volume on mixing for liquid mixtures, and gas-phase PVT measurements for nitrogen+methane have been reviewed and where possible evaluated for consistency. The derived properties chosen for analysis and correlation were liquid mixture excess Gibbs free energies, and Henry's constants.

Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction–diffusion systems

NASA Astrophysics Data System (ADS)

Fellner, Klemens; Tang, Bao Quoc

2018-06-01

The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.

Dynamics of Axially Symmetric Perturbed Hamiltonians in 1:1:1 Resonance

NASA Astrophysics Data System (ADS)

Carrasco, D.; Palacián, J. F.; Vidal, C.; Vidarte, J.; Yanguas, P.

2018-03-01

We study the dynamics of a family of perturbed three-degree-of-freedom Hamiltonian systems which are in 1:1:1 resonance. The perturbation consists of axially symmetric cubic and quartic arbitrary polynomials. Our analysis is performed by normalisation, reduction and KAM techniques. Firstly, the system is reduced by the axial symmetry, and then, periodic solutions and KAM 3-tori of the full system are determined from the relative equilibria. Next, the oscillator symmetry is extended by normalisation up to terms of degree 4 in rectangular coordinates; after truncation of higher orders and reduction to the orbit space, some relative equilibria are established and periodic solutions and KAM 3-tori of the original system are obtained. As a third step, the reduction in the two symmetries leads to a one-degree-of-freedom system that is completely analysed in the twice reduced space. All the relative equilibria together with the stability and parametric bifurcations are determined. Moreover, the invariant 2-tori (related to the critical points of the twice reduced space), some periodic solutions and the KAM 3-tori, all corresponding to the full system, are established. Additionally, the bifurcations of equilibria occurring in the twice reduced space are reconstructed as quasi-periodic bifurcations involving 2-tori and periodic solutions of the full system.

Gas chemistry of Icelandic thermal fluids

NASA Astrophysics Data System (ADS)

Stefánsson, Andri

2017-10-01

The chemistry of gases in thermal fluids from Iceland was studied in order to evaluate the sources and processes affecting volatile concentrations in volcanic geothermal systems at divergent plate boundaries. The fluids included vapor fumaroles and two-phase well discharges with temperatures of 100-340 °C. The vapor was dominated by H2O accounting for 62-100 mol% and generally for > 99 mol%, with CO2, H2S and H2 being the dominant gases followed by N2, CH4, and Ar. Overall mineral-gas and gas-gas equilibria were not observed for the major gases, including CO2, H2S, H2 and CH4 within the geothermal reservoirs. Instead the system proved to be controlled by source(s) and their ratios and various metastable equilibria along a fluid-rock reaction progress with gas concentrations controlled by such metastable equilibria varying at particular temperatures as a functional extent of reaction. The concentrations of H2S and H2 closely reflect mineral-fluid metastable equilibria, whereas CO2 concentrations are controlled by the input of magma gas corresponding to > 0.1 to < 5% mass input. With fluid ascent to the surface, boiling and condensation may occur, further changing the gas concentrations and hence surface fumaroles may not reflect the reservoir fluid characteristics but rather secondary processes.

Use of reconstructed 3D equilibria to determine onset conditions of helical cores in tokamaks for extrapolation to ITER

NASA Astrophysics Data System (ADS)

Wingen, A.; Wilcox, R. S.; Seal, S. K.; Unterberg, E. A.; Cianciosa, M. R.; Delgado-Aparicio, L. F.; Hirshman, S. P.; Lao, L. L.

2018-03-01

Large, spontaneous m/n  =  1/1 helical cores are shown to be expected in tokamaks such as ITER with extended regions of low- or reversed- magnetic shear profiles and q near 1 in the core. The threshold for this spontaneous symmetry breaking is determined using VMEC scans, beginning with reconstructed 3D equilibria from DIII-D and Alcator C-Mod based on observed internal 3D deformations. The helical core is a saturated internal kink mode (Wesson 1986 Plasma Phys. Control. Fusion 28 243); its onset threshold is shown to be proportional to (dp/dρ)/B_t2 around q  =  1. Below the threshold, applied 3D fields can drive a helical core to finite size, as in DIII-D. The helical core size thereby depends on the magnitude of the applied perturbation. Above it, a small, random 3D kick causes a bifurcation from axisymmetry and excites a spontaneous helical core, which is independent of the kick size. Systematic scans of the q-profile show that the onset threshold is very sensitive to the q-shear in the core. Helical cores occur frequently in Alcator C-Mod during ramp-up when slow current penetration results in a reversed shear q-profile, which is favorable for helical core formation. Finally, a comparison of the helical core onset threshold for discharges from DIII-D, Alcator C-Mod and ITER confirms that while DIII-D is marginally stable, Alcator C-Mod and especially ITER are highly susceptible to helical core formation without being driven by an externally applied 3D magnetic field.

Use of reconstructed 3D equilibria to determine onset conditions of helical cores in tokamaks for extrapolation to ITER

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

Wingen, A.; Wilcox, R. S.; Seal, S. K.

In this paper, large, spontaneous m/n = 1/1 helical cores are shown to be expected in tokamaks such as ITER with extended regions of low- or reversed- magnetic shear profiles and q near 1 in the core. The threshold for this spontaneous symmetry breaking is determined using VMEC scans, beginning with reconstructed 3D equilibria from DIII-D and Alcator C-Mod based on observed internal 3D deformations. The helical core is a saturated internal kink mode (Wesson 1986 Plasma Phys. Control. Fusion 28 243); its onset threshold is shown to be proportional tomore » $$({\\rm d}p/{\\rm d}\\rho)/B_t^2$$ around q = 1. Below the threshold, applied 3D fields can drive a helical core to finite size, as in DIII-D. The helical core size thereby depends on the magnitude of the applied perturbation. Above it, a small, random 3D kick causes a bifurcation from axisymmetry and excites a spontaneous helical core, which is independent of the kick size. Systematic scans of the q-profile show that the onset threshold is very sensitive to the q-shear in the core. Helical cores occur frequently in Alcator C-Mod during ramp-up when slow current penetration results in a reversed shear q-profile, which is favorable for helical core formation. In conclusion, a comparison of the helical core onset threshold for discharges from DIII-D, Alcator C-Mod and ITER confirms that while DIII-D is marginally stable, Alcator C-Mod and especially ITER are highly susceptible to helical core formation without being driven by an externally applied 3D magnetic field.« less

On the Basic Principles of Igneous Petrology

NASA Astrophysics Data System (ADS)

Marsh, B. D.

2014-12-01

How and why Differentiation occurs has dominated Igneous Petrology since its beginning (~1880) even though many of the problems associated with it have been thoroughly solved. Rediscovery of the proverbial wheel with new techniques impedes progress. As soon as thin section petrography was combined with rock and mineral chemistry, rock diversity, compositional suites, and petrographic provinces all became obvious. The masterful 1902 CIPW norm in a real sense solved the chemical mystery of differentiation: rocks are related by the addition and subtraction of minerals in the anciently appreciated process of fractional crystallization. Yet few believed this, even after phase equilibria arrived. Assimilation, gas transfer, magma mixing, Soret diffusion, immiscibility, and other processes had strong adherents, even though by 1897 Becker conclusively showed the ineffectiveness of molecular diffusion in large-scale processes. The enormity of heat to molecular diffusion (today's Lewis no.) should have been convincing; but few paid attention. Bowen did, and he refined and restated the result; few still paid attention. And in spite of his truly masterful command of experiment and field relations in promoting fractional crystallization, Fenner and others fought him with odd arguments. The beauty of phase equilibria eventually dominated at the expense of knowing the physical side of differentiation. Bowen himself saw and struggled with the connection between physical and chemical processes. Progress has come from new concepts in heat transfer, kinetics, and slurry dynamics. The key approach is understanding the dynamic competition between spatial rates of solidification and all other processes. The lesson is clear: Scholarship and combined field, laboratory and technical expertise are critical to understanding magmatic processes. Magma is a limitlessly enchanting and challenging material wherein physical processes buttressed by chemistry govern.

Use of reconstructed 3D equilibria to determine onset conditions of helical cores in tokamaks for extrapolation to ITER

DOE PAGES

Wingen, A.; Wilcox, R. S.; Seal, S. K.; ...

2018-01-15

In this paper, large, spontaneous m/n = 1/1 helical cores are shown to be expected in tokamaks such as ITER with extended regions of low- or reversed- magnetic shear profiles and q near 1 in the core. The threshold for this spontaneous symmetry breaking is determined using VMEC scans, beginning with reconstructed 3D equilibria from DIII-D and Alcator C-Mod based on observed internal 3D deformations. The helical core is a saturated internal kink mode (Wesson 1986 Plasma Phys. Control. Fusion 28 243); its onset threshold is shown to be proportional tomore » $$({\\rm d}p/{\\rm d}\\rho)/B_t^2$$ around q = 1. Below the threshold, applied 3D fields can drive a helical core to finite size, as in DIII-D. The helical core size thereby depends on the magnitude of the applied perturbation. Above it, a small, random 3D kick causes a bifurcation from axisymmetry and excites a spontaneous helical core, which is independent of the kick size. Systematic scans of the q-profile show that the onset threshold is very sensitive to the q-shear in the core. Helical cores occur frequently in Alcator C-Mod during ramp-up when slow current penetration results in a reversed shear q-profile, which is favorable for helical core formation. In conclusion, a comparison of the helical core onset threshold for discharges from DIII-D, Alcator C-Mod and ITER confirms that while DIII-D is marginally stable, Alcator C-Mod and especially ITER are highly susceptible to helical core formation without being driven by an externally applied 3D magnetic field.« less

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.

Contact discontinuities in a cold collision-free two-beam plasma

NASA Technical Reports Server (NTRS)

Kirkland, K. B.; Sonnerup, B. U. O.

1982-01-01

The structure of contact discontinuities in a collision-free plasma is examined using a model of a plasma which consists of two oppositely directed cold ion beams and a background of cold massless electrons such that exact charge neutrality is maintained and that the electric field is zero. The basic equations describing self-consistent equilibria are obtained for the more general situation where a net flow across the layer takes place and where the magnetic field has two nonzero tangential components but where the electric field remains zero. These equations are then specialized to the case of no net plasma flow where one of the tangential components is zero, and four different classes of sheets are obtained, all having thickness the order of the ion inertial length. The first class is for layers separating two identical plasma and magnetic field regions, the second is for an infinite array of parallel layers producing an undulated magnetic field, the third is for layers containing trapped ions in closed orbits which separate two vacuum regions with uniform identical magnetic fields, and the fourth is for layers which reflect a single plasma beam, leaving a vacuum with a reversed and compressed tangential field on the other side.

ON ESTIMATING FORCE-FREENESS BASED ON OBSERVED MAGNETOGRAMS

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

Zhang, X. M.; Zhang, M.; Su, J. T., E-mail: xmzhang@nao.cas.cn

It is a common practice in the solar physics community to test whether or not measured photospheric or chromospheric vector magnetograms are force-free, using the Maxwell stress as a measure. Some previous studies have suggested that magnetic fields of active regions in the solar chromosphere are close to being force-free whereas there is no consistency among previous studies on whether magnetic fields of active regions in the solar photosphere are force-free or not. Here we use three kinds of representative magnetic fields (analytical force-free solutions, modeled solar-like force-free fields, and observed non-force-free fields) to discuss how measurement issues such asmore » limited field of view (FOV), instrument sensitivity, and measurement error could affect the estimation of force-freeness based on observed magnetograms. Unlike previous studies that focus on discussing the effect of limited FOV or instrument sensitivity, our calculation shows that just measurement error alone can significantly influence the results of estimates of force-freeness, due to the fact that measurement errors in horizontal magnetic fields are usually ten times larger than those in vertical fields. This property of measurement errors, interacting with the particular form of a formula for estimating force-freeness, would result in wrong judgments of the force-freeness: a truly force-free field may be mistakenly estimated as being non-force-free and a truly non-force-free field may be estimated as being force-free. Our analysis calls for caution when interpreting estimates of force-freeness based on measured magnetograms, and also suggests that the true photospheric magnetic field may be further away from being force-free than it currently appears to be.« less

The equation of state of n-pentane in the atomistic model TraPPE-EH

NASA Astrophysics Data System (ADS)

Valeev, B. U.; Pisarev, V. V.

2018-01-01

In this work, we study the vapor-liquid equilibrium in n-pentane. We use the TraPPE-EH (transferable potentials for phase equilibria-explicit hydrogen) forcefield, where each hydrogen and carbon atom is considered as independent center of force. The fluid behavior was investigated with different values of density and temperature by molecular dynamics method. The n-pentane evaporation curve was calculated in the temperature range of 290 to 390 K. The densities of the coexisting phases are also calculated. The compression curve at 370 K was calculated and isothermal bulk modulus was found. The simulated properties of n-pentane are in good agreement with data from a database of the National Institute of Standards and Technology, so the TraPPE-EH model can be recommended for simulations of hydrocarbons.

A conserved quantity in thin body dynamics

NASA Astrophysics Data System (ADS)

Hanna, J. A.; Pendar, H.

2016-02-01

Thin, solid bodies with metric symmetries admit a restricted form of reparameterization invariance. Their dynamical equilibria include motions with both rigid and flowing aspects. On such configurations, a quantity is conserved along the intrinsic coordinate corresponding to the symmetry. As an example of its utility, this conserved quantity is combined with linear and angular momentum currents to construct solutions for the equilibria of a rotating, flowing string, for which it is akin to Bernoulli's constant.

Free boundary skin current magnetohydrodynamic equilibria

NASA Astrophysics Data System (ADS)

Reusch, Michael F.

1988-10-01

Function theoretic methods in the complex plane are used to develop simple parametric hodograph formulas that generate sharp boundary equilibria of arbitrary shape. The related method of Gorenflo [Z. Angew. Math. Phys. 16, 279 (1965)] and Merkel (Ph.D. thesis, University of Munich, 1965) is discussed. A numerical technique for the construction of solutions, based on one of the methods, is presented. A study is made of the bifurcations of an equilibrium of general form.

Medium-β free-boundary equilibria of a quasi-isodynamic stellarator

NASA Astrophysics Data System (ADS)

Mikhailov, M. I.; Drevlak, M.; Nührenberg, J.; Shafranov, V. D.

2012-06-01

Free-boundary MHD equilibria with magnetic surfaces in the vacuum region surrounding the plasma [E. Strumberger, Nucl. Fusion 37, 19 (1997); M. Drevlak, D. Monticello, and A. Reiman, Nucl. Fusion 45, 731 (2005)] are obtained for a quasi-isodynamic stellarator [A. A. Subbotin, M. I. Mikhailov, V. D. Shafranov et al., Nucl. Fusion 46, 921 (2006); M. I. Mikhailov, J. Nuhrenberg, and V. D. Shafranov, Plasma Phys. Rep. 35, 529 (2009)].

Medium-{beta} free-boundary equilibria of a quasi-isodynamic stellarator

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

Mikhailov, M. I.; Drevlak, M.; Nuehrenberg, J.

Free-boundary MHD equilibria with magnetic surfaces in the vacuum region surrounding the plasma [E. Strumberger, Nucl. Fusion 37, 19 (1997); M. Drevlak, D. Monticello, and A. Reiman, Nucl. Fusion 45, 731 (2005)] are obtained for a quasi-isodynamic stellarator [A. A. Subbotin, M. I. Mikhailov, V. D. Shafranov et al., Nucl. Fusion 46, 921 (2006); M. I. Mikhailov, J. Nuhrenberg, and V. D. Shafranov, Plasma Phys. Rep. 35, 529 (2009)].

Gyrokinetic magnetohydrodynamics and the associated equilibria

NASA Astrophysics Data System (ADS)

Lee, W. W.; Hudson, S. R.; Ma, C. H.

2017-12-01

The gyrokinetic magnetohydrodynamic (MHD) equations, related to the recent paper by W. W. Lee ["Magnetohydrodynamics for collisionless plasmas from the gyrokinetic perspective," Phys. Plasmas 23, 070705 (2016)], and their associated equilibria properties are discussed. This set of equations consists of the time-dependent gyrokinetic vorticity equation, the gyrokinetic parallel Ohm's law, and the gyrokinetic Ampere's law as well as the equations of state, which are expressed in terms of the electrostatic potential, ϕ, and the vector potential, A , and support both spatially varying perpendicular and parallel pressure gradients and the associated currents. The corresponding gyrokinetic MHD equilibria can be reached when ϕ→0 and A becomes constant in time, which, in turn, gives ∇.(J∥+J⊥)=0 and the associated magnetic islands, if they exist. Examples of simple cylindrical geometry are given. These gyrokinetic MHD equations look quite different from the conventional MHD equations, and their comparisons will be an interesting topic in the future.

Self-organization in a distributed coordination game through heuristic rules

NASA Astrophysics Data System (ADS)

Agarwal, Shubham; Ghosh, Diptesh; Chakrabarti, Anindya S.

2016-12-01

In this paper, we consider a distributed coordination game played by a large number of agents with finite information sets, which characterizes emergence of a single dominant attribute out of a large number of competitors. Formally, N agents play a coordination game repeatedly, which has exactly N pure strategy Nash equilibria, and all of the equilibria are equally preferred by the agents. The problem is to select one equilibrium out of N possible equilibria in the least number of attempts. We propose a number of heuristic rules based on reinforcement learning to solve the coordination problem. We see that the agents self-organize into clusters with varying intensities depending on the heuristic rule applied, although all clusters but one are transitory in most cases. Finally, we characterize a trade-off in terms of the time requirement to achieve a degree of stability in strategies versus the efficiency of such a solution.

Origins of the temperature dependence of hammerhead ribozyme catalysis.

PubMed Central

Peracchi, A

1999-01-01

The difficulties in interpreting the temperature dependence of protein enzyme reactions are well recognized. Here, the hammerhead ribozyme cleavage was investigated under single-turnover conditions between 0 and 60 degrees C as a model for RNA-catalyzed reactions. Under the adopted conditions, the chemical step appears to be rate-limiting. However, the observed rate of cleavage is affected by pre-catalytic equilibria involving deprotonation of an essential group and binding of at least one low-affinity Mg2+ion. Thus, the apparent entropy and enthalpy of activation include contributions from the temperature dependence of these equilibria, precluding a simple physical interpretation of the observed activation parameters. Similar pre-catalytic equilibria likely contribute to the observed activation parameters for ribozyme reactions in general. The Arrhenius plot for the hammerhead reaction is substantially curved over the temperature range considered, which suggests the occurrence of a conformational change of the ribozyme ground state around physiological temperatures. PMID:10390528

Strategic trade between two regions with partial local consumer protection - General setup and nash equilibria

NASA Astrophysics Data System (ADS)

Iordanov, Iordan V.; Vassilev, Andrey A.

2017-12-01

We construct a model of the trade relations between two regions for the case when the trading entities (consumers) compete for a scarce good and there is an element of strategic interdependence in the trading process. Additionally, local consumers enjoy partial protection in the form of guaranteed access to a part of the locally-supplied quantity of the good. The model is formulated for the general asymmetric case, where the two regions differ in terms of parameters such as income, size of the local market supply, degree of protection and transportation costs. For this general model we establish the existence of Nash equilibria and obtain their form as a function of the model parameters, producing a typology of the equilibria. This is a required step in order to rigorously study various types of price dynamics for the model.

Thermodynamic calculations in the system CH4-H2O and methane hydrate phase equilibria

USGS Publications Warehouse

Circone, S.; Kirby, S.H.; Stern, L.A.

2006-01-01

Using the Gibbs function of reaction, equilibrium pressure, temperature conditions for the formation of methane clathrate hydrate have been calculated from the thermodynamic properties of phases in the system CH4-H 2O. The thermodynamic model accurately reproduces the published phase-equilibria data to within ??2 K of the observed equilibrium boundaries in the range 0.08-117 MPa and 190-307 K. The model also provides an estimate of the third-law entropy of methane hydrate at 273.15 K, 0.1 MPa of 56.2 J mol-1 K-1 for 1/n CH4??H 2O, where n is the hydrate number. Agreement between the calculated and published phase-equilibria data is optimized when the hydrate composition is fixed and independent of the pressure and temperature for the conditions modeled. ?? 2006 American Chemical Society.

Gyrokinetic magnetohydrodynamics and the associated equilibria

DOE PAGES

Lee, W. W.; Hudson, S. R.; Ma, C. H.

2017-12-27

The gyrokinetic magnetohydrodynamic (MHD) equations, related to the recent paper by W. W. Lee, and their associated equilibria properties are discussed. This set of equations consists of the time-dependent gyrokinetic vorticity equation, the gyrokinetic parallel Ohm's law, and the gyrokinetic Ampere's law as well as the equations of state, which are expressed in terms of the electrostatic potential, Φ, and the vector potential, A, and support both spatially varying perpendicular and parallel pressure gradients and the associated currents. The corresponding gyrokinetic MHD equilibria can be reached when Φ → 0 and A becomes constant in time, which, in turn, givesmore » ∇· (J ∥+J ⊥) = 0 and the associated magnetic islands, if they exist. Examples of simple cylindrical geometry are given. In conclusion, these gyrokinetic MHD equations look quite different from the conventional MHD equations, and their comparisons will be an interesting topic in the future.« less

Gyrokinetic magnetohydrodynamics and the associated equilibria

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

Lee, W. W.; Hudson, S. R.; Ma, C. H.

