Stability of the iterative solutions of integral equations as one phase freezing criterion.

PubMed

Fantoni, R; Pastore, G

2003-10-01

A recently proposed connection between the threshold for the stability of the iterative solution of integral equations for the pair correlation functions of a classical fluid and the structural instability of the corresponding real fluid is carefully analyzed. Direct calculation of the Lyapunov exponent of the standard iterative solution of hypernetted chain and Percus-Yevick integral equations for the one-dimensional (1D) hard rods fluid shows the same behavior observed in 3D systems. Since no phase transition is allowed in such 1D system, our analysis shows that the proposed one phase criterion, at least in this case, fails. We argue that the observed proximity between the numerical and the structural instability in 3D originates from the enhanced structure present in the fluid but, in view of the arbitrary dependence on the iteration scheme, it seems uneasy to relate the numerical stability analysis to a robust one-phase criterion for predicting a thermodynamic phase transition.

Universality of bridge functions and its relation to variational perturbation theory and additivity of equations of state

NASA Astrophysics Data System (ADS)

Rosenfeld, Yaakov

1984-05-01

Featuring the modified hypernetted-chain (MHNC) scheme as a variational fitting procedure, we demonstrate that the accuracy of the variational perturbation theory (VPT) and of the method based on additivity of equations of state is determined by the excess entropy dependence of the bridge-function parameters [i.e., η(s) when the Percus-Yevick hard-sphere bridge functions are employed]. It is found that η(s) is nearly universal for all soft (i.e., "physical") potentials while it is distinctly different for the hard spheres, providing a graphical display of the "jump" in pair-potential space (with respect to accuracy of VPT) from "hard" to "soft" behavior. The universality of η(s) provides a local criterion for the MHNC scheme that should be useful for inverting structure-factor data in order to obtain the potential. An alternative local MHNC criterion due to Lado is rederived and extended, and it is also analyzed in light of the plot of η(s).

Structure of highly asymmetric hard-sphere mixtures: an efficient closure of the Ornstein-Zernike equations.

PubMed

Amokrane, S; Ayadim, A; Malherbe, J G

2005-11-01

A simple modification of the reference hypernetted chain (RHNC) closure of the multicomponent Ornstein-Zernike equations with bridge functions taken from Rosenfeld's hard-sphere bridge functional is proposed. Its main effect is to remedy the major limitation of the RHNC closure in the case of highly asymmetric mixtures--the wide domain of packing fractions in which it has no solution. The modified closure is also much faster, while being of similar complexity. This is achieved with a limited loss of accuracy, mainly for the contact value of the big sphere correlation functions. Comparison with simulation shows that inside the RHNC no-solution domain, it provides a good description of the structure, while being clearly superior to all the other closures used so far to study highly asymmetric mixtures. The generic nature of this closure and its good accuracy combined with a reduced no-solution domain open up the possibility to study the phase diagram of complex fluids beyond the hard-sphere model.

Ionic structures and transport properties of hot dense W and U plasmas

NASA Astrophysics Data System (ADS)

Hou, Yong; Yuan, Jianmin

2016-10-01

We have combined the average-atom model with the hyper-netted chain approximation (AAHNC) to describe the electronic and ionic structure of uranium and tungsten in the hot dense matter regime. When the electronic structure is described within the average-atom model, the effects of others ions on the electronic structure are considered by the correlation functions. And the ionic structure is calculated though using the hyper-netted chain (HNC) approximation. The ion-ion pair potential is calculated using the modified Gordon-Kim model based on the electronic density distribution in the temperature-depended density functional theory. And electronic and ionic structures are determined self-consistently. On the basis of the ion-ion pair potential, we perform the classical (CMD) and Langevin (LMD) molecular dynamics to simulate the ionic transport properties, such as ionic self-diffusion and shear viscosity coefficients, through the ionic velocity correlation functions. Due that the free electrons become more and more with increasing the plasma temperature, the influence of the electron-ion collisions on the transport properties become more and more important.

Optimum free energy in the reference functional approach for the integral equations theory

NASA Astrophysics Data System (ADS)

Ayadim, A.; Oettel, M.; Amokrane, S.

2009-03-01

We investigate the question of determining the bulk properties of liquids, required as input for practical applications of the density functional theory of inhomogeneous systems, using density functional theory itself. By considering the reference functional approach in the test particle limit, we derive an expression of the bulk free energy that is consistent with the closure of the Ornstein-Zernike equations in which the bridge functions are obtained from the reference system bridge functional. By examining the connection between the free energy functional and the formally exact bulk free energy, we obtain an improved expression of the corresponding non-local term in the standard reference hypernetted chain theory derived by Lado. In this way, we also clarify the meaning of the recently proposed criterion for determining the optimum hard-sphere diameter in the reference system. This leads to a theory in which the sole input is the reference system bridge functional both for the homogeneous system and the inhomogeneous one. The accuracy of this method is illustrated with the standard case of the Lennard-Jones fluid and with a Yukawa fluid with very short range attraction.

The force distribution probability function for simple fluids by density functional theory.

PubMed

Rickayzen, G; Heyes, D M

2013-02-28

Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.

Use of Two-Body Correlated Basis Functions with van der Waals Interaction to Study the Shape-Independent Approximation for a Large Number of Trapped Interacting Bosons

NASA Astrophysics Data System (ADS)

Lekala, M. L.; Chakrabarti, B.; Das, T. K.; Rampho, G. J.; Sofianos, S. A.; Adam, R. M.; Haldar, S. K.

2017-05-01

We study the ground-state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small (˜ 3) to very large (˜ 10^7) particle numbers. We use the two-body correlated basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground-state energy and the one-body density for different values of the van der Waals parameter C6. We compare our results with those of the modified Gross-Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross-Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit.

From square-well to Janus: Improved algorithm for integral equation theory and comparison with thermodynamic perturbation theory within the Kern-Frenkel model

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

Giacometti, Achille, E-mail: achille.giacometti@unive.it; Gögelein, Christoph, E-mail: christoph.goegelein@ds.mpg.de; Lado, Fred, E-mail: lado@ncsu.edu

2014-03-07

Building upon past work on the phase diagram of Janus fluids [F. Sciortino, A. Giacometti, and G. Pastore, Phys. Rev. Lett. 103, 237801 (2009)], we perform a detailed study of integral equation theory of the Kern-Frenkel potential with coverage that is tuned from the isotropic square-well fluid to the Janus limit. An improved algorithm for the reference hypernetted-chain (RHNC) equation for this problem is implemented that significantly extends the range of applicability of RHNC. Results for both structure and thermodynamics are presented and compared with numerical simulations. Unlike previous attempts, this algorithm is shown to be stable down to themore » Janus limit, thus paving the way for analyzing the frustration mechanism characteristic of the gas-liquid transition in the Janus system. The results are also compared with Barker-Henderson thermodynamic perturbation theory on the same model. We then discuss the pros and cons of both approaches within a unified treatment. On balance, RHNC integral equation theory, even with an isotropic hard-sphere reference system, is found to be a good compromise between accuracy of the results, computational effort, and uniform quality to tackle self-assembly processes in patchy colloids of complex nature. Further improvement in RHNC however clearly requires an anisotropic reference bridge function.« less

Electron and Nuclear Pressures in Electron-Nucleus Mixtures

NASA Astrophysics Data System (ADS)

Chihara, J.; Yamagiwa, M.

2007-12-01

For a solid metal with frozen nuclei, the density-functional theory provides a unique definition of the electron pressure in an electron-nucleus mixture, and the total pressure of this mixture is represented as the sum of the electron and nuclear pressures. This fact leads to definitions of the electron and nuclear pressures on the basis of the virial theorem in terms of the wall potentials confining the electrons and nuclei. These definitions take a general form applicable without use of the adiabatic approximation. In this situation, we show that Janak's definition of the electron pressure in terms of the nuclear virial term is inappropriate; a similar statement holds for the definition of the stress tensor in this mixture. It is also demonstrated that both the electron and nuclear pressures become zero individually for a metal in vacuum, in contrast to the conventional understanding, according to which zero pressure is realized as a result of a cancellation of the elect ron and nuclear pressures. On the basis of these facts, a simple equation of state for liquid metals is derived, and it is examined numerically for the case of liquid alkaline metals by use of the quantum hypernetted chain equation and the Ashcroft model potential.

Coulomb Logarithm in Nonideal and Degenerate Plasmas

NASA Astrophysics Data System (ADS)

Filippov, A. V.; Starostin, A. N.; Gryaznov, V. K.

2018-03-01

Various methods for determining the Coulomb logarithm in the kinetic theory of transport and various variants of the choice of the plasma screening constant, taking into account and disregarding the contribution of the ion component and the boundary value of the electron wavevector are considered. The correlation of ions is taken into account using the Ornstein-Zernike integral equation in the hypernetted-chain approximation. It is found that the effect of ion correlation in a nondegenerate plasma is weak, while in a degenerate plasma, this effect must be taken into account when screening is determined by the electron component alone. The calculated values of the electrical conductivity of a hydrogen plasma are compared with the values determined experimentally in the megabar pressure range. It is shown that the values of the Coulomb logarithm can indeed be smaller than unity. Special experiments are proposed for a more exact determination of the Coulomb logarithm in a magnetic field for extremely high pressures, for which electron scattering by ions prevails.

Optimized theory for simple and molecular fluids.

PubMed

Marucho, M; Montgomery Pettitt, B

2007-03-28

An optimized closure approximation for both simple and molecular fluids is presented. A smooth interpolation between Perkus-Yevick and hypernetted chain closures is optimized by minimizing the free energy self-consistently with respect to the interpolation parameter(s). The molecular version is derived from a refinement of the method for simple fluids. In doing so, a method is proposed which appropriately couples an optimized closure with the variant of the diagrammatically proper integral equation recently introduced by this laboratory [K. M. Dyer et al., J. Chem. Phys. 123, 204512 (2005)]. The simplicity of the expressions involved in this proposed theory has allowed the authors to obtain an analytic expression for the approximate excess chemical potential. This is shown to be an efficient tool to estimate, from first principles, the numerical value of the interpolation parameters defining the aforementioned closure. As a preliminary test, representative models for simple fluids and homonuclear diatomic Lennard-Jones fluids were analyzed, obtaining site-site correlation functions in excellent agreement with simulation data.

Correlational and thermodynamic properties of finite-temperature electron liquids in the hypernetted-chain approximation.

PubMed

Tanaka, Shigenori

2016-12-07

Correlational and thermodynamic properties of homogeneous electron liquids at finite temperatures are theoretically analyzed in terms of dielectric response formalism with the hypernetted-chain (HNC) approximation and its modified version. The static structure factor and the local-field correction to describe the strong Coulomb-coupling effects beyond the random-phase approximation are self-consistently calculated through solution to integral equations in the paramagnetic (spin unpolarized) and ferromagnetic (spin polarized) states. In the ground state with the normalized temperature θ=0, the present HNC scheme well reproduces the exchange-correlation energies obtained by quantum Monte Carlo (QMC) simulations over the whole fluid phase (the coupling constant r s ≤100), i.e., within 1% and 2% deviations from putative best QMC values in the paramagnetic and ferromagnetic states, respectively. As compared with earlier studies based on the Singwi-Tosi-Land-Sjölander and modified convolution approximations, some improvements on the correlation energies and the correlation functions including the compressibility sum rule are found in the intermediate to strong coupling regimes. When applied to the electron fluids at intermediate Fermi degeneracies (θ≈1), the static structure factors calculated in the HNC scheme show good agreements with the results obtained by the path integral Monte Carlo (PIMC) simulation, while a small negative region in the radial distribution function is observed near the origin, which may be associated with a slight overestimation for the exchange-correlation hole in the HNC approximation. The interaction energies are calculated for various combinations of density and temperature parameters ranging from strong to weak degeneracy and from weak to strong coupling, and the HNC values are then parametrized as functions of r s and θ. The HNC exchange-correlation free energies obtained through the coupling-constant integration show reasonable agreements with earlier results including the PIMC-based fitting over the whole fluid region at finite degeneracies in the paramagnetic state. In contrast, a systematic difference between the HNC and PIMC results is observed in the ferromagnetic state, which suggests a necessity of further studies on the exchange-correlation free energies from both aspects of analytical theory and simulation.

Radial Distribution Functions of Strongly Coupled Two-Temperature Plasmas

NASA Astrophysics Data System (ADS)

Shaffer, Nathaniel R.; Tiwari, Sanat Kumar; Baalrud, Scott D.

2017-10-01

We present tests of three theoretical models for the radial distribution functions (RDFs) in two-temperature strongly coupled plasmas. RDFs are useful in extending plasma thermodynamics and kinetic theory to strong coupling, but they are usually known only for thermal equilibrium or for approximate one-component model plasmas. Accurate two-component modeling is necessary to understand the impact of strong coupling on inter-species transport, e.g., ambipolar diffusion and electron-ion temperature relaxation. We demonstrate that the Seuferling-Vogel-Toeppfer (SVT) extension of the hypernetted chain equations not only gives accurate RDFs (as compared with classical molecular dynamics simulations), but also has a simple connection with the Yukawa OCP model. This connection gives a practical means to recover the structure of the electron background from knowledge of the ion-ion RDF alone. Using the model RDFs in Effective Potential Theory, we report the first predictions of inter-species transport coefficients of strongly coupled plasmas far from equilibrium. This work is supported by NSF Grant No. PHY-1453736, AFSOR Award No. FA9550-16-1-0221, and used XSEDE computational resources.

Generalized Jastrow Variational Method for Liquid HELIUM-3-HELIUM-4 Mixtures at T = 0 K.

NASA Astrophysics Data System (ADS)

Mirabbaszadeh, Kavoos

Microscopic theory of dilute liquid { ^3 He}-{^4 He} mixtures is of great interest, because it provides a physical realization of a nearly degenerate weakly interacting Fermion system. An understanding of properties of the mixtures has received considerable attention both theoretically and experimentally over the past thirty years. We present here a variational procedure based on the Jastrow function for the ground state of {^3 He}- {^4 He} mixtures by minimizing the total energy of the mixture using the hypernetted-chain (HNC) approximation and the Percus-Yevick (PY) approximation for the two body correlation functions. Our goal is to compute from first principles the internal energy of the system and the various two body correlation functions at various densities and compare the results with experiment. The Jastrow variational method for the ground state energy of liquid {^4 He} consists of the following ansatz for the wave function Psi_alpha {rm(vec r_{1 alpha},} {vec r_{2alpha},} dots, {vec r_{N _alpha})} = prod _{rm i < j} {rm f_ {alphaalpha}(r_{ij}). } For a {^3 He } system the corresponding ansatz is Psi_beta {rm( vec r_{1beta},} {vec r_{2beta },} dots, {vec r_{N_beta})} = {[prod _{i < j} f_{betabeta }(r_{ij})]} Phi {rm( vec r_{1beta},} {vec r_{2beta },} dots, {vec r_{Nbeta}),} where Phi is a Slater determinant of plane waves for the ground state of the Fermion system. The total energy per particle can be written in the form: E = x_sp{alpha}{2} E_{alphaalpha} + x_sp{beta}{2 }E_{betabeta } + 2x_{alpha} x_{beta}E _{alphabeta}, where E_{alphaalpha} , E_{betabeta} , E_{alphabeta} are unknown parameters to be determined from a microscopic theory. Using the Jastrow wave function Psi for the mixture, a general expression is given for the ground state energy in terms of the two body potential and two and three body correlation functions. The Kirkwood Super-position Approximation (KSA) is used for the three-body correlation functions. The antisymmetry of the wave function for Fermions is incorporated following the procedure given earlier by Lado, Inguva and Smith. This procedure for treating the antisymmetry of the wave function simplifies the equations for the two-body correlation functions considerably. The equations for the correlation functions are solved in the hypernetted-chain approximation. Once the two-particle correlation functions for the mixture ( ^3He-^4He) have been obtained, the energy is minimized with respect to the variational parameters involved in the Jastrow wave function. The binding energy and the optimal correlation functions are then obtained as a function of the concentration of ^3He atoms in the mixture. (Abstract shortened with permission of author.).

Test of simple fluid theories for the Lennard-Jones system

NASA Astrophysics Data System (ADS)

Malijevský, A.; Labik, S.

1988-03-01

A test is made of a new version of the reference-hypernetted chain approximation (RHNC) with minimized free energy proposed by Lado, Foiles and Ashcroft. An accurate relationship is used for the bridge function of the reference hard spheres. The calculated values of the compressibility factor and the internal energy are compared with simulation data, with results of the exponential approximation of Andersen et al., and with results of the Madden-Fitts approximation. The RHNC provides the most reliable results over wide ranges of reduced temperatures and densities.

Effective Mass Calculations for Two-dimensional Gas of Dipolar Fermions

NASA Astrophysics Data System (ADS)

Seydi, I.; Abedinpour, S. H.; Tanatar, B.

2017-06-01

We consider a two-dimensional system of ultracold dipolar fermions with dipole moments aligned in the perpendicular direction. We use the static structure factor information from Fermi-Hypernetted-Chain calculations to obtain the effective many-body dipole-dipole interaction and calculate the many-body effective mass of the system within the G0W approximation to the self-energy. A large cancellation between different contributions to the self-energy results in a weak dependence of the effective mass on the interaction strength over a large range of coupling constants.

Elementary diagrams in nuclear and neutron matter

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

Wiringa, R.B.

1995-08-01

Variational calculations of nuclear and neutron matter are currently performed using a diagrammatic cluster expansion with the aid of nonlinear integral equations for evaluating expectation values. These are the Fermi hypernetted chain (FHNC) and single-operator chain (SOC) equations, which are a way of doing partial diagram summations to infinite order. A more complete summation can be made by adding elementary diagrams to the procedure. The simplest elementary diagrams appear at the four-body cluster level; there is one such E{sub 4} diagram in Bose systems, but 35 diagrams in Fermi systems, which gives a level of approximation called FHNC/4. We developedmore » a novel technique for evaluating these diagrams, by computing and storing 6 three-point functions, S{sub xyz}(r{sub 12}, r{sub 13}, r{sub 23}), where xyz (= ccd, cce, ddd, dde, dee, or eee) denotes the exchange character at the vertices 1, 2, and 3. All 35 Fermi E{sub 4} diagrams can be constructed from these 6 functions and other two-point functions that are already calculated. The elementary diagrams are known to be important in some systems like liquid {sup 3}He. We expect them to be small in nuclear matter at normal density, but they might become significant at higher densities appropriate for neutron star calculations. This year we programmed the FHNC/4 contributions to the energy and tested them in a number of simple model cases, including liquid {sup 3}He and Bethe`s homework problem. We get reasonable, but not exact agreement with earlier published work. In nuclear and neutron matter with the Argonne v{sub 14} interaction these contributions are indeed small corrections at normal density and grow to only 5-10 MeV/nucleon at 5 times normal density.« less

Spin polarization of two-dimensional electron system in parabolic potential

NASA Astrophysics Data System (ADS)

Miyake, Takashi; Totsuji, Chieko; Nakanishi, Kenta; Tsuruta, Kenji; Totsuji, Hiroo

2008-09-01

We analyze the ground state of the two-dimensional quantum system of electrons confined in a parabolic potential with the system size around 100 at 0 K. We map the system onto a classical system on the basis of the classical-map hypernetted-chain (CHNC) method which has been proven to work in the integral-equation-based analyses of uniform systems and apply classical Monte Carlo and molecular dynamics simulations. We find that, when we decrease the strength of confinement keeping the number of confined electrons fixed, the energy of the spin-polarized state with somewhat lower average density becomes smaller than that of the spin-unpolarized state with somewhat higher average density. This system thus undergoes the transition from the spin-unpolarized state to the spin polarized state and the corresponding critical value of r estimated from the average density is as low as r∼0.4 which is much smaller than the r value for the Wigner lattice formation. When we compare the energies of spin-unpolarized and spin-polarized states for given average density, our data give the critical r value for the transition between unpolarized and polarized states around 10 which is close to but still smaller than the known possibility of polarization at r∼27. The advantage of our method is a direct applicability to geometrically complex systems which are difficult to analyze by integral equations and this is an example.

Nonlocal screening in metal surfaces

NASA Technical Reports Server (NTRS)

Krotscheck, E.; Kohn, W.

1986-01-01

Due to the effect of the nonuniform environment on the static screening of the Coulomb potential, the local-density approximation for the particle-hole interaction is found to be inadequate to determine the surface energy of simple metals. Use of the same set of single-particle states, and thus the same one-body density and the same work function, has eliminated the single-electron states in favor of the structure of the short-ranged correlations as the basis of this effect. A posteriori simplifications of the Fermi hypernetted-chain theory may be found to allow the same calculational accuracy with simpler computational tools.

Demixing in simple dipolar mixtures: Integral equation versus density functional results

NASA Astrophysics Data System (ADS)

Range, Gabriel M.; Klapp, Sabine H. L.

2004-09-01

Using reference hypernetted chain (RHNC) integral equations and density functional theory in the modified mean-field (MMF) approximation we investigate the phase behavior of binary mixtures of dipolar hard spheres. The two species ( A and B ) differ only in their dipole moments mA and mB , and the central question investigated is under which conditions these asymmetric mixtures can exhibit demixing phase transitions in the fluid phase regime. Results from our two theoretical approaches turn out to strongly differ. Within the RHNC (which we apply to the isotropic high-temperature phase) demixing does indeed occur for dense systems with small interaction parameters Γ=mB2/mA2 . This result generalizes previously reported observations on demixing in mixtures of dipolar and neutral hard spheres (Γ=0) to the case of true dipolar hard sphere mixtures. The RHNC approach also indicates that these demixed fluid phases are isotropic at temperatures accessible by the theory, whereas isotropic-to-ferroelectric transitions occur only at larger Γ . The MMF theory, on the other hand, yields a different picture in which demixing occurs in combination with spontaneous ferroelectricity at all Γ considered. This discrepancy underlines the relevance of correlational effects for the existence of demixing transitions in dipolar systems without dispersive interactions. Indeed, supplementing the dipolar interactions by small, asymmetric amounts of van der Waals-like interactions (and thereby supporting the systems tendency to demix) one finally reaches good agreement between MMF and RHNC results.

Fluids Density Functional Theory of Salt-Doped Block Copolymers

NASA Astrophysics Data System (ADS)

Brown, Jonathan R.; Hall, Lisa M.

Block copolymers have attracted a great deal of recent interest as potential non-flammable, solid-state, electrolyte materials for batteries or other charge carrying applications. The microphase separation in block copolymers combines the properties of a conductive (though mechanically soft) polymer with a mechanically robust (though non-conductive) polymer. We use fluids density functional theory (fDFT) to study the phase behavior of salt-doped block copolymers. Because the salt prefers to preferentially solvate into the conductive phase, salt doping effectively enhances the segregation strength between the two polymer types. We consider the effects of this preferential solvation and of charge correlations by separately modeling the ion-rich phase, without bonding, using the Ornstein-Zernike equation and the hypernetted-chain closure. We use the correlations from this subsystem in the inhomogeneous fDFT calculations. Initial addition of salt increases the domain spacing and sharpens the interfacial region, but for high salt loadings the interface can broaden. Addition of salt can also drive a system with a low copolymer segregation strength to order by first passing through a two phase regime with a salt-rich ordered phase and a salt-poor disordered phase. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award Number DE-SC0014209.

Theory and simulation of electrolyte mixtures

NASA Astrophysics Data System (ADS)

Lee, B. Hribar; Vlachy, V.; Bhuiyan, L. B.; Outhwaite, C. W.; Molero, M.

Monte Carlo simulation and theoretical results on some aspects of thermodynamics of mixtures of electrolytes with a common species are presented. Both charge symmetric mixtures, where ions differ only in size, and charge asymmetric but size symmetric mixtures at ionic strength ranging generally from I = 10-4 to 1.0 M, and in a few cases up to I = M, are examined. The theoretical methods explored are: (i) the symmetric Poisson-Boltzmann theory, (ii) the modified Poisson-Boltzmann theory and (iii) the hypernetted-chain integral equation. The first two electrolyte mixing coefficients w0 and w1 of the various mixtures are calculated from an accurate determination of their osmotic pressure data. The theories are seen to be consistent among themselves, and with certain limiting laws in the literature, in predicting the trends of the mixing coefficients with respect to ionic strength. Some selected relevant experimental data have been analysed and compared with the theoretical and simulation trends. In addition the mean activity coefficients for a model mimicking the mixture of KCl and KF electrolytes are calculated and hence the Harned coefficients obtained for this system. These calculations are compared with the experimental data and Monte Carlo results available in the literature. The theoretically predicted Harned coefficients are in good agreement with the simulation results for the model KCl-KF mixture.

Simple electrolyte solutions: Comparison of DRISM and molecular dynamics results for alkali halide solutions

PubMed Central

Joung, In Suk; Luchko, Tyler; Case, David A.

2013-01-01

Using the dielectrically consistent reference interaction site model (DRISM) of molecular solvation, we have calculated structural and thermodynamic information of alkali-halide salts in aqueous solution, as a function of salt concentration. The impact of varying the closure relation used with DRISM is investigated using the partial series expansion of order-n (PSE-n) family of closures, which includes the commonly used hypernetted-chain equation (HNC) and Kovalenko-Hirata closures. Results are compared to explicit molecular dynamics (MD) simulations, using the same force fields, and to experiment. The mean activity coefficients of ions predicted by DRISM agree well with experimental values at concentrations below 0.5 m, especially when using the HNC closure. As individual ion activities (and the corresponding solvation free energies) are not known from experiment, only DRISM and MD results are directly compared and found to have reasonably good agreement. The activity of water directly estimated from DRISM is nearly consistent with values derived from the DRISM ion activities and the Gibbs-Duhem equation, but the changes in the computed pressure as a function of salt concentration dominate these comparisons. Good agreement with experiment is obtained if these pressure changes are ignored. Radial distribution functions of NaCl solution at three concentrations were compared between DRISM and MD simulations. DRISM shows comparable water distribution around the cation, but water structures around the anion deviate from the MD results; this may also be related to the high pressure of the system. Despite some problems, DRISM-PSE-n is an effective tool for investigating thermodynamic properties of simple electrolytes. PMID:23387564

Thomson scattering from a three-component plasma.

PubMed

Johnson, W R; Nilsen, J

2014-02-01

A model for a three-component plasma consisting of two distinct ionic species and electrons is developed and applied to study x-ray Thomson scattering. Ions of a specific type are assumed to be identical and are treated in the average-atom approximation. Given the plasma temperature and density, the model predicts mass densities, effective ionic charges, and cell volumes for each ionic type, together with the plasma chemical potential and free-electron density. Additionally, the average-atom treatment of individual ions provides a quantum-mechanical description of bound and continuum electrons. The model is used to obtain parameters needed to determine the dynamic structure factors for x-ray Thomson scattering from a three-component plasma. The contribution from inelastic scattering by free electrons is evaluated in the random-phase approximation. The contribution from inelastic scattering by bound electrons is evaluated using the bound-state and scattering wave functions obtained from the average-atom calculations. Finally, the partial static structure factors for elastic scattering by ions are evaluated using a two-component version of the Ornstein-Zernike equations with hypernetted chain closure, in which electron-ion interactions are accounted for using screened ion-ion interaction potentials. The model is used to predict the x-ray Thomson scattering spectrum from a CH plasma and the resulting spectrum is compared with experimental results obtained by Feltcher et al. [Phys. Plasmas 20, 056316 (2013)].

Advances in visual representation of molecular potentials.

PubMed

Du, Qi-Shi; Huang, Ri-Bo; Chou, Kuo-Chen

2010-06-01

The recent advances in visual representations of molecular properties in 3D space are summarized, and their applications in molecular modeling study and rational drug design are introduced. The visual representation methods provide us with detailed insights into protein-ligand interactions, and hence can play a major role in elucidating the structure or reactivity of a biomolecular system. Three newly developed computation and visualization methods for studying the physical and chemical properties of molecules are introduced, including their electrostatic potential, lipophilicity potential and excess chemical potential. The newest application examples of visual representations in structure-based rational drug are presented. The 3D electrostatic potentials, calculated using the empirical method (EM-ESP), in which the classical Coulomb equation and traditional atomic partial changes are discarded, are highly consistent with the results by the higher level quantum chemical method. The 3D lipophilicity potentials, computed by the heuristic molecular lipophilicity potential method based on the principles of quantum mechanics and statistical mechanics, are more accurate and reliable than those by using the traditional empirical methods. The 3D excess chemical potentials, derived by the reference interaction site model-hypernetted chain theory, provide a new tool for computational chemistry and molecular modeling. For structure-based drug design, the visual representations of molecular properties will play a significant role in practical applications. It is anticipated that the new advances in computational chemistry will stimulate the development of molecular modeling methods, further enriching the visual representation techniques for rational drug design, as well as other relevant fields in life science.

Cooling without contact in bilayer dipolar Fermi gases

NASA Astrophysics Data System (ADS)

Tanatar, Bilal; Renklioglu, Basak; Oktel, M. Ozgur

2016-05-01

We consider two parallel layers of dipolar ultracold Fermi gases at different temperatures and calculate the heat transfer between them. The effective interactions describing screening and correlation effects between the dipoles in a single layer are modelled within the Euler-Lagrange Fermi-hypernetted chain approximation. The random-phase approximation is employed for the interactions across the layers. We investigate the amount of transferred power between the layers as a function of the temperature difference. Energy transfer proceeds via the long-range dipole-dipole interactions. A simple thermal model is developed to investigate the feasibility of using the contactless sympathetic cooling of the ultracold polar atoms/molecules. Our calculations indicate that dipolar heat transfer is effective for typical polar molecule experiments and may be utilized as a cooling process. Supported by TUBA and TUBITAK (112T974).

Average-atom model for two-temperature states and ionic transport properties of aluminum in the warm dense matter regime

NASA Astrophysics Data System (ADS)

Hou, Yong; Fu, Yongsheng; Bredow, Richard; Kang, Dongdong; Redmer, Ronald; Yuan, Jianmin

2017-03-01

The average-atom model combined with the hyper-netted chain approximation is an efficient tool for electronic and ionic structure calculations for warm dense matter. Here we generalize this method in order to describe non-equilibrium states with different electron and ion temperature as produced in laser-matter interactions on ultra-short time scales. In particular, the electron-ion and ion-ion correlation effects are considered when calculating the electron structure. We derive an effective ion-ion pair-potential using the electron densities in the framework of temperature-depended density functional theory. Using this ion-ion potential we perform molecular dynamics simulations in order to determine the ionic transport properties such as the ionic diffusion coefficient and the shear viscosity through the ionic velocity autocorrelation functions.

Water based on a molecular model behaves like a hard-sphere solvent for a nonpolar solute when the reference interaction site model and related theories are employed

NASA Astrophysics Data System (ADS)

Hayashi, Tomohiko; Oshima, Hiraku; Harano, Yuichi; Kinoshita, Masahiro

2016-09-01

For neutral hard-sphere solutes, we compare the reduced density profile of water around a solute g(r), solvation free energy μ, energy U, and entropy S under the isochoric condition predicted by the two theories: dielectrically consistent reference interaction site model (DRISM) and angle-dependent integral equation (ADIE) theories. A molecular model for water pertinent to each theory is adopted. The hypernetted-chain (HNC) closure is employed in the ADIE theory, and the HNC and Kovalenko-Hirata (K-H) closures are tested in the DRISM theory. We also calculate g(r), U, S, and μ of the same solute in a hard-sphere solvent whose molecular diameter and number density are set at those of water, in which case the radial-symmetric integral equation (RSIE) theory is employed. The dependences of μ, U, and S on the excluded volume and solvent-accessible surface area are analyzed using the morphometric approach (MA). The results from the ADIE theory are in by far better agreement with those from computer simulations available for g(r), U, and μ. For the DRISM theory, g(r) in the vicinity of the solute is quite high and becomes progressively higher as the solute diameter d U increases. By contrast, for the ADIE theory, it is much lower and becomes further lower as d U increases. Due to unphysically positive U and significantly larger |S|, μ from the DRISM theory becomes too high. It is interesting that μ, U, and S from the K-H closure are worse than those from the HNC closure. Overall, the results from the DRISM theory with a molecular model for water are quite similar to those from the RSIE theory with the hard-sphere solvent. Based on the results of the MA analysis, we comparatively discuss the different theoretical methods for cases where they are applied to studies on the solvation of a protein.

The A in SAFT: developing the contribution of association to the Helmholtz free energy within a Wertheim TPT1 treatment of generic Mie fluids

NASA Astrophysics Data System (ADS)

Dufal, Simon; Lafitte, Thomas; Haslam, Andrew J.; Galindo, Amparo; Clark, Gary N. I.; Vega, Carlos; Jackson, George

2015-05-01

An accurate representation of molecular association is a vital ingredient of advanced equations of state (EOSs), providing a description of thermodynamic properties of complex fluids where hydrogen bonding plays an important role. The combination of the first-order thermodynamic perturbation theory (TPT1) of Wertheim for associating systems with an accurate description of the structural and thermodynamic properties of the monomer fluid forms the basis of the statistical associating fluid theory (SAFT) family of EOSs. The contribution of association to the free energy in SAFT and related EOSs is very sensitive to the nature of intermolecular potential used to describe the monomers and, crucially, to the accuracy of the representation of the thermodynamic and structural properties. Here we develop an accurate description of the association contribution for use within the recently developed SAFT-VR Mie framework for chain molecules formed from segments interacting through a Mie potential [T. Lafitte, A. Apostolakou, C. Avendaño, A, Galindo, C. S. Adjiman, E. A. Müller, and G. Jackson, J. Chem. Phys. 139, 154504 (2013)]. As the Mie interaction represents a soft-core potential model, a method similar to that adopted for the Lennard-Jones potential [E. A. Müller and K. E. Gubbins, Ind. Eng. Chem. Res. 34, 3662 (1995)] is employed to describe the association contribution to the Helmholtz free energy. The radial distribution function (RDF) of the Mie fluid (which is required for the evaluation of the integral at the heart of the association term) is determined for a broad range of thermodynamic conditions (temperatures and densities) using the reference hyper-netted chain (RHNC) integral-equation theory. The numerical data for the association kernel of Mie fluids with different association geometries are then correlated for a range of thermodynamic states to obtain a general expression for the association contribution which can be applied for varying values of the Mie repulsive exponent. The resulting SAFT-VR Mie EOS allows for a much improved description of the vapour-liquid equilibria and single-phase properties of associating fluids such as water, methanol, ammonia, hydrogen sulphide, and their mixtures. A comparison is also made between the theoretical predictions of the degree of association for water and the extent of hydrogen bonding obtained from molecular simulations of the SPC/E and TIP4P/2005 atomistic models.

Spin-dependent analysis of two-dimensional electron liquids

NASA Astrophysics Data System (ADS)

Bulutay, C.; Tanatar, B.

2002-05-01

Two-dimensional electron liquid (2D EL) at full Fermi degeneracy is revisited, giving special attention to the spin-polarization effects. First, we extend the recently proposed classical-map hypernetted-chain (CHNC) technique to the 2D EL, while preserving the simplicity of the original proposal. An efficient implementation of CHNC is given utilizing Lado's quadrature expressions for the isotropic Fourier transforms. Our results indicate that the paramagnetic phase stays to be the ground state until the Wigner crystallization density, even though the energy separation with the ferromagnetic and other partially polarized states become minute. We analyze compressibility and spin stiffness variations with respect to density and spin polarization, the latter being overlooked until now. Spin-dependent static structure factor and pair-distribution functions are computed; agreement with the available quantum Monte Carlo data persists even in the strong-coupling regime of the 2D EL.

Theory of the interface between a classical plasma and a hard wall

NASA Astrophysics Data System (ADS)

Ballone, P.; Pastore, G.; Tosi, M. P.

1983-09-01

The interfacial density profile of a classical one-component plasma confined by a hard wall is studied in planar and spherical geometries. The approach adapts to interfacial problems a modified hypernetted-chain approximation developed by Lado and by Rosenfeld and Ashcroft for the bulk structure of simple liquids. The specific new aim is to embody selfconsistently into the theory a contact theorem, fixing the plasma density at the wall through an equilibrium condition which involves the electrical potential drop across the interface and the bulk pressure. The theory is brought into fully quantitative contact with computer simulation data for a plasma confined in a spherical cavity of large but finite radius. The interfacial potential at the point of zero charge is accurately reproduced by suitably combining the contact theorem with relevant bulk properties in a simple, approximate representation of the interfacial charge density profile.

Theory of the interface between a classical plasma and a hard wall

NASA Astrophysics Data System (ADS)

Ballone, P.; Pastore, G.; Tosi, M. P.

1984-12-01

The interfacial density profile of a classical one-component plasma confined by a hard wall is studied in planar and spherical geometries. The approach adapts to interfacial problems a modified hypernetted-chain approximation developed by Lado and by Rosenfeld and Ashcroft for the bulk structure of simple liquids. The specific new aim is to embody self-consistently into the theory a “contact theorem”, fixing the plasma density at the wall through an equilibrium condition which involves the electrical potential drop across the interface and the bulk pressure. The theory is brought into fully quantitative contact with computer simulation data for a plasma confined in a spherical cavity of large but finite radius. It is also shown that the interfacial potential at the point of zero charge is accurately reproduced by suitably combining the contact theorem with relevant bulk properties in a simple, approximate representation of the interfacial charge density profile.

Pair potentials for warm dense matter and their application to x-ray Thomson scattering in aluminum and beryllium.

PubMed

Harbour, L; Dharma-Wardana, M W C; Klug, D D; Lewis, L J

2016-11-01

Ultrafast laser experiments yield increasingly reliable data on warm dense matter, but their interpretation requires theoretical models. We employ an efficient density functional neutral-pseudoatom hypernetted-chain (NPA-HNC) model with accuracy comparable to ab initio simulations and which provides first-principles pseudopotentials and pair potentials for warm-dense matter. It avoids the use of (i) ad hoc core-repulsion models and (ii) "Yukawa screening" and (iii) need not assume ion-electron thermal equilibrium. Computations of the x-ray Thomson scattering (XRTS) spectra of aluminum and beryllium are compared with recent experiments and with density-functional-theory molecular-dynamics (DFT-MD) simulations. The NPA-HNC structure factors, compressibilities, phonons, and conductivities agree closely with DFT-MD results, while Yukawa screening gives misleading results. The analysis of the XRTS data for two of the experiments, using two-temperature quasi-equilibrium models, is supported by calculations of their temperature relaxation times.

A pressure consistent bridge correction of Kovalenko-Hirata closure in Ornstein-Zernike theory for Lennard-Jones fluids by apparently adjusting sigma parameter

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

Ebato, Yuki; Miyata, Tatsuhiko, E-mail: miyata.tatsuhiko.mf@ehime-u.ac.jp

Ornstein-Zernike (OZ) integral equation theory is known to overestimate the excess internal energy, U{sup ex}, pressure through the virial route, P{sub v}, and excess chemical potential, μ{sup ex}, for one-component Lennard-Jones (LJ) fluids under hypernetted chain (HNC) and Kovalenko-Hirata (KH) approximatons. As one of the bridge correction methods to improve the precision of these thermodynamic quantities, it was shown in our previous paper that the method to apparently adjust σ parameter in the LJ potential is effective [T. Miyata and Y. Ebato, J. Molec. Liquids. 217, 75 (2016)]. In our previous paper, we evaluated the actual variation in the σmore » parameter by using a fitting procedure to molecular dynamics (MD) results. In this article, we propose an alternative method to determine the actual variation in the σ parameter. The proposed method utilizes a condition that the virial and compressibility pressures coincide with each other. This method can correct OZ theory without a fitting procedure to MD results, and possesses characteristics of keeping a form of HNC and/or KH closure. We calculate the radial distribution function, pressure, excess internal energy, and excess chemical potential for one-component LJ fluids to check the performance of our proposed bridge function. We discuss the precision of these thermodynamic quantities by comparing with MD results. In addition, we also calculate a corrected gas-liquid coexistence curve based on a corrected KH-type closure and compare it with MD results.« less

Coarse-Grained Models for Automated Fragmentation and Parametrization of Molecular Databases.

PubMed

Fraaije, Johannes G E M; van Male, Jan; Becherer, Paul; Serral Gracià, Rubèn

2016-12-27

We calibrate coarse-grained interaction potentials suitable for screening large data sets in top-down fashion. Three new algorithms are introduced: (i) automated decomposition of molecules into coarse-grained units (fragmentation); (ii) Coarse-Grained Reference Interaction Site Model-Hypernetted Chain (CG RISM-HNC) as an intermediate proxy for dissipative particle dynamics (DPD); and (iii) a simple top-down coarse-grained interaction potential/model based on activity coefficient theories from engineering (using COSMO-RS). We find that the fragment distribution follows Zipf and Heaps scaling laws. The accuracy in Gibbs energy of mixing calculations is a few tenths of a kilocalorie per mole. As a final proof of principle, we use full coarse-grained sampling through DPD thermodynamics integration to calculate log P OW for 4627 compounds with an average error of 0.84 log unit. The computational speeds per calculation are a few seconds for CG RISM-HNC and a few minutes for DPD thermodynamic integration.

Dressed ion theory of size-asymmetric electrolytes: effective ionic charges and the decay length of screened Coulomb potential and pair correlations.

PubMed

Forsberg, Björn; Ulander, Johan; Kjellander, Roland

2005-02-08

The effects of ionic size asymmetry on long-range electrostatic interactions in electrolyte solutions are investigated within the primitive model. Using the formalism of dressed ion theory we analyze correlation functions from Monte Carlo simulations and the hypernetted chain approximation for size asymmetric 1:1 electrolytes. We obtain decay lengths of the screened Coulomb potential, effective charges of ions, and effective permittivity of the solution. It is found that the variation of these quantities with the degree of size asymmetry depends in a quite intricate manner on the interplay between the electrostatic coupling and excluded volume effects. In most cases the magnitude of the effective charge of the small ion species is larger than that of the large species; the difference increases with increasing size asymmetry. The effective charges of both species are larger (in absolute value) than the bare ionic charge, except for high asymmetry where the effective charge of the large ions can become smaller than the bare charge.

Heat Transfer Through Dipolar Coupling: Sympathetic cooling without contact

NASA Astrophysics Data System (ADS)

Oktel, Mehmet; Renklioglu, Basak; Tanatar, Bilal

We consider two parallel layers of dipolar ultracold gases at different temperatures and calculate the heat transfer through dipolar coupling. As the simplest model we consider a system in which both of the layers contain two-dimensional spin-polarized Fermi gases. The effective interactions describing the correlation effects and screening between the dipoles are obtained by the Euler-Lagrange Fermi-hypernetted-chain approximation in a single layer. We use the random-phase approximation (RPA) for the interactions across the layers. We find that heat transfer through dipolar coupling becomes efficient when the layer separation is comparable to dipolar interaction length scale. We characterize the heat transfer by calculating the time constant for temperature equilibration between the layers and find that for the typical experimental parameter regime of dipolar molecules this is on the order of milliseconds. We generalize the initial model to Boson-Boson and Fermion-Boson layers and suggest that contactless sympathetic cooling may be used for ultracold dipolar molecules. Supported by TUBITAK 1002-116F030.

Models of the elastic x-ray scattering feature for warm dense aluminum

DOE PAGES

Starrett, Charles Edward; Saumon, Didier

2015-09-03

The elastic feature of x-ray scattering from warm dense aluminum has recently been measured by Fletcher et al. [Nature Photonics 9, 274 (2015)] with much higher accuracy than had hitherto been possible. This measurement is a direct test of the ionic structure predicted by models of warm dense matter. We use the method of pseudoatom molecular dynamics to predict this elastic feature for warm dense aluminum with temperatures of 1–100 eV and densities of 2.7–8.1g/cm 3. We compare these predictions to experiments, finding good agreement with Fletcher et al. and corroborating the discrepancy found in analyses of an earlier experimentmore » of Ma et al. [Phys. Rev. Lett. 110, 065001 (2013)]. Lastly, we also evaluate the validity of the Thomas-Fermi model of the electrons and of the hypernetted chain approximation in computing the elastic feature and find them both wanting in the regime currently probed by experiments.« less

Penetrable square-well fluids: exact results in one dimension.

PubMed

Santos, Andrés; Fantoni, Riccardo; Giacometti, Achille

2008-05-01

We introduce a model of attractive penetrable spheres by adding a short-range attractive square well outside a penetrable core, and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact impenetrable counterpart as a starting point. The model is expected to describe star polymers in regimes of good and moderate solvent under dilute conditions. We derive the exact coefficients of a low-density expansion up to second order for the radial distribution function and up to fourth order in the virial expansion. These exact results are used as a benchmark to test the reliability of approximate theories (Percus-Yevick and hypernetted chain). Notwithstanding the lack of an exact solution for arbitrary densities, our results are expected to be rather precise within a wide range of temperatures and densities. A detailed analysis of some limiting cases is carried out. In particular, we provide a complete solution of the sticky penetrable-sphere model in one dimension up to the same order in density. The issue of Ruelle's thermodynamics stability is analyzed and the region of a well-defined thermodynamic limit is identified.

Thermodynamic Theory of Spherically Trapped Coulomb Clusters

NASA Astrophysics Data System (ADS)

Wrighton, Jeffrey; Dufty, James; Bonitz, Michael; K"{A}Hlert, Hanno

2009-11-01

The radial density profile of a finite number of identical charged particles confined in a harmonic trap is computed over a wide ranges of temperatures (Coulomb coupling) and particle numbers. At low temperatures these systems form a Coulomb crystal with spherical shell structure which has been observed in ultracold trapped ions and in dusty plasmas. The shell structure is readily reproduced in simulations. However, analytical theories which used a mean field approachfootnotetext[1]C. Henning et al., Phys. Rev. E 74, 056403 (2006) or a local density approximationfootnotetext[2]C. Henning et al., Phys. Rev. E 76, 036404 (2007) have, so far, only been able to reproduce the average density profile. Here we present an approach to Coulomb correlations based on the hypernetted chain approximation with additional bridge diagrams. It is demonstrated that this model reproduces the correct shell structure within a few percent and provides the basis for a thermodynamic theory of Coulomb clusters in the strongly coupled fluid state.footnotetext[3]J. Wrighton, J.W. Dufty, H. K"ahlert and M. Bonitz, J. Phys. A 42, 214052 (2009) and Phys. Rev. E (2009) (to be submitted)

Construction of Chained True Score Equipercentile Equatings under the Kernel Equating (KE) Framework and Their Relationship to Levine True Score Equating. Research Report. ETS RR-09-24

ERIC Educational Resources Information Center

Chen, Haiwen; Holland, Paul

2009-01-01

In this paper, we develop a new chained equipercentile equating procedure for the nonequivalent groups with anchor test (NEAT) design under the assumptions of the classical test theory model. This new equating is named chained true score equipercentile equating. We also apply the kernel equating framework to this equating design, resulting in a…

Efficient molecular density functional theory using generalized spherical harmonics expansions.

PubMed

Ding, Lu; Levesque, Maximilien; Borgis, Daniel; Belloni, Luc

2017-09-07

We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r≡(x,y,z) and of the three Euler angles Ω≡(θ,ϕ,ψ) describing the solvent orientation. The standard density functional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r,Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water.

Theory and computer simulation of hard-core Yukawa mixtures: thermodynamical, structural and phase coexistence properties.

PubMed

Mkanya, Anele; Pellicane, Giuseppe; Pini, Davide; Caccamo, Carlo

2017-09-13

We report extensive calculations, based on the modified hypernetted chain (MHNC) theory, on the hierarchical reference theory (HRT), and on Monte Carlo simulations, of thermodynamical, structural and phase coexistence properties of symmetric binary hard-core Yukawa mixtures (HCYM) with attractive interactions at equal species concentration. The obtained results are throughout compared with those available in the literature for the same systems. It turns out that the MHNC predictions for thermodynamic and structural quantities are quite accurate in comparison with the MC data. The HRT is equally accurate for thermodynamics, and slightly less accurate for structure. Liquid-vapor (LV) and liquid-liquid (LL) consolute coexistence conditions as emerging from simulations, are also highly satisfactorily reproduced by both the MHNC and HRT for relatively long ranged potentials. When the potential range reduces, the MHNC faces problems in determining the LV binodal line; however, the LL consolute line and the critical end point (CEP) temperature and density turn out to be still satisfactorily predicted within this theory. The HRT also predicts with good accuracy the CEP position. The possibility of employing liquid state theories HCYM for the purpose of reliably determining phase equilibria in multicomponent colloidal fluids of current technological interest, is discussed.

Theory and computer simulation of hard-core Yukawa mixtures: thermodynamical, structural and phase coexistence properties

NASA Astrophysics Data System (ADS)

Mkanya, Anele; Pellicane, Giuseppe; Pini, Davide; Caccamo, Carlo

2017-09-01

We report extensive calculations, based on the modified hypernetted chain (MHNC) theory, on the hierarchical reference theory (HRT), and on Monte Carlo simulations, of thermodynamical, structural and phase coexistence properties of symmetric binary hard-core Yukawa mixtures (HCYM) with attractive interactions at equal species concentration. The obtained results are throughout compared with those available in the literature for the same systems. It turns out that the MHNC predictions for thermodynamic and structural quantities are quite accurate in comparison with the MC data. The HRT is equally accurate for thermodynamics, and slightly less accurate for structure. Liquid-vapor (LV) and liquid-liquid (LL) consolute coexistence conditions as emerging from simulations, are also highly satisfactorily reproduced by both the MHNC and HRT for relatively long ranged potentials. When the potential range reduces, the MHNC faces problems in determining the LV binodal line; however, the LL consolute line and the critical end point (CEP) temperature and density turn out to be still satisfactorily predicted within this theory. The HRT also predicts with good accuracy the CEP position. The possibility of employing liquid state theories HCYM for the purpose of reliably determining phase equilibria in multicomponent colloidal fluids of current technological interest, is discussed.

The LOCV asymmetric nuclear matter two-body density distributions versus those of FHNC

NASA Astrophysics Data System (ADS)

Tafrihi, Azar

2018-05-01

The theoretical computations of the electron-nucleus scattering can be improved, by employing the asymmetric nuclear matter (ASM) two-body density distributions (TBDD) . But, due to the sophistications of the calculations, the TBDD with arbitrary isospin asymmetry have not yet been computed in the Fermi Hypernetted Chain (FHNC) or the Monte Carlo (MC) approaches. So, in the present work, we intend to find the ASM TBDD, in the states with isospin T, spin S and spin projection Sz, in the Lowest Order Constrained Variational (LOCV) method. It is demonstrated that, at small relative distances, independent of the proton to neutron ratio β, the state-dependent TBDD have a universal shape. Expectedly, it is observed that, at low (high) β values, the nucleons prefer to make a pair in the T = 1(0) states. In addition, the strength of the tensor-dependent correlations is investigated, using the ratio of the TBDD in the TSSz = 010 state with θ = π / 2 and that of θ = 0. The mentioned ratios peak at r ∼ 0 . 9 fm, considering different β values. It is hoped that, the present results could help a better reproduction of the experimental data of the electron-nucleus scattering.

Integrable Seven-Point Discrete Equations and Second-Order Evolution Chains

NASA Astrophysics Data System (ADS)

Adler, V. E.

2018-04-01

We consider differential-difference equations defining continuous symmetries for discrete equations on a triangular lattice. We show that a certain combination of continuous flows can be represented as a secondorder scalar evolution chain. We illustrate the general construction with a set of examples including an analogue of the elliptic Yamilov chain.

Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating

ERIC Educational Resources Information Center

Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen

2012-01-01

This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…

An Evaluation of Kernel Equating: Parallel Equating with Classical Methods in the SAT Subject Tests[TM] Program. Research Report. ETS RR-09-06

ERIC Educational Resources Information Center

Grant, Mary C.; Zhang, Lilly; Damiano, Michele

2009-01-01

This study investigated kernel equating methods by comparing these methods to operational equatings for two tests in the SAT Subject Tests[TM] program. GENASYS (ETS, 2007) was used for all equating methods and scaled score kernel equating results were compared to Tucker, Levine observed score, chained linear, and chained equipercentile equating…

Analytical expression for the correlation function of a hard sphere chain fluid

NASA Astrophysics Data System (ADS)

Chang, Jaeeon; Kim, Hwayong

A closed form expression is given for the correlation function of flexible hard sphere chain fluid. A set of integral equations obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with the polymer Percus-Yevick ideal chain approximation is considered. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of individual correlation functions are obtained. By inverse Laplace transformation the inter- and intramolecular radial distribution functions (RDFs) are obtained in closed forms up to 3D(D is segment diameter). These analytical expressions for the RDFs would be useful in developing the perturbation theory of chain fluids.

Theoretical study of solvent effects on the coil-globule transition

NASA Astrophysics Data System (ADS)

Polson, James M.; Opps, Sheldon B.; Abou Risk, Nicholas

2009-06-01

The coil-globule transition of a polymer in a solvent has been studied using Monte Carlo simulations of a single chain subject to intramolecular interactions as well as a solvent-mediated effective potential. This solvation potential was calculated using several different theoretical approaches for two simple polymer/solvent models, each employing hard-sphere chains and hard-sphere solvent particles as well as attractive square-well potentials between some interaction sites. For each model, collapse is driven by variation in a parameter which changes the energy mismatch between monomers and solvent particles. The solvation potentials were calculated using two fundamentally different methodologies, each designed to predict the conformational behavior of polymers in solution: (1) the polymer reference interaction site model (PRISM) theory and (2) a many-body solvation potential (MBSP) based on scaled particle theory introduced by Grayce [J. Chem. Phys. 106, 5171 (1997)]. For the PRISM calculations, two well-studied solvation monomer-monomer pair potentials were employed, each distinguished by the closure relation used in its derivation: (i) a hypernetted-chain (HNC)-type potential and (ii) a Percus-Yevick (PY)-type potential. The theoretical predictions were each compared to results obtained from explicit-solvent discontinuous molecular dynamics simulations on the same polymer/solvent model systems [J. Chem. Phys. 125, 194904 (2006)]. In each case, the variation in the coil-globule transition properties with solvent density is mostly qualitatively correct, though the quantitative agreement between the theory and prediction is typically poor. The HNC-type potential yields results that are more qualitatively consistent with simulation. The conformational behavior of the polymer upon collapse predicted by the MBSP approach is quantitatively correct for low and moderate solvent densities but is increasingly less accurate for higher densities. At high solvent densities, the PRISM-HNC and MBSP approaches tend to overestimate, while the PRISM-PY approach underestimates the tendency of the solvent to drive polymer collapse.

Magnonic analog of relativistic Zitterbewegung in an antiferromagnetic spin chain

NASA Astrophysics Data System (ADS)

Wang, Weiwei; Gu, Chenjie; Zhou, Yan; Fangohr, Hans

2017-07-01

We theoretically investigate the spin-wave (magnon) excitations in a classical antiferromagnetic spin chain with easy-axis anisotropy. We obtain a Dirac-like equation by linearizing the Landau-Lifshitz-Gilbert equation in this antiferromagnetic system, in contrast to the ferromagnetic system in which a Schrödinger-type equation is derived. The Hamiltonian operator in the Dirac-like equation is a pseudo-Hermitian. We compute and demonstrate relativistic Zitterbewegung (trembling motion) in the antiferromagnetic spin chain by measuring the expectation values of the wave-packet position.

Comparison of the One- and Bi-Direction Chained Equipercentile Equating

ERIC Educational Resources Information Center

Oh, Hyeonjoo; Moses, Tim

2012-01-01

This study investigated differences between two approaches to chained equipercentile (CE) equating (one- and bi-direction CE equating) in nearly equal groups and relatively unequal groups. In one-direction CE equating, the new form is linked to the anchor in one sample of examinees and the anchor is linked to the reference form in the other…

Quantum spectral curve for ( q, t)-matrix model

NASA Astrophysics Data System (ADS)

Zenkevich, Yegor

2018-02-01

We derive quantum spectral curve equation for ( q, t)-matrix model, which turns out to be a certain difference equation. We show that in Nekrasov-Shatashvili limit this equation reproduces the Baxter TQ equation for the quantum XXZ spin chain. This chain is spectral dual to the Seiberg-Witten integrable system associated with the AGT dual gauge theory.

Dual chain perturbation theory: A new equation of state for polyatomic molecules

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

Marshall, Bennett D., E-mail: bennett.d.marshall@exxonmobil.com

In the development of equations of state for polyatomic molecules, thermodynamic perturbation theory (TPT) is widely used to calculate the change in free energy due to chain formation. TPT is a simplification of a more general and exact multi-density cluster expansion for associating fluids. In TPT, all contributions to the cluster expansion which contain chain–chain interactions are neglected. That is, all inter-chain interactions are treated at the reference fluid level. This allows for the summation of the cluster theory in terms of reference system correlation functions only. The resulting theory has been shown to be accurate and has been widelymore » employed as the basis of many engineering equations of state. While highly successful, TPT has many handicaps which result from the neglect of chain–chain contributions. The subject of this document is to move beyond the limitations of TPT and include chain–chain contributions to the equation of state.« less

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

Harstad, E. N.; Harlow, Francis Harvey,; Schreyer, H. L.

Our goal is to develop constitutive relations for the behavior of a solid polymer during high-strain-rate deformations. In contrast to the classic thermodynamic techniques for deriving stress-strain response in static (equilibrium) circumstances, we employ a statistical-mechanics approach, in which we evolve a probability distribution function (PDF) for the velocity fluctuations of the repeating units of the chain. We use a Langevin description for the dynamics of a single repeating unit and a Lioville equation to describe the variations of the PDF. Moments of the PDF give the conservation equations for a single polymer chain embedded in other similar chains. Tomore » extract single-chain analytical constitutive relations these equations have been solved for representative loading paths. By this process we discover that a measure of nonuniform chain link displacement serves this purpose very well. We then derive an evolution equation for the descriptor function, with the result being a history-dependent constitutive relation.« less

Verifying the Hanging Chain Model

ERIC Educational Resources Information Center

Karls, Michael A.

2013-01-01

The wave equation with variable tension is a classic partial differential equation that can be used to describe the horizontal displacements of a vertical hanging chain with one end fixed and the other end free to move. Using a web camera and TRACKER software to record displacement data from a vibrating hanging chain, we verify a modified version…

Thermodynamics of Inozemtsev's elliptic spin chain

NASA Astrophysics Data System (ADS)

Klabbers, Rob

2016-06-01

We study the thermodynamic behaviour of Inozemtsev's long-range elliptic spin chain using the Bethe ansatz equations describing the spectrum of the model in the infinite-length limit. We classify all solutions of these equations in that limit and argue which of these solutions determine the spectrum in the thermodynamic limit. Interestingly, some of the solutions are not selfconjugate, which puts the model in sharp contrast to one of the model's limiting cases, the Heisenberg XXX spin chain. Invoking the string hypothesis we derive the thermodynamic Bethe ansatz equations (TBA-equations) from which we determine the Helmholtz free energy in thermodynamic equilibrium and derive the associated Y-system. We corroborate our results by comparing numerical solutions of the TBA-equations to a direct computation of the free energy for the finite-length hamiltonian. In addition we confirm numerically the interesting conjecture put forward by Finkel and González-López that the original and supersymmetric versions of Inozemtsev's elliptic spin chain are equivalent in the thermodynamic limit.

Comparative study of the LOCV and the FHNC approaches for the nucleonic matter problem

NASA Astrophysics Data System (ADS)

Tafrihi, Azar; Modarres, Majid

2016-03-01

The nucleonic matter problem is investigated by comparing the lowest order constrained variational (LOCV) method with the Fermi hypernetted chain (FHNC) theory, emphasizing the role of the LOCV correlation functions. In this way, the central correlation functions are used in the LOCV formalism, for the Bethe homework problem. It is shown that the LOCV computations reasonably agree with those of FHNC. Moreover, the FHNC calculations are performed with the LOCV correlation functions. It is found that, assuming the LOCV or the parametrized correlation functions, the FHNC computations do not change significantly. So, one may conclude that the mentioned consistencies refer to the choice of the LOCV correlation functions. Because, the contribution of the many-body cluster terms can be ignored, if the LOCV correlation functions satisfy the normalization constraint. Then, using the AV 18 interaction, the operator-dependent (OD) correlation functions are employed in the LOCV calculations. Note that the LOCV OD correlation functions are obtained by averaging over the states. It turns out that the overall behaviour of the LOCV OD correlation functions are similar to those of FHNC. Although, due to the many-body effects which are considered in the FHNC calculations, the LOCV results fairly differ from those of FHNC. Finally, it is worth mentioning that, unlike the recent FHNC calculations, the spin-orbit-dependent correlation functions are included in the LOCV approach.

Joint modelling rationale for chained equations

PubMed Central

2014-01-01

Background Chained equations imputation is widely used in medical research. It uses a set of conditional models, so is more flexible than joint modelling imputation for the imputation of different types of variables (e.g. binary, ordinal or unordered categorical). However, chained equations imputation does not correspond to drawing from a joint distribution when the conditional models are incompatible. Concurrently with our work, other authors have shown the equivalence of the two imputation methods in finite samples. Methods Taking a different approach, we prove, in finite samples, sufficient conditions for chained equations and joint modelling to yield imputations from the same predictive distribution. Further, we apply this proof in four specific cases and conduct a simulation study which explores the consequences when the conditional models are compatible but the conditions otherwise are not satisfied. Results We provide an additional “non-informative margins” condition which, together with compatibility, is sufficient. We show that the non-informative margins condition is not satisfied, despite compatible conditional models, in a situation as simple as two continuous variables and one binary variable. Our simulation study demonstrates that as a consequence of this violation order effects can occur; that is, systematic differences depending upon the ordering of the variables in the chained equations algorithm. However, the order effects appear to be small, especially when associations between variables are weak. Conclusions Since chained equations is typically used in medical research for datasets with different types of variables, researchers must be aware that order effects are likely to be ubiquitous, but our results suggest they may be small enough to be negligible. PMID:24559129

Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions

DOE PAGES

Kim, K. S.; Nakae, L. F.; Prasad, M. K.; ...

2015-11-01

Here, we solve a simple theoretical model of time evolving fission chains due to Feynman that generalizes and asymptotically approaches the point model theory. The point model theory has been used to analyze thermal neutron counting data. This extension of the theory underlies fast counting data for both neutrons and gamma rays from metal systems. Fast neutron and gamma-ray counting is now possible using liquid scintillator arrays with nanosecond time resolution. For individual fission chains, the differential equations describing three correlated probability distributions are solved: the time-dependent internal neutron population, accumulation of fissions in time, and accumulation of leaked neutronsmore » in time. Explicit analytic formulas are given for correlated moments of the time evolving chain populations. The equations for random time gate fast neutron and gamma-ray counting distributions, due to randomly initiated chains, are presented. Correlated moment equations are given for both random time gate and triggered time gate counting. There are explicit formulas for all correlated moments are given up to triple order, for all combinations of correlated fast neutrons and gamma rays. The nonlinear differential equations for probabilities for time dependent fission chain populations have a remarkably simple Monte Carlo realization. A Monte Carlo code was developed for this theory and is shown to statistically realize the solutions to the fission chain theory probability distributions. Combined with random initiation of chains and detection of external quanta, the Monte Carlo code generates time tagged data for neutron and gamma-ray counting and from these data the counting distributions.« less

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

Kim, K. S.; Nakae, L. F.; Prasad, M. K.

Here, we solve a simple theoretical model of time evolving fission chains due to Feynman that generalizes and asymptotically approaches the point model theory. The point model theory has been used to analyze thermal neutron counting data. This extension of the theory underlies fast counting data for both neutrons and gamma rays from metal systems. Fast neutron and gamma-ray counting is now possible using liquid scintillator arrays with nanosecond time resolution. For individual fission chains, the differential equations describing three correlated probability distributions are solved: the time-dependent internal neutron population, accumulation of fissions in time, and accumulation of leaked neutronsmore » in time. Explicit analytic formulas are given for correlated moments of the time evolving chain populations. The equations for random time gate fast neutron and gamma-ray counting distributions, due to randomly initiated chains, are presented. Correlated moment equations are given for both random time gate and triggered time gate counting. There are explicit formulas for all correlated moments are given up to triple order, for all combinations of correlated fast neutrons and gamma rays. The nonlinear differential equations for probabilities for time dependent fission chain populations have a remarkably simple Monte Carlo realization. A Monte Carlo code was developed for this theory and is shown to statistically realize the solutions to the fission chain theory probability distributions. Combined with random initiation of chains and detection of external quanta, the Monte Carlo code generates time tagged data for neutron and gamma-ray counting and from these data the counting distributions.« less

Monte Carlo simulation and equation of state for flexible charged hard-sphere chain fluids: polyampholyte and polyelectrolyte solutions.

PubMed

Jiang, Hao; Adidharma, Hertanto

2014-11-07

The thermodynamic modeling of flexible charged hard-sphere chains representing polyampholyte or polyelectrolyte molecules in solution is considered. The excess Helmholtz energy and osmotic coefficients of solutions containing short polyampholyte and the osmotic coefficients of solutions containing short polyelectrolytes are determined by performing canonical and isobaric-isothermal Monte Carlo simulations. A new equation of state based on the thermodynamic perturbation theory is also proposed for flexible charged hard-sphere chains. For the modeling of such chains, the use of solely the structure information of monomer fluid for calculating the chain contribution is found to be insufficient and more detailed structure information must therefore be considered. Two approaches, i.e., the dimer and dimer-monomer approaches, are explored to obtain the contribution of the chain formation to the Helmholtz energy. By comparing with the simulation results, the equation of state with either the dimer or dimer-monomer approach accurately predicts the excess Helmholtz energy and osmotic coefficients of polyampholyte and polyelectrolyte solutions except at very low density. It also well captures the effect of temperature on the thermodynamic properties of these solutions.

Overcharging and charge reversal in the electrical double layer around the point of zero charge.

PubMed

Guerrero-García, G Iván; González-Tovar, Enrique; Chávez-Páez, Martín; Lozada-Cassou, Marcelo

2010-02-07

The ionic adsorption around a weakly charged spherical colloid, immersed in size-asymmetric 1:1 and 2:2 salts, is studied. We use the primitive model (PM) of an electrolyte to perform Monte Carlo simulations as well as theoretical calculations by means of the hypernetted chain/mean spherical approximation (HNC/MSA) and the unequal-radius modified Gouy-Chapman (URMGC) integral equations. Structural quantities such as the radial distribution functions, the integrated charge, and the mean electrostatic potential are reported. Our Monte Carlo "experiments" evidence that near the point of zero charge, the smallest ionic species is preferentially adsorbed onto the macroparticle, independently of the sign of the charge carried by this tiniest electrolytic component, giving rise to the appearance of the phenomena of charge reversal (CR) and overcharging (OC). Accordingly, colloidal CR, due to an excessive attachment of counterions, is observed when the macroion is slightly charged and the coions are larger than the counterions. In the opposite situation, i.e., if the counterions are larger than the coions, the central macroion acquires additional like-charge (coions) and hence becomes "overcharged," a feature theoretically predicted in the past [F. Jiménez-Angeles and M. Lozada-Cassou, J. Phys. Chem. B 108, 7286 (2004)]. In other words, here we present the first simulation data on OC in the PM electrical double layer, showing that close to the point of zero charge, this novel effect surges as a consequence of the ionic size asymmetry. We also find that the HNC/MSA theory captures well the CR and OC phenomena exhibited by the computer experiments, especially as the macroion's charge increases. On the contrary, even if URMGC also displays CR and OC, its predictions do not compare favorably with the Monte Carlo data, evidencing that the inclusion of hard-core correlations in Monte Carlo and HNC/MSA enhances and extends those effects. We explain our findings in terms of the energy-entropy balance. In the field of electrophoresis, it has been generally agreed that the charge of a colloid in motion is partially decreased by counterion adsorption. Depending on the location of the macroion's slipping surface, the OC results of this paper could imply an increase in the expected electrophoretic mobility. These observations aware about the interpretation of electrokinetic measurements using the standard Poisson-Boltzmann approximation beyond its validity region.

Structure des fluides de bâtonnets polaires et polarisables dans l'approximation des chaînes hypertressées avec amplification du potentiel répulsif. Un modèle simple d'acétonitrile liquide.

NASA Astrophysics Data System (ADS)

Salamito, B.; Fries, P. H.

1991-07-01

We study fluids of rigid rods which are generated by a distribution of line sites and which carry a polarizable electric point dipole at their centre. We examine the difficulties for solving the integral equations, which result from truncating the rotational invariant expansion of the usual intermolecular rapidly varying shape potentials. In order to overcome these convergence problems, soft shape potentials are used in addition to an approximation HNCAR, of the hypernetted chain (HNC) type, which Amplifies these soft Repulsive effects. The polarization due to all the molecules is treated at a self-consistent mean field level. This formalism is applied to a model of liquid acetonitrile at 291K. The Kirkwood factors, the dielectric constant, and the cross sections of neutron or X-rays diffraction studies are in good agreement with experiment. This justifies the theoretical molecular pair distribution, from which the local molecular order is carefully analyzed. On étudie des fluides de bâtonnets rigides engendrés par une distribution de sites alignés et portant en leur centre un dipôle électrique ponctuel polarisable. On examine les difficultés de résolution des équations intégrales liées à la troncature du développement en invariants rotationnels des potentiels de forme intermoléculaires usuels à variation rapide. Pour contourner ces problèmes de convergence on utilise des potentiels de forme molle combinés à une approximation HNCAR, du type des chaînes hypertressées (HNC), qui Amplifie ces effets Répulsifs mous. On traite la polarisation due à l'ensemble des molécules par une approximation auto-cohérente de champ moyen. On applique ce formalisme à un modèle d'acétonitrile liquide à 291K. Les facteurs de Kirkwood, la constante diélectrique et les sections efficaces de diffusion des neutrons ou des rayons X calculés sont en bon accord avec l'expérience. Ceci justifie la distribution théorique de paires de molécules à partir de laquelle on analyse en détail l'ordre moléculaire local.

On the dynamics of chain systems. [applications in manipulator and human body models

NASA Technical Reports Server (NTRS)

Huston, R. L.; Passerello, C. E.

1974-01-01

A computer-oriented method for obtaining dynamical equations of motion for chain systems is presented. A chain system is defined as an arbitrarily assembled set of rigid bodies such that adjoining bodies have at least one common point and such that closed loops are not formed. The equations of motion are developed through the use of Lagrange's form of d'Alembert's principle. The method and procedure is illustrated with an elementary study of a tripod space manipulator. The method is designed for application with systems such as human body models, chains and cables, and dynamic finite-segment models.

Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density-functional theory.

PubMed

Likos, Christos N; Mladek, Bianca M; Gottwald, Dieter; Kahl, Gerhard

2007-06-14

We demonstrate the accuracy of the hypernetted chain closure and of the mean-field approximation for the calculation of the fluid-state properties of systems interacting by means of bounded and positive pair potentials with oscillating Fourier transforms. Subsequently, we prove the validity of a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same systems. On the basis of this functional, we calculate analytically the freezing parameters of the latter. We demonstrate explicitly that the stable crystals feature a lattice constant that is independent of density and whose value is dictated by the position of the negative minimum of the Fourier transform of the pair potential. This property is equivalent with the existence of clusters, whose population scales proportionally to the density. We establish that regardless of the form of the interaction potential and of the location on the freezing line, all cluster crystals have a universal Lindemann ratio Lf=0.189 at freezing. We further make an explicit link between the aforementioned density functional and the harmonic theory of crystals. This allows us to establish an equivalence between the emergence of clusters and the existence of negative Fourier components of the interaction potential. Finally, we make a connection between the class of models at hand and the system of infinite-dimensional hard spheres, when the limits of interaction steepness and space dimension are both taken to infinity in a particularly described fashion.

Solute-solvent cavity and bridge functions. I. Varying size of the solute

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

Vyalov, I., E-mail: ivan.vyalov@iit.it; Chuev, G., E-mail: genchuev@rambler.ru; Georgi, N., E-mail: georgi@mis.mpg.de

2014-08-21

In this work we present the results of the extensive molecular simulations of solute-solvent cavity and bridge functions. The mixtures of Lennard-Jones solvent with Lennard-Jones solute at infinite dilution are considered for different solute-solvent size ratios—up to 4:1. The Percus-Yevick and hypernetted chain closures deviate substantially from simulation results in the investigated temperature and density ranges. We also find that the behavior of the indirect and cavity correlation functions is non-monotonous within the hard-core region, but the latter can be successfully approximated by mean-field theory if the solute-solvent interaction energy is divided into repulsive and attractive contribution, according to Weeks-Chandler-Andersenmore » theory. Furthermore, in spite of the non-monotonous behavior of logarithm of the cavity function and the indirect correlation function, their difference, i.e., the bridge function remains constant within the hard-core region. Such behavior of the bridge and indirect correlation functions at small distances and for small values of indirect correlation function is well known from the Duh-Haymet plots, where the non-unique relationship results in loops of the bridge function vs. indirect correlation function graphs. We show that the same pathological behavior appears also when distance is small and indirect correlation function is large. We further show that the unique functional behavior of the bridge function can be established when bridge is represented as a function of the renormalized, repulsive indirect correlation function.« less

Topics in Bethe Ansatz

NASA Astrophysics Data System (ADS)

Wang, Chunguang

Integrable quantum spin chains have close connections to integrable quantum field. theories, modern condensed matter physics, string and Yang-Mills theories. Bethe. ansatz is one of the most important approaches for solving quantum integrable spin. chains. At the heart of the algebraic structure of integrable quantum spin chains is. the quantum Yang-Baxter equation and the boundary Yang-Baxter equation. This. thesis focuses on four topics in Bethe ansatz. The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N. sites have solutions containing ±i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions must be carefully regularized. We consider a regularization involving a parameter that can be. determined using a generalization of the Bethe equations. These generalized Bethe. equations provide a practical way of determining which singular solutions correspond. to eigenvectors of the model. The Bethe equations for the periodic XXX and XXZ spin chains admit singular. solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to bephysical, in which case they correspond to genuine eigenvalues and eigenvectors of. the Hamiltonian. We analyze the ground state of the open spin-1/2 isotropic quantum spin chain. with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots. split evenly into two sets: those that remain finite, and those that become infinite. We. argue that the former satisfy conventional Bethe equations, while the latter satisfy a. generalization of the Richardson-Gaudin equations. We derive an expression for the. leading correction to the boundary energy in terms of the boundary parameters. We argue that the Hamiltonians for A(2) 2n open quantum spin chains corresponding. to two choices of integrable boundary conditions have the symmetries Uq(Bn) and. Uq(Cn), respectively. The deformation of Cn is novel, with a nonstandard coproduct. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of. each type. With the help of this formula, we verify numerically (for a generic value of. the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.

Monte Carlo simulation and equation of state for flexible charged hard-sphere chain fluids: Polyampholyte and polyelectrolyte solutions

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

Jiang, Hao; Adidharma, Hertanto, E-mail: adidharm@uwyo.edu

The thermodynamic modeling of flexible charged hard-sphere chains representing polyampholyte or polyelectrolyte molecules in solution is considered. The excess Helmholtz energy and osmotic coefficients of solutions containing short polyampholyte and the osmotic coefficients of solutions containing short polyelectrolytes are determined by performing canonical and isobaric-isothermal Monte Carlo simulations. A new equation of state based on the thermodynamic perturbation theory is also proposed for flexible charged hard-sphere chains. For the modeling of such chains, the use of solely the structure information of monomer fluid for calculating the chain contribution is found to be insufficient and more detailed structure information must thereforemore » be considered. Two approaches, i.e., the dimer and dimer-monomer approaches, are explored to obtain the contribution of the chain formation to the Helmholtz energy. By comparing with the simulation results, the equation of state with either the dimer or dimer-monomer approach accurately predicts the excess Helmholtz energy and osmotic coefficients of polyampholyte and polyelectrolyte solutions except at very low density. It also well captures the effect of temperature on the thermodynamic properties of these solutions.« less

Derivation of stiffness matrix in constitutive modeling of magnetorheological elastomer

NASA Astrophysics Data System (ADS)

Leng, D.; Sun, L.; Sun, J.; Lin, Y.

2013-02-01

Magnetorheological elastomers (MREs) are a class of smart materials whose mechanical properties change instantly by the application of a magnetic field. Based on the specially orthotropic, transversely isotropic stress-strain relationships and effective permeability model, the stiffness matrix of constitutive equations for deformable chain-like MRE is considered. To valid the components of shear modulus in this stiffness matrix, the magnetic-structural simulations with finite element method (FEM) are presented. An acceptable agreement is illustrated between analytical equations and numerical simulations. For the specified magnetic field, sphere particle radius, distance between adjacent particles in chains and volume fractions of ferrous particles, this constitutive equation is effective to engineering application to estimate the elastic behaviour of chain-like MRE in an external magnetic field.

A molecular model for cohesive slip at polymer melt/solid interfaces.

PubMed

Tchesnokov, M A; Molenaar, J; Slot, J J M; Stepanyan, R

2005-06-01

A molecular model is proposed which predicts wall slip by disentanglement of polymer chains adsorbed on a wall from those in the polymer bulk. The dynamics of the near-wall boundary layer is found to be governed by a nonlinear equation of motion, which accounts for such mechanisms on surface chains as convection, retraction, constraint release, and thermal fluctuations. This equation is valid over a wide range of grafting regimes, including those in which interactions between neighboring adsorbed molecules become essential. It is not closed since the dynamics of adsorbed chains is shown to be coupled to that of polymer chains in the bulk via constraint release. The constitutive equations for the layer and bulk, together with continuity of stress and velocity, are found to form a closed system of equations which governs the dynamics of the whole "bulk+boundary layer" ensemble. Its solution provides a stick-slip law in terms of the molecular parameters and extruder geometry. The model is quantitative and contains only those parameters that can be measured directly, or extracted from independent rheological measurements. The model predictions show a good agreement with available experimental data.

A non-additive repulsive contribution in an equation of state: The development for homonuclear square well chains equation of state validated against Monte Carlo simulation

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

Trinh, Thi-Kim-Hoang; Laboratoire de Science des Procédés et des Matériaux; Passarello, Jean-Philippe, E-mail: Jean-Philippe.Passarello@lspm.cnrs.fr

This work consists of the adaptation of a non-additive hard sphere theory inspired by Malakhov and Volkov [Polym. Sci., Ser. A 49(6), 745–756 (2007)] to a square-well chain. Using the thermodynamic perturbation theory, an additional term is proposed that describes the effect of perturbing the chain of square well spheres by a non-additive parameter. In order to validate this development, NPT Monte Carlo simulations of thermodynamic and structural properties of the non-additive square well for a pure chain and a binary mixture of chains are performed. Good agreements are observed between the compressibility factors originating from the theory and thosemore » from molecular simulations.« less

The Missing Data Assumptions of the NEAT Design and Their Implications for Test Equating

ERIC Educational Resources Information Center

Sinharay, Sandip; Holland, Paul W.

2010-01-01

The Non-Equivalent groups with Anchor Test (NEAT) design involves "missing data" that are "missing by design." Three nonlinear observed score equating methods used with a NEAT design are the "frequency estimation equipercentile equating" (FEEE), the "chain equipercentile equating" (CEE), and the "item-response-theory observed-score-equating" (IRT…

The Bethe ansatz

NASA Astrophysics Data System (ADS)

Levkovich-Maslyuk, Fedor

2016-08-01

We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based on the exact S-matrix. Then we illustrate this method in several concrete theories. The first case we study is the SU(2) chiral Gross-Neveu model. We derive the Bethe equations via algebraic Bethe ansatz, solving in the process the Heisenberg XXX spin chain. We discuss this famous spin chain model in some detail, covering in particular the coordinate Bethe ansatz, some properties of Bethe states, and the classical scaling limit leading to finite-gap equations. Then we proceed to the more involved SU(3) chiral Gross-Neveu model and derive the Bethe equations using nested algebraic Bethe ansatz to solve the arising SU(3) spin chain. Finally we show how a method similar to the Bethe ansatz works in a completely different setting, namely for the 1D oscillator in quantum mechanics.

Singular eigenstates in the even(odd) length Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Ranjan Giri, Pulak; Deguchi, Tetsuo

2015-05-01

We study the implications of the regularization for the singular solutions on the even(odd) length spin-1/2 XXX chains in some specific down-spin sectors. In particular, the analytic expressions of the Bethe eigenstates for three down-spin sector have been obtained along with their numerical forms in some fixed length chains. For an even-length chain if the singular solutions \\{{{λ }α }\\} are invariant under the sign changes of their rapidities \\{{{λ }α }\\}=\\{-{{λ }α }\\}, then the Bethe ansatz equations are reduced to a system of (M-2)/2((M-3)/2) equations in an even (odd) down-spin sector. For an odd N length chain in the three down-spin sector, it has been analytically shown that there exist singular solutions in any finite length of the spin chain of the form N=3(2k+1) with k=1,2,3,\\cdots . It is also shown that there exist no singular solutions in the four down-spin sector for some odd-length spin-1/2 XXX chains.

The Effectiveness of Circular Equating as a Criterion for Evaluating Equating.

ERIC Educational Resources Information Center

Wang, Tianyou; Hanson, Bradley A.; Harris, Deborah J.

Equating a test form to itself through a chain of equatings, commonly referred to as circular equating, has been widely used as a criterion to evaluate the adequacy of equating. This paper uses both analytical methods and simulation methods to show that this criterion is in general invalid in serving this purpose. For the random groups design done…

A fresh look at the catenary

NASA Astrophysics Data System (ADS)

Behroozi, F.

2014-09-01

A hanging chain takes the familiar form known as the catenary which is one of the most ubiquitous curves students encounter in their daily life. Yet most introductory physics and mathematics texts ignore the subject entirely. In more advanced texts the catenary equation is usually derived as an application of the calculus of variations. Although the variational approach is mathematically elegant, it is suitable for more advanced students. Here we derive the catenary equation in special and rectangular coordinates by considering the equilibrium conditions for an element of the hanging chain and without resorting to the calculus of variations. One advantage of this approach is its simplicity which makes it accessible to undergraduate students; another is the concurrent derivation of a companion equation which gives the tension along the chain. These solutions provide an excellent opportunity for undergraduates to explore the underlying physics. One interesting result is that the shape of a hanging chain does not depend on its linear mass density or on the strength of the gravitational field. Therefore, within a scale factor, all catenaries are copies of the same universal curve. We give the functional dependence of the scale factor on the length and terminal angle of the hanging chain.

Evaluating Equating Accuracy and Assumptions for Groups that Differ in Performance

ERIC Educational Resources Information Center

Powers, Sonya; Kolen, Michael J.

2014-01-01

Accurate equating results are essential when comparing examinee scores across exam forms. Previous research indicates that equating results may not be accurate when group differences are large. This study compared the equating results of frequency estimation, chained equipercentile, item response theory (IRT) true-score, and IRT observed-score…

Motions, efforts and actuations in constrained dynamic systems: a multi-link open-chain example

NASA Astrophysics Data System (ADS)

Duke Perreira, N.

1999-08-01

The effort-motion method, which describes the dynamics of open- and closed-chain topologies of rigid bodies interconnected with revolute and prismatic pairs, is interpreted geometrically. Systems are identified for which the simultaneous control of forces and velocities is desirable, and a representative open-chain system is selected for use in the ensuing analysis. Gauge invariant transformations are used to recast the commonly used kinetic and kinematic equations into a dimensional gauge invariant form. Constraint elimination techniques based on singular value decompositions then recast the invariant equations into orthogonal and reciprocal sets of motion and effort equations written in state variable form. The ideal actuation is found that simultaneously achieves the obtainable portions of the desired constraining efforts and motions. The performance is then evaluated of using the actuation closest to the ideal actuation.

Conformational statistics of stiff macromolecules as solutions to partial differential equations on the rotation and motion groups

PubMed

Chirikjian; Wang

2000-07-01

Partial differential equations (PDE's) for the probability density function (PDF) of the position and orientation of the distal end of a stiff macromolecule relative to its proximal end are derived and solved. The Kratky-Porod wormlike chain, the Yamakawa helical wormlike chain, and the original and revised Marko-Siggia models are examples of stiffness models to which the present formulation is applied. The solution technique uses harmonic analysis on the rotation and motion groups to convert PDE's governing the PDF's of interest into linear algebraic equations which have mathematically elegant solutions.

Chained versus Post-Stratification Equating in a Linear Context: An Evaluation Using Empirical Data. Research Report. ETS RR-10-06

ERIC Educational Resources Information Center

Puhan, Gautam

2010-01-01

This study used real data to construct testing conditions for comparing results of chained linear, Tucker, and Levine-observed score equatings. The comparisons were made under conditions where the new- and old-form samples were similar in ability and when they differed in ability. The length of the anchor test was also varied to enable examination…

Gauge equivalence of the Gross Pitaevskii equation and the equivalent Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Radha, R.; Kumar, V. Ramesh

2007-11-01

In this paper, we construct an equivalent spin chain for the Gross-Pitaevskii equation with quadratic potential and exponentially varying scattering lengths using gauge equivalence. We have then generated the soliton solutions for the spin components S3 and S-. We find that the spin solitons for S3 and S- can be compressed for exponentially growing eigenvalues while they broaden out for decaying eigenvalues.

Optical solitons and modulation instability analysis of an integrable model of (2+1)-Dimensional Heisenberg ferromagnetic spin chain equation

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru

2017-12-01

This paper addresses the nonlinear Schrödinger type equation (NLSE) in (2+1)-dimensions which describes the nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) with anisotropic and bilinear interactions in the semiclassical limit. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the generalized tanh methods. Dark, dark-bright or combined optical and singular soliton solutions of the equation are derived. Furthermore, the modulational instability (MI) is studied based on the standard linear-stability analysis and the MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions.

Methods for Equating Mental Tests.

DTIC Science & Technology

1984-11-01

1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth

Efficient dynamic modeling of manipulators containing closed kinematic loops

NASA Astrophysics Data System (ADS)

Ferretti, Gianni; Rocco, Paolo

An approach to efficiently solve the forward dynamics problem for manipulators containing closed chains is proposed. The two main distinctive features of this approach are: the dynamics of the equivalent open loop tree structures (any closed loop can be in general modeled by imposing some additional kinematic constraints to a suitable tree structure) is computed through an efficient Newton Euler formulation; the constraint equations relative to the most commonly adopted closed chains in industrial manipulators are explicitly solved, thus, overcoming the redundancy of Lagrange's multipliers method while avoiding the inefficiency due to a numerical solution of the implicit constraint equations. The constraint equations considered for an explicit solution are those imposed by articulated gear mechanisms and planar closed chains (pantograph type structures). Articulated gear mechanisms are actually used in all industrial robots to transmit motion from actuators to links, while planar closed chains are usefully employed to increase the stiffness of the manipulators and their load capacity, as well to reduce the kinematic coupling of joint axes. The accuracy and the efficiency of the proposed approach are shown through a simulation test.

Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

NASA Astrophysics Data System (ADS)

Cherstvy, A. G.; Winkler, R. G.

2006-08-01

We investigate the complexation of long thin polyelectrolyte (PE) chains with oppositely charged spheres. In the limit of strong adsorption, when strongly charged PE chains adapt a definite wrapped conformation on the sphere surface, we analytically solve the linear Poisson-Boltzmann equation and calculate the electrostatic potential and the energy of the complex. We discuss some biological applications of the obtained results. For weak adsorption, when a flexible weakly charged PE chain is localized next to the sphere in solution, we solve the Edwards equation for PE conformations in the Hulthén potential, which is used as an approximation for the screened Debye-Hückel potential of the sphere. We predict the critical conditions for PE adsorption. We find that the critical sphere charge density exhibits a distinctively different dependence on the Debye screening length than for PE adsorption onto a flat surface. We compare our findings with experimental measurements on complexation of various PEs with oppositely charged colloidal particles. We also present some numerical results of the coupled Poisson-Boltzmann and self-consistent field equation for PE adsorption in an assembly of oppositely charged spheres.

Shocks, Rarefaction Waves, and Current Fluctuations for Anharmonic Chains

DOE PAGES

Mendl, Christian B.; Spohn, Herbert

2016-10-04

The nonequilibrium dynamics of anharmonic chains is studied by imposing an initial domain-wall state, in which the two half lattices are prepared in equilibrium with distinct parameters. Here, we analyse the Riemann problem for the corresponding Euler equations and, in specific cases, compare with molecular dynamics. Additionally, the fluctuations of time-integrated currents are investigated. In analogy with the KPZ equation, their typical fluctuations should be of size t 1/3 and have a Tracy–Widom GUE distributed amplitude. The proper extension to anharmonic chains is explained and tested through molecular dynamics. Our results are calibrated against the stochastic LeRoux lattice gas.

Kernel and Traditional Equipercentile Equating with Degrees of Presmoothing. Research Report. ETS RR-07-15

ERIC Educational Resources Information Center

Moses, Tim; Holland, Paul

2007-01-01

The purpose of this study was to empirically evaluate the impact of loglinear presmoothing accuracy on equating bias and variability across chained and post-stratification equating methods, kernel and percentile-rank continuization methods, and sample sizes. The results of evaluating presmoothing on equating accuracy generally agreed with those of…

The Importance of Content Representation for Common-Item Equating with Nonrandom Groups.

ERIC Educational Resources Information Center

Klein, Lawrence W.; Jarjoura, David

1985-01-01

The test equating accuracy of content-representative anchors (subsets of items in common) versus nonrepresentative, but substantially longer, anchors was compared for a professional certification examination. Through a chain of equatings, it was found that content representation in anchors was critical. (Author/GDC)

The Missing Data Assumptions of the Nonequivalent Groups with Anchor Test (NEAT) Design and Their Implications for Test Equating. Research Report. ETS RR-09-16

ERIC Educational Resources Information Center

Sinharay, Sandip; Holland, Paul W.

2008-01-01

The nonequivalent groups with anchor test (NEAT) design involves missing data that are missing by design. Three popular equating methods that can be used with a NEAT design are the poststratification equating method, the chain equipercentile equating method, and the item-response-theory observed-score-equating method. These three methods each…

Concatenons as the solutions for non-linear partial differential equations

NASA Astrophysics Data System (ADS)

Kudryashov, N. A.; Volkov, A. K.

2017-07-01

New class of solutions for nonlinear partial differential equations is introduced. We call them the concaten solutions. As an example we consider equations for the description of wave processes in the Fermi-Pasta-Ulam mass chain and construct the concatenon solutions for these equation. Stability of the concatenon-type solutions is investigated numerically. Interaction between the concatenon and solitons is discussed.

Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods

DOE PAGES

Motta, Mario; Ceperley, David M.; Chan, Garnet Kin-Lic; ...

2017-09-28

We present numerical results for the equation of state of an infinite chain of hydrogen atoms. A variety of modern many-body methods are employed, with exhaustive cross-checks and validation. Approaches for reaching the continuous space limit and the thermodynamic limit are investigated, proposed, and tested. The detailed comparisons provide a benchmark for assessing the current state of the art in many-body computation, and for the development of new methods. The ground-state energy per atom in the linear chain is accurately determined versus bond length, with a confidence bound given on all uncertainties.

Matrix-valued Boltzmann equation for the nonintegrable Hubbard chain.

PubMed

Fürst, Martin L R; Mendl, Christian B; Spohn, Herbert

2013-07-01

The standard Fermi-Hubbard chain becomes nonintegrable by adding to the nearest neighbor hopping additional longer range hopping amplitudes. We assume that the quartic interaction is weak and investigate numerically the dynamics of the chain on the level of the Boltzmann type kinetic equation. Only the spatially homogeneous case is considered. We observe that the huge degeneracy of stationary states in the case of nearest neighbor hopping is lost and the convergence to the thermal Fermi-Dirac distribution is restored. The convergence to equilibrium is exponentially fast. However for small next-nearest neighbor hopping amplitudes one has a rapid relaxation towards the manifold of quasistationary states and slow relaxation to the final equilibrium state.

Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods

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

Motta, Mario; Ceperley, David M.; Chan, Garnet Kin-Lic

We present numerical results for the equation of state of an infinite chain of hydrogen atoms. A variety of modern many-body methods are employed, with exhaustive cross-checks and validation. Approaches for reaching the continuous space limit and the thermodynamic limit are investigated, proposed, and tested. The detailed comparisons provide a benchmark for assessing the current state of the art in many-body computation, and for the development of new methods. The ground-state energy per atom in the linear chain is accurately determined versus bond length, with a confidence bound given on all uncertainties.

The dynamics of a forced coupled network of active elements

NASA Astrophysics Data System (ADS)

Parks, Helen F.; Ermentrout, Bard; Rubin, Jonathan E.

2011-03-01

This paper presents the derivation and analysis of mathematical models motivated by the experimental induction of contour phosphenes in the retina. First, a spatially discrete chain of periodically forced coupled oscillators is considered via reduction to a chain of scalar phase equations. Each isolated oscillator locks in a 1:2 manner with the forcing so that there is intrinsic bistability, with activity peaking on either the odd or even cycles of the forcing. If half the chain is started on the odd cycle and half on the even cycle (“split state”), then with sufficiently strong coupling, a wave can be produced that can travel in either direction due to symmetry. Numerical and analytic methods are employed to determine the size of coupling necessary for the split state solution to destabilize such that waves appear. Taking a continuum limit, we reduce the chain to a partial differential equation. We use a Melnikov function to compute, to leading order, the speed of the traveling wave solution to the partial differential equation as a function of the form of coupling and the forcing parameters and compare our result to the numerically computed discrete and continuum wave speeds.

Manipulator interactive design with interconnected flexible elements

NASA Technical Reports Server (NTRS)

Singh, R. P.; Likins, P. W.

1983-01-01

This paper describes the development of an analysis tool for the interactive design of control systems for manipulators and similar electro-mechanical systems amenable to representation as structures in a topological chain. The chain consists of a series of elastic bodies subject to small deformations and arbitrary displacements. The bodies are connected by hinges which permit kinematic constraints, control, or relative motion with six degrees of freedom. The equations of motion for the chain configuration are derived via Kane's method, extended for application to interconnected flexible bodies with time-varying boundary conditions. A corresponding set of modal coordinates has been selected. The motion equations are imbedded within a simulation that transforms the vector-dyadic equations into scalar form for numerical integration. The simulation also includes a linear, time-invariant controler specified in transfer function format and a set of sensors and actuators that interface between the structure and controller. The simulation is driven by an interactive set-up program resulting in an easy-to-use analysis tool.

Item Response Theory Equating Using Bayesian Informative Priors.

ERIC Educational Resources Information Center

de la Torre, Jimmy; Patz, Richard J.

This paper seeks to extend the application of Markov chain Monte Carlo (MCMC) methods in item response theory (IRT) to include the estimation of equating relationships along with the estimation of test item parameters. A method is proposed that incorporates estimation of the equating relationship in the item calibration phase. Item parameters from…

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

NASA Astrophysics Data System (ADS)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Inhibitory effects of cardols and related compounds on superoxide anion generation by xanthine oxidase.

PubMed

Masuoka, Noriyoshi; Nihei, Ken-ichi; Maeta, Ayami; Yamagiwa, Yoshiro; Kubo, Isao

2015-01-01

5-Pentadecatrienylresorcinol, isolated from cashew nuts and commonly known as cardol (C₁₅:₃), prevented the generation of superoxide radicals catalysed by xanthine oxidase without the inhibition of uric acid formation. The inhibition kinetics did not follow the Michelis-Menten equation, but instead followed the Hill equation. Cardol (C₁₀:₀) also inhibited superoxide anion generation, but resorcinol and cardol (C₅:₀) did not inhibit superoxide anion generation. The related compounds 3,5-dihydroxyphenyl alkanoates and alkyl 2,4-dihydroxybenzoates, had more than a C9 chain, cooperatively inhibited but alkyl 3,5-dihydroxybenzoates, regardless of their alkyl chain length, did not inhibit the superoxide anion generation. These results suggested that specific inhibitors for superoxide anion generation catalysed by xanthine oxidase consisted of an electron-rich resorcinol group and an alkyl chain having longer than C9 chain. Copyright © 2014 Elsevier Ltd. All rights reserved.

Ring[bond]chain tautomerism of 2-Aryl-substituted cis- and trans-decahydroquinazolines.

PubMed

Lázár, László; Göblyös, Anikó; Martinek, Tamás A; Fülöp, Ferenc

2002-07-12

In CDCl(3) at 300 K, 2-aryl-substituted cis- and trans-3-isopropyldecahydroquinazolines and trans-3-phenyldecahydroquinazolines proved to be three-component (r(1)[bond]o[bond]r(2)) ring[bond]chain tautomeric mixtures, whereas only ring-closed tautomers could be detected for the 3-methyl-substituted analogues. The proportions of the ring-chain tautomeric forms at equilibrium were strongly influenced by the N-substitutents and the cis-trans ring junction and could be described by the equation log K(X) = rho sigma(+) + log K(X=H). These are the first examples among 2-aryl-1,3-N,N-heterocycles of a three-component ring-chain tautomeric equilibrium characterized by a Hammett-type equation. The stabilities of the ring-closed forms of cis- and trans-2-aryldecahydroquinazolines and the corresponding 3,1-benzoxazines were found to increase in the following sequence of the heteroatom at position 3: NPh < N-i-Pr < O < NMe.

Explicit solutions for exit-only radioactive decay chains

NASA Astrophysics Data System (ADS)

Yuan, Ding; Kernan, Warnick

2007-05-01

In this study, we extended Bateman's [Proc. Cambridge Philos. Soc. 15, 423 (1910)] original work for solving radioactive decay chains and explicitly derived analytic solutions for generic exit-only radioactive decay problems under given initial conditions. Instead of using the conventional Laplace transform for solving Bateman's equations, we used a much simpler algebraic approach. Finally, we discuss methods of breaking down certain classes of large decay chains into collections of simpler chains for easy handling.

A reference-modified density functional theory: An application to solvation free-energy calculations for a Lennard-Jones solution.

PubMed

Sumi, Tomonari; Maruyama, Yutaka; Mitsutake, Ayori; Koga, Kenichiro

2016-06-14

In the conventional classical density functional theory (DFT) for simple fluids, an ideal gas is usually chosen as the reference system because there is a one-to-one correspondence between the external field and the density distribution function, and the exact intrinsic free-energy functional is available for the ideal gas. In this case, the second-order density functional Taylor series expansion of the excess intrinsic free-energy functional provides the hypernetted-chain (HNC) approximation. Recently, it has been shown that the HNC approximation significantly overestimates the solvation free energy (SFE) for an infinitely dilute Lennard-Jones (LJ) solution, especially when the solute particles are several times larger than the solvent particles [T. Miyata and J. Thapa, Chem. Phys. Lett. 604, 122 (2014)]. In the present study, we propose a reference-modified density functional theory as a systematic approach to improve the SFE functional as well as the pair distribution functions. The second-order density functional Taylor series expansion for the excess part of the intrinsic free-energy functional in which a hard-sphere fluid is introduced as the reference system instead of an ideal gas is applied to the LJ pure and infinitely dilute solution systems and is proved to remarkably improve the drawbacks of the HNC approximation. Furthermore, the third-order density functional expansion approximation in which a factorization approximation is applied to the triplet direct correlation function is examined for the LJ systems. We also show that the third-order contribution can yield further refinements for both the pair distribution function and the excess chemical potential for the pure LJ liquids.

The solvation of ions in acetonitrile and acetone. II. Monte Carlo simulations using polarizable solvent models

NASA Astrophysics Data System (ADS)

Fischer, R.; Richardi, J.; Fries, P. H.; Krienke, H.

2002-11-01

Structural properties and energies of solvation are simulated for alkali and halide ions. The solvation structure is discussed in terms of various site-site distribution functions, of solvation numbers, and of orientational correlation functions of the solvent molecules around the ions. The solvent polarizability has notable effects which cannot be intuitively predicted. In particular, it is necessary to reproduce the experimental solvation numbers of small ions. The changes of solvation properties are investigated along the alkali and halide series. By comparing the solvation of ions in acetone to that in acetonitrile, it is shown that the spatial correlations among the solvent molecules around an ion result in a strong screening of the ion-solvent direct intermolecular potential and are essential to understand the changes in the solvation structures and energies between different solvents. The solvation properties derived from the simulations are compared to earlier predictions of the hypernetted chain (HNC) approximation of the molecular Ornstein-Zernike (MOZ) theory [J. Richardi, P. H. Fries, and H. Krienke, J. Chem. Phys. 108, 4079 (1998)]. The MOZ(HNC) formalism gives an overall qualitatively correct picture of the solvation and its various unexpected findings are corroborated. For the larger ions, its predictions become quantitative. The MOZ approach allows to calculate solvent-solvent and ion-solvent potentials of mean force, which shed light on the 3D labile molecular and ionic architectures in the solution. These potentials of mean force convey a unique information which is necessary to fully interpret the angle-averaged structural functions computed from the simulations. Finally, simulations of solutions at finite concentrations show that the solvent-solvent and ion-solvent spatial correlations at infinite dilution are marginally altered by the introduction of fair amounts of ions.

Detecting and Correcting Scale Drift in Test Equating: An Illustration from a Large Scale Testing Program

ERIC Educational Resources Information Center

Puhan, Gautam

2009-01-01

The purpose of this study is to determine the extent of scale drift on a test that employs cut scores. It was essential to examine scale drift for this testing program because new forms in this testing program are often put on scale through a series of intermediate equatings (known as equating chains). This process may cause equating error to…

Scale Drift in Equating on a Test That Employs Cut Scores. Research Report. ETS RR-07-34

ERIC Educational Resources Information Center

Puhan, Gautam

2007-01-01

The purpose of this study is to determine the extent of scale drift on a test that employs cut scores. It is essential to examine scale drift in a testing program using new forms that are often put on scale through a series of intermediate equatings (known as equating chains). This may cause equating error to accumulate to a point where scale…

In Praise of the Catenary

NASA Astrophysics Data System (ADS)

Behroozi, F.

2018-04-01

When a chain hangs loosely from its end points, it takes the familiar form known as the catenary. Power lines, clothes lines, and chain links are familiar examples of the catenary in everyday life. Nevertheless, the subject is conspicuously absent from current introductory physics and calculus courses. Even in upper-level physics and math courses, the catenary equation is usually introduced as an example of hyperbolic functions or discussed as an application of the calculus of variations. We present a new derivation of the catenary equation that is suitable for introductory physics and mathematics courses.

Q-operators for the open Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Frassek, Rouven; Szécsényi, István M.

2015-12-01

We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang-Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation and derive the explicit form of their eigenvalues in terms of the Bethe roots.

Linear Equating for the NEAT Design: Parameter Substitution Models and Chained Linear Relationship Models

ERIC Educational Resources Information Center

Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.

2009-01-01

This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…

Collateral Information for Equating in Small Samples: A Preliminary Investigation

ERIC Educational Resources Information Center

Kim, Sooyeon; Livingston, Samuel A.; Lewis, Charles

2011-01-01

This article describes a preliminary investigation of an empirical Bayes (EB) procedure for using collateral information to improve equating of scores on test forms taken by small numbers of examinees. Resampling studies were done on two different forms of the same test. In each study, EB and non-EB versions of two equating methods--chained linear…

An examination on the influence of small and medium enterprise (SME) stakeholder on green supply chain management practices

NASA Astrophysics Data System (ADS)

Shahlan, M. Z.; Sidek, A. A.; Suffian, S. A.; Hazza, M. H. F. A.; Daud, M. R. C.

2018-01-01

In this paper, climate change and global warming are the biggest current issues in the industrial sectors. The green supply chain managements (GSCM) is one of the crucial input to these issues. Effective GSCM can potentially secure the organization’s competitive advantage and improve the environmental performance of the network activities. In this study, the aim is to investigate and examine how a small and medium enterprises (SMEs) stakeholder pressure and top management influence green supply chain management practices. The study is further advance green supply chain management research in Malaysia focusing on SMEs manufacturing sector using structural equation modelling. Structural equation modelling is a multivariate statistical analysis technique used to examine structural relationship. It is the combination of factor analysis and multi regression analysis and used to analyse structural relationship between measure variable and latent factor. This research found that top management support and stakeholder pressure is the major influence for SMEs to adopt green supply chain management. The research also found that top management is fully mediate with the relationship between stakeholder pressure and monitoring supplier environmental performance.

Interaction of a magnetic island chain in a tokamak plasma with a resonant magnetic perturbation of rapidly oscillating phase

NASA Astrophysics Data System (ADS)

Fitzpatrick, Richard

2017-12-01

An investigation is made into the interaction of a magnetic island chain, embedded in a tokamak plasma, with an externally generated magnetic perturbation of the same helicity whose helical phase is rapidly oscillating. The analysis is similar in form to the classic analysis used by Kapitza [Sov. Phys. JETP 21, 588 (1951)] to examine the angular motion of a rigid pendulum whose pivot point undergoes rapid vertical oscillations. The phase oscillations are found to modify the existing terms, and also to give rise to new terms, in the equations governing the secular evolution of the island chain's radial width and helical phase. An examination of the properties of the new secular evolution equation reveals that it is possible to phase-lock an island chain to an external magnetic perturbation with an oscillating helical phase in a stabilizing phase relation provided that the amplitude, ɛ, of the phase oscillations (in radians) is such that |J0(ɛ )|≪1 , and the mean angular frequency of the perturbation closely matches the natural angular frequency of the island chain.

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

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

Granita, E-mail: granitafc@gmail.com; Bahar, A.

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

A generic rate equation for catalysed, template-directed polymerisation.

PubMed

Hofmeyr, Jan-Hendrik S; Gqwaka, Olona P C; Rohwer, Johann M

2013-09-02

Biosynthetic networks link to growth and reproduction processes through template-directed synthesis of macromolecules such as polynucleotides and polypeptides. No rate equation exists that captures this link in a way that it can effectively be incorporated into a single computational model of the overall process. This paper describes the derivation of such a generic steady-state rate equation for catalysed, template-directed polymerisation reactions with varying monomer stoichiometry and varying chain length. The derivation is based on a classical Michaelis-Menten mechanism with template binding and an arbitrary number of chain elongation steps that produce a polymer composed of an arbitrary number of monomer types. The rate equation only requires the identity of the first dimer in the polymer sequence; for the remainder only the monomer composition needs be known. Further simplification of a term in the denominator yielded an equation requiring no positional information at all, only the monomer composition of the polymer; this equation still gave an excellent estimate of the reaction rate provided that either the monomer concentrations are at least half-saturating, or the polymer is very long. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Energy transport in the three coupled α-polypeptide chains of collagen molecule with long-range interactions effect

NASA Astrophysics Data System (ADS)

Mvogo, Alain; Ben-Bolie, G. H.; Kofané, T. C.

2015-06-01

The dynamics of three coupled α-polypeptide chains of a collagen molecule is investigated with the influence of power-law long-range exciton-exciton interactions. The continuum limit of the discrete equations reveal that the collagen dynamics is governed by a set of three coupled nonlinear Schrödinger equations, whose dispersive coefficient depends on the LRI parameter r. We construct the analytic symmetric and asymmetric (antisymmetric) soliton solutions, which match with the structural features of collagen related with the acupuncture channels. These solutions are used as initial conditions for the numerical simulations of the discrete equations, which reveal a coherent transport of energy in the molecule for r > 3. The results also indicate that the width of the solitons is a decreasing function of r, which help to stabilize the solitons propagating in the molecule. To confirm further the efficiency of energy transport in the molecule, the modulational instability of the system is performed and the numerical simulations show that the energy can flow from one polypeptide chain to another in the form of nonlinear waves.

Nonequilibrium steady state in open quantum systems: Influence action, stochastic equation and power balance

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

Hsiang, J.-T., E-mail: cosmology@gmail.com; Department of Physics, National Dong Hwa University, Hualien 97401, Taiwan; Hu, B.L.

2015-11-15

The existence and uniqueness of a steady state for nonequilibrium systems (NESS) is a fundamental subject and a main theme of research in statistical mechanics for decades. For Gaussian systems, such as a chain of classical harmonic oscillators connected at each end to a heat bath, and for classical anharmonic oscillators under specified conditions, definitive answers exist in the form of proven theorems. Answering this question for quantum many-body systems poses a challenge for the present. In this work we address this issue by deriving the stochastic equations for the reduced system with self-consistent backaction from the two baths, calculatingmore » the energy flow from one bath to the chain to the other bath, and exhibiting a power balance relation in the total (chain + baths) system which testifies to the existence of a NESS in this system at late times. Its insensitivity to the initial conditions of the chain corroborates to its uniqueness. The functional method we adopt here entails the use of the influence functional, the coarse-grained and stochastic effective actions, from which one can derive the stochastic equations and calculate the average values of physical variables in open quantum systems. This involves both taking the expectation values of quantum operators of the system and the distributional averages of stochastic variables stemming from the coarse-grained environment. This method though formal in appearance is compact and complete. It can also easily accommodate perturbative techniques and diagrammatic methods from field theory. Taken all together it provides a solid platform for carrying out systematic investigations into the nonequilibrium dynamics of open quantum systems and quantum thermodynamics. -- Highlights: •Nonequilibrium steady state (NESS) for interacting quantum many-body systems. •Derivation of stochastic equations for quantum oscillator chain with two heat baths. •Explicit calculation of the energy flow from one bath to the chain to the other bath. •Power balance relation shows the existence of NESS insensitive to initial conditions. •Functional method as a viable platform for issues in quantum thermodynamics.« less

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

Mendl, Christian B.; Spohn, Herbert

The nonequilibrium dynamics of anharmonic chains is studied by imposing an initial domain-wall state, in which the two half lattices are prepared in equilibrium with distinct parameters. Here, we analyse the Riemann problem for the corresponding Euler equations and, in specific cases, compare with molecular dynamics. Additionally, the fluctuations of time-integrated currents are investigated. In analogy with the KPZ equation, their typical fluctuations should be of size t 1/3 and have a Tracy–Widom GUE distributed amplitude. The proper extension to anharmonic chains is explained and tested through molecular dynamics. Our results are calibrated against the stochastic LeRoux lattice gas.

Polymer scaling and dynamics in steady-state sedimentation at infinite Péclet number.

PubMed

Lehtola, V; Punkkinen, O; Ala-Nissila, T

2007-11-01

We consider the static and dynamical behavior of a flexible polymer chain under steady-state sedimentation using analytic arguments and computer simulations. The model system comprises a single coarse-grained polymer chain of N segments, which resides in a Newtonian fluid as described by the Navier-Stokes equations. The chain is driven into nonequilibrium steady state by gravity acting on each segment. The equations of motion for the segments and the Navier-Stokes equations are solved simultaneously using an immersed boundary method, where thermal fluctuations are neglected. To characterize the chain conformation, we consider its radius of gyration RG(N). We find that the presence of gravity explicitly breaks the spatial symmetry leading to anisotropic scaling of the components of RG with N along the direction of gravity RG, parallel and perpendicular to it RG, perpendicular, respectively. We numerically estimate the corresponding anisotropic scaling exponents nu parallel approximately 0.79 and nu perpendicular approximately 0.45, which differ significantly from the equilibrium scaling exponent nue=0.588 in three dimensions. This indicates that on the average, the chain becomes elongated along the sedimentation direction for large enough N. We present a generalization of the Flory scaling argument, which is in good agreement with the numerical results. It also reveals an explicit dependence of the scaling exponents on the Reynolds number. To study the dynamics of the chain, we compute its effective diffusion coefficient D(N), which does not contain Brownian motion. For the range of values of N used here, we find that both the parallel and perpendicular components of D increase with the chain length N, in contrast to the case of thermal diffusion in equilibrium. This is caused by the fluid-driven fluctuations in the internal configuration of the polymer that are magnified as polymer size becomes larger.

Doubly self-consistent field theory of grafted polymers under simple shear in steady state.

PubMed

Suo, Tongchuan; Whitmore, Mark D

2014-03-21

We present a generalization of the numerical self-consistent mean-field theory of polymers to the case of grafted polymers under simple shear. The general theoretical framework is presented, and then applied to three different chain models: rods, Gaussian chains, and finitely extensible nonlinear elastic (FENE) chains. The approach is self-consistent at two levels. First, for any flow field, the polymer density profile and effective potential are calculated self-consistently in a manner similar to the usual self-consistent field theory of polymers, except that the calculation is inherently two-dimensional even for a laterally homogeneous system. Second, through the use of a modified Brinkman equation, the flow field and the polymer profile are made self-consistent with respect to each other. For all chain models, we find that reasonable levels of shear cause the chains to tilt, but it has very little effect on the overall thickness of the polymer layer, causing a small decrease for rods, and an increase of no more than a few percent for the Gaussian and FENE chains. Using the FENE model, we also probe the individual bond lengths, bond correlations, and bond angles along the chains, the effects of the shear on them, and the solvent and bonded stress profiles. We find that the approximations needed within the theory for the Brinkman equation affect the bonded stress, but none of the other quantities.

Nonequilibrium generalised Langevin equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths.

PubMed

Ness, H; Stella, L; Lorenz, C D; Kantorovich, L

2017-04-28

We use a generalised Langevin equation scheme to study the thermal transport of low dimensional systems. In this approach, the central classical region is connected to two realistic thermal baths kept at two different temperatures [H. Ness et al., Phys. Rev. B 93, 174303 (2016)]. We consider model Al systems, i.e., one-dimensional atomic chains connected to three-dimensional baths. The thermal transport properties are studied as a function of the chain length N and the temperature difference ΔT between the baths. We calculate the transport properties both in the linear response regime and in the non-linear regime. Two different laws are obtained for the linear conductance versus the length of the chains. For large temperatures (T≳500 K) and temperature differences (ΔT≳500 K), the chains, with N>18 atoms, present a diffusive transport regime with the presence of a temperature gradient across the system. For lower temperatures (T≲500 K) and temperature differences (ΔT≲400 K), a regime similar to the ballistic regime is observed. Such a ballistic-like regime is also obtained for shorter chains (N≤15). Our detailed analysis suggests that the behaviour at higher temperatures and temperature differences is mainly due to anharmonic effects within the long chains.

Observed Methods for Felling Hardwood Trees with Chain Saws

Treesearch

Jerry L. Koger

1983-01-01

The angles and lengths of the cutting surfaces made by chain saw operators on hardwood tree stumps are described by means, standard deviations, ranges, and regression equations. Recommended felling guidelines are compared with observed felling methods used by experienced timber cutters in the southern Appalachian Mountains.

a Numerical Comparison of Langrange and Kane's Methods of AN Arm Segment

NASA Astrophysics Data System (ADS)

Rambely, Azmin Sham; Halim, Norhafiza Ab.; Ahmad, Rokiah Rozita

A 2-D model of a two-link kinematic chain is developed using two dynamics equations of motion, namely Kane's and Lagrange Methods. The dynamics equations are reduced to first order differential equation and solved using modified Euler and fourth order Runge Kutta to approximate the shoulder and elbow joint angles during a smash performance in badminton. Results showed that Runge-Kutta produced a better and exact approximation than that of modified Euler and both dynamic equations produced better absolute errors.