The gyrokinetic magnetohydrodynamic (MHD) equations, related to the recent paper by W. W. Lee, and their associated equilibria properties are discussed. This set of equations consists of the time-dependent gyrokinetic vorticity equation, the gyrokinetic parallel Ohm's law, and the gyrokinetic Ampere's law as well as the equations of state, which are expressed in terms of the electrostatic potential, Φ, and the vector potential, A, and support both spatially varying perpendicular and parallel pressure gradients and the associated currents. The corresponding gyrokinetic MHD equilibria can be reached when Φ → 0 and A becomes constant in time, which, in turn, givesmore » ∇· (J ∥+J ⊥) = 0 and the associated magnetic islands, if they exist. Examples of simple cylindrical geometry are given. In conclusion, these gyrokinetic MHD equations look quite different from the conventional MHD equations, and their comparisons will be an interesting topic in the future.« less

Prediction of vapour-liquid and vapour-liquid-liquid equilibria of nitrogen-hydrocarbon mixtures used in J-T refrigerators

NASA Astrophysics Data System (ADS)

Narayanan, Vineed; Venkatarathnam, G.

2018-03-01

Nitrogen-hydrocarbon mixtures are widely used as refrigerants in J-T refrigerators operating with mixtures, as well as in natural gas liquefiers. The Peng-Robinson equation of state has traditionally been used to simulate the above cryogenic process. Multi parameter Helmholtz energy equations are now preferred for determining the properties of natural gas. They have, however, been used only to predict vapour-liquid equilibria, and not vapour-liquid-liquid equilibria that can occur in mixtures used in cryogenic mixed refrigerant processes. In this paper the vapour-liquid equilibrium of binary mixtures of nitrogen-methane, nitrogen-ethane, nitrogen-propane, nitrogen-isobutane and three component mixtures of nitrogen-methane-ethane and nitrogen-methane-propane have been studied with the Peng-Robinson and the Helmholtz energy equations of state of NIST REFPROP and compared with experimental data available in the literature.

Thermodynamic assessment of hydrothermal alkali feldspar-mica-aluminosilicate equilibria

USGS Publications Warehouse

Sverjensky, D.A.; Hemley, J.J.; d'Angelo, W. M.

1991-01-01

The thermodynamic properties of minerals retrieved from consideration of solid-solid and dehydration equilibria with calorimetric reference values, and those of aqueous species derived from studies of electrolytes, are not consistent with experimentally measured high-temperature solubilities in the systems K2O- and Na2O-Al2O3-SiO2-H2O-HCl (e.g., K-fs - Ms - Qtz - K+ - H+). This introduces major inaccuracies into the computation of ionic activity ratios and the acidities of diagenetic, metamorphic, and magmatic hydrothermal fluids buffered by alkali silicate-bearing assemblages. We report a thermodynamic analysis of revised solubility equilibria in these systems that integrates the thermodynamic properties of minerals obtained from phase equilibria studies (Berman, 1988) with the properties of aqueous species calculated from a calibrated equation of state (Shock and Helgeson, 1988). This was achieved in two separate steps. First, new values of the free energies and enthalpies of formation at 25??C and 1 bar for the alkali silicates muscovite and albite were retrieved from the experimental solubility equilibria at 300??C and Psat. Because the latter have stoichiometric reaction coefficients different from those for solid-solid and dehydration equilibria, our procedure preserves exactly the relative thermodynamic properties of the alkali-bearing silicates (Berman, 1988). Only simple arithmetic adjustments of -1,600 and -1,626 (??500) cal/mol to all the K- and Na-bearing silicates, respectively, in Berman (1988) are required. In all cases, the revised values are within ??0.2% of calorimetric values. Similar adjustments were derived for the properties of minerals from Helgeson et al. (1978). Second, new values of the dissociation constant of HCl were retrieved from the solubility equilibria at temperatures and pressures from 300-600??C and 0.5-2.0 kbars using a simple model for aqueous speciation. The results agree well with the conductance-derived dissociation constants from Franck (1956a,b) for temperatures from 300-550??C. Compared to the conductance-derived results of Frantz and Marshall (1984), our dissociation constants agree well at the highest densities, but are greater at lower densities. At the lowest density, at 600??C and 1 kbar, the discrepancy of 0.9 log units is within the overall uncertainties associated with our experimental results and those associated with deriving dissociation constants from conductance measurements in highly associated solutions (Oelkers and Helgeson, 1988). Finally, we also report an equation of state fit to the standard thermodynamic properties of the aqueous HCl molecule that is consistent with a wide array of independently determined dissociation constants of HCl and permits interpolation and extrapolation of the dissociation constant of HCl to 1000??C and 5.0 kbars. ?? 1991.

CHARMM additive and polarizable force fields for biophysics and computer-aided drug design

PubMed Central

Vanommeslaeghe, K.

2014-01-01

Background Molecular Mechanics (MM) is the method of choice for computational studies of biomolecular systems owing to its modest computational cost, which makes it possible to routinely perform molecular dynamics (MD) simulations on chemical systems of biophysical and biomedical relevance. Scope of Review As one of the main factors limiting the accuracy of MD results is the empirical force field used, the present paper offers a review of recent developments in the CHARMM additive force field, one of the most popular bimolecular force fields. Additionally, we present a detailed discussion of the CHARMM Drude polarizable force field, anticipating a growth in the importance and utilization of polarizable force fields in the near future. Throughout the discussion emphasis is placed on the force fields’ parametrization philosophy and methodology. Major Conclusions Recent improvements in the CHARMM additive force field are mostly related to newly found weaknesses in the previous generation of additive force fields. Beyond the additive approximation is the newly available CHARMM Drude polarizable force field, which allows for MD simulations of up to 1 microsecond on proteins, DNA, lipids and carbohydrates. General Significance Addressing the limitations ensures the reliability of the new CHARMM36 additive force field for the types of calculations that are presently coming into routine computational reach while the availability of the Drude polarizable force fields offers a model that is an inherently more accurate model of the underlying physical forces driving macromolecular structures and dynamics. PMID:25149274

Effect of scrape-off-layer current on reconstructed tokamak equilibrium

DOE PAGES

King, J. R.; Kruger, S. E.; Groebner, R. J.; ...

2017-01-13

Methods are described that extend fields from reconstructed equilibria to include scrape-off-layer current through extrapolated parametrized and experimental fits. The extrapolation includes both the effects of the toroidal-field and pressure gradients which produce scrape-off-layer current after recomputation of the Grad-Shafranov solution. To quantify the degree that inclusion of scrape-off-layer current modifies the equilibrium, the χ-squared goodness-of-fit parameter is calculated for cases with and without scrape-off-layer current. The change in χ-squared is found to be minor when scrape-off-layer current is included however flux surfaces are shifted by up to 3 cm. Here the impact on edge modes of these scrape-off-layer modificationsmore » is also found to be small and the importance of these methods to nonlinear computation is discussed.« less

Plasma Disks and Rings with ``High'' Magnetic Energy Densities

NASA Astrophysics Data System (ADS)

Coppi, B.; Rousseau, F.

2006-04-01

The nonlinear theory of rotating axisymmetric thin structures in which the magnetic field energy density is comparable with the thermal plasma energy density is formulated. The only flow velocity included in the theory is the velocity of rotation around a central object whose gravity is dominant. The periodic sequence, in the radial direction, of pairs of opposite current channels that can form is shown to lead to relatively large plasma density and pressure modulations, while the relevant magnetic surfaces can acquire a ``crystal structure.'' A new class of equilibria consisting of a series of plasma rings is identified, in the regimes where the plasma pressure is comparable to the magnetic pressure associated with the fields produced by the internal currents. The possible relevance of this result to the formation of dusty plasma rings is pointed out.

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

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

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

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

Transport properties of interacting magnetic islands in tokamak plasmas

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

Gianakon, T.A.; Callen, J.D.; Hegna, C.C.

1993-10-01

This paper explores the equilibrium and transient transport properties of a mixed magnetic topology model for tokamak equilibria. The magnetic topology is composed of a discrete set of mostly non-overlapping magnetic islands centered on the low-order rational surfaces. Transport across the island regions is fast due to parallel transport along the stochastic magnetic field lines about the separatrix of each island. Transport between island regions is assumed to be slow due to a low residual cross-field transport. In equilibrium, such a model leads to: a nonlinear dependence of the heat flux on the pressure gradient; a power balance diffusion coefficientmore » which increases from core to edge; and profile resiliency. Transiently, such a model also exhibits a heat pulse diffusion coefficient larger than the power balance diffusion coefficient.« less

Heteroclinic tangle phenomena in nanomagnets subject to time-harmonic excitations

NASA Astrophysics Data System (ADS)

Serpico, C.; Quercia, A.; Bertotti, G.; d'Aquino, M.; Mayergoyz, I.; Perna, S.; Ansalone, P.

2015-05-01

Magnetization dynamics in uniformly magnetized nanomagnets excited by time-harmonic (AC) external fields or spin-polarized injected currents is considered. The analysis is focused on the behaviour of the AC-excited dynamics near saddle equilibria. It turns out that this dynamics has a chaotic character at moderately low power level. This chaotic and fractal nature is due to the phenomenon of heteroclinic tangle which is produced by the combined effect of AC-excitations and saddle type dynamics. By using the perturbation technique based on Melnikov function, analytical formulas for the threshold AC excitation amplitudes necessary to create the heteroclinic tangle are derived. Both the cases of AC applied fields and AC spin-polarized injected currents are treated. Then, by means of numerical simulations, we show how heteroclinic tangle is accompanied by the erosion of the safe basin around the stable regimes.

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

DOE PAGES

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

2016-03-03

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

CHARMM additive and polarizable force fields for biophysics and computer-aided drug design.

PubMed

Vanommeslaeghe, K; MacKerell, A D

2015-05-01

Molecular Mechanics (MM) is the method of choice for computational studies of biomolecular systems owing to its modest computational cost, which makes it possible to routinely perform molecular dynamics (MD) simulations on chemical systems of biophysical and biomedical relevance. As one of the main factors limiting the accuracy of MD results is the empirical force field used, the present paper offers a review of recent developments in the CHARMM additive force field, one of the most popular biomolecular force fields. Additionally, we present a detailed discussion of the CHARMM Drude polarizable force field, anticipating a growth in the importance and utilization of polarizable force fields in the near future. Throughout the discussion emphasis is placed on the force fields' parametrization philosophy and methodology. Recent improvements in the CHARMM additive force field are mostly related to newly found weaknesses in the previous generation of additive force fields. Beyond the additive approximation is the newly available CHARMM Drude polarizable force field, which allows for MD simulations of up to 1μs on proteins, DNA, lipids and carbohydrates. Addressing the limitations ensures the reliability of the new CHARMM36 additive force field for the types of calculations that are presently coming into routine computational reach while the availability of the Drude polarizable force fields offers an inherently more accurate model of the underlying physical forces driving macromolecular structures and dynamics. This article is part of a Special Issue entitled "Recent developments of molecular dynamics". Copyright © 2014 Elsevier B.V. All rights reserved.

Pendulum motions of extended lunar space elevator

NASA Astrophysics Data System (ADS)

Burov, A. A.; Kosenko, I. I.

2014-09-01

In the usual everyday life, it is well known that the inverted pendulum is unstable and is ready to fall to "all four sides," to the left and to the right, forward and backward. The theoretical studies and the lunar experience of moon robots and astronauts also confirms this property. The question arises: Is this property preserved if the pendulum is "very, very long"? It turns out that the answer is negative; namely, if the pendulum length significantly exceeds the Moon radius, then the radial equilibria at which the pendulum is located along the straight line connecting the Earth and Moon centers are Lyapunov stable and the pendulum does not fall in any direction at all. Moreover, if the pendulum goes beyond the collinear libration points, then it can be extended and manufactured from cables. This property was noted by F. A. Tsander and underlies the so-called lunar space elevator (e.g., see [1]). In the plane of the Earth and Moon orbits, there are some other equilibria which turn out to be unstable. The question is, Are there equilibria at which the pendulum is located outside the orbital plane? In this paper, we show that the answer is positive, but such equilibria are unstable in the secular sense. We also study necessary conditions for the stability of lunar pendulum oscillations in the plane of the lunar orbit. It was numerically discovered that stable and unstable equilibria alternate depending on the oscillation amplitude and the angular velocity of rotation. The study of the lunar elevator dynamics originates in [2]. The concept of lunar elevator was developed in detail in [3, 4]. Several classes of equilibria with the finiteness of the Moon size taken into account were studied in [5]. The possibility of location of an orbital station fixed to the Moon surface by a pair of tethers was investigated in [6]. The problem of orientation of the terminal station of the lunar space elevator was studied in [7]. The influence of the tether length variations on the motion of the lunar tether system was considered in [8]. The alternation of stable and unstable flat oscillations is well known in the problem of satellite oscillations in a circular orbit [9, 10].

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

Moroz, P.E.

A new stellarator configuration, the Double-Helix Stellarator (DHS), is introduced. This novel configuration features a double-helix center post as the only helical element of the stellarator coil system. The DHS configuration has many unique characteristics. One of them is the extreme low plasma aspect ratio, A {approx} 1--1.2. Other advantages include a high enclosed volume, appreciable rotational transform, and a possibility of extreme-high-{beta} MHD equilibria. Moreover, the DHS features improved transport characteristics caused by the absence of the magnetic field ripple on the outboard of the torus. Compactness, simplicity and modularity of the coil system add to the DHS advantagesmore » for fusion applications.« less

Dynamic analyses, FPGA implementation and engineering applications of multi-butterfly chaotic attractors generated from generalised Sprott C system

NASA Astrophysics Data System (ADS)

Lai, Qiang; Zhao, Xiao-Wen; Rajagopal, Karthikeyan; Xu, Guanghui; Akgul, Akif; Guleryuz, Emre

2018-01-01

This paper considers the generation of multi-butterfly chaotic attractors from a generalised Sprott C system with multiple non-hyperbolic equilibria. The system is constructed by introducing an additional variable whose derivative has a switching function to the Sprott C system. It is numerically found that the system creates two-, three-, four-, five-butterfly attractors and any other multi-butterfly attractors. First, the dynamic analyses of multi-butterfly chaotic attractors are presented. Secondly, the field programmable gate array implementation, electronic circuit realisation and random number generator are done with the multi-butterfly chaotic attractors.

Continuum limit of electrostatic gyrokinetic absolute equilibrium

NASA Astrophysics Data System (ADS)

Zhu, Jian-Zhou

2012-06-01

Electrostatic gyrokinetic absolute equilibria with continuum velocity field are obtained through the partition function and through the Green function of the functional integral. The new results justify and explain the prescription for quantization/discretization or taking the continuum limit of velocity. The mistakes in the Appendix D of our earlier work [J.-Z. Zhu and G. W. Hammett, Phys. Plasmas 17, 122307 (2010)] are explained and corrected. If the lattice spacing for discretizing velocity is big enough, all the invariants could concentrate at the lowest Fourier modes in a negative-temperature state, which might indicate a possible variation of the dual cascade picture in 2D plasma turbulence.

Spinal lordosis optimizes the requirements for a stable erect posture.

PubMed

Wagner, Heiko; Liebetrau, Anne; Schinowski, David; Wulf, Thomas; de Lussanet, Marc H E

2012-04-16

Lordosis is the bending of the lumbar spine that gives the vertebral column of humans its characteristic ventrally convex curvature. Infants develop lordosis around the time when they acquire bipedal locomotion. Even macaques develop a lordosis when they are trained to walk bipedally. The aim of this study was to investigate why humans and some animals develop a lumbar lordosis while learning to walk bipedally. We developed a musculoskeletal model of the lumbar spine, that includes an asymmetric, dorsally shifted location of the spinal column in the body, realistic moment arms, and physiological cross-sectional areas (PCSA) of the muscles as well as realistic force-length and force-velocity relationships. The model was used to analyze the stability of an upright body posture. According to our results, lordosis reduces the local joint torques necessary for an equilibrium of the vertebral column during an erect posture. At the same time lordosis increases the demands on the global muscles to provide stability. We conclude that the development of a spinal lordosis is a compromise between the stability requirements of an erect posture and the necessity of torque equilibria at each spinal segment.

Spinal lordosis optimizes the requirements for a stable erect posture

PubMed Central

2012-01-01

Background Lordosis is the bending of the lumbar spine that gives the vertebral column of humans its characteristic ventrally convex curvature. Infants develop lordosis around the time when they acquire bipedal locomotion. Even macaques develop a lordosis when they are trained to walk bipedally. The aim of this study was to investigate why humans and some animals develop a lumbar lordosis while learning to walk bipedally. Results We developed a musculoskeletal model of the lumbar spine, that includes an asymmetric, dorsally shifted location of the spinal column in the body, realistic moment arms, and physiological cross-sectional areas (PCSA) of the muscles as well as realistic force-length and force-velocity relationships. The model was used to analyze the stability of an upright body posture. According to our results, lordosis reduces the local joint torques necessary for an equilibrium of the vertebral column during an erect posture. At the same time lordosis increases the demands on the global muscles to provide stability. Conclusions We conclude that the development of a spinal lordosis is a compromise between the stability requirements of an erect posture and the necessity of torque equilibria at each spinal segment. PMID:22507595

The Mathematics of Aggregation, Interdependence, Organizations and Systems of Nash Equilibria (NE): A Replacement for Game Theory

DTIC Science & Technology

2011-06-01

there a free-market economist in the House?, American Journal of Economics and Sociology, 66(2): 309-334. Jasny, B. R., Zahn, L.M., & Marshall, E...1   The Mathematics of Aggregation, Interdependence, Organizations and Systems of Nash equilibria (NE): A replacement for Game Theory...level data to group, organization and systems levels, making it one of social science’s biggest challenges, if not the most important (Giles, 2011). For

Beltrami–Bernoulli equilibria in plasmas with degenerate electrons

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

Berezhiani, V. I., E-mail: vazhab@yahoo.com; Shatashvili, N. L., E-mail: shatash@ictp.it; Mahajan, S. M., E-mail: mahajan@mail.utexas.edu

2015-02-15

A new class of Double Beltrami–Bernoulli equilibria, sustained by electron degeneracy pressure, is investigated. It is shown that due to electron degeneracy, a nontrivial Beltrami–Bernoulli equilibrium state is possible even for a zero temperature plasma. These states are, conceptually, studied to show the existence of new energy transformation pathways converting, for instance, the degeneracy energy into fluid kinetic energy. Such states may be of relevance to compact astrophysical objects like white dwarfs, neutron stars, etc.

Enduring Rivalry in the Philippines and the Application of Amnesty, Reintegration and Reconciliation (AR2)

DTIC Science & Technology

2008-05-22

equilibrium is a theory in paleobiology introduced by Steven Jay Gould and Niles Elderage in 1972 as an alternative to Darwin’s relatively smooth...Equilibria: The Tempo and Mode of Evolution Reconsidered," Paleobiology 3, no. 2 (1972). 3 Stephen Krasner, "Approaches to the State: Alternative...34Punctuated Equilibria: The Tempo and Mode of Evolution Reconsidered." Paleobiology 3, no. 2 (1972): 37. Ferrer, Miriam Coronel. "Philippines National

Vapor-liquid equilibria for 1,1-difluoroethane + acetylene and 1,1-difluoroethane + 1,1-dichloroethane at 303.2 K and 323.2 K

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

Lim, J.S.; Lee, Y.W.; Kim, J.D.

1996-09-01

Isothermal vapor-liquid equilibria for 1,1-difluoroethane (HFC-152a) + acetylene and 1,1-difluoroethane + 1,1-dichloroethane (HCC-150a) were measured in a circulation type apparatus at 303.2 K and 323.2 K. The experimental data were correlated with the Peng-Robinson equation of state using the Wong and Sandler mixing rule, and the relevant parameters are presented.

Technical Information, Returns to Scale, and the Existence of Competitive Equilibrium.

DTIC Science & Technology

1985-05-01

Economies, Part I. Existence of Bequest Equilibria Part II. Properties of Bequest Equilibria" by Debraj Ray and Douglas Bernheim. 420. "On the Existence...Dasgupta and Debraj Ray . 455. "Procurement, Cost Overruns and Severance: A Study in Commitment and Renegotiation," by Jean Tirole. 456. "Multiparty...Consistent Plans Under Production Uncertainty," by B. Douglas Bernheiu and Debraj Ray . 463 "Free Entry and Stability in a Cournot Model," by Gabrielle Demange

Recent Developments and Applications of the CHARMM force fields

PubMed Central

Zhu, Xiao; Lopes, Pedro E.M.; MacKerell, Alexander D.