Integrability of conformal fishnet theory

NASA Astrophysics Data System (ADS)

Gromov, Nikolay; Kazakov, Vladimir; Korchemsky, Gregory; Negro, Stefano; Sizov, Grigory

2018-01-01

We study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed N = 4 SYM theory. We show that the transfer matrix "building" the fishnet graphs emerges from the R-matrix of non-compact conformal SU(2 , 2) Heisenberg spin chain with spins belonging to principal series representations of the four-dimensional conformal group. We demonstrate explicitly a relationship between this integrable spin chain and the Quantum Spectral Curve (QSC) of N = 4 SYM. Using QSC and spin chain methods, we construct Baxter equation for Q-functions of the conformal spin chain needed for computation of the anomalous dimensions of operators of the type tr( ϕ 1 J ) where ϕ 1 is one of the two scalars of the theory. For J = 3 we derive from QSC a quantization condition that fixes the relevant solution of Baxter equation. The scaling dimensions of the operators only receive contributions from wheel-like graphs. We develop integrability techniques to compute the divergent part of these graphs and use it to present the weak coupling expansion of dimensions to very high orders. Then we apply our exact equations to calculate the anomalous dimensions with J = 3 to practically unlimited precision at any coupling. These equations also describe an infinite tower of local conformal operators all carrying the same charge J = 3. The method should be applicable for any J and, in principle, to any local operators of bi-scalar theory. We show that at strong coupling the scaling dimensions can be derived from semiclassical quantization of finite gap solutions describing an integrable system of noncompact SU(2 , 2) spins. This bears similarities with the classical strings arising in the strongly coupled limit of N = 4 SYM.

Note: A simple picture of subdiffusive polymer motion from stochastic simulations

NASA Astrophysics Data System (ADS)

Gniewek, Pawel; Kolinski, Andrzej

2011-02-01

Entangled polymer solutions and melts exhibit unusual frictional properties. In the entanglement limit self-diffusion coefficient of long flexible polymers decays with the second power of chain length and viscosity increases with 3-3.5 power of chain length.1 It is very difficult to provide detailed molecular-level explanation of the entanglement effect.2 Perhaps, the problem of many entangled polymer chains is the most complex multibody issue of classical physics. There are different approaches to polymer melt dynamics. Some of these recognize hydrodynamic interactions as a dominant term, while topological constraints for polymer chains are assumed as a secondary factor. Other theories consider the topological constraints as the most important factors controlling polymer dynamics. Herman and co-workers describe polymer dynamics in melts, as a lateral sliding of a chain along other chains until complete mutual disentanglement. Despite the success in explaining the power-laws for viscosity, the model has some limitations. First of all, memory effects are ignored, that is, polymer segments are treated independently. Also, each entanglement/obstacle is treated as a separate entity, which is certainly a simplification of the memory effect problem. In addition to that, correlated motions of segments are addressed within the framework of renormalized Rouse-chain theory,7 without calling any topological entanglements in advance. This approach leads to the generalized Langevin equation characterized by distinct memory kernels describing local and nonlocal segment correlations or to the Smoluchowski equation in which the segments' mobility is treated as a stochastic variable.11 Both models describe the polymer segments motion at a microscopic level. An interesting alternative is to solve the integrodifferential equation for the chain relaxation with a sophisticated kernel function.12 The design of the kernel function is based on a mesoscopic description of the polymer melt. These theories explain some experimental data, although the description of the crossover between the Rouse and non-Rouse behavior is not satisfactory. Obviously, within the scope of a short note we cannot review all theoretical concepts of the polymer melt dynamics. Here we focus just on the interpretation of the observed single segment autocorrelation function.

Collision of Identical Solitary Waves in Hertzian Chains

NASA Astrophysics Data System (ADS)

Sen, Surajit; Manciu, Marian; Hurd, Alan J.

2000-03-01

We consider a chain of elastic beads, which repel upon contact according to the non-linear Hertz potential. We further assume that the chain is under zero loading, i.e., the grains have zero initial overlap. We show via careful numerical solution of the equations of motion that an impulse propagates as a solitary wave and that the collision of identical solitary waves propagating in opposite directions along the chain spawns a hierarchy of multiple weak solitary waves [1]. [1] M. Manciu, S. Sen and A.J. Hurd, Phys Lett A (submitted).

Conformal invariance of the Lungren-Monin-Novikov equations for vorticity fields in 2D turbulence

NASA Astrophysics Data System (ADS)

Grebenev, V. N.; Wacławczyk, M.; Oberlack, M.

2017-10-01

We study the statistical properties of the vorticity field in two-dimensional turbulence. The field is described in terms of the infinite Lundgren-Monin-Novikov (LMN) chain of equations for multi-point probability density functions (pdf’s) of vorticity. We perform a Lie group analysis of the first equation in this chain using the direct method based on the canonical Lie-Bäcklund transformations devised for integro-differential equations. We analytically show that the conformal group is broken for the first LMN equation i.e. for the 1-point pdf at least for the inviscid case but the equation is still conformally invariant on the associated characteristic with zero-vorticity. Then, we demonstrate that this characteristic is conformally transformed. We find this outcome coincides with the numerical results about the conformal invariance of the statistics of zero-vorticity isolines, see e.g. Falkovich (2007 Russian Math. Surv. 63 497-510). The conformal symmetry can be understood as a ‘local scaling’ and its traces in two-dimensional turbulence were already discussed in the literature, i.e. it was conjectured more than twenty years ago in Polyakov (1993 Nucl. Phys. B 396 367-85) and clearly validated experimentally in Bernard et al (2006 Nat. Phys. 2 124-8).

Constrained multibody system dynamics: An automated approach

NASA Technical Reports Server (NTRS)

Kamman, J. W.; Huston, R. L.

1982-01-01

The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. The closed loop problem of multibody chain systems is addressed. The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. The modifications is based upon a solution of the constraint equations obtained through a zero eigenvalues theorem, is a contraction of the dynamical equations. For a system with n-generalized coordinates and m-constraint equations, the coefficients in the constraint equations may be viewed as constraint vectors in n-dimensional space. In this setting the system itself is free to move in the n-m directions which are orthogonal to the constraint vectors.

Traveling-wave solutions in continuous chains of unidirectionally coupled oscillators

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Kolesov, A. Yu; Rozov, N. Kh

2017-12-01

Proposed is a mathematical model of a continuous annular chain of unidirectionally coupled generators given by certain nonlinear advection-type hyperbolic boundary value problem. Such problems are constructed by a limit transition from annular chains of unidirectionally coupled ordinary differential equations with an unbounded increase in the number of links. It is shown that any preassigned finite number of stable periodic motions of the traveling-wave type can coexist in the model.

Flux-vector splitting algorithm for chain-rule conservation-law form

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Nguyen, H. L.; Willis, E. A.; Steinthorsson, E.; Li, Z.

1991-01-01

A flux-vector splitting algorithm with Newton-Raphson iteration was developed for the 'full compressible' Navier-Stokes equations cast in chain-rule conservation-law form. The algorithm is intended for problems with deforming spatial domains and for problems whose governing equations cannot be cast in strong conservation-law form. The usefulness of the algorithm for such problems was demonstrated by applying it to analyze the unsteady, two- and three-dimensional flows inside one combustion chamber of a Wankel engine under nonfiring conditions. Solutions were obtained to examine the algorithm in terms of conservation error, robustness, and ability to handle complex flows on time-dependent grid systems.

Nonlinear dispersive waves in repulsive lattices

NASA Astrophysics Data System (ADS)

Mehrem, A.; Jiménez, N.; Salmerón-Contreras, L. J.; García-Andrés, X.; García-Raffi, L. M.; Picó, R.; Sánchez-Morcillo, V. J.

2017-07-01

The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting of an array of coupled magnetic dipoles. By driving harmonically the lattice at one boundary, we excite propagating waves and demonstrate different regimes of mode conversion into higher harmonics, strongly influenced by dispersion and discreteness. The phenomenon of acoustic dilatation of the chain is also predicted and discussed. The results are compared with the theoretical predictions of the α -Fermi-Pasta-Ulam equation, describing a chain of masses connected by nonlinear quadratic springs and numerical simulations. The results can be extrapolated to other systems described by this equation.

Thermodynamic perturbation theory for fused sphere hard chain fluids using nonadditive interactions

NASA Astrophysics Data System (ADS)

Abu-Sharkh, Basel F.; Sunaidi, Abdallah; Hamad, Esam Z.

2004-03-01

A model is developed for the equation of state of fused chains based on Wertheim thermodynamic perturbation theory and nonadditive size interactions. The model also assumes that the structure (represented by the radial distribution function) of the fused chain fluid is the same as that of the touching hard sphere chain fluid. The model is completely based on spherical additive and nonadditive size interactions. The model has the advantage of offering good agreement with simulation data while at the same time being independent of fitted parameters. The model is most accurate for short chains, small values of Δ (slightly fused spheres) and at intermediate (liquidlike) densities.

Polymer dynamics in turbulent flow

NASA Astrophysics Data System (ADS)

Muthukumar, Murugappan

2014-03-01

Presence of dilute amounts of high-molecular weight polymers in liquids undergoing turbulent wall-bounded shear flows leads to significant drag reduction. There are two major proposed mechanisms of drag reduction in the literature. One is based on enhanced viscosity due to chain extension; the other is based on the assumption that elastic energy stored in polymer conformations is comparable to the kinetic energy in some eddies. Using the Navier-Stokes equation for the fluid and the Kirkwood-Riseman-Zimm equation for polymer chains, we have addressed the coupling between the near-wall turbulence dynamics and polymer dynamics. Our theoretical results show that the torque associated with polymer conformations contributes more significantly than the chain stretching and that the characteristic dimensions of polymer coils are much smaller than eddy sizes required for possible exchange of energy. We thus emphasize an additional mechanism to the existing two schools of thought in the search of an understanding of drag reduction.

Doubly self-consistent field theory of grafted polymers under simple shear in steady state

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

Suo, Tongchuan; Whitmore, Mark D., E-mail: mark-whitmore@umanitoba.ca

2014-03-21

We present a generalization of the numerical self-consistent mean-field theory of polymers to the case of grafted polymers under simple shear. The general theoretical framework is presented, and then applied to three different chain models: rods, Gaussian chains, and finitely extensible nonlinear elastic (FENE) chains. The approach is self-consistent at two levels. First, for any flow field, the polymer density profile and effective potential are calculated self-consistently in a manner similar to the usual self-consistent field theory of polymers, except that the calculation is inherently two-dimensional even for a laterally homogeneous system. Second, through the use of a modified Brinkmanmore » equation, the flow field and the polymer profile are made self-consistent with respect to each other. For all chain models, we find that reasonable levels of shear cause the chains to tilt, but it has very little effect on the overall thickness of the polymer layer, causing a small decrease for rods, and an increase of no more than a few percent for the Gaussian and FENE chains. Using the FENE model, we also probe the individual bond lengths, bond correlations, and bond angles along the chains, the effects of the shear on them, and the solvent and bonded stress profiles. We find that the approximations needed within the theory for the Brinkman equation affect the bonded stress, but none of the other quantities.« less

Recursive thoughts on the simulation of the flexible multibody dynamics of slender offshore structures

NASA Astrophysics Data System (ADS)

Schilder, J.; Ellenbroek, M.; de Boer, A.

2017-12-01

In this work, the floating frame of reference formulation is used to create a flexible multibody model of slender offshore structures such as pipelines and risers. It is shown that due to the chain-like topology of the considered structures, the equation of motion can be expressed in terms of absolute interface coordinates. In the presented form, kinematic constraint equations are satisfied explicitly and the Lagrange multipliers are eliminated from the equations. Hence, the structures can be conveniently coupled to finite element or multibody models of for example seabed and vessel. The chain-like topology enables the efficient use of recursive solution procedures for both transient dynamic analysis and equilibrium analysis. For this, the transfer matrix method is used. In order to improve the convergence of the equilibrium analysis, the analytical solution of an ideal catenary is used as an initial configuration, reducing the number of required iterations.

A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space

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

Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel

2006-01-15

Given a discrete-time Markov chain with finite state space and a stationary transition matrix, a system of 'local' Poisson equations characterizing the (exponential) Varadhan's functional J(.) is given. The main results, which are derived for an arbitrary transition structure so that J(.) may be nonconstant, are as follows: (i) Any solution to the local Poisson equations immediately renders Varadhan's functional, and (ii) a solution of the system always exist. The proof of this latter result is constructive and suggests a method to solve the local Poisson equations.

Twisting singular solutions of Betheʼs equations

NASA Astrophysics Data System (ADS)

Nepomechie, Rafael I.; Wang, Chunguang

2014-12-01

The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.

Efficient quantum state transfer in an engineered chain of quantum bits

NASA Astrophysics Data System (ADS)

Sandberg, Martin; Knill, Emanuel; Kapit, Eliot; Vissers, Michael R.; Pappas, David P.

2016-03-01

We present a method of performing quantum state transfer in a chain of superconducting quantum bits. Our protocol is based on engineering the energy levels of the qubits in the chain and tuning them all simultaneously with an external flux bias. The system is designed to allow sequential adiabatic state transfers, resulting in on-demand quantum state transfer from one end of the chain to the other. Numerical simulations of the master equation using realistic parameters for capacitive nearest-neighbor coupling, energy relaxation, and dephasing show that fast, high-fidelity state transfer should be feasible using this method.

Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range. Part 1: constitutive equations

NASA Astrophysics Data System (ADS)

Kari, Leif

2017-09-01

The constitutive equations of chemically and physically ageing rubber in the audible frequency range are modelled as a function of ageing temperature, ageing time, actual temperature, time and frequency. The constitutive equations are derived by assuming nearly incompressible material with elastic spherical response and viscoelastic deviatoric response, using Mittag-Leffler relaxation function of fractional derivative type, the main advantage being the minimum material parameters needed to successfully fit experimental data over a broad frequency range. The material is furthermore assumed essentially entropic and thermo-mechanically simple while using a modified William-Landel-Ferry shift function to take into account temperature dependence and physical ageing, with fractional free volume evolution modelled by a nonlinear, fractional differential equation with relaxation time identical to that of the stress response and related to the fractional free volume by Doolittle equation. Physical ageing is a reversible ageing process, including trapping and freeing of polymer chain ends, polymer chain reorganizations and free volume changes. In contrast, chemical ageing is an irreversible process, mainly attributed to oxygen reaction with polymer network either damaging the network by scission or reformation of new polymer links. The chemical ageing is modelled by inner variables that are determined by inner fractional evolution equations. Finally, the model parameters are fitted to measurements results of natural rubber over a broad audible frequency range, and various parameter studies are performed including comparison with results obtained by ordinary, non-fractional ageing evolution differential equations.

Shadowing of non-transversal heteroclinic chains

NASA Astrophysics Data System (ADS)

Delshams, Amadeu; Simon, Adrià; Zgliczyński, Piotr

2018-03-01

We present a new result about the shadowing of non-transversal chain of heteroclinic connections based on the idea of dropping dimensions. We illustrate this new mechanism with several examples. As an application we discuss this mechanism in a simplification of a toy model system derived by Colliander et al. in the context of cubic defocusing nonlinear Schrödinger equation.

A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis

ERIC Educational Resources Information Center

Edwards, Michael C.

2010-01-01

Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show…

Pseudo Bayes Estimates for Test Score Distributions and Chained Equipercentile Equating. Research Report. ETS RR-09-47

ERIC Educational Resources Information Center

Moses, Tim; Oh, Hyeonjoo J.

2009-01-01

Pseudo Bayes probability estimates are weighted averages of raw and modeled probabilities; these estimates have been studied primarily in nonpsychometric contexts. The purpose of this study was to evaluate pseudo Bayes probability estimates as applied to the estimation of psychometric test score distributions and chained equipercentile equating…

Buffering effect in continuous chains of unidirectionally coupled generators

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Kolesov, A. Yu.; Rozov, N. Kh.

2014-11-01

We propose a mathematical model of a continuous annular chain of unidirectionally coupled generators given by some nonlinear advection-type hyperbolic boundary value problem. Such problems are constructed by a limit transition from annular chains of unidirectionally coupled ordinary differential equations with an unbounded increase in the number of links. We find that a certain buffering phenomenon is realized in our boundary value problem. Namely, we show that any preassigned finite number of stable periodic motions of the traveling-wave type can coexist in the model.

Translocation time of a polymer chain through an energy gradient nanopore

NASA Astrophysics Data System (ADS)

Luo, Meng-Bo; Zhang, Shuang; Wu, Fan; Sun, Li-Zhen

2017-06-01

The translocation time of a polymer chain through an interaction energy gradient nanopore was studied by Monte Carlo simulations and the Fokker-Planck equation with double-absorbing boundary conditions. Both the simulation and calculation revealed three different behaviors for polymer translocation. These behaviors can be explained qualitatively from free-energy landscapes obtained for polymer translocation at different parameters. Results show that the translocation time of a polymer chain through a nanopore can be tuned by suitably designing the interaction energy gradient.

Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

NASA Astrophysics Data System (ADS)

Cirilo António, N.; Manojlović, N.; Salom, I.

2014-12-01

We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.

Non-recursive augmented Lagrangian algorithms for the forward and inverse dynamics of constrained flexible multibodies

NASA Technical Reports Server (NTRS)

Bayo, Eduardo; Ledesma, Ragnar

1993-01-01

A technique is presented for solving the inverse dynamics of flexible planar multibody systems. This technique yields the non-causal joint efforts (inverse dynamics) as well as the internal states (inverse kinematics) that produce a prescribed nominal trajectory of the end effector. A non-recursive global Lagrangian approach is used in formulating the equations for motion as well as in solving the inverse dynamics equations. Contrary to the recursive method previously presented, the proposed method solves the inverse problem in a systematic and direct manner for both open-chain as well as closed-chain configurations. Numerical simulation shows that the proposed procedure provides an excellent tracking of the desired end effector trajectory.

Quantum criticality and duality in the Sachdev-Ye-Kitaev/AdS2 chain

NASA Astrophysics Data System (ADS)

Jian, Shao-Kai; Xian, Zhuo-Yu; Yao, Hong

2018-05-01

We show that the quantum critical point (QCP) between a diffusive metal and ferromagnetic (or antiferromagnetic) phases in the SYK chain has a gravitational description corresponding to the double-trace deformation in an AdS2 chain. Specifically, by studying a double-trace deformation of a Z2 scalar in an AdS2 chain where the Z2 scalar is dual to the order parameter in the SYK chain, we find that the susceptibility and renormalization group equation describing the QCP in the SYK chain can be exactly reproduced in the holographic model. Our results suggest that the infrared geometry in the gravity theory dual to the diffusive metal of the SYK chain is also an AdS2 chain. We further show that the transition in SYK model captures universal information about double-trace deformation in generic black holes with near horizon AdS2 space-time.

Kinks, loops, and protein folding, with protein A as an example

PubMed Central

Krokhotin, Andrey; Liwo, Adam; Maisuradze, Gia G.; Niemi, Antti J.; Scheraga, Harold A.

2014-01-01

The dynamics and energetics of formation of loops in the 46-residue N-terminal fragment of the B-domain of staphylococcal protein A has been studied. Numerical simulations have been performed using coarse-grained molecular dynamics with the united-residue (UNRES) force field. The results have been analyzed in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrödinger (DNLS) equation. In the case of proteins, the DNLS equation arises from a Cα-trace-based energy function. Three individual kink profiles were identified in the experimental three-α-helix structure of protein A, in the range of the Glu16-Asn29, Leu20-Asn29, and Gln33-Asn44 residues, respectively; these correspond to two loops in the native structure. UNRES simulations were started from the full right-handed α-helix to obtain a clear picture of kink formation, which would otherwise be blurred by helix formation. All three kinks emerged during coarse-grained simulations. It was found that the formation of each is accompanied by a local free energy increase; this is expressed as the change of UNRES energy which has the physical sense of the potential of mean force of a polypeptide chain. The increase is about 7 kcal/mol. This value can thus be considered as the free energy barrier to kink formation in full α-helical segments of polypeptide chains. During the simulations, the kinks emerge, disappear, propagate, and annihilate each other many times. It was found that the formation of a kink is initiated by an abrupt change in the orientation of a pair of consecutive side chains in the loop region. This resembles the formation of a Bloch wall along a spin chain, where the Cα backbone corresponds to the chain, and the amino acid side chains are interpreted as the spin variables. This observation suggests that nearest-neighbor side chain–side chain interactions are responsible for initiation of loop formation. It was also found that the individual kinks are reflected as clear peaks in the principal modes of the analyzed trajectory of protein A, the shapes of which resemble the directional derivatives of the kinks along the chain. These observations suggest that the kinks of the DNLS equation determine the functionally important motions of proteins. PMID:24437917

ℤ3 parafermionic chain emerging from Yang-Baxter equation.

PubMed

Yu, Li-Wei; Ge, Mo-Lin

2016-02-23

We construct the 1D ℤ3 parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the ℤ3 parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the ℤ3 parafermionic model is a direct generalization of 1D ℤ2 Kitaev model. Both the ℤ2 and ℤ3 model can be obtained from Yang-Baxter equation. On the other hand, to show the algebra of parafermionic tripling intuitively, we define a new 3-body Hamiltonian H123 based on Yang-Baxter equation. Different from the Majorana doubling, the H123 holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, ω-parity P [formula in text] and emergent parafermionic operator Γ, which are the generalizations of parity PM and emergent Majorana operator in Lee-Wilczek model, respectively. Both the ℤ3 parafermionic model and H123 can be viewed as SU(3) models in color space. In comparison with the Majorana models for SU(2), it turns out that the SU(3) models are truly the generalization of Majorana models resultant from Yang-Baxter equation.

Rotational waves in geodynamics

NASA Astrophysics Data System (ADS)

Gerus, Artyom; Vikulin, Alexander

2015-04-01

The rotation model of a geoblock with intrinsic momentum was constructed by A.V. Vikulin and A.G. Ivanchin [9, 10] to describe seismicity within the Pacific Ocean margin. It is based on the idea of a rotational motion of geoblocks as the parts of the rotating body of the Earth that generates rotary deformation waves. The law of the block motion was derived in the form of the sine-Gordon equation (SG) [5, 9]; the dimensionless form of the equation is: δ2θ δ2θ δξ2 - δη2 = sinθ, (1) where θ = β/2, ξ = k0z and η = v0k0t are dimensionless coordinates, z - length of the chain of masses (blocks), t - time, β - turn angle, ν0 - representative velocity of the process, k0 - wave number. Another case analyzed was a chain of nonuniformly rotating blocks, with deviation of force moments from equilibrium positions μ, considering friction forces α along boundaries, which better matched a real-life seismic process. As a result, the authors obtained the law of motion for a block in a chain in the form of the modified SG equation [8]: δ2θ δ2θ δθ- δξ2 - δ η2 = sin θ+ α δη + μδ(ξ)sin θ (2)

Hierarchical imputation of systematically and sporadically missing data: An approximate Bayesian approach using chained equations.

PubMed

Jolani, Shahab

2018-03-01

In health and medical sciences, multiple imputation (MI) is now becoming popular to obtain valid inferences in the presence of missing data. However, MI of clustered data such as multicenter studies and individual participant data meta-analysis requires advanced imputation routines that preserve the hierarchical structure of data. In clustered data, a specific challenge is the presence of systematically missing data, when a variable is completely missing in some clusters, and sporadically missing data, when it is partly missing in some clusters. Unfortunately, little is known about how to perform MI when both types of missing data occur simultaneously. We develop a new class of hierarchical imputation approach based on chained equations methodology that simultaneously imputes systematically and sporadically missing data while allowing for arbitrary patterns of missingness among them. Here, we use a random effect imputation model and adopt a simplification over fully Bayesian techniques such as Gibbs sampler to directly obtain draws of parameters within each step of the chained equations. We justify through theoretical arguments and extensive simulation studies that the proposed imputation methodology has good statistical properties in terms of bias and coverage rates of parameter estimates. An illustration is given in a case study with eight individual participant datasets. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Standard Error Estimation of 3PL IRT True Score Equating with an MCMC Method

ERIC Educational Resources Information Center

Liu, Yuming; Schulz, E. Matthew; Yu, Lei

2008-01-01

A Markov chain Monte Carlo (MCMC) method and a bootstrap method were compared in the estimation of standard errors of item response theory (IRT) true score equating. Three test form relationships were examined: parallel, tau-equivalent, and congeneric. Data were simulated based on Reading Comprehension and Vocabulary tests of the Iowa Tests of…

Statistical mechanics of Fermi-Pasta-Ulam chains with the canonical ensemble

NASA Astrophysics Data System (ADS)

Demirel, Melik C.; Sayar, Mehmet; Atılgan, Ali R.

1997-03-01

Low-energy vibrations of a Fermi-Pasta-Ulam-Β (FPU-Β) chain with 16 repeat units are analyzed with the aid of numerical experiments and the statistical mechanics equations of the canonical ensemble. Constant temperature numerical integrations are performed by employing the cubic coupling scheme of Kusnezov et al. [Ann. Phys. 204, 155 (1990)]. Very good agreement is obtained between numerical results and theoretical predictions for the probability distributions of the generalized coordinates and momenta both of the chain and of the thermal bath. It is also shown that the average energy of the chain scales linearly with the bath temperature.

Gaussian solitary waves and compactons in Fermi–Pasta–Ulam lattices with Hertzian potentials

PubMed Central

James, Guillaume; Pelinovsky, Dmitry

2014-01-01

We consider a class of fully nonlinear Fermi–Pasta–Ulam (FPU) lattices, consisting of a chain of particles coupled by fractional power nonlinearities of order α>1. This class of systems incorporates a classical Hertzian model describing acoustic wave propagation in chains of touching beads in the absence of precompression. We analyse the propagation of localized waves when α is close to unity. Solutions varying slowly in space and time are searched with an appropriate scaling, and two asymptotic models of the chain of particles are derived consistently. The first one is a logarithmic Korteweg–de Vries (KdV) equation and possesses linearly orbitally stable Gaussian solitary wave solutions. The second model consists of a generalized KdV equation with Hölder-continuous fractional power nonlinearity and admits compacton solutions, i.e. solitary waves with compact support. When , we numerically establish the asymptotically Gaussian shape of exact FPU solitary waves with near-sonic speed and analytically check the pointwise convergence of compactons towards the limiting Gaussian profile. PMID:24808748

Imidazoline phosphonic acids

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

Redmore, D.

1972-07-04

Nitrogen-heterocyclic phosphonic acids and derivatives are characterized by aminomethyl (or substituted methyl) phosphonic acids or derivatives thereof bonded directly or indirectly, i.e., through a N-side chain to the nitrogen atom in the heterocyclic ring, for example those containing in the molecule at least one of the following units: ..pi..Equation/sup -/ where represents a heterocyclic ring having a nitrogen atom on the ring; -R'N- represents an amino- terminated side chain attached directly to the ring nitrogen (which side chain may or may not be present); and ..pi..Equation/sup -/ represents a methyl (or substituted methyl) phosphonic acid group where M is hydrogen,more » an alcohol or a salt moiety, and X and Y are hydrogen or a substituted group such as alkyl, aryl, etc., of which one or 2 units may be present depending on the available nitrogen bonded by hydrogens, and to uses for these compounds, for example, as scale inhibitors, corrosion inhibitors, etc. (5 claims)« less

Characterizing traveling-wave collisions in granular chains starting from integrable limits: the case of the Korteweg-de Vries equation and the Toda lattice.

PubMed

Shen, Y; Kevrekidis, P G; Sen, S; Hoffman, A

2014-08-01

Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To that effect, we aim to quantify approximations of the relevant Hertzian FPU-type lattice through both the Korteweg-de Vries (KdV) equation and the Toda lattice. Using the availability in such settings of both one-soliton and two-soliton solutions in explicit analytical form, we initialize such coherent structures in the granular chain and observe the proximity of the resulting evolution to the underlying integrable (KdV or Toda) model. While the KdV offers the possibility to accurately capture collisions of solitary waves propagating in the same direction, the Toda lattice enables capturing both copropagating and counterpropagating soliton collisions. The error in the approximation is quantified numerically and connections to bounds established in the mathematical literature are also given.

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations

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

Dascaliuc, Radu; Thomann, Enrique; Waymire, Edward C., E-mail: waymire@math.oregonstate.edu

2015-07-15

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturallymore » arise as a result of this investigation.« less

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations.

PubMed

Dascaliuc, Radu; Michalowski, Nicholas; Thomann, Enrique; Waymire, Edward C

2015-07-01

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.

Applications of IBSOM and ETEM for solving the nonlinear chains of atoms with long-range interactions

NASA Astrophysics Data System (ADS)

Foroutan, Mohammadreza; Zamanpour, Isa; Manafian, Jalil

2017-10-01

This paper presents a number of new solutions obtained for solving a complex nonlinear equation describing dynamics of nonlinear chains of atoms via the improved Bernoulli sub-ODE method (IBSOM) and the extended trial equation method (ETEM). The proposed solutions are kink solitons, anti-kink solitons, soliton solutions, hyperbolic solutions, trigonometric solutions, and bellshaped soliton solutions. Then our new results are compared with the well-known results. The methods used here are very simple and succinct and can be also applied to other nonlinear models. The balance number of these methods is not constant contrary to other methods. The proposed methods also allow us to establish many new types of exact solutions. By utilizing the Maple software package, we show that all obtained solutions satisfy the conditions of the studied model. More importantly, the solutions found in this work can have significant applications in Hamilton's equations and generalized momentum where solitons are used for long-range interactions.

Paramagnetic particles and mixing in micro-scale flows.

PubMed

Calhoun, R; Yadav, A; Phelan, P; Vuppu, A; Garcia, A; Hayes, M

2006-02-01

Mixing in microscale flows with rotating chains of paramagnetic particles can be enhanced by adjusting the ratio of viscous to magnetic forces so that chains dynamically break and reform. Lattice Boltzmann (LB) simulations were used to calculate the interaction between the fluid and suspended paramagnetic particles under the influence of a rotating magnetic field. Fluid velocities obtained from the LB simulations are used to solve the advection diffusion equation for massless tracer particles. At relatively high Mason numbers, small chains result in low edge velocities, and hence mixing is slower than at other Mason numbers. At low Mason numbers, long, stable chains form and produce little mixing toward the center of the chains. A peak in mixing rate is observed when chains break and reform. The uniformity of mixing is greater at higher Mason numbers because more small chains result in a larger number of small mixing areas.

Analysis of scattering by a linear chain of spherical inclusions in an optical fiber

NASA Astrophysics Data System (ADS)

Chremmos, Ioannis D.; Uzunoglu, Nikolaos K.

2006-12-01

The scattering by a linear chain of spherical dielectric inclusions, embedded along the axis of an optical fiber, is analyzed using a rigorous integral equation formulation, based on the dyadic Green's function theory. The coupled electric field integral equations are solved by applying the Galerkin technique with Mie-type expansion of the field inside the spheres in terms of spherical waves. The analysis extends the previously studied case of a single spherical inhomogeneity inside a fiber to the multisphere-scattering case, by utilizing the classic translational addition theorems for spherical waves in order to analytically extract the direct-intersphere-coupling coefficients. Results for the transmitted and reflected power, on incidence of the fundamental HE11 mode, are presented for several cases.

Modeling qRT-PCR dynamics with application to cancer biomarker quantification.

PubMed

Chervoneva, Inna; Freydin, Boris; Hyslop, Terry; Waldman, Scott A

2017-01-01

Quantitative reverse transcription polymerase chain reaction (qRT-PCR) is widely used for molecular diagnostics and evaluating prognosis in cancer. The utility of mRNA expression biomarkers relies heavily on the accuracy and precision of quantification, which is still challenging for low abundance transcripts. The critical step for quantification is accurate estimation of efficiency needed for computing a relative qRT-PCR expression. We propose a new approach to estimating qRT-PCR efficiency based on modeling dynamics of polymerase chain reaction amplification. In contrast, only models for fluorescence intensity as a function of polymerase chain reaction cycle have been used so far for quantification. The dynamics of qRT-PCR efficiency is modeled using an ordinary differential equation model, and the fitted ordinary differential equation model is used to obtain effective polymerase chain reaction efficiency estimates needed for efficiency-adjusted quantification. The proposed new qRT-PCR efficiency estimates were used to quantify GUCY2C (Guanylate Cyclase 2C) mRNA expression in the blood of colorectal cancer patients. Time to recurrence and GUCY2C expression ratios were analyzed in a joint model for survival and longitudinal outcomes. The joint model with GUCY2C quantified using the proposed polymerase chain reaction efficiency estimates provided clinically meaningful results for association between time to recurrence and longitudinal trends in GUCY2C expression.

Thermal diffusion of Boussinesq solitons.

PubMed

Arévalo, Edward; Mertens, Franz G

2007-10-01

We consider the problem of the soliton dynamics in the presence of an external noisy force for the Boussinesq type equations. A set of ordinary differential equations (ODEs) of the relevant coordinates of the system is derived. We show that for the improved Boussinesq (IBq) equation the set of ODEs has limiting cases leading to a set of ODEs which can be directly derived either from the ill-posed Boussinesq equation or from the Korteweg-de Vries (KdV) equation. The case of a soliton propagating in the presence of damping and thermal noise is considered for the IBq equation. A good agreement between theory and simulations is observed showing the strong robustness of these excitations. The results obtained here generalize previous results obtained in the frame of the KdV equation for lattice solitons in the monatomic chain of atoms.

An analytical equation of state for describing isotropic-nematic phase equilibria of Lennard-Jones chain fluids with variable degree of molecular flexibility

NASA Astrophysics Data System (ADS)

van Westen, Thijs; Oyarzún, Bernardo; Vlugt, Thijs J. H.; Gross, Joachim

2015-06-01

We develop an equation of state (EoS) for describing isotropic-nematic (IN) phase equilibria of Lennard-Jones (LJ) chain fluids. The EoS is developed by applying a second order Barker-Henderson perturbation theory to a reference fluid of hard chain molecules. The chain molecules consist of tangentially bonded spherical segments and are allowed to be fully flexible, partially flexible (rod-coil), or rigid linear. The hard-chain reference contribution to the EoS is obtained from a Vega-Lago rescaled Onsager theory. For the description of the (attractive) dispersion interactions between molecules, we adopt a segment-segment approach. We show that the perturbation contribution for describing these interactions can be divided into an "isotropic" part, which depends only implicitly on orientational ordering of molecules (through density), and an "anisotropic" part, for which an explicit dependence on orientational ordering is included (through an expansion in the nematic order parameter). The perturbation theory is used to study the effect of chain length, molecular flexibility, and attractive interactions on IN phase equilibria of pure LJ chain fluids. Theoretical results for the IN phase equilibrium of rigid linear LJ 10-mers are compared to results obtained from Monte Carlo simulations in the isobaric-isothermal (NPT) ensemble, and an expanded formulation of the Gibbs-ensemble. Our results show that the anisotropic contribution to the dispersion attractions is irrelevant for LJ chain fluids. Using the isotropic (density-dependent) contribution only (i.e., using a zeroth order expansion of the attractive Helmholtz energy contribution in the nematic order parameter), excellent agreement between theory and simulations is observed. These results suggest that an EoS contribution for describing the attractive part of the dispersion interactions in real LCs can be obtained from conventional theoretical approaches designed for isotropic fluids, such as a Perturbed-Chain Statistical Associating Fluid Theory approach.

Network Polymers Formed Under Nonideal Conditions.

DTIC Science & Technology

1986-12-01

the system or the limited ability of the statistical model to account for stochastic correlations. The viscosity of the reacting system was measured as...based on competing reactions (ring, chain) and employs equilibrium chain statistics . The work thus far has been limited to single cycle growth on an...polymerizations, because a large number of differential equations must be solved. The Makovian approach (sometimes referred to as the statistical or

Chaotic dynamics of Heisenberg ferromagnetic spin chain with bilinear and biquadratic interactions

NASA Astrophysics Data System (ADS)

Blessy, B. S. Gnana; Latha, M. M.

2017-10-01

We investigate the chaotic dynamics of one dimensional Heisenberg ferromagnetic spin chain by constructing the Hamiltonian equations of motion. We present the trajectory and phase plots of the system with bilinear and also biquadratic interactions. The stability of the system is analysed in both cases by constructing the Jacobian matrix and by measuring the Lyapunov exponents. The results are illustrated graphically.

Classical integrable defects as quasi Bäcklund transformations

NASA Astrophysics Data System (ADS)

Doikou, Anastasia

2016-10-01

We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the ;equations of motion; on the defect point via the space-like and time-like description. We then exploit the structural similarity of these equations with the discrete and continuous Bäcklund transformations. And although these equations are similar they are not exactly the same to the Bäcklund transformations. We also consider specific examples of integrable models to demonstrate our construction, i.e. the Toda chain and the sine-Gordon model. The equations of the time (space) evolution of the defect (discontinuity) degrees of freedom for these models are explicitly derived.

Modeling of Nonlinear Hydrodynamics of the Coastal Areas of the Black Sea by the Chain of the Proprietary and Open Source Models

NASA Astrophysics Data System (ADS)

Kantardgi, Igor; Zheleznyak, Mark; Demchenko, Raisa; Dykyi, Pavlo; Kivva, Sergei; Kolomiets, Pavlo; Sorokin, Maxim

2014-05-01

The nearshore hydrodynamic fields are produced by the nonlinear interactions of the shoaling waves of different time scales and currents. To simulate the wind wave and swells propagated to the coasts, wave generated near shore currents, nonlinear-dispersive wave transformation and wave diffraction in interaction with coastal and port structure, sediment transport and coastal erosion the chains of the models should be used. The objective of this presentation is to provide an overview of the results of the application of the model chains for the assessment of the wave impacts on new construction designed at the Black Sea coasts and the impacts of these constructions on the coastal erosion/ accretion processes to demonstrate needs for further development of the nonlinear models for the coastal engineering applications. The open source models Wave Watch III and SWAN has been used to simulate wave statistics of the dedicated areas of the Black Sea in high resolution to calculated the statistical parameters of the extreme wave approaching coastal zone construction in accordance with coastal engineering standards. As the main tool for the costal hydrodynamic simulations the modeling system COASTOX-MORPHO has been used, that includes the following models. HWAVE -code based on hyperbolic version of mild slope equations., HWAVE-S - spectral version of HWAVE., BOUSS-FNL - fully nonlinear system of Boussinesq equations for simulation wave nonlinear -dispersive wave transformation in coastal areas. COASTOX-CUR - the code provided the numerical solution of the Nonlinear Shallow Water Equations (NLSWE) by finite-volume methods on the unstructured grid describing the long wave transformation in the coastal zone with the efficient drying -wetting algorithms to simulate the inundation of the coastal areas including tsunami wave runup. Coastox -Cur equations with the radiation stress term calculated via near shore wave fields simulate the wave generated nearhore currents. COASTOX-SED - the module of the simulation of the sediment transport in which the suspended sediments are simulated on the basis of the solution of 2-D advection -diffusion equation and the bottom sediment transport calculations are provided the basis of a library of the most popular semi-empirical formulas. MORPH - the module of the simulation of the morphological transformation of coastal zone based on the mass balance equation, on the basis of the sediment fluxes, calculated in the SED module. MORPH management submodel is responsible for the execution of the model chain "waves- current- sediments - morphodynamics- waves". The open source model SWASH has been used to simulate nonlinear resonance phenomena in coastal waters. The model chain was applied to simulate the potential impact of the designed shore protection structures at the Sochi Olympic Park on coastal morphodynamics, the wave parameters and nonlinear oscillations in the new ports designed in Gelenddjik and Taman at North-East coast of the Black Sea. The modeling results are compared with the results of the physical modeling in the hydraulic flumes of Moscow University of Civil Engineering.

Solitons riding on solitons and the quantum Newton's cradle.

PubMed

Ma, Manjun; Navarro, R; Carretero-González, R

2016-02-01

The reduced dynamics for dark and bright soliton chains in the one-dimensional nonlinear Schrödinger equation is used to study the behavior of collective compression waves corresponding to Toda lattice solitons. We coin the term hypersoliton to describe such solitary waves riding on a chain of solitons. It is observed that in the case of dark soliton chains, the formulated reduction dynamics provides an accurate an robust evolution of traveling hypersolitons. As an application to Bose-Einstein condensates trapped in a standard harmonic potential, we study the case of a finite dark soliton chain confined at the center of the trap. When the central chain is hit by a dark soliton, the energy is transferred through the chain as a hypersoliton that, in turn, ejects a dark soliton on the other end of the chain that, as it returns from its excursion up the trap, hits the central chain repeating the process. This periodic evolution is an analog of the classical Newton's cradle.

Solution of the Lindblad equation for spin helix states.

PubMed

Popkov, V; Schütz, G M

2017-04-01

Using Lindblad dynamics we study quantum spin systems with dissipative boundary dynamics that generate a stationary nonequilibrium state with a nonvanishing spin current that is locally conserved except at the boundaries. We demonstrate that with suitably chosen boundary target states one can solve the many-body Lindblad equation exactly in any dimension. As solution we obtain pure states at any finite value of the dissipation strength and any system size. They are characterized by a helical stationary magnetization profile and a ballistic spin current which is independent of system size, even when the quantum spin system is not integrable. These results are derived in explicit form for the one-dimensional spin-1/2 Heisenberg chain and its higher-spin generalizations, which include the integrable spin-1 Zamolodchikov-Fateev model and the biquadratic Heisenberg chain.

Quantum integrability and functional equations

NASA Astrophysics Data System (ADS)

Volin, Dmytro

2010-03-01

In this thesis a general procedure to represent the integral Bethe Ansatz equations in the form of the Reimann-Hilbert problem is given. This allows us to study in simple way integrable spin chains in the thermodynamic limit. Based on the functional equations we give the procedure that allows finding the subleading orders in the solution of various integral equations solved to the leading order by the Wiener-Hopf technics. The integral equations are studied in the context of the AdS/CFT correspondence, where their solution allows verification of the integrability conjecture up to two loops of the strong coupling expansion. In the context of the two-dimensional sigma models we analyze the large-order behavior of the asymptotic perturbative expansion. Obtained experience with the functional representation of the integral equations allowed us also to solve explicitly the crossing equations that appear in the AdS/CFT spectral problem.

The fifth-order partial differential equation for the description of the α + β Fermi-Pasta-Ulam model

NASA Astrophysics Data System (ADS)

Kudryashov, Nikolay A.; Volkov, Alexandr K.

2017-01-01

We study a new nonlinear partial differential equation of the fifth order for the description of perturbations in the Fermi-Pasta-Ulam mass chain. This fifth-order equation is an expansion of the Gardner equation for the description of the Fermi-Pasta-Ulam model. We use the potential of interaction between neighbouring masses with both quadratic and cubic terms. The equation is derived using the continuous limit. Unlike the previous works, we take into account higher order terms in the Taylor series expansions. We investigate the equation using the Painlevé approach. We show that the equation does not pass the Painlevé test and can not be integrated by the inverse scattering transform. We use the logistic function method and the Laurent expansion method to find travelling wave solutions of the fifth-order equation. We use the pseudospectral method for the numerical simulation of wave processes, described by the equation.

Geometry and combinatorics of Julia sets of real quadratic maps

NASA Astrophysics Data System (ADS)

Barnsley, M. F.; Geronimo, J. S.; Harrington, A. N.

1984-10-01

For real λ a correspondence is made between the Julia set B λ for z→( z- λ)2, in the hyperbolic case, and the set of λ-chains λ±√(λ±√(λ±..., with the aid of Cremer's theorem. It is shown how a number of features of Bλ can be understood in terms of λ-chains. The structure of B λ is determined by certain equivalence classes of λ-chains, fixed by orders of visitation of certain real cycles; and the bifurcation history of a given cycle can be conveniently computed via the combinatorics of λ-chains. The functional equations obeyed by attractive cycles are investigated, and their relation to λ-chains is given. The first cascade of period-doubling bifurcations is described from the point of view of the associated Julia sets and λ-chains. Certain "Julia sets" associated with the Feigenbaum function and some theorems of Lanford are discussed.

Event-chain Monte Carlo algorithms for three- and many-particle interactions

NASA Astrophysics Data System (ADS)

Harland, J.; Michel, M.; Kampmann, T. A.; Kierfeld, J.

2017-02-01

We generalize the rejection-free event-chain Monte Carlo algorithm from many-particle systems with pairwise interactions to systems with arbitrary three- or many-particle interactions. We introduce generalized lifting probabilities between particles and obtain a general set of equations for lifting probabilities, the solution of which guarantees maximal global balance. We validate the resulting three-particle event-chain Monte Carlo algorithms on three different systems by comparison with conventional local Monte Carlo simulations: i) a test system of three particles with a three-particle interaction that depends on the enclosed triangle area; ii) a hard-needle system in two dimensions, where needle interactions constitute three-particle interactions of the needle end points; iii) a semiflexible polymer chain with a bending energy, which constitutes a three-particle interaction of neighboring chain beads. The examples demonstrate that the generalization to many-particle interactions broadens the applicability of event-chain algorithms considerably.

On extinction time of a generalized endemic chain-binomial model.

PubMed

Aydogmus, Ozgur

2016-09-01

We considered a chain-binomial epidemic model not conferring immunity after infection. Mean field dynamics of the model has been analyzed and conditions for the existence of a stable endemic equilibrium are determined. The behavior of the chain-binomial process is probabilistically linked to the mean field equation. As a result of this link, we were able to show that the mean extinction time of the epidemic increases at least exponentially as the population size grows. We also present simulation results for the process to validate our analytical findings. Copyright © 2016 Elsevier Inc. All rights reserved.

Low-temperature transport in out-of-equilibrium XXZ chains

NASA Astrophysics Data System (ADS)

Bertini, Bruno; Piroli, Lorenzo

2018-03-01

We study the low-temperature transport properties of out-of-equilibrium XXZ spin-1/2 chains. We consider the protocol where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. We focus on the qualitative and quantitative features of the profiles of local observables, which at large times t and distances x from the junction become functions of the ratio \\zeta=x/t . By means of the generalized hydrodynamic equations, we analyse the rich phenomenology arising by considering different regimes of the phase diagram. In the gapped phases, variations of the profiles are found to be exponentially small in the temperatures, but described by non-trivial functions of ζ. We provide analytical formulae for the latter, which give accurate results also for small but finite temperatures. In the gapless regime, we show how the three-step conformal predictions for the profiles of energy density and energy current are naturally recovered from the hydrodynamic equations. Moreover, we also recover the recent non-linear Luttinger liquid predictions for low-temperature transport: universal peaks of width \

Radiative transfer calculated from a Markov chain formalism

NASA Technical Reports Server (NTRS)

Esposito, L. W.; House, L. L.

1978-01-01

The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.

The role of higher-order terms in perturbation approaches to the monomer and\\xA0bonding contributions in a SAFT-type equation of state for square-well chain\\xA0fluids

NASA Astrophysics Data System (ADS)

Solana, J. R.; Akhouri, B. P.

2018-07-01

A perturbation theory for square-well chain fluids is developed within the scheme of the (generalised) Wertheim thermodynamic perturbation theory. The theory is based on the Pavlyukhin parametrisations [Y. T. Pavlyukhin, J. Struct. Chem. 53, 476 (2012)] of their simulation data for the first four perturbation terms in the high temperature expansion of the Helmholtz free energy of square-well monomer fluids combined with a second-order perturbation theory for the contact value of the radial distribution function of the square-well monomer fluid that enters into bonding contribution. To obtain the latter perturbation terms, we have performed computer simulations in the hard-sphere reference system. The importance of the perturbation terms beyond the second-order one for the monomer fluid and of the approximations of different orders in the bonding contribution for the chain fluids in the predicted equation of state, excess energy and liquid-vapour coexistence densities is analysed.

Modelling Evolutionary Algorithms with Stochastic Differential Equations.

PubMed

Heredia, Jorge Pérez

2017-11-20

There has been renewed interest in modelling the behaviour of evolutionary algorithms (EAs) by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogues of the additive and multiplicative drift theorems from runtime analysis. In addition, we derive a new more general multiplicative drift theorem that also covers non-elitist EAs. This theorem simultaneously allows for positive and negative results, providing information on the algorithm's progress even when the problem cannot be optimised efficiently. Finally, we provide results for some well-known heuristics namely Random Walk (RW), Random Local Search (RLS), the (1+1) EA, the Metropolis Algorithm (MA), and the Strong Selection Weak Mutation (SSWM) algorithm.

On a numerical method for solving integro-differential equations with variable coefficients with applications in finance

NASA Astrophysics Data System (ADS)

Kudryavtsev, O.; Rodochenko, V.

2018-03-01

We propose a new general numerical method aimed to solve integro-differential equations with variable coefficients. The problem under consideration arises in finance where in the context of pricing barrier options in a wide class of stochastic volatility models with jumps. To handle the effect of the correlation between the price and the variance, we use a suitable substitution for processes. Then we construct a Markov-chain approximation for the variation process on small time intervals and apply a maturity randomization technique. The result is a system of boundary problems for integro-differential equations with constant coefficients on the line in each vertex of the chain. We solve the arising problems using a numerical Wiener-Hopf factorization method. The approximate formulae for the factors are efficiently implemented by means of the Fast Fourier Transform. Finally, we use a recurrent procedure that moves backwards in time on the variance tree. We demonstrate the convergence of the method using Monte-Carlo simulations and compare our results with the results obtained by the Wiener-Hopf method with closed-form expressions of the factors.

Supersymmetric quantum spin chains and classical integrable systems

NASA Astrophysics Data System (ADS)

Tsuboi, Zengo; Zabrodin, Anton; Zotov, Andrei

2015-05-01

For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y( gl( N| M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of generating function for the family of commuting quantum transfer matrices. Any eigenvalue of the master T-operator is the tau-function of the classical mKP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0-th time of the hierarchy. This implies a remarkable relation between the quantum supersymmetric spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, we obtain a system of algebraic equations for the spectrum of the spin chain Hamiltonians.

Asymptotic study of pulsating evolution of overdriven and CJ detonation with a chain-branching kinetics model

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

Short, Mark; Chliquete, Carlos

2011-01-20

The pulsating dynamics of gaseous detonations with a model two-step chain-branching kinetic mechanism are studied both numerically and asymptotically. The model studied here was also used in [4], [3] and [2] and mimics the attributes of some chain-branching reaction mechanisms. Specifically, the model comprises a chain-initiationlbranching zone with an Arrhenius temperature-sensitive rate behind the detonation shock where fuel is converted into chain-radical with no heat release. This is followed by a chain-termination zone having a temperature insensitive rate where the exothermic heat of reaction is released. The lengths of these two zones depend on the relative rates of each stage.more » It was determined in [4] and [3] via asymptotic and numerical analysis that the ratio of the length of the chain-branching zone to that of the chain-initation zone relative to the size of the von Neumann state scaled activation energy in the chain initiation/branching zone has a primary influence of the stability of one-dimensional pulsating instability behavior for this model. In [2], the notion of a specific stability parameter related to this ratio was proposed that determines the boundary between stable and unstable waves. In [4], a slow-time varying asymptotic study was conducted of pulsating instability of Chapman-Jouguet (CJ) detonations with the above two-step rate model, assuming a large activation energy for the chain-initiation zone and a chain-termination zone longer than the chain-initiation zone. Deviations D{sub n}{sup (1)} ({tau}) of the detonation velocity from Chapman-Jouguet were of the order of the non-dimensional activation energy. Solutions were sought for a pulsation timescale of the order of the non-dimensional activation energy times the particle transit time through the induction zone. On this time-scale, the evolution of the chain-initation zone is quasi-steady. In [4], a time-dependent non-linear evolution equation for D{sub n}{sup (1)} ({tau}) was then constructed via a perturbation procedure for cases where the ratio of the length of the chain-termination zone to chain-initiation zone was less than the non-dimensional activation energy. To leading order, the steady CJ detonation was found to be unstable; higher-order corrections lead to the construction of a stability limit between stable and unsteady pulsating solutions. One conclusion from this study is that for a stability limit to occur at leading order, the period of pulsation of the detonation must occur on the time scale of particle passage through the longer chain-termination zone, while the length of the chain-termination zone must be of order of the non-dimensional activation energy longer than the chain-initiation zone. The relevance of these suggested scalings was verified via numerical solutions of the full Euler system in [3], and formed the basis of the stability parameter criteria suggested in [2]. In the following, we formulate an asymptotic study based on these new suggested scales, studying the implications for describing pulsating behavior in gaseous chain-branching detonations. Specifically, we find that the chain-induction zone structure is the same as that studied in [4]. However, the study of unsteady evolution in the chain-termination region is now governed by a set of asymptotically derived nonlinear POEs. Equations for the linear stablity behavior of this set of POE's is obtained, while the nonlinear POEs are solved numerically using a shock-attached, shock-fitting method developed by Henrick et aJ. [1]. The results thus far show that the stability threshold calculated using the new ratio of the chain-termination zone length to that of the chain-initiation zone yields a marked improvement over [2]. Additionally, solutions will be compared with predictions obtained from the solution of the full Euler system. Finally, the evolution equation previously derived in [4] has been generalized to consider both arbitrary reaction orders and any degree of overdrive.« less

Design and Implementation of a Numerical Technique to Inform Anisotropic Hyperelastic Finite Element Models using Diffusion-Weighted Imaging

DTIC Science & Technology

2011-10-01

the deviatoric part of a tensor in the reference configuration and p = −∂Ψ ∂J is the hydrostatic pressure. Using the chain 4 rule, equation 13 can be...Kirchoff stress tensor S to the current configuration, and a scaling with the inverse of the volume ratio, transforms equation 16 to the Cauchy stress ...a characteristic of most soft tissues. Then, similar to equation 13, the second Piola-Kirchoff stress is given by: S = 2J−2/3DEV [ ∂Ψisoc ( C ) ∂C

Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory

DOE PAGES

Mendl, Christian B.; Lu, Jianfeng; Lukkarinen, Jani

2016-12-02

We perform microscopic molecular dynamics simulations of particle chains with an onsite anharmonicity to study relaxation of spatially homogeneous states to equilibrium, and directly compare the simulations with the corresponding Boltzmann-Peierls kinetic theory. The Wigner function serves as a common interface between the microscopic and kinetic level. We demonstrate quantitative agreement after an initial transient time interval. In particular, besides energy conservation, we observe the additional quasiconservation of the phonon density, defined via an ensemble average of the related microscopic field variables and exactly conserved by the kinetic equations. On superkinetic time scales, density quasiconservation is lost while energy remainsmore » conserved, and we find evidence for eventual relaxation of the density to its canonical ensemble value. Furthermore, the precise mechanism remains unknown and is not captured by the Boltzmann-Peierls equations.« less

Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory

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

Mendl, Christian B.; Lu, Jianfeng; Lukkarinen, Jani

We perform microscopic molecular dynamics simulations of particle chains with an onsite anharmonicity to study relaxation of spatially homogeneous states to equilibrium, and directly compare the simulations with the corresponding Boltzmann-Peierls kinetic theory. The Wigner function serves as a common interface between the microscopic and kinetic level. We demonstrate quantitative agreement after an initial transient time interval. In particular, besides energy conservation, we observe the additional quasiconservation of the phonon density, defined via an ensemble average of the related microscopic field variables and exactly conserved by the kinetic equations. On superkinetic time scales, density quasiconservation is lost while energy remainsmore » conserved, and we find evidence for eventual relaxation of the density to its canonical ensemble value. Furthermore, the precise mechanism remains unknown and is not captured by the Boltzmann-Peierls equations.« less

Stability in chemical and biological systems: Multistage polyenzymatic reactions

NASA Astrophysics Data System (ADS)

Varfolomeev, S. D.; Lukovenkov, A. V.

2010-08-01

General principles of the theory of stability of solutions to differential equations are considered. The stability of equations describing the dynamics of changes in reagent concentrations in polyenzymatic biochemical chains is analyzed. Various mechanisms of formation of stable and unstable stationary states are considered, and unbalanced regimes and collapse are analyzed. The influence of systems of toxins and drugs on stability is studied. An interpretation of pathological processes based on stability theory is given.

Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory

NASA Astrophysics Data System (ADS)

Sciarappa, Antonio

2017-10-01

We provide a proposal, motivated by Separation of Variables and gauge theory arguments, for constructing exact solutions to the quantum Baxter equation associated to the N-particle relativistic Toda chain and test our proposal against numerical results. Quantum Mechanical non-perturbative corrections, essential in order to obtain a sensible solution, are taken into account in our gauge theory approach by considering codimension two defects on curved backgrounds (squashed S 5 and degenerate limits) rather than flat space; this setting also naturally incorporates exact quantization conditions and energy spectrum of the relativistic Toda chain as well as its modular dual structure.

Effect of Structure on Transport Properties (Viscosity, Ionic Conductivity, and Self-Diffusion Coefficient) of Aprotic Heterocyclic Anion (AHA) Room Temperature Ionic Liquids. 2. Variation of Alkyl Chain Length in the Phosphonium Cation.

PubMed

Sun, Liyuan; Morales-Collazo, Oscar; Xia, Han; Brennecke, Joan F

2016-06-30

A series of room-temperature ionic liquids (ILs) composed of triethyl(alkyl)phosphonium cations paired with three different aprotic heterocyclic anions (AHAs) (alkyl = butyl ([P2224](+)) and octyl ([P2228](+))) were prepared to investigate the effect of cationic alkyl chain length on transport properties. The transport properties and density of these ILs were measured from 283.15 to 343.15 K at ambient pressure. The dependence of the transport properties (viscosity, ionic conductivity, diffusivity, and molar conductivity) on temperature can be described by the Vogel-Fulcher-Tamman (VFT) equation. The ratio of the molar conductivity obtained from the molar concentration and ionic conductivity measurements to that calculated from self-diffusion coefficients (measured by pulsed gradient spin-echo nuclear magnetic resonance spectroscopy) using the Nernst-Einstein equation was used to quantify the ionicity of these ILs. The molar conductivity ratio decreases with increasing number of carbon atoms in the alkyl chain, indicating that the reduced Coulombic interactions resulting from lower density are more than balanced by the increased van der Waals interactions between the alkyl chains. The results of this study may provide insight into the design of ILs with enhanced dynamics that may be suitable as electrolytes in lithium ion batteries and other electrochemical applications.

Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations.

PubMed

Martirosyan, A; Saakian, David B

2011-08-01

We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.