2011-01-01

Empirical force fields commonly used to describe the condensed phase properties of complex systems such as biological macromolecules are continuously being updated. Improvements in quantum mechanical (QM) methods used to generate target data, availability of new experimental target data, incorporation of new classes of compounds and new theoretical developments (eg. polarizable methods) make force-field development a dynamic domain of research. Accordingly, a number of improvements and extensions of the CHARMM force fields have occurred over the years. The objective of the present review is to provide an up-to-date overview of the CHARMM force fields. A limited presentation on the historical aspects of force fields will be given, including underlying methodologies and principles, along with a brief description of the strategies used for parameter development. This is followed by information on the CHARMM additive and polarizable force fields, including examples of recent applications of those force fields. PMID:23066428

The effect of force feedback delay on stiffness perception and grip force modulation during tool-mediated interaction with elastic force fields

PubMed Central

Karniel, Amir; Nisky, Ilana

2015-01-01

During interaction with objects, we form an internal representation of their mechanical properties. This representation is used for perception and for guiding actions, such as in precision grip, where grip force is modulated with the predicted load forces. In this study, we explored the relationship between grip force adjustment and perception of stiffness during interaction with linear elastic force fields. In a forced-choice paradigm, participants probed pairs of virtual force fields while grasping a force sensor that was attached to a haptic device. For each pair, they were asked which field had higher level of stiffness. In half of the pairs, the force feedback of one of the fields was delayed. Participants underestimated the stiffness of the delayed field relatively to the nondelayed, but their grip force characteristics were similar in both conditions. We analyzed the magnitude of the grip force and the lag between the grip force and the load force in the exploratory probing movements within each trial. Right before answering which force field had higher level of stiffness, both magnitude and lag were similar between delayed and nondelayed force fields. These results suggest that an accurate internal representation of environment stiffness and time delay was used for adjusting the grip force. However, this representation did not help in eliminating the bias in stiffness perception. We argue that during performance of a perceptual task that is based on proprioceptive feedback, separate neural mechanisms are responsible for perception and action-related computations in the brain. PMID:25717155

The effect of force feedback delay on stiffness perception and grip force modulation during tool-mediated interaction with elastic force fields.

PubMed

Leib, Raz; Karniel, Amir; Nisky, Ilana

2015-05-01

During interaction with objects, we form an internal representation of their mechanical properties. This representation is used for perception and for guiding actions, such as in precision grip, where grip force is modulated with the predicted load forces. In this study, we explored the relationship between grip force adjustment and perception of stiffness during interaction with linear elastic force fields. In a forced-choice paradigm, participants probed pairs of virtual force fields while grasping a force sensor that was attached to a haptic device. For each pair, they were asked which field had higher level of stiffness. In half of the pairs, the force feedback of one of the fields was delayed. Participants underestimated the stiffness of the delayed field relatively to the nondelayed, but their grip force characteristics were similar in both conditions. We analyzed the magnitude of the grip force and the lag between the grip force and the load force in the exploratory probing movements within each trial. Right before answering which force field had higher level of stiffness, both magnitude and lag were similar between delayed and nondelayed force fields. These results suggest that an accurate internal representation of environment stiffness and time delay was used for adjusting the grip force. However, this representation did not help in eliminating the bias in stiffness perception. We argue that during performance of a perceptual task that is based on proprioceptive feedback, separate neural mechanisms are responsible for perception and action-related computations in the brain. Copyright © 2015 the American Physiological Society.

Emergence and equilibration of jets in planetary turbulence

NASA Astrophysics Data System (ADS)

Constantinou, Navid; Ioannou, Petros; Farrell, Brian

2013-04-01

Spatially and temporally coherent large scale jets that are not forced directly at the jet scale are prominent feature of rotating turbulence. A familiar example is the midlatitude jet in the Earth's atmosphere and the banded winds of the giants planets. These jets arise and are supported by the systematic organisation of the turbulent Reynolds stresses. Understanding the mechanism producing the required eddy momentum flux convergence, and how the jets and associated eddy field mutually adjust to maintain a steady jet structure at finite amplitude, constitute fundamental theoretical problems. Stochastic Structural Stability Theory (SSST) gives an explanation for jet formation that is fundamentally based on the interaction between jets and their associated field of turbulent eddies. SSST combines the full dynamics of the zonal mean flow with the second order statistics of the turbulent field obtained from a stochastic turbulence model (STM). The quasi-linear (QL) approximation to the full nonlinear dynamics (NL) results when the perturbation-perturbation interactions are parameterized in the perturbation equations, while interaction between the perturbations and the zonal mean flow is retained in the zonal mean equation. SSST consists of an infinite ensemble of perturbations evolving under QL. Therefore, SSST provides a set of dynamical equations for the mean flow and the second order statistics of the second cummulant of the perturbation vorticity field, which are autonomous and fluctuation free and can facilitate analytic study of turbulent equilibria and their stability as a function of parameters. Thus, jet formation in homogeneous beta-turbulence can be identified with an SSST structural instability of a homogeneous (mean flow free) SSTT equilibrium. We investigate the emergence and equilibration of jets from homogeneous barotropic beta-plane turbulence in the absence of coherent external forcing. SSST predicts that infinitesimal perturbations with zonal jet form organise homogeneous turbulence to produce systematic upgradient fluxes, giving rise to exponential jet growth and eventually to the establishment of finite amplitude equilibrium jets. We compare these predictions with simulations of the NL equations and their QL approximation in order to examine further the mechanism of emergence and equilibration of jets from turbulence. We concentrate on the effects of perturbation-perturbation nonlinearity on jet bifurcation and equilibration, and on the influence of perturbations in exciting the manifold of SSST modes with jet structure. We find that the bifurcation structure predicted by SSST for the emergence of zonal jets from a homogeneous turbulent state is confirmed by both QL and NL simulations. Moreover, we show that the finite amplitude equilibrium jets found in NL and QL simulations are as predicted by the fixed point solutions of SSST. Obtaining this agreement between NL and both SSST and QL simulations required in some cases that the modification of the turbulent spectrum caused by the perturbation-perturbation nonlinearity in NL be accounted for in the specification of the stochastic forcing in QL and SSST. These results confirm that jet emergence in barotropic beta-plane turbulence can be traced to the cooperative mean flow/perturbation instability that is captured by SSST.

Eigenvalue problems for Beltrami fields arising in a three-dimensional toroidal magnetohydrodynamic equilibrium problem

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

Hudson, S. R.; Hole, M. J.; Dewar, R. L.

2007-05-15

A generalized energy principle for finite-pressure, toroidal magnetohydrodynamic (MHD) equilibria in general three-dimensional configurations is proposed. The full set of ideal-MHD constraints is applied only on a discrete set of toroidal magnetic surfaces (invariant tori), which act as barriers against leakage of magnetic flux, helicity, and pressure through chaotic field-line transport. It is argued that a necessary condition for such invariant tori to exist is that they have fixed, irrational rotational transforms. In the toroidal domains bounded by these surfaces, full Taylor relaxation is assumed, thus leading to Beltrami fields {nabla}xB={lambda}B, where {lambda} is constant within each domain. Two distinctmore » eigenvalue problems for {lambda} arise in this formulation, depending on whether fluxes and helicity are fixed, or boundary rotational transforms. These are studied in cylindrical geometry and in a three-dimensional toroidal region of annular cross section. In the latter case, an application of a residue criterion is used to determine the threshold for connected chaos.« less

Gas chemistry and thermometry of the Cerro Prieto, Mexico, geothermal field

USGS Publications Warehouse

Nehring, N.L.; D'Amore, F.

1984-01-01

Gas compositions of Cerro Prieto wells in 1977 reflected strong boiling in the reservoir around wells M-20 and M-25. This boiling zone appeared to be collapsing in 1982 when a number of wells in this area of the field were shut-in. In 1977 and 1982, gas compositions also showed boiling zones corresponding to faults H and L postulated by Halfman et al. (1982). Four gas geothermometers were applied, based on reservoir equilibria and calculated fugacities. The Fisher - Tropsch reaction predicted high temperatures and appeared to re-equilibrate slowly, whereas the H2S reaction predicted low temperatures and appeared to re-equilibrate rapidly. Hydrogen and NH3 reactions were intermediate. Like gas compositions, the geothermometers reflected reservoir processes, such as boiling. Surface gas compositions are related to well compositions, but contain large concentrations of N2 originating from air dissolved in groundwater. The groundwater appears to originate in the east and flow over the production field before mixing with reservoir gases near the surface. ?? 1984.

Gyrofluid modeling and phenomenology of low-βe Alfvén wave turbulence

NASA Astrophysics Data System (ADS)

Passot, T.; Sulem, P. L.; Tassi, E.

2018-04-01

A two-field reduced gyrofluid model including electron inertia, ion finite Larmor radius corrections, and parallel magnetic field fluctuations is derived from the model of Brizard [Brizard, Phys. Fluids B 4, 1213 (1992)]. It assumes low βe, where βe indicates the ratio between the equilibrium electron pressure and the magnetic pressure exerted by a strong uniform magnetic guide field, but permits an arbitrary ion-to-electron equilibrium temperature ratio. It is shown to have a noncanonical Hamiltonian structure and provides a convenient framework for studying kinetic Alfvén wave turbulence, from magnetohydrodynamics to sub-de scales (where de holds for the electron skin depth). Magnetic energy spectra are phenomenologically determined within energy and generalized cross-helicity cascades in the perpendicular spectral plane. Arguments based on absolute statistical equilibria are used to predict the direction of the transfers, pointing out that, within the sub-ion range, the generalized cross-helicity could display an inverse cascade if injected at small scales, for example by reconnection processes.

Phase Equilibria and Crystal Chemistry in Portions of the System SrO-CaO-Bi2O3-CuO, Part II—The System SrO-Bi2O3-CuO

PubMed Central

Roth, R. S.; Rawn, C. J.; Burton, B. P.; Beech, F.

1990-01-01

New data are presented on the phase equilibria and crystal chemistry of the binary systems Sr0-Bi203 and SrO-CuO and the ternary system SrO-Bi2O3-CuO. Symmetry data and unit cell dimensions based on single crystal and powder x-ray diffraction measurements are reported for all the binary SrO-Bi2O3 phases, including a new phase identified as Sr6Bi2O9. The ternary system contains at least four ternary phases which can be formed in air at ~900 °C. These are identified as Sr2Bi2CuO6, Sr8Bi4Cu5O19+x, Sr3Bi2Cu2O8 and a solid solution (the Raveau phase) which, for equilibrium conditions at ~900 °C, corresponds approximately to the formula Sr1.8−xBi2.2+xCu1±x/2Oz.(0.0⩽x⩽~0.15). Superconductivity in this phase apparently occurs only in compositions that correspond to negative values of x. Compositions that lie outside the equilibrium Raveau-phase field often form nearly homogeneous Raveau-phase products. Typically this occurs after relatively brief heat treatments, or in crystallization of a quenched melt. PMID:28179779

Singular Isothermal Disks. Paper 2; Nonaxiymmetric Bifurcations and Equilibria

NASA Technical Reports Server (NTRS)

Galli, Danielle; Shu, Frank H.; Laughlin, Gregory; Lizano, Susana

2000-01-01

We review the difficulties of the classical fission and fragmentation hypotheses for the formation of binary and multiple stars. A crucial missing ingredient in previous theoretical studies is the inclusion of dynamically important levels of magnetic fields. As a minimal model for a candidate presursor to the formation of binary and multiple stars, we therefore formulate and solve the problem of the equilibria of isopedically magnetized, singular isothermal disks, without the assumption of axial symmetry. Considerable analytical progress can be made if we restrict our attention to models that are scale-free, i.e., that have surface densities that vary inversely with distance omega from the rotation axis of the system. In agreement with earlier analysis by Syer and Tremaine, we find that lopsided (M = 1) configurations exist at any dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4, ...) configurations bifurcate from an underlying axisymmetric sequence at progressively higher dimensionless rates of rotation, but such nonaxisymmetric sequences always terminate in shockwaves before they have a chance to fission into M = 2, 3, 4, ... separate bodies. On the basis of our experience in this paper, we advance the hypothesis that binary and multiple star-formation from smooth (i.e., not highly turbulent) starting states that are supercritical but in unstable mechanical balance requires the rapid (i.e., dynamical) loss of magnetic flux at some stage of the ensuing gravitational collapse.

MMA-EoS: A Computational Framework for Mineralogical Thermodynamics

NASA Astrophysics Data System (ADS)

Chust, T. C.; Steinle-Neumann, G.; Dolejš, D.; Schuberth, B. S. A.; Bunge, H.-P.

2017-12-01

We present a newly developed software framework, MMA-EoS, that evaluates phase equilibria and thermodynamic properties of multicomponent systems by Gibbs energy minimization, with application to mantle petrology. The code is versatile in terms of the equation-of-state and mixing properties and allows for the computation of properties of single phases, solution phases, and multiphase aggregates. Currently, the open program distribution contains equation-of-state formulations widely used, that is, Caloric-Murnaghan, Caloric-Modified-Tait, and Birch-Murnaghan-Mie-Grüneisen-Debye models, with published databases included. Through its modular design and easily scripted database, MMA-EoS can readily be extended with new formulations of equations-of-state and changes or extensions to thermodynamic data sets. We demonstrate the application of the program by reproducing and comparing physical properties of mantle phases and assemblages with previously published work and experimental data, successively increasing complexity, up to computing phase equilibria of six-component compositions. Chemically complex systems allow us to trace the budget of minor chemical components in order to explore whether they lead to the formation of new phases or extend stability fields of existing ones. Self-consistently computed thermophysical properties for a homogeneous mantle and a mechanical mixture of slab lithologies show no discernible differences that require a heterogeneous mantle structure as has been suggested previously. Such examples illustrate how thermodynamics of mantle mineralogy can advance the study of Earth's interior.

Uranium nitride as LWR TRISO fuel: Thermodynamic modeling of U-C-N

NASA Astrophysics Data System (ADS)

Besmann, Theodore M.; Shin, Dongwon; Lindemer, Terrence B.

2012-08-01

TRISO coated particle fuel is envisioned as a next generation replacement for current urania pellet fuel in LWR applications. To obtain adequate fissile loading the kernel of the TRISO particle will likely need to be UN instead of UO2. In support of the necessary development effort for this new fuel system, an assessment of phase regions of interest in the U-C-N system was undertaken as the fuel will be prepared by the carbothermic reduction of the oxide followed by nitriding, will be in equilibrium with carbon within the TRISO particle, and will react with minor actinides and fission products. The phase equilibria and thermochemistry of the U-C-N system is reviewed, including nitrogen pressure measurements above various phase fields. Measurements were used to confirm an ideal solution model of UN and UC adequately represents the UC1-xNx phase. Agreement with the data was significantly improved by effectively adjusting the Gibbs free energy of UN by +12 kJ/mol. This also required adjustment of the value for the sesquinitride by +17 kJ/mol to obtain agreement with phase equilibria. The resultant model together with reported values for other phases in the system was used to generate isothermal sections of the U-C-N phase diagram. Nitrogen partial pressures were also computed for regions of interest.

Geometric criteria for the non-existence of cycles in predator-prey systems with group defense.

PubMed

Liu, Yaping

2007-07-01

In this paper, we study the existence of cycles in a predator-prey system in which the prey species is equipped with the group defense capability. Some geometric criteria are developed, relating the location of the two positive equilibria on the prey isocline and the non-existence of cycles. We show that under a general geometric condition, if both positive equilibria lie on a downslope or both lie on an upslope of the prey isocline, cycles do not exist.

Equilibria of a Two-Person Non-Zerosum Noisy Game of Timing,

DTIC Science & Technology

1981-01-01

AD-A097 158 YALE UNIV NEW HAVEN CT COWLES FOUNDATION FOR RESEARC -ETC F/B 12/1 EQUILIBRIA OF A TWO-PERSON ON-ZEROSUN OISY GAME OF TIMING, CUb .JAN al...pubUo zeleale Distribution Unlimited. 1. Introduction Two toothpaste manufacturers are competing for a larger share of the dentifrice market . Each is...successfully capturing a share of the market , if its product hits the stores first. (This is assuming that the toothpaste is being technologically

Vapor-liquid equilibria for difluoromethane + dichloromethane at 303.2 and 313.2 K and 1,1-difluoroethane + vinyl chloride at 303.2 and 323.2 K

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

Lim, J.S.; Lee, Y.W.; Lee, Y.Y.

1997-05-01

Isothermal vapor-liquid equilibria for difluoromethane (HFC-32) + dichloromethane at 303.2 K and 313.2 K and 1,1-difluoroethane (HFC-152a) + vinyl chloride at 303.2 K and 323.2 K were measured in a circulation-type apparatus. The experimental data were correlated with the Peng-Robinson equation of state using the Wong and Sandler mixing rule, and the relevant parameters are presented.

Phase equilibria of CFC alternative refrigerant mixtures: Binary systems of isobutane + 1,1,1,2-tetrafluoroethane, + 1,1-difluoroethane, and + difluoromethane

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

Lim, J.S.; Park, J.Y.; Lee, B.G.

1999-12-01

Isothermal vapor-liquid equilibria were measured in the binary systems 1,1,1,2-tetrafluoroethane + isobutane at 303.2 and 323.2 K, 1,1-difluoroethane + isobutane at 303.2, 313.2, 323.2, and 333.2 K, and difluoromethane + isobutane at 301.8 and 321.8 K in a circulation-type equilibrium apparatus. The experimental data were well correlated with the Peng-Robinson equation of state using the Wong and Sandler mixing rules.

Isothermal vapor-liquid equilibria for the systems 1-chloro-1,1-difluoroethane + hydrogen fluoride, 1,1-dichloro-1-fluoroethane + hydrogen fluoride, and chlorodifluoromethane + hydrogen fluoride

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

Kang, Y.W.; Lee, Y.Y.

1997-03-01

Isothermal vapor-liquid equilibria for the three binary systems (1-chloro-1,1-difluoroethane + hydrogen fluoride, 1,1-dichloro-1-fluoroethane + hydrogen fluoride, and chlorodifluoromethane + hydrogen fluoride) have been measured. The experimental data for the binary systems are correlated with the NRTL equation with the vapor-phase association model for the mixtures containing hydrogen fluoride, and the relevant parameters are presented. All of the systems form minimum boiling heterogeneous azeotropes.

Existence of equilibria in quantum Bertrand-Edgeworth duopoly game

NASA Astrophysics Data System (ADS)

Sekiguchi, Yohei; Sakahara, Kiri; Sato, Takashi

2012-12-01

Both classical and quantum version of two models of price competition in duopoly market, the one is realistic and the other is idealized, are investigated. The pure strategy Nash equilibria of the realistic model exists under stricter condition than that of the idealized one in the classical form game. This is the problem known as Edgeworth paradox in economics. In the quantum form game, however, the former converges to the latter as the measure of entanglement goes to infinity.

Phase equilibria and crystal chemistry of rubidium niobates and rubidium tantalates

NASA Technical Reports Server (NTRS)

Minor, D. B.; Roth, R. S.; Parker, H. S.; Brower, W. S.

1977-01-01

The phase equilibria relations and crystal chemistry of portions of the Rb2O-Nb2O5 and Rb2O-Ta2O5 systems were investigated for structures potentially useful as ionic conductors. A hexagonal tungsten bronze-type (HTB) structure was found in both systems as well as three hexagonal phases with mixed HTB-pyrochlore type structures. Ion exchange experiments between various alkali ions are described for several phases. Unit cell dimensions and X-ray diffraction powder patterns are reported.

Reparameterization of RNA chi Torsion Parameters for the AMBER Force Field and Comparison to NMR Spectra for Cytidine and Uridine.

PubMed

Yildirim, Ilyas; Stern, Harry A; Kennedy, Scott D; Tubbs, Jason D; Turner, Douglas H

2010-05-11

A reparameterization of the torsional parameters for the glycosidic dihedral angle, chi, for the AMBER99 force field in RNA nucleosides is used to provide a modified force field, AMBER99chi. Molecular dynamics simulations of cytidine, uridine, adenosine, and guanosine in aqueous solution using the AMBER99 and AMBER99chi force fields are compared with NMR results. For each nucleoside and force field, 10 individual molecular dynamics simulations of 30 ns each were run. For cytidine with AMBER99chi force field, each molecular dynamics simulation time was extended to 120 ns for convergence purposes. Nuclear magnetic resonance (NMR) spectroscopy, including one-dimensional (1D) (1)H, steady-state 1D (1)H nuclear Overhauser effect (NOE), and transient 1D (1)H NOE, was used to determine the sugar puckering and preferred base orientation with respect to the ribose of cytidine and uridine. The AMBER99 force field overestimates the population of syn conformations of the base orientation and of C2'-endo sugar puckering of the pyrimidines, while the AMBER99chi force field's predictions are more consistent with NMR results. Moreover, the AMBER99 force field prefers high anti conformations with glycosidic dihedral angles around 310 degrees for the base orientation of purines. The AMBER99chi force field prefers anti conformations around 185 degrees , which is more consistent with the quantum mechanical calculations and known 3D structures of folded ribonucleic acids (RNAs). Evidently, the AMBER99chi force field predicts the structural characteristics of ribonucleosides better than the AMBER99 force field and should improve structural and thermodynamic predictions of RNA structures.

Phase Equilibria and Magnetic Phases in the Ce-Fe-Co-B System

PubMed Central

Wang, Tian; Kevorkov, Dmytro; Medraj, Mamoun

2016-01-01

Ce-Fe-Co-B is a promising system for permanent magnets. A high-throughput screening method combining diffusion couples, key alloys, Scanning Electron Microscope/Wavelength Dispersive X-ray Spectroscope (SEM/WDS), and Magnetic Force Microscope (MFM) is used in this research to understand the phase equilibria and to explore promising magnetic phases in this system. Three magnetic phases were detected and their homogeneity ranges were determined at 900 °C, which were presented by the formulae: Ce2Fe14−xCoxB (0 ≤ x ≤ 4.76), CeCo4−xFexB (0 ≤ x ≤ 3.18), and Ce3Co11−x FexB4 (0 ≤ x ≤ 6.66). The phase relations among the magnetic phases in this system have been studied. Ce2(Fe, Co)14B appears to have stronger magnetization than Ce(Co, Fe)4B and Ce3(Co, Fe)11B4 from MFM analysis when comparing the magnetic interactions of selected key alloys. Also, a non-magnetic CeCo12−xFexB6 (0 ≤ x ≤ 8.74) phase was detected in this system. A boron-rich solid solution with Ce13FexCoyB45 (32 ≤ x ≤ 39, 3 ≤ y ≤ 10) chemical composition was also observed. However, the crystal structure of this phase could not be found in the literature. Moreover, ternary solid solutions ε1 (Ce2Fe17−xCox (0 ≤ x ≤ 12.35)) and ε2 (Ce2Co17−xFex (0 ≤ x ≤ 3.57)) were found to form between Ce2Fe17 and Ce2Co17 in the Ce-Fe-Co ternary system at 900 °C. PMID:28772374

Liquid-liquid equilibria of binary mixtures of a lipidic ionic liquid with hydrocarbons.

PubMed

Green, Blane D; Badini, Alexander J; O'Brien, Richard A; Davis, James H; West, Kevin N

2016-01-28

Although structurally diverse, many ionic liquids (ILs) are polar in nature due to the strong coulombic forces inherent in ionic compounds. However, the overall polarity of the IL can be tuned by incorporating significant nonpolar content into one or more of the constituent ions. In this work, the binary liquid-liquid equilibria of one such IL, 1-methyl-3-(Z-octadec-9-enyl)imidazolium bistriflimide, with several hydrocarbons (n-hexane, n-octane, n-decane, cyclohexane, methylcyclohexane, 1-octene) is measured over the temperature range 0-70 °C at ambient pressure using a combination of cloud point and gravimetric techniques. The phase behavior of the systems are similar in that they exhibit two phases: one that is 60-90 mole% hydrocarbon and a second phase that is nearly pure hydrocarbon. Each phase exhibits a weak dependence of composition on temperature (steep curve) above ∼10 °C, likely due to swelling and restructuring of the nonpolar nano-domains of the IL being limited by energetically unfavorable restructuring in the polar nano-domains. The solubility of the n-alkanes decreases with increasing size (molar volume), a trend that continues for the cyclic alkanes, for which upper critical solution temperatures are observed below 70 °C. 1-Octene is found to be more soluble than n-octane, attributable to a combination of its lower molar volume and slightly higher polarity. The COSMO-RS model is used to predict the T-x'-x'' diagrams and gives good qualitative agreement of the observed trends. This work presents the highest known solubility of n-alkanes in an IL to date and tuning the structure of the ionic liquid to maximize the size/shape trends observed may provide the basis for enhanced separations of nonpolar species.

Submicron magnetite grains and carbon compounds in Martian meteorite ALH84001: inorganic, abiotic formation by shock and thermal metamorphism.

PubMed

Treiman, Allan H

2003-01-01

Purported biogenic features of the ALH84001 Martian meteorite (the carbonate globules, their submicron magnetite grains, and organic matter) have reasonable inorganic origins, and a comprehensive hypothesis is offered here. The carbonate globules were deposited from hydrothermal water, without biological mediation. Thereafter, ALH84001 was affected by an impact shock event, which raised its temperature nearly instantaneously to 500-700K, and induced iron-rich carbonate in the globules to decompose to magnetite and other minerals. The rapidity of the temperature increase caused magnetite grains to nucleate in abundance; hence individual crystals were very small. Nucleation and growth of magnetite crystals were fastest along edges and faces of the precursor carbonate grains, forcing the magnetite grains to be platy or elongated, including the "truncated hexa-octahedra" shape. ALH84001 had formed at some depth within Mars where the lithostatic pressure was significantly above that of Mars' surface. Also, because the rock was at depth, the impact heat dissipated slowly. During this interval, magnetite crystals approached chemical equilibria with surrounding minerals and gas. Their composition, nearly pure Fe(3)O(4), reflects those of equilibria; elements that substitute into magnetite are either absent from iron-rich carbonate (e.g., Ti, Al, Cr), or partitioned into other minerals during magnetite formation (Mg, Mn). Many microstructural imperfections in the magnetite grains would have annealed out as the rock cooled. In this post-shock thermal regime, carbon-bearing gas from the decomposition of iron carbonates reacted with water in the rock (or from its surroundings) to produce organic matter via Fischer-Tropschlike reactions. Formation of such organic compounds like polycyclic aromatic hydrocarbons would have been catalyzed by the magnetite (formation of graphite, the thermochemically stable phase, would be kinetically hindered).

Flow Shear Effects in the Onset Physics of Resistive MHD Instabilities in Tokamaks. Final report

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

Brennan, Dylan P.

The progress in this research centers around the computational analysis of flow shear effects in the onset of a 3/2 mode driven by a 1/1 mode in DIII-D equilibria. The initial idea was to try and calculate, via nonlinear simulations with NIMROD, the effects of rotation shear on driven 3/2 and 2/1 seed island physics, in experimentally relevant DIIID equilibria. The simulations indicated that very small seed islands were directly driven, as shielding between the sawtooth and the surfaces is significant at the high Lundquist numbers of the experiment. Instead, long after the initial crash the difference in linear stabilitymore » of the 3/2, which remained prevalent despite the flattening of the core profiles from the sawtooth, contributed to a difference in the eventual seed island evolution. Essentially the seed islands grew or decayed long after the sawtooth crash, and not directly from it. Effectively the dominant 1/1 mode was found to be dragging the coupled modes surrounding it at a high rate through the plasma at their surfaces. The 1/1 mode is locked to the local frame of the plasma in the core, where the flow rate is greatest. The resonant perturbations at the surrounding surfaces propagate in the 'high slip regime' in the language of Fitzpatrick. Peaked flux averaged jxb forces (see Figs. 1 and 2) agree with localized flow modifications at the surfaces in analogy with Ebrahimi, PRL 2007. We track the mode into nonlinear saturation and have found oscillatory states in the evolution. During a visit (11/09) to Tulsa by R.J. LaHaye (GA), it became clear that similar oscillatory states are observed in DIII-D for these types of discharges.« less

Validating empirical force fields for molecular-level simulation of cellulose dissolution

USDA-ARS?s Scientific Manuscript database

The calculations presented here, which include dynamics simulations using analytical force fields and first principles studies, indicate that the COMPASS force field is preferred over the Dreiding and Universal force fields for studying dissolution of large cellulose structures. The validity of thes...

Hierarchical atom type definitions and extensible all-atom force fields.

PubMed

Jin, Zhao; Yang, Chunwei; Cao, Fenglei; Li, Feng; Jing, Zhifeng; Chen, Long; Shen, Zhe; Xin, Liang; Tong, Sijia; Sun, Huai

2016-03-15

The extensibility of force field is a key to solve the missing parameter problem commonly found in force field applications. The extensibility of conventional force fields is traditionally managed in the parameterization procedure, which becomes impractical as the coverage of the force field increases above a threshold. A hierarchical atom-type definition (HAD) scheme is proposed to make extensible atom type definitions, which ensures that the force field developed based on the definitions are extensible. To demonstrate how HAD works and to prepare a foundation for future developments, two general force fields based on AMBER and DFF functional forms are parameterized for common organic molecules. The force field parameters are derived from the same set of quantum mechanical data and experimental liquid data using an automated parameterization tool, and validated by calculating molecular and liquid properties. The hydration free energies are calculated successfully by introducing a polarization scaling factor to the dispersion term between the solvent and solute molecules. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Estimating Values of H2O-ACTIVITIES in the Mantle Using Amphibole Equilibria

NASA Astrophysics Data System (ADS)

Lamb, W. M.; Hunt, L. E.

2017-12-01

Determining values of H2O activity (aH2O) for mantle rocks will yield a better understanding of those mantle processes that are controlled, in part, by the availability of H2O (e.g., melting and deformation). The H contents of the upper mantle can be estimated from amount of H contained in nominally anhydrous minerals (NAMs). However, for many common NAMs, the relation between aH2O and H content is not well known, and certain NAMs may be prone to retrograde H loss. The activities of H2O and other fluids species (e.g., CO2) may be estimated using mineral equilibria. Equilibria involving amphibole can, for example, be used to estimate values of aH2O and hydrogen fugacity (ƒH2). Spinel equilibria can be applied to estimate values of oxygen fugacity (ƒO2) that, when combined with ƒH2, will provide a second estimate of aH2O. We have characterized mineral chemistries in 11 amphibole-bearing peridotite xenoliths from the southwestern U.S.A. The compositions of co-existing pyroxenes ± garnet yield P-T conditions of ≈ 1.1 GPa, and 880 to 980˚C, and application of dehydration equilibria yields values of aH2O ranging from 0.04 to 0.19. The compositions of coexisting spinel + olivine + opx yield DlogƒO2(FMQ) of -0.2 to +0.9. Values of ƒH2, estimated using amphibole dehydrogenation equilibria (6 to 91 bars) were combined with values of ƒO2 to estimate aH2O in nine samples (≈ 0.02 to 0.12). The difference between these two values of aH2O, estimated using dehydration equilibria versus ƒH2 + ƒO2, is generally < 0.1, suggesting that the amphiboles experienced little or no retrograde H-loss. All samples equilibrated at low values of aH2O, and these values may be used to predict NAM H-contents. For example, according to Gaetani et al. (2014, Cont. Min. Pet., p. 965), the concentration of H in olivine is a function of P, T, the fugacities of H2O and O2, and olivine composition. Their relation yields relatively low predicted H-contents of 10 to 28 wt. ppm for olivine in our samples. These results suggest that if P, T, and bulk composition are appropriate to stabilize amphibole in the mantle, this mineral may act to consume much of the available H and equilibrate at low values of aH2O. The NAMs in these rocks will have relatively low H-contents and, if these NAMs control the rheology the rock, this portion of the mantle will have a relatively high viscosity.

A force field for dynamic Cu-BTC metal-organic framework.

PubMed

Zhao, Lei; Yang, Qingyuan; Ma, Qintian; Zhong, Chongli; Mi, Jianguo; Liu, Dahuan

2011-02-01

A new force field that can describe the flexibility of Cu-BTC metal-organic framework (MOF) was developed in this work. Part of the parameters were obtained using density functional theory calculations, and the others were taken from other force fields. The new force field could reproduce well the experimental crystal structure, negative thermal expansion, vibrational properties as well as adsorption behavior in Cu-BTC. In addition, the bulk modulus of Cu-BTC was predicted using the new force field. We believe the new force field is useful in understanding the structure-property relationships for MOFs, and the approach can be extended to other MOFs.

Containerless Processing Studies in the MSFC Electrostatic Levitator

NASA Technical Reports Server (NTRS)

Rogers, J. R.; SanSoucie, M. P.

2012-01-01

Levitation or containerless processing represents an important tool in materials research. Levitated specimens are free from contact with a container, which permits studies of deeply undercooled melts, and high-temperature, highly reactive materials. Containerless processing provides data for studies of thermophysical properties, phase equilibria, metastable state formation, microstructure formation, undercooling, and nucleation. Levitation techniques include: acoustic, aero-acoustic, electromagnetic, and electrostatic. In microgravity, levitation can be achieved with greatly reduced positioning forces. Microgravity also reduces the effects of buoyancy and sedimentation in melts. The European Space Agency (ESA) and the German Aerospace Center (DLR) jointly developed an electromagnetic levitator facility (MSL-EML) for containerless materials processing in space. The MSL-EML will be accommodated in the European Columbus Facility on the International Space Station (ISS). The electrostatic levitator (ESL) facility at the Marshall Space Flight Center provides support for the development of containerless processing studies for the ISS. The capabilities of the facility and recent results will be discussed.

Molecular origin of urea driven hydrophobic polymer collapse and unfolding depending on side chain chemistry.

PubMed

Nayar, Divya; Folberth, Angelina; van der Vegt, Nico F A

2017-07-19

Osmolytes affect hydrophobic collapse and protein folding equilibria. The underlying mechanisms are, however, not well understood. We report large-scale conformational sampling of two hydrophobic polymers with secondary and tertiary amide side chains using extensive molecular dynamics simulations. The calculated free energy of unfolding increases with urea for the secondary amide, yet decreases for the tertiary amide, in agreement with experiment. The underlying mechanism is rooted in opposing entropic driving forces: while urea screens the hydrophobic macromolecular interface and drives unfolding of the tertiary amide, urea's concomitant loss in configurational entropy drives collapse of the secondary amide. Only at sufficiently high urea concentrations bivalent urea hydrogen bonding interactions with the secondary amide lead to further stabilisation of its collapsed state. The observations provide a new angle on the interplay between side chain chemistry, urea hydrogen bonding, and the role of urea in attenuating or strengthening the hydrophobic effect.

Fixed-Charge Atomistic Force Fields for Molecular Dynamics Simulations in the Condensed Phase: An Overview.

PubMed

Riniker, Sereina

2018-03-26

In molecular dynamics or Monte Carlo simulations, the interactions between the particles (atoms) in the system are described by a so-called force field. The empirical functional form of classical fixed-charge force fields dates back to 1969 and remains essentially unchanged. In a fixed-charge force field, the polarization is not modeled explicitly, i.e. the effective partial charges do not change depending on conformation and environment. This simplification allows, however, a dramatic reduction in computational cost compared to polarizable force fields and in particular quantum-chemical modeling. The past decades have shown that simulations employing carefully parametrized fixed-charge force fields can provide useful insights into biological and chemical questions. This overview focuses on the four major force-field families, i.e. AMBER, CHARMM, GROMOS, and OPLS, which are based on the same classical functional form and are continuously improved to the present day. The overview is aimed at readers entering the field of (bio)molecular simulations. More experienced users may find the comparison and historical development of the force-field families interesting.

Thermodynamic analysis of reaction equilibria in ionic and molecular liquid systems by high-temperature Raman spectroscopy.

PubMed

Kalampounias, Angelos G; Boghosian, Soghomon

2009-09-01

A formalism for correlating relative Raman band intensities with the stoichiometric coefficients, the equilibrium constant, and the thermodynamics of reaction equilibria in solution is derived. The proposed method is used for studying: (1) the thermal dissociation of molten KHSO(4) in the temperature range 240-450 degrees C; (2) the dinuclear complex formation in molten TaCl(5)-AlCl(3) mixtures at temperatures between 125 and 235 degrees C. The experimental and calculational procedures for exploiting the temperature-dependent Raman band intensities in the molten phase as well as (if applicable) in the vapors thereof are described and used for determining the enthalpy of the equilibria: (1) 2HSO(4)(-)(l) <--> S(2)O(7)(2-)(l) + H(2)O(g), DeltaH(0)=64.9 +/- 2.9 kJ mol(-1); and (2) 1/2Ta(2)Cl(10)(l) + 1/2Al(2)Cl(6)(l) <--> TaAlCl(8)(l), DeltaH(0)=-12.1 +/- 1.5 kJ mol(-1).

Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation

NASA Astrophysics Data System (ADS)

Khajanchi, Subhas; Das, Dhiraj Kumar; Kar, Tapan Kumar

2018-05-01

We propose and analyze a mathematical model for tuberculosis (TB) transmission to study the role of exogenous reinfection and endogenous reactivation. The model exhibits two equilibria: a disease free and an endemic equilibria. We observe that the TB model exhibits transcritical bifurcation when basic reproduction number R0 = 1. Our results demonstrate that the disease transmission rate β and exogenous reinfection rate α plays an important role to change the qualitative dynamics of TB. The disease transmission rate β give rises to the possibility of backward bifurcation for R0 < 1, and hence the existence of multiple endemic equilibria one of which is stable and another one is unstable. Our analysis suggests that R0 < 1 may not be sufficient to completely eliminate the disease. We also investigate that our TB transmission model undergoes Hopf-bifurcation with respect to the contact rate β and the exogenous reinfection rate α. We conducted some numerical simulations to support our analytical findings.

Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games.

PubMed

Duong, Manh Hong; Han, The Anh

2016-12-01

In this paper, we study the distribution and behaviour of internal equilibria in a d-player n-strategy random evolutionary game where the game payoff matrix is generated from normal distributions. The study of this paper reveals and exploits interesting connections between evolutionary game theory and random polynomial theory. The main contributions of the paper are some qualitative and quantitative results on the expected density, [Formula: see text], and the expected number, E(n, d), of (stable) internal equilibria. Firstly, we show that in multi-player two-strategy games, they behave asymptotically as [Formula: see text] as d is sufficiently large. Secondly, we prove that they are monotone functions of d. We also make a conjecture for games with more than two strategies. Thirdly, we provide numerical simulations for our analytical results and to support the conjecture. As consequences of our analysis, some qualitative and quantitative results on the distribution of zeros of a random Bernstein polynomial are also obtained.

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

PubMed Central

Li, Jiawei; Kendall, Graham

2015-01-01

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

The Cu-Li-Sn Phase Diagram: Isopleths, Liquidus Projection and Reaction Scheme

PubMed Central

Flandorfer, Hans

2016-01-01

The Cu-Li-Sn phase diagram was constructed based on XRD and DTA data of 60 different alloy compositions. Eight ternary phases and 14 binary solid phases form 44 invariant ternary reactions, which are illustrated by a Scheil-Schulz reaction scheme and a liquidus projection. Phase equilibria as a function of concentration and temperature are shown along nine isopleths. This report together with an earlier publication of our group provides for the first time comprehensive investigations of phase equilibria and respective phase diagrams. Most of the phase equilibria could be established based on our experimental results. Only in the Li-rich part where many binary and ternary compounds are present estimations had to be done which are all indicated by dashed lines. A stable ternary miscibility gap could be found which was predicted by modelling the liquid ternary phase in a recent work. The phase diagrams are a crucial input for material databases and thermodynamic optimizations regarding new anode materials for high-power Li-ion batteries. PMID:27788175

Redox equilibria of multivalent ions in silicate glasses

NASA Technical Reports Server (NTRS)

Lauer, H. V., Jr.; Morris, R. V.

1977-01-01

Experimental studies were made on the compositional dependence of the redox equilibrium of Eu in synthetic silicate liquids, together with an empirical model describing the observed compositional dependence. Electron paramagnetic resonance (EPR) was used to measure the concentration ratio of Eu(2+) to Eu(3+) in various glasses formed by rapidly quenching silicate liquids. The compositional field studied comprised mixtures of SiO2, TiO2, Al2O3, CaO, MgO, and Na2O. The proposed model describes the Eu(2+)/Eu(3+) ratio over the entire compositional field in terms of parameters easily related to each glass composition. The general applicability and utility of the model is further demonstrated by its application to the Fe(2+)-Fe(3+), Ce(3+)-Ce(4+), and Cr(3+)-Cr(6+) redox reactions in binary alkali oxide silicate glasses of Li, Na, and K.

Scrutinizing Molecular Mechanics Force Fields on the Submicrosecond Timescale with NMR Data

PubMed Central

Lange, Oliver F.; van der Spoel, David; de Groot, Bert L.

2010-01-01

Abstract Protein dynamics on the atomic level and on the microsecond timescale has recently become accessible from both computation and experiment. To validate molecular dynamics (MD) at the submicrosecond timescale against experiment we present microsecond MD simulations in 10 different force-field configurations for two globular proteins, ubiquitin and the gb3 domain of protein G, for which extensive NMR data is available. We find that the reproduction of the measured NMR data strongly depends on the chosen force field and electrostatics treatment. Generally, particle-mesh Ewald outperforms cut-off and reaction-field approaches. A comparison to measured J-couplings across hydrogen bonds suggests that there is room for improvement in the force-field description of hydrogen bonds in most modern force fields. Our results show that with current force fields, simulations beyond hundreds of nanoseconds run an increased risk of undergoing transitions to nonnative conformational states or will persist within states of high free energy for too long, thus skewing the obtained population frequencies. Only for the AMBER99sb force field have such transitions not been observed. Thus, our results have significance for the interpretation of data obtained with long MD simulations, for the selection of force fields for MD studies and for force-field development. We hope that this comprehensive benchmark based on NMR data applied to many popular MD force fields will serve as a useful resource to the MD community. Finally, we find that for gb3, the force-field AMBER99sb reaches comparable accuracy in back-calculated residual dipolar couplings and J-couplings across hydrogen bonds to ensembles obtained by refinement against NMR data. PMID:20643085

Phase-field modeling of chemical control of polarization stability and switching dynamics in ferroelectric thin films

DOE PAGES

Cao, Ye; Kalinin, Sergei V.