Equations of state for the fully flexible WCA chains in the fluid and solid phases based on Wertheims-TPT2

NASA Astrophysics Data System (ADS)

Mirzaeinia, Ali; Feyzi, Farzaneh; Hashemianzadeh, Seyed Majid

2018-03-01

Based on Wertheim's second order thermodynamic perturbation theory (TPT2), equations of state (EOSs) are presented for the fluid and solid phases of tangent, freely jointed spheres. It is considered that the spheres interact with each other through the Weeks-Chandler-Anderson (WCA) potential. The developed TPT2 EOS is the sum of a monomeric reference term and a perturbation contribution due to bonding. MC NVT simulations are performed to determine the structural properties of the reference system in the reduced temperature range of 0.6 ≤ T* ≤ 4.0 and the packing fraction range of 0.1 ≤ η ≤ 0.72. Mathematical functions are fitted to the simulation results of the reference system and employed in the framework of Wertheim's theory to develop TPT2 EOSs for the fluid and solid phases. The extended EOSs are compared to the MC NPT simulation results of the compressibility factor and internal energy of the fully flexible chain systems. Simulations are performed for the WCA chain system for chain lengths of up to 15 at T* = 1.0, 1.5, 2.0, 3.0. Across all the reduced temperatures, the agreement between the results of the TPT2 EOS and MC simulations is remarkable. Overall Average Absolute Relative Percent Deviation at T* = 1.0 for the compressibility factor in the entire chain lengths we covered is 0.51 and 0.77 for the solid and fluid phases, respectively. Similar features are observed in the case of residual internal energy.

Equations of state for the fully flexible WCA chains in the fluid and solid phases based on Wertheims-TPT2.

PubMed

Mirzaeinia, Ali; Feyzi, Farzaneh; Hashemianzadeh, Seyed Majid

2018-03-14

Based on Wertheim's second order thermodynamic perturbation theory (TPT2), equations of state (EOSs) are presented for the fluid and solid phases of tangent, freely jointed spheres. It is considered that the spheres interact with each other through the Weeks-Chandler-Anderson (WCA) potential. The developed TPT2 EOS is the sum of a monomeric reference term and a perturbation contribution due to bonding. MC NVT simulations are performed to determine the structural properties of the reference system in the reduced temperature range of 0.6 ≤ T* ≤ 4.0 and the packing fraction range of 0.1 ≤ η ≤ 0.72. Mathematical functions are fitted to the simulation results of the reference system and employed in the framework of Wertheim's theory to develop TPT2 EOSs for the fluid and solid phases. The extended EOSs are compared to the MC NPT simulation results of the compressibility factor and internal energy of the fully flexible chain systems. Simulations are performed for the WCA chain system for chain lengths of up to 15 at T* = 1.0, 1.5, 2.0, 3.0. Across all the reduced temperatures, the agreement between the results of the TPT2 EOS and MC simulations is remarkable. Overall Average Absolute Relative Percent Deviation at T* = 1.0 for the compressibility factor in the entire chain lengths we covered is 0.51 and 0.77 for the solid and fluid phases, respectively. Similar features are observed in the case of residual internal energy.

Orientation of chain molecules in ionotropic gels: a Brownian dynamics model

NASA Astrophysics Data System (ADS)

Woelki, Stefan; Kohler, Hans-Helmut

2003-09-01

As is known from birefringence measurements, polysaccharide molecules of ionotropic gels are preferentially orientated normal to the direction of gel growth. In this paper the orientation effect is investigated by means of an off-lattice Brownian dynamics model simulating the gel formation process. The model describes the integration of a single coarse grained phantom chain into the growing gel. The equations of motion of the chain are derived. The computer simulations show that, during the process of integration, the chain is contracting normal to the direction of gel growth. A scaling relation is obtained for the degree of contraction as a function of the length parameters of the chain, the velocity of the gel formation front and the rate constant of the crosslinking reaction. It is shown that the scaling relation, if applied to the example of ionotropic copper alginate gel, leads to reasonable predictions of the time course of the degree of contraction of the alginate chains.

Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model

NASA Astrophysics Data System (ADS)

Manojlović, N.; Salom, I.

2017-10-01

The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, used previously in the case of the XXX Heisenberg chain. As expected, these Bethe vectors yield the strikingly simple expression for the off-shell action of the transfer matrix of the chain as well as the spectrum of the transfer matrix and the corresponding Bethe equations. As in the XXX case, the so-called quasi-classical limit gives the off-shell action of the generating function of the corresponding trigonometric Gaudin Hamiltonians with boundary terms.

An Exactly Solvable Spin Chain Related to Hahn Polynomials

NASA Astrophysics Data System (ADS)

Stoilova, Neli I.; van der Jeugt, Joris

2011-03-01

We study a linear spin chain which was originally introduced by Shi et al. [Phys. Rev. A 71 (2005), 032309, 5 pages], for which the coupling strength contains a parameter α and depends on the parity of the chain site. Extending the model by a second parameter β, it is shown that the single fermion eigenstates of the Hamiltonian can be computed in explicit form. The components of these eigenvectors turn out to be Hahn polynomials with parameters (α,β) and (α+1,β-1). The construction of the eigenvectors relies on two new difference equations for Hahn polynomials. The explicit knowledge of the eigenstates leads to a closed form expression for the correlation function of the spin chain. We also discuss some aspects of a q-extension of this model.

Evaluation of the path integral for flow through random porous media

NASA Astrophysics Data System (ADS)

Westbroek, Marise J. E.; Coche, Gil-Arnaud; King, Peter R.; Vvedensky, Dimitri D.

2018-04-01

We present a path integral formulation of Darcy's equation in one dimension with random permeability described by a correlated multivariate lognormal distribution. This path integral is evaluated with the Markov chain Monte Carlo method to obtain pressure distributions, which are shown to agree with the solutions of the corresponding stochastic differential equation for Dirichlet and Neumann boundary conditions. The extension of our approach to flow through random media in two and three dimensions is discussed.

Transit and lifespan in neutrophil production: implications for drug intervention.

PubMed

Câmara De Souza, Daniel; Craig, Morgan; Cassidy, Tyler; Li, Jun; Nekka, Fahima; Bélair, Jacques; Humphries, Antony R

2018-02-01

A comparison of the transit compartment ordinary differential equation modelling approach to distributed and discrete delay differential equation models is studied by focusing on Quartino's extension to the Friberg transit compartment model of myelosuppression, widely relied upon in the pharmaceutical sciences to predict the neutrophil response after chemotherapy, and on a QSP delay differential equation model of granulopoiesis. An extension to the Quartino model is provided by considering a general number of transit compartments and introducing an extra parameter that allows for the decoupling of the maturation time from the production rate of cells. An overview of the well established linear chain technique, used to reformulate transit compartment models with constant transit rates as distributed delay differential equations (DDEs), is then given. A state-dependent time rescaling of the Quartino model is performed to apply the linear chain technique and rewrite the Quartino model as a distributed DDE, yielding a discrete DDE model in a certain parameter limit. Next, stability and bifurcation analyses are undertaken in an effort to situate such studies in a mathematical pharmacology context. We show that both the original Friberg and the Quartino extension models incorrectly define the mean maturation time, essentially treating the proliferative pool as an additional maturation compartment. This misspecification can have far reaching consequences on the development of future models of myelosuppression in PK/PD.

Harmonic Chain with Velocity Flips: Thermalization and Kinetic Theory

NASA Astrophysics Data System (ADS)

Lukkarinen, Jani; Marcozzi, Matteo; Nota, Alessia

2016-12-01

We consider the detailed structure of correlations in harmonic chains with pinning and a bulk velocity flip noise during the heat relaxation phase which occurs on diffusive time scales, for t=O(L^2) where L is the chain length. It has been shown earlier that for non-degenerate harmonic interactions these systems thermalize, and the dominant part of the correlations is given by local thermal equilibrium determined by a temperature profile which satisfies a linear heat equation. Here we are concerned with two new aspects about the thermalization process: the first order corrections in 1 / L to the local equilibrium correlations and the applicability of kinetic theory to study the relaxation process. Employing previously derived explicit uniform estimates for the temperature profile, we first derive an explicit form for the first order corrections to the particle position-momentum correlations. By suitably revising the definition of the Wigner transform and the kinetic scaling limit we derive a phonon Boltzmann equation whose predictions agree with the explicit computation. Comparing the two results, the corrections can be understood as arising from two different sources: a current-related term and a correction to the position-position correlations related to spatial changes in the phonon eigenbasis.

The coupling effects of kinematics and flexibility on the Lagrangian dynamic formulation of open chain deformable links

NASA Technical Reports Server (NTRS)

Changizi, Koorosh

1989-01-01

A nonlinear Lagrangian formulation for the spatial kinematic and dynamic analysis of open chain deformable links consisting of cylindrical joints that connect pairs of flexible links is developed. The special cases of revolute or prismatic joint can also be obtained from the kinematic equations. The kinematic equations are described using a 4x4 matrix method. The configuration of each deformable link in the open loop kinematic chain is identified using a coupled set of relative joint variables, constant geometric parameters, and elastic coordinates. The elastic coordinates define the link deformation with respect to a selected joint coordinate system that is consistent with the kinematic constraints on the boundary of the deformable link. These coordinates can be introduced using approximation techniques such as Rayleigh-Ritz method, finite element technique or any other desired approach. The large relative motion between two neighboring links are defined by a set of joint coordinates which describes the large relative translational and rotational motion between two neighboring joint coordinate systems. The origin of these coordinate systems are rigidly attached to the neighboring links at the joint definition points along the axis of motion.

Breathers in a locally resonant granular chain with precompression

DOE PAGES

Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; ...

2016-09-01

Here we study a locally resonant granular material in the form of a precompressed Hertzian chain with linear internal resonators. Using an asymptotic reduction, we derive an effective nonlinear Schrödinger (NLS) modulation equation. In turn, this leads us to provide analytical evidence, subsequently corroborated numerically, for the existence of two distinct types of discrete breathers related to acoustic or optical modes: (a) traveling bright breathers with a strain profile exponentially vanishing at infinity and (b) stationary and traveling dark breathers, exponentially localized, time-periodic states mounted on top of a non-vanishing background. Moreover, the stability and bifurcation structure of numerically computedmore » exact stationary dark breathers is also examined. Stationary bright breathers cannot be identified using the NLS equation, which is defocusing at the upper edges of the phonon bands and becomes linear at the lower edge of the optical band.« less

Counterion accumulation effects on a suspension of DNA molecules: Equation of state and pressure-driven denaturation

NASA Astrophysics Data System (ADS)

Nicasio-Collazo, Luz Adriana; Delgado-González, Alexandra; Hernández-Lemus, Enrique; Castañeda-Priego, Ramón

2017-04-01

The study of the effects associated with the electrostatic properties of DNA is of fundamental importance to understand both its molecular properties at the single molecule level, like the rigidity of the chain, and its interaction with other charged bio-molecules, including other DNA molecules; such interactions are crucial to maintain the thermodynamic stability of the intra-cellular medium. In the present work, we combine the Poisson-Boltzmann mean-field theory with an irreversible thermodynamic approximation to analyze the effects of counterion accumulation inside DNA on both the denaturation profile of the chain and the equation of state of the suspension. To this end, we model the DNA molecule as a porous charged cylinder immersed in an aqueous solution. These thermo-electrostatic effects are explicitly studied in the particular case of some genes for which damage in their sequence is associated with diffuse large B-cell lymphoma.

Nurse staffing and deficiencies in the largest for-profit nursing home chains and chains owned by private equity companies.

PubMed

Harrington, Charlene; Olney, Brian; Carrillo, Helen; Kang, Taewoon

2012-02-01

To compare staffing levels and deficiencies of the 10 largest U.S. for-profit nursing home chains with five other ownership groups and chain staffing and deficiencies before and after purchase by four private equity (PE) companies. Facilities for the largest for-profit chains were identified through Internet searches and company reports and matched with federal secondary data for 2003-2008 for each ownership group. Descriptive statistics and generalized estimation equation panel regression models examined staffing and deficiencies by ownership groups in the 2003-2008 period, controlling for facility characteristics, resident acuity, and market factors with state fixed effects. The top 10 for-profit chains had lower registered nurse and total nurse staffing hours than government facilities, controlling for other factors. The top 10 chains received 36 percent higher deficiencies and 41 percent higher serious deficiencies than government facilities. Other for-profit facilities also had lower staffing and higher deficiencies than government facilities. The chains purchased by PE companies showed little change in staffing levels, but the number of deficiencies and serious deficiencies increased in some postpurchase years compared with the prepurchase period. There is a need for greater study of large for-profit chains as well as those chains purchased by PE companies. © Health Research and Educational Trust.

Integrable discretisations for a class of nonlinear Schrödinger equations on Grassmann algebras

NASA Astrophysics Data System (ADS)

Grahovski, Georgi G.; Mikhailov, Alexander V.

2013-12-01

Integrable discretisations for a class of coupled (super) nonlinear Schrödinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are constructed. As a result, Grassmann generalisations of the Toda lattice and the NLS dressing chain are obtained. The compatibility (Bianchi commutativity) of these Darboux transformations leads to integrable Grassmann generalisations of the difference Toda and NLS equations. The resulting systems will have discrete Lax representations provided by the set of two consistent elementary Darboux transformations. For the two discrete systems obtained, initial value and initial-boundary problems are formulated.

COLLABORATIVE RESEARCH AND DEVELOPMENT (CR&D) Delivery Order 0034: Aircraft Coatings Modeling and Simulation

DTIC Science & Technology

2008-03-01

bonded potentials used. The interactions between the beads were described using 6-12 Lennard - Jones (LJ) potential (Equation (1)) with a 2.5 d cutoff...in Lennard - Jones potential for the non-bonded interactions is at 1.12 d in line with the second peak. The remainder of the g(r)chain-chain has...Simulator). 40 Lennard - Jones and Coulombic interactions for pairs of organic atoms were computed using a switching function with inner and outer cutoffs of

Protonic transport through solitons in hydrogen-bonded systems

NASA Astrophysics Data System (ADS)

Kavitha, L.; Jayanthi, S.; Muniyappan, A.; Gopi, D.

2011-09-01

We offer an alternative route for investigating soliton solutions in hydrogen-bonded (HB) chains. We invoke the modified extended tangent hyperbolic function method coupled with symbolic computation to solve the governing equation of motion for proton dynamics. We investigate the dynamics of proton transfer in HB chains through bell-shaped soliton excitations, which trigger the bio-energy transport in most biological systems. This solitonic mechanism of proton transfer could play functional roles in muscular contraction, enzymatic activity and oxidative phosphorylation.

Slavnov and Gaudin-Korepin Formulas for Models without U(1) Symmetry: the Twisted XXX Chain

NASA Astrophysics Data System (ADS)

Belliard, Samuel; Pimenta, Rodrigo A.

2015-12-01

We consider the XXX spin-1/2 Heisenberg chain on the circle with an arbitrary twist. We characterize its spectral problem using the modified algebraic Bethe anstaz and study the scalar product between the Bethe vector and its dual. We obtain modified Slavnov and Gaudin-Korepin formulas for the model. Thus we provide a first example of such formulas for quantum integrable models without U(1) symmetry characterized by an inhomogenous Baxter T-Q equation.

One-electron propagation in Fermi, Pasta, Ulam disordered chains with Gaussian acoustic pulse pumping

NASA Astrophysics Data System (ADS)

Silva, L. D. Da; Dos Santos, J. L. L.; Ranciaro Neto, A.; Sales, M. O.; de Moura, F. A. B. F.

In this work, we consider a one-electron moving on a Fermi, Pasta, Ulam disordered chain under effect of electron-phonon interaction and a Gaussian acoustic pulse pumping. We describe electronic dynamics using quantum mechanics formalism and the nonlinear atomic vibrations using standard classical physics. Solving numerical equations related to coupled quantum/classical behavior of this system, we study electronic propagation properties. Our calculations suggest that the acoustic pumping associated with the electron-lattice interaction promote a sub-diffusive electronic dynamics.

Modeling of the morphological change of cellulose microfibrils caused with aqueous NaOH solution: the longitudinal contraction and laterally swelling during decrystallization.

PubMed

Nakano, Takato

2017-04-01

The conformation of cellulose microfibrils treated with aqueous NaOH was modeled as partially decrystallized cellulose chains before completing conversion to cellulose II, in order to elucidate the change in morphology of ramie fiber caused by NaOH treatment. Equations for the relative length and width of the microfibrils were derived on the basis of partially decrystallized microfibrils modeling. Each equation contains four parameters, n, β, w c , and c r , which correspond to the number of glucose residues between periodic defects along the untreated ramie cellulose microfibrils, the extension ratio of amorphous cellulose chain along length, the cross-section crystallinity, and the correction term of crystallinity, respectively. The validity of the derived equations was confirmed by two types of simulations. One is performed using experimental data L/L 0 and W/W 0 as a function of crystallinity, while the other is done using the relationship between the relative length and width obtained from the experimental data, which is independent of crystallinity, was performed. The best-fit simulation was obtained under n = 277, β = 2.813, and c r w c  = 0.671 for the former and under n = 301 and β = 2.792 for the latter. These values of n and β correspond closely to the values reported in references for ramie microfibrils. Both simulation results show that macroscopic changes in the morphology of ramie fibers is attributable to the changes in cellulose chain conformation in the decrystallized regions created along the microfibrils upon NaOH treatment.

Fourier's law of heat conduction: quantum mechanical master equation analysis.

PubMed

Wu, Lian-Ao; Segal, Dvira

2008-06-01

We derive the macroscopic Fourier's Law of heat conduction from the exact gain-loss time convolutionless quantum master equation under three assumptions for the interaction kernel. To second order in the interaction, we show that the first two assumptions are natural results of the long time limit. The third assumption can be satisfied by a family of interactions consisting of an exchange effect. The pure exchange model directly leads to energy diffusion in a weakly coupled spin- 12 chain.

A class of generalized Ginzburg-Landau equations with random switching

NASA Astrophysics Data System (ADS)

Wu, Zheng; Yin, George; Lei, Dongxia

2018-09-01

This paper focuses on a class of generalized Ginzburg-Landau equations with random switching. In our formulation, the nonlinear term is allowed to have higher polynomial growth rate than the usual cubic polynomials. The random switching is modeled by a continuous-time Markov chain with a finite state space. First, an explicit solution is obtained. Then properties such as stochastic-ultimate boundedness and permanence of the solution processes are investigated. Finally, two-time-scale models are examined leading to a reduction of complexity.

Equatorial irregularity belt and its movement during a magnetic storm

NASA Technical Reports Server (NTRS)

Vats, H. O.; Chandra, H.; Deshpande, M. R.; Rastogi, R. G.; Murthy, B. S.; Janve, A. V.; Rai, R. K.; Singh, M.; Gurm, H. S.; Jain, A. R.

1978-01-01

Evidence for an equatorial irregularity belt and its movement during a magnetic storm has been obtained from Faraday rotation measurements at a chain of 140-MHz radio beacons receiving from the ATS-6 satellite. The stations covered a latitude region from the magnetic equator to the 45 deg N dip on the Indian subcontinent. An irregularity belt extending from the magnetic equator to about 27 deg N latitude was observed during the main phase of the magnetic storm of 10 January, 1976.

Aspects of the inverse problem for the Toda chain

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

Kozlowski, K. K., E-mail: karol.kozlowski@u-bourgogne.fr

We generalize Babelon's approach to equations in dual variables so as to be able to treat new types of operators which we build out of the sub-constituents of the model's monodromy matrix. Further, we also apply Sklyanin's recent monodromy matrix identities so as to obtain equations in dual variables for yet other operators. The schemes discussed in this paper appear to be universal and thus, in principle, applicable to many models solvable through the quantum separation of variables.

N-soliton interactions: Effects of linear and nonlinear gain and loss

NASA Astrophysics Data System (ADS)

Carretero-González, R.; Gerdjikov, V. S.; Todorov, M. D.

2017-10-01

We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the nonlinear Schrödinger equation perturbed simultaneously by linear and nonlinear gain/loss terms. We derive the corresponding perturbed complex Toda chain in the case of a combination of linear, cubic, and/or quintic terms. We show that the soliton interactions dynamics for this reduced PCTC model compares favorably to full numerical results of the original perturbed nonlinear Schrödinger equation.

Diverging conductance at the contact between random and pure quantum XX spin chains

NASA Astrophysics Data System (ADS)

Chatelain, Christophe

2017-11-01

A model consisting of two quantum XX spin chains, one homogeneous and the second with random couplings drawn from a binary distribution, is considered. The two chains are coupled to two different non-local thermal baths and their dynamics is governed by a Lindblad equation. In the steady state, a current J is induced between the two chains by coupling them together by their edges and imposing different chemical potentials μ to the two baths. While a regime of linear characteristics J versus Δμ is observed in the absence of randomness, a gap opens as the disorder strength is increased. In the infinite-randomness limit, this behavior is related to the density of states of the localized states contributing to the current. The conductance is shown to diverge in this limit.

Stress stiffening and approximate equations in flexible multibody dynamics

NASA Technical Reports Server (NTRS)

Padilla, Carlos E.; Vonflotow, Andreas H.

1993-01-01

A useful model for open chains of flexible bodies undergoing large rigid body motions, but small elastic deformations, is one in which the equations of motion are linearized in the small elastic deformations and deformation rates. For slow rigid body motions, the correctly linearized, or consistent, set of equations can be compared to prematurely linearized, or inconsistent, equations and to 'oversimplified,' or ruthless, equations through the use of open loop dynamic simulations. It has been shown that the inconsistent model should never be used, while the ruthless model should be used whenever possible. The consistent and inconsistent models differ by stress stiffening terms. These are due to zeroth-order stresses effecting virtual work via nonlinear strain-displacement terms. In this paper we examine in detail the nature of these stress stiffening terms and conclude that they are significant only when the associated zeroth-order stresses approach 'buckling' stresses. Finally it is emphasized that when the stress stiffening terms are negligible the ruthlessly linearized equations should be used.

Energy exchange dynamics of the discrete nonlinear Schrödinger equation lattice and intrinsic formation of strongly localized states

NASA Astrophysics Data System (ADS)

Hennig, D.

1997-09-01

We study the dynamics of excitation energy transfer along a lattice chain modeled by the discrete nonlinear Schrödinger (DNLS) equation. We prove that a segment carrying resonant motion can be decoupled from the remainder of the chain supporting quasiperiodic dynamics. The resonant segment from the extended chain is taken to be a four-site element, viz., a tetramer. First, we focus interest on the energy exchange dynamics along the tetramer viewed as two weakly coupled DNLS dimers. Hamiltonian methods are used to investigate the phase-space dynamics. We pay special attention to the role of the diffusion of the action variables inside resonance layers for the energy migration. When distributing the energy initially equally between the two dimers one observes a directed irreversible flow of energy from one dimer into the other assisted by action diffusion. Eventually on one dimer a stable self-trapped excitation of large amplitude forms at a single site while the other dimer exhibits equal energy partition over its two sites. Finally, we study the formation of localized structure on an extended DNLS lattice chain. In particular we explore the stability of the so-called even-parity and odd-parity localized modes, respectively, and explain their different stability properties by means of phase-space dynamics. The global instability of the even-parity mode is shown. For the excited even-parity mode a symmetry-breaking perturbation of the pattern leads to an intrinsic collapse of the even-parity mode to the odd-parity one. The latter remains stable with respect to symmetry-breaking perturbations. In this way we demonstrate that the favored stable localized states for the DNLS lattice chain correspond to one-site localized excitations.

A recursive approach to the equations of motion for the maneuvering and control of flexible multi-body systems

NASA Technical Reports Server (NTRS)

Kwak, Moon K.; Meirovitch, Leonard

1991-01-01

Interest lies in a mathematical formulation capable of accommodating the problem of maneuvering a space structure consisting of a chain of articulated flexible substructures. Simultaneously, any perturbations from the 'rigid body' maneuvering and any elastic vibration must be suppressed. The equations of motion for flexible bodies undergoing rigid body motions and elastic vibrations can be obtained conveniently by means of Lagrange's equations in terms of quasi-coordinates. The advantage of this approach is that it yields equations in terms of body axes, which are the same axes that are used to express the control forces and torques. The equations of motion are nonlinear hybrid differential quations. The partial differential equations can be discretized (in space) by means of the finite element method or the classical Rayleigh-Ritz method. The result is a set of nonlinear ordinary differential equations of high order. The nonlinearity can be traced to the rigid body motions and the high order to the elastic vibration. Elastic motions tend to be small when compared with rigid body motions.

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

Nekrasov, Nikita; ITEP, Moscow; Shatashvili, Samson

Supersymmetric vacua of two dimensional N = 4 gauge theories with matter, softly broken by the twisted masses down to N = 2, are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. Examples include: the Heisenberg SU(2)XXX spin chain which is mapped to the two dimensional U(N) theory with fundamental hypermultiplets, the XXZ spin chain which is mapped to the analogous three dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model which are related to the four dimensional theory compactified on T{sup 2}. A consequence of our correspondence ismore » the isomorphism of the quantum cohomology ring of various quiver varieties, such as cotangent bundles to (partial) flag varieties and the ring of quantum integrals of motion of various spin chains. The correspondence extends to any spin group, representations, boundary conditions, and inhomogeneity, it includes Sinh-Gordon and non-linear Schroedinger models as well as the dynamical spin chains like Hubbard model. Compactifications of four dimensional N = 2 theories on a two-sphere lead to the instanton-corrected Bethe equations.« less

Nurse Staffing and Deficiencies in the Largest For-Profit Nursing Home Chains and Chains Owned by Private Equity Companies

PubMed Central

Harrington, Charlene; Olney, Brian; Carrillo, Helen; Kang, Taewoon

2012-01-01

Objective To compare staffing levels and deficiencies of the 10 largest U.S. for-profit nursing home chains with five other ownership groups and chain staffing and deficiencies before and after purchase by four private equity (PE) companies. Data Sources Facilities for the largest for-profit chains were identified through Internet searches and company reports and matched with federal secondary data for 2003–2008 for each ownership group. Study Design Descriptive statistics and generalized estimation equation panel regression models examined staffing and deficiencies by ownership groups in the 2003–2008 period, controlling for facility characteristics, resident acuity, and market factors with state fixed effects. Principal Findings The top 10 for-profit chains had lower registered nurse and total nurse staffing hours than government facilities, controlling for other factors. The top 10 chains received 36 percent higher deficiencies and 41 percent higher serious deficiencies than government facilities. Other for-profit facilities also had lower staffing and higher deficiencies than government facilities. The chains purchased by PE companies showed little change in staffing levels, but the number of deficiencies and serious deficiencies increased in some postpurchase years compared with the prepurchase period. Conclusions There is a need for greater study of large for-profit chains as well as those chains purchased by PE companies. PMID:22091627

Structure and thermodynamics of a simple fluid

NASA Astrophysics Data System (ADS)

Stell, G.; Weis, J. J.

1980-02-01

Monte Carlo results are found for a simple fluid with a pair potential consisting of a hard-sphere core and a Lennard-Jones attractive tail. They are compared with several of the most promising recent theoretical treatments of simple fluids, all of which involve the decomposition of the pair potential into a hard-sphere-core term and an attractive-tail term. This direct comparison avoids the use of a second perturbation scheme associated with softening the core, which would introduce an ambiguity in the significance of the differences found between the theoretical and Monte Carlo results. The study includes the optimized random-phase approximation (ORPA) and exponential (EXP) approximations of Andersen and Chandler, an extension of the latter approximation to nodal order three (the N3 approximation), the linear-plus-square (LIN + SQ) approximation of Høye and Stell, the renormalized hypernetted chain (RHNC) approximation of Lado, and the quadratic (QUAD) approximation suggested by second-order self-consistent Γ ordering, the lowest order of which is identical to the ORPA. As anticipated on the basis of earlier studies, it is found that the EXP approximation yields radial distribution functions and structure factors of excellent overall accuracy in the liquid state, where the RHNC results are also excellent and the EXP, QUAD, and LIN + SQ results prove to be virtually indistinguishable from one another. For all the approximations, however, the thermodynamics from the compressibility relation are poor and the virial-theorem results are not uniformly reliable. Somewhat more surprisingly, it is found that the EXP results yield a negative structure factor S(k) for very small k in the liquid state and poor radial distribution functions at low densities. The RHNC results are nowhere worse than the EXP results and in some states (e.g., at low densities) much better. In contrast, the N3 results are better in some respects than the EXP results but worse in others. The authors briefly comment on the RHNC and EXP approximations applied to the full Lennard-Jones potential, for which the EXP approximation appears somewhat improved in the liquid state as a result of the softening of the potential core.

Effective electrostatic interactions among charged thermo-responsive microgels immersed in a simple electrolyte

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

González-Mozuelos, P.

This work explores the nature and thermodynamic behavior of the effective electrostatic interactions among charged microgels immersed in a simple electrolyte, taking special interest in the effects due to the thermally induced variation of the microgel size while the remaining parameters (microgel charge and concentration, plus the amount of added salt) are kept constant. To this end, the rigorous approach obtained from applying the precise methodology of the dressed ion theory to the proper definition of the effective direct correlation functions, which emerge from tracing-out the degrees of freedom of the microscopic ions, is employed to provide an exact descriptionmore » of the parameters characterizing such interactions: screening length, effective permittivity, and renormalized charges. A model solution with three components is assumed: large permeable anionic spheres for the microgels, plus small charged hard spheres of equal size for the monovalent cations and anions. The two-body correlations among the components of this model suspension, used as the input for the determination of the effective interaction parameters, are here calculated by using the hyper-netted chain approximation. It is then found that at finite microgel concentrations the values of these parameters change as the microgel size increases, even though the ionic strength of the supporting electrolyte and the bare charge of the microgels remain fixed during this process. The variation of the screening length, as well as that of the effective permittivity, is rather small, but still interesting in view of the fact that the corresponding Debye length stays constant. The renormalized charges, in contrast, increase markedly as the microgels swell. The ratio of the renormalized charge to the corresponding analytic result obtained in the context of an extended linear response theory allows us to introduce an effective charge that accounts for the non-linear effects induced by the short-ranged association of microions to the microgels. The behavior of these effective charges as a function of the amount of added salt and the macroion charge, size, and concentration reveals the interplay among all these system parameters.« less

Thermodynamics of Oligonucleotide Duplex Melting

ERIC Educational Resources Information Center

Schreiber-Gosche, Sherrie; Edwards, Robert A.

2009-01-01

Melting temperatures of oligonucleotides are useful for a number of molecular biology applications, such as the polymerase chain reaction (PCR). Although melting temperatures are often calculated with simplistic empirical equations, application of thermodynamics provides more accurate melting temperatures and an opportunity for students to apply…

Algebraic geometry and Bethe ansatz. Part I. The quotient ring for BAE

NASA Astrophysics Data System (ADS)

Jiang, Yunfeng; Zhang, Yang

2018-03-01

In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and powerful tools for understanding the structure of solution space of Bethe ansatz equations. In particular, we find novel efficient methods to count the number of solutions of Bethe ansatz equations based on Gröbner basis and quotient ring. We also develop analytical approach based on companion matrix to perform the sum of on-shell quantities over all physical solutions without solving Bethe ansatz equations explicitly. To demonstrate the power of our method, we revisit the completeness problem of Bethe ansatz of Heisenberg spin chain, and calculate the sum rules of OPE coefficients in planar N=4 super-Yang-Mills theory.

Optimal Harvesting in a Periodic Food Chain Model with Size Structures in Predators

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

Zhang, Feng-Qin, E-mail: zhafq@263.net; Liu, Rong; Chen, Yuming, E-mail: ychen@wlu.ca

In this paper, we investigate a periodic food chain model with harvesting, where the predators have size structures and are described by first-order partial differential equations. First, we establish the existence of a unique non-negative solution by using the Banach fixed point theorem. Then, we provide optimality conditions by means of normal cone and adjoint system. Finally, we derive the existence of an optimal strategy by means of Ekeland’s variational principle. Here the objective functional represents the net economic benefit yielded from harvesting.

Chain Rule Approach for Calculating the Time-Derivative of Flux

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

Langenbrunner, James R.; Booker, Jane M.

The reaction history (gamma-flux observable) is mathematically studied by using the chain rule for taking the total-time derivatives. That is, the total time-derivative of flux is written as the product of the ion temperature derivative with respect to time and the derivative of the flux with respect to ion temperature. Some equations are derived using the further simplification that the fusion reactivity is a parametrized function of ion temperature, T. Deuterium-tritium (D-T) fusion is used as the application with reactivity calculations from three established reactivity parametrizations.

An analytical approach to top predator interference on the dynamics of a food chain model

NASA Astrophysics Data System (ADS)

Senthamarai, R.; Vijayalakshmi, T.

2018-04-01

In this paper, a nonlinear mathematical model is proposed and analyzed to study of top predator interference on the dynamics of a food chain model. The mathematical model is formulated using the system of non-linear ordinary differential equations. In this model, there are three state dimensionless variables, viz, size of prey population x, size of intermediate predator y and size of top predator population z. The analytical results are compared with the numerical simulation using MATLAB software and satisfactory results are noticed.

Simulation of economic agents interaction in a trade chain

NASA Astrophysics Data System (ADS)

Gimanova, I. A.; Dulesov, A. S.; Litvin, N. V.

2017-01-01

The mathematical model of economic agents interaction is offered in the work. It allowsconsidering the change of price and sales volumesin dynamics according to the process of purchase and sale in the single-product market of the trade and intermediary network. The description of data-flow processes is based on the use of the continuous dynamic market model. The application of ordinary differential equations during the simulation allows one to define areas of coefficients - characteristics of agents - and to investigate their interaction in a chain on stability.

Loss of tubular creatinine secretion as the only sign of tubular proximal cell dysfunction in light chain proximal tubulopathy: A case report.

PubMed

Stehlé, Thomas; Vignon, Marguerite; Flamant, Martin; Figueres, Marie-Lucile; Rabant, Marion; Rodenas, Anita; Noël, Laure-Hélène; Arnulf, Bertrand; Vidal-Petiot, Emmanuelle

2016-06-01

Light chain proximal tubulopathy (LCPT) is a rare disease, characterized by cytoplasmic inclusions of light chain (usually kappa) immunoglobulins. Clinical presentation is usually a Fanconi syndrome. The proximal tubular dysfunction can be incomplete, and exceptional cases of LCPT without any tubular dysfunction have even been described. Here, we report a case of LCPT in which the only sign of proximal tubulopathy is the absence of secretion of creatinine, as assessed by the simultaneous measurement of renal clearance of creatinine and CrEDTA. The loss of tubular creatinine secretion as a sign of tubular proximal cell dysfunction ought to be identified in patients with light chain proximal tubulopathy as it leads to a clinically relevant underestimation of GFR by the creatinine-derived equations. The prevalence and prognostic significance of this particular proximal tubular damage in LCPT remain to be determined.

Study on the supply chain of an enterprise based on axiomatic design

NASA Astrophysics Data System (ADS)

Fan, Shu-hai; Lin, Chao-qun; Ji, Chun; Zhou, Ce; Chen, Peng

2018-06-01

This paper first expounds the basic theoretical knowledge of axiomatic design, and then designs and improves the enterprise supply chain through two design axioms (axiom of independence and information axiom). In the axiomatic design of the axiom of independence, the user needs to determine the needs and problems to be solved, to determine the top total goals, the total goal decomposition, and to determine their own design equations. In the application of information axiom, the concept of cloud is used to quantify the amount of information, and the two schemes are evaluated and compared. Finally, through axiomatic design, we can get the best solution for the improvement of supply chain design. Axiomatic design is a generic, systematic and sophisticated approach to design that addresses the needs of different customers. Using this method to improve the level of supply chain management is creative. As a mature method, it will make the process efficient and convenient.

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

Alexeev, A. V.; Maltseva, D. V.; Ivanov, V. A., E-mail: ivanov@polly.phys.msu.ru

We study force-extension curves of a single semiflexible chain consisting of several rigid rods connected by flexible spacers. The atomic force microscopy and laser optical or magnetic tweezers apparatus stretching these rod-coil macromolecules are discussed. In addition, the stretching by external isotropic force is analyzed. The main attention is focused on computer simulation and analytical results. We demonstrate that the force-extension curves for rod-coil chains composed of two or three rods of equal length differ not only quantitatively but also qualitatively in different probe methods. These curves have an anomalous shape for a chain of two rods. End-to-end distributions ofmore » rod-coil chains are calculated by Monte Carlo method and compared with analytical equations. The influence of the spacer’s length on the force-extension curves in different probe methods is analyzed. The results can be useful for interpreting experiments on the stretching of rod-coil block-copolymers.« less

It's hard to be green: Reverse green value chain.

PubMed

Couto, João; Tiago, Teresa; Gil, Artur; Tiago, Flávio; Faria, Sandra

2016-08-01

Firms have recently discovered that it is not enough to optimize internal processes and relationships with partners along the value chain to create a sustainable competitive market position. A clear customer orientation, which acknowledges that consumer buying behavior is complex and includes many elements implied in the value chain, is required. As companies offering green products are no exception to this rule, this study analyzes consumer behavior in Europe from a reserve green supply chain management perspective, using descriptive analyses and a structural equation model, with data collected by Flash Barometer comprising 26,573 responses from 28 European countries. The results suggest that European consumers are conscious of the green concept, but are not willing to buy or pay more for these products since the value is unclear. Companies offering green products must therefore rethink their strategies, especially in terms of value proposition, communication strategies, and eco-labeling. Copyright © 2016 Elsevier Inc. All rights reserved.

Symplectic integration of closed chain rigid body dynamics with internal coordinate equations of motion

NASA Astrophysics Data System (ADS)

Mazur, Alexey K.

1999-07-01

Internal coordinate molecular dynamics (ICMD) is a recent efficient method for modeling polymer molecules which treats them as chains of rigid bodies rather than ensembles of point particles as in Cartesian MD. Unfortunately, it is readily applicable only to linear or tree topologies without closed flexible loops. Important examples violating this condition are sugar rings of nucleic acids, proline residues in proteins, and also disulfide bridges. This paper presents the first complete numerical solution of the chain closure problem within the context of ICMD. The method combines natural implicit fixation of bond lengths and bond angles by the choice of internal coordinates with explicit constraints similar to Cartesian dynamics used to maintain the chain closure. It is affordable for large molecules and makes possible 3-5 times faster dynamics simulations of molecular systems with flexible rings, including important biological objects like nucleic acids and disulfide-bonded proteins.

Bushes of vibrational modes for Fermi-Pasta-Ulam chains

NASA Astrophysics Data System (ADS)

Chechin, G. M.; Novikova, N. V.; Abramenko, A. A.

2002-06-01

Some exact solutions and multimode invariant submanifolds were found for the Fermi-Pasta-Ulam (FPU)- β model by Poggi and Ruffo [Physica D 103 (1997) 251]. In the present paper we demonstrate how results of such a type can be obtained for an arbitraryN-particle chain with periodic boundary conditions with the aid of our group-theoretical approach [Physica D 117 (1998) 43] based on the concept of bushes of normal modes in mechanical systems with discrete symmetry. The integro-differential equation describing the FPU- α dynamics in the modal space is derived. The loss of stability of the bushes of modes for the FPU- α model, in particular, for the limiting case N→∞ for the dynamical regime with displacement pattern having period twice the lattice spacing ( π-mode) is studied. Our results for the FPU- α chain are compared with those by Poggi and Ruffo for the FPU- β chain.

Modeling chain folding in protein-constrained circular DNA.

PubMed Central

Martino, J A; Olson, W K

1998-01-01

An efficient method for sampling equilibrium configurations of DNA chains binding one or more DNA-bending proteins is presented. The technique is applied to obtain the tertiary structures of minimal bending energy for a selection of dinucleosomal minichromosomes that differ in degree of protein-DNA interaction, protein spacing along the DNA chain contour, and ring size. The protein-bound portions of the DNA chains are represented by tight, left-handed supercoils of fixed geometry. The protein-free regions are modeled individually as elastic rods. For each random spatial arrangement of the two nucleosomes assumed during a stochastic search for the global minimum, the paths of the flexible connecting DNA segments are determined through a numerical solution of the equations of equilibrium for torsionally relaxed elastic rods. The minimal energy forms reveal how protein binding and spacing and plasmid size differentially affect folding and offer new insights into experimental minichromosome systems. PMID:9591675

Influence of macromolecular architecture on necking in polymer extrusion film casting process

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

Pol, Harshawardhan; Banik, Sourya; Azad, Lal Busher

2015-05-22

Extrusion film casting (EFC) is an important polymer processing technique that is used to produce several thousand tons of polymer films/coatings on an industrial scale. In this research, we are interested in understanding quantitatively how macromolecular chain architecture (for example long chain branching (LCB) or molecular weight distribution (MWD or PDI)) influences the necking and thickness distribution of extrusion cast films. We have used different polymer resins of linear and branched molecular architecture to produce extrusion cast films under controlled experimental conditions. The necking profiles of the films were imaged and the velocity profiles during EFC were monitored using particlemore » tracking velocimetry (PTV) technique. Additionally, the temperature profiles were captured using an IR thermography and thickness profiles were calculated. The experimental results are compared with predictions of one-dimensional flow model of Silagy et al{sup 1} wherein the polymer resin rheology is modeled using molecular constitutive equations such as the Rolie-Poly (RP) and extended Pom Pom (XPP). We demonstrate that the 1-D flow model containing the molecular constitutive equations provides new insights into the role of macromolecular chain architecture on film necking.{sup 1}D. Silagy, Y. Demay, and J-F. Agassant, Polym. Eng. Sci., 36, 2614 (1996)« less

Structure of Poly(dialkylsiloxane) Melts:  Comparisons of Wide-Angle X-ray Scattering, Molecular Dynamics Simulations, and Integral Equation Theory

DOE PAGES

Habenschuss, Anton; Tsige, Mesfin; Curro, John G.; ...

2007-08-21

Here, wide-angle X-ray scattering, molecular dynamics (MD) simulations, and integral equation theory are used to study the structure of poly(diethylsiloxane) (PDES), poly(ethylmethylsiloxane) (PEMS), and poly(dimethylsiloxane) (PDMS) melts. The structure functions of PDES, PEMS, and PDMS are similar, but systematic trends in the intermolecular packing are observed. The local intramolecular structure is extracted from the experimental structure functions. The bond distances and bond angles obtained, including the large Si-O-Si angle, are in good agreement with the explicit atom (EA) and united atom (UA) potentials used in the simulations and theory and from other sources. Very good agreement is found between themore » MD simulations using the EA potentials and the experimental scattering results. Good agreement is also found between the polymer reference interaction site model (PRISM theory) and the UA MD simulations. The intermolecular structure is examined experimentally using an appropriately weighted radial distribution function and with theory and simulation using intermolecular site/site pair correlation functions. Finally, experiment, simulation, and theory show systematic increases in the chain/chain packing distances in the siloxanes as the number of sites in the pendant side chains is increased.« less

Baxter operators and Hamiltonians for "nearly all" integrable closed gl(n) spin chains

NASA Astrophysics Data System (ADS)

Frassek, Rouven; Łukowski, Tomasz; Meneghelli, Carlo; Staudacher, Matthias

2013-09-01

We continue our systematic construction of Baxter Q-operators for spin chains, which is based on certain degenerate solutions of the Yang-Baxter equation. Here we generalize our approach from the fundamental representation of gl(n) to generic finite-dimensional representations in quantum space. The results equally apply to non-compact representations of highest or lowest weight type. We furthermore fill an apparent gap in the literature, and provide the nearest-neighbor Hamiltonians of the spin chains in question for all cases where the gl(n) representations are described by rectangular Young diagrams, as well as for their infinite-dimensional generalizations. They take the form of digamma functions depending on operator-valued shifted weights. We believe that this condition follows from [R0,I,Jba]=0, [R0,I,Jb˙a˙]=0, [R0,I,Jbc˙Jc˙a]=0, which are specializations, respectively, of the last equation in (2.14), (2.16) and (2.19) in the case of minimal representations. Clearly R0,I can be considered as a function of the Casimir operators of gl(n) as well. These are just constants in a given irreducible representation and will not enter the discussion regarding the determination of R0,I.

Patchwork sampling of stochastic differential equations

NASA Astrophysics Data System (ADS)

Kürsten, Rüdiger; Behn, Ulrich

2016-03-01

We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The method is based on a complete, nonoverlapping partition of the state space into patches on which the stochastic process is ergodic. On each of these patches we run simulations of the process strictly truncated to the corresponding patch, which allows effective simulations also in rarely visited regions. The correct weight for each patch is obtained by counting the attempted transitions between all different patches. The results are patchworked to cover the whole state space. We extend the concept of truncated Markov chains which is originally formulated for processes which obey detailed balance to processes not fulfilling detailed balance. The method is illustrated by three examples, describing the one-dimensional diffusion of an overdamped particle in a double-well potential, a system of many globally coupled overdamped particles in double-well potentials subject to additive Gaussian white noise, and the overdamped motion of a particle on the circle in a periodic potential subject to a deterministic drift and additive noise. In an appendix we explain how other well-known Markov chain Monte Carlo algorithms can be related to truncated Markov chains.

From the quantum transfer matrix to the quench action: the Loschmidt echo in XXZ Heisenberg spin chains

NASA Astrophysics Data System (ADS)

Piroli, Lorenzo; Pozsgay, Balázs; Vernier, Eric

2017-02-01

We consider the computation of the Loschmidt echo after quantum quenches in the interacting XXZ Heisenberg spin chain both for real and imaginary times. We study two-site product initial states, focusing in particular on the Néel and tilted Néel states. We apply the quantum transfer matrix (QTM) approach to derive generalized TBA equations, which follow from the fusion hierarchy of the appropriate QTM’s. Our formulas are valid for arbitrary imaginary time and for real times at least up to a time t 0, after which the integral equations have to be modified. In some regimes, t 0 is seen to be either very large or infinite, allowing to explore in detail the post-quench dynamics of the system. As an important part of our work, we show that for the Néel state our imaginary time results can be recovered by means of the quench action approach, unveiling a direct connection with the quantum transfer matrix formalism. In particular, we show that in the zero-time limit, the study of our TBA equations allows for a simple alternative derivation of the recently obtained Bethe ansatz distribution functions for the Néel, tilted Néel and tilted ferromagnet states.

Stochastic entangled chain dynamics of dense polymer solutions.

PubMed

Kivotides, Demosthenes; Wilkin, S Louise; Theofanous, Theo G

2010-10-14

We propose an adjustable-parameter-free, entangled chain dynamics model of dense polymer solutions. The model includes the self-consistent dynamics of molecular chains and solvent by describing the former via coarse-grained polymer dynamics that incorporate hydrodynamic interaction effects, and the latter via the forced Stokes equation. Real chain elasticity is modeled via the inclusion of a Pincus regime in the polymer's force-extension curve. Excluded volume effects are taken into account via the combined action of coarse-grained intermolecular potentials and explicit geometric tracking of chain entanglements. We demonstrate that entanglements are responsible for a new (compared to phantom chain dynamics), slow relaxation mode whose characteristic time scale agrees very well with experiment. Similarly good agreement between theory and experiment is also obtained for the equilibrium chain size. We develop methods for the solution of the model in periodic flow domains and apply them to the computation of entangled polymer solutions in equilibrium. We show that the number of entanglements Π agrees well with the number of entanglements expected on the basis of tube theory, satisfactorily reproducing the latter's scaling of Π with the polymer volume fraction φ. Our model predicts diminishing chain size with concentration, thus vindicating Flory's suggestion of excluded volume effects screening in dense solutions. The predicted scaling of chain size with φ is consistent with the heuristic, Flory theory based value.

Leading to Learning and Competitive Intelligence

ERIC Educational Resources Information Center

Luu, Trong Tuan

2013-01-01

Purpose: This research aims to examine whether there is the chain effect from corporate social responsibility (CSR) and emotional intelligence (EI) to organizational learning and competitive intelligence in chemical companies in a Vietnam business setting. Design/methodology/approach: Structural equation modeling (SEM) approach was used to analyze…

General phase spaces: from discrete variables to rotor and continuum limits

NASA Astrophysics Data System (ADS)

Albert, Victor V.; Pascazio, Saverio; Devoret, Michel H.

2017-12-01

We provide a basic introduction to discrete-variable, rotor, and continuous-variable quantum phase spaces, explaining how the latter two can be understood as limiting cases of the first. We extend the limit-taking procedures used to travel between phase spaces to a general class of Hamiltonians (including many local stabilizer codes) and provide six examples: the Harper equation, the Baxter parafermionic spin chain, the Rabi model, the Kitaev toric code, the Haah cubic code (which we generalize to qudits), and the Kitaev honeycomb model. We obtain continuous-variable generalizations of all models, some of which are novel. The Baxter model is mapped to a chain of coupled oscillators and the Rabi model to the optomechanical radiation pressure Hamiltonian. The procedures also yield rotor versions of all models, five of which are novel many-body extensions of the almost Mathieu equation. The toric and cubic codes are mapped to lattice models of rotors, with the toric code case related to U(1) lattice gauge theory.

Classical r matrix of the su(2 vertical bar 2) super Yang-Mills spin chain

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

Torrielli, Alessandro

2007-05-15

In this note we straightforwardly derive and make use of the quantum R matrix for the su(2 vertical bar 2) super Yang-Mills spin chain in the manifest su(1 vertical bar 2)-invariant formulation, which solves the standard quantum Yang-Baxter equation, in order to obtain the correspondent (undressed) classical r matrix from the first order expansion in the 'deformation' parameter 2{pi}/{radical}({lambda}) and check that this last solves the standard classical Yang-Baxter equation. We analyze its bialgebra structure, its dependence on the spectral parameters, and its pole structure. We notice that it still preserves an su(1 vertical bar 2) subalgebra, thereby admitting anmore » expression in terms of a combination of projectors, which spans only a subspace of su(1 vertical bar 2)xsu(1 vertical bar 2). We study the residue at its simple pole at the origin and comment on the applicability of the classical Belavin-Drinfeld type of analysis.« less

Strong diffusion formulation of Markov chain ensembles and its optimal weaker reductions

NASA Astrophysics Data System (ADS)

Güler, Marifi

2017-10-01

Two self-contained diffusion formulations, in the form of coupled stochastic differential equations, are developed for the temporal evolution of state densities over an ensemble of Markov chains evolving independently under a common transition rate matrix. Our first formulation derives from Kurtz's strong approximation theorem of density-dependent Markov jump processes [Stoch. Process. Their Appl. 6, 223 (1978), 10.1016/0304-4149(78)90020-0] and, therefore, strongly converges with an error bound of the order of lnN /N for ensemble size N . The second formulation eliminates some fluctuation variables, and correspondingly some noise terms, within the governing equations of the strong formulation, with the objective of achieving a simpler analytic formulation and a faster computation algorithm when the transition rates are constant or slowly varying. There, the reduction of the structural complexity is optimal in the sense that the elimination of any given set of variables takes place with the lowest attainable increase in the error bound. The resultant formulations are supported by numerical simulations.

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

Gevorkyan, A. S., E-mail: g-ashot@sci.am; Sahakyan, V. V.

We study the classical 1D Heisenberg spin glasses in the framework of nearest-neighboring model. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from the first principles of classical mechanics lead to ℕℙ hard problem, that however in the limit of the statistical equilibrium can be calculated by ℙ algorithm. For the partition function of the ensemble a new representation is offered in the form of one-dimensional integral of spin-chains’ energy distribution.

Dynamics of generalized sine-Gordon soliton in inhomogeneous media

NASA Astrophysics Data System (ADS)

Gharaati, A.; Khordad, R.

2011-03-01

In this paper we introduce a few novel generalized sine-Gordon equations and study the dynamics of its solitons in inhomogeneous media. We consider length, mass, gravitational acceleration and spring stiffness of a coupled pendulums chain as a function of position x. Then in the continuum limit we derive semi-analytical and numerical soliton solutions of the modified sine-Gordon equation in the inhomogeneous media. The obtained results confirm that the behavior of solitons in these media is similar to that of a classical point particle moved in an external potential.

Solutions of the Bethe ansatz equations for XXX antiferromagnet of arbitrary spin in the case of a finite number of sites

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

Avdeev, L.V.; Doerfel, B.D.

1987-11-01

The exactly integrable isotropic Heisenberg chain of N spins s is studied, and numerical solutions to the Bethe ansatz equations corresponding to the antiferromagnetic vacuum (for sN less than or equal to 128) and the simplest excitations have been obtained. For s = 1, a complete set of states for N = 6 is given, and the vacuum solution for finite N is estimated analytically. The deviations from the string picture at large N are discussed.

Time-local equation for exact time-dependent optimized effective potential in time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Liao, Sheng-Lun; Ho, Tak-San; Rabitz, Herschel; Chu, Shih-I.

2017-04-01

Solving and analyzing the exact time-dependent optimized effective potential (TDOEP) integral equation has been a longstanding challenge due to its highly nonlinear and nonlocal nature. To meet the challenge, we derive an exact time-local TDOEP equation that admits a unique real-time solution in terms of time-dependent Kohn-Sham orbitals and effective memory orbitals. For illustration, the dipole evolution dynamics of a one-dimension-model chain of hydrogen atoms is numerically evaluated and examined to demonstrate the utility of the proposed time-local formulation. Importantly, it is shown that the zero-force theorem, violated by the time-dependent Krieger-Li-Iafrate approximation, is fulfilled in the current TDOEP framework. This work was partially supported by DOE.

Higher-order automatic differentiation of mathematical functions

NASA Astrophysics Data System (ADS)

Charpentier, Isabelle; Dal Cappello, Claude

2015-04-01

Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

A parallel algorithm for step- and chain-growth polymerization in molecular dynamics.

PubMed

de Buyl, Pierre; Nies, Erik

2015-04-07

Classical Molecular Dynamics (MD) simulations provide insight into the properties of many soft-matter systems. In some situations, it is interesting to model the creation of chemical bonds, a process that is not part of the MD framework. In this context, we propose a parallel algorithm for step- and chain-growth polymerization that is based on a generic reaction scheme, works at a given intrinsic rate and produces continuous trajectories. We present an implementation in the ESPResSo++ simulation software and compare it with the corresponding feature in LAMMPS. For chain growth, our results are compared to the existing simulation literature. For step growth, a rate equation is proposed for the evolution of the crosslinker population that compares well to the simulations for low crosslinker functionality or for short times.

A parallel algorithm for step- and chain-growth polymerization in molecular dynamics

NASA Astrophysics Data System (ADS)

de Buyl, Pierre; Nies, Erik

2015-04-01

Classical Molecular Dynamics (MD) simulations provide insight into the properties of many soft-matter systems. In some situations, it is interesting to model the creation of chemical bonds, a process that is not part of the MD framework. In this context, we propose a parallel algorithm for step- and chain-growth polymerization that is based on a generic reaction scheme, works at a given intrinsic rate and produces continuous trajectories. We present an implementation in the ESPResSo++ simulation software and compare it with the corresponding feature in LAMMPS. For chain growth, our results are compared to the existing simulation literature. For step growth, a rate equation is proposed for the evolution of the crosslinker population that compares well to the simulations for low crosslinker functionality or for short times.

A neoclassical drift-magnetohydrodynamical fluid model of the interaction of a magnetic island chain with a resonant error-field in a high temperature tokamak plasma

NASA Astrophysics Data System (ADS)

Fitzpatrick, Richard

2018-04-01

A two-fluid, neoclassical theory of the interaction of a single magnetic island chain with a resonant error-field in a quasi-cylindrical, low-β, tokamak plasma is presented. The plasmas typically found in large hot tokamaks lie in the so-called weak neoclassical flow-damping regime in which the neoclassical ion stress tensor is not the dominant term in the ion parallel equation of motion. Nevertheless, flow-damping in such plasmas dominates ion perpendicular viscosity, and is largely responsible for determining the phase velocity of a freely rotating island chain (which is in the ion diamagnetic direction relative to the local E × B frame at the rational surface). The critical vacuum island width required to lock the island chain is mostly determined by the ion neoclassical poloidal flow damping rate at the rational surface. The stabilizing effect of the average field-line curvature, as well as the destabilizing effect of the perturbed bootstrap current, is the same for a freely rotating, a non-uniformly rotating, and a locked island chain. The destabilizing effect of the error-field averages to zero when the chain is rotating and only manifests itself when the chain locks. The perturbed ion polarization current has a small destabilizing effect on a freely rotating island chain, but a large destabilizing effect on both a non-uniformly rotating and a locked island chain. This behavior may account for the experimentally observed fact that locked island chains are much more unstable than corresponding freely rotating chains.

Determinants of supply chain coordination of milk and dairy industries in Ethiopia: a case of Addis Ababa and its surroundings.

PubMed

Lemma, Habtamu Regassa; Singh, Rajwinder; Kaur, Navjot

2015-01-01

Coordination of different business activities among units becomes vital as organizations pay much attention to their core activities. Thus, their fruitfulness constantly relies on their capacity to coordinate their internal and external activities in the supply chain outside their own boundaries. Giving consideration to these obvious reasons, this paper aims to investigate the determinants of supply chain coordination of milk and dairy industries. The data were collected from 330 milk suppliers, processors, and retailers in the central part of Ethiopia. The structural equation modeling has been employed to develop the structural relationship between key constructs and measured variables. In total, 15 measured variables for coordination in the supply chain have been identified. These are further grouped into four factors namely, non-price coordination, price coordination, relationships and product development decision. It has been observed that the implementation of these factors could maximize the coordination linkage among supply chain members. Thus, dairy sectors should take the identified coordination factors into account in each of their business dealings.

Role of short-range correlation in facilitation of wave propagation in a long-range ladder chain

NASA Astrophysics Data System (ADS)

Farzadian, O.; Niry, M. D.

2018-09-01

We extend a new method for generating a random chain, which has a kind of short-range correlation induced by a repeated sequence while retaining long-range correlation. Three distinct methods are considered to study the localization-delocalization transition of mechanical waves in one-dimensional disordered media with simultaneous existence of short and long-range correlation. First, a transfer-matrix method was used to calculate numerically the localization length of a wave in a binary chain. We found that the existence of short-range correlation in a long-range correlated chain can increase the localization length at the resonance frequency Ωc. Then, we carried out an analytical study of the delocalization properties of the waves in correlated disordered media around Ωc. Finally, we apply a dynamical method based on the direct numerical simulation of the wave equation to study the propagation of waves in the correlated chain. Imposing short-range correlation on the long-range background will lead the propagation to super-diffusive transport. The results obtained with all three methods are in agreement with each other.

Heat conduction in one-dimensional aperiodic quantum Ising chains.

PubMed

Li, Wenjuan; Tong, Peiqing

2011-03-01

The heat conductivity of nonperiodic quantum Ising chains whose ends are connected with heat baths at different temperatures are studied numerically by solving the Lindblad master equation. The chains are subjected to a uniform transverse field h, while the exchange coupling J{m} between the nearest-neighbor spins takes the two values J{A} and J{B} arranged in Fibonacci, generalized Fibonacci, Thue-Morse, and period-doubling sequences. We calculate the energy-density profile and energy current of the resulting nonequilibrium steady states to study the heat-conducting behavior of finite but large systems. Although these nonperiodic quantum Ising chains are integrable, it is clearly found that energy gradients exist in all chains and the energy currents appear to scale as the system size ~N{α}. By increasing the ratio of couplings, the exponent α can be modulated from α > -1 to α < -1 corresponding to the nontrivial transition from the abnormal heat transport to the heat insulator. The influences of the temperature gradient and the magnetic field to heat conduction have also been discussed.

Soliton Analysis in Complex Molecular Systems: A Zig-Zag Chain

NASA Astrophysics Data System (ADS)

Christiansen, P. L.; Savin, A. V.; Zolotaryuk, A. V.

1997-06-01

A simple numerical method for seeking solitary wavesolutions of a permanent profile in molecular systems of big complexity is presented. The method is essentially based on the minimization of a finite-dimensional function which is chosen under an appropriate discretization of time derivatives in equations of motion. In the present paper, it is applied to a zig-zag chain backbone of coupled particles, each of which has twodegrees of freedom (longitudinal and transverse). Both topological and nontopological soliton solutions are treated for this chain when it is (i) subjected to a two-dimensional periodic substrate potential or (ii) considered as an isolated object, respectively. In the first case, which may be considered as a zig-zag generalization of the Frenkel-Kontorova chain model, two types of kink solutions with different topological charges, describing vacancies of one or two atoms (I- or II-kinks) and defects with excess one or two atoms in the chain (I- or II-antikinks), have been found. The second case (isolated chain) is a generalization of the well-known Fermi-Pasta-Ulam chain model, which takes into account transverse degrees of freedom of the chain molecules. Two types of stable nontopological soliton solutions which describe either (i) a supersonic solitary wave of longitudinal stretching accompanied by transverse slendering or (ii) supersonic pulses of longitudinal compression propagating together with localized transverse thickening (bulge) have been obtained.

Effect of fluid inertia on the motion of a collinear swimmer.

PubMed

Felderhof, B U

2016-12-01

The swimming of a two-sphere system and of a three-sphere chain in an incompressible viscous fluid is studied on the basis of simplified equations of motion which take account of both Stokes friction and added mass effects. The analysis is based on an explicit expression for the asymptotic periodic swimming velocity and a corresponding evaluation of the mean rate of dissipation. The mean swimming velocity of the two-sphere system is found to be nonvanishing provided that the two spheres are not identical. The swimming of a comparable chain of three identical spheres is much more efficient.

Study of the time evolution of correlation functions of the transverse Ising chain with ring frustration by perturbative theory

NASA Astrophysics Data System (ADS)

Zheng, Zhen-Yu; Li, Peng

2018-04-01

We consider the time evolution of two-point correlation function in the transverse-field Ising chain (TFIC) with ring frustration. The time-evolution procedure we investigated is equivalent to a quench process in which the system is initially prepared in a classical kink state and evolves according to the time-dependent Schrödinger equation. Within a framework of perturbative theory (PT) in the strong kink phase, the evolution of the correlation function is disclosed to demonstrate a qualitatively new behavior in contrast to the traditional case without ring frustration.

Nonequilibrium Phase Transition in a Periodically Driven XY Spin Chain

NASA Astrophysics Data System (ADS)

Prosen, Tomaž; Ilievski, Enej

2011-08-01

We present a general formulation of Floquet states of periodically time-dependent open Markovian quasifree fermionic many-body systems in terms of a discrete Lyapunov equation. Illustrating the technique, we analyze periodically kicked XY spin-(1)/(2) chain which is coupled to a pair of Lindblad reservoirs at its ends. A complex phase diagram is reported with reentrant phases of long range and exponentially decaying spin-spin correlations as some of the system’s parameters are varied. The structure of phase diagram is reproduced in terms of counting nontrivial stationary points of Floquet quasiparticle dispersion relation.

Stateline: Critical Mass

ERIC Educational Resources Information Center

Christie, Kathy

2005-01-01

In Physics "critical mass" refers to the minimum amount of fissionable material required to sustain a chain reaction. The adoption of state education policy isn't often equated with this concept, but occasionally solutions and ideas seem to gather around a common problem. If the solution at hand is simple, easily understood, and…

An equal force theory for network models of soft materials with arbitrary molecular weight distribution

NASA Astrophysics Data System (ADS)

Verron, E.; Gros, A.

2017-09-01

Most network models for soft materials, e.g. elastomers and gels, are dedicated to idealized materials: all chains admit the same number of Kuhn segments. Nevertheless, such standard models are not appropriate for materials involving multiple networks, and some specific constitutive equations devoted to these materials have been derived in the last few years. In nearly all cases, idealized networks of different chain lengths are assembled following an equal strain assumption; only few papers adopt an equal stress assumption, although some authors argue that such hypothesis would reflect the equilibrium of the different networks in contact. In this work, a full-network model with an arbitrary chain length distribution is derived by considering that chains of different lengths satisfy the equal force assumption in each direction of the unit sphere. The derivation is restricted to non-Gaussian freely jointed chains and to affine deformation of the sphere. Firstly, after a proper definition of the undeformed configuration of the network, we demonstrate that the equal force assumption leads to the equality of a normalized stretch in chains of different lengths. Secondly, we establish that the network with chain length distribution behaves as an idealized full-network of which both chain length and density of are provided by the chain length distribution. This approach is finally illustrated with two examples: the derivation of a new expression for the Young modulus of bimodal interpenetrated polymer networks, and the prediction of the change in fluorescence during deformation of mechanochemically responsive elastomers.

Mapping of uncertainty relations between continuous and discrete time

NASA Astrophysics Data System (ADS)

Chiuchiú, Davide; Pigolotti, Simone

2018-03-01

Lower bounds on fluctuations of thermodynamic currents depend on the nature of time, discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master equations. We prove that current fluctuations in the master equations are always more likely, due to random timings of transitions. This comparison leads to a mapping of the moments of a current between discrete and continuous time. We exploit this mapping to obtain uncertainty bounds. Our results reduce the quests for uncertainty bounds in discrete and continuous time to a single problem.

Mapping of uncertainty relations between continuous and discrete time.

PubMed

Chiuchiù, Davide; Pigolotti, Simone

2018-03-01

Lower bounds on fluctuations of thermodynamic currents depend on the nature of time, discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master equations. We prove that current fluctuations in the master equations are always more likely, due to random timings of transitions. This comparison leads to a mapping of the moments of a current between discrete and continuous time. We exploit this mapping to obtain uncertainty bounds. Our results reduce the quests for uncertainty bounds in discrete and continuous time to a single problem.

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR).

PubMed

Forte, Esther; Llovell, Felix; Vega, Lourdes F; Trusler, J P Martin; Galindo, Amparo

2011-04-21

An accurate prediction of phase behavior at conditions far and close to criticality cannot be accomplished by mean-field based theories that do not incorporate long-range density fluctuations. A treatment based on renormalization-group (RG) theory as developed by White and co-workers has proven to be very successful in improving the predictions of the critical region with different equations of state. The basis of the method is an iterative procedure to account for contributions to the free energy of density fluctuations of increasing wavelengths. The RG method has been combined with a number of versions of the statistical associating fluid theory (SAFT), by implementing White's earliest ideas with the improvements of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters: a cutoff wavelength L for density fluctuations and an average gradient of the wavelet function Φ. In this work, the SAFT-VR (variable range) equation of state is extended with a similar crossover treatment which, however, follows closely the most recent improvements introduced by White. The interpretation of White's latter developments allows us to establish a straightforward method which enables Φ to be evaluated; only the cutoff wavelength L then needs to be adjusted. The approach used here begins with an initial free energy incorporating only contributions from short-wavelength fluctuations, which are treated locally. The contribution from long-wavelength fluctuations is incorporated through an iterative procedure based on attractive interactions which incorporate the structure of the fluid following the ideas of perturbation theories and using a mapping that allows integration of the radial distribution function. Good agreement close and far from the critical region is obtained using a unique fitted parameter L that can be easily related to the range of the potential. In this way the thermodynamic properties of a square-well (SW) fluid are given by the same number of independent intermolecular model parameters as in the classical equation. Far from the critical region the approach provides the correct limiting behavior reducing to the classical equation (SAFT-VR). In the critical region the β critical exponent is calculated and is found to take values close to the universal value. In SAFT-VR the free energy of an associating chain fluid is obtained following the thermodynamic perturbation theory of Wertheim from the knowledge of the free energy and radial distribution function of a reference monomer fluid. By determining L for SW fluids of varying well width a unique equation of state is obtained for chain and associating systems without further adjustment of critical parameters. We use computer simulation data of the phase behavior of chain and associating SW fluids to test the accuracy of the new equation.

Wave-packet rectification in nonlinear electronic systems: A tunable Aharonov-Bohm diode

PubMed Central

Li, Yunyun; Zhou, Jun; Marchesoni, Fabio; Li, Baowen

2014-01-01

Rectification of electron wave-packets propagating along a quasi-one dimensional chain is commonly achieved via the simultaneous action of nonlinearity and longitudinal asymmetry, both confined to a limited portion of the chain termed wave diode. However, it is conceivable that, in the presence of an external magnetic field, spatial asymmetry perpendicular to the direction of propagation suffices to ensure rectification. This is the case of a nonlinear ring-shaped lattice with different upper and lower halves (diode), which is attached to two elastic chains (leads). The resulting device is mirror symmetric with respect to the ring vertical axis, but mirror asymmetric with respect to the chain direction. Wave propagation along the two diode paths can be modeled for simplicity by a discrete Schrödinger equation with cubic nonlinearities. Numerical simulations demonstrate that, thanks to the Aharonov-Bohm effect, such a diode can be operated by tuning the magnetic flux across the ring. PMID:24691462

Energy exchange and transition to localization in the asymmetric Fermi-Pasta-Ulam oscillatory chain

NASA Astrophysics Data System (ADS)

Smirnov, Valeri V.; Shepelev, Denis S.; Manevitch, Leonid I.

2013-01-01

A finite (periodic) FPU chain is chosen as a convenient model for investigating the energy exchange phenomenon in nonlinear oscillatory systems. As we have recently shown, this phenomenon may occur as a consequence of the resonant interaction between high-frequency nonlinear normal modes. This interaction determines both the complete energy exchange between different parts of the chain and the transition to energy localization in an excited group of particles. In the paper, we demonstrate that this mechanism can exist in realistic (asymmetric) models of atomic or molecular oscillatory chains. Also, we study the resonant interaction of conjugated nonlinear normal modes and prove a possibility of linearization of the equations of motion. The theoretical constructions developed in this paper are based on the concepts of "effective particles" and Limiting Phase Trajectories. In particular, an analytical description of energy exchange between the "effective particles" in the terms of non-smooth functions is presented. The analytical results are confirmed with numerical simulations.

Soliton switching in a site-dependent ferromagnet

NASA Astrophysics Data System (ADS)

Senjudarvannan, R.; Sathishkumar, P.; Vijayalakshmi, S.

2017-02-01

Switching of soliton in a ferromagnetic medium offers the possibility of developing a new innovative approach for information storage technologies. The nonlinear spin dynamics of a site-dependent Heisenberg ferromagnetic spin chain with Gilbert damping under the influence of external magnetic field is expressed in the form of the Landau-Lifshitz-Gilbert equation in the classical continuum limit. The corresponding evolution equation is developed through stereographic projection technique by projecting the unit sphere of spin onto a complex plane. The exact soliton solutions are constructed by solving the associated evolution equation through the modified extended tanh-function method. The impact of damping and external magnetic field on the magnetic soliton under the invariant inhomogeneity is investigated and finally, the magnetization switching in the form of shape changing solitons are demonstrated.

Position and force control of coordinated multiple arms

NASA Technical Reports Server (NTRS)

Hayati, Samad A.

1988-01-01

A technique is presented for controlling multiple manipulators which are holding a single object and therefore form a closed kinematic chain. The object, which may or may not be in contact with a rigid environment, is assumed to be held rigidly by n robot end-effectors. The derivation is based on setting up constraint equations which reduce the 6 x n degrees of freedom of n manipulators each having six joints. Additional constraint equations are considered when one or more degrees of freedom of the object are reduced due to external constraints. Utilizing the operational space dynamic equations, a decoupling controller is designed to control both the position and the interaction forces of the object with the environment. Simulation results for the control of a pair of two-link manipulators are presented.

A theory for fracture of polymeric gels

NASA Astrophysics Data System (ADS)

Mao, Yunwei; Anand, Lallit

2018-06-01

A polymeric gel is a cross-linked polymer network swollen with a solvent. If the concentration of the solvent or the deformation is increased to substantial levels, especially in the presence of flaws, then the gel may rupture. Although various theoretical aspects of coupling of fluid permeation with large deformation of polymeric gels are reasonably well-understood and modeled in the literature, the understanding and modeling of the effects of fluid diffusion on the damage and fracture of polymeric gels is still in its infancy. In this paper we formulate a thermodynamically-consistent theory for fracture of polymeric gels - a theory which accounts for the coupled effects of fluid diffusion, large deformations, damage, and also the gradient effects of damage. The particular constitutive equations for fracture of a gel proposed in our paper, contain two essential new ingredients: (i) Our constitutive equation for the change in free energy of a polymer network accounts for not only changes in the entropy, but also changes in the internal energy due the stretching of the Kuhn segments of the polymer chains in the network. (ii) The damage and failure of the polymer network is taken to occur by chain-scission, a process which is driven by the changes in the internal energy of the stretched polymer chains in the network, and not directly by changes in the configurational entropy of the polymer chains. The theory developed in this paper is numerically implemented in an open-source finite element code MOOSE, by writing our own application. Using this simulation capability we report on our study of the fracture of a polymeric gel, and some interesting phenomena which show the importance of the diffusion of the fluid on fracture response of the gel are highlighted.

Momentum-Based Dynamics for Spacecraft with Chained Revolute Appendages

NASA Technical Reports Server (NTRS)

Queen, Steven; London, Ken; Gonzalez, Marcelo

2005-01-01

An efficient formulation is presented for a sub-class of multi-body dynamics problems that involve a six degree-of-freedom base body and a chain of N rigid linkages connected in series by single degree-of-freedom revolute joints. This general method is particularly well suited for simulations of spacecraft dynamics and control that include the modeling of an orbiting platform with or without internal degrees of freedom such as reaction wheels, dampers, and/or booms. In the present work, particular emphasis is placed on dynamic simulation of multi-linkage robotic manipulators. The differential equations of motion are explicitly given in terms of linear and angular momentum states, which can be evaluated recursively along a serial chain of linkages for an efficient real-time solution on par with the best of the O(N3) methods.

Coupled pendula chains under parametric PT-symmetric driving force

NASA Astrophysics Data System (ADS)

Destyl, E.; Nuiro, S. P.; Pelinovsky, D. E.; Poullet, P.

2017-12-01

We consider a chain of coupled pendula pairs, where each pendulum is connected to the nearest neighbors in the longitudinal and transverse directions. The common strings in each pair are modulated periodically by an external force. In the limit of small coupling and near the 1 : 2 parametric resonance, we derive a novel system of coupled PT-symmetric discrete nonlinear Schrödinger equations, which has Hamiltonian symmetry but has no phase invariance. By using the conserved energy, we find the parameter range for the linear and nonlinear stability of the zero equilibrium. Numerical experiments illustrate how destabilization of the zero equilibrium takes place when the stability constraints are not satisfied. The central pendulum excites nearest pendula and this process continues until a dynamical equilibrium is reached where each pendulum in the chain oscillates at a finite amplitude.

Bethe-Boltzmann hydrodynamics and spin transport in the XXZ chain

NASA Astrophysics Data System (ADS)

Bulchandani, Vir B.; Vasseur, Romain; Karrasch, Christoph; Moore, Joel E.

2018-01-01

Quantum integrable systems, such as the interacting Bose gas in one dimension and the XXZ quantum spin chain, have an extensive number of local conserved quantities that endow them with exotic thermalization and transport properties. We discuss recently introduced hydrodynamic approaches for such integrable systems from the viewpoint of kinetic theory and extend the previous works by proposing a numerical scheme to solve the hydrodynamic equations for finite times and arbitrary locally equilibrated initial conditions. We then discuss how such methods can be applied to describe nonequilibrium steady states involving ballistic heat and spin currents. In particular, we show that the spin Drude weight in the XXZ chain, previously accessible only by rigorous techniques of limited scope or controversial thermodynamic Bethe ansatz arguments, may be evaluated from hydrodynamics in very good agreement with density-matrix renormalization group calculations.

Integration within the Felsenstein equation for improved Markov chain Monte Carlo methods in population genetics

PubMed Central

Hey, Jody; Nielsen, Rasmus

2007-01-01

In 1988, Felsenstein described a framework for assessing the likelihood of a genetic data set in which all of the possible genealogical histories of the data are considered, each in proportion to their probability. Although not analytically solvable, several approaches, including Markov chain Monte Carlo methods, have been developed to find approximate solutions. Here, we describe an approach in which Markov chain Monte Carlo simulations are used to integrate over the space of genealogies, whereas other parameters are integrated out analytically. The result is an approximation to the full joint posterior density of the model parameters. For many purposes, this function can be treated as a likelihood, thereby permitting likelihood-based analyses, including likelihood ratio tests of nested models. Several examples, including an application to the divergence of chimpanzee subspecies, are provided. PMID:17301231

Compression induced phase transition of nematic brush: A mean-field theory study

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

Tang, Jiuzhou; Zhang, Xinghua, E-mail: zhangxh@bjtu.edu.cn; Yan, Dadong, E-mail: yandd@bnu.edu.cn

2015-11-28

Responsive behavior of polymer brush to the external compression is one of the most important characters for its application. For the flexible polymer brush, in the case of low grafting density, which is widely studied by the Gaussian chain model based theory, the compression leads to a uniform deformation of the chain. However, in the case of high grafting density, the brush becomes anisotropic and the nematic phase will be formed. The normal compression tends to destroy the nematic order, which leads to a complex responsive behaviors. Under weak compression, chains in the nematic brush are buckled, and the bendingmore » energy and Onsager interaction give rise to the elasticity. Under deep compression, the responsive behaviors of the nematic polymer brush depend on the chain rigidity. For the compressed rigid polymer brush, the chains incline to re-orientate randomly to maximize the orientational entropy and its nematic order is destroyed. For the compressed flexible polymer brush, the chains incline to fold back to keep the nematic order. A buckling-folding transition takes place during the compressing process. For the compressed semiflexible brush, the chains are collectively tilted to a certain direction, which leads to the breaking of the rotational symmetry in the lateral plane. These responsive behaviors of nematic brush relate to the properties of highly frustrated worm-like chain, which is hard to be studied by the traditional self-consistent field theory due to the difficulty to solve the modified diffusion equation. To overcome this difficulty, a single chain in mean-field theory incorporating Monte Carlo simulation and mean-field theory for the worm-like chain model is developed in present work. This method shows high performance for entire region of chain rigidity in the confined condition.« less

Integrable open spin chains from flavored ABJM theory

NASA Astrophysics Data System (ADS)

Bai, Nan; Chen, Hui-Huang; He, Song; Wu, Jun-Bao; Yang, Wen-Li; Zhu, Meng-Qi

2017-08-01

We compute the two-loop anomalous dimension matrix in the scalar sector of planar N=3 flavored ABJM theory. Using coordinate Bethe ansatz, we obtain the reflection matrices and confirm that the boundary Yang-Baxter equations are satisfied. This establishes the integrability of this theory in the scalar sector at the two-loop order.

Factorized three-body S-matrix restrained by the Yang–Baxter equation and quantum entanglements

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

Yu, Li-Wei, E-mail: NKyulw@gmail.com; Zhao, Qing, E-mail: qzhaoyuping@bit.edu.cn; Ge, Mo-Lin, E-mail: geml@nankai.edu.cn

2014-09-15

This paper investigates the physical effects of the Yang–Baxter equation (YBE) to quantum entanglements through the 3-body S-matrix in entangling parameter space. The explicit form of 3-body S-matrix Ř{sub 123}(θ,φ) based on the 2-body S-matrices is given due to the factorization condition of YBE. The corresponding chain Hamiltonian has been obtained and diagonalized, also the Berry phase for 3-body system is given. It turns out that by choosing different spectral parameters the Ř(θ,φ)-matrix gives GHZ and W states respectively. The extended 1-D Kitaev toy model has been derived. Examples of the role of the model in entanglement transfer are discussed.more » - Highlights: • We give the relation between 3-body S-matrix and 3-qubit entanglement. • The relation between 3-qubit and 2-qubit entanglements is investigated via YBE. • 1D Kitaev toy model is derived by the Type-II solution of YBE. • The condition of YBE kills the “Zero boundary mode” in our chain model.« less

Bilinear forms and soliton solutions for a fourth-order variable-coefficient nonlinear Schrödinger equation in an inhomogeneous Heisenberg ferromagnetic spin chain or an alpha helical protein

NASA Astrophysics Data System (ADS)

Yang, Jin-Wei; Gao, Yi-Tian; Wang, Qi-Min; Su, Chuan-Qi; Feng, Yu-Jie; Yu, Xin

2016-01-01

In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation is studied, which might describe a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain with the octuple-dipole interaction or an alpha helical protein with higher-order excitations and interactions under continuum approximation. With the aid of auxiliary function, we derive the bilinear forms and corresponding constraints on the variable coefficients. Via the symbolic computation, we obtain the Lax pair, infinitely many conservation laws, one-, two- and three-soliton solutions. We discuss the influence of the variable coefficients on the solitons. With different choices of the variable coefficients, we obtain the parabolic, cubic, and periodic solitons, respectively. We analyse the head-on and overtaking interactions between/among the two and three solitons. Interactions between a bound state and a single soliton are displayed with different choices of variable coefficients. We also derive the quasi-periodic formulae for the three cases of the bound states.

Validation of optimization strategies using the linear structured production chains

NASA Astrophysics Data System (ADS)

Kusiak, Jan; Morkisz, Paweł; Oprocha, Piotr; Pietrucha, Wojciech; Sztangret, Łukasz

2017-06-01

Different optimization strategies applied to sequence of several stages of production chains were validated in this paper. Two benchmark problems described by ordinary differential equations (ODEs) were considered. A water tank and a passive CR-RC filter were used as the exemplary objects described by the first and the second order differential equations, respectively. Considered in the work optimization problems serve as the validators of strategies elaborated by the Authors. However, the main goal of research is selection of the best strategy for optimization of two real metallurgical processes which will be investigated in an on-going projects. The first problem will be the oxidizing roasting process of zinc sulphide concentrate where the sulphur from the input concentrate should be eliminated and the minimal concentration of sulphide sulphur in the roasted products has to be achieved. Second problem will be the lead refining process consisting of three stages: roasting to the oxide, oxide reduction to metal and the oxidizing refining. Strategies, which appear the most effective in considered benchmark problems will be candidates for optimization of the mentioned above industrial processes.

Analysis of laser energy characteristics of laser guided weapons based on the hardware-in-the-loop simulation system

NASA Astrophysics Data System (ADS)

Zhu, Yawen; Cui, Xiaohong; Wang, Qianqian; Tong, Qiujie; Cui, Xutai; Li, Chenyu; Zhang, Le; Peng, Zhong

2016-11-01

The hardware-in-the-loop simulation system, which provides a precise, controllable and repeatable test conditions, is an important part of the development of the semi-active laser (SAL) guided weapons. In this paper, laser energy chain characteristics were studied, which provides a theoretical foundation for the SAL guidance technology and the hardware-in-the-loop simulation system. Firstly, a simplified equation was proposed to adjust the radar equation according to the principles of the hardware-in-the-loop simulation system. Secondly, a theoretical model and calculation method were given about the energy chain characteristics based on the hardware-in-the-loop simulation system. We then studied the reflection characteristics of target and the distance between the missile and target with major factors such as the weather factors. Finally, the accuracy of modeling was verified by experiment as the values measured experimentally generally follow the theoretical results from the model. And experimental results revealed that ratio of attenuation of the laser energy exhibited a non-linear change vs. pulse number, which were in accord with the actual condition.

Handling target obscuration through Markov chain observations

NASA Astrophysics Data System (ADS)

Kouritzin, Michael A.; Wu, Biao

2008-04-01

Target Obscuration, including foliage or building obscuration of ground targets and landscape or horizon obscuration of airborne targets, plagues many real world filtering problems. In particular, ground moving target identification Doppler radar, mounted on a surveillance aircraft or unattended airborne vehicle, is used to detect motion consistent with targets of interest. However, these targets try to obscure themselves (at least partially) by, for example, traveling along the edge of a forest or around buildings. This has the effect of creating random blockages in the Doppler radar image that move dynamically and somewhat randomly through this image. Herein, we address tracking problems with target obscuration by building memory into the observations, eschewing the usual corrupted, distorted partial measurement assumptions of filtering in favor of dynamic Markov chain assumptions. In particular, we assume the observations are a Markov chain whose transition probabilities depend upon the signal. The state of the observation Markov chain attempts to depict the current obscuration and the Markov chain dynamics are used to handle the evolution of the partially obscured radar image. Modifications of the classical filtering equations that allow observation memory (in the form of a Markov chain) are given. We use particle filters to estimate the position of the moving targets. Moreover, positive proof-of-concept simulations are included.

A kinetic theory description of the viscosity of dense fluids consisting of chain molecules.

PubMed

de Wijn, Astrid S; Vesovic, Velisa; Jackson, George; Trusler, J P Martin

2008-05-28

An expression for the viscosity of a dense fluid is presented that includes the effect of molecular shape. The molecules of the fluid are approximated by chains of equal-sized, tangentially jointed, rigid spheres. It is assumed that the collision dynamics in such a fluid can be approximated by instantaneous collisions between two rigid spheres belonging to different chains. The approach is thus analogous to that of Enskog for a fluid consisting of rigid spheres. The description is developed in terms of two molecular parameters, the diameter sigma of the spherical segment and the chain length (number of segments) m. It is demonstrated that an analysis of viscosity data of a particular pure fluid alone cannot be used to obtain independently effective values of both sigma and m. Nevertheless, the chain lengths of n-alkanes are determined by assuming that the diameter of each rigid sphere making up the chain can be represented by the diameter of a methane molecule. The effective chain lengths of n-alkanes are found to increase linearly with the number C of carbon atoms present. The dependence can be approximated by a simple relationship m=1+(C-1)3. The same relationship was reported within the context of a statistical associating fluid theory equation of state treatment of the fluid, indicating that both the equilibrium thermodynamic properties and viscosity yield the same value for the chain lengths of n-alkanes.

Double-exponential decay of orientational correlations in semiflexible polyelectrolytes.

PubMed

Bačová, P; Košovan, P; Uhlík, F; Kuldová, J; Limpouchová, Z; Procházka, K

2012-06-01

In this paper we revisited the problem of persistence length of polyelectrolytes. We performed a series of Molecular Dynamics simulations using the Debye-Hückel approximation for electrostatics to test several equations which go beyond the classical description of Odijk, Skolnick and Fixman (OSF). The data confirm earlier observations that in the limit of large contour separations the decay of orientational correlations can be described by a single-exponential function and the decay length can be described by the OSF relation. However, at short countour separations the behaviour is more complex. Recent equations which introduce more complicated expressions and an additional length scale could describe the results very well on both the short and the long length scale. The equation of Manghi and Netz when used without adjustable parameters could capture the qualitative trend but deviated in a quantitative comparison. Better quantitative agreement within the estimated error could be obtained using three equations with one adjustable parameter: 1) the equation of Manghi and Netz; 2) the equation proposed by us in this paper; 3) the equation proposed by Cannavacciuolo and Pedersen. Two characteristic length scales can be identified in the data: the intrinsic or bare persistence length and the electrostatic persistence length. All three equations use a single parameter to describe a smooth crossover from the short-range behaviour dominated by the intrinsic stiffness of the chain to the long-range OSF-like behaviour.

A multi-level solution algorithm for steady-state Markov chains

NASA Technical Reports Server (NTRS)

Horton, Graham; Leutenegger, Scott T.

1993-01-01

A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.

Excitations of breathers and rogue wave in the Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Qi, Jian-Wen; Duan, Liang; Yang, Zhan-Ying; Yang, Wen-Li

2018-01-01

We study the excitations of breathers and rogue wave in a classical Heisenberg spin chain with twist interaction, which is governed by a fourth-order integrable nonlinear Schrödinger equation. The dynamics of these waves have been extracted from an exact solution. In particular, the corresponding existence conditions based on the parameters of perturbation wave number K, magnon number N, background wave vector ks and amplitude c are presented explicitly. Furthermore, the characteristics of magnetic moment distribution corresponding to these nonlinear waves are also investigated in detail. Finally, we discussed the state transition of three types nonlinear localized waves under the different excitation conditions.

Geodesic Monte Carlo on Embedded Manifolds

PubMed Central

Byrne, Simon; Girolami, Mark

2013-01-01

Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton–Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices. PMID:25309024

Statistical Physics on the Eve of the 21st Century: in Honour of J B McGuire on the Occasion of His 65th Birthday

NASA Astrophysics Data System (ADS)

Batchelor, Murray T.; Wille, Luc T.

The Table of Contents for the book is as follows: * Preface * Modelling the Immune System - An Example of the Simulation of Complex Biological Systems * Brief Overview of Quantum Computation * Quantal Information in Statistical Physics * Modeling Economic Randomness: Statistical Mechanics of Market Phenomena * Essentially Singular Solutions of Feigenbaum- Type Functional Equations * Spatiotemporal Chaotic Dynamics in Coupled Map Lattices * Approach to Equilibrium of Chaotic Systems * From Level to Level in Brain and Behavior * Linear and Entropic Transformations of the Hydrophobic Free Energy Sequence Help Characterize a Novel Brain Polyprotein: CART's Protein * Dynamical Systems Response to Pulsed High-Frequency Fields * Bose-Einstein Condensates in the Light of Nonlinear Physics * Markov Superposition Expansion for the Entropy and Correlation Functions in Two and Three Dimensions * Calculation of Wave Center Deflection and Multifractal Analysis of Directed Waves Through the Study of su(1,1)Ferromagnets * Spectral Properties and Phases in Hierarchical Master Equations * Universality of the Distribution Functions of Random Matrix Theory * The Universal Chiral Partition Function for Exclusion Statistics * Continuous Space-Time Symmetries in a Lattice Field Theory * Quelques Cas Limites du Problème à N Corps Unidimensionnel * Integrable Models of Correlated Electrons * On the Riemann Surface of the Three-State Chiral Potts Model * Two Exactly Soluble Lattice Models in Three Dimensions * Competition of Ferromagnetic and Antiferromagnetic Order in the Spin-l/2 XXZ Chain at Finite Temperature * Extended Vertex Operator Algebras and Monomial Bases * Parity and Charge Conjugation Symmetries and S Matrix of the XXZ Chain * An Exactly Solvable Constrained XXZ Chain * Integrable Mixed Vertex Models Ftom the Braid-Monoid Algebra * From Yang-Baxter Equations to Dynamical Zeta Functions for Birational Tlansformations * Hexagonal Lattice Directed Site Animals * Direction in the Star-Triangle Relations * A Self-Avoiding Walk Through Exactly Solved Lattice Models in Statistical Mechanics

Current of interacting particles inside a channel of exponential cavities: Application of a modified Fick-Jacobs equation.

PubMed

Suárez, G; Hoyuelos, M; Mártin, H

2016-06-01

Recently a nonlinear Fick-Jacobs equation has been proposed for the description of transport and diffusion of particles interacting through a hard-core potential in tubes or channels of varying cross section [Suárez et al., Phys. Rev. E 91, 012135 (2015)]PLEEE81539-375510.1103/PhysRevE.91.012135. Here we focus on the analysis of the current and mobility when the channel is composed by a chain of asymmetric cavities and a force is applied in one or the opposite direction, for both interacting and noninteracting particles, and compare analytical and Monte Carlo simulation results. We consider a cavity with a shape given by exponential functions; the linear Fick-Jacobs equation for noninteracting particles can be exactly solved in this case. The results of the current difference (when a force is applied in opposite directions) are more accurate for the modified Fick-Jacobs equation for particles with hard-core interaction than for noninteracting ones.

Physics, stability, and dynamics of supply networks

NASA Astrophysics Data System (ADS)

Helbing, Dirk; Lämmer, Stefan; Seidel, Thomas; Šeba, Pétr; Płatkowski, Tadeusz

2004-12-01

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the nonlinear behavior is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed “bullwhip effect” in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by damped or growing oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.

Allometric constraints on Sr/Ca and Ba/Ca partitioning in terrestrial mammalian trophic chains.

PubMed

Balter, Vincent

2004-03-01

In biological systems, strontium (Sr) and barium (Ba) are two non-essential elements, in comparison to calcium (Ca) which is essential. The Sr/Ca and Ba/Ca ratios tend to decrease in biochemical pathways which include Ca as an essential element, and these processes are termed biopurification of Ca. The quantitative pathway of the biopurification of Ca in relation to Sr and Ba between two biological reservoirs ( Rn and R(n -1)) is measured with an observed ratio (OR) expressed by the (Sr/Ca) Rn /(Sr/Ca)( Rn-1) and (Ba/Ca) Rn /(Ba/Ca)( Rn-1) ratios. For a mammalian organism, during the whole biopurification of Ca starting with the diet to the ultimate reservoir of Ca which is the bone, the mean values for ORSr and ORBa are 0.25 and 0.2, respectively. In this study, published Sr/Ca and Ba/Ca ratios are used for three sets of soils, plants, and bones of herbivorous and carnivorous mammals, each comprising a trophic chain, to illustrate the biopurification of Ca at the level of trophic chains. Calculated ORSr and ORBa of herbivore bones in relation to plants and of bones of carnivores in relation to bones of herbivores give ORSr=0.30+/-0.08 and ORBa=0.16+/-0.08, thus suggesting that trophic chains reflect the Sr/Ca and Ba/Ca fluxes that are prevalent at the level of a mammalian organism. The slopes of the three regression equations of log(Sr/Ca) vs. log(Ba/Ca) are similar, indicating that the process of biopurification of Ca with respect to Sr and Ba is due to biological processes and is independent of the geological settings. Modifications of the logarithmic expression of the Sr/Ca and Ba/Ca relationship allow a new formula of the biopurification process to be deduced, leading to the general equation ORBa=ORSr(1.79+/-0.33), where the allometric coefficient is the mean of the slopes of the three regression equations. Some recent examples are used to illustrate this new analysis of predator-prey relations between mammals. This opens up new possibilities for the utilization of Ba/Ca and Sr/Ca in addition to stable isotope ratios (delta13C and delta15N) for the determination of the relative contribution of different food sources to an animal's diet.

Universal calculational recipe for solvent-mediated potential: based on a combination of integral equation theory and density functional theory

NASA Astrophysics Data System (ADS)

Zhou, Shiqi

2004-07-01

A universal formalism, which enables calculation of solvent-mediated potential (SMP) between two equal or non-equal solute particles with any shape immersed in solvent reservior consisting of atomic particle and/or polymer chain or their mixture, is proposed by importing a density functional theory externally into OZ equation systems. Only if size asymmetry of the solvent bath components is moderate, the present formalism can calculate the SMP in any complex fluids at the present development stage of statistical mechanics, and therefore avoids all of limitations of previous approaches for SMP. Preliminary calculation indicates the reliability of the present formalism.

An Elementary Introduction to Recently Developed Computational Methods for Solving Singularly Perturbed Partial Differential Equations Arising in Science and Engineering

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Srivastava, Akanksha

2013-01-01

This paper presents a survey of innovative approaches of the most effective computational techniques for solving singular perturbed partial differential equations, which are useful because of their numerical and computer realizations. Many applied problems appearing in semiconductors theory, biochemistry, kinetics, theory of electrical chains, economics, solid mechanics, fluid dynamics, quantum mechanics, and many others can be modelled as singularly perturbed systems. Here, we summarize a wide range of research articles published by numerous researchers during the last ten years to get a better view of the present scenario in this area of research.

Spatial operator algebra framework for multibody system dynamics

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Jain, Abhinandan; Kreutz, K.

1989-01-01

The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.

Spatial Operator Algebra for multibody system dynamics

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.

1992-01-01

The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.

Design-Parameters Setup for Power-Split Dual-Regime IVT

NASA Astrophysics Data System (ADS)

Preda, Ion; Ciolan, Gheorghe; Covaciu, Dinu

2017-10-01

To analyze the working possibilities of power-split infinitely variable transmissions (IVTs) it is necessary to follow a systematic approach. The method proposed in this paper consists of generating a block diagram of the transmission and then, based on this diagram, to derive the kinematics and dynamics equations of the transmission. For an actual numerical case, the derived equations are used to find characteristic values of the transmission components (gear and chain drives, planetary units) necessary to calculate the speed ratios, the speeds, torques and powers acting on the shafts and coupling (control) elements, and even to estimate the overall efficiency of the transmission.

Energy localization in the phi4 oscillator chain.

PubMed

Ponno, A; Ruggiero, J; Drigo, E; De Luca, J

2006-05-01

We study energy localization in a finite one-dimensional phi(4) oscillator chain with initial energy in a single oscillator of the chain. We numerically calculate the effective number of degrees of freedom sharing the energy on the lattice as a function of time. We find that for energies smaller than a critical value, energy equipartition among the oscillators is reached in a relatively short time. On the other hand, above the critical energy, a decreasing number of particles sharing the energy is observed. We give an estimate of the effective number of degrees of freedom as a function of the energy. Our results suggest that localization is due to the appearance, above threshold, of a breather-like structure. Analytic arguments are given, based on the averaging theory and the analysis of a discrete nonlinear Schrödinger equation approximating the dynamics, to support and explain the numerical results.

Effects of internal friction on contact formation dynamics of polymer chain

NASA Astrophysics Data System (ADS)

Bian, Yukun; Li, Peng; Zhao, Nanrong

2018-04-01

A theoretical framework is presented to study the contact formation dynamics of polymer chains, in accompany with an electron-transfer quenching. Based on a non-Markovian Smoluchowski equation supplemented with an exponential sink term, we derive the mean time of contact formation under Wilemski-Fixman approximation. Our particular attentions are paid to the effect of internal friction. We find out that internal friction induces a novel fractional viscosity dependence, which will become more remarkable as internal friction increases. Furthermore, we clarify that internal friction inevitably promotes a diffusion-controlled mechanism by slowing the chain relaxation. Finally, we apply our theory to rationalise the experimental investigation for contact formation of a single-stranded DNA. The theoretical results can reproduce the experimental data very well with quite reasonable estimation for the intrinsic parameters. Such good agreements clearly demonstrate the validity of our theory which has appropriately addressed the very role of internal friction to the relevant dynamics.

Soliton-impurity interaction in two Ablowitz-Ladik chains with different coupling

NASA Astrophysics Data System (ADS)

Kamburova, R. S.; Primatarowa, M. T.

2014-12-01

The interaction of solitons with point defects in a system of coupled Ablowitz- Ladik (AL) chains is studied numerically. The system is a discrete analog of coupled nonlinear Schrodinger equations. Two types of interchain coupling are investigated: one which admits reduction of the system to the standard integrable AL model (dispersive coupling) and one which couples opposite sites of the chains and does not admit reduction to the AL model (nondispersive coupling). The action of the two coupling types is additive and they can compensate each other in some cases. We have obtained that the single-peak bound soliton-defect solution (attractive impurity) is stable against perturbations, while the double-peak bound soliton-defect solution (repulsive impurity) is unstable and can be easily destroyed. Linear point defects do not influence the period of energy transfer and it is close to the period for the homogeneous case.

Experiments and kinematics analysis of a hand rehabilitation exoskeleton with circuitous joints.

PubMed

Zhang, Fuhai; Fu, Yili; Zhang, Qinchao; Wang, Shuguo

2015-01-01

Aiming at the hand rehabilitation of stroke patients, a wearable hand exoskeleton with circuitous joint is proposed. The circuitous joint adopts the symmetric pinion and rack mechanism (SPRM) with the parallel mechanism. The exoskeleton finger is a serial mechanism composed of three closed-chain SPRM joints in series. The kinematic equations of the open chain of the finger and the closed chains of the SPRM joints were built to analyze the kinematics of the hand rehabilitation exoskeleton. The experimental setup of the hand rehabilitation exoskeleton was built and the continuous passive motion (CPM) rehabilitation experiment and the test of human-robot interaction force measurement were conducted. Experiment results show that the mechanical design of the hand rehabilitation robot is reasonable and that the kinematic analysis is correct, thus the exoskeleton can be used for the hand rehabilitation of stroke patients.

An Adjoint State Method for Three-Dimensional Transmission Traveltime Tomography Using First-Arrivals

DTIC Science & Technology

2006-01-30

detail next. 3.2 Fast Sweeping Method for Equation (1) The fast sweeping method was originated in Boue and Dupis [5], its first PDE formulation was in...Geophysics, 50:903–923, 1985. [5] M. Boue and P. Dupuis. Markov chain approximations for deterministic control prob- lems with affine dynamics and

Collective effects on activated segmental relaxation in supercooled polymer melts

NASA Astrophysics Data System (ADS)

Mirigian, Stephen; Schweizer, Kenneth

2013-03-01

We extend the polymer nonlinear Langevin equation (NLE) theory of activated segmental dynamics in supercooled polymer melts in two new directions. First, a well-defined mapping from real monomers to a freely-jointed chain is formulated that retains information about chain stiffness, monomer volume, and the amplitude of thermal density fluctuations. Second, collective effects beyond the local cage scale are included based on an elastic solid-state perspective in the ``shoving model'' spirit which accounts for longer range contributions to the activation barrier. In contrast to previous phenomenological treatments of this model, we formulate an explicit microscopic picture of the hopping event, and derive, not assume, that the collective barrier is directly related to the elastic shear modulus. Local hopping is thus renormalized by collective motions of the surroundings that are required to physically accommodate it. Using the PRISM theory of structure, and known compressibility and chain statistics information, quantitative applications of the new theory to predict the temperature and chain length dependence of the alpha time, shear modulus, and fragility are carried out for a range of real polymer liquids and compared to experiment.

Subsampled Numerical Experiments as a Guide for Field Deployment of Thermistor Chains

NASA Astrophysics Data System (ADS)

Shaw, Justin; Stastna, Marek

2017-11-01

Thermistor chains are a standard tool for recording temperature profiles in geophysical flows. Density values can be inferred from readings and the resulting density field analyzed for the passage of internal waves, Kelvin-Helmholtz billows, and other dynamic events. The number and spacing of the thermistors, both on and between chains, determines which events can be identified in the dataset. We examine the effect of changing these variables by subsampling a set of numerical experiments to simulate thermistor chain locations. A pseudo spectral method was used to solve the incompressible Navier-Stokes equations under the Boussinesq approximation. The resulting flows are a set of high resolution seiches where the depth was held constant across experiments, and the length was varied. Sampling a known, commonly occurring flow with relatively simple geometry allows for a clear analysis of the effects of thermistor placement in the capture of dynamic events. We will discuss three dimensional deployment strategies, as well as EOF and DMD analyses if there is time. Funded by a Grant from the National Sciences and Engineering Research Council of Canada.

The isotropic-nematic and nematic-nematic phase transition of binary mixtures of tangent hard-sphere chain fluids: An analytical equation of state

NASA Astrophysics Data System (ADS)

van Westen, Thijs; Vlugt, Thijs J. H.; Gross, Joachim

2014-01-01

An analytical equation of state (EoS) is derived to describe the isotropic (I) and nematic (N) phase of linear- and partially flexible tangent hard-sphere chain fluids and their mixtures. The EoS is based on an extension of Onsager's second virial theory that was developed in our previous work [T. van Westen, B. Oyarzún, T. J. H. Vlugt, and J. Gross, J. Chem. Phys. 139, 034505 (2013)]. Higher virial coefficients are calculated using a Vega-Lago rescaling procedure, which is hereby generalized to mixtures. The EoS is used to study (1) the effect of length bidispersity on the I-N and N-N phase behavior of binary linear tangent hard-sphere chain fluid mixtures, (2) the effect of partial molecular flexibility on the binary phase diagram, and (3) the solubility of hard-sphere solutes in I- and N tangent hard-sphere chain fluids. By changing the length bidispersity, two types of phase diagrams were found. The first type is characterized by an I-N region at low pressure and a N-N demixed region at higher pressure that starts from an I-N-N triphase equilibrium. The second type does not show the I-N-N equilibrium. Instead, the N-N region starts from a lower critical point at a pressure above the I-N region. The results for the I-N region are in excellent agreement with the results from molecular simulations. It is shown that the N-N demixing is driven both by orientational and configurational/excluded volume entropy. By making the chains partially flexible, it is shown that the driving force resulting from the configurational entropy is reduced (due to a less anisotropic pair-excluded volume), resulting in a shift of the N-N demixed region to higher pressure. Compared to linear chains, no topological differences in the phase diagram were found. We show that the solubility of hard-sphere solutes decreases across the I-N phase transition. Furthermore, it is shown that by using a liquid crystal mixture as the solvent, the solubility difference can by maximized by tuning the composition. Theoretical results for the Henry's law constant of the hard-sphere solute are in good agreement with the results from molecular simulation.

Excess entropy scaling for the segmental and global dynamics of polyethylene melts.

PubMed

Voyiatzis, Evangelos; Müller-Plathe, Florian; Böhm, Michael C

2014-11-28

The range of validity of the Rosenfeld and Dzugutov excess entropy scaling laws is analyzed for unentangled linear polyethylene chains. We consider two segmental dynamical quantities, i.e. the bond and the torsional relaxation times, and two global ones, i.e. the chain diffusion coefficient and the viscosity. The excess entropy is approximated by either a series expansion of the entropy in terms of the pair correlation function or by an equation of state for polymers developed in the context of the self associating fluid theory. For the whole range of temperatures and chain lengths considered, the two estimates of the excess entropy are linearly correlated. The scaled bond and torsional relaxation times fall into a master curve irrespective of the chain length and the employed scaling scheme. Both quantities depend non-linearly on the excess entropy. For a fixed chain length, the reduced diffusion coefficient and viscosity scale linearly with the excess entropy. An empirical reduction to a chain length-independent master curve is accessible for both dynamic quantities. The Dzugutov scheme predicts an increased value of the scaled diffusion coefficient with increasing chain length which contrasts physical expectations. The origin of this trend can be traced back to the density dependence of the scaling factors. This finding has not been observed previously for Lennard-Jones chain systems (Macromolecules, 2013, 46, 8710-8723). Thus, it limits the applicability of the Dzugutov approach to polymers. In connection with diffusion coefficients and viscosities, the Rosenfeld scaling law appears to be of higher quality than the Dzugutov approach. An empirical excess entropy scaling is also proposed which leads to a chain length-independent correlation. It is expected to be valid for polymers in the Rouse regime.

Study of fracture and stress-induced morphological instabilities in polymeric materials

NASA Astrophysics Data System (ADS)

Sabouri-Ghomi, Mohsen

We study the phenomena of fracture in polymers at the molecular and continuum level. At a molecular level, we study the failure of polymer/polymer interfaces. Our main focus is on a specific mode of failure known as chain pull-out fracture, which is common to weak adhesive junctions, and polymer blends and mixtures. In the case of the interface between incompatible polymers, reinforcement is achieved by adding a block copolymer to the interface. We introduce a microscopic model based on Brownian dynamics to investigate the effect of the polymerization index N, of the block connector chain, on fracture toughness of such reinforced polymeric junctions. We consider the mushroom regime, where connector chains are grafted with low surface density, for the case of large pulling velocity. We find that for short chains the interface fracture toughness depends linearly on the polymerization index N of the connector chains, while for longer chains the dependence becomes N 3/2. We propose a scaling argument, based on the geometry of the initial configuration, that accounts for both short and long chains and the crossover between them. At the continuum level, we study the pattern selection mechanism of finger-like crack growth phenomena in gradient driven growth problems in general, and the structure of stress-induced morphological instabilities in crazing of polymer glasses in particular. We simulate solidification in a narrow channel through the use of a phase-field model with an adaptive grid. By tuning a dimensionless parameter, the Peclet number, we show a continuous crossover from a free dendrite at high Peclet numbers to anisotropic viscous fingering at low Peclet numbers. At low Peclet numbers we find good agreement between our results, theoretical predictions, and experiment, providing the first quantitative test of solvability theory for anisotropic viscous fingers. For high undercoolings, we find new phenomena, a solid forger which satisfies stability and thermodynamic criterion. We further provide an analytical form for the shape of these fingers, based on local models of solidification, which fits our numerical results from simulation. Later we study the growth of crazes in polymer glasses by deriving the equations of motion of plastic flow at the craze tip, and the steady-state velocity profile of this flow. By developing a phenomenological model, we solve the full time-dependent equations of motion of this highly non-linear phenomena. Our simulation produces the steady-state cellular pattern observed in experiments. We further show that polymer glasses with lower yield stress produce cellular patterns with sharper tips and more cells, indicating instabilities with smaller wavelengths.

The meaning of the "universal" WLF parameters of glass-forming polymer liquids

NASA Astrophysics Data System (ADS)

Dudowicz, Jacek; Douglas, Jack F.; Freed, Karl F.

2015-01-01

Although the Williams-Landell-Ferry (WLF) equation for the segmental relaxation time τ(T) of glass-forming materials is one of the most commonly encountered relations in polymer physics, its molecular basis is not well understood. The WLF equation is often claimed to be equivalent to the Vogel-Fulcher-Tammann (VFT) equation, even though the WLF expression for τ(T) contains no explicit dependence on the fragility parameter D of the VFT equation, while the VFT equation lacks any explicit reference to the glass transition temperature Tg, the traditionally chosen reference temperature in the WLF equation. The observed approximate universality of the WLF parameters C1 ( g ) and C2 ( g ) implies that τ(T) depends only on T-Tg, a conclusion that seems difficult to reconcile with the VFT equation where the fragility parameter D largely governs the magnitude of τ(T). The current paper addresses these apparent inconsistencies by first evaluating the macroscopic WLF parameters C1 ( g ) and C2 ( g ) from the generalized entropy theory of glass-formation and then by determining the dependence of C1 ( g ) and C2 ( g ) on the microscopic molecular parameters (including the strength of the cohesive molecular interactions and the degree of chain stiffness) and on the molar mass of the polymer. Attention in these calculations is restricted to the temperature range (Tg < T < Tg + 100 K), where both the WLF and VFT equations apply.

The isotropic-nematic phase transition of tangent hard-sphere chain fluids—Pure components

NASA Astrophysics Data System (ADS)

van Westen, Thijs; Oyarzún, Bernardo; Vlugt, Thijs J. H.; Gross, Joachim

2013-07-01

An extension of Onsager's second virial theory is developed to describe the isotropic-nematic phase transition of tangent hard-sphere chain fluids. Flexibility is introduced by the rod-coil model. The effect of chain-flexibility on the second virial coefficient is described using an accurate, analytical approximation for the orientation-dependent pair-excluded volume. The use of this approximation allows for an analytical treatment of intramolecular flexibility by using a single pure-component parameter. Two approaches to approximate the effect of the higher virial coefficients are considered, i.e., the Vega-Lago rescaling and Scaled Particle Theory (SPT). The Onsager trial function is employed to describe the orientational distribution function. Theoretical predictions for the equation of state and orientational order parameter are tested against the results from Monte Carlo (MC) simulations. For linear chains of length 9 and longer, theoretical results are in excellent agreement with MC data. For smaller chain lengths, small errors introduced by the approximation of the higher virial coefficients become apparent, leading to a small under- and overestimation of the pressure and density difference at the phase transition, respectively. For rod-coil fluids of reasonable rigidity, a quantitative comparison between theory and MC simulations is obtained. For more flexible chains, however, both the Vega-Lago rescaling and SPT lead to a small underestimation of the location of the phase transition.

Dependence and power in healthcare equipment supply chains.

PubMed

de Jong, Jurriaan L; Benton, W C

2018-03-05

Most healthcare organizations (HCOs) engage Group Purchasing Organizations (GPOs) as an outsourcing strategy to secure their supplies and materials. When an HCO outsources the procurement function to a GPO, this GPO will directly interact with the HCO's supplier on the HCO's behalf. This study investigates how an HCO's dependence on a GPO affects supply chain relationships and power in the healthcare medical equipment supply chain. Hypotheses are tested through factor analysis and structural equation modeling, using primary survey data from HCO procurement managers. An HCO's dependence on a GPO is found to be positively associated with a GPO's reliance on mediated power, but, surprisingly, negatively associated with a GPO's mediated power. Furthermore, analysis indicates that an HCO's dependence on a GPO is positively associated with an HCO's dependence on a GPO-contracted Original Equipment Manufacturer (OEM). HCO reliance on GPOs may lead to a buyer's dependence trap, where HCOs are increasingly dependent on GPOs and OEMs. Implications for HCO procurement managers and recommended steps for mitigation are offered. Power-dependence relationships in the medical equipment supply chain are not consistent with relationships in other, more traditional, supply chains. While dependence in a supply chain relationship typically leads to an increase in reliance on mediated power, GPO-dependent HCOs instead perceive a decrease in GPO mediated power. Furthermore, HCOs that rely on procurement service from GPOs are increasingly dependent on the OEMs.

Kinematics and dynamics of a six-degree-of-freedom robot manipulator with closed kinematic chain mechanism

NASA Technical Reports Server (NTRS)

Nguyen, Charles C.; Pooran, Farhad J.

1989-01-01

This paper deals with a class of robot manipulators built based on the kinematic chain mechanism (CKCM). This class of CKCM manipulators consists of a fixed and a moving platform coupled together via a number of in-parallel actuators. A closed-form solution is derived for the inverse kinematic problem of a six-degre-of-freedom CKCM manipulator designed to study robotic applications in space. Iterative Newton-Raphson method is employed to solve the forward kinematic problem. Dynamics of the above manipulator is derived using the Lagrangian approach. Computer simulation of the dynamical equations shows that the actuating forces are strongly dependent on the mass and centroid of the robot links.

On fundamental quality of fission chain reaction to oppose rapid runaways of nuclear reactors

NASA Astrophysics Data System (ADS)

Kulikov, G. G.; Shmelev, A. N.; Apse, V. A.; Kulikov, E. G.

2017-01-01

It has been shown that the in-hour equation characterizes the barriers and resistibility of fission chain reaction (FCR) against rapid runaways in nuclear reactors. Traditionally, nuclear reactors are characterized by the presence of barriers based on delayed and prompt neutrons. A new barrier based on the reflector neutrons that can occur when the fast reactor core is surrounded by a weakly absorbing neutron reflector with heavy atomic weight was proposed. It has been shown that the safety of this fast reactor is substantially improved, and considerable elongation of prompt neutron lifetime "devalues" the role of delayed neutron fraction as the maximum permissible reactivity for the reactor safety.

Complex behavior in chains of nonlinear oscillators.

PubMed

Alonso, Leandro M

2017-06-01

This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally. The results presented here suggest that in networks composed of many oscillatory units with local interactions, excitability together with balanced interactions is sufficient to give rise to complex emergent features. For values of the parameters where complex behavior occurs, the system also displays a high-dimensional bifurcation where an exponentially large number of equilibria are borne in pairs out of multiple saddle-node bifurcations.

Electrostatic Interactions Between Glycosaminoglycan Molecules

NASA Astrophysics Data System (ADS)

Song, Fan; Moyne, Christian; Bai, Yi-Long

2005-02-01

The electrostatic interactions between nearest-neighbouring chondroitin sulfate glycosaminoglycan (CS-GAG) molecular chains are obtained on the bottle brush conformation of proteoglycan aggrecan based on an asymptotic solution of the Poisson-Boltzmann equation the CS-GAGs satisfy under the physiological conditions of articular cartilage. The present results show that the interactions are associated intimately with the minimum separation distance and mutual angle between the molecular chains themselves. Further analysis indicates that the electrostatic interactions are not only expressed to be purely exponential in separation distance and decrease with the increasing mutual angle but also dependent sensitively on the saline concentration in the electrolyte solution within the tissue, which is in agreement with the existed relevant conclusions.

Electronic transport in disordered chains with saturable nonlinearity

NASA Astrophysics Data System (ADS)

dos Santos, J. L. L.; Nguyen, Ba Phi; de Moura, F. A. B. F.

2015-10-01

In this work we study numerically the dynamics of an initially localized wave packet in one-dimensional disordered chains with saturable nonlinearity. By using the generalized discrete nonlinear Schrödinger equation, we calculate two different physical quantities as a function of time, which are the participation number and the mean square displacement from the excitation site. From detailed numerical analysis, we find that the saturable nonlinearity can promote a sub-diffusive spreading of the wave packet even in the presence of diagonal disorder for a long time. In addition, we also investigate the effect of the saturated nonlinearity for initial times of the electronic evolution thus showing the possibility of mobile breather-like modes.