2016-12-15

Phase-field simulation (PFS) has revolutionized the understanding of domain structure and switching behavior in ferroelectric thin films and ceramics. Generally, PFS is based on the solution of (a set of) Landau-Ginzburg-Devonshire equations for a defined order parameter field(s) under physical boundary conditions (BCs) of fixed potential or charge. While well matched to the interfaces in bulk materials and devices, these BCs are generally not applicable to free ferroelectric surfaces. Here, we developed a self-consistent phase-field model with BCs based on electrochemical equilibria. We chose Pb(Zr 0.2Ti 0.8)O 3 ultrathin film consisting of (001) oriented single tetragonal domain ( Pz) asmore » a model system and systematically studied the effects of oxygen partial pressure, temperature, and surface ions on the ferroelectric state and compared it with the case of complete screening. We have further explored the polarization switching induced by the oxygen partial pressure and observed pronounced size effect induced by chemical screening. Finally, our paper thus helps to understand the emergent phenomena in ferroelectric thin films brought about by the electrochemical ionic surface compensations.« less

Phase-field modeling of chemical control of polarization stability and switching dynamics in ferroelectric thin films

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

Cao, Ye; Kalinin, Sergei V.

Phase-field simulation (PFS) has revolutionized the understanding of domain structure and switching behavior in ferroelectric thin films and ceramics. Generally, PFS is based on the solution of (a set of) Landau-Ginzburg-Devonshire equations for a defined order parameter field(s) under physical boundary conditions (BCs) of fixed potential or charge. While well matched to the interfaces in bulk materials and devices, these BCs are generally not applicable to free ferroelectric surfaces. Here, we developed a self-consistent phase-field model with BCs based on electrochemical equilibria. We chose Pb(Zr 0.2Ti 0.8)O 3 ultrathin film consisting of (001) oriented single tetragonal domain ( Pz) asmore » a model system and systematically studied the effects of oxygen partial pressure, temperature, and surface ions on the ferroelectric state and compared it with the case of complete screening. We have further explored the polarization switching induced by the oxygen partial pressure and observed pronounced size effect induced by chemical screening. Finally, our paper thus helps to understand the emergent phenomena in ferroelectric thin films brought about by the electrochemical ionic surface compensations.« less

Improved Design of Stellarator Coils for Current Carrying Plasmas

NASA Astrophysics Data System (ADS)

Drevlak, M.; Strumberger, E.; Hirshman, S.; Boozer, A.; Brooks, A.; Valanju, P.

1998-11-01

The method of automatic optimization (P. Merkel, Nucl. Fus. 27), (1987) 867; P. Merkel, M. Drevlak, Proc 25th EPS Conf. on Cont. Fus. and Plas. Phys., Prague, in print. for the design of stellarator coils consists essentially of determining filaments such that the average relative field error int dS [ (B_coil + B_j) \\cdot n]^2/B^2_coil is minimized on the prescribed plasma boundary. Bj is the magnetic field produced by the plasma currents of the given finite β fixed boundary equilibrium. For equilibria of the W7-X type, Bj can be neglected, because of the reduced parallel plasma currents. This is not true for quasi-axisymmetric stellarator (QAS) configurations (A. Reiman, et al., to be published.) with large equilibrium and net plasma (bootstrap) currents. Although the coils for QAS exhibit low values of the field error, free boundary calculations indicate that the shape of the plasma is usually not accurately reproduced , particularly when saddle coils are used. We investigate if the surface reconstruction can be improved by introducing a modified measure of the field error based on a measure of the resonant components of the normal field.

Game-Theoretic Models of Information Overload in Social Networks

NASA Astrophysics Data System (ADS)

Borgs, Christian; Chayes, Jennifer; Karrer, Brian; Meeder, Brendan; Ravi, R.; Reagans, Ray; Sayedi, Amin

We study the effect of information overload on user engagement in an asymmetric social network like Twitter. We introduce simple game-theoretic models that capture rate competition between celebrities producing updates in such networks where users non-strategically choose a subset of celebrities to follow based on the utility derived from high quality updates as well as disutility derived from having to wade through too many updates. Our two variants model the two behaviors of users dropping some potential connections (followership model) or leaving the network altogether (engagement model). We show that under a simple formulation of celebrity rate competition, there is no pure strategy Nash equilibrium under the first model. We then identify special cases in both models when pure rate equilibria exist for the celebrities: For the followership model, we show existence of a pure rate equilibrium when there is a global ranking of the celebrities in terms of the quality of their updates to users. This result also generalizes to the case when there is a partial order consistent with all the linear orders of the celebrities based on their qualities to the users. Furthermore, these equilibria can be computed in polynomial time. For the engagement model, pure rate equilibria exist when all users are interested in the same number of celebrities, or when they are interested in at most two. Finally, we also give a finite though inefficient procedure to determine if pure equilibria exist in the general case of the followership model.

Generalization of Solovev’s approach to finding equilibrium solutions for axisymmetric plasmas with flow

NASA Astrophysics Data System (ADS)

M, S. CHU; Yemin, HU; Wenfeng, GUO

2018-03-01

Solovev’s approach of finding equilibrium solutions was found to be extremely useful for generating a library of linear-superposable equilibria for the purpose of shaping studies. This set of solutions was subsequently expanded to include the vacuum solutions of Zheng, Wootton and Solano, resulting in a set of functions {SOLOVEV_ZWS} that were usually used for all toroidally symmetric plasmas, commonly recognized as being able to accommodate any desired plasma shapes (complete-shaping capability). The possibility of extending the Solovev approach to toroidal equilibria with a general plasma flow is examined theoretically. We found that the only meaningful extension is to plasmas with a pure toroidal rotation and with a constant Mach number. We also show that the simplification ansatz made to the current profiles, which was the basis of the Solovev approach, should be applied more systematically to include an internal boundary condition at the magnetic axis; resulting in a modified and more useful set {SOLOVEV_ZWSm}. Explicit expressions of functions in this set are given for equilibria with a quasi-constant current density profile, with a toroidal flow at a constant Mach number and with specific heat capacity 1. The properties of {SOLOVEV_ZWSm} are studied analytically. Numerical examples of achievable equilibria are demonstrated. Although the shaping capability of the set {SOLOVE_ZWSm} is quite extensive, it nevertheless still does not have complete shaping capability, particularly for plasmas with negative curvature points on the plasma boundary such as the doublets or indented bean shaped tokamaks.

Accelerating Multiagent Reinforcement Learning by Equilibrium Transfer.

PubMed

Hu, Yujing; Gao, Yang; An, Bo

2015-07-01

An important approach in multiagent reinforcement learning (MARL) is equilibrium-based MARL, which adopts equilibrium solution concepts in game theory and requires agents to play equilibrium strategies at each state. However, most existing equilibrium-based MARL algorithms cannot scale due to a large number of computationally expensive equilibrium computations (e.g., computing Nash equilibria is PPAD-hard) during learning. For the first time, this paper finds that during the learning process of equilibrium-based MARL, the one-shot games corresponding to each state's successive visits often have the same or similar equilibria (for some states more than 90% of games corresponding to successive visits have similar equilibria). Inspired by this observation, this paper proposes to use equilibrium transfer to accelerate equilibrium-based MARL. The key idea of equilibrium transfer is to reuse previously computed equilibria when each agent has a small incentive to deviate. By introducing transfer loss and transfer condition, a novel framework called equilibrium transfer-based MARL is proposed. We prove that although equilibrium transfer brings transfer loss, equilibrium-based MARL algorithms can still converge to an equilibrium policy under certain assumptions. Experimental results in widely used benchmarks (e.g., grid world game, soccer game, and wall game) show that the proposed framework: 1) not only significantly accelerates equilibrium-based MARL (up to 96.7% reduction in learning time), but also achieves higher average rewards than algorithms without equilibrium transfer and 2) scales significantly better than algorithms without equilibrium transfer when the state/action space grows and the number of agents increases.

Thermodynamic foundations of applications of ab initio methods for determination of the adsorbate equilibria: hydrogen at the GaN(0001) surface.

PubMed

Kempisty, Pawel; Strąk, Paweł; Sakowski, Konrad; Kangawa, Yoshihiro; Krukowski, Stanisław

2017-11-08

Thermodynamic foundations of ab initio modeling of vapor-solid and vapor-surface equilibria are introduced. The chemical potential change is divided into enthalpy and entropy terms. The enthalpy path passes through vapor-solid transition at zero temperature. The entropy path avoids the singular point at zero temperature passing a solid-vapor transition under normal conditions, where evaporation entropy is employed. In addition, the thermal changes are calculated. The chemical potential difference contribution of the following terms: vaporization enthalpy, vaporization entropy, the temperature-entropy related change, the thermal enthalpy change and mechanical pressure is obtained. The latter term is negligibly small for the pressure typical for epitaxy. The thermal enthalpy change is two orders smaller than the first three terms which have to be taken into account explicitly. The configurational vaporization entropy change is derived for adsorption processes. The same formulation is derived for vapor-surface equilibria using hydrogen at the GaN(0001) surface as an example. The critical factor is the dependence of the enthalpy of evaporation (desorption energy) on the pinning of the Fermi level bringing a drastic change of the value from 2.24 eV to -2.38 eV. In addition it is shown that entropic contributions considerable change the hydrogen equilibrium pressure over the GaN(0001) surface by several orders of magnitude. Thus a complete and exact formulation of vapor-solid and vapor-surface equilibria is presented.

Experimental Investigation of Gas/Slag/Matte/Tridymite Equilibria in the Cu-Fe-O-S-Si System in Controlled Gas Atmosphere: Experimental Results at 1523 K (1250 °C) and P(SO2) = 0.25 atm

NASA Astrophysics Data System (ADS)

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

2018-04-01

To assist in the optimization of copper smelting and converting processes, accurate new measurements of the phase equilibria of the Cu-Fe-O-S-Si system have been undertaken. The experimental investigation was focused on the characterization of gas/slag/matte/tridymite equilibria in the Cu-Fe-O-S-Si system at 1523 K (1250 °C), P(SO2) = 0.25 atm, and a range of P(O2)s. The experimental methodology, developed in PYROSEARCH, includes high-temperature equilibration of samples on substrate made from the silica primary phase in controlled gas atmospheres (CO/CO2/SO2/Ar) followed by rapid quenching of the equilibrium condensed phases and direct measurement of the phase compositions with electron-probe X-ray microanalysis (EPMA). The data provided in the present study at 1523 K (1250 °C) and the previous study by the authors at 1473 K (1200 °C) has enabled the determination of the effects of temperature on the phase equilibria of the multicomponent multiphase system, including such characteristics as the chemically dissolved copper in slag and Fe/SiO2 ratio at silica saturation as a function of copper concentration in matte. The new data will be used in the optimization of the thermodynamic database for the copper-containing systems.

Stepwise formation of H3O(+)(H2O)n in an ion drift tube: Empirical effective temperature of association/dissociation reaction equilibrium in an electric field.

PubMed

Nakai, Yoichi; Hidaka, Hiroshi; Watanabe, Naoki; Kojima, Takao M

2016-06-14

We measured equilibrium constants for H3O(+)(H2O)n-1 + H2O↔H3O(+)(H2O)n (n = 4-9) reactions taking place in an ion drift tube with various applied electric fields at gas temperatures of 238-330 K. The zero-field reaction equilibrium constants were determined by extrapolation of those obtained at non-zero electric fields. From the zero-field reaction equilibrium constants, the standard enthalpy and entropy changes, ΔHn,n-1 (0) and ΔSn,n-1 (0), of stepwise association for n = 4-8 were derived and were in reasonable agreement with those measured in previous studies. We also examined the electric field dependence of the reaction equilibrium constants at non-zero electric fields for n = 4-8. An effective temperature for the reaction equilibrium constants at non-zero electric field was empirically obtained using a parameter describing the electric field dependence of the reaction equilibrium constants. Furthermore, the size dependence of the parameter was thought to reflect the evolution of the hydrogen-bond structure of H3O(+)(H2O)n with the cluster size. The reflection of structural information in the electric field dependence of the reaction equilibria is particularly noteworthy.

Prediction of Mechanical Properties of Polymers With Various Force Fields

NASA Technical Reports Server (NTRS)

Odegard, Gregory M.; Clancy, Thomas C.; Gates, Thomas S.

2005-01-01

The effect of force field type on the predicted elastic properties of a polyimide is examined using a multiscale modeling technique. Molecular Dynamics simulations are used to predict the atomic structure and elastic properties of the polymer by subjecting a representative volume element of the material to bulk and shear finite deformations. The elastic properties of the polyimide are determined using three force fields: AMBER, OPLS-AA, and MM3. The predicted values of Young s modulus and shear modulus of the polyimide are compared with experimental values. The results indicate that the mechanical properties of the polyimide predicted with the OPLS-AA force field most closely matched those from experiment. The results also indicate that while the complexity of the force field does not have a significant effect on the accuracy of predicted properties, small differences in the force constants and the functional form of individual terms in the force fields determine the accuracy of the force field in predicting the elastic properties of the polyimide.

Force Field for Water Based on Neural Network.

PubMed

Wang, Hao; Yang, Weitao

2018-05-18

We developed a novel neural network based force field for water based on training with high level ab initio theory. The force field was built based on electrostatically embedded many-body expansion method truncated at binary interactions. Many-body expansion method is a common strategy to partition the total Hamiltonian of large systems into a hierarchy of few-body terms. Neural networks were trained to represent electrostatically embedded one-body and two-body interactions, which require as input only one and two water molecule calculations at the level of ab initio electronic structure method CCSD/aug-cc-pVDZ embedded in the molecular mechanics water environment, making it efficient as a general force field construction approach. Structural and dynamic properties of liquid water calculated with our force field show good agreement with experimental results. We constructed two sets of neural network based force fields: non-polarizable and polarizable force fields. Simulation results show that the non-polarizable force field using fixed TIP3P charges has already behaved well, since polarization effects and many-body effects are implicitly included due to the electrostatic embedding scheme. Our results demonstrate that the electrostatically embedded many-body expansion combined with neural network provides a promising and systematic way to build the next generation force fields at high accuracy and low computational costs, especially for large systems.

Different elution modes and field programming in gravitational field-flow fractionation. III. Field programming by flow-rate gradient generated by a programmable pump.

PubMed

Plocková, J; Chmelík, J

2001-05-25

Gravitational field-flow fractionation (GFFF) utilizes the Earth's gravitational field as an external force that causes the settlement of particles towards the channel accumulation wall. Hydrodynamic lift forces oppose this action by elevating particles away from the channel accumulation wall. These two counteracting forces enable modulation of the resulting force field acting on particles in GFFF. In this work, force-field programming based on modulating the magnitude of hydrodynamic lift forces was implemented via changes of flow-rate, which was accomplished by a programmable pump. Several flow-rate gradients (step gradients, linear gradients, parabolic, and combined gradients) were tested and evaluated as tools for optimization of the separation of a silica gel particle mixture. The influence of increasing amount of sample injected on the peak resolution under flow-rate gradient conditions was also investigated. This is the first time that flow-rate gradients have been implemented for programming of the resulting force field acting on particles in GFFF.

Non-axisymmetric ideal equilibrium and stability of ITER plasmas with rotating RMPs

NASA Astrophysics Data System (ADS)

Ham, C. J.; Cramp, R. G. J.; Gibson, S.; Lazerson, S. A.; Chapman, I. T.; Kirk, A.

2016-08-01

The magnetic perturbations produced by the resonant magnetic perturbation (RMP) coils will be rotated in ITER so that the spiral patterns due to strike point splitting which are locked to the RMP also rotate. This is to ensure even power deposition on the divertor plates. VMEC equilibria are calculated for different phases of the RMP rotation. It is demonstrated that the off harmonics rotate in the opposite direction to the main harmonic. This is an important topic for future research to control and optimize ITER appropriately. High confinement mode (H-mode) is favourable for the economics of a potential fusion power plant and its use is planned in ITER. However, the high pressure gradient at the edge of the plasma can trigger periodic eruptions called edge localized modes (ELMs). ELMs have the potential to shorten the life of the divertor in ITER (Loarte et al 2003 Plasma Phys. Control. Fusion 45 1549) and so methods for mitigating or suppressing ELMs in ITER will be important. Non-axisymmetric RMP coils will be installed in ITER for ELM control. Sampling theory is used to show that there will be significant a {{n}\\text{coils}}-{{n}\\text{rmp}} harmonic sideband. There are nine coils toroidally in ITER so {{n}\\text{coils}}=9 . This results in a significant n  =  6 component to the {{n}\\text{rmp}}=3 applied field and a significant n  =  5 component to the {{n}\\text{rmp}}=4 applied field. Although the vacuum field has similar amplitudes of these harmonics the plasma response to the various harmonics dictates the final equilibrium. Magnetic perturbations with toroidal mode number n  =  3 and n  =  4 are applied to a 15 MA, {{q}95}≈ 3 burning ITER plasma. We use a three-dimensional ideal magnetohydrodynamic model (VMEC) to calculate ITER equilibria with applied RMPs and to determine growth rates of infinite n ballooning modes (COBRA). The {{n}\\text{rmp}}=4 case shows little change in ballooning mode growth rate as the RMP is rotated, however there is a change with rotation for the {{n}\\text{rmp}}=3 case.

Theory of Dust Voids in Plasmas

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

Epidemic spreading on adaptively weighted scale-free networks.

PubMed

Sun, Mengfeng; Zhang, Haifeng; Kang, Huiyan; Zhu, Guanghu; Fu, Xinchu

2017-04-01

We introduce three modified SIS models on scale-free networks that take into account variable population size, nonlinear infectivity, adaptive weights, behavior inertia and time delay, so as to better characterize the actual spread of epidemics. We develop new mathematical methods and techniques to study the dynamics of the models, including the basic reproduction number, and the global asymptotic stability of the disease-free and endemic equilibria. We show the disease-free equilibrium cannot undergo a Hopf bifurcation. We further analyze the effects of local information of diseases and various immunization schemes on epidemic dynamics. We also perform some stochastic network simulations which yield quantitative agreement with the deterministic mean-field approach.

Phase Diagram of Quaternary System NaBr-KBr-CaBr2-H2O at 323 K

NASA Astrophysics Data System (ADS)

Cui, Rui-Zhi; Wang, Wei; Yang, Lei; Sang, Shi-Hua

2018-03-01

The phase equilibria in the system NaBr-KBr-CaBr2-H2O at 323 K were studied using the isothermal dissolution equilibrium method. Using the experimental solubilities of salts data, phase diagram was constructed. The phase diagram have two invariant points, five univariant curves, and four crystallization fields. The equilibrium solid phases in the system are NaBr, NaBr · 2H2O, KBr, and CaBr2 · 4H2O. The solubilities of salts in the system at 323 K were calculated by Pitzer's equation. There is shown that the calculated solubilities agree well with experimental data.

Improved method for calculating neoclassical transport coefficients in the banana regime

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

Taguchi, M., E-mail: taguchi.masayoshi@nihon-u.ac.jp

The conventional neoclassical moment method in the banana regime is improved by increasing the accuracy of approximation to the linearized Fokker-Planck collision operator. This improved method is formulated for a multiple ion plasma in general tokamak equilibria. The explicit computation in a model magnetic field shows that the neoclassical transport coefficients can be accurately calculated in the full range of aspect ratio by the improved method. The some neoclassical transport coefficients for the intermediate aspect ratio are found to appreciably deviate from those obtained by the conventional moment method. The differences between the transport coefficients with these two methods aremore » up to about 20%.« less

Modeling mass drug treatment and resistant filaria disease transmission

NASA Astrophysics Data System (ADS)

Fuady, A. M.; Nuraini, N.; Soewono, E.; Tasman, H.; Supriatna, A. K.

2014-03-01

It has been indicated that a long term application of combined mass drug treatment may contribute to the development of drug resistance in lymphatic filariasis. This phenomenon is not well understood due to the complexity of filaria life cycle. In this paper we formulate a mathematical model for the spread of mass drug resistant in a filaria endemic region. The model is represented in a 13-dimensional Host-Vector system. The basic reproductive ratio of the system which is obtained from the next generation matrix, and analysis of stability of both the disease free equilibrium and the coexistence equilibria are shown. Numerical simulation for long term dynamics for possible field conditions is also shown.

Effects of gravity reduction on phase equilibria. Part 1: Unary and binary isostructural solids

NASA Technical Reports Server (NTRS)

Larson, D. J., Jr.

1975-01-01

Analysis of the Skylab II M553 Experiment samples resulted in the hypothesis that the reduced gravity environment was altering the melting and solidification reactions. A theoretical study was conducted to define the conditions under which such alteration of phase relations is feasible, determine whether it is restricted to space processing, and, if so, ascertain which alloy systems or phase reactions are most likely to demonstrate such effects. Phase equilibria of unary and binary systems with a single solid phase (unary and isomorphous) were considered.

Chemistry of uranium in aluminophosphate glasses

NASA Technical Reports Server (NTRS)

Schreiber, H. D.; Balazs, G. B.; Williams, B. J.