A modified Lotka-Volterra model for the evolution of coordinate symbiosis in energy enterprise

NASA Astrophysics Data System (ADS)

Zhou, Li; Wang, Teng; Lyu, Xiaohuan; Yu, Jing

2018-02-01

Recent developments in energy markets make the operating industries more dynamic and complex, and energy enterprises cooperate more closely in the industrial chain and symbiosis. In order to further discuss the evolution of coordinate symbiosis in energy enterprises, a modified Lotka-Volterra equation is introduced to develop a symbiosis analysis model of energy groups. According to the equilibrium and stability analysis, a conclusion is obtained that if the upstream energy group and the downstream energy group are in symbiotic state, the growth of their utility will be greater than their independent value. Energy enterprises can get mutual benefits and positive promotions in industrial chain by their cooperation.

On the Multilevel Solution Algorithm for Markov Chains

NASA Technical Reports Server (NTRS)

Horton, Graham

1997-01-01

We discuss the recently introduced multilevel algorithm for the steady-state solution of Markov chains. The method is based on an aggregation principle which is well established in the literature and features a multiplicative coarse-level correction. Recursive application of the aggregation principle, which uses an operator-dependent coarsening, yields a multi-level method which has been shown experimentally to give results significantly faster than the typical methods currently in use. When cast as a multigrid-like method, the algorithm is seen to be a Galerkin-Full Approximation Scheme with a solution-dependent prolongation operator. Special properties of this prolongation lead to the cancellation of the computationally intensive terms of the coarse-level equations.

Actuation for simultaneous motions and constraining efforts: an open chain example

NASA Astrophysics Data System (ADS)

Perreira, N. Duke

1997-06-01

A brief discussion on systems where simultaneous control of forces and velocities are desirable is given and an example linkage with revolute and prismatic joint is selected for further analysis. The Newton-Euler approach for dynamic system analysis is applied to the example to provide a basis of comparison. Gauge invariant transformations are used to convert the dynamic equations into invariant form suitable for use in a new dynamic system analysis method known as the motion-effort approach. This approach uses constraint elimination techniques based on singular value decompositions to recast the invariant form of dynamic system equations into orthogonal sets of motion and effort equations. Desired motions and constraining efforts are partitioned into ideally obtainable and unobtainable portions which are then used to determine the required actuation. The method is applied to the example system and an analytic estimate to its success is made.

Modeling self-consistent multi-class dynamic traffic flow

NASA Astrophysics Data System (ADS)

Cho, Hsun-Jung; Lo, Shih-Ching

2002-09-01

In this study, we present a systematic self-consistent multiclass multilane traffic model derived from the vehicular Boltzmann equation and the traffic dispersion model. The multilane domain is considered as a two-dimensional space and the interaction among vehicles in the domain is described by a dispersion model. The reason we consider a multilane domain as a two-dimensional space is that the driving behavior of road users may not be restricted by lanes, especially motorcyclists. The dispersion model, which is a nonlinear Poisson equation, is derived from the car-following theory and the equilibrium assumption. Under the concept that all kinds of users share the finite section, the density is distributed on a road by the dispersion model. In addition, the dynamic evolution of the traffic flow is determined by the systematic gas-kinetic model derived from the Boltzmann equation. Multiplying Boltzmann equation by the zeroth, first- and second-order moment functions, integrating both side of the equation and using chain rules, we can derive continuity, motion and variance equation, respectively. However, the second-order moment function, which is the square of the individual velocity, is employed by previous researches does not have physical meaning in traffic flow. Although the second-order expansion results in the velocity variance equation, additional terms may be generated. The velocity variance equation we propose is derived from multiplying Boltzmann equation by the individual velocity variance. It modifies the previous model and presents a new gas-kinetic traffic flow model. By coupling the gas-kinetic model and the dispersion model, a self-consistent system is presented.

Mean-field calculations of chain packing and conformational statistics in lipid bilayers: comparison with experiments and molecular dynamics studies.

PubMed Central

Fattal, D R; Ben-Shaul, A

1994-01-01

A molecular, mean-field theory of chain packing statistics in aggregates of amphiphilic molecules is applied to calculate the conformational properties of the lipid chains comprising the hydrophobic cores of dipalmitoyl-phosphatidylcholine (DPPC), dioleoyl-phosphatidylcholine (DOPC), and palmitoyl-oleoyl-phosphatidylcholine (POPC) bilayers in their fluid state. The central quantity in this theory, the probability distribution of chain conformations, is evaluated by minimizing the free energy of the bilayer assuming only that the segment density within the hydrophobic region is uniform (liquidlike). Using this distribution we calculate chain conformational properties such as bond orientational order parameters and spatial distributions of the various chain segments. The lipid chains, both the saturated palmitoyl (-(CH2)14-CH3) and the unsaturated oleoyl (-(CH2)7-CH = CH-(CH2)7-CH3) chains are modeled using rotational isomeric state schemes. All possible chain conformations are enumerated and their statistical weights are determined by the self-consistency equations expressing the condition of uniform density. The hydrophobic core of the DPPC bilayer is treated as composed of single (palmitoyl) chain amphiphiles, i.e., the interactions between chains originating from the same lipid headgroup are assumed to be the same as those between chains belonging to different molecules. Similarly, the DOPC system is treated as a bilayer of oleoyl chains. The POPC bilayer is modeled as an equimolar mixture of palmitoyl and oleoyl chains. Bond orientational order parameter profiles, and segment spatial distributions are calculated for the three systems above, for several values of the bilayer thickness (or, equivalently, average area/headgroup) chosen, where possible, so as to allow for comparisons with available experimental data and/or molecular dynamics simulations. In most cases the agreement between the mean-field calculations, which are relatively easy to perform, and the experimental and simulation data is very good, supporting their use as an efficient tool for analyzing a variety of systems subject to varying conditions (e.g., bilayers of different compositions or thicknesses at different temperatures). PMID:7811955

On Matrix Sampling and Imputation of Context Questionnaires with Implications for the Generation of Plausible Values in Large-Scale Assessments

ERIC Educational Resources Information Center

Kaplan, David; Su, Dan

2016-01-01

This article presents findings on the consequences of matrix sampling of context questionnaires for the generation of plausible values in large-scale assessments. Three studies are conducted. Study 1 uses data from PISA 2012 to examine several different forms of missing data imputation within the chained equations framework: predictive mean…

The Weak Link HP-41C hand-held calculator program

Treesearch

Ross A. Phillips; Penn A. Peters; Gary D. Falk

1982-01-01

The Weak Link hand-held calculator program (HP-41C) quickly analyzes a system for logging production and costs. The production equations model conventional chain saw, skidder, loader, and tandemaxle truck operations in eastern mountain areas. Production of each function of the logging system may be determined so that the system may be balanced for minimum cost. The...

Multiple imputation by chained equations for systematically and sporadically missing multilevel data.

PubMed

Resche-Rigon, Matthieu; White, Ian R

2018-06-01

In multilevel settings such as individual participant data meta-analysis, a variable is 'systematically missing' if it is wholly missing in some clusters and 'sporadically missing' if it is partly missing in some clusters. Previously proposed methods to impute incomplete multilevel data handle either systematically or sporadically missing data, but frequently both patterns are observed. We describe a new multiple imputation by chained equations (MICE) algorithm for multilevel data with arbitrary patterns of systematically and sporadically missing variables. The algorithm is described for multilevel normal data but can easily be extended for other variable types. We first propose two methods for imputing a single incomplete variable: an extension of an existing method and a new two-stage method which conveniently allows for heteroscedastic data. We then discuss the difficulties of imputing missing values in several variables in multilevel data using MICE, and show that even the simplest joint multilevel model implies conditional models which involve cluster means and heteroscedasticity. However, a simulation study finds that the proposed methods can be successfully combined in a multilevel MICE procedure, even when cluster means are not included in the imputation models.

Source term evaluation model for high-level radioactive waste repository with decay chain build-up.

PubMed

Chopra, Manish; Sunny, Faby; Oza, R B

2016-09-18

A source term model based on two-component leach flux concept is developed for a high-level radioactive waste repository. The long-lived radionuclides associated with high-level waste may give rise to the build-up of activity because of radioactive decay chains. The ingrowths of progeny are incorporated in the model using Bateman decay chain build-up equations. The model is applied to different radionuclides present in the high-level radioactive waste, which form a part of decay chains (4n to 4n + 3 series), and the activity of the parent and daughter radionuclides leaching out of the waste matrix is estimated. Two cases are considered: one when only parent is present initially in the waste and another where daughters are also initially present in the waste matrix. The incorporation of in situ production of daughter radionuclides in the source is important to carry out realistic estimates. It is shown that the inclusion of decay chain build-up is essential to avoid underestimation of the radiological impact assessment of the repository. The model can be a useful tool for evaluating the source term of the radionuclide transport models used for the radiological impact assessment of high-level radioactive waste repositories.

Fast analytic solver of rational Bethe equations

NASA Astrophysics Data System (ADS)

Marboe, C.; Volin, D.

2017-05-01

In this note we propose an approach for a fast analytic determination of all possible sets of Bethe roots corresponding to eigenstates of rational {GL}({N}\\vert {M}) integrable spin chains of given not too large length, in terms of Baxter Q-functions. We observe that all exceptional solutions, if any, are automatically correctly accounted. The key intuition behind the approach is that the equations on the Q-functions are determined solely by the Young diagram, and not by the choice of the rank of the {GL} symmetry. Hence we can choose arbitrary {N} and {M} that accommodate the desired representation. Then we consider all distinguished Q-functions at once, not only those following a certain Kac-Dynkin path.

Comparative Analysis of InSAR Digital Surface Models for Test Area Bucharest

NASA Astrophysics Data System (ADS)

Dana, Iulia; Poncos, Valentin; Teleaga, Delia

2010-03-01

This paper presents the results of the interferometric processing of ERS Tandem, ENVISAT and TerraSAR- X for digital surface model (DSM) generation. The selected test site is Bucharest (Romania), a built-up area characterized by the usual urban complex pattern: mixture of buildings with different height levels, paved roads, vegetation, and water bodies. First, the DSMs were generated following the standard interferometric processing chain. Then, the accuracy of the DSMs was analyzed against the SPOT HRS model (30 m resolution at the equator). A DSM derived by optical stereoscopic processing of SPOT 5 HRG data and also the SRTM (3 arc seconds resolution at the equator) DSM have been included in the comparative analysis.

Deep learning beyond Lefschetz thimbles

NASA Astrophysics Data System (ADS)

Alexandru, Andrei; Bedaque, Paulo F.; Lamm, Henry; Lawrence, Scott

2017-11-01

The generalized thimble method to treat field theories with sign problems requires repeatedly solving the computationally expensive holomorphic flow equations. We present a machine learning technique to bypass this problem. The central idea is to obtain a few field configurations via the flow equations to train a feed-forward neural network. The trained network defines a new manifold of integration which reduces the sign problem and can be rapidly sampled. We present results for the 1 +1 dimensional Thirring model with Wilson fermions on sizable lattices. In addition to the gain in speed, the parametrization of the integration manifold we use avoids the "trapping" of Monte Carlo chains which plagues large-flow calculations, a considerable shortcoming of the previous attempts.

Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures.

PubMed

Khusnutdinova, Karima R; Samsonov, Alexander M; Zakharov, Alexey S

2009-05-01

We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.

Heat of capillary condensation in nanopores: new insights from the equation of state.

PubMed

Tan, Sugata P; Piri, Mohammad

2017-02-15

Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) coupled with the Young-Laplace equation is a recently developed equation of state (EOS) that successfully presents not only the capillary condensation but also the pore critical phenomena. The development of this new EOS allows further investigation of the heats involved in condensation. Compared to the conventional approaches, the EOS calculations present the temperature-dependent behavior of the heat of capillary condensation as well as that of the contributing effects. The confinement effect was found to be the strongest at the pore critical point. Therefore, contrary to the bulk heat condensation that vanishes at the critical point, the heat of capillary condensation in small pores shows a minimum and then increases with temperature when approaching the pore critical temperature. Strong support for the existence of the pore critical point is also discussed as the volume expansivity of the condensed phase in confinement was found to increase dramatically near the pore critical temperature. At high reduced temperatures, the Clausius-Clapeyron equation was found to apply better for confined fluids than it does for bulk fluids.

Abelian Toda field theories on the noncommutative plane

NASA Astrophysics Data System (ADS)

Cabrera-Carnero, Iraida

2005-10-01

Generalizations of GL(n) abelian Toda and GL with tilde above(n) abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by algebra-valued gauge potentials dependent on the fields. This condition can be expressed as noncommutative Leznov-Saveliev equations which make possible to define the noncommutative generalizations as systems of second order differential equations, with an infinite chain of conserved currents. The actions corresponding to these field theories are also provided. The special cases of GL(2) Liouville and GL with tilde above(2) sinh/sine-Gordon are explicitly studied. It is also shown that from the noncommutative (anti-)self-dual Yang-Mills equations in four dimensions it is possible to obtain by dimensional reduction the equations of motion of the two-dimensional models constructed. This fact supports the validity of the noncommutative version of the Ward conjecture. The relation of our proposal to previous versions of some specific Toda field theories reported in the literature is presented as well.

Mathematical Analysis of Vehicle Delivery Scale of Bike-Sharing Rental Nodes

NASA Astrophysics Data System (ADS)

Zhai, Y.; Liu, J.; Liu, L.

2018-04-01

Aiming at the lack of scientific and reasonable judgment of vehicles delivery scale and insufficient optimization of scheduling decision, based on features of the bike-sharing usage, this paper analyses the applicability of the discrete time and state of the Markov chain, and proves its properties to be irreducible, aperiodic and positive recurrent. Based on above analysis, the paper has reached to the conclusion that limit state (steady state) probability of the bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then this paper analyses the difficulty of the transition probability matrix parameter statistics and the linear equations group solution in the traditional solving algorithm of the bike-sharing Markov chain. In order to improve the feasibility, this paper proposes a "virtual two-node vehicle scale solution" algorithm which considered the all the nodes beside the node to be solved as a virtual node, offered the transition probability matrix, steady state linear equations group and the computational methods related to the steady state scale, steady state arrival time and scheduling decision of the node to be solved. Finally, the paper evaluates the rationality and accuracy of the steady state probability of the proposed algorithm by comparing with the traditional algorithm. By solving the steady state scale of the nodes one by one, the proposed algorithm is proved to have strong feasibility because it lowers the level of computational difficulty and reduces the number of statistic, which will help the bike-sharing companies to optimize the scale and scheduling of nodes.

The relationship between odd- and branched-chain fatty acids and microbial nucleic acid bases in rumen

PubMed Central

Liu, Keyuan; Hao, Xiaoyan; Li, Yang; Luo, Guobin; Zhang, Yonggen; Xin, Hangshu

2017-01-01

Objective This study aims to identify the relationship between odd- and branched-chain fatty acids (OBCFAs) and microbial nucleic acid bases in the rumen, and to establish a model to accurately predict microbial protein flow by using OBCFA. Methods To develop the regression equations, data on the rumen contents of individual cows were obtained from 2 feeding experiments. In the first experiment, 3 rumen-fistulated dry dairy cows arranged in a 3×3 Latin square were fed diets of differing forage to concentration ratios (F:C). The second experiment consisted of 9 lactating Holstein dairy cows of similar body weights at the same stage of pregnancy. For each lactation stage, 3 cows with similar milk production were selected. The rumen contents were sampled at 4 time points of every two hours after morning feeding 6 h, and then to analyse the concentrations of OBCFA and microbial nucleic acid bases in the rumen samples. Results The ruminal bacteria nucleic acid bases were significantly influenced by feeding diets of differing forge to concentration ratios and lactation stages of dairy cows (p<0.05). The concentrations of OBCFAs, especially odd-chain fatty acids and C15:0 isomers, strongly correlated with the microbial nucleic acid bases in the rumen (p<0.05). The equations of ruminal microbial nucleic acid bases established by ruminal OBCFAs contents showed a good predictive capacity, as indicated by reasonably low standard errors and high R-squared values. Conclusion This finding suggests that the rumen OBCFA composition could be used as an internal marker of rumen microbial matter. PMID:28728386

The relationship between odd- and branched-chain fatty acids and microbial nucleic acid bases in rumen.

PubMed

Liu, Keyuan; Hao, Xiaoyan; Li, Yang; Luo, Guobin; Zhang, Yonggen; Xin, Hangshu

2017-11-01

This study aims to identify the relationship between odd- and branched-chain fatty acids (OBCFAs) and microbial nucleic acid bases in the rumen, and to establish a model to accurately predict microbial protein flow by using OBCFA. To develop the regression equations, data on the rumen contents of individual cows were obtained from 2 feeding experiments. In the first experiment, 3 rumen-fistulated dry dairy cows arranged in a 3×3 Latin square were fed diets of differing forage to concentration ratios (F:C). The second experiment consisted of 9 lactating Holstein dairy cows of similar body weights at the same stage of pregnancy. For each lactation stage, 3 cows with similar milk production were selected. The rumen contents were sampled at 4 time points of every two hours after morning feeding 6 h, and then to analyse the concentrations of OBCFA and microbial nucleic acid bases in the rumen samples. The ruminal bacteria nucleic acid bases were significantly influenced by feeding diets of differing forge to concentration ratios and lactation stages of dairy cows (p<0.05). The concentrations of OBCFAs, especially odd-chain fatty acids and C15:0 isomers, strongly correlated with the microbial nucleic acid bases in the rumen (p<0.05). The equations of ruminal microbial nucleic acid bases established by ruminal OBCFAs contents showed a good predictive capacity, as indicated by reasonably low standard errors and high R-squared values. This finding suggests that the rumen OBCFA composition could be used as an internal marker of rumen microbial matter.

Hospital employment of physicians and supply chain performance: An empirical investigation.

PubMed

Young, Gary J; Nyaga, Gilbert N; Zepeda, E David

2016-01-01

As hospital employment of physicians becomes increasingly common in the United States, much speculation exists as to whether this type of arrangement will promote hospital operating efficiency in such areas as supply chain management. Little empirical research has been conducted to address this question. The aim of this study was to provide an exploratory assessment of whether hospital employment of physicians is associated with better supply chain performance. Drawing from both agency and stewardship theories, we examined whether hospitals with a higher proportion of employed medical staff members have relatively better supply chain performance based on two performance measures, supply chain expenses and inventory costs. We conducted the study using a pooled, cross-sectional sample of hospitals located in California between 2007 and 2009. Key data sources were hospital annual financial reports from California's Office of Statewide Health Policy and Development and the American Hospital Association annual survey of hospitals. To examine the relationship between physician employment and supply chain performance, we specified physician employment as the proportion of total employed medical staff members as well as the proportion of employed medical staff members within key physician subgroups. We analyzed the data using generalized estimating equations. Study results generally supported our hypothesis that hospital employment of physicians is associated with better supply chain performance. Although the results of our study should be viewed as preliminary, the trend in the United States toward hospital employment of physicians may be a positive development for improved hospital operating efficiency. Hospital managers should also be attentive to training and educational resources that medical staff members may need to strengthen their role in supply chain activities.

The binding of analogs of porphyrins and chlorins with elongated side chains to albumin

PubMed Central

Ben Dror, Shimshon; Bronshtein, Irena; Weitman, Hana; Smith, Kevin M.; O’Neal, William G.; Jacobi, Peter A.; Ehrenberg, Benjamin

2012-01-01

In previous studies, we demonstrated that elongation of side chains of several sensitizers endowed them with higher affinity for artificial and natural membranes and caused their deeper localization in membranes. In the present study, we employed eight hematoporphyrin and protoporphyrin analogs and four groups containing three chlorin analogs each, all synthesized with variable numbers of methylenes in their alkyl carboxylic chains. We show that these tetrapyrroles’ affinity for bovine serum albumin (BSA) and their localization in the binding site are also modulated by chain lengths. The binding constants of the hematoporphyrins and protoporphyrins to BSA increased as the number of methylenes was increased. The binding of the chlorins depended on the substitution at the meso position opposite to the chains. The quenching of the sensitizers’ florescence by external iodide ions decreased as the side chains became longer, indicating to deeper insertion of the molecules into the BSA binding pocket. To corroborate this conclusion, we studied the efficiency of photodamage caused to tryptophan in BSA upon illumination of the bound sensitizers. The efficiency was found to depend on the side-chain lengths of the photosensitizer. We conclude that the protein site that hosts these sensitizers accommodates different analogs at positions that differ slightly from each other. These differences are manifested in the ease of access of iodide from the external aqueous phase, and in the proximity of the photosensitizers to the tryptophan. In the course of this study, we developed the kinetic equations that have to be employed when the sensitizer itself is being destroyed. PMID:19330323

Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order

DOE PAGES

Favalli, Andrea; Croft, Stephen; Santi, Peter

2015-06-15

Various methods of autocorrelation neutron analysis may be used to extract information about a measurement item containing spontaneously fissioning material. The two predominant approaches being the time correlation analysis (that make use of a coincidence gate) methods of multiplicity shift register logic and Feynman sampling. The common feature is that the correlated nature of the pulse train can be described by a vector of reduced factorial multiplet rates. We call these singlets, doublets, triplets etc. Within the point reactor model the multiplet rates may be related to the properties of the item, the parameters of the detector, and basic nuclearmore » data constants by a series of coupled algebraic equations – the so called point model equations. Solving, or inverting, the point model equations using experimental calibration model parameters is how assays of unknown items is performed. Currently only the first three multiplets are routinely used. In this work we develop the point model equations to higher order multiplets using the probability generating functions approach combined with the general derivative chain rule, the so called Faà di Bruno Formula. Explicit expression up to 5th order are provided, as well the general iterative formula to calculate any order. This study represents the first necessary step towards determining if higher order multiplets can add value to nondestructive measurement practice for nuclear materials control and accountancy.« less

Testing lyoequivalency for three commercially sustained-release tablets containing diltiazem hydrochloride.

PubMed

Maswadeh, Hamzah A; Al-Hanbali, Othman A; Kanaan, Reem A; Shakya, Ashok K; Maraqa, Anwar

2010-01-01

In vitro release kinetics of three commercially available sustained release tablets (SR) diltiazem hydrochloride were studied at pH 1.1 for 2 h and for another 6 h at pH 6.8 using the USP dissolution apparatus with the paddle assemble. The kinetics of the dissolution process was studied by analyzing the dissolution data using five kinetic equations: the zero-order equation, the first-order equation, the Higuchi square root equation, the Hixson-Crowell cube root law and the Peppas equation. Analyses of the dissolution kinetic data for diltiazem hydrochloride commercial SR tablets showed that both Dilzacard and Dilzem SR tablets released drug by Non-Fickian (Anomalous transport) release with release exponent (n) equal to 0.59 and 0.54, respectively, which indicate the summation of both diffusion and dissolution controlled drug release. Bi-Tildiem SR tablets released drug by super case II (n = 1.29) which indicate zero-order release due to the dissolution of polymeric matrix and relaxation of the polymer chain. This finding was also in agreement with results obtained from application of zero-order and Hixson-Crowell equations. A dissolution profile comparative study was done to test the lyoequivelancy of the three products by using the mean dissolution time (MDT), dissimilarity factor f1 and similarity factor f2. Results showed that the three products are different and not lyoequivalent.

Exact master equation and non-Markovian decoherence dynamics of Majorana zero modes under gate-induced charge fluctuations

NASA Astrophysics Data System (ADS)

Lai, Hon-Lam; Yang, Pei-Yun; Huang, Yu-Wei; Zhang, Wei-Min

2018-02-01

In this paper, we use the exact master equation approach to investigate the decoherence dynamics of Majorana zero modes in the Kitaev model, a 1D p -wave spinless topological superconducting chain (TSC) that is disturbed by gate-induced charge fluctuations. The exact master equation is derived by extending Feynman-Vernon influence functional technique to fermionic open systems involving pairing excitations. We obtain the exact master equation for the zero-energy Bogoliubov quasiparticle (bogoliubon) in the TSC, and then transfer it into the master equation for the Majorana zero modes. Within this exact master equation formalism, we can describe in detail the non-Markovian decoherence dynamics of the zero-energy bogoliubon as well as Majorana zero modes under local perturbations. We find that at zero temperature, local charge fluctuations induce level broadening to one of the Majorana zero modes but there is an isolated peak (localized bound state) located at zero energy that partially protects the Majorana zero mode from decoherence. At finite temperatures, the zero-energy localized bound state does not precisely exist, but the coherence of the Majorana zero mode can still be partially but weakly protected, due to the sharp dip of the spectral density near the zero frequency. The decoherence will be enhanced as one increases the charge fluctuations and/or the temperature of the gate.

Dual Effects on Choice of Conditioned Reinforcement Frequency and Conditioned Reinforcement Value

ERIC Educational Resources Information Center

McDevitt, Margaret A.; Williams, Ben A.

2010-01-01

Pigeons were presented with a concurrent-chains schedule in which the total time to primary reinforcement was equated for the two alternatives (VI 30 s VI 60 s vs. VI 60 s VI 30 s). In one set of conditions, the terminal links were signaled by the same stimulus, and in another set of conditions they were signaled by different stimuli. Choice was…

Functions Character

NASA Astrophysics Data System (ADS)

Dugave, Maxime; Göhmann, Frank; Kozlowski, Karol Kajetan

2014-04-01

We establish several properties of the solutions to the linear integral equations describing the infinite volume properties of the XXZ spin-1/2 chain in the disordered regime. In particular, we obtain lower and upper bounds for the dressed energy, dressed charge and density of Bethe roots. Furthermore, we establish that given a fixed external magnetic field (or a fixed magnetization) there exists a unique value of the boundary of the Fermi zone.

Simple Model of Sickle Hemoglobin

NASA Astrophysics Data System (ADS)

Shiryayev, Andrey; Li, Xiaofei; Gunton, James

2006-03-01

A microscopic model is proposed for the interactions between sickle hemoglobin molecules based on information from the protein data bank. A Monte Carlo simulation of a simplified two patch model is carried out, with the goal of understanding fiber formation. A gradual transition from monomers to one dimensional chains is observed as one varies the density of molecules at fixed temperature, somewhat similar to the transition from monomers to polymer fibers in sickle hemoglobin molecules in solution. An observed competition between chain formation and crystallization for the model is also discussed. The results of the simulation of the equation of state are shown to be in excellent agreement with a theory for a model of globular proteins, for the case of two interacting sites.

Cytoplasmic motion induced by cytoskeleton stretching and its effect on cell mechanics.

PubMed

Zhang, T

2011-09-01

Cytoplasmic motion assumed as a steady state laminar flow induced by cytoskeleton stretching in a cell is determined and its effect on the mechanical behavior of the cell under externally applied forces is demonstrated. Non-Newtonian fluid is assumed for the multiphase cytoplasmic fluid and the analytical velocity field around the macromolecular chain is obtained by solving the reduced nonlinear momentum equation using homotopy technique. The entropy generation by the fluid internal friction is calculated and incorporated into the entropic elasticity based 8-chain constitutive relations. Numerical examples showed strengthening behavior of cells in response to externally applied mechanical stimuli. The spatial distribution of the stresses within a cell under externally applied fluid flow forces were also studied.

The Effects of Partnership Management on Supply Chain Cooperative Performance: A Case Study of High-Tech Industry

NASA Astrophysics Data System (ADS)

Wu, Mei-Ying; Chang, Yun-Ju; Weng, Yung-Chien

2009-08-01

With the structural change of global supply chains, the relationship between manufacturers and suppliers has transformed into a long-term partnership. Thus, this study aims to explore the partnership between manufacturers and suppliers in Taiwan's high-tech industry. Four constructs, including partner characteristic, partnership quality, partnership closeness, and cooperative performance, induced from previous literatures are used to construct the research framework and hypotheses. A questionnaire survey is then performed on executives and staffs involved in the high-tech industry. The proposed framework and hypotheses are empirically validated through confirmatory factory analysis and structural equation modeling. It is expected that the research findings can serve as a reference for Taiwan's high-tech industry on building partnerships.

Integrability in heavy quark effective theory

NASA Astrophysics Data System (ADS)

Braun, Vladimir M.; Ji, Yao; Manashov, Alexander N.

2018-06-01

It was found that renormalization group equations in the heavy-quark effective theory (HQET) for the operators involving one effective heavy quark and light degrees of freedom are completely integrable in some cases and are related to spin chain models with the Hamiltonian commuting with the nondiagonal entry C( u) of the monodromy matrix. In this work we provide a more complete mathematical treatment of such spin chains in the QISM framework. We also discuss the relation of integrable models that appear in the HQET context with the large-spin limit of integrable models in QCD with light quarks. We find that the conserved charges and the "ground state" wave functions in HQET models can be obtained from the light-quark counterparts in a certain scaling limit.

Robustness of assembly supply chain networks by considering risk propagation and cascading failure

NASA Astrophysics Data System (ADS)

Tang, Liang; Jing, Ke; He, Jie; Stanley, H. Eugene

2016-10-01

An assembly supply chain network (ASCN) is composed of manufacturers located in different geographical regions. To analyze the robustness of this ASCN when it suffers from catastrophe disruption events, we construct a cascading failure model of risk propagation. In our model, different disruption scenarios s are considered and the probability equation of all disruption scenarios is developed. Using production capability loss as the robustness index (RI) of an ASCN, we conduct a numerical simulation to assess its robustness. Through simulation, we compare the network robustness at different values of linking intensity and node threshold and find that weak linking intensity or high node threshold increases the robustness of the ASCN. We also compare network robustness levels under different disruption scenarios.

Hopf and Bautin Bifurcation in a Tritrophic Food Chain Model with Holling Functional Response Types III and IV

NASA Astrophysics Data System (ADS)

Castellanos, Víctor; Castillo-Santos, Francisco Eduardo; Dela-Rosa, Miguel Angel; Loreto-Hernández, Iván

In this paper, we analyze the Hopf and Bautin bifurcation of a given system of differential equations, corresponding to a tritrophic food chain model with Holling functional response types III and IV for the predator and superpredator, respectively. We distinguish two cases, when the prey has linear or logistic growth. In both cases we guarantee the existence of a limit cycle bifurcating from an equilibrium point in the positive octant of ℝ3. In order to do so, for the Hopf bifurcation we compute explicitly the first Lyapunov coefficient, the transversality Hopf condition, and for the Bautin bifurcation we also compute the second Lyapunov coefficient and verify the regularity conditions.

Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator

DOE PAGES

Lobos, Alejandro M.; Dobry, Ariel O.; Galitski, Victor

2015-05-22

Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model).We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chainmore » acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter U = 0). Furthermore, at low enough temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-1/2 end states for chains with open boundary conditions. In conclusion, our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.« less

Modelling electro-active polymers with a dispersion-type anisotropy

NASA Astrophysics Data System (ADS)

Hossain, Mokarram; Steinmann, Paul

2018-02-01

We propose a novel constitutive framework for electro-active polymers (EAPs) that can take into account anisotropy with a chain dispersion. To enhance actuation behaviour, particle-filled EAPs become promising candidates nowadays. Recent studies suggest that particle-filled EAPs, which can be cured under an electric field during the manufacturing time, do not necessarily form perfect anisotropic composites, rather they create composites with dispersed chains. Hence in this contribution, an electro-mechanically coupled constitutive model is devised that considers the chain dispersion with a probability distribution function in an integral form. To obtain relevant quantities in discrete form, numerical integration over the unit sphere is utilized. Necessary constitutive equations are derived exploiting the basic laws of thermodynamics that result in a thermodynamically consistent formulation. To demonstrate the performance of the proposed electro-mechanically coupled framework, we analytically solve a non-homogeneous boundary value problem, the extension and inflation of an axisymmetric cylindrical tube under electro-mechanically coupled load. The results capture various electro-mechanical couplings with the formulation proposed for EAP composites.

The rate dependent response of a bistable chain at finite temperature

NASA Astrophysics Data System (ADS)

Benichou, Itamar; Zhang, Yaojun; Dudko, Olga K.; Givli, Sefi

2016-10-01

We study the rate dependent response of a bistable chain subjected to thermal fluctuations. The study is motivated by the fact that the behavior of this model system is prototypical to a wide range of nonlinear processes in materials physics, biology and chemistry. To account for the stochastic nature of the system response, we formulate a set of governing equations for the evolution of the probability density of meta-stable configurations. Based on this approach, we calculate the behavior for a wide range of parametric values, such as rate, temperature, overall stiffness, and number of elements in the chain. Our results suggest that fundamental characteristics of the response, such as average transition stress and hysteresis, can be captured by a simple law which folds the influence of all these factors into a single non-dimensional quantity. We also show that the applicability of analytical results previously obtained for single-well systems can be extended to systems having multiple wells by proper definition of rate and of the transition stress.

Phi-value analysis of a linear, sequential reaction mechanism: theory and application to ion channel gating.

PubMed

Zhou, Yu; Pearson, John E; Auerbach, Anthony

2005-12-01

We derive the analytical form of a rate-equilibrium free-energy relationship (with slope Phi) for a bounded, linear chain of coupled reactions having arbitrary connecting rate constants. The results confirm previous simulation studies showing that Phi-values reflect the position of the perturbed reaction within the chain, with reactions occurring earlier in the sequence producing higher Phi-values than those occurring later in the sequence. The derivation includes an expression for the transmission coefficients of the overall reaction based on the rate constants of an arbitrary, discrete, finite Markov chain. The results indicate that experimental Phi-values can be used to calculate the relative heights of the energy barriers between intermediate states of the chain but provide no information about the energies of the wells along the reaction path. Application of the equations to the case of diliganded acetylcholine receptor channel gating suggests that the transition-state ensemble for this reaction is nearly flat. Although this mechanism accounts for many of the basic features of diliganded and unliganded acetylcholine receptor channel gating, the experimental rate-equilibrium free-energy relationships appear to be more linear than those predicted by the theory.

A novel pendulum test for measuring roller chain efficiency

NASA Astrophysics Data System (ADS)

Wragge-Morley, R.; Yon, J.; Lock, R.; Alexander, B.; Burgess, S.

2018-07-01

This paper describes a novel pendulum decay test for determining the transmission efficiency of chain drives. The test involves releasing a pendulum with an initial potential energy and measuring its decaying oscillations: under controlled conditions the decay reveals the losses in the transmission to a high degree of accuracy. The main advantage over motorised rigs is that there are significantly fewer sources of friction and inertia and hence measurement error. The pendulum rigs have an accuracy around 0.6% for the measurement of the coefficient of friction, giving an accuracy of transmission efficiency measurement around 0.012%. A theoretical model of chain friction combined with the equations of motion enables the coefficient of friction to be determined from the decay rate of pendulum velocity. The pendulum rigs operate at relatively low speeds. However, they allow an accurate determination of the coefficient of friction to estimate transmission efficiency at higher speeds. The pendulum rig revealed a previously undetected rocking behaviour in the chain links at very small articulation angles. In this regime, the link interfaces were observed to roll against one another rather than slide. This observation indicates that a very high-efficiency transmission can be achieved if the articulation angle is very low.

Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field.

PubMed

Carmelo, J M P; Sacramento, P D; Machado, J D P; Campbell, D K

2015-10-14

We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the 'pseudofermion dynamical theory' (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents ζ(τ)(k) controlling the singularities for both the longitudinal (τ = l) and transverse (τ = t) dynamical structure factors for the whole momentum range k ∈ ]0,π[, in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.

Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field

NASA Astrophysics Data System (ADS)

Carmelo, J. M. P.; Sacramento, P. D.; Machado, J. D. P.; Campbell, D. K.

2015-10-01

We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the ‘pseudofermion dynamical theory’ (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents {{\\zeta}τ}(k) controlling the singularities for both the longitudinal ≤ft(τ =l\\right) and transverse ≤ft(τ =t\\right) dynamical structure factors for the whole momentum range k\\in ]0,π[ , in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.

Exact quantum numbers of collapsed and non-collapsed two-string solutions in the spin-1/2 Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Deguchi, Tetsuo; Ranjan Giri, Pulak

2016-04-01

Every solution of the Bethe-ansatz equations (BAEs) is characterized by a set of quantum numbers, by which we can evaluate it numerically. However, no general rule is known how to give quantum numbers for the physical solutions of BAE. For the spin-1/2 XXX chain we rigorously derive all the quantum numbers for the complete set of the Bethe-ansatz eigenvectors in the two down-spin sector with any chain length N. Here we obtain them both for real and complex solutions. We also show that all the solutions associated with them are distinct. Consequently, we prove the completeness of the Bethe ansatz and give an exact expression for the number of real solutions which correspond to collapsed bound-state solutions (i.e., two-string solutions) in the sector: 2[(N-1)/2-(N/π ){{tan}}-1(\\sqrt{N-1})] in terms of Gauss’ symbol. Moreover, we prove in the sector the scheme conjectured by Takahashi for solving BAE systematically. We also suggest that by applying the present method we can derive the quantum numbers for the spin-1/2 XXZ chain.

Dynamics of hot random quantum spin chains: from anyons to Heisenberg spins

NASA Astrophysics Data System (ADS)

Parameswaran, Siddharth; Potter, Andrew; Vasseur, Romain

2015-03-01

We argue that the dynamics of the random-bond Heisenberg spin chain are ergodic at infinite temperature, in contrast to the many-body localized behavior seen in its random-field counterpart. First, we show that excited-state real-space renormalization group (RSRG-X) techniques suffer from a fatal breakdown of perturbation theory due to the proliferation of large effective spins that grow without bound. We repair this problem by deforming the SU (2) symmetry of the Heisenberg chain to its `anyonic' version, SU(2)k , where the growth of effective spins is truncated at spin S = k / 2 . This enables us to construct a self-consistent RSRG-X scheme that is particularly simple at infinite temperature. Solving the flow equations, we compute the excited-state entanglement and show that it crosses over from volume-law to logarithmic scaling at a length scale ξk ~eαk3 . This reveals that (a) anyon chains have random-singlet-like excited states for any finite k; and (b) ergodicity is restored in the Heisenberg limit k --> ∞ . We acknowledge support from the Quantum Materials program of LBNL (RV), the Gordon and Betty Moore Foundation (ACP), and UC Irvine startup funds (SAP).

Exact Correlation Functions in S U (2 ) N =2 Superconformal QCD

NASA Astrophysics Data System (ADS)

Baggio, Marco; Niarchos, Vasilis; Papadodimas, Kyriakos

2014-12-01

We report an exact solution of 2- and 3-point functions of chiral primary fields in S U (2 ) N =2 super-Yang-Mills theory coupled to four hypermultiplets. It is shown that these correlation functions are nontrivial functions of the gauge coupling, obeying differential equations which take the form of the semi-infinite Toda chain. We solve these equations recursively in terms of the Zamolodchikov metric that can be determined exactly from supersymmetric localization on the four-sphere. Our results are verified independently in perturbation theory with a Feynman diagram computation up to 2 loops. This is a short version of a companion paper that contains detailed technical remarks, additional material, and aspects of an extension to the S U (N ) gauge group.

Looping probabilities of elastic chains: a path integral approach.

PubMed

Cotta-Ramusino, Ludovica; Maddocks, John H

2010-11-01

We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit continuum mechanics models for the computation of DNA looping probabilities, but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula. Accordingly, and for simplicity, the current presentation is limited to the illustrative case of planar configurations. A path integral formalism is adopted, and, in the standard way, the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions. Then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function. The original aspects of our analysis are twofold. First, the quadratic Lagrangian describing the fluctuations has cross-terms that are linear in first derivatives. This, seemingly small, deviation from the structure of standard path integral examples complicates the necessary analysis significantly. Nevertheless, after a nonlinear change of variable of Riccati type, we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of Jacobi ordinary differential equations associated with the second variation. The second novel aspect of our analysis is that we show that the Hamiltonian form of these linear Jacobi equations still provides the appropriate correction term in the inextensible, unshearable limit that is commonly adopted in polymer physics models of, e.g. DNA. Prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end points. Our approximation formula for the looping pdf is of quite general applicability as, in contrast to most prior approaches, no assumption is made of either uniformity of the elastic chain, nor of a straight intrinsic shape. If the chain is uniform the Jacobi system evaluated at certain minimum energy configurations has constant coefficients. In such cases our approximate pdf can be evaluated in an entirely explicit, closed form. We illustrate our analysis with a planar example of this type and compute an approximate probability of cyclization, i.e., of forming a closed loop, from a uniform elastic chain whose intrinsic shape is an open circular arc.

Phase Radio Engineering Systems (Selected Pages),

DTIC Science & Technology

1983-04-28

that if on the linear network functions the delta-function, which has the uniform spectrum, then the spectrum of response repeats frequency DOC...integrator can be used, for example, chain/ network RC with the slow response. Page 222. As the being congruent/equating cascade/stage can be used, for example...the elements of the networks which are ensured with the great technical difficulties or not at all can be achieved/reached. !.( .... . 2

Evaluation of an Empirical Traction Equation for Forestry Tires

Treesearch

C.R. Vechinski; C.E. Johnson; R.L. Raper

1998-01-01

Variable load test data were used to evaluate the applicability of an existing forestry tire traction model for a new forestry tire and a worn tire of the same size with and without tire chains in a range of soil conditions. `The clay and sandy soi!s ranged in moisture content from 17 to 28%. Soil bulk density varied between 1.1 and 1.4g cm-3...

On boundary fusion and functional relations in the Baxterized affine Hecke algebra

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

Babichenko, A., E-mail: babichen@weizmann.ac.il; Regelskis, V., E-mail: v.regelskis@surrey.ac.uk

2014-04-15

We construct boundary type operators satisfying fused reflection equation for arbitrary representations of the Baxterized affine Hecke algebra. These operators are analogues of the fused reflection matrices in solvable half-line spin chain models. We show that these operators lead to a family of commuting transfer matrices of Sklyanin type. We derive fusion type functional relations for these operators for two families of representations.

Transport in simple networks described by an integrable discrete nonlinear Schrödinger equation.

PubMed

Nakamura, K; Sobirov, Z A; Matrasulov, D U; Sawada, S

2011-08-01

We elucidate the case in which the Ablowitz-Ladik (AL)-type discrete nonlinear Schrödinger equation (NLSE) on simple networks (e.g., star graphs and tree graphs) becomes completely integrable just as in the case of a simple one-dimensional (1D) discrete chain. The strength of cubic nonlinearity is different from bond to bond, and networks are assumed to have at least two semi-infinite bonds with one of them working as an incoming bond. The present work is a nontrivial extension of our preceding one [Sobirov et al., Phys. Rev. E 81, 066602 (2010)] on the continuum NLSE to the discrete case. We find (1) the solution on each bond is a part of the universal (bond-independent) AL soliton solution on the 1D discrete chain, but it is multiplied by the inverse of the square root of bond-dependent nonlinearity; (2) nonlinearities at individual bonds around each vertex must satisfy a sum rule; and (3) under findings 1 and 2, there exist an infinite number of constants of motion. As a practical issue, with the use of an AL soliton injected through the incoming bond, we obtain transmission probabilities inversely proportional to the strength of nonlinearity on the outgoing bonds.

The ISI distribution of the stochastic Hodgkin-Huxley neuron.

PubMed

Rowat, Peter F; Greenwood, Priscilla E

2014-01-01

The simulation of ion-channel noise has an important role in computational neuroscience. In recent years several approximate methods of carrying out this simulation have been published, based on stochastic differential equations, and all giving slightly different results. The obvious, and essential, question is: which method is the most accurate and which is most computationally efficient? Here we make a contribution to the answer. We compare interspike interval histograms from simulated data using four different approximate stochastic differential equation (SDE) models of the stochastic Hodgkin-Huxley neuron, as well as the exact Markov chain model simulated by the Gillespie algorithm. One of the recent SDE models is the same as the Kurtz approximation first published in 1978. All the models considered give similar ISI histograms over a wide range of deterministic and stochastic input. Three features of these histograms are an initial peak, followed by one or more bumps, and then an exponential tail. We explore how these features depend on deterministic input and on level of channel noise, and explain the results using the stochastic dynamics of the model. We conclude with a rough ranking of the four SDE models with respect to the similarity of their ISI histograms to the histogram of the exact Markov chain model.

PDB_Hydro: incorporating dipolar solvents with variable density in the Poisson-Boltzmann treatment of macromolecule electrostatics.

PubMed

Azuara, Cyril; Lindahl, Erik; Koehl, Patrice; Orland, Henri; Delarue, Marc

2006-07-01

We describe a new way to calculate the electrostatic properties of macromolecules which eliminates the assumption of a constant dielectric value in the solvent region, resulting in a Generalized Poisson-Boltzmann-Langevin equation (GPBLE). We have implemented a web server (http://lorentz.immstr.pasteur.fr/pdb_hydro.php) that both numerically solves this equation and uses the resulting water density profiles to place water molecules at preferred sites of hydration. Surface atoms with high or low hydration preference can be easily displayed using a simple PyMol script, allowing for the tentative prediction of the dimerization interface in homodimeric proteins, or lipid binding regions in membrane proteins. The web site includes options that permit mutations in the sequence as well as reconstruction of missing side chain and/or main chain atoms. These tools are accessible independently from the electrostatics calculation, and can be used for other modeling purposes. We expect this web server to be useful to structural biologists, as the knowledge of solvent density should prove useful to get better fits at low resolution for X-ray diffraction data and to computational biologists, for whom these profiles could improve the calculation of interaction energies in water between ligands and receptors in docking simulations.

Modeling pH-Responsive Adsorption of Polyelectrolytes at Oil-Water Interfaces

NASA Astrophysics Data System (ADS)

Qin, Shiyi; Yong, Xin

We use dissipative particle dynamics (DPD) to discover the interfacial adsorption of pH-responsive polyelectrolytes in oil-water binary systems under different pH values. The electrostatic interactions between charged beads and the dielectric discontinuity across the interface are modeled by exploiting a modified Particle-Particle-Particle-Mesh (PPPM) method, which uses an iterative method to solve the Poisson equation on a uniform grid. We first model the adsorption behavior of a single linear polyelectrolyte from the aqueous phase. The Henderson-Hasselbalch equation describes the relation between pH and the degree of ionization of the modeled polyelectrolytes. Through changing the degree of ionization, we explore the influence of pH on the adsorption behavior and show that the electrostatic interactions significantly modulate the adsorption. Time evolutions of the position and conformation of the polyelectrolytes and the variation in the oil-water surface tension will be measured to characterize the adsorption behavior. Furthermore, we model the pH-dependent adsorption behavior of polyelectrolytes with more complicated structures, namely, branched polyelectrolytes with hydrophobic backbones and hydrophilic side chains. We also find that the addition of salts in the medium and the lengths of the backbone and ionized side chain affect the adsorption. This research supported by the American Chemical Society Petroleum Research Fund (Award 56884-DNI9).

Stable and dynamic microtubules coordinately shape the myosin activation zone during cytokinetic furrow formation

PubMed Central

Foe, Victoria E.; von Dassow, George

2008-01-01

The cytokinetic furrow arises from spatial and temporal regulation of cortical contractility. To test the role microtubules play in furrow specification, we studied myosin II activation in echinoderm zygotes by assessing serine19-phosphorylated regulatory light chain (pRLC) localization after precisely timed drug treatments. Cortical pRLC was globally depressed before cytokinesis, then elevated only at the equator. We implicated cell cycle biochemistry (not microtubules) in pRLC depression, and differential microtubule stability in localizing the subsequent myosin activation. With no microtubules, pRLC accumulation occurred globally instead of equatorially, and loss of just dynamic microtubules increased equatorial pRLC recruitment. Nocodazole treatment revealed a population of stable astral microtubules that formed during anaphase; among these, those aimed toward the equator grew longer, and their tips coincided with cortical pRLC accumulation. Shrinking the mitotic apparatus with colchicine revealed pRLC suppression near dynamic microtubule arrays. We conclude that opposite effects of stable versus dynamic microtubules focuses myosin activation to the cell equator during cytokinesis. PMID:18955555

Langevin Equation for DNA Dynamics

NASA Astrophysics Data System (ADS)

Grych, David; Copperman, Jeremy; Guenza, Marina

Under physiological conditions, DNA oligomers can contain well-ordered helical regions and also flexible single-stranded regions. We describe the site-specific motion of DNA with a modified Rouse-Zimm Langevin equation formalism that describes DNA as a coarse-grained polymeric chain with global structure and local flexibility. The approach has successfully described the protein dynamics in solution and has been extended to nucleic acids. Our approach provides diffusive mode analytical solutions for the dynamics of global rotational diffusion and internal motion. The internal DNA dynamics present a rich energy landscape that accounts for an interior where hydrogen bonds and base-stacking determine structure and experience limited solvent exposure. We have implemented several models incorporating different coarse-grained sites with anisotropic rotation, energy barrier crossing, and local friction coefficients that include a unique internal viscosity and our models reproduce dynamics predicted by atomistic simulations. The models reproduce bond autocorrelation along the sequence as compared to that directly calculated from atomistic molecular dynamics simulations. The Langevin equation approach captures the essence of DNA dynamics without a cumbersome atomistic representation.

A Kinetic Approach to Propagation and Stability of Detonation Waves

NASA Astrophysics Data System (ADS)

Monaco, R.; Bianchi, M. Pandolfi; Soares, A. J.

2008-12-01

The problem of the steady propagation and linear stability of a detonation wave is formulated in the kinetic frame for a quaternary gas mixture in which a reversible bimolecular reaction takes place. The reactive Euler equations and related Rankine-Hugoniot conditions are deduced from the mesoscopic description of the process. The steady propagation problem is solved for a Zeldovich, von Neuman and Doering (ZND) wave, providing the detonation profiles and the wave thickness for different overdrive degrees. The one-dimensional stability of such detonation wave is then studied in terms of an initial value problem coupled with an acoustic radiation condition at the equilibrium final state. The stability equations and their initial data are deduced from the linearized reactive Euler equations and related Rankine-Hugoniot conditions through a normal mode analysis referred to the complex disturbances of the steady state variables. Some numerical simulations for an elementary reaction of the hydrogen-oxygen chain are proposed in order to describe the time and space evolution of the instabilities induced by the shock front perturbation.

Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows

NASA Astrophysics Data System (ADS)

Zhao, Lifei; Li, Zhen; Caswell, Bruce; Ouyang, Jie; Karniadakis, George Em

2018-06-01

We simulate complex fluids by means of an on-the-fly coupling of the bulk rheology to the underlying microstructure dynamics. In particular, a continuum model of polymeric fluids is constructed without a pre-specified constitutive relation, but instead it is actively learned from mesoscopic simulations where the dynamics of polymer chains is explicitly computed. To couple the bulk rheology of polymeric fluids and the microscale dynamics of polymer chains, the continuum approach (based on the finite volume method) provides the transient flow field as inputs for the (mesoscopic) dissipative particle dynamics (DPD), and in turn DPD returns an effective constitutive relation to close the continuum equations. In this multiscale modeling procedure, we employ an active learning strategy based on Gaussian process regression (GPR) to minimize the number of expensive DPD simulations, where adaptively selected DPD simulations are performed only as necessary. Numerical experiments are carried out for flow past a circular cylinder of a non-Newtonian fluid, modeled at the mesoscopic level by bead-spring chains. The results show that only five DPD simulations are required to achieve an effective closure of the continuum equations at Reynolds number Re = 10. Furthermore, when Re is increased to 100, only one additional DPD simulation is required for constructing an extended GPR-informed model closure. Compared to traditional message-passing multiscale approaches, applying an active learning scheme to multiscale modeling of non-Newtonian fluids can significantly increase the computational efficiency. Although the method demonstrated here obtains only a local viscosity from the polymer dynamics, it can be extended to other multiscale models of complex fluids whose macro-rheology is unknown.

Survival condition for low-frequency quasi-one-dimensional breathers in a two-dimensional strongly anisotropic crystal

NASA Astrophysics Data System (ADS)

Savin, A. V.; Zubova, E. A.; Manevitch, L. I.

2005-06-01

We investigate a two-dimensional (2D) strongly anisotropic crystal (2D SAC) on substrate: 2D system of coupled linear chains of particles with strong intrachain and weak interchain interactions, each chain being subjected to the sine background potential. Nonlinear dynamics of one of these chains when the rest of them are fixed is reduced to the well known Frenkel-Kontorova (FK) model. Depending on strengh of the substrate, the 2D SAC models a variety of physical systems: polymer crystals with identical chains having light side groups, an array of inductively coupled long Josephson junctions, anisotropic crystals having light and heavy sublattices. Continuum limit of the FK model, the sine-Gordon (sG) equation, allows two types of soliton solutions: topological solitons and breathers. It is known that the quasi-one-dimensional topological solitons can propagate also in a chain of 2D system of coupled chains and even in a helix chain in a three-dimensional model of polymer crystal. In contrast to this, numerical simulation shows that the long-living breathers inherent to the FK model do not exist in the 2D SAC with weak background potential. The effect changes scenario of kink-antikink collision with small relative velocity: at weak background potential the collision always results only in intensive phonon radiation while kink-antikink recombination in the FK model results in long-living low-frequency sG breather creation. We found the survival condition for breathers in the 2D SAC on substrate depending on breather frequency and strength of the background potential. The survival condition bears no relation to resonances between breather frequency and frequencies of phonon band—contrary to the case of the FK model.

General approach to polymer chains confined by interacting boundaries

NASA Astrophysics Data System (ADS)

Freed, Karl F.; Dudowicz, Jacek; Stukalin, Evgeny B.; Douglas, Jack F.

2010-09-01

Polymer chains, confined to cavities or polymer layers with dimensions less than the chain radius of gyration, appear in many phenomena, such as gel chromatography, rubber elasticity, viscolelasticity of high molar mass polymer melts, the translocation of polymers through nanopores and nanotubes, polymer adsorption, etc. Thus, the description of how the constraints alter polymer thermodynamic properties is a recurrent theoretical problem. A realistic treatment requires the incorporation of impenetrable interacting (attractive or repulsive) boundaries, a process that introduces significant mathematical complications. The standard approach involves developing the generalized diffusion equation description of the interaction of flexible polymers with impenetrable confining surfaces into a discrete eigenfunction expansion, where the solutions are normally truncated at the first mode (the "ground state dominance" approximation). This approximation is mathematically well justified under conditions of strong confinement, i.e., a confinement length scale much smaller than the chain radius of gyration, but becomes unreliable when the polymers are confined to dimensions comparable to their typically nanoscale size. We extend a general approach to describe polymers under conditions of weak to moderate confinement and apply this semianalytic method specifically to determine the thermodynamics and static structure factor for a flexible polymer confined between impenetrable interacting parallel plate boundaries. The method is first illustrated by analyzing chain partitioning between a pore and a large external reservoir, a model system with application to chromatography. Improved agreement is found for the partition coefficients of a polymer chain in the pore geometry. An expression is derived for the structure factor S(k ) in a slit geometry to assist in more accurately estimating chain dimensions from scattering measurements for thin polymer films.

How electronic dynamics with Pauli exclusion produces Fermi-Dirac statistics.

PubMed

Nguyen, Triet S; Nanguneri, Ravindra; Parkhill, John

2015-04-07

It is important that any dynamics method approaches the correct population distribution at long times. In this paper, we derive a one-body reduced density matrix dynamics for electrons in energetic contact with a bath. We obtain a remarkable equation of motion which shows that in order to reach equilibrium properly, rates of electron transitions depend on the density matrix. Even though the bath drives the electrons towards a Boltzmann distribution, hole blocking factors in our equation of motion cause the electronic populations to relax to a Fermi-Dirac distribution. These factors are an old concept, but we show how they can be derived with a combination of time-dependent perturbation theory and the extended normal ordering of Mukherjee and Kutzelnigg for a general electronic state. The resulting non-equilibrium kinetic equations generalize the usual Redfield theory to many-electron systems, while ensuring that the orbital occupations remain between zero and one. In numerical applications of our equations, we show that relaxation rates of molecules are not constant because of the blocking effect. Other applications to model atomic chains are also presented which highlight the importance of treating both dephasing and relaxation. Finally, we show how the bath localizes the electron density matrix.

Ergodicity of the Stochastic Nosé-Hoover Heat Bath

NASA Astrophysics Data System (ADS)

Wei Chung Lo,; Baowen Li,

2010-07-01

We numerically study the ergodicity of the stochastic Nosé-Hoover heat bath whose formalism is based on the Markovian approximation for the Nosé-Hoover equation [J. Phys. Soc. Jpn. 77 (2008) 103001]. The approximation leads to a Langevin-like equation driven by a fluctuating dissipative force and multiplicative Gaussian white noise. The steady state solution of the associated Fokker-Planck equation is the canonical distribution. We investigate the dynamics of this method for the case of (i) free particle, (ii) nonlinear oscillators and (iii) lattice chains. We derive the Fokker-Planck equation for the free particle and present approximate analytical solution for the stationary distribution in the context of the Markovian approximation. Numerical simulation results for nonlinear oscillators show that this method results in a Gaussian distribution for the particles velocity. We also employ the method as heat baths to study nonequilibrium heat flow in one-dimensional Fermi-Pasta-Ulam (FPU-β) and Frenkel-Kontorova (FK) lattices. The establishment of well-defined temperature profiles are observed only when the lattice size is large. Our results provide numerical justification for such Markovian approximation for classical single- and many-body systems.

Chains of risk for alcohol use disorder: Mediators of exposure to neighborhood deprivation in early and middle childhood.

PubMed

Karriker-Jaffe, Katherine J; Lönn, Sara L; Cook, Won K; Kendler, Kenneth S; Sundquist, Kristina

2018-03-01

Our goal was to test a cascade model to identify developmental pathways, or chains of risk, from neighborhood deprivation in childhood to alcohol use disorder (AUD) in young adulthood. Using Swedish general population data, we examined whether exposure to neighborhood deprivation during early and middle childhood was associated with indicators of social functioning in adolescence and emerging adulthood, and whether these were predictive of AUD. Structural equation models showed exposure to neighborhood deprivation was associated with lower school achievement during adolescence, poor social functioning during emerging adulthood, and the development of AUD for both males and females. Understanding longitudinal pathways from early exposure to adverse environments to later AUD can inform prevention and intervention efforts. Copyright © 2018 Elsevier Ltd. All rights reserved.

Nonequilibrium thermodynamic potentials for continuous-time Markov chains.

PubMed

Verley, Gatien

2016-01-01

We connect the rare fluctuations of an equilibrium (EQ) process and the typical fluctuations of a nonequilibrium (NE) stationary process. In the framework of large deviation theory, this observation allows us to introduce NE thermodynamic potentials. For continuous-time Markov chains, we identify the relevant pairs of conjugated variables and propose two NE ensembles: one with fixed dynamics and fluctuating time-averaged variables, and another with fixed time-averaged variables, but a fluctuating dynamics. Accordingly, we show that NE processes are equivalent to conditioned EQ processes ensuring that NE potentials are Legendre dual. We find a variational principle satisfied by the NE potentials that reach their maximum in the NE stationary state and whose first derivatives produce the NE equations of state and second derivatives produce the NE Maxwell relations generalizing the Onsager reciprocity relations.

Thermal rectification in anharmonic chains under an energy-conserving noise.

PubMed

Guimarães, Pedro H; Landi, Gabriel T; de Oliveira, Mário J

2015-12-01

Systems in which the heat flux depends on the direction of the flow are said to present thermal rectification. This effect has attracted much theoretical and experimental interest in recent years. However, in most theoretical models the effect is found to vanish in the thermodynamic limit, in disagreement with experiment. The purpose of this paper is to show that the rectification may be restored by including an energy-conserving noise which randomly flips the velocity of the particles with a certain rate λ. It is shown that as long as λ is nonzero, the rectification remains finite in the thermodynamic limit. This is illustrated in a classical harmonic chain subject to a quartic pinning potential (the Φ(4) model) and coupled to heat baths by Langevin equations.

Projection methods for the numerical solution of Markov chain models

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.

Adapting Poisson-Boltzmann to the self-consistent mean field theory: Application to protein side-chain modeling

NASA Astrophysics Data System (ADS)

Koehl, Patrice; Orland, Henri; Delarue, Marc

2011-08-01

We present an extension of the self-consistent mean field theory for protein side-chain modeling in which solvation effects are included based on the Poisson-Boltzmann (PB) theory. In this approach, the protein is represented with multiple copies of its side chains. Each copy is assigned a weight that is refined iteratively based on the mean field energy generated by the rest of the protein, until self-consistency is reached. At each cycle, the variational free energy of the multi-copy system is computed; this free energy includes the internal energy of the protein that accounts for vdW and electrostatics interactions and a solvation free energy term that is computed using the PB equation. The method converges in only a few cycles and takes only minutes of central processing unit time on a commodity personal computer. The predicted conformation of each residue is then set to be its copy with the highest weight after convergence. We have tested this method on a database of hundred highly refined NMR structures to circumvent the problems of crystal packing inherent to x-ray structures. The use of the PB-derived solvation free energy significantly improves prediction accuracy for surface side chains. For example, the prediction accuracies for χ1 for surface cysteine, serine, and threonine residues improve from 68%, 35%, and 43% to 80%, 53%, and 57%, respectively. A comparison with other side-chain prediction algorithms demonstrates that our approach is consistently better in predicting the conformations of exposed side chains.

Analytical theory of the shear Alfvén continuum in the presence of a magnetic island

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

Cook, C. R., E-mail: cook@physics.wisc.edu; Hegna, C. C.

2015-04-15

The effect of a magnetic island chain on the shear Alfvén continuum is calculated analytically. Using a WKB approximation of the linearized ideal MHD equations, the island is shown to cause an upshift in the continuum accumulation point frequency. This minimum of the frequency spectrum is shifted from the rational surface to the island separatrix. The structure of the eigenmodes is also presented.

RadVel: General toolkit for modeling Radial Velocities

NASA Astrophysics Data System (ADS)

Fulton, Benjamin J.; Petigura, Erik A.; Blunt, Sarah; Sinukoff, Evan

2018-01-01

RadVel models Keplerian orbits in radial velocity (RV) time series. The code is written in Python with a fast Kepler's equation solver written in C. It provides a framework for fitting RVs using maximum a posteriori optimization and computing robust confidence intervals by sampling the posterior probability density via Markov Chain Monte Carlo (MCMC). RadVel can perform Bayesian model comparison and produces publication quality plots and LaTeX tables.

APL-UW Deep Water Propagation 2015-2017: Philippine Sea Data Analysis

DTIC Science & Technology

independent Monte Carlo parabolic equation simulations . The autospectrum of normalized intensity had an excellent match to that of a time-dependent Monte...ambient noise; systems along the Aleutian chain have either no significant trendor a slight increasing trend; systems in the central Pacific Ocean...At the end of the grant, it was determined that the Kauai cable had suffered a break in the shallow near-shore region. Additional contractual

Entanglement dynamics following a sudden quench: An exact solution

NASA Astrophysics Data System (ADS)

Ghosh, Supriyo; Gupta, Kumar S.; Srivastava, Shashi C. L.

2017-12-01

We present an exact and fully analytical treatment of the entanglement dynamics for an isolated system of N coupled oscillators following a sudden quench of the system parameters. The system is analyzed using the solutions of the time-dependent Schrodinger's equation, which are obtained by solving the corresponding nonlinear Ermakov equations. The entanglement entropies exhibit a multi-oscillatory behaviour, where the number of dynamically generated time scales increases with N. The harmonic chains exhibit entanglement revival and for larger values of N (> 10), we find near-critical logarithmic scaling for the entanglement entropy, which is modulated by a time-dependent factor. The N = 2 case is equivalent to the two-site Bose-Hubbard model in the tunneling regime, which is amenable to empirical realization in cold-atom systems.

Sound Clocks and Sonic Relativity

NASA Astrophysics Data System (ADS)

Todd, Scott L.; Menicucci, Nicolas C.

2017-10-01

Sound propagation within certain non-relativistic condensed matter models obeys a relativistic wave equation despite such systems admitting entirely non-relativistic descriptions. A natural question that arises upon consideration of this is, "do devices exist that will experience the relativity in these systems?" We describe a thought experiment in which `acoustic observers' possess devices called sound clocks that can be connected to form chains. Careful investigation shows that appropriately constructed chains of stationary and moving sound clocks are perceived by observers on the other chain as undergoing the relativistic phenomena of length contraction and time dilation by the Lorentz factor, γ , with c the speed of sound. Sound clocks within moving chains actually tick less frequently than stationary ones and must be separated by a shorter distance than when stationary to satisfy simultaneity conditions. Stationary sound clocks appear to be length contracted and time dilated to moving observers due to their misunderstanding of their own state of motion with respect to the laboratory. Observers restricted to using sound clocks describe a universe kinematically consistent with the theory of special relativity, despite the preferred frame of their universe in the laboratory. Such devices show promise in further probing analogue relativity models, for example in investigating phenomena that require careful consideration of the proper time elapsed for observers.

Evaluation of the operatorial Q-system for non-compact super spin chains

NASA Astrophysics Data System (ADS)

Frassek, Rouven; Marboe, Christian; Meidinger, David

2017-09-01

We present an approach to evaluate the full operatorial Q-system of all u(p,q\\Big|r+s) -invariant spin chains with representations of Jordan-Schwinger type. In particular, this includes the super spin chain of planar N=4 super Yang-Mills theory at one loop in the presence of a diagonal twist. Our method is based on the oscillator construction of Q-operators. The Q-operators are built as traces over Lax operators which are degenerate solutions of the Yang-Baxter equation. For non-compact representations these Lax operators may contain multiple infinite sums that conceal the form of the resulting functions. We determine these infinite sums and calculate the matrix elements of the lowest level Q-operators. Transforming the Lax operators corresponding to the Q-operators into a representation involving only finite sums allows us to take the supertrace and to obtain the explicit form of the Q-operators in terms of finite matrices for a given magnon sector. Imposing the functional relations, we then bootstrap the other Q-operators from those of the lowest level. We exemplify this approach for non-compact spin - s spin chains and apply it to N=4 at the one-loop level using the BMN vacuum as an example.

Effects of alkyl chain length and solvents on thermodynamic dissociation constants of the ionic liquids with one carboxyl group in the alkyl chain of imidazolium cations.

PubMed

Chen, Yuehua; Wang, Huiyong; Wang, Jianji

2014-05-01

Thermodynamic dissociation constants of the Brønsted acidic ionic liquids (ILs) are important for their catalytic and separation applications. In this work, a series of imidazolium bromides with one carboxylic acid substitute group in their alkyl chain ([{(CH2)nCOOH}mim]Br, n = 1,3,5,7) have been synthesized, and their dissociation constants (pKa) at different ionic strengths have been determined in aqueous and aqueous organic solvents at 0.1 mole fraction (x) of ethanol, glycol, iso-propanol, and dimethyl sulfoxide by potentiometric titrations at 298.2 K. The standard thermodynamic dissociation constants (pKa(T)) of the ILs in these solvents were calculated from the extended Debye-Hückel equation. It was found that the pKa values increased with the increase of ionic strength of the media and of the addition of organic solvent in water. The pKa(T) values also increased with the increase of the alkyl chain length of cations of the ILs. In addition, the effect of solvent nature on pKa(T) values is interpreted from solvation of the dissociation components and their Gibbs energy of transfer from water to aqueous organic solutions.

Modelling biochemical reaction systems by stochastic differential equations with reflection.

PubMed

Niu, Yuanling; Burrage, Kevin; Chen, Luonan

2016-05-07

In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. Copyright © 2016 Elsevier Ltd. All rights reserved.

Fast analysis of radionuclide decay chain migration

NASA Astrophysics Data System (ADS)

Chen, J. S.; Liang, C. P.; Liu, C. W.; Li, L.

2014-12-01

A novel tool for rapidly predicting the long-term plume behavior of an arbitrary length radionuclide decay chain is presented in this study. This fast tool is achieved based on generalized analytical solutions in compact format derived for a set of two-dimensional advection-dispersion equations coupled with sequential first-order decay reactions in groundwater system. The performance of the developed tool is evaluated by a numerical model using a Laplace transform finite difference scheme. The results of performance evaluation indicate that the developed model is robust and accurate. The developed model is then used to fast understand the transport behavior of a four-member radionuclide decay chain. Results show that the plume extents and concentration levels of any target radionuclide are very sensitive to longitudinal, transverse dispersion, decay rate constant and retardation factor. The developed model are useful tools for rapidly assessing the ecological and environmental impact of the accidental radionuclide releases such as the Fukushima nuclear disaster where multiple radionuclides leaked through the reactor, subsequently contaminating the local groundwater and ocean seawater in the vicinity of the nuclear plant.

Biomimetics of throwing at basketball

NASA Astrophysics Data System (ADS)

Merticaru, E.; Budescu, E.; Iacob, R. M.

2016-08-01

The paper deals with the inverse dynamics of a kinematic chain of the human upper limb when throwing the ball at the basketball, aiming to calculate the torques required to put in action the technical system. The kinematic chain respects the anthropometric features regarding the length and mass of body segments. The kinematic parameters of the motion were determined by measuring the angles of body segments during a succession of filmed pictures of a throw, and the interpolation of these values and determination of the interpolating polynomials for each independent geometric coordinate. Using the Lagrange equations, there were determined the variations with time of the required torques to put in motion the kinematic chain of the type of triple physical pendulum. The obtained values show, naturally, the fact that the biggest torque is that for mimetic articulation of the shoulder, being comparable with those obtained by the brachial biceps muscle of the analyzed human subject. Using the obtained data, there can be conceived the mimetic technical system, of robotic type, with application in sports, so that to perform the motion of ball throwing, from steady position, at the basket.

Block-accelerated aggregation multigrid for Markov chains with application to PageRank problems

NASA Astrophysics Data System (ADS)

Shen, Zhao-Li; Huang, Ting-Zhu; Carpentieri, Bruno; Wen, Chun; Gu, Xian-Ming

2018-06-01

Recently, the adaptive algebraic aggregation multigrid method has been proposed for computing stationary distributions of Markov chains. This method updates aggregates on every iterative cycle to keep high accuracies of coarse-level corrections. Accordingly, its fast convergence rate is well guaranteed, but often a large proportion of time is cost by aggregation processes. In this paper, we show that the aggregates on each level in this method can be utilized to transfer the probability equation of that level into a block linear system. Then we propose a Block-Jacobi relaxation that deals with the block system on each level to smooth error. Some theoretical analysis of this technique is presented, meanwhile it is also adapted to solve PageRank problems. The purpose of this technique is to accelerate the adaptive aggregation multigrid method and its variants for solving Markov chains and PageRank problems. It also attempts to shed some light on new solutions for making aggregation processes more cost-effective for aggregation multigrid methods. Numerical experiments are presented to illustrate the effectiveness of this technique.

FOR STIMULI-RESPONSIVE POLYMERS WITH ENHANCED EFFICIENCY IN RESERVOIR RECOVERY PROCESSES

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

Charles McCormick; Roger Hester

To date, our synthetic research efforts have been focused on the development of stimuli-responsive water-soluble polymers designed for use in enhanced oil recovery (EOR) applications. These model systems are structurally tailored for potential application as viscosifiers and/or mobility control agents for secondary and tertiary EOR methods. The following report discloses the progress of our ongoing research of polyzwitterions, polymers derived from monomers bearing both positive and negative charges, that show the ability to sustain or increase their hydrodynamic volume (and thus, solution viscosity) in the presence of electrolytes. Such polymers appear to be well-suited for use under conditions similar tomore » those encountered in EOR operations. Additionally, we disclose the synthesis and characterization of a well-defined set of polyacrylamide (PAM) homopolymers that vary by MW. The MW of the PAM samples is controlled by addition of sodium formate to the polymerization medium as a conventional chain transfer agent. Data derived from polymer characterization is used to determine the kinetic parameter C{sub CT}, the chain transfer constant to sodium formate under the given polymerization conditions. The PAM homopolymer series will be employed in future set of experiments designed to test a simplified intrinsic viscosity equation. The flow resistance of a polymer solution through a porous medium is controlled by the polymer's hydrodynamic volume, which is strongly related to it's intrinsic viscosity. However, the hydrodynamic volume of a polymer molecule in an aqueous solution varies with fluid temperature, solvent composition, and polymer structure. This report on the theory of polymer solubility accentuates the importance of developing polymer solutions that increase in intrinsic viscosity when fluid temperatures are elevated above room conditions. The intrinsic viscosity response to temperature and molecular weight variations of three polymer solutions verified the modeling capability of a simplified intrinsic viscosity equation. These results imply that the simplified intrinsic viscosity equation is adequate in modeling polymer coil size response to solvent composition, temperature and polymer molecular weight. The equation can be used to direct efforts to produce superior polymers for mobility control during flooding of reservoirs at elevated temperatures.« less

Stochastic dynamics of time correlation in complex systems with discrete time

NASA Astrophysics Data System (ADS)

Yulmetyev, Renat; Hänggi, Peter; Gafarov, Fail

2000-11-01

In this paper we present the concept of description of random processes in complex systems with discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations for time correlation functions (TCFs). We have introduced the dynamic (time dependent) information Shannon entropy Si(t) where i=0,1,2,3,..., as an information measure of stochastic dynamics of time correlation (i=0) and time memory (i=1,2,3,...). The set of functions Si(t) constitute the quantitative measure of time correlation disorder (i=0) and time memory disorder (i=1,2,3,...) in complex system. The theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states. We examine two stochastic processes involving the creation and annihilation of time correlation (or time memory) in details. We carry out the analysis of vectors' dynamics employing finite-difference equations for random variables and the evolution operator describing their natural motion. The existence of TCF results in the construction of the set of projection operators by the usage of scalar product operation. Harnessing the infinite set of orthogonal dynamic random variables on a basis of Gram-Shmidt orthogonalization procedure tends to creation of infinite chain of finite-difference non-Markov kinetic equations for discrete TCFs and memory functions (MFs). The solution of the equations above thereof brings to the recurrence relations between the TCF and MF of senior and junior orders. This offers new opportunities for detecting the frequency spectra of power of entropy function Si(t) for time correlation (i=0) and time memory (i=1,2,3,...). The results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems. Application of this technique on the analysis of stochastic dynamics of RR intervals from human ECG's shows convincing evidence for a non-Markovian phenomemena associated with a peculiarities in short- and long-range scaling. This method may be of use in distinguishing healthy from pathologic data sets based in differences in these non-Markovian properties.

Discrete breathers dynamic in a model for DNA chain with a finite stacking enthalpy

NASA Astrophysics Data System (ADS)

Gninzanlong, Carlos Lawrence; Ndjomatchoua, Frank Thomas; Tchawoua, Clément

2018-04-01

The nonlinear dynamics of a homogeneous DNA chain based on site-dependent finite stacking and pairing enthalpies is studied. A new variant of extended discrete nonlinear Schrödinger equation describing the dynamics of modulated wave is derived. The regions of discrete modulational instability of plane carrier waves are studied, and it appears that these zones depend strongly on the phonon frequency of Fourier's mode. The staggered/unstaggered discrete breather (SDB/USDB) is obtained straightforwardly without the staggering transformation, and it is demonstrated that SDBs are less unstable than USDB. The instability of discrete multi-humped SDB/USDB solution does not depend on the number of peaks of the discrete breather (DB). By using the concept of Peierls-Nabarro energy barrier, it appears that the low-frequency DBs are more mobile.

Inhomogeneous Heisenberg spin chain and quantum vortex filament as non-holonomically deformed NLS systems

NASA Astrophysics Data System (ADS)

Abhinav, Kumar; Guha, Partha

2018-03-01

Through the Hasimoto map, various dynamical systems can be mapped to different integrodifferential generalizations of Nonlinear Schrödinger (NLS) family of equations some of which are known to be integrable. Two such continuum limits, corresponding to the inhomogeneous XXX Heisenberg spin chain [J. Phys. C 15, L1305 (1982)] and that of a thin vortex filament moving in a superfluid with drag [Eur. Phys. J. B 86, 275 (2013) 86; Phys. Rev. E 91, 053201 (2015)], are shown to be particular non-holonomic deformations (NHDs) of the standard NLS system involving generalized parameterizations. Crucially, such NHDs of the NLS system are restricted to specific spectral orders that exactly complements NHDs of the original physical systems. The specific non-holonomic constraints associated with these integrodifferential generalizations additionally posses distinct semi-classical signature.

Quasi-soliton scattering in quantum spin chains

NASA Astrophysics Data System (ADS)

Vlijm, R.; Ganahl, M.; Fioretto, D.; Brockmann, M.; Haque, M.; Evertz, H. G.; Caux, J.-S.

2015-12-01

The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time-evolution fits on the displacements. The time-evolved block decimation algorithm allows for the study of scattering displacements from spin-block states, showing similar scattering displacement features.

Quasi-soliton scattering in quantum spin chains

NASA Astrophysics Data System (ADS)

Fioretto, Davide; Vljim, Rogier; Ganahl, Martin; Brockmann, Michael; Haque, Masud; Evertz, Hans-Gerd; Caux, Jean-Sébastien

The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time evolution fits on the displacements. The TEBD algorithm allows for the study of scattering displacements from spin-block states, showing similar displacement scattering features.

Traveling solitons in long-range oscillator chains

NASA Astrophysics Data System (ADS)

Miloshevich, George; Nguenang, Jean Pierre; Dauxois, Thierry; Khomeriki, Ramaz; Ruffo, Stefano

2017-03-01

We investigate the existence and propagation of solitons in a long-range extension of the quartic Fermi-Pasta-Ulam (FPU) chain of anharmonic oscillators. The coupling in the linear term decays as a power-law with an exponent 1<α ≤slant 3 . We obtain an analytic perturbative expression of traveling envelope solitons by introducing a non linear Schrödinger equation for the slowly varying amplitude of short wavelength modes. Due to the non analytic properties of the dispersion relation, it is crucial to develop the theory using discrete difference operators. Those properties are also the ultimate reason why kink-solitons may exist but are unstable, at variance with the short-range FPU model. We successfully compare these approximate analytic results with numerical simulations for the value α =2 which was chosen as a case study.

First-Principles Propagation of Geoelectric Fields from Ionosphere to Ground using LANLGeoRad

NASA Astrophysics Data System (ADS)

Jeffery, C. A.; Woodroffe, J. R.; Henderson, M. G.

2017-12-01

A notable deficiency in the current SW forecasting chain is the propagation of geoelectric fields from ionosphere to ground using Biot-Savart integrals, which ignore the localized complexity of lithospheric electrical conductivity and the relatively high conductivity of ocean water compared to the lithosphere. Three-dimensional models of Earth conductivity with mesoscale spatial resolution are being developed, but a new approach is needed to incorporate this information into the SW forecast chain. We present initial results from a first-principles geoelectric propagation model call LANLGeoRad, which solves Maxwell's equations on an unstructured geodesic grid. Challenges associated with the disparate response times of millisecond electromagnetic propagation and 10-second geomagnetic fluctuations are highlighted, and a novel rescaling of the ionosphere/ground system is presented that renders this geoelectric system computationally tractable.

The Nosé–Hoover looped chain thermostat for low temperature thawed Gaussian wave-packet dynamics

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

Coughtrie, David J.; Tew, David P.

2014-05-21

We have used a generalised coherent state resolution of the identity to map the quantum canonical statistical average for a general system onto a phase-space average over the centre and width parameters of a thawed Gaussian wave packet. We also propose an artificial phase-space density that has the same behaviour as the canonical phase-space density in the low-temperature limit, and have constructed a novel Nosé–Hoover looped chain thermostat that generates this density in conjunction with variational thawed Gaussian wave-packet dynamics. This forms a new platform for evaluating statistical properties of quantum condensed-phase systems that has an explicit connection to themore » time-dependent Schrödinger equation, whilst retaining many of the appealing features of path-integral molecular dynamics.« less

Adsorption of a single polymer chain on a surface: Effects of the potential range

NASA Astrophysics Data System (ADS)

Klushin, Leonid I.; Polotsky, Alexey A.; Hsu, Hsiao-Ping; Markelov, Denis A.; Binder, Kurt; Skvortsov, Alexander M.

2013-02-01

We investigate the effects of the range of adsorption potential on the equilibrium behavior of a single polymer chain end-attached to a solid surface. The exact analytical theory for ideal lattice chains interacting with a planar surface via a box potential of depth U and width W is presented and compared to continuum model results and to Monte Carlo (MC) simulations using the pruned-enriched Rosenbluth method for self-avoiding chains on a simple cubic lattice. We show that the critical value Uc corresponding to the adsorption transition scales as W-1/ν, where the exponent ν=1/2 for ideal chains and ν≈3/5 for self-avoiding walks. Lattice corrections for finite W are incorporated in the analytical prediction of the ideal chain theory Uc≈((π2)/(24))(W+1/2)-2 and in the best-fit equation for the MC simulation data Uc=0.585(W+1/2)-5/3. Tail, loop, and train distributions at the critical point are evaluated by MC simulations for 1≤W≤10 and compared to analytical results for ideal chains and with scaling theory predictions. The behavior of a self-avoiding chain is remarkably close to that of an ideal chain in several aspects. We demonstrate that the bound fraction θ and the related properties of finite ideal and self-avoiding chains can be presented in a universal reduced form: θ(N,U,W)=θ(NUc,U/Uc). By utilizing precise estimations of the critical points we investigate the chain length dependence of the ratio of the normal and lateral components of the gyration radius. Contrary to common expectations this ratio attains a limiting universal value /=0.320±0.003 only at N˜5000. Finite-N corrections for this ratio turn out to be of the opposite sign for W=1 and for W≥2. We also study the N dependence of the apparent crossover exponent ϕeff(N). Strong corrections to scaling of order N-0.5 are observed, and the extrapolated value ϕ=0.483±0.003 is found for all values of W. The strong correction to scaling effects found here explain why for smaller values of N, as used in most previous work, misleadingly large values of ϕeff(N) were identified as the asymptotic value for the crossover exponent.

String limit of the isotropic Heisenberg chain in the four-particle sector

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

Antipov, A. G., E-mail: aga2@csa.ru; Komarov, I. V., E-mail: ivkoma@rambler.r

2008-05-15

The quantum method of variable separation is applied to the spectral problem of the isotropic Heisenberg model. The Baxter difference equation is resolved by means of a special quasiclassical asymptotic expansion. States are identified by multiplicities of limiting values of the Bethe parameters. The string limit of the four-particle sector is investigated. String solutions are singled out and classified. It is shown that only a minor fraction of solutions demonstrate string behavior.

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics.

PubMed

Aguayo-Ortiz, A; Mendoza, S; Olvera, D

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics

PubMed Central

Mendoza, S.; Olvera, D.

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and “Rankine-Hugoniot” jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges. PMID:29659602

Giant frequency down-conversion of the dancing acoustic bubble

PubMed Central

Deymier, P. A.; Keswani, M.; Jenkins, N.; Tang, C.; Runge, K.

2016-01-01

We have demonstrated experimentally the existence of a giant frequency down-conversion of the translational oscillatory motion of individual submillimeter acoustic bubbles in water in the presence of a high frequency (500 kHz) ultrasonic standing wave. The frequency of the translational oscillations (~170 Hz) is more than three orders of magnitude smaller than that of the driving acoustic wave. We elucidate the mechanism of this very slow oscillation with an analytical model leading to an equation of translational motion of a bubble taking the form of Mathieu’s equation. This equation illuminates the origin of the giant down conversion in frequency as arising from an unstable equilibrium. We also show that bubbles that form chains along the direction of the acoustic standing wave due to radiation interaction forces exhibit also translation oscillations that form a spectral band. This band extends approximately from 130 Hz up to nearly 370 Hz, a frequency range that is still at least three orders of magnitude lower than the frequency of the driving acoustic wave. PMID:27857217

Giant frequency down-conversion of the dancing acoustic bubble

NASA Astrophysics Data System (ADS)

Deymier, P. A.; Keswani, M.; Jenkins, N.; Tang, C.; Runge, K.

2016-11-01

We have demonstrated experimentally the existence of a giant frequency down-conversion of the translational oscillatory motion of individual submillimeter acoustic bubbles in water in the presence of a high frequency (500 kHz) ultrasonic standing wave. The frequency of the translational oscillations (~170 Hz) is more than three orders of magnitude smaller than that of the driving acoustic wave. We elucidate the mechanism of this very slow oscillation with an analytical model leading to an equation of translational motion of a bubble taking the form of Mathieu’s equation. This equation illuminates the origin of the giant down conversion in frequency as arising from an unstable equilibrium. We also show that bubbles that form chains along the direction of the acoustic standing wave due to radiation interaction forces exhibit also translation oscillations that form a spectral band. This band extends approximately from 130 Hz up to nearly 370 Hz, a frequency range that is still at least three orders of magnitude lower than the frequency of the driving acoustic wave.

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

Krasnobaeva, L. A., E-mail: kla1983@mail.ru; Siberian State Medical University Moscowski Trakt 2, Tomsk, 634050; Shapovalov, A. V.

Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on dynamics local conformational perturbations (kink) propagating along the DNA molecule is investigated. Such waves have an important role in the regulation of important biological processes in living systems at the molecular level. As a dynamic model of DNA was used a modified sine-Gordon equation, simulating the rotational oscillations of bases in one of the chains DNA. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the frameworkmore » of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker– Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum. Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on the kink dynamics is investigated in the sine–Gordon model. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the framework of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker–Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum.« less

The effect of atmospheric diabatic heating on low-frequency oscillations

NASA Astrophysics Data System (ADS)

Yen, Ming-Cheng

A diagnostic scheme is devised to illustrate a chain relationship between diabatic heating and planetary-scale divergent and rotational circulations. The scheme consists of the velocity-potential maintenance equation, which relates diabatic heating and velocity potential, and the streamfunction budget equation, which depicts the streamfunction tendency caused by the imbalance between streamfunction tendencies induced by vorticity advection and source. The proposed scheme is employed to examine the effect of tropical diabatic heating on the annual variation of subtropical jet streams. It was found that annual variations of both tropical diabatic heating and planetary-scale divergent circulation exhibit an annual in-phase seesaw oscillation between the winter and summer hemispheres. The annual variation of subtropical jet streams is caused by the adjustment of atmospheric rotational flow through planetary-scale divergent circulation in response to the annual cycle of tropical diabatic heating.

Bright, dark and W-shaped solitons with extended nonlinear Schrödinger's equation for odd and even higher-order terms

NASA Astrophysics Data System (ADS)

Bendahmane, Issam; Triki, Houria; Biswas, Anjan; Saleh Alshomrani, Ali; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj

2018-02-01

We present solitary wave solutions of an extended nonlinear Schrödinger equation with higher-order odd (third-order) and even (fourth-order) terms by using an ansatz method. The including high-order dispersion terms have significant physical applications in fiber optics, the Heisenberg spin chain, and ocean waves. Exact envelope solutions comprise bright, dark and W-shaped solitary waves, illustrating the potentially rich set of solitary wave solutions of the extended model. Furthermore, we investigate the properties of these solitary waves in nonlinear and dispersive media. Moreover, specific constraints on the system parameters for the existence of these structures are discussed exactly. The results show that the higher-order dispersion and nonlinear effects play a crucial role for the formation and properties of propagating waves.

Simulation of cooperating robot manipulators on a mobile platform

NASA Technical Reports Server (NTRS)

Murphy, Stephen H.; Wen, John Ting-Yung; Saridis, George N.

1991-01-01

The dynamic equations of motion are presented for two or more cooperating manipulators on a freely moving mobile platform. The system of cooperating robot manipulators forms a closed kinematic chain where the force of interaction must be included in the formulation of robot and platform dynamics. The formulation includes the full dynamic interactions from arms to platform and arm tip to arm tip, and the possible translation and rotation of the platform. The equations of motion are shown to be identical in structure to the fixed-platform cooperative manipulator dynamics. The number of DOFs of the system is sufficiently large to make recursive dynamic calculation methods potentially more efficient than closed-form solutions. A complete simulation with two 6-DOF manipulators of a free-floating platform is presented along a with a multiple-arm controller to position the common load.

Global Patterns of Tectonism on Titan from Mountain Chains and Virgae

NASA Technical Reports Server (NTRS)

Cook, C.; Barnes, J. W.; Radebaugh, J.; Hurford, T.; Ktatenhorn, S. A.

2012-01-01

This research is based on the exploration of tectonic patterns on Titan from a global perspective. Several moons in the outer solar system display patterns of surface tectonic features that imply global stress fields driven or modified by global forces. Patterns such as these are seen in Europa's tidally induced fracture patterns, Enceladus's tiger stripes, and Ganymede's global expansion induced normal fault bands. Given its proximity to Saturn, as well as its eccentric orbit, tectonic features and global stresses may be present on Titan as well. Titan displays possible tectonic structures, such as mountain chains along its equator (Radebaugh et al. 2007), as well as the unexplored dark linear streaks termed virgae by the IAU. Imaged by Cassini with the RADAR instrument, mountain chains near the equator are observed with a predominante east-west orientation (Liu et al. 2012, Mitri et al. 2010). Orientations such as these can be explained by modifications in the global tidal stress field induced by global contraction followed by rotational spin-up. Also, due to Titan's eccentric orbit, its current rotation rate may be in an equilibrium between tidal spin-up near periapsis and spin-down near apoapsis (Barnes and Fortney 2003). Additional stress from rotational spin-up provides an asymmetry to the stress field. This, combined with an isotropic stress from radial contraction, favors the formation of equatorial mountain chains in an east-west direction. The virgae, which have been imaged by Cassini with both the Visual and Infrared Mapping Spectrometer (VIMS) and Imaging Science Subsystem (ISS) instruments, are located predominately near 30 degrees latitude in either hemisphere. Oriented with a pronounced elongation in the east-west direction, all observed virgae display similar characteristics: similar relative albedos as the surrounding terrain however darkened with an apparent neutral absorber, broken-linear or rounded sharp edges, and connected, angular elements with distinct, linear edges. Virgae imaged during northern latitude passes are oriented with their long dimensions toward Titan's antiSaturn point. If the virgae are of tectonic origin, for instance if the turn out to be i.e. grabens, they could serve as markers to Titan's global stress field. Using them in this way allows for a mapping of global tectonic patterns. These patterns will be tested for consistency against the various sources of global stress and orientations of mountain chains. By determining what drives Titan's tectonics globally, we will be able to place Titan within the context of the other outer planet icy satellites.

Load balancing and closed chain multiple arm control

NASA Technical Reports Server (NTRS)

Kreutz, Kenneth; Lokshin, Anatole

1988-01-01

The authors give the general dynamical equations for several rigid link manipulators rigidly grasping a commonly held rigid object. It is shown that the number of arm-configuration degrees of freedom lost due to imposing the closed-loop kinematic constraints is the same as the number of degrees of freedom gained for controlling the internal forces of the closed-chain system. This number is equal to the dimension of the kernel of the Jacobian operator which transforms contact forces to the net forces acting on the held object, and it is shown that this kernel can be identified with the subspace of controllable internal forces of the closed-chain system. Control of these forces makes it possible to regulate the grasping forces imparted to the held object or to control the load taken by each arm. It is shown that the internal forces can be influenced without affecting the control of the configuration degrees of freedom. Control laws of the feedback linearization type are shown to be useful for controlling the location and attitude of a frame fixed with respect to the held object, while simultaneously controlling the internal forces of the closed-chain system. Force feedback can be used to linearize and control the system even when the held object has unknown mass properties. If saturation effects are ignored, an unconstrained quadratic optimization can be performed to distribute the load optimally among the joint actuators.

Liquid crystalline phase behavior in systems of hard-sphere chains

NASA Astrophysics Data System (ADS)

Williamson, Dave C.; Jackson, George

1998-06-01

A study of the liquid crystalline phase transitions in a system of hard-sphere chains is presented. The chains comprise m=7 tangentially bonded hard-sphere segments in a linear conformation (LHSC). The isothermal-isobaric Monte Carlo simulation technique is used to obtain the equation of state of the system both by compressing the isotropic (I) liquid and by expanding the solid (K). As well as the usual isotropic and solid phases, nematic and smectic-A liquid crystalline states are seen. A large degree of hysteresis is found in the neighborhood of the I-N transition. The results for the rigid LHSC system were compared with existing data for the corresponding semiflexible hard-sphere chains (FHSC): the flexibility has a large destabilizing effect on the nematic phase and consequently it postpones the I-N transition. The results of the simulations are also compared with rescaled Onsager theories for the I-N transition. It is rather surprising to find that the Parsons approach, which has been so successful for other hard-core models such as spherocylinders and ellipsoids, gives very poor results. The related approach of Vega and Lago gives a good description of the I-N phase transition. The procedure of Vega and Lago, as with all two-body resummations of the Onsager theory, only gives a qualitative description of the nematic order.

Lattice cluster theory for dense, thin polymer films.

PubMed

Freed, Karl F

2015-04-07

While the application of the lattice cluster theory (LCT) to study the miscibility of polymer blends has greatly expanded our understanding of the monomer scale molecular details influencing miscibility, the corresponding theory for inhomogeneous systems has not yet emerged because of considerable technical difficulties and much greater complexity. Here, we present a general formulation enabling the extension of the LCT to describe the thermodynamic properties of dense, thin polymer films using a high dimension, high temperature expansion. Whereas the leading order of the LCT for bulk polymer systems is essentially simple Flory-Huggins theory, the highly non-trivial leading order inhomogeneous LCT (ILCT) for a film with L layers already involves the numerical solution of 3(L - 1) coupled, highly nonlinear equations for the various density profiles in the film. The new theory incorporates the essential "transport" constraints of Helfand and focuses on the strict imposition of excluded volume constraints, appropriate to dense polymer systems, rather than the maintenance of chain connectivity as appropriate for lower densities and as implemented in self-consistent theories of polymer adsorption at interfaces. The ILCT is illustrated by presenting examples of the computed profiles of the density, the parallel and perpendicular bonds, and the chain ends for free standing and supported films as a function of average film density, chain length, temperature, interaction with support, and chain stiffness. The results generally agree with expected general trends.

The open XXX spin chain in the SoV framework: scalar product of separate states

NASA Astrophysics Data System (ADS)

Kitanine, N.; Maillet, J. M.; Niccoli, G.; Terras, V.

2017-06-01

We consider the XXX open spin-1/2 chain with the most general non-diagonal boundary terms, that we solve by means of the quantum separation of variables (SoV) approach. We compute the scalar products of separate states, a class of states which notably contains all the eigenstates of the model. As usual for models solved by SoV, these scalar products can be expressed as some determinants with a non-trivial dependance in terms of the inhomogeneity parameters that have to be introduced for the method to be applicable. We show that these determinants can be transformed into alternative ones in which the homogeneous limit can easily be taken. These new representations can be considered as generalizations of the well-known determinant representation for the scalar products of the Bethe states of the periodic chain. In the particular case where a constraint is applied on the boundary parameters, such that the transfer matrix spectrum and eigenstates can be characterized in terms of polynomial solutions of a usual T-Q equation, the scalar product that we compute here corresponds to the scalar product between two off-shell Bethe-type states. If in addition one of the states is an eigenstate, the determinant representation can be simplified, hence leading in this boundary case to direct analogues of algebraic Bethe ansatz determinant representations of the scalar products for the periodic chain.

Serum neurofilament as a predictor of disease worsening and brain and spinal cord atrophy in multiple sclerosis.

PubMed

Barro, Christian; Benkert, Pascal; Disanto, Giulio; Tsagkas, Charidimos; Amann, Michael; Naegelin, Yvonne; Leppert, David; Gobbi, Claudio; Granziera, Cristina; Yaldizli, Özgür; Michalak, Zuzanna; Wuerfel, Jens; Kappos, Ludwig; Parmar, Katrin; Kuhle, Jens

2018-05-30

Neuro-axonal injury is a key factor in the development of permanent disability in multiple sclerosis. Neurofilament light chain in peripheral blood has recently emerged as a biofluid marker reflecting neuro-axonal damage in this disease. We aimed at comparing serum neurofilament light chain levels in multiple sclerosis and healthy controls, to determine their association with measures of disease activity and their ability to predict future clinical worsening as well as brain and spinal cord volume loss. Neurofilament light chain was measured by single molecule array assay in 2183 serum samples collected as part of an ongoing cohort study from 259 patients with multiple sclerosis (189 relapsing and 70 progressive) and 259 healthy control subjects. Clinical assessment, serum sampling and MRI were done annually; median follow-up time was 6.5 years. Brain volumes were quantified by structural image evaluation using normalization of atrophy, and structural image evaluation using normalization of atrophy, cross-sectional, cervical spinal cord volumes using spinal cord image analyser (cordial). Results were analysed using ordinary linear regression models and generalized estimating equation modelling. Serum neurofilament light chain was higher in patients with a clinically isolated syndrome or relapsing remitting multiple sclerosis as well as in patients with secondary or primary progressive multiple sclerosis than in healthy controls (age adjusted P < 0.001 for both). Serum neurofilament light chain above the 90th percentile of healthy controls values was an independent predictor of Expanded Disability Status Scale worsening in the subsequent year (P < 0.001). The probability of Expanded Disability Status Scale worsening gradually increased by higher serum neurofilament light chain percentile category. Contrast enhancing and new/enlarging lesions were independently associated with increased serum neurofilament light chain (17.8% and 4.9% increase per lesion respectively; P < 0.001). The higher the serum neurofilament light chain percentile level, the more pronounced was future brain and cervical spinal volume loss: serum neurofilament light chain above the 97.5th percentile was associated with an additional average loss in brain volume of 1.5% (P < 0.001) and spinal cord volume of 2.5% over 5 years (P = 0.009). Serum neurofilament light chain correlated with concurrent and future clinical and MRI measures of disease activity and severity. High serum neurofilament light chain levels were associated with both brain and spinal cord volume loss. Neurofilament light chain levels are a real-time, easy to measure marker of neuro-axonal injury that is conceptually more comprehensive than brain MRI.

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

Cirilo Antonio, N.; Manojlovic, N.; Departamento de Matematica, FCT, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro

sl{sub 2} Gaudin model with jordanian twist is studied. This system can be obtained as the semiclassical limit of the XXX spin chain deformed by the jordanian twist. The appropriate creation operators that yield the Bethe states of the Gaudin model and consequently its spectrum are defined. Their commutation relations with the generators of the corresponding loop algebra as well as with the generating function of integrals of motion are given. The inner products and norms of Bethe states and the relation to the solutions of the Knizhnik-Zamolodchikov equations are discussed.

The algebraic theory of latent projectors in lambda matrices

NASA Technical Reports Server (NTRS)

Denman, E. D.; Leyva-Ramos, J.; Jeon, G. J.

1981-01-01

Multivariable systems such as a finite-element model of vibrating structures, control systems, and large-scale systems are often formulated in terms of differential equations which give rise to lambda matrices. The present investigation is concerned with the formulation of the algebraic theory of lambda matrices and the relationship of latent roots, latent vectors, and latent projectors to the eigenvalues, eigenvectors, and eigenprojectors of the companion form. The chain rule for latent projectors and eigenprojectors for the repeated latent root or eigenvalues is given.

A Decision Analysis Perspective on Multiple Response Robust Optimization

DTIC Science & Technology

2012-03-01

the utility function in question is monotonically increasing and is twice differentiable . If γ(y) = 0, the utility function is describing risk neutral...twice differentiable , the risk aversion function with respect to a single attribute, yi, i = 1, . . . , n, is given in Equation 2.9, γUyi = − U ′′yi U...UV (V (y1, y2)) and fol- lowing the chain rule of differentiation , Matheson and Abbas [31] show that the risk aversion with respect to a single

Just in Time - Expecting Failure: Do JIT Principles Run Counter to DoD’s Business Nature?

DTIC Science & Technology

2014-04-01

Regiment. The last several years witnessed both commercial industry and the Department of Defense (DoD) logistics supply chains trending to-ward an...moving items through a production system only when needed. Equating inventory to an avoidable waste instead of adding value to a company directly...Louisiana plant for a week, Honda Motor Company to suspend orders for Japanese-built Honda and Acura models, and pro- ducers of Boeing’s 787 to run billions

Complex absorbing potential based Lorentzian fitting scheme and time dependent quantum transport.

PubMed

Xie, Hang; Kwok, Yanho; Jiang, Feng; Zheng, Xiao; Chen, GuanHua

2014-10-28

Based on the complex absorbing potential (CAP) method, a Lorentzian expansion scheme is developed to express the self-energy. The CAP-based Lorentzian expansion of self-energy is employed to solve efficiently the Liouville-von Neumann equation of one-electron density matrix. The resulting method is applicable for both tight-binding and first-principles models and is used to simulate the transient currents through graphene nanoribbons and a benzene molecule sandwiched between two carbon-atom chains.

When the feasibility of an ecosystem is sufficient for global stability?

PubMed

Porati, A; Granero, M I

2000-01-01

We show via a Liapunov function that in every model ecosystem governed by generalized Lotka-Volterra equations, a feasible steady state is globally asymptotically stable if the number of interaction branches equals n-1, where n is the number of species. This means that the representative graph for which the theorem holds is a 'tree' and not only an alimentary chain. Our result is valid also in the case of non-homogeneous systems, which model situations in which input fluxes are present.

Chain pooling to minimize prediction error in subset regression. [Monte Carlo studies using population models

NASA Technical Reports Server (NTRS)

Holms, A. G.

1974-01-01

Monte Carlo studies using population models intended to represent response surface applications are reported. Simulated experiments were generated by adding pseudo random normally distributed errors to population values to generate observations. Model equations were fitted to the observations and the decision procedure was used to delete terms. Comparison of values predicted by the reduced models with the true population values enabled the identification of deletion strategies that are approximately optimal for minimizing prediction errors.

Combine Flash-Based FPGA TID and Long-Term Retention Reliabilities Through VT Shift

NASA Astrophysics Data System (ADS)

Wang, Jih-Jong; Rezzak, Nadia; Dsilva, Durwyn; Xue, Fengliang; Samiee, Salim; Singaraju, Pavan; Jia, James; Nguyen, Victor; Hawley, Frank; Hamdy, Esmat

2016-08-01

Reliability test results of data retention and total ionizing dose (TID) in 65 nm Flash-based field programmable gate array (FPGA) are presented. Long-chain inverter design is recommended for reliability evaluation because it is the worst case design for both effects. Based on preliminary test data, both issues are unified and modeled by one natural decay equation. The relative contributions of TID induced threshold-voltage shift and retention mechanisms are evaluated by analyzing test data.

Service quality and parents' willingness to get adolescents HPV vaccine from pharmacists.

PubMed

Shah, Parth D; Calo, William A; Marciniak, Macary W; Golin, Carol E; Sleath, Betsy L; Brewer, Noel T

2018-04-01

We sought to examine whether pharmacy service quality was associated with parents' willingness to have immunizing pharmacists administer human papillomavirus (HPV) vaccine to their adolescent children. Participants were a national sample of 1504 US parents of adolescents ages 11 to 17 who completed an online survey in 2014. Analyses used structural equation modeling. Parents rated service quality and feelings of satisfaction with their pharmacies as moderate to high. Many (44%) were willing to get HPV vaccine from immunizing pharmacists for their adolescent children. Compared with parents who went to chain pharmacies, parents who went to independent pharmacies gave higher ratings of service quality (professionalism, confidentiality, milieu, all p < .001). Parents who went to clinic pharmacies, compared with parents who went to chain pharmacies gave lower ratings for milieu (p < .01). Parents who went to independent pharmacies had lower willingness to get HPV vaccine from pharmacists compared to parents who went to chain pharmacies (p = .001), but there was no difference in willingness for parents who went to clinic versus chain pharmacies. Service quality and satisfaction partially mediated the effect between independent pharmacies compared to chain pharmacies and willingness (p < .05). Parents who knew their pharmacists or expressed more confidence in HPV vaccine also had higher willingness to get their children HPV vaccine from pharmacist. Many parents were willing to go to immunizing pharmacists for their children's HPV vaccination. Pharmacies that are considering offering HPV vaccine may be able to improve vaccine uptake by increasing perception of service quality. Copyright © 2018 Elsevier Inc. All rights reserved.

Simple model of sickle hemogloblin

NASA Astrophysics Data System (ADS)

Shiryayev, Andrey; Li, Xiaofei; Gunton, J. D.

2006-07-01

A microscopic model is proposed for the interactions between sickle hemoglobin molecules based on information from the protein data bank. A solution of this model, however, requires accurate estimates of the interaction parameters which are currently unavailable. Therefore, as a first step toward a molecular understanding of the nucleation mechanisms in sickle hemoglobin, a Monte Carlo simulation of a simplified two patch model is carried out. A gradual transition from monomers to one dimensional chains is observed as one varies the density of molecules at fixed temperature, somewhat similar to the transition from monomers to polymer fibers in sickle hemoglobin molecules in solution. An observed competition between chain formation and crystallization for the model is also discussed. The results of the simulation of the equation of state are shown to be in excellent agreement with a theory for a model of globular proteins, for the case of two interacting sites.

Study on transport packages used for food freshness preservation based on thermal analysis

NASA Astrophysics Data System (ADS)

Yu, Ying

2016-12-01

In recent time, as the Chinese consumption level increases, the consumption quantity of high-value fruits, vegetables and seafood products have been increasing year by year. As a consequence, the traffic volume of refrigerated products also increases yearly and the popularization degree of the cold-chain transportation enhances. A low-temperature environment should be guaranteed during transportation, thus there is about 40% of diesel oil should be consumed by the refrigerating system and the cold-chain transportation becomes very costly. This study aimed to explore methods that could reduce the cost of transport packages of refrigerated products. On the basis of the heat transfer theory and the fluid mechanics theory, the heat exchanging process of corrugated cases during the operation of refrigerating system was analyzed, the heat transfer process of corrugated cases and refrigerator van was theoretically analyzed and the heat balance equation of corrugated cases was constructed.

Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo

PubMed Central

Golightly, Andrew; Wilkinson, Darren J.

2011-01-01

Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka–Volterra system and a prokaryotic auto-regulatory network. PMID:23226583

Molecular origins of anisotropic shock propagation in crystalline and amorphous polyethylene

NASA Astrophysics Data System (ADS)

O'Connor, Thomas C.; Elder, Robert M.; Sliozberg, Yelena R.; Sirk, Timothy W.; Andzelm, Jan W.; Robbins, Mark O.

2018-03-01

Molecular dynamics simulations are used to analyze shock propagation in amorphous and crystalline polyethylene. Results for the shock velocity Us are compared to predictions from Pastine's equation of state and hydrostatic theory. The results agree with Pastine at high impact velocities. At low velocities the yield stress becomes important, increasing the shock velocity and leading to anisotropy in the crystalline response. Detailed analysis of changes in atomic order reveals the origin of the anisotropic response. For shock along the polymer backbone, an elastic front is followed by a plastic front where chains buckle with a characteristic wavelength. Shock perpendicular to the chain backbone can produce plastic deformation or transitions to different orthorhombic or monoclinic structures, depending on the impact speed and direction. Tensile loading does not produce stable shocks: Amorphous systems craze and fracture while for crystals the front broadens linearly with time.

Modeling nonlinear dynamic properties of dielectric elastomers with various crosslinks, entanglements, and finite deformations

NASA Astrophysics Data System (ADS)

Zhang, Junshi; Chen, Hualing; Li, Dichen

2018-02-01

Subject to an AC voltage, dielectric elastomers (DEs) behave as a nonlinear vibration, implying potential applications as soft dynamical actuators and robots. In this article, by utilizing the Lagrange's equation, a theoretical model is deduced to investigate the dynamic performances of DEs by considering three internal properties, including crosslinks, entanglements, and finite deformations of polymer chains. Numerical calculations are employed to describe the dynamic response, stability, periodicity, and resonance properties of DEs. It is observed that the frequency and nonlinearity of dynamic response are tuned by the internal properties of DEs. Phase paths and Poincaré maps are utilized to detect the stability and periodicity of the nonlinear vibrations of DEs, which demonstrate that transitions between aperiodic and quasi-periodic vibrations may occur when the three internal properties vary. The resonance of DEs involving the three internal properties of polymer chains is also investigated.

Spinon excitation spectra of the J1-J2 chain from analytical calculations in the dimer basis and exact diagonalization

NASA Astrophysics Data System (ADS)

Lavarélo, Arthur; Roux, Guillaume

2014-10-01

The excitation spectrum of the frustrated spin-1/2 Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted which yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at J 2 = 0.25 J 1 and an onset of incommensurability in the dispersion relation at J 2 = 9/17 J 1 as in [S. Brehmer et al., J. Phys.: Condens. Matter 10, 1103 (1998)]. These analytical results provide a good support for the understanding of exact diagonalization spectra, assuming an independent spinons picture.

Skeletal Muscle Fatigability and Myosin Heavy Chain Fiber Type in Resistance Trained Men.

PubMed

Bagley, James R; McLeland, Kathryn A; Arevalo, Jose A; Brown, Lee E; Coburn, Jared W; Galpin, Andrew J

2017-03-01

Bagley, JR, McLeland, KA, Arevalo, JA, Brown, LE, Coburn, JW, and Galpin, AJ. Skeletal muscle fatigability and myosin heavy chain fiber type in resistance trained men. J Strength Cond Res 31(3): 602-607, 2017-Forty years ago, Thorstensson and Karlsson in 1976 described the link between muscle fatigability and fiber type, finding that more fast-twitch fibers were associated with a quicker onset of quadriceps fatigue. This provided the foundation for the Classic Thorstensson Test of fatigability and subsequent noninvasive fiber type prediction equation. This equation was developed with data from recreationally active (REC) men but has been implemented in participants with heterogeneous physical activity/exercise backgrounds. The accuracy of this approach in resistance trained (RET) men has not been established. Moreover, muscle fiber typing techniques have evolved considerably since this seminal work. Therefore, we reexamined this relationship using RET men and a more sensitive fiber typing method (single fiber myosin heavy chain [MHC] isoform classification). Fifteen RET men (age = 24.8 ± 1.3 years) performed maximal knee extensions (via isokinetic dynamometry) to determine peak torque (PT) and quadriceps fatigue percentage (FP) after 30 and 50 repetitions. Vastus lateralis (VL) single fiber MHC type was determined and fibers were grouped as %Fast (expressing MHC IIa, IIa/IIX, or IIx; no MHC I containing fibers). Resistance trained men exhibited 46% greater PT (RET = 207 ± 28 N·m vs. REC = 130 ± 8 N·m) and 28% more %Fast (RET = 61 ± 4% vs. REC = 44 ± 4%) than REC men. Additionally, RET men had a relatively homogeneous FP (64 ± 1%) ranging from 53 to 72%. No relationship was found between FP and MHC fiber type (R = 0.01, p > 0.05). The Classic Thorstensson Test may not accurately estimate VL fiber type composition in RET men, highlighting the (a) unique phenotypical/functional adaptations induced by chronic RET and (b) the need for more sensitive cellular/molecular analyses in RET muscle.

Recursive mass matrix factorization and inversion: An operator approach to open- and closed-chain multibody dynamics

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Kreutz, K.

1988-01-01

This report advances a linear operator approach for analyzing the dynamics of systems of joint-connected rigid bodies.It is established that the mass matrix M for such a system can be factored as M=(I+H phi L)D(I+H phi L) sup T. This yields an immediate inversion M sup -1=(I-H psi L) sup T D sup -1 (I-H psi L), where H and phi are given by known link geometric parameters, and L, psi and D are obtained recursively by a spatial discrete-step Kalman filter and by the corresponding Riccati equation associated with this filter. The factors (I+H phi L) and (I-H psi L) are lower triangular matrices which are inverses of each other, and D is a diagonal matrix. This factorization and inversion of the mass matrix leads to recursive algortihms for forward dynamics based on spatially recursive filtering and smoothing. The primary motivation for advancing the operator approach is to provide a better means to formulate, analyze and understand spatial recursions in multibody dynamics. This is achieved because the linear operator notation allows manipulation of the equations of motion using a very high-level analytical framework (a spatial operator algebra) that is easy to understand and use. Detailed lower-level recursive algorithms can readily be obtained for inspection from the expressions involving spatial operators. The report consists of two main sections. In Part 1, the problem of serial chain manipulators is analyzed and solved. Extensions to a closed-chain system formed by multiple manipulators moving a common task object are contained in Part 2. To retain ease of exposition in the report, only these two types of multibody systems are considered. However, the same methods can be easily applied to arbitrary multibody systems formed by a collection of joint-connected regid bodies.

Predicting maximal strength of quadriceps from submaximal performance in individuals with knee joint osteoarthritis.

PubMed

McNair, Peter J; Colvin, Matt; Reid, Duncan

2011-02-01

To compare the accuracy of 12 maximal strength (1-repetition maximum [1-RM]) equations for predicting quadriceps strength in people with osteoarthritis (OA) of the knee joint. Eighteen subjects with OA of the knee joint attended a rehabilitation gymnasium on 3 occasions: 1) a familiarization session, 2) a session where the 1-RM of the quadriceps was established using a weights machine for an open-chain knee extension exercise and a leg press exercise, and 3) a session where the subjects performed with a load at which they could lift for approximately 10 repetitions only. The data were used in 12 prediction equations to calculate 1-RM strength and compared to the actual 1-RM data. Data were examined using Bland and Altman graphs and statistics, intraclass correlation coefficients (ICCs), and typical error values between the actual 1-RM and the respective 1-RM prediction equation data. Difference scores (predicted 1-RM--actual 1-RM) across the injured and control legs were also compared. For the knee extension exercise, the Brown, Brzycki, Epley, Lander, Mayhew et al, Poliquin, and Wathen prediction equations demonstrated the greatest levels of predictive accuracy. All of the ICCs were high (range 0.96–0.99), and typical errors were between 3% and 4%. For the knee press exercise, the Adams, Berger, Kemmler et al, and O'Conner et al equations demonstrated the greatest levels of predictive accuracy. All of the ICCs were high (range 0.95-0.98), and the typical errors ranged from 5.9-6.3%. This study provided evidence supporting the use of prediction equations to assess maximal strength in individuals with a knee joint with OA.

Enhancements of Nucleate Boiling Under Microgravity Conditions

NASA Technical Reports Server (NTRS)

Zhang, Nengli; Chao, David F.; Yang, W. J.

2000-01-01

This paper presents two means for enhancing nucleate boiling and critical heat flux under microgravity conditions: using micro-configured metal-graphite composites as the boiling surface and dilute aqueous solutions of long-chain alcohols as the working fluid. In the former, thermocapillary force induced by temperature difference between the graphite-fiber tips and the metal matrix plays an important role in bubble detachment. Thus boiling-heat transfer performance does not deteriorate in a reduced-gravity environment. In the latter cases, the surface tension-temperature gradient of the long-chain alcohol solutions turns positive as the temperature exceeds a certain value. Consequently, the Marangoni effect does not impede, but rather aids in bubble departure from the heating surface. This feature is most favorable in microgravity. As a result, the bubble size of departure is substantially reduced at higher frequencies. Based on the existing experimental data, and a two-tier theoretical model, correlation formulas are derived for nucleate boiling on the copper-graphite and aluminum-graphite composite surfaces, in both the isolated and coalesced bubble regimes. In addition, performance equations for nucleate boiling and critical heat flux in dilute aqueous solutions of long-chain alcohols are obtained.

Dielectric relaxation spectrum of undiluted poly(4-chlorostyrene), T≳Tg

NASA Astrophysics Data System (ADS)

Yoshihara, M.; Work, R. N.