1982-01-01

The U(VI)-U(V)-U(IV) redox equilibria are investigated in two sodium aluminophosphate base compositions at a variety of melt temperatures, imposed oxygen fugacities, and uranium contents. Results show that the higher redox states of uranium are quite soluble in the phosphate glasses, although U(IV) readily precipitates from the melts as UO2. In addition, comparisons of the uranium redox equilibria established in phosphate melts versus those in silicate melts shows that the coordination sites of the individual uranium species are generally the same in both solvent systems although they differ in detail.

Solid-phase equilibria on Pluto's surface

NASA Astrophysics Data System (ADS)

Tan, Sugata P.; Kargel, Jeffrey S.

2018-03-01

Pluto's surface is covered by volatile ices that are in equilibrium with the atmosphere. Multicomponent phase equilibria may be calculated using a thermodynamic equation of state and, without additional assumptions, result in methane-rich and nitrogen-rich solid phases. The former is formed at temperature range between the atmospheric pressure-dependent sublimation and condensation points, while the latter is formed at temperatures lower than the sublimation point. The results, calculated for the observed 11 μbar atmospheric pressure and composition, are consistent with recent work derived from observations by New Horizons.

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.

Modelling the effect of immigration on drinking behaviour.

PubMed

Xiang, Hong; Zhu, Cheng-Cheng; Huo, Hai-Feng

2017-12-01

A drinking model with immigration is constructed. For the model with problem drinking immigration, the model admits only one problem drinking equilibrium. For the model without problem drinking immigration, the model has two equilibria, one is problem drinking-free equilibrium and the other is problem drinking equilibrium. By employing the method of Lyapunov function, stability of all kinds of equilibria is obtained. Numerical simulations are also provided to illustrate our analytical results. Our results show that alcohol immigrants increase the difficulty of the temperance work of the region.

Force field development with GOMC, a fast new Monte Carlo molecular simulation code

NASA Astrophysics Data System (ADS)

Mick, Jason Richard

In this work GOMC (GPU Optimized Monte Carlo) a new fast, flexible, and free molecular Monte Carlo code for the simulation atomistic chemical systems is presented. The results of a large Lennard-Jonesium simulation in the Gibbs ensemble is presented. Force fields developed using the code are also presented. To fit the models a quantitative fitting process is outlined using a scoring function and heat maps. The presented n-6 force fields include force fields for noble gases and branched alkanes. These force fields are shown to be the most accurate LJ or n-6 force fields to date for these compounds, capable of reproducing pure fluid behavior and binary mixture behavior to a high degree of accuracy.

Idealized Cloud-System Resolving Modeling for Tropical Convection Studies

NASA Astrophysics Data System (ADS)

Anber, Usama M.

A three-dimensional limited-domain Cloud-Resolving Model (CRM) is used in idealized settings to study the interaction between tropical convection and the large scale dynamics. The model domain is doubly periodic and the large-scale circulation is parameterized using the Weak Temperature Gradient (WTG) Approximation and Damped Gravity Wave (DGW) methods. The model simulations fall into two main categories: simulations with a prescribed radiative cooling profile, and others in which radiative cooling profile interacts with clouds and water vapor. For experiments with a prescribed radiative cooling profile, radiative heating is taken constant in the vertical in the troposphere. First, the effect of turbulent surface fluxes and radiative cooling on tropical deep convection is studied. In the precipitating equilibria, an increment in surface fluxes produces a greater increase in precipitation than an equal increment in column-integrated radiative heating. The gross moist stability remains close to constant over a wide range of forcings. With dry initial conditions, the system exhibits hysteresis, and maintains a dry state with for a wide range of net energy inputs to the atmospheric column under WTG. However, for the same forcings the system admits a rainy state when initialized with moist conditions, and thus multiple equilibria exist under WTG. When the net forcing is increased enough that simulations, which begin dry, eventually develop precipitation. DGW, on the other hand, does not have the tendency to develop multiple equilibria under the same conditions. The effect of vertical wind shear on tropical deep convection is also studied. The strength and depth of the shear layer are varied as control parameters. Surface fluxes are prescribed. For weak wind shear, time-averaged rainfall decreases with shear and convection remains disorganized. For larger wind shear, rainfall increases with shear, as convection becomes organized into linear mesoscale systems. This non-monotonic dependence of rainfall on shear is observed when the imposed surface fluxes are moderate. For larger surface fluxes, convection in the unsheared basic state is already strongly organized, but increasing wind shear still leads to increasing rainfall. In addition to surface rainfall, the impacts of shear on the parameterized large-scale vertical velocity, convective mass fluxes, cloud fraction, and momentum transport are also discussed. For experiments with interactive radiative cooling profile, the effect of cloud-radiation interaction on cumulus ensemble is examined in sheared and unsheared environments with both fixed and interactive sea surface temperature (SST). For fixed SST, interactive radiation, when compared to simulations in which radiative profile has the same magnitude and vertical shape but does not interact with clouds or water vapor, is found to suppress mean precipitation by inducing strong descent in the lower troposphere, increasing the gross moist stability. For interactive SST, using a slab ocean mixed layer, there exists a shear strength above which the system becomes unstable and develops oscillatory behavior. Oscillations have periods of wet precipitating states followed by periods of dry non-precipitating states. The frequencies of oscillations are intraseasonal to subseasonal, depending on the mixed layer depth. Finally, the model is coupled to a land surface model with fully interactive radiation and surface fluxes to study the diurnal and seasonal radiation and water cycles in the Amazon basin. The model successfully captures the afternoon precipitation and cloud cover peak and the greater latent heat flux in the dry season for the first time; two major biases in GCMs with implications for correct estimates of evaporation and gross primary production in the Amazon. One of the key findings is that the fog layer near the surface in the west season is crucial for determining the surface energy budget and precipitation. This suggests that features on the diurnal time scale can significantly impact climate on the seasonal time scale.

Comparison of Cellulose Iβ Simulations with Three Carbohydrate Force Fields.

PubMed

Matthews, James F; Beckham, Gregg T; Bergenstråhle-Wohlert, Malin; Brady, John W; Himmel, Michael E; Crowley, Michael F

2012-02-14

Molecular dynamics simulations of cellulose have recently become more prevalent due to increased interest in renewable energy applications, and many atomistic and coarse-grained force fields exist that can be applied to cellulose. However, to date no systematic comparison between carbohydrate force fields has been conducted for this important system. To that end, we present a molecular dynamics simulation study of hydrated, 36-chain cellulose Iβ microfibrils at room temperature with three carbohydrate force fields (CHARMM35, GLYCAM06, and Gromos 45a4) up to the near-microsecond time scale. Our results indicate that each of these simulated microfibrils diverge from the cellulose Iβ crystal structure to varying degrees under the conditions tested. The CHARMM35 and GLYCAM06 force fields eventually result in structures similar to those observed at 500 K with the same force fields, which are consistent with the experimentally observed high-temperature behavior of cellulose I. The third force field, Gromos 45a4, produces behavior significantly different from experiment, from the other two force fields, and from previously reported simulations with this force field using shorter simulation times and constrained periodic boundary conditions. For the GLYCAM06 force field, initial hydrogen-bond conformations and choice of electrostatic scaling factors significantly affect the rate of structural divergence. Our results suggest dramatically different time scales for convergence of properties of interest, which is important in the design of computational studies and comparisons to experimental data. This study highlights that further experimental and theoretical work is required to understand the structure of small diameter cellulose microfibrils typical of plant cellulose.

Three Dimensional Distribution of Sensitive Field and Stress Field Inversion of Force Sensitive Materials under Constant Current Excitation.

PubMed

Zhao, Shuanfeng; Liu, Min; Guo, Wei; Zhang, Chuanwei

2018-02-28

Force sensitive conductive composite materials are functional materials which can be used as the sensitive material of force sensors. However, the existing sensors only use one-dimensional electrical properties of force sensitive conductive materials. Even in tactile sensors, the measurement of contact pressure is achieved by large-scale arrays and the units of a large-scale array are also based on the one-dimensional electrical properties of force sensitive materials. The main contribution of this work is to study the three-dimensional electrical properties and the inversion method of three-dimensional stress field of a force sensitive material (conductive rubber), which pushes the application of force sensitive material from one dimensional to three-dimensional. First, the mathematical model of the conductive rubber current field distribution under a constant force is established by the effective medium theory, and the current field distribution model of conductive rubber with different geometry, conductive rubber content and conductive rubber relaxation parameters is deduced. Secondly, the inversion method of the three-dimensional stress field of conductive rubber is established, which provides a theoretical basis for the design of a new tactile sensor, three-dimensional stress field and space force based on force sensitive materials.

Comparison of three empirical force fields for phonon calculations in CdSe quantum dots

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

Kelley, Anne Myers

Three empirical interatomic force fields are parametrized using structural, elastic, and phonon dispersion data for bulk CdSe and their predictions are then compared for the structures and phonons of CdSe quantum dots having average diameters of ~2.8 and ~5.2 nm (~410 and ~2630 atoms, respectively). The three force fields include one that contains only two-body interactions (Lennard-Jones plus Coulomb), a Tersoff-type force field that contains both two-body and three-body interactions but no Coulombic terms, and a Stillinger-Weber type force field that contains Coulombic interactions plus two-body and three-body terms. While all three force fields predict nearly identical peak frequencies formore » the strongly Raman-active “longitudinal optical” phonon in the quantum dots, the predictions for the width of the Raman peak, the peak frequency and width of the infrared absorption peak, and the degree of disorder in the structure are very different. The three force fields also give very different predictions for the variation in phonon frequency with radial position (core versus surface). The Stillinger-Weber plus Coulomb type force field gives the best overall agreement with available experimental data.« less

Optimized molecular dynamics force fields applied to the helix-coil transition of polypeptides.

PubMed

Best, Robert B; Hummer, Gerhard

2009-07-02

Obtaining the correct balance of secondary structure propensities is a central priority in protein force-field development. Given that current force fields differ significantly in their alpha-helical propensities, a correction to match experimental results would be highly desirable. We have determined simple backbone energy corrections for two force fields to reproduce the fraction of helix measured in short peptides at 300 K. As validation, we show that the optimized force fields produce results in excellent agreement with nuclear magnetic resonance experiments for folded proteins and short peptides not used in the optimization. However, despite the agreement at ambient conditions, the dependence of the helix content on temperature is too weak, a problem shared with other force fields. A fit of the Lifson-Roig helix-coil theory shows that both the enthalpy and entropy of helix formation are too small: the helix extension parameter w agrees well with experiment, but its entropic and enthalpic components are both only about half the respective experimental estimates. Our structural and thermodynamic analyses point toward the physical origins of these shortcomings in current force fields, and suggest ways to address them in future force-field development.

A Statistical Analysis of the PPII Propensity of Amino Acid Guests in Proline-Rich Peptides

PubMed Central

Moradi, Mahmoud; Babin, Volodymyr; Sagui, Celeste; Roland, Christopher

2011-01-01

There has been considerable debate about the intrinsic PPII propensity of amino-acid residues in denatured polypeptides. Experimentally, the propensity scale is based on the behavior of guest amino-acid residues placed in the middle of polyproline hosts. We have used classical molecular dynamics simulations, with state-of-the-art force fields to carry out a comprehensive analysis of the conformational equilibria of the proline-based host oligopeptides with single guests. The tracked structural characteristics include the PPII content, the cis/trans isomerization of the prolyl bonds, the puckering of the pyrrolidine rings of the proline residues, and the secondary structural motifs. We find no evidence for an intrinsic PPII propensity in any of the guest amino acids other than proline. Instead, the PPII content as derived from experiments may be explained in terms of: 1), a local correlation between the dihedral angles of the guest amino acid and the proline residue immediately preceding it; and 2), a nonlocal correlation between the cis/trans states of the peptide bonds. In terms of the latter, we find that the presence of a guest (other than proline, tyrosine, or tryptophan) increases the trans content of most of the prolyl bonds, which results in an effective increase of the peptide PPII content. With respect to the local dihedral correlations, we find that these are well described in terms of the so-called odds-ratio statistic. Expressed in terms of free energy language, the PPII content based on the odds-ratio of the relevant residues correlate well with the experimentally measured PPII content. PMID:21320454

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

J.A. Krommes

Fusion physics poses an extremely challenging, practically complex problem that does not yield readily to simple paradigms. Nevertheless, various of the theoretical tools and conceptual advances emphasized at the KaufmanFest 2007 have motivated and/or found application to the development of fusion-related plasma turbulence theory. A brief historical commentary is given on some aspects of that specialty, with emphasis on the role (and limitations) of Hamiltonian/symplectic approaches, variational methods, oscillation-center theory, and nonlinear dynamics. It is shown how to extract a renormalized ponderomotive force from the statistical equations of plasma turbulence, and the possibility of a renormalized K-χ theorem is discussed.more » An unusual application of quasilinear theory to the problem of plasma equilibria in the presence of stochastic magnetic fields is described. The modern problem of zonal-flow dynamics illustrates a confluence of several techniques, including (i) the application of nonlinear-dynamics methods, especially center-manifold theory, to the problem of the transition to plasma turbulence in the face of self-generated zonal flows; and (ii) the use of Hamiltonian formalism to determine the appropriate (Casimir) invariant to be used in a novel wave-kinetic analysis of systems of interacting zonal flows and drift waves. Recent progress in the theory of intermittent chaotic statistics and the generation of coherent structures from turbulence is mentioned, and an appeal is made for some new tools to cope with these interesting and difficult problems in nonlinear plasma physics. Finally, the important influence of the intellectually stimulating research environment fostered by Prof. Allan Kaufman on the author's thinking and teaching methodology is described.« less

Influence of electric field on the hydrogen bond network of water.

PubMed

Suresh, S J; Satish, A V; Choudhary, A

2006-02-21

Understanding the inherent response of water to an external electric (E)-field is useful towards decoupling the role of E-field and surface in several practically encountered situations, such as that near an ion, near a charged surface, or within a biological nanopore. While this problem has been studied in some detail through simulations in the past, it has not been very amenable for theoretical analysis owing to the complexities presented by the hydrogen (H) bond interactions in water. It is also difficult to perform experiments with water in externally imposed, high E-fields owing to dielectric breakdown problems; it is hence all the more important that theoretical progress in this area complements the progress achieved through simulations. In an attempt to fill this lacuna, we develop a theory based on relatively simple concepts of reaction equilibria and Boltzmann distribution. The results are discussed in three parts: one pertaining to a comparison of the key features of the theory vis a vis published simulation/experimental results; second pertaining to insights into the H-bond stoichiometry and molecular orientations at different field strengths and temperatures; and the third relating to a surprising but explainable finding that H-bonds can stabilize molecules whose dipoles are oriented perpendicular to the direction of field (in addition to the E-field and H-bonds both stabilizing molecules with dipoles aligned in the direction of the field).

Empirical temperature-dependent intermolecular potentials determined by data mining from crystal data

NASA Astrophysics Data System (ADS)

Hofmann, D. W. M.; Kuleshova, L. N.

2018-05-01

Modern force fields are accurate enough to describe thermal effects in molecular crystals. Here, we have extended our earlier approach to discrete force fields for various temperatures to a force field with a continuous function. For the parametrisation of the force field, we used data mining on experimental structures with the temperature as an additional descriptor. The obtained force field can be used to minimise energy at a finite temperature and for molecular dynamics with zero-K potentials. The applicability of the method has been demonstrated for the prediction of crystal density, temperature density gradients and transition temperature.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Linear calculations of edge current driven kink modes with BOUT++ code

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

Li, G. Q., E-mail: ligq@ipp.ac.cn; Xia, T. Y.; Lawrence Livermore National Laboratory, Livermore, California 94550

This work extends previous BOUT++ work to systematically study the impact of edge current density on edge localized modes, and to benchmark with the GATO and ELITE codes. Using the CORSICA code, a set of equilibria was generated with different edge current densities by keeping total current and pressure profile fixed. Based on these equilibria, the effects of the edge current density on the MHD instabilities were studied with the 3-field BOUT++ code. For the linear calculations, with increasing edge current density, the dominant modes are changed from intermediate-n and high-n ballooning modes to low-n kink modes, and the linearmore » growth rate becomes smaller. The edge current provides stabilizing effects on ballooning modes due to the increase of local shear at the outer mid-plane with the edge current. For edge kink modes, however, the edge current does not always provide a destabilizing effect; with increasing edge current, the linear growth rate first increases, and then decreases. In benchmark calculations for BOUT++ against the linear results with the GATO and ELITE codes, the vacuum model has important effects on the edge kink mode calculations. By setting a realistic density profile and Spitzer resistivity profile in the vacuum region, the resistivity was found to have a destabilizing effect on both the kink mode and on the ballooning mode. With diamagnetic effects included, the intermediate-n and high-n ballooning modes can be totally stabilized for finite edge current density.« less

Phase Equilibria of the Ternary Sn-Pb-Co System at 250°C and Interfacial Reactions of Co with Sn-Pb Alloys

NASA Astrophysics Data System (ADS)

Wang, Chao-hong; Kuo, Chun-yi; Yang, Nian-cih

2015-11-01

The isothermal section of the ternary Sn-Pb-Co system at 250°C was experimentally determined through a series of the equilibrated Sn-Pb-Co alloys of various compositions. The equilibrium phases were identified on the basis of compositional analysis. For the Sn-Co intermetallic compounds (IMCs), CoSn3, CoSn2, CoSn and Co3Sn2, the Pb solubility was very limited. There exist five tie-triangle regions. The Co-Pb system involves one monotectic reaction, so the phase separation of liquid alloys near the Co-Pb side occurred prior to solidification. The immiscibility field was also determined. Additionally, interfacial reactions between Co and Sn-Pb alloys were conducted. The reaction phase for the Sn-48 at.%Pb and Sn-58 at.%Pb at 250°C was CoSn3 and CoSn2, respectively. Both of them were simultaneously formed in the Sn-53 at.%Pb/Co. The formed IMCs were closely associated to the phase equilibria relationship of the liquid-CoSn3-CoSn2 tie-triangle. Furthermore, with increasing temperatures, the phase formed in equilibrium with Sn-37 wt.%Pb was found to transit from CoSn3 to CoSn2 at 275°C. We propose a simple method of examining the phase transition temperature in the interfacial reactions to determine the boundaries of the liquid-CoSn3-CoSn2 tie-triangles at different temperatures.

Kinetic description of rotating Tokamak plasmas with anisotropic temperatures in the collisionless regime

NASA Astrophysics Data System (ADS)

Cremaschini, Claudio; Tessarotto, Massimo

2011-11-01

A largely unsolved theoretical issue in controlled fusion research is the consistent kinetic treatment of slowly-time varying plasma states occurring in collisionless and magnetized axisymmetric plasmas. The phenomenology may include finite pressure anisotropies as well as strong toroidal and poloidal differential rotation, characteristic of Tokamak plasmas. Despite the fact that physical phenomena occurring in fusion plasmas depend fundamentally on the microscopic particle phase-space dynamics, their consistent kinetic treatment remains still essentially unchallenged to date. The goal of this paper is to address the problem within the framework of Vlasov-Maxwell description. The gyrokinetic treatment of charged particles dynamics is adopted for the construction of asymptotic solutions for the quasi-stationary species kinetic distribution functions. These are expressed in terms of the particle exact and adiabatic invariants. The theory relies on a perturbative approach, which permits to construct asymptotic analytical solutions of the Vlasov-Maxwell system. In this way, both diamagnetic and energy corrections are included consistently into the theory. In particular, by imposing suitable kinetic constraints, the existence of generalized bi-Maxwellian asymptotic kinetic equilibria is pointed out. The theory applies for toroidal rotation velocity of the order of the ion thermal speed. These solutions satisfy identically also the constraints imposed by the Maxwell equations, i.e., quasi-neutrality and Ampere's law. As a result, it is shown that, in the presence of nonuniform fluid and EM fields, these kinetic equilibria can sustain simultaneously toroidal differential rotation, quasi-stationary finite poloidal flows and temperature anisotropy.

Stellar dynamics around a massive black hole - II. Resonant relaxation

NASA Astrophysics Data System (ADS)

Sridhar, S.; Touma, Jihad R.

2016-06-01

We present a first-principles theory of resonant relaxation (RR) of a low-mass stellar system orbiting a more massive black hole (MBH). We first extend the kinetic theory of Gilbert to include the Keplerian field of a black hole of mass M•. Specializing to a Keplerian stellar system of mass M ≪ M•, we use the orbit-averaging method of Sridhar & Touma to derive a kinetic equation for RR. This describes the collisional evolution of a system of N ≫ 1 Gaussian rings in a reduced 5-dim space, under the combined actions of self-gravity, 1 post-Newtonian (PN) and 1.5 PN relativistic effects of the MBH and an arbitrary external potential. In general geometries, RR is driven by both apsidal and nodal resonances, so the distinction between scalar RR and vector RR disappears. The system passes through a sequence of quasi-steady secular collisionless equilibria, driven by irreversible two-ring correlations that accrue through gravitational interactions, both direct and collective. This correlation function is related to a `wake function', which is the linear response of the system to the perturbation of a chosen ring. The wake function is easier to appreciate, and satisfies a simpler equation, than the correlation function. We discuss general implications for the interplay of secular dynamics and non-equilibrium statistical mechanics in the evolution of Keplerian stellar systems towards secular thermodynamic equilibria, and set the stage for applications to the RR of axisymmetric discs in Paper III.