1980-06-01

Dielectric relaxation characteristics of undiluted, atactic poly(4-chlorostyrene), P4CS, have been determined at temperatures 406 K⩽T⩽446 K from measurements made at frequencies 0.2 Hz⩽f⩽0.2 MHz. After effects of electrical conductivity are subtracted, it is found that the normalized complex dielectric constant K*=K'-i K″ can be represented quantitatively by the Havriliak-Negami (H-N) equation K*=[1+(iωτ0)1-α]-β, 0⩽α, β⩽1, except for a small, high frequency tail that appears in measurements made near the glass transition temperature, Tg. The parameter β is nearly constant, and α depends linearly on log τ0, where τ0 is a characteristic relaxation time. The parameters α and β extrapolate through values obtained from published data from P4CS solutions, and extrapolation to α=0 yields a value of τ0 which compares favorably with a published value for crankshaft motions of an equivalent isolated chain segment. These observations suggest that β may characterize effects of chain connectivity and α may describe effects of interactions of the surroundings with the chain. Experimental results are compared with alternative empirical and model-based representations of dielectric relaxation in polymers.

Complex dynamics in the Leslie-Gower type of the food chain system with multiple delays

NASA Astrophysics Data System (ADS)

Guo, Lei; Song, Zi-Gen; Xu, Jian

2014-08-01

In this paper, we present a Leslie-Gower type of food chain system composed of three species, which are resource, consumer, and predator, respectively. The digestion time delays corresponding to consumer-eat-resource and predator-eat-consumer are introduced for more realistic consideration. It is called the resource digestion delay (RDD) and consumer digestion delay (CDD) for simplicity. Analyzing the corresponding characteristic equation, the stabilities of the boundary and interior equilibrium points are studied. The food chain system exhibits the species coexistence for the small values of digestion delays. Large RDD/CDD may destabilize the species coexistence and induce the system dynamic into recurrent bloom or system collapse. Further, the present of multiple delays can control species population into the stable coexistence. To investigate the effect of time delays on the recurrent bloom of species population, the Hopf bifurcation and periodic solution are investigated in detail in terms of the central manifold reduction and normal form method. Finally, numerical simulations are performed to display some complex dynamics, which include multiple periodic solution and chaos motion for the different values of system parameters. The system dynamic behavior evolves into the chaos motion by employing the period-doubling bifurcation.

Density matrix renormalization group simulations of SU(N ) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz

NASA Astrophysics Data System (ADS)

Nataf, Pierre; Mila, Frédéric

2018-04-01

We develop an efficient method to perform density matrix renormalization group simulations of the SU(N ) Heisenberg chain with open boundary conditions taking full advantage of the SU(N ) symmetry of the problem. This method is an extension of the method previously developed for exact diagonalizations and relies on a systematic use of the basis of standard Young tableaux. Concentrating on the model with the fundamental representation at each site (i.e., one particle per site in the fermionic formulation), we have benchmarked our results for the ground-state energy up to N =8 and up to 420 sites by comparing them with Bethe ansatz results on open chains, for which we have derived and solved the Bethe ansatz equations. The agreement for the ground-state energy is excellent for SU(3) (12 digits). It decreases with N , but it is still satisfactory for N =8 (six digits). Central charges c are also extracted from the entanglement entropy using the Calabrese-Cardy formula and agree with the theoretical values expected from the SU (N) 1 Wess-Zumino-Witten conformal field theories.

From bead to rod: Comparison of theories by measuring translational drag coefficients of micron-sized magnetic bead-chains in Stokes flow

PubMed Central

Lu, Chen; Zhao, Xiaodan; Kawamura, Ryo

2017-01-01

Frictional drag force on an object in Stokes flow follows a linear relationship with the velocity of translation and a translational drag coefficient. This drag coefficient is related to the size, shape, and orientation of the object. For rod-like objects, analytical solutions of the drag coefficients have been proposed based on three rough approximations of the rod geometry, namely the bead model, ellipsoid model, and cylinder model. These theories all agree that translational drag coefficients of rod-like objects are functions of the rod length and aspect ratio, but differ among one another on the correction factor terms in the equations. By tracking the displacement of the particles through stationary fluids of calibrated viscosity in magnetic tweezers setup, we experimentally measured the drag coefficients of micron-sized beads and their bead-chain formations with chain length of 2 to 27. We verified our methodology with analytical solutions of dimers of two touching beads, and compared our measured drag coefficient values of rod-like objects with theoretical calculations. Our comparison reveals several analytical solutions that used more appropriate approximation and derived formulae that agree with our measurement better. PMID:29145447

Spontaneous healing and growth of locked magnetic island chains in toroidal plasmas

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

Fitzpatrick, R.; Waelbroeck, F. L.

2012-11-15

Recent experiments have demonstrated that locked magnetic island chains in stellarator plasmas spontaneously heal under certain conditions, and spontaneously grow under others. A formalism initially developed to study magnetic island dynamics in tokamak plasmas is employed to investigate this phenomenon. It is found that island healing/growth transitions can be caused either by a breakdown in torque balance in the vicinity of the island chain, or by an imbalance between the various terms in the island width evolution equation. The scaling of the healing/growth thresholds with the standard dimensionless plasma parameters {beta}, {nu}{sub *}, and {rho}{sub *} is determined. In accordancemore » with the experimental data, it is found that island healing generally occurs at high {beta} and low {nu}{sub *}, and island growth at low {beta} and high {nu}{sub *}. In further agreement, it is found that island healing is accompanied an ion poloidal velocity shift in the electron diamagnetic direction, and island growth by a velocity shift in the ion diamagnetic direction. Finally, it is found that there is considerable hysteresis in the healing/growth cycle, as is also seen experimentally.« less

Identification of rice supply chain risk to DKI Jakarta through Cipinang primary rice market

NASA Astrophysics Data System (ADS)

Sugiarto, D.; Ariwibowo, A.; Mardianto, I.; Surjasa, D.

2018-01-01

This paper identifies several sources of risks in DKI Jakarta rice supply chain that through Cipinang Primary Rice Market (CPRM). Secondary data from several sources were collected and analysed using pareto chart and time series analysis. Based on the pareto analysis, it was known that there was a change in the order of suppliers whereas in 2011, 80% of the supply came only from Cirebon, Karawang and Bandung (West Java Province). While in 2015 the main source of supply changed to Cirebon, Central Java and Karawang. Linear trend equation using decomposition model for Cirebon and Karawang showed trend of decreasing monthly supply while Central Java had a positive trend. Harvest area of wetland paddy in Cirebon and Karawang showed a negative trend in the last 6 years. The data also showed that West Java Province was the province with the largest rice crop area affected by plant organism attack and drought disaster in 2015. DKI Jakarta had several potential supply chain risks from rice supply, drought risk and pests risk where the province of West Java, which previously could become a major supplier began to require supply assistance from other provinces, especially Central Java.

Synchronized Molecular-Dynamics simulation for thermal lubrication of a polymeric liquid between parallel plates

NASA Astrophysics Data System (ADS)

Yasuda, Shugo; Yamamoto, Ryoichi

2015-11-01

The Synchronized Molecular-Dynamics simulation which was recently proposed by authors is applied to the analysis of polymer lubrication between parallel plates. In the SMD method, the MD simulations are assigned to small fluid elements to calculate the local stresses and temperatures and are synchronized at certain time intervals to satisfy the macroscopic heat- and momentum-transport equations.The rheological properties and conformation of the polymer chains coupled with local viscous heating are investigated with a non-dimensional parameter, the Nahme-Griffith number, which is defined as the ratio of the viscous heating to the thermal conduction at the characteristic temperature required to sufficiently change the viscosity. The present simulation demonstrates that strong shear thinning and a transitional behavior of the conformation of the polymer chains are exhibited with a rapid temperature rise when the Nahme-Griffith number exceeds unity.The results also clarify that the reentrant transition of the linear stress-optical relation occurs for large shear stresses due to the coupling of the conformation of polymer chains with heat generation under shear flows. This study was financially supported by JSPS KAKENHI Grant Nos. 26790080 and 26247069.

Breathers and rogue waves in a Heisenberg ferromagnetic spin chain or an alpha helical protein

NASA Astrophysics Data System (ADS)

Yang, Jin-Wei; Gao, Yi-Tian; Su, Chuan-Qi; Wang, Qi-Min; Lan, Zhong-Zhou

2017-07-01

In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation for a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain or an alpha helical protein has been investigated. Breathers and rogue waves are constructed via the Darboux transformation and generalized Darboux transformation, respectively. Results of the breathers and rogue waves are presented: (1) The first- and second-order Akhmediev breathers and Kuznetsov-Ma solitons are presented with different values of variable coefficients which are related to the energy transfer or higher-order excitations and interactions in the helical protein, or related to the spin excitations resulting from the lowest order continuum approximation and octupole-dipole interaction in a Heisenberg ferromagnetic spin chain, and the nonlinear periodic breathers resulting from the Akhmediev breathers are studied as well; (2) For the first- and second-order rogue waves, we find that they can be split into many similar components when the variable coefficients are polynomial functions of time; (3) Rogue waves can also be split when the variable coefficients are hyperbolic secant functions of time, but the profile of each component in such a case is different.

Effect of magnetic islands on the localization of kinetic Alfvén wave

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

Rai, Rajesh Kumar, E-mail: rajanraj.rai7@gmail.com; Sharma, Swati, E-mail: swati.sharma704@gmail.com; Yadav, Nitin

2015-12-15

Recent studies have revealed an intimate link between magnetic reconnection and turbulence. Observations show that kinetic Alfvén waves (KAWs) play a very crucial role in magnetic reconnection and have been a topic of interest from decades in the context of turbulence and particle heating. In the present paper, we study the role that KAW plays in the formation of coherent structures/current sheets when KAW is propagating in the pre-existing fully developed chain of magnetic islands. We derived the dynamical equation of KAW in the presence of chain of magnetic islands and solved it using numerical simulations well as analytic tools.more » Due to pre-existing chain of magnetic islands, KAW splits into coherent structures and the scale size of these structures along transverse directions (with respect to background magnetic field) comes out to be either less than or greater than ion gyro radius. Therefore, the present work may be the first step towards understanding how magnetic reconnection generated islands may affect the KAW localization and eventually contribute to magnetic turbulence. In this way the present approach may be helpful to understand the interplay between magnetic reconnection and turbulence in ion diffusion region.« less

Dielectric spectroscopy investigation of proton transfer processes in carboxymethyl alpha-cyclodextrin polymer cross-linked by epichlorohydrin

NASA Astrophysics Data System (ADS)

Papaioannou, Panagoula K.; Karagianni, Chaido S.; Kakali, Glykeria; Charalampopoulos, Vasileios G.

2018-03-01

The carboxymethyl-α-cyclodextrin polymer (cross-linked by epichlorohydrin) is investigated by dielectric spectroscopy over a frequency range of 0.1-100 kHz and the temperature ranges of 137.2-297.6 K (cooling) and 137.2-472 K (heating). Upon cooling to 288.1 K, the ac-conductivity invariance is attributed to slight changes in the topology of the H-bonded chains. From 288.1 to 244.0 K, the ac-conductivity decreases abruptly (following the Arrhenius law with Eα = 0.40 eV), whereas below 244.0 K it presents no important variations. During heating from 137.2 to 302.6 K, no thermal hysteresis is observed. From 302.6 to 364.9 K, the ac-conductivity increases (Eα = 0.71 eV), whereas above 383 K it decreases up to 436.7 K since the dehydration process has been completed and the H-bonded chains can no longer be retained. From 436.7 to 472 K, the ac-conductivity increases again (Eα = 0.76 eV) indicating the formation of "new" H-bonded chains. Curve fitting of various relaxation processes is done by Havriliak-Negami equation at selective temperatures.

Theory of coherent van der Waals matter.

PubMed

Kulić, Igor M; Kulić, Miodrag L

2014-12-01

We explain in depth the previously proposed theory of the coherent van der Waals (cvdW) interaction, the counterpart of van der Waals (vdW) force, emerging in spatially coherently fluctuating electromagnetic fields. We show that cvdW driven matter is dominated by many-body interactions, which are significantly stronger than those found in standard van der Waals (vdW) systems. Remarkably, the leading two- and three-body interactions are of the same order with respect to the distance (∝R(-6)), in contrast to the usually weak vdW three-body effects (∝R(-9)). From a microscopic theory we show that the anisotropic cvdW many-body interactions drive the formation of low-dimensional structures such as chains, membranes, and vesicles with very unusual, nonlocal properties. In particular, cvdW chains display a logarithmically growing stiffness with the chain length, while cvdW membranes have a bending modulus growing linearly with their size. We argue that the cvdW anisotropic many-body forces cause local cohesion but also a negative effective "surface tension." We conclude by deriving the equation of state for cvdW materials and propose experiments to test the theory, in particular the unusual three-body nature of cvdW.

Theory of coherent van der Waals matter

NASA Astrophysics Data System (ADS)

Kulić, Igor M.; Kulić, Miodrag L.

2014-12-01

We explain in depth the previously proposed theory of the coherent van der Waals (cvdW) interaction, the counterpart of van der Waals (vdW) force, emerging in spatially coherently fluctuating electromagnetic fields. We show that cvdW driven matter is dominated by many-body interactions, which are significantly stronger than those found in standard van der Waals (vdW) systems. Remarkably, the leading two- and three-body interactions are of the same order with respect to the distance (∝R-6) , in contrast to the usually weak vdW three-body effects (∝R-9 ). From a microscopic theory we show that the anisotropic cvdW many-body interactions drive the formation of low-dimensional structures such as chains, membranes, and vesicles with very unusual, nonlocal properties. In particular, cvdW chains display a logarithmically growing stiffness with the chain length, while cvdW membranes have a bending modulus growing linearly with their size. We argue that the cvdW anisotropic many-body forces cause local cohesion but also a negative effective "surface tension." We conclude by deriving the equation of state for cvdW materials and propose experiments to test the theory, in particular the unusual three-body nature of cvdW.

Retardation effects on the dispersion and propagation of plasmons in metallic nanoparticle chains

NASA Astrophysics Data System (ADS)

Downing, Charles A.; Mariani, Eros; Weick, Guillaume

2018-01-01

We consider a chain of regularly-spaced spherical metallic nanoparticles, where each particle supports three degenerate localized surface plasmons. Due to the dipolar interaction between the nanoparticles, the localized plasmons couple to form extended collective modes. Using an open quantum system approach in which the collective plasmons are interacting with vacuum electromagnetic modes and which, importantly, readily incorporates retardation via the light-matter coupling, we analytically evaluate the resulting radiative frequency shifts of the plasmonic bandstructure. For subwavelength-sized nanoparticles, our analytical treatment provides an excellent quantitative agreement with the results stemming from laborious numerical calculations based on fully-retarded solutions to Maxwell’s equations. Indeed, the explicit expressions for the plasmonic spectrum which we provide showcase how including retardation gives rise to a logarithmic singularity in the bandstructure of transverse-polarized plasmons. We further study the impact of retardation effects on the propagation of plasmonic excitations along the chain. While for the longitudinal modes, retardation has a negligible effect, we find that the retarded dipolar interaction can significantly modify the plasmon propagation in the case of transverse-polarized modes. Moreover, our results elucidate the analogy between radiative effects in nanoplasmonic systems and the cooperative Lamb shift in atomic physics.

Cholic acid accumulation and its diminution by short-chain fatty acids in bifidobacteria.

PubMed

Kurdi, Peter; Tanaka, Hiroshi; Van Veen, Hendrik W; Asano, Kozo; Tomita, Fusao; Yokota, Atsushi

2003-08-01

Cholic acid (CA) transport was investigated in nine intestinal Bifidobacterium strains. Upon energization with glucose, all of the bifidobacteria accumulated CA. The driving force behind CA accumulation was found to be the transmembrane proton gradient (Delta pH, alkaline interior). The levels of accumulated CA generally coincided with the theoretical values, which were calculated by the Henderson-Hasselbalch equation using the measured internal pH values of the bifidobacteria, and a pK(a) value of 6.4 for CA. These results suggest that the mechanism of CA accumulation is based on the diffusion of a hydrophobic weak acid across the bacterial cell membrane, and its dissociation according to the Delta pH value. A mixture of short-chain fatty acids (acetate, propionate and butyrate) at the appropriate colonic concentration (117 mM in total) reduced CA accumulation in Bifidobacterium breve JCM 1192(T). These short-chain fatty acids, which are weak acids, reduced the Delta pH, thereby decreasing CA accumulation in a dose-dependent manner. The bifidobacteria did not alter or modify the CA molecule. The probiotic potential of CA accumulation in vivo is discussed in relation to human bile acid metabolism.

Simulating the Transfer of Strontium-90 from Soil to Leafy Vegetables by Using Strontium-88.

PubMed

Kuke, Ding; Shujuan, Liu; Yingxue, He; Dong, Yan; Fengshou, Zhang; Shuifeng, Wang; Jinghua, Guo; Wei, Zhang; Xin, Wang; Xiaoyan, Jiang

The transfer, from soil to Chinese cabbage and spinach, of radioactive strontium-90 released as a result of accidents in nuclear power stations was studied using a stable isotope of strontium, namely nuclide strontium-88 ( 88 Sr). The study led to an experimental model for assessing the hazard of radionuclide strontium-90 ( 90 Sr) entering the food chain and for predicting the risk to food safety. Chinese cabbage and spinach were grown in pots in a greenhouse and irrigated with deionized water containing known quantities of strontium. Based on the strontium content of that water, the plants were divided into five groups (treatments) and strontium content of the soil, and 30-day-old plants were determined by inductively coupled plasma atomic emission spectroscopy instrument (ICP-AES). Data on the strontium content of soil and plants enabled the development of a model using MATLAB, a mathematical software package, which included curve fitting and problem solving using regression equations and differential equations. Although strontium curves for leaves, stems, and roots of Chinese cabbage were not exactly the same, all showed a non-linear increase when compared with the increase in the content of strontium in soil. Strontium curves for leaves, stems, and roots of spinach were very similar and showed an initial increase followed by a decrease. Strontium concentrations in both Chinese cabbage and spinach were initially related to the concentrations of sodium and sulfur, the next two relevant nuclides being calcium and magnesium. The relationship between calcium and strontium in Chinese cabbage was different from that in spinach. By using 88 Sr to simulate the transfer of radionuclide 90 Sr from soil to a crop, the relevant data required to deal with accidental release of strontium can be obtained using a fitting curve and regression equations, thereby providing some experimental basis for evaluating the potential hazards posed by such accidents to the food chain.

Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations

DOE PAGES

Zhang, Yang; Chong, Edwin K. P.; Hannig, Jan; ...

2013-01-01

We inmore » troduce a continuum modeling method to approximate a class of large wireless networks by nonlinear partial differential equations (PDEs). This method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N , the number of nodes in the network. As N goes to infinity, the sequence converges to a continuum limit, which is the solution of a certain nonlinear PDE. We first describe PDE models for networks with uniformly located nodes and then generalize to networks with nonuniformly located, and possibly mobile, nodes. Based on the PDE models, we develop a method to control the transmissions in nonuniform networks so that the continuum limit is invariant under perturbations in node locations. This enables the networks to maintain stable global characteristics in the presence of varying node locations.« less

Problems with indirect determinations of peak streamflows in steep, desert stream channels

USGS Publications Warehouse

Glancy, Patrick A.; Williams, Rhea P.

1994-01-01

Many peak streamflow values used in flood analyses for desert areas are derived using the Manning equation. Data used in the equation are collected after the flow has subsided, and peak flow is thereby determined indirectly. Most measurement problems and associated errors in peak-flow determinations result from (1) channel erosion or deposition that cannot be discerned or properly evaluated after the fact, (2) unsteady and non-uniform flow that rapidly changes in magnitude, and (3) appreciable sediment transport that has unknown effects on energy dissipation. High calculated velocities and Froude numbers are unacceptable to some investigators. Measurement results could be improved by recording flows with a video camera, installing a recording stream gage and recording rain gages, measuring channel scour with buried chains, analyzing measured data by multiple techniques, and supplementing indirect measurements with direct measurements of stream velocities in similar ephemeral streams.

An Efficient Solution Method for Multibody Systems with Loops Using Multiple Processors

NASA Technical Reports Server (NTRS)

Ghosh, Tushar K.; Nguyen, Luong A.; Quiocho, Leslie J.

2015-01-01

This paper describes a multibody dynamics algorithm formulated for parallel implementation on multiprocessor computing platforms using the divide-and-conquer approach. The system of interest is a general topology of rigid and elastic articulated bodies with or without loops. The algorithm divides the multibody system into a number of smaller sets of bodies in chain or tree structures, called "branches" at convenient joints called "connection points", and uses an Order-N (O (N)) approach to formulate the dynamics of each branch in terms of the unknown spatial connection forces. The equations of motion for the branches, leaving the connection forces as unknowns, are implemented in separate processors in parallel for computational efficiency, and the equations for all the unknown connection forces are synthesized and solved in one or several processors. The performances of two implementations of this divide-and-conquer algorithm in multiple processors are compared with an existing method implemented on a single processor.

PICASSO: an end-to-end image simulation tool for space and airborne imaging systems II. Extension to the thermal infrared: equations and methods

NASA Astrophysics Data System (ADS)

Cota, Stephen A.; Lomheim, Terrence S.; Florio, Christopher J.; Harbold, Jeffrey M.; Muto, B. Michael; Schoolar, Richard B.; Wintz, Daniel T.; Keller, Robert A.

2011-10-01

In a previous paper in this series, we described how The Aerospace Corporation's Parameterized Image Chain Analysis & Simulation SOftware (PICASSO) tool may be used to model space and airborne imaging systems operating in the visible to near-infrared (VISNIR). PICASSO is a systems-level tool, representative of a class of such tools used throughout the remote sensing community. It is capable of modeling systems over a wide range of fidelity, anywhere from conceptual design level (where it can serve as an integral part of the systems engineering process) to as-built hardware (where it can serve as part of the verification process). In the present paper, we extend the discussion of PICASSO to the modeling of Thermal Infrared (TIR) remote sensing systems, presenting the equations and methods necessary to modeling in that regime.

Dark and antidark soliton interactions in the nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential.

PubMed

Li, Min; Xu, Tao

2015-03-01

Via the Nth Darboux transformation, a chain of nonsingular localized-wave solutions is derived for a nonlocal nonlinear Schrödinger equation with the self-induced parity-time (PT) -symmetric potential. It is found that the Nth iterated solution in general exhibits a variety of elastic interactions among 2N solitons on a continuous-wave background and each interacting soliton could be the dark or antidark type. The interactions with an arbitrary odd number of solitons can also be obtained under different degenerate conditions. With N=1 and 2, the two-soliton and four-soliton interactions and their various degenerate cases are discussed in the asymptotic analysis. Numerical simulations are performed to support the analytical results, and the stability analysis indicates that the PT-symmetry breaking can also destroy the stability of the soliton interactions.

IT vendor selection model by using structural equation model & analytical hierarchy process

NASA Astrophysics Data System (ADS)

Maitra, Sarit; Dominic, P. D. D.

2012-11-01

Selecting and evaluating the right vendors is imperative for an organization's global marketplace competitiveness. Improper selection and evaluation of potential vendors can dwarf an organization's supply chain performance. Numerous studies have demonstrated that firms consider multiple criteria when selecting key vendors. This research intends to develop a new hybrid model for vendor selection process with better decision making. The new proposed model provides a suitable tool for assisting decision makers and managers to make the right decisions and select the most suitable vendor. This paper proposes a Hybrid model based on Structural Equation Model (SEM) and Analytical Hierarchy Process (AHP) for long-term strategic vendor selection problems. The five steps framework of the model has been designed after the thorough literature study. The proposed hybrid model will be applied using a real life case study to assess its effectiveness. In addition, What-if analysis technique will be used for model validation purpose.

Arnold Diffusion of Charged Particles in ABC Magnetic Fields

NASA Astrophysics Data System (ADS)

Luque, Alejandro; Peralta-Salas, Daniel

2017-06-01

We prove the existence of diffusing solutions in the motion of a charged particle in the presence of ABC magnetic fields. The equations of motion are modeled by a 3DOF Hamiltonian system depending on two parameters. For small values of these parameters, we obtain a normally hyperbolic invariant manifold and we apply the so-called geometric methods for a priori unstable systems developed by A. Delshams, R. de la Llave and T.M. Seara. We characterize explicitly sufficient conditions for the existence of a transition chain of invariant tori having heteroclinic connections, thus obtaining global instability (Arnold diffusion). We also check the obtained conditions in a computer-assisted proof. ABC magnetic fields are the simplest force-free-type solutions of the magnetohydrodynamics equations with periodic boundary conditions, and can be considered as an elementary model for the motion of plasma-charged particles in a tokamak.

Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos.

PubMed

Basko, D M

2014-02-01

We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.

Markov Chain Monte Carlo from Lagrangian Dynamics.

PubMed

Lan, Shiwei; Stathopoulos, Vasileios; Shahbaba, Babak; Girolami, Mark

2015-04-01

Hamiltonian Monte Carlo (HMC) improves the computational e ciency of the Metropolis-Hastings algorithm by reducing its random walk behavior. Riemannian HMC (RHMC) further improves the performance of HMC by exploiting the geometric properties of the parameter space. However, the geometric integrator used for RHMC involves implicit equations that require fixed-point iterations. In some cases, the computational overhead for solving implicit equations undermines RHMC's benefits. In an attempt to circumvent this problem, we propose an explicit integrator that replaces the momentum variable in RHMC by velocity. We show that the resulting transformation is equivalent to transforming Riemannian Hamiltonian dynamics to Lagrangian dynamics. Experimental results suggests that our method improves RHMC's overall computational e ciency in the cases considered. All computer programs and data sets are available online (http://www.ics.uci.edu/~babaks/Site/Codes.html) in order to allow replication of the results reported in this paper.

Effect of dynamic disorder on charge transport along a pentacene chain

NASA Astrophysics Data System (ADS)

Böhlin, J.; Linares, M.; Stafström, S.

2011-02-01

The lattice equation of motion and a numerical solution of the time-dependent Schrödinger equation provide us with a microscopic picture of charge transport in highly ordered molecular crystals. We have chosen the pentacene single crystal as a model system, and we study charge transport as a function of phonon-mode time-dependent fluctuations in the intermolecular electron transfer integral. For comparison, we include similar fluctuations also in the intramolecular potentials. The variance in these energy quantities is closely related to the temperature of the system. The pentacene system is shown to be very sensitive to fluctuation in the intermolecular transfer integral, revealing a transition from adiabatic to nonadiabatic polaron transport for increasing temperatures. The extension of the polaron at temperatures above 200 K is limited by the electron localization length rather than the interplay between the electron transfer integral and the electron-phonon coupling strength.

Adsorption of a single polymer chain on a surface: effects of the potential range.

PubMed

Klushin, Leonid I; Polotsky, Alexey A; Hsu, Hsiao-Ping; Markelov, Denis A; Binder, Kurt; Skvortsov, Alexander M

2013-02-01

We investigate the effects of the range of adsorption potential on the equilibrium behavior of a single polymer chain end-attached to a solid surface. The exact analytical theory for ideal lattice chains interacting with a planar surface via a box potential of depth U and width W is presented and compared to continuum model results and to Monte Carlo (MC) simulations using the pruned-enriched Rosenbluth method for self-avoiding chains on a simple cubic lattice. We show that the critical value U(c) corresponding to the adsorption transition scales as W(-1/ν), where the exponent ν=1/2 for ideal chains and ν≈3/5 for self-avoiding walks. Lattice corrections for finite W are incorporated in the analytical prediction of the ideal chain theory U(c)≈(π(2)/24)(W+1/2)(-2) and in the best-fit equation for the MC simulation data U(c)=0.585(W+1/2)(-5/3). Tail, loop, and train distributions at the critical point are evaluated by MC simulations for 1≤W≤10 and compared to analytical results for ideal chains and with scaling theory predictions. The behavior of a self-avoiding chain is remarkably close to that of an ideal chain in several aspects. We demonstrate that the bound fraction θ and the related properties of finite ideal and self-avoiding chains can be presented in a universal reduced form: θ(N,U,W)=θ(NU(c),U/U(c)). By utilizing precise estimations of the critical points we investigate the chain length dependence of the ratio of the normal and lateral components of the gyration radius. Contrary to common expectations this ratio attains a limiting universal value /=0.320±0.003 only at N~5000. Finite-N corrections for this ratio turn out to be of the opposite sign for W=1 and for W≥2. We also study the N dependence of the apparent crossover exponent φ(eff)(N). Strong corrections to scaling of order N(-0.5) are observed, and the extrapolated value φ=0.483±0.003 is found for all values of W. The strong correction to scaling effects found here explain why for smaller values of N, as used in most previous work, misleadingly large values of φ(eff)(N) were identified as the asymptotic value for the crossover exponent.

Characteristics of Total Electron Content (TEC) observed from a chain of stations near the northern crest of the Equatorial Ionization Anomaly (EIA) along 88.5°E meridian in India

NASA Astrophysics Data System (ADS)

Paul, K. S.; Das, A.; Ray, S.; Paul, A.

2016-01-01

The equatorial ionosphere presents some of the highest TEC values in the world coupled with observations of periodic structures. Total Electron Content (TEC) and scintillation data were analyzed from a chain of stations Calcutta (22.58°N, 88.38°E geographic; 32°N magnetic dip), Baharampore (24.09°N, 88.25°E geographic; 35°N magnetic dip) and Farakka (24.79°N, 87.89°E geographic; 36.04°N magnetic dip) situated almost same meridian (88.5°E) during September 2011 and March-April 2012 for elevation greater than 20° so that the ionosphere can be tracked from the 15.50°N south of Calcutta to 31.80°N north of Farakka. Periodic variation of TEC was noticed before TEC bite out, predominantly within a particular latitudinal swath (19°N ‒26°N) along 88.5°E meridian. No periodic structures were observed over the magnetic equator during the observation period on ionosonde records from the magnetic equator station Trivandrum and COSMIC, GRACE and C/NOFS electron density measurements. The present paper reports, perhaps for the first time from the Indian longitude sector, confinement of such periodic structures in TEC primarily within a latitude swath of 19.00-26.00 °N almost along the same longitude of 88.5 °E.

The multiple imputation method: a case study involving secondary data analysis.

PubMed

Walani, Salimah R; Cleland, Charles M

2015-05-01

To illustrate with the example of a secondary data analysis study the use of the multiple imputation method to replace missing data. Most large public datasets have missing data, which need to be handled by researchers conducting secondary data analysis studies. Multiple imputation is a technique widely used to replace missing values while preserving the sample size and sampling variability of the data. The 2004 National Sample Survey of Registered Nurses. The authors created a model to impute missing values using the chained equation method. They used imputation diagnostics procedures and conducted regression analysis of imputed data to determine the differences between the log hourly wages of internationally educated and US-educated registered nurses. The authors used multiple imputation procedures to replace missing values in a large dataset with 29,059 observations. Five multiple imputed datasets were created. Imputation diagnostics using time series and density plots showed that imputation was successful. The authors also present an example of the use of multiple imputed datasets to conduct regression analysis to answer a substantive research question. Multiple imputation is a powerful technique for imputing missing values in large datasets while preserving the sample size and variance of the data. Even though the chained equation method involves complex statistical computations, recent innovations in software and computation have made it possible for researchers to conduct this technique on large datasets. The authors recommend nurse researchers use multiple imputation methods for handling missing data to improve the statistical power and external validity of their studies.

Application of classical simulations for the computation of vibrational properties of free molecules.

PubMed

Tikhonov, Denis S; Sharapa, Dmitry I; Schwabedissen, Jan; Rybkin, Vladimir V

2016-10-12

In this study, we investigate the ability of classical molecular dynamics (MD) and Monte-Carlo (MC) simulations for modeling the intramolecular vibrational motion. These simulations were used to compute thermally-averaged geometrical structures and infrared vibrational intensities for a benchmark set previously studied by gas electron diffraction (GED): CS 2 , benzene, chloromethylthiocyanate, pyrazinamide and 9,12-I 2 -1,2-closo-C 2 B 10 H 10 . The MD sampling of NVT ensembles was performed using chains of Nose-Hoover thermostats (NH) as well as the generalized Langevin equation thermostat (GLE). The performance of the theoretical models based on the classical MD and MC simulations was compared with the experimental data and also with the alternative computational techniques: a conventional approach based on the Taylor expansion of potential energy surface, path-integral MD and MD with quantum-thermal bath (QTB) based on the generalized Langevin equation (GLE). A straightforward application of the classical simulations resulted, as expected, in poor accuracy of the calculated observables due to the complete neglect of quantum effects. However, the introduction of a posteriori quantum corrections significantly improved the situation. The application of these corrections for MD simulations of the systems with large-amplitude motions was demonstrated for chloromethylthiocyanate. The comparison of the theoretical vibrational spectra has revealed that the GLE thermostat used in this work is not applicable for this purpose. On the other hand, the NH chains yielded reasonably good results.

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

Unseren, M.A.

The report reviews a method for modeling and controlling two serial link manipulators which mutually lift and transport a rigid body object in a three dimensional workspace. A new vector variable is introduced which parameterizes the internal contact force controlled degrees of freedom. A technique for dynamically distributing the payload between the manipulators is suggested which yields a family of solutions for the contact forces and torques the manipulators impart to the object. A set of rigid body kinematic constraints which restricts the values of the joint velocities of both manipulators is derived. A rigid body dynamical model for themore » closed chain system is first developed in the joint space. The model is obtained by generalizing the previous methods for deriving the model. The joint velocity and acceleration variables in the model are expressed in terms of independent pseudovariables. The pseudospace model is transformed to obtain reduced order equations of motion and a separate set of equations governing the internal components of the contact forces and torques. A theoretic control architecture is suggested which explicitly decouples the two sets of equations comprising the model. The controller enables the designer to develop independent, non-interacting control laws for the position control and internal force control of the system.« less

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

Unseren, M.A.

The paper reviews a method for modeling and controlling two serial link manipulators which mutually lift and transport a rigid body object in a three dimensional workspace. A new vector variable is introduced which parameterizes the internal contact force controlled degrees of freedom. A technique for dynamically distributing the payload between the manipulators is suggested which yields a family of solutions for the contact forces and torques the manipulators impart to the object. A set of rigid body kinematic constraints which restrict the values of the joint velocities of both manipulators is derived. A rigid body dynamical model for themore » closed chain system is first developed in the joint space. The model is obtained by generalizing the previous methods for deriving the model. The joint velocity and acceleration variables in the model are expressed in terms of independent pseudovariables. The pseudospace model is transformed to obtain reduced order equations of motion and a separate set of equations governing the internal components of the contact forces and torques. A theoretic control architecture is suggested which explicitly decouples the two sets of equations comprising the model. The controller enables the designer to develop independent, non-interacting control laws for the position control and internal force control of the system.« less

A symplectic integration method for elastic filaments

NASA Astrophysics Data System (ADS)

Ladd, Tony; Misra, Gaurav

2009-03-01

Elastic rods are a ubiquitous coarse-grained model of semi-flexible biopolymers such as DNA, actin, and microtubules. The Worm-Like Chain (WLC) is the standard numerical model for semi-flexible polymers, but it is only a linearized approximation to the dynamics of an elastic rod, valid for small deflections; typically the torsional motion is neglected as well. In the standard finite-difference and finite-element formulations of an elastic rod, the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin. We present numerical results for the deterministic and stochastic motion of single filaments.

Linear and nonlinear response of a rotating tokamak plasma to a resonant error-field

NASA Astrophysics Data System (ADS)

Fitzpatrick, Richard

2014-09-01

An in-depth investigation of the effect of a resonant error-field on a rotating, quasi-cylindrical, tokamak plasma is preformed within the context of constant-ψ, resistive-magnetohydrodynamical theory. General expressions for the response of the plasma at the rational surface to the error-field are derived in both the linear and nonlinear regimes, and the extents of these regimes mapped out in parameter space. Torque-balance equations are also obtained in both regimes. These equations are used to determine the steady-state plasma rotation at the rational surface in the presence of the error-field. It is found that, provided the intrinsic plasma rotation is sufficiently large, the torque-balance equations possess dynamically stable low-rotation and high-rotation solution branches, separated by a forbidden band of dynamically unstable solutions. Moreover, bifurcations between the two stable solution branches are triggered as the amplitude of the error-field is varied. A low- to high-rotation bifurcation is invariably associated with a significant reduction in the width of the magnetic island chain driven at the rational surface, and vice versa. General expressions for the bifurcation thresholds are derived and their domains of validity mapped out in parameter space.

Implicit chaining in cotton-top tamarins (Saguinus oedipus) with elements equated for probability of reinforcement

PubMed Central

Dillon, Laura; Collins, Meaghan; Conway, Maura; Cunningham, Kate

2013-01-01

Three experiments examined the implicit learning of sequences under conditions in which the elements comprising a sequence were equated in terms of reinforcement probability. In Experiment 1 cotton-top tamarins (Saguinus oedipus) experienced a five-element sequence displayed serially on a touch screen in which reinforcement probability was equated across elements at .16 per element. Tamarins demonstrated learning of this sequence with higher latencies during a random test as compared to baseline sequence training. In Experiments 2 and 3, manipulations of the procedure used in the first experiment were undertaken to rule out a confound owing to the fact that the elements in Experiment 1 bore different temporal relations to the intertrial interval (ITI), an inhibitory period. The results of Experiments 2 and 3 indicated that the implicit learning observed in Experiment 1 was not due to temporal proximity between some elements and the inhibitory ITI. The results taken together support two conclusion: First that tamarins engaged in sequence learning whether or not there was contingent reinforcement for learning the sequence, and second that this learning was not due to subtle differences in associative strength between the elements of the sequence. PMID:23344718

Transient response of nonlinear polymer networks: A kinetic theory

NASA Astrophysics Data System (ADS)

Vernerey, Franck J.

2018-06-01

Dynamic networks are found in a majority of natural materials, but also in engineering materials, such as entangled polymers and physically cross-linked gels. Owing to their transient bond dynamics, these networks display a rich class of behaviors, from elasticity, rheology, self-healing, or growth. Although classical theories in rheology and mechanics have enabled us to characterize these materials, there is still a gap in our understanding on how individuals (i.e., the mechanics of each building blocks and its connection with others) affect the emerging response of the network. In this work, we introduce an alternative way to think about these networks from a statistical point of view. More specifically, a network is seen as a collection of individual polymer chains connected by weak bonds that can associate and dissociate over time. From the knowledge of these individual chains (elasticity, transient attachment, and detachment events), we construct a statistical description of the population and derive an evolution equation of their distribution based on applied deformation and their local interactions. We specifically concentrate on nonlinear elastic response that follows from the strain stiffening response of individual chains of finite size. Upon appropriate averaging operations and using a mean field approximation, we show that the distribution can be replaced by a so-called chain distribution tensor that is used to determine important macroscopic measures such as stress, energy storage and dissipation in the network. Prediction of the kinetic theory are then explored against known experimental measurement of polymer responses under uniaxial loading. It is found that even under the simplest assumptions of force-independent chain kinetics, the model is able to reproduce complex time-dependent behaviors of rubber and self-healing supramolecular polymers.

Polymer translocation through a nanopore: a showcase of anomalous diffusion.

PubMed

Milchev, A; Dubbeldam, Johan L A; Rostiashvili, Vakhtang G; Vilgis, Thomas A

2009-04-01

We investigate the translocation dynamics of a polymer chain threaded through a membrane nanopore by a chemical potential gradient that acts on the chain segments inside the pore. By means of diverse methods (scaling theory, fractional calculus, and Monte Carlo and molecular dynamics simulations), we demonstrate that the relevant dynamic variable, the transported number of polymer segments, s(t), displays an anomalous diffusive behavior, both with and without an external driving force being present. We show that in the absence of drag force the time tau, needed for a macromolecule of length N to thread from the cis into the trans side of a cell membrane, scales as tauN(2/alpha) with the chain length. The anomalous dynamics of the translocation process is governed by a universal exponent alpha= 2/(2nu + 2 - gamma(1)), which contains the basic universal exponents of polymer physics, nu (the Flory exponent) and gamma(1) (the surface entropic exponent). A closed analytic expression for the probability to find s translocated segments at time t in terms of chain length N and applied drag force f is derived from the fractional Fokker-Planck equation, and shown to provide analytic results for the time variation of the statistical moments and . It turns out that the average translocation time scales as tau proportional, f(-1)N(2/alpha-1). These results are tested and found to be in perfect agreement with extensive Monte Carlo and molecular dynamics computer simulations.

Cost Effectiveness Trade-Offs in Software Support Environment Standardization.

DTIC Science & Technology

1986-09-30

IIIIIEEEIIIIIE MiII I U..2 2 ma MICROCOPY RESOLUTION TEST CHART 911C FILE C y, o FINAL REPORT - September 30, 1986 G- TECHNION INTERNATIONAL, INC. Cost...Summary description of econometric model B-I C. Causal chain used as basis for model C-I D. Excerpts from [Wer185) D-1 LIST OF FIGURES S-1 USAF MCCR...Productivity cost drivers D-4 LIST OF TASL3$ I-1 Summary of Tangible Benefits in Econometric Equations 1-9 1-2 Summary of Tangible Costs in Econometric

Intelligent Automated Process Planning and Code Generation for Computer-Controlled Inspection

DTIC Science & Technology

1994-01-01

from the design and tolerance feature combinations of the FBDE via the UP. Obviously, the properties of the MR contain the tolerance and fe ~ature types...rule to ge- h i edrvtv fE VV,..V) The second line is obtained from the substitution of equation (4.5) into the first line. The third line is a chain...2 Feb., Pasadena. CA. G. Rodriguez and H. Seraji (eds.), JPL Pubi. 89-7, 1/, 367-376. Joshi, Sanjay. and Tien-Chien Chang, 1990. "Feature Extraction

A Bayesian nonparametric approach to dynamical noise reduction

NASA Astrophysics Data System (ADS)

Kaloudis, Konstantinos; Hatjispyros, Spyridon J.

2018-06-01

We propose a Bayesian nonparametric approach for the noise reduction of a given chaotic time series contaminated by dynamical noise, based on Markov Chain Monte Carlo methods. The underlying unknown noise process (possibly) exhibits heavy tailed behavior. We introduce the Dynamic Noise Reduction Replicator model with which we reconstruct the unknown dynamic equations and in parallel we replicate the dynamics under reduced noise level dynamical perturbations. The dynamic noise reduction procedure is demonstrated specifically in the case of polynomial maps. Simulations based on synthetic time series are presented.

Collinear swimmer propelling a cargo sphere at low Reynolds number.

PubMed

Felderhof, B U

2014-11-01

The swimming velocity and rate of dissipation of a linear chain consisting of two or three little spheres and a big sphere is studied on the basis of low Reynolds number hydrodynamics. The big sphere is treated as a passive cargo, driven by the tail of little spheres via hydrodynamic and direct elastic interaction. The fundamental solution of Stokes equations in the presence of a sphere with a no-slip boundary condition, as derived by Oseen, is used to model the hydrodynamic interactions between the big sphere and the little spheres.

Retrieve the Bethe states of quantum integrable models solved via the off-diagonal Bethe Ansatz

NASA Astrophysics Data System (ADS)

Zhang, Xin; Li, Yuan-Yuan; Cao, Junpeng; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng

2015-05-01

Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, a systematic method for retrieving the Bethe-type eigenstates of integrable models without obvious reference state is developed by employing certain orthogonal basis of the Hilbert space. With the XXZ spin torus model and the open XXX spin- \\frac{1}{2} chain as examples, we show that for a given inhomogeneous T-Q relation and the associated Bethe Ansatz equations, the constructed Bethe-type eigenstate has a well-defined homogeneous limit.

RANDOM EVOLUTIONS, MARKOV CHAINS, AND SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS

PubMed Central

Griego, R. J.; Hersh, R.

1969-01-01

Several authors have considered Markov processes defined by the motion of a particle on a fixed line with a random velocity1, 6, 8, 10 or a random diffusivity.5, 12 A “random evolution” is a natural but apparently new generalization of this notion. In this note we hope to show that this concept leads to simple and powerful applications of probabilistic tools to initial-value problems of both parabolic and hyperbolic type. We obtain existence theorems, representation theorems, and asymptotic formulas, both old and new. PMID:16578690

Marker-based reconstruction of the kinematics of a chain of segments: a new method that incorporates joint kinematic constraints.

PubMed

Klous, Miriam; Klous, Sander

2010-07-01

The aim of skin-marker-based motion analysis is to reconstruct the motion of a kinematical model from noisy measured motion of skin markers. Existing kinematic models for reconstruction of chains of segments can be divided into two categories: analytical methods that do not take joint constraints into account and numerical global optimization methods that do take joint constraints into account but require numerical optimization of a large number of degrees of freedom, especially when the number of segments increases. In this study, a new and largely analytical method for a chain of rigid bodies is presented, interconnected in spherical joints (chain-method). In this method, the number of generalized coordinates to be determined through numerical optimization is three, irrespective of the number of segments. This new method is compared with the analytical method of Veldpaus et al. [1988, "A Least-Squares Algorithm for the Equiform Transformation From Spatial Marker Co-Ordinates," J. Biomech., 21, pp. 45-54] (Veldpaus-method, a method of the first category) and the numerical global optimization method of Lu and O'Connor [1999, "Bone Position Estimation From Skin-Marker Co-Ordinates Using Global Optimization With Joint Constraints," J. Biomech., 32, pp. 129-134] (Lu-method, a method of the second category) regarding the effects of continuous noise simulating skin movement artifacts and regarding systematic errors in joint constraints. The study is based on simulated data to allow a comparison of the results of the different algorithms with true (noise- and error-free) marker locations. Results indicate a clear trend that accuracy for the chain-method is higher than the Veldpaus-method and similar to the Lu-method. Because large parts of the equations in the chain-method can be solved analytically, the speed of convergence in this method is substantially higher than in the Lu-method. With only three segments, the average number of required iterations with the chain-method is 3.0+/-0.2 times lower than with the Lu-method when skin movement artifacts are simulated by applying a continuous noise model. When simulating systematic errors in joint constraints, the number of iterations for the chain-method was almost a factor 5 lower than the number of iterations for the Lu-method. However, the Lu-method performs slightly better than the chain-method. The RMSD value between the reconstructed and actual marker positions is approximately 57% of the systematic error on the joint center positions for the Lu-method compared with 59% for the chain-method.

Molecular Dynamics Studies of Polyethylene Oxide and Polyethylene Glycol: Hydrodynamic Radius and Shape Anisotropy

PubMed Central

Lee, Hwankyu; Venable, Richard M.; MacKerell, Alexander D.; Pastor, Richard W.

2008-01-01

A revision (C35r) to the CHARMM ether force field is shown to reproduce experimentally observed conformational populations of dimethoxyethane. Molecular dynamics simulations of 9, 18, 27, and 36-mers of polyethylene oxide (PEO) and 27-mers of polyethylene glycol (PEG) in water based on C35r yield a persistence length λ = 3.7 Å, in quantitative agreement with experimentally obtained values of 3.7 Å for PEO and 3.8 Å for PEG; agreement with experimental values for hydrodynamic radii of comparably sized PEG is also excellent. The exponent υ relating the radius of gyration and molecular weight (\\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\usepackage[Euler]{upgreek} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}R_{{\\mathrm{g}}}{\\propto}M_{{\\mathrm{w}}}^{{\\upsilon}}\\end{equation*}\\end{document}) of PEO from the simulations equals 0.515 ± 0.023, consistent with experimental observations that low molecular weight PEG behaves as an ideal chain. The shape anisotropy of hydrated PEO is 2.59:1.44:1.00. The dimension of the middle length for each of the polymers nearly equals the hydrodynamic radius \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\usepackage[Euler]{upgreek} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}R_{{\\mathrm{h}}}\\end{equation*}\\end{document}obtained from diffusion measurements in solution. This explains the correspondence of \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\usepackage[Euler]{upgreek} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}R_{{\\mathrm{h}}}\\end{equation*}\\end{document} and \\documentclass[10pt]{article} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{pmc} \\usepackage[Euler]{upgreek} \\pagestyle{empty} \\oddsidemargin -1.0in \\begin{document} \\begin{equation*}R_{{\\mathrm{p}}},\\end{equation*}\\end{document} the pore radius of membrane channels: a polymer such as PEG diffuses with its long axis parallel to the membrane channel, and passes through the channel without substantial distortion. PMID:18456821

Time-resolved studies of energy transfer from meso-tetrakis(N-methylpyridinium-4-yl)- porphyrin to 3,3'-diethyl-2,2'-thiatricarbocyanine iodide along deoxyribonucleic acid Chain.

PubMed

Kakiuchi, Toshifumi; Ito, Fuyuki; Nagamura, Toshihiko

2008-04-03

The excitation energy transfer from meso-tetrakis(N-methylpyridinium-4-yl)porphyrin (TMPyP) to 3,3'-diethyl-2,2'-thiatricarbocyanine iodide (DTTCI) along the deoxyribonucleic acid (DNA) double strand was investigated by the steady-state absorption and fluorescence measurements and time-resolved fluorescence measurements. The steady-state fluorescence spectra showed that the near-infrared fluorescence of DTTCI was strongly enhanced up to 86 times due to the energy transfer from the excited TMPyP molecule in DNA buffer solution. Furthermore, we elucidated the mechanism of fluorescence quenching and enhancement by the direct observation of energy transfer using the time-resolved measurements. The fluorescence quenching of TMPyP chiefly consists of a static component due to the formation of complex and dynamic components due to the excitation energy transfer. In a heterogeneous one-dimensional system such as a DNA chain, it was proved that the energy transfer process only carries out within the critical distance based on the Förster theory and within a threshold value estimated from the modified Stern-Volmer equation. The present results showed that DNA chain is one of the most powerful tools for nanoassemblies and will give a novel concepts of material design.

Time-dependent real space RG on the spin-1/2 XXZ chain

NASA Astrophysics Data System (ADS)

Mason, Peter; Zagoskin, Alexandre; Betouras, Joseph

In order to measure the spread of information in a system of interacting fermions with nearest-neighbour couplings and strong bond disorder, one could utilise a dynamical real space renormalisation group (RG) approach on the spin-1/2 XXZ chain. Under such a procedure, a many-body localised state is established as an infinite randomness fixed point and the entropy scales with time as log(log(t)). One interesting further question that results from such a study is the case when the Hamiltonian explicitly depends on time. Here we answer this question by considering a dynamical renormalisation group treatment on the strongly disordered random spin-1/2 XXZ chain where the couplings are time-dependent and chosen to reflect a (slow) evolution of the governing Hamiltonian. Under the condition that the renormalisation process occurs at fixed time, a set of coupled second order, nonlinear PDE's can be written down in terms of the random distributions of the bonds and fields. Solution of these flow equations at the relevant critical fixed points leads us to establish the dynamics of the flow as we sweep through the quantum critical point of the Hamiltonian. We will present these critical flows as well as discussing the issues of duality, entropy and many-body localisation.

Determinants of choice for pigeons and humans on concurrent-chains schedules of reinforcement.

PubMed

Belke, T W; Pierce, W D; Powell, R A

1989-09-01

Concurrent-chains schedules of reinforcement were arranged for humans and pigeons. Responses of humans were reinforced with tokens exchangeable for money, and key pecks of 4 birds were reinforced with food. Variable-interval 30-s and 40-s schedules operated in the terminal links of the chains. Condition 1 exposed subjects to variable-interval 90-s and variable-interval 30-s initial links, respectively. Conditions 2 and 3 arranged equal initial-link schedules of 40 s or 120 s. Experimental conditions tested the descriptive adequacy of five equations: reinforcement density, delay reduction, modified delay reduction, matching and maximization. Results based on choice proportions and switch rates during the initial links showed that pigeons behaved in accord with delay-reduction models, whereas humans maximized overall rate of reinforcement. As discussed by Logue and associates in self-control research, different types of reinforcement may affect sensitivity to delay differentially. Pigeons' responses were reinforced with food, a reinforcer that is consumable upon presentation. Humans' responses were reinforced with money, a reinforcer exchanged for consumable reinforcers after it was earned. Reinforcers that are immediately consumed may generate high sensitivity to delay and behavior described as delay reduction. Reinforces with longer times to consumption may generate low sensitivity to delay and behavior that maximizes overall payoff.

Pseudo hard-sphere potential for use in continuous molecular-dynamics simulation of spherical and chain molecules

NASA Astrophysics Data System (ADS)

Jover, J.; Haslam, A. J.; Galindo, A.; Jackson, G.; Müller, E. A.

2012-10-01

We present a continuous pseudo-hard-sphere potential based on a cut-and-shifted Mie (generalized Lennard-Jones) potential with exponents (50, 49). Using this potential one can mimic the volumetric, structural, and dynamic properties of the discontinuous hard-sphere potential over the whole fluid range. The continuous pseudo potential has the advantage that it may be incorporated directly into off-the-shelf molecular-dynamics code, allowing the user to capitalise on existing hardware and software advances. Simulation results for the compressibility factor of the fluid and solid phases of our pseudo hard spheres are presented and compared both to the Carnahan-Starling equation of state of the fluid and published data, the differences being indistinguishable within simulation uncertainty. The specific form of the potential is employed to simulate flexible chains formed from these pseudo hard spheres at contact (pearl-necklace model) for mc = 4, 5, 7, 8, 16, 20, 100, 201, and 500 monomer segments. The compressibility factor of the chains per unit of monomer, mc, approaches a limiting value at reasonably small values, mc < 50, as predicted by Wertheim's first order thermodynamic perturbation theory. Simulation results are also presented for highly asymmetric mixtures of pseudo hard spheres, with diameter ratios of 3:1, 5:1, 20:1 over the whole composition range.

Sampled-data chain-observer design for a class of delayed nonlinear systems

NASA Astrophysics Data System (ADS)

Kahelras, M.; Ahmed-Ali, T.; Giri, F.; Lamnabhi-Lagarrigue, F.

2018-05-01

The problem of observer design is addressed for a class of triangular nonlinear systems with not-necessarily small delay and sampled output measurements. One more difficulty is that the system state matrix is dependent on the un-delayed output signal which is not accessible to measurement, making existing observers inapplicable. A new chain observer, composed of m elementary observers in series, is designed to compensate for output sampling and arbitrary large delays. The larger the time-delay the larger the number m. Each elementary observer includes an output predictor that is conceived to compensate for the effects of output sampling and a fractional delay. The predictors are defined by first-order ordinary differential equations (ODEs) much simpler than those of existing predictors which involve both output and state predictors. Using a small gain type analysis, sufficient conditions for the observer to be exponentially convergent are established in terms of the minimal number m of elementary observers and the maximum sampling interval.

Modeling the Commuting Travel Activities within Historic Districts in Chinese Cities

PubMed Central

Yin, Fengjun; Hu, Qizhou

2014-01-01

The primary objective of this study is to analyze the characteristics of commuting activities within the historical districts in cities of China. The impacts of various explanatory variables on commuters' travels are evaluated using the structural equation modeling (SEM) approach. The household survey was conducted in the historical districts in Yangzhou, China. Based on the data, various individual and household attributes were considered exogenous variables, while the subsistence activity characteristics, travel times, numbers of three typical home-based trip chains, trip chains, and travel mode were considered as the endogenous variables. Commuters in our study were classified into two main groups according to their working location, which were the commuters in the historic district and those out of the district. The modeling results show that several individual and household attributes of commuters in historic district have significant impacts on the characteristics of travel activities. Additionally, the characteristics of travel activities within the two groups are quite different, and the contributing factors related to commuting travels are different as well. PMID:25435864

Exact Markov chain and approximate diffusion solution for haploid genetic drift with one-way mutation.

PubMed

Hössjer, Ola; Tyvand, Peder A; Miloh, Touvia

2016-02-01

The classical Kimura solution of the diffusion equation is investigated for a haploid random mating (Wright-Fisher) model, with one-way mutations and initial-value specified by the founder population. The validity of the transient diffusion solution is checked by exact Markov chain computations, using a Jordan decomposition of the transition matrix. The conclusion is that the one-way diffusion model mostly works well, although the rate of convergence depends on the initial allele frequency and the mutation rate. The diffusion approximation is poor for mutation rates so low that the non-fixation boundary is regular. When this happens we perturb the diffusion solution around the non-fixation boundary and obtain a more accurate approximation that takes quasi-fixation of the mutant allele into account. The main application is to quantify how fast a specific genetic variant of the infinite alleles model is lost. We also discuss extensions of the quasi-fixation approach to other models with small mutation rates. Copyright © 2015 Elsevier Inc. All rights reserved.

Experimental and Chemoinformatics Study of Tautomerism in a Database of Commercially Available Screening Samples

PubMed Central

2016-01-01

We investigated how many cases of the same chemical sold as different products (at possibly different prices) occurred in a prototypical large aggregated database and simultaneously tested the tautomerism definitions in the chemoinformatics toolkit CACTVS. We applied the standard CACTVS tautomeric transforms plus a set of recently developed ring–chain transforms to the Aldrich Market Select (AMS) database of 6 million screening samples and building blocks. In 30 000 cases, two or more AMS products were found to be just different tautomeric forms of the same compound. We purchased and analyzed 166 such tautomer pairs and triplets by 1H and 13C NMR to determine whether the CACTVS transforms accurately predicted what is the same “stuff in the bottle”. Essentially all prototropic transforms with examples in the AMS were confirmed. Some of the ring–chain transforms were found to be too “aggressive”, i.e. to equate structures with one another that were different compounds. PMID:27669079

N-body scattering. I. The algebraic structure of transition amplitude and integral equations (in Chinese)

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

Pao, C.K.

1975-05-01

An assessment of wave energy as a source of electrical power in the United Kingdom is reported. British Hovercraft Corporation has conducted some tank tests for Wavepower Limited, studying various simple float systems. It aims to develop a wave-power device that is simple, cheap, made up of small mass- produced units, can be installed in sections, and can be easily maintained. A chain of floats, hinged together, with waves traveling down the chain, was investigated. Pumps on the hinges absorb power from the relative rotation of adjacent floats. A wave-power device could also serve as an effective breakwater. Direct generationmore » of electricity is a feasible application of wave power. The system is compared with a rocking boom concept. Wave energy could be used in conjunction with thermal stations to provide sufficient capacity when wave power is low. Wave power has a high availability when compared with wind power. (MCW)« less