Sapphirine-bearing granulites from the Tongbai orogen, China: Petrology, phase equilibria, zircon U-Pb geochronology and implications for Paleozoic ultrahigh temperature metamorphism

NASA Astrophysics Data System (ADS)

Xiang, Hua; Zhong, Zeng-Qiu; Li, Ye; Qi, Min; Zhou, Han-Wen; Zhang, Li; Zhang, Ze-Ming; Santosh, M.

2014-11-01

We report here for the first time the occurrence of sapphirine-bearing granulites within the Qinling Group of the Qinling-Tongbai orogen and provide robust evidence for extreme crustal metamorphism at ultrahigh-temperature (UHT) conditions. We document the UHT indicator of sapphirine and spinel in a mafic granulite consisting of orthopyroxene, biotite, plagioclase, amphibole and rutile/ilmenite. The ferromagnesian minerals in the sapphirine-bearing granulite have high XMg [Mg/(Mg + Fe)] (orthopyroxene XMg = 0.84-0.95; biotite XMg = 0.81; amphibole XMg = 0.87-0.96). The phase equilibria modeling demonstrates that the early spinel-bearing assemblage is stable at 923-950 °C and 6.7-8.9 kbar, and the peak assemblage of Opx + Pl + Spr/Spl + Amp + Bt + Ilm (+ melt) defines a field at 922-947 °C and 8.4-10.2 kbar. Rutiles have variable Zr concentrations but mostly cluster at ca. 1,500 and 3400 ppm. Zr-in-rutile geothermometry yielded high temperatures of up to 890-940 °C. Zircon U-Pb dating of the granulite constrains the timing of the immediate post-peak and retrograde metamorphic stages as 429 ± 7 Ma and 412 ± 4 Ma, respectively. The UHT metamorphism, together with extensive occurrence of coeval magmatic suites suggests that the Tongbai orogen experienced a Paleozoic Andean-type orogeny probably derived from mid-oceanic ridge subduction of the Qinling Ocean.

Analysis of recruitment and industrial human resources management for optimal productivity in the presence of the HIV/AIDS epidemic.

PubMed

Okosun, Kazeem O; Makinde, Oluwole D; Takaidza, Isaac

2013-01-01

The aim of this paper is to analyze the recruitment effects of susceptible and infected individuals in order to assess the productivity of an organizational labor force in the presence of HIV/AIDS with preventive and HAART treatment measures in enhancing the workforce output. We consider constant controls as well as time-dependent controls. In the constant control case, we calculate the basic reproduction number and investigate the existence and stability of equilibria. The model is found to exhibit backward and Hopf bifurcations, implying that for the disease to be eradicated, the basic reproductive number must be below a critical value of less than one. We also investigate, by calculating sensitivity indices, the sensitivity of the basic reproductive number to the model's parameters. In the time-dependent control case, we use Pontryagin's maximum principle to derive necessary conditions for the optimal control of the disease. Finally, numerical simulations are performed to illustrate the analytical results. The cost-effectiveness analysis results show that optimal efforts on recruitment (HIV screening of applicants, etc.) is not the most cost-effective strategy to enhance productivity in the organizational labor force. Hence, to enhance employees' productivity, effective education programs and strict adherence to preventive measures should be promoted.

A Comparison of Classical Force-Fields for Molecular Dynamics Simulations of Lubricants

PubMed Central

Ewen, James P.; Gattinoni, Chiara; Thakkar, Foram M.; Morgan, Neal; Spikes, Hugh A.; Dini, Daniele

2016-01-01

For the successful development and application of lubricants, a full understanding of their complex nanoscale behavior under a wide range of external conditions is required, but this is difficult to obtain experimentally. Nonequilibrium molecular dynamics (NEMD) simulations can be used to yield unique insights into the atomic-scale structure and friction of lubricants and additives; however, the accuracy of the results depend on the chosen force-field. In this study, we demonstrate that the use of an accurate, all-atom force-field is critical in order to; (i) accurately predict important properties of long-chain, linear molecules; and (ii) reproduce experimental friction behavior of multi-component tribological systems. In particular, we focus on n-hexadecane, an important model lubricant with a wide range of industrial applications. Moreover, simulating conditions common in tribological systems, i.e., high temperatures and pressures (HTHP), allows the limits of the selected force-fields to be tested. In the first section, a large number of united-atom and all-atom force-fields are benchmarked in terms of their density and viscosity prediction accuracy of n-hexadecane using equilibrium molecular dynamics (EMD) simulations at ambient and HTHP conditions. Whilst united-atom force-fields accurately reproduce experimental density, the viscosity is significantly under-predicted compared to all-atom force-fields and experiments. Moreover, some all-atom force-fields yield elevated melting points, leading to significant overestimation of both the density and viscosity. In the second section, the most accurate united-atom and all-atom force-field are compared in confined NEMD simulations which probe the structure and friction of stearic acid adsorbed on iron oxide and separated by a thin layer of n-hexadecane. The united-atom force-field provides an accurate representation of the structure of the confined stearic acid film; however, friction coefficients are consistently under-predicted and the friction-coverage and friction-velocity behavior deviates from that observed using all-atom force-fields and experimentally. This has important implications regarding force-field selection for NEMD simulations of systems containing long-chain, linear molecules; specifically, it is recommended that accurate all-atom potentials, such as L-OPLS-AA, are employed. PMID:28773773

A Comparison of Classical Force-Fields for Molecular Dynamics Simulations of Lubricants.

PubMed

Ewen, James P; Gattinoni, Chiara; Thakkar, Foram M; Morgan, Neal; Spikes, Hugh A; Dini, Daniele

2016-08-02

For the successful development and application of lubricants, a full understanding of their complex nanoscale behavior under a wide range of external conditions is required, but this is difficult to obtain experimentally. Nonequilibrium molecular dynamics (NEMD) simulations can be used to yield unique insights into the atomic-scale structure and friction of lubricants and additives; however, the accuracy of the results depend on the chosen force-field. In this study, we demonstrate that the use of an accurate, all-atom force-field is critical in order to; (i) accurately predict important properties of long-chain, linear molecules; and (ii) reproduce experimental friction behavior of multi-component tribological systems. In particular, we focus on n -hexadecane, an important model lubricant with a wide range of industrial applications. Moreover, simulating conditions common in tribological systems, i.e., high temperatures and pressures (HTHP), allows the limits of the selected force-fields to be tested. In the first section, a large number of united-atom and all-atom force-fields are benchmarked in terms of their density and viscosity prediction accuracy of n -hexadecane using equilibrium molecular dynamics (EMD) simulations at ambient and HTHP conditions. Whilst united-atom force-fields accurately reproduce experimental density, the viscosity is significantly under-predicted compared to all-atom force-fields and experiments. Moreover, some all-atom force-fields yield elevated melting points, leading to significant overestimation of both the density and viscosity. In the second section, the most accurate united-atom and all-atom force-field are compared in confined NEMD simulations which probe the structure and friction of stearic acid adsorbed on iron oxide and separated by a thin layer of n -hexadecane. The united-atom force-field provides an accurate representation of the structure of the confined stearic acid film; however, friction coefficients are consistently under-predicted and the friction-coverage and friction-velocity behavior deviates from that observed using all-atom force-fields and experimentally. This has important implications regarding force-field selection for NEMD simulations of systems containing long-chain, linear molecules; specifically, it is recommended that accurate all-atom potentials, such as L-OPLS-AA, are employed.

Thermobarometry of Whangarei volcanic field lavas, New Zealand: Constraints on plumbing systems of small monogenetic basalt volcanoes

NASA Astrophysics Data System (ADS)

Shane, Phil; Coote, Alisha

2018-04-01

The intra-plate, basaltic Whangarei volcanic field (WVF) is a little-studied cluster of Quaternary monogenetic volcanoes in northern New Zealand. Clinopyroxene-melt equilibria provides an insight to the ascent and storage of the magmas that is not evident from whole-rock-scale geochemistry. Basalts from two of the younger volcanoes contain a population of equilibrium and disequilibrium clinopyroxene phenocrysts. Many of the crystals are resorbed, and are characterised by diffuse, patchy zoning, and low MgO (Mg#70-80) and Cr2O3 contents. Such crystals also occur as relic cores in other phenocrysts. These grew in a magma that was more evolved than that of the host rock composition. Equilibrium clinopyroxenes are enriched in MgO (Mg#83-88) and Cr2O3 ( 0.4-0.9 wt%), and occur as reverse-zoned crystals, and rim/mantle overgrowths on relic cores of other crystals. These crystals and rim/mantles zones nucleated in magma with a composition similar to that of the host rock. The textural relationships demonstrate that a mafic magma intruded a more silicic resident magma, resulting in crystal-exchange and entrainment of antecrysts. Clinopyroxene-melt equilibria indicate that the crystallisation occurred at temperatures in the range 1135-1195 °C, and pressures in the range 290-680 MPa. The dominant pressure mode (400-550 MPa) equates to depths of about 15-19 km which coincides with a present-day body of partial melt in the crust. Higher pressures indicated by subordinate crystal populations indicate staged ascent and crystallisation above the Moho ( 26 km depth). Thus, the magmatic system is envisaged as a crystal mush column through the lower and mid crust. Such crystallisation histories are perhaps not expected in low flux, monogenetic magma systems, and reflect the importance of the crustal density structure beneath the volcanoes. Future activity could be preceded by seismic events in the lower crust as the magmas intrude localised crystal mush bodies.

Le Chatelier's principle in replicator dynamics

NASA Astrophysics Data System (ADS)

Allahverdyan, Armen E.; Galstyan, Aram

2011-10-01

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

Le Chatelier's principle in replicator dynamics.

PubMed

Allahverdyan, Armen E; Galstyan, Aram

2011-10-01

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

Acid-Base Chemistry of White Wine: Analytical Characterisation and Chemical Modelling

PubMed Central

Prenesti, Enrico; Berto, Silvia; Toso, Simona; Daniele, Pier Giuseppe

2012-01-01

A chemical model of the acid-base properties is optimized for each white wine under study, together with the calculation of their ionic strength, taking into account the contributions of all significant ionic species (strong electrolytes and weak one sensitive to the chemical equilibria). Coupling the HPLC-IEC and HPLC-RP methods, we are able to quantify up to 12 carboxylic acids, the most relevant substances responsible of the acid-base equilibria of wine. The analytical concentration of carboxylic acids and of other acid-base active substances was used as input, with the total acidity, for the chemical modelling step of the study based on the contemporary treatment of overlapped protonation equilibria. New protonation constants were refined (L-lactic and succinic acids) with respect to our previous investigation on red wines. Attention was paid for mixed solvent (ethanol-water mixture), ionic strength, and temperature to ensure a thermodynamic level to the study. Validation of the chemical model optimized is achieved by way of conductometric measurements and using a synthetic “wine” especially adapted for testing. PMID:22566762

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.

The Effect of CaO on Gas/Slag/Matte/Tridymite Equilibria in Fayalite-Based Copper Smelting Slags at 1473 K (1200 °C) and P(SO2) = 0.25 Atm

NASA Astrophysics Data System (ADS)

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

2018-04-01

Fundamental experimental studies have been undertaken to determine the effect of CaO on the equilibria between the gas phase (CO/CO2/SO2/Ar) and slag/matte/tridymite phases in the Cu-Fe-O-S-Si-Ca system at 1473 K (1200 °C) and P(SO2) = 0.25 atm. The experimental methodology developed in the Pyrometallurgy Innovation Centre was used. New experimental data have been obtained for the four-phase equilibria system for fixed concentrations of CaO (up to 4 wt pct) in the slag phase as a function of copper concentration in matte, including the concentrations of dissolved sulfur and copper in slag, and Fe/SiO2 ratios in slag at tridymite saturation. The new data provided in the present study are of direct relevance to the pyrometallurgical processing of copper and will be used as an input to optimize the thermodynamic database for the copper-containing multi-component multi-phase system.

Initial condition-dependent dynamics and transient period in memristor-based hypogenetic jerk system with four line equilibria

NASA Astrophysics Data System (ADS)

Bao, Han; Wang, Ning; Bao, Bocheng; Chen, Mo; Jin, Peipei; Wang, Guangyi

2018-04-01

Memristor-based nonlinear dynamical system easily presents the initial condition-dependent dynamical phenomenon of extreme multistability, i.e., coexisting infinitely many attractors, which has been received much attention in recent years. By introducing an ideal and active flux-controlled memristor into an existing hypogenetic chaotic jerk system, an interesting memristor-based chaotic system with hypogenetic jerk equation and circuit forms is proposed. The most striking feature is that this system has four line equilibria and exhibits the extreme multistability phenomenon of coexisting infinitely many attractors. Stability of these line equilibria are analyzed, and coexisting infinitely many attractors' behaviors with the variations of the initial conditions are investigated by bifurcation diagrams, Lyapunov exponent spectra, attraction basins, and phased portraits, upon which the forming mechanism of extreme multistablity in the memristor-based hypogenetic jerk system is explored. Specially, unusual transition behavior of long term transient period with steady chaos, completely different from the phenomenon of transient chaos, can be also found for some initial conditions. Moreover, a hardware circuit is design and fabricated and its experimental results effectively verify the truth of extreme multistablity.

The effect of pressure anisotropy on ballooning modes in tokamak plasmas

NASA Astrophysics Data System (ADS)

Johnston, A.; Hole, M. J.; Qu, Z. S.; Hezaveh, H.

2018-06-01

Edge Localised Modes are thought to be caused by a spectrum of magnetohydrodynamic instabilities, including the ballooning mode. While ballooning modes have been studied extensively both theoretically and experimentally, the focus of the vast majority of this research has been on isotropic plasmas. The prevalence of pressure anisotropy in modern tokamaks thus motivates further study of these modes. This paper presents a numerical analysis of ballooning modes in anisotropic equilibria. The investigation was conducted using the newly-developed codes HELENA+ATF and MISHKA-A, which adds anisotropic physics to equilibria and stability analysis. We have examined the impact of anisotropy on the stability of an n = 30 ballooning mode, confirming results conform to previous calculations in the isotropic limit. Growth rates of ballooning modes in equilibria with different levels of anisotropy were then calculated using the stability code MISHKA-A. The key finding was that the level of anisotropy had a significant impact on ballooning mode growth rates. For {T}\\perp > {T}| | , typical of ICRH heating, the growth rate increases, while for {T}\\perp < {T}| | , typical of neutral beam heating, the growth rate decreases.

Acid-base chemistry of white wine: analytical characterisation and chemical modelling.

PubMed

Prenesti, Enrico; Berto, Silvia; Toso, Simona; Daniele, Pier Giuseppe

2012-01-01

A chemical model of the acid-base properties is optimized for each white wine under study, together with the calculation of their ionic strength, taking into account the contributions of all significant ionic species (strong electrolytes and weak one sensitive to the chemical equilibria). Coupling the HPLC-IEC and HPLC-RP methods, we are able to quantify up to 12 carboxylic acids, the most relevant substances responsible of the acid-base equilibria of wine. The analytical concentration of carboxylic acids and of other acid-base active substances was used as input, with the total acidity, for the chemical modelling step of the study based on the contemporary treatment of overlapped protonation equilibria. New protonation constants were refined (L-lactic and succinic acids) with respect to our previous investigation on red wines. Attention was paid for mixed solvent (ethanol-water mixture), ionic strength, and temperature to ensure a thermodynamic level to the study. Validation of the chemical model optimized is achieved by way of conductometric measurements and using a synthetic "wine" especially adapted for testing.

High-beta analytic equilibria in circular, elliptical, and D-shaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows

NASA Astrophysics Data System (ADS)

López, O. E.; Guazzotto, L.

2017-03-01

The Grad-Shafranov-Bernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for high-beta equilibria in circular, elliptical, and D-shaped cross sections in the high aspect ratio approximation are found, which include finite toroidal and poloidal flows. Assuming a polynomial dependence of the free functions on the poloidal flux, the equilibrium problem is reduced to an inhomogeneous Helmholtz partial differential equation (PDE) subject to homogeneous Dirichlet conditions. An application of the Green's function method leads to a closed form for the circular solution and to a series solution in terms of Mathieu functions for the elliptical case, which is valid for arbitrary elongations. To extend the elliptical solution to a D-shaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604-614 (2004)] is presented for relevant scenarios.

Equilibria of perceptrons for simple contingency problems.

PubMed

Dawson, Michael R W; Dupuis, Brian

2012-08-01

The contingency between cues and outcomes is fundamentally important to theories of causal reasoning and to theories of associative learning. Researchers have computed the equilibria of Rescorla-Wagner models for a variety of contingency problems, and have used these equilibria to identify situations in which the Rescorla-Wagner model is consistent, or inconsistent, with normative models of contingency. Mathematical analyses that directly compare artificial neural networks to contingency theory have not been performed, because of the assumed equivalence between the Rescorla-Wagner learning rule and the delta rule training of artificial neural networks. However, recent results indicate that this equivalence is not as straightforward as typically assumed, suggesting a strong need for mathematical accounts of how networks deal with contingency problems. One such analysis is presented here, where it is proven that the structure of the equilibrium for a simple network trained on a basic contingency problem is quite different from the structure of the equilibrium for a Rescorla-Wagner model faced with the same problem. However, these structural differences lead to functionally equivalent behavior. The implications of this result for the relationships between associative learning, contingency theory, and connectionism are discussed.

Effects of force fields on the conformational and dynamic properties of amyloid β(1-40) dimer explored by replica exchange molecular dynamics simulations.

PubMed

Watts, Charles R; Gregory, Andrew; Frisbie, Cole; Lovas, Sándor

2018-03-01

The conformational space and structural ensembles of amyloid beta (Aβ) peptides and their oligomers in solution are inherently disordered and proven to be challenging to study. Optimum force field selection for molecular dynamics (MD) simulations and the biophysical relevance of results are still unknown. We compared the conformational space of the Aβ(1-40) dimers by 300 ns replica exchange MD simulations at physiological temperature (310 K) using: the AMBER-ff99sb-ILDN, AMBER-ff99sb*-ILDN, AMBER-ff99sb-NMR, and CHARMM22* force fields. Statistical comparisons of simulation results to experimental data and previously published simulations utilizing the CHARMM22* and CHARMM36 force fields were performed. All force fields yield sampled ensembles of conformations with collision cross sectional areas for the dimer that are statistically significantly larger than experimental results. All force fields, with the exception of AMBER-ff99sb-ILDN (8.8 ± 6.4%) and CHARMM36 (2.7 ± 4.2%), tend to overestimate the α-helical content compared to experimental CD (5.3 ± 5.2%). Using the AMBER-ff99sb-NMR force field resulted in the greatest degree of variance (41.3 ± 12.9%). Except for the AMBER-ff99sb-NMR force field, the others tended to under estimate the expected amount of β-sheet and over estimate the amount of turn/bend/random coil conformations. All force fields, with the exception AMBER-ff99sb-NMR, reproduce a theoretically expected β-sheet-turn-β-sheet conformational motif, however, only the CHARMM22* and CHARMM36 force fields yield results compatible with collapse of the central and C-terminal hydrophobic cores from residues 17-21 and 30-36. Although analyses of essential subspace sampling showed only minor variations between force fields, secondary structures of lowest energy conformers are different. © 2017 Wiley Periodicals, Inc.

Catch trials in force field learning influence adaptation and consolidation of human motor memory

PubMed Central

Stockinger, Christian; Focke, Anne; Stein, Thorsten

2014-01-01

Force field studies are a common tool to investigate motor adaptation and consolidation. Thereby, subjects usually adapt their reaching movements to force field perturbations induced by a robotic device. In this context, so-called catch trials, in which the disturbing forces are randomly turned off, are commonly used to detect after-effects of motor adaptation. However, catch trials also produce sudden large motor errors that might influence the motor adaptation and the consolidation process. Yet, the detailed influence of catch trials is far from clear. Thus, the aim of this study was to investigate the influence of catch trials on motor adaptation and consolidation in force field experiments. Therefore, 105 subjects adapted their reaching movements to robot-generated force fields. The test groups adapted their reaching movements to a force field A followed by learning a second interfering force field B before retest of A (ABA). The control groups were not exposed to force field B (AA). To examine the influence of diverse catch trial ratios, subjects received catch trials during force field adaptation with a probability of either 0, 10, 20, 30, or 40%, depending on the group. First, the results on motor adaptation revealed significant differences between the diverse catch trial ratio groups. With increasing amount of catch trials, the subjects' motor performance decreased and subjects' ability to accurately predict the force field—and therefore internal model formation—was impaired. Second, our results revealed that adapting with catch trials can influence the following consolidation process as indicated by a partial reduction to interference. Here, the optimal catch trial ratio was 30%. However, detection of consolidation seems to be biased by the applied measure of performance. PMID:24795598

The multiscale coarse-graining method. II. Numerical implementation for coarse-grained molecular models

PubMed Central

Noid, W. G.; Liu, Pu; Wang, Yanting; Chu, Jhih-Wei; Ayton, Gary S.; Izvekov, Sergei; Andersen, Hans C.; Voth, Gregory A.

2008-01-01

The multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005);J. Chem. Phys. 123, 134105 (2005)] employs a variational principle to determine an interaction potential for a CG model from simulations of an atomically detailed model of the same system. The companion paper proved that, if no restrictions regarding the form of the CG interaction potential are introduced and if the equilibrium distribution of the atomistic model has been adequately sampled, then the MS-CG variational principle determines the exact many-body potential of mean force (PMF) governing the equilibrium distribution of CG sites generated by the atomistic model. In practice, though, CG force fields are not completely flexible, but only include particular types of interactions between CG sites, e.g., nonbonded forces between pairs of sites. If the CG force field depends linearly on the force field parameters, then the vector valued functions that relate the CG forces to these parameters determine a set of basis vectors that span a vector subspace of CG force fields. The companion paper introduced a distance metric for the vector space of CG force fields and proved that the MS-CG variational principle determines the CG force force field that is within that vector subspace and that is closest to the force field determined by the many-body PMF. The present paper applies the MS-CG variational principle for parametrizing molecular CG force fields and derives a linear least squares problem for the parameter set determining the optimal approximation to this many-body PMF. Linear systems of equations for these CG force field parameters are derived and analyzed in terms of equilibrium structural correlation functions. Numerical calculations for a one-site CG model of methanol and a molecular CG model of the EMIM+∕NO3− ionic liquid are provided to illustrate the method. PMID:18601325

QuickFF: A program for a quick and easy derivation of force fields for metal-organic frameworks from ab initio input.

PubMed

Vanduyfhuys, Louis; Vandenbrande, Steven; Verstraelen, Toon; Schmid, Rochus; Waroquier, Michel; Van Speybroeck, Veronique

2015-05-15

QuickFF is a software package to derive accurate force fields for isolated and complex molecular systems in a quick and easy manner. Apart from its general applicability, the program has been designed to generate force fields for metal-organic frameworks in an automated fashion. The force field parameters for the covalent interaction are derived from ab initio data. The mathematical expression of the covalent energy is kept simple to ensure robustness and to avoid fitting deficiencies as much as possible. The user needs to produce an equilibrium structure and a Hessian matrix for one or more building units. Afterward, a force field is generated for the system using a three-step method implemented in QuickFF. The first two steps of the methodology are designed to minimize correlations among the force field parameters. In the last step, the parameters are refined by imposing the force field parameters to reproduce the ab initio Hessian matrix in Cartesian coordinate space as accurate as possible. The method is applied on a set of 1000 organic molecules to show the easiness of the software protocol. To illustrate its application to metal-organic frameworks (MOFs), QuickFF is used to determine force fields for MIL-53(Al) and MOF-5. For both materials, accurate force fields were already generated in literature but they requested a lot of manual interventions. QuickFF is a tool that can easily be used by anyone with a basic knowledge of performing ab initio calculations. As a result, accurate force fields are generated with minimal effort. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Toward polarizable AMOEBA thermodynamics at fixed charge efficiency using a dual force field approach: application to organic crystals.

PubMed

Nessler, Ian J; Litman, Jacob M; Schnieders, Michael J

2016-11-09

First principles prediction of the structure, thermodynamics and solubility of organic molecular crystals, which play a central role in chemical, material, pharmaceutical and engineering sciences, challenges both potential energy functions and sampling methodologies. Here we calculate absolute crystal deposition thermodynamics using a novel dual force field approach whose goal is to maintain the accuracy of advanced multipole force fields (e.g. the polarizable AMOEBA model) while performing more than 95% of the sampling in an inexpensive fixed charge (FC) force field (e.g. OPLS-AA). Absolute crystal sublimation/deposition phase transition free energies were determined using an alchemical path that grows the crystalline state from a vapor reference state based on sampling with the OPLS-AA force field, followed by dual force field thermodynamic corrections to change between FC and AMOEBA resolutions at both end states (we denote the three step path as AMOEBA/FC). Importantly, whereas the phase transition requires on the order of 200 ns of sampling per compound, only 5 ns of sampling was needed for the dual force field thermodynamic corrections to reach a mean statistical uncertainty of 0.05 kcal mol -1 . For five organic compounds, the mean unsigned error between direct use of AMOEBA and the AMOEBA/FC dual force field path was only 0.2 kcal mol -1 and not statistically significant. Compared to experimental deposition thermodynamics, the mean unsigned error for AMOEBA/FC (1.4 kcal mol -1 ) was more than a factor of two smaller than uncorrected OPLS-AA (3.2 kcal mol -1 ). Overall, the dual force field thermodynamic corrections reduced condensed phase sampling in the expensive force field by a factor of 40, and may prove useful for protein stability or binding thermodynamics in the future.

The electromagnetic force field, fluid flow field and temperature profiles in levitated metal droplets

NASA Technical Reports Server (NTRS)

El-Kaddah, N.; Szekely, J.

1982-01-01

A mathematical representation was developed for the electromagnetic force field, the flow field, the temperature field (and for transport controlled kinetics), in a levitation melted metal droplet. The technique of mutual inductances was employed for the calculation of the electromagnetic force field, while the turbulent Navier - Stokes equations and the turbulent convective transport equations were used to represent the fluid flow field, the temperature field and the concentration field. The governing differential equations, written in spherical coordinates, were solved numerically. The computed results were in good agreement with measurements, regarding the lifting force, and the average temperature of the specimen and carburization rates, which were transport controlled.

Extracting the potential-well of a near-field optical trap using the Helmholtz-Hodge decomposition

NASA Astrophysics Data System (ADS)

Zaman, Mohammad Asif; Padhy, Punnag; Hansen, Paul C.; Hesselink, Lambertus

2018-02-01

The non-conservative nature of the force field generated by a near-field optical trap is analyzed. A plasmonic C-shaped engraving on a gold film is considered as the trap. The force field is calculated using the Maxwell stress tensor method. The Helmholtz-Hodge decomposition is used to extract the conservative and the non-conservative component of the force. Due to the non-negligible non-conservative component, it is found that the conventional approach of extracting the potential by direct integration of the force is not accurate. Despite the non-conservative nature of the force field, it is found that the statistical properties of a trapped nanoparticle can be estimated from the conservative component of the force field alone. Experimental and numerical results are presented to support the claims.

Analysis of nonlocal neural fields for both general and gamma-distributed connectivities

NASA Astrophysics Data System (ADS)

Hutt, Axel; Atay, Fatihcan M.

2005-04-01

This work studies the stability of equilibria in spatially extended neuronal ensembles. We first derive the model equation from statistical properties of the neuron population. The obtained integro-differential equation includes synaptic and space-dependent transmission delay for both general and gamma-distributed synaptic connectivities. The latter connectivity type reveals infinite, finite, and vanishing self-connectivities. The work derives conditions for stationary and nonstationary instabilities for both kernel types. In addition, a nonlinear analysis for general kernels yields the order parameter equation of the Turing instability. To compare the results to findings for partial differential equations (PDEs), two typical PDE-types are derived from the examined model equation, namely the general reaction-diffusion equation and the Swift-Hohenberg equation. Hence, the discussed integro-differential equation generalizes these PDEs. In the case of the gamma-distributed kernels, the stability conditions are formulated in terms of the mean excitatory and inhibitory interaction ranges. As a novel finding, we obtain Turing instabilities in fields with local inhibition-lateral excitation, while wave instabilities occur in fields with local excitation and lateral inhibition. Numerical simulations support the analytical results.

Full-field drift Hamiltonian particle orbits in 3D geometry

NASA Astrophysics Data System (ADS)

Cooper, W. A.; Graves, J. P.; Brunner, S.; Isaev, M. Yu

2011-02-01

A Hamiltonian/Lagrangian theory to describe guiding centre orbit drift motion which is canonical in the Boozer coordinate frame has been extended to include full electromagnetic perturbed fields in anisotropic pressure 3D equilibria with nested magnetic flux surfaces. A redefinition of the guiding centre velocity to eliminate the motion due to finite equilibrium radial magnetic fields and the choice of a gauge condition that sets the radial component of the electromagnetic vector potential to zero are invoked to guarantee that the Boozer angular coordinates retain the canonical structure. The canonical momenta are identified and the guiding centre particle radial drift motion and parallel gyroradius evolution are derived. The particle coordinate position is linearly modified by wave-particle interactions. All the nonlinear wave-wave interactions appear explicitly only in the evolution of the parallel gyroradius. The radial variation of the electrostatic potential is related to the binormal component of the displacement vector for MHD-type perturbations. The electromagnetic vector potential projections can then be determined from the electrostatic potential and the radial component of the MHD displacement vector.

Equilibrium reconstruction with 3D eddy currents in the Lithium Tokamak eXperiment

DOE PAGES

Hansen, C.; Boyle, D. P.; Schmitt, J. C.; ...

2017-04-18

Axisymmetric free-boundary equilibrium reconstructions of tokamak plasmas in the Lithium Tokamak eXperiment (LTX) are performed using the PSI-Tri equilibrium code. Reconstructions in LTX are complicated by the presence of long-lived non-axisymmetric eddy currents generated by a vacuum vessel and first wall structures. To account for this effect, reconstructions are performed with additional toroidal current sources in these conducting regions. The eddy current sources are fixed in their poloidal distributions, but their magnitude is adjusted as part of the full reconstruction. Eddy distributions are computed by toroidally averaging currents, generated by coupling to vacuum field coils, from a simplified 3D filamentmore » model of important conducting structures. The full 3D eddy current fields are also used to enable the inclusion of local magnetic field measurements, which have strong 3D eddy current pick-up, as reconstruction constraints. Using this method, equilibrium reconstruction yields good agreement with all available diagnostic signals. Here, an accompanying field perturbation produced by 3D eddy currents on the plasma surface with a primarily n = 2, m = 1 character is also predicted for these equilibria.« less

3D Field Modifications of Core Neutral Fueling In the EMC3-EIRENE Code

NASA Astrophysics Data System (ADS)

Waters, Ian; Frerichs, Heinke; Schmitz, Oliver; Ahn, Joon-Wook; Canal, Gustavo; Evans, Todd; Feng, Yuehe; Kaye, Stanley; Maingi, Rajesh; Soukhanovskii, Vsevolod

2017-10-01

The application of 3-D magnetic field perturbations to the edge plasmas of tokamaks has long been seen as a viable way to control damaging Edge Localized Modes (ELMs). These 3-D fields have also been correlated with a density drop in the core plasmas of tokamaks; known as `pump-out'. While pump-out is typically explained as the result of enhanced outward transport, degraded fueling of the core may also play a role. By altering the temperature and density of the plasma edge, 3-D fields will impact the distribution function of high energy neutral particles produced through ion-neutral energy exchange processes. Starved of the deeply penetrating neutral source, the core density will decrease. Numerical studies carried out with the EMC3-EIRENE code on National Spherical Tokamak eXperiment-Upgrade (NSTX-U) equilibria show that this change to core fueling by high energy neutrals may be a significant contributor to the overall particle balance in the NSTX-U tokamak: deep core (Ψ < 0.5) fueling from neutral ionization sources is decreased by 40-60% with RMPs. This work was funded by the US Department of Energy under Grant DE-SC0012315.

Muscle co-contraction patterns in robot-mediated force field learning to guide specific muscle group training.

PubMed

Pizzamiglio, Sara; Desowska, Adela; Shojaii, Pegah; Taga, Myriam; Turner, Duncan L

2017-01-01

Muscle co-contraction is a strategy of increasing movement accuracy and stability employed in dealing with force perturbation of movement. It is often seen in neuropathological populations. The direction of movement influences the pattern of co-contraction, but not all movements are easily achievable for populations with motor deficits. Manipulating the direction of the force instead, may be a promising rehabilitation protocol to train movement with use of a co-contraction reduction strategy. Force field learning paradigms provide a well described procedure to evoke and test muscle co-contraction. The aim of this study was to test the muscle co-contraction pattern in a wide range of arm muscles in different force-field directions utilising a robot-mediated force field learning paradigm of motor adaptation. Forty-two participants volunteered to participate in a study utilising robot-mediated force field motor adaptation paradigm with a clockwise or counter-clockwise force field. Kinematics and surface electromyography (EMG) of eight arm muscles were measured. Both muscle activation and co-contraction was earlier and stronger in flexors in the clockwise condition and in extensors in the counter-clockwise condition. Manipulating the force field direction leads to changes in the pattern of muscle co-contraction.

Nanomaterials for in vivo imaging of mechanical forces and electrical fields

NASA Astrophysics Data System (ADS)

Mehlenbacher, Randy D.; Kolbl, Rea; Lay, Alice; Dionne, Jennifer A.

2018-02-01

Cellular signalling is governed in large part by mechanical forces and electromagnetic fields. Mechanical forces play a critical role in cell differentiation, tissue organization and diseases such as cancer and heart disease; electrical fields are essential for intercellular communication, muscle contraction, neural signalling and sensory perception. Therefore, quantifying a biological system's forces and fields is crucial for understanding physiology and disease pathology and for developing medical tools for repair and recovery. This Review highlights advances in sensing mechanical forces and electrical fields in vivo, focusing on optical probes. The emergence of biocompatible optical probes, such as genetically encoded voltage indicators, molecular rotors, fluorescent dyes, semiconducting nanoparticles, plasmonic nanoparticles and lanthanide-doped upconverting nanoparticles, offers exciting opportunities to push the limits of spatial and temporal resolution, stability, multi-modality and stimuli sensitivity in bioimaging. We further discuss the materials design principles behind these probes and compare them across various metrics to facilitate sensor selection. Finally, we examine which advances are necessary to fully unravel the role of mechanical forces and electrical fields in vivo, such as the ability to probe the vectorial nature of forces, the development of combined force and field sensors, and the design of efficient optical actuators.

Multistability in bidirectional associative memory neural networks

NASA Astrophysics Data System (ADS)

Huang, Gan; Cao, Jinde

2008-04-01

In this Letter, the multistability issue is studied for Bidirectional Associative Memory (BAM) neural networks. Based on the existence and stability analysis of the neural networks with or without delay, it is found that the 2 n-dimensional networks can have 3 equilibria and 2 equilibria of them are locally exponentially stable, where each layer of the BAM network has n neurons. Furthermore, the results has been extended to (n+m)-dimensional BAM neural networks, where there are n and m neurons on the two layers respectively. Finally, two numerical examples are presented to illustrate the validity of our results.

Regenerable biocide delivery unit, volume 2

NASA Technical Reports Server (NTRS)

Atwater, James E.; Wheeler, Richard R., Jr.

1992-01-01

Source code for programs dealing with the following topics are presented: (1) life cycle test stand-parametric test stand control (in BASIC); (2) simultaneous aqueous iodine equilibria-true equilibrium (in C); (3) simultaneous aqueous iodine equilibria-pseudo-equilibrium (in C); (4) pseudo-(fast)-equilibrium with iodide initially present (in C); (5) solution of simultaneous iodine rate expressions (Mathematica); (6) 2nd order kinetics of I2-formic acid in humidity condensate (Mathematica); (7) prototype RMCV onboard microcontroller (CAMBASIC); (8) prototype RAM data dump to PC (in BASIC); and (9) prototype real time data transfer to PC (in BASIC).

TET Offensive II Field Force Vietnam After Action Report 31 January - 18 February 1968

DTIC Science & Technology

1968-03-01

and the 5th VC Division. V During this same period of time there were no majur shifts in ARVN forces . However III Corps shifted three...8217-".•: ’ ’SSIFJED U.S. ARMY. VIETNAM. II FIELD FORCE . TET OFFENSIVE II FIELD FORCE VIETNAM AFTER ACTION REPORT, 31 JANUARY-18 FEB- RUARY 1968...H FIELD FORCE VIETNAM AFTER ACTION REPORT 31 January-18 February 1968 RECORD K0- ! FlSjl fi-.-A-,>-•: it tT*\\ : *si h s» -wP Mr-, £< St

Accuracy Test of the OPLS-AA Force Field for Calculating Free Energies of Mixing and Comparison with PAC-MAC

PubMed Central

2017-01-01

We have calculated the excess free energy of mixing of 1053 binary mixtures with the OPLS-AA force field using two different methods: thermodynamic integration (TI) of molecular dynamics simulations and the Pair Configuration to Molecular Activity Coefficient (PAC-MAC) method. PAC-MAC is a force field based quasi-chemical method for predicting miscibility properties of various binary mixtures. The TI calculations yield a root mean squared error (RMSE) compared to experimental data of 0.132 kBT (0.37 kJ/mol). PAC-MAC shows a RMSE of 0.151 kBT with a calculation speed being potentially 1.0 × 104 times greater than TI. OPLS-AA force field parameters are optimized using PAC-MAC based on vapor–liquid equilibrium data, instead of enthalpies of vaporization or densities. The RMSE of PAC-MAC is reduced to 0.099 kBT by optimizing 50 force field parameters. The resulting OPLS-PM force field has a comparable accuracy as the OPLS-AA force field in the calculation of mixing free energies using TI. PMID:28418655

Magnetic moment of solar plasma and the Kelvin force: -The driving force of plasma up-flow -

NASA Astrophysics Data System (ADS)

Shibasaki, Kiyoto

2017-04-01

Thermal plasma in the solar atmosphere is magnetized (diamagnetic). The magnetic moment does not disappear by collisions because complete gyration is not a necessary condition to have magnetic moment. Magnetized fluid is subjected to Kelvin force in non-uniform magnetic field. Generally, magnetic field strength decreases upwards in the solar atmosphere, hence the Kelvin force is directed upwards along the field. This force is not included in the fluid treatment of MHD. By adding the Kelvin force to the MHD equation of motion, we can expect temperature dependent plasma flows along the field which are reported by many observations. The temperature dependence of the flow speed is explained by temperature dependence of magnetic moment. From the observed parameters, we can infer physical parameters in the solar atmosphere such as scale length of the magnetic field strength and the friction force acting on the flowing plasma. In case of closed magnetic field lines, loop-top concentration of hot plasma is expected which is frequently observed.

Communication: Multiple atomistic force fields in a single enhanced sampling simulation

NASA Astrophysics Data System (ADS)

Hoang Viet, Man; Derreumaux, Philippe; Nguyen, Phuong H.

2015-07-01

The main concerns of biomolecular dynamics simulations are the convergence of the conformational sampling and the dependence of the results on the force fields. While the first issue can be addressed by employing enhanced sampling techniques such as simulated tempering or replica exchange molecular dynamics, repeating these simulations with different force fields is very time consuming. Here, we propose an automatic method that includes different force fields into a single advanced sampling simulation. Conformational sampling using three all-atom force fields is enhanced by simulated tempering and by formulating the weight parameters of the simulated tempering method in terms of the energy fluctuations, the system is able to perform random walk in both temperature and force field spaces. The method is first demonstrated on a 1D system and then validated by the folding of the 10-residue chignolin peptide in explicit water.

Primary Phase Field of the Pb-Doped 2223 High-Tc Superconductor in the (Bi, Pb)-Sr-Ca-Cu-O System

PubMed Central

Wong-Ng, W.; Cook, L. P.; Kearsley, A.; Greenwood, W.

1999-01-01

Both liquidus and subsolidus phase equilibrium data are of central importance for applications of high temperature superconductors in the (Bi, Pb)-Sr-Ca-Cu-O system, including material synthesis, melt processing and single crystal growth. The subsolidus equilibria of the 110 K high-Tc Pb-doped 2223 ([Bi, Pb], Sr, Ca, Cu) phase and the location of the primary phase field (crystallization field) have been determined in this study. For the quantitative determination of liquidus data, a wicking technique was developed to capture the melt for quantitative microchemical analysis. A total of 29 five-phase volumes that include the 2223 phase as a component was obtained. The initial melt compositions of these volumes range from a mole fraction of 7.3 % to 28.0 % for Bi, 11.3 % to 27.8 % for Sr, 1.2 % to 19.4 % for Pb, 9.8 % to 30.8 % for Ca, and 17.1 % to 47.0 % for Cu. Based on these data, the crystallization field for the 2223 phase was constructed using the convex hull technique. A section of this “volume” was obtained by holding two components of the composition at the median value, allowing projection on the other three axes to show the extent of the field.

Persistency-field Eh-pH diagrams for sulfides and their application to supergene oxidation and enrichment of sulfide ore bodies

USGS Publications Warehouse

Sato, M.

1992-01-01

At temperatures prevailing near the Earth's surface, metastable co-existence of chemical substances is common because chemical reactions that would directly lead to the attainment of thermody-namically most stable equilibria are often blocked by high activation energy barriers. The persistency of a metastable assemblage is then governed by alternative reaction paths that provide lower activation energy barriers. Comparison of observed mineral assemblages in the supergene oxidized and enriched sulfide ores with corresponding stability Eh-pH diagrams reveals that the supergene assemblages are mostly metastable due primarily to the persistency of sulfide minerals beyond stability boundaries. A new set of diagrams called persistency-field Eh-pH diagrams has been constructed for binary metal sulfides on the basis of electrochemical and other experimental data. Each diagram delineates the persistency field, which is a combined field of thermodynamic stability and reaction path-controlled metastability, for a specific sulfide mineral. When applied to the supergene assemblages, these new diagrams show much better correspondence to the field observations. Although there may still be room for further refinement, the new diagrams appear to provide a strong visual aid to the understanding of the behavior of sulfide minerals in the supergene conditions. ?? 1992.