On Kronecker-Capelli type theorems for infinite systems

NASA Astrophysics Data System (ADS)

Fedorov, Foma M.; Potapova, Sargylana V.

2017-11-01

On the basis of the new concept of the decrement of an infinite matrices and determinants, we studied the inconsistency of a general infinite systems of linear algebraic equations. We proved the theorem on inconsistency of a infinite system when the decrement of its matrix is nonzero.

Markov chains of infinite order and asymptotic satisfaction of balance: application to the adaptive integration method.

PubMed

Earl, David J; Deem, Michael W

2005-04-14

Adaptive Monte Carlo methods can be viewed as implementations of Markov chains with infinite memory. We derive a general condition for the convergence of a Monte Carlo method whose history dependence is contained within the simulated density distribution. In convergent cases, our result implies that the balance condition need only be satisfied asymptotically. As an example, we show that the adaptive integration method converges.

Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations.

NASA Technical Reports Server (NTRS)

Sloss, J. M.; Kranzler, S. K.

1972-01-01

The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.

Microporous Materials of Metal Carboxylates

NASA Astrophysics Data System (ADS)

Mori, Wasuke; Takamizawa, Satoshi

2000-06-01

Copper(II) terephthalate absorbs a large amount of gases such as N2, Ar, O2, and Xe. The maximum amounts of absorption of gases were 1.8, 1.9, 2.2, and 0.9 mole per mole of the copper(II) salt for N2, Ar, O2, and Xe, respectively, indicating that the gases were not adsorbed on the surface but occluded within the solid. Other microporous copper(II) dicarboxylates are also reviewed. The porous structure of copper(II) terephthalate, in which the gas is occluded, is deduced from the temperature dependence of magnetic susceptibilities and the linear structure of terephthalate. Microporous molybdenum(II) and ruthenium(II, III) dicarboxylates are discussed. We describe that rhodium(II) monocarboxylate bridged by pyrazine form stable micropores by self-assembly of infinite linear chain complexes.

The finite scaling for S = 1 XXZ chains with uniaxial single-ion-type anisotropy

NASA Astrophysics Data System (ADS)

Wang, Honglei; Xiong, Xingliang

2014-03-01

The scaling behavior of criticality for spin-1 XXZ chains with uniaxial single-ion-type anisotropy is investigated by employing the infinite matrix product state representation with the infinite time evolving block decimation method. At criticality, the accuracy of the ground state of a system is limited by the truncation dimension χ of the local Hilbert space. We present four evidences for the scaling of the entanglement entropy, the largest eigenvalue of the Schmidt decomposition, the correlation length, and the connection between the actual correlation length ξ and the energy. The result shows that the finite scalings are governed by the central charge of the critical system. Also, it demonstrates that the infinite time evolving block decimation algorithm by the infinite matrix product state representation can be a quite accurate method to simulate the critical properties at criticality.

Gacs quantum algorithmic entropy in infinite dimensional Hilbert spaces

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

Benatti, Fabio, E-mail: benatti@ts.infn.it; Oskouei, Samad Khabbazi, E-mail: kh.oskuei@ut.ac.ir; Deh Abad, Ahmad Shafiei, E-mail: shafiei@khayam.ut.ac.ir

We extend the notion of Gacs quantum algorithmic entropy, originally formulated for finitely many qubits, to infinite dimensional quantum spin chains and investigate the relation of this extension with two quantum dynamical entropies that have been proposed in recent years.

Electrostatic persistence length.

PubMed

Fixman, Marshall

2010-03-11

The persistence length is calculated for polyelectrolyte chains with fixed bond lengths and bond angles (pi-theta), and a potential energy consisting of the screened Coulomb interaction between beads, potential wells alpha phi(i)2 for the dihedral angles phi(i), and coupling terms beta phi(i) phi(i+/-1). This model defines a librating chain that reduces in appropriate limits to the freely rotating or wormlike chains, it can accommodate local crumpling or extreme stiffness, and it is easy to simulate. A planar-quadratic (pq), analytic approximation is based on an expansion of the electrostatic energy in eigenfunctions of the quadratic form that describes the backbone energy, and on the assumption that the quadratic form not only is positive but also adequately confines the chain in an infinite phase space of dihedral angles to the physically unique part with all |phi(i)| < pi. The pq approximation is available under these weak constraints, but the simulations confirm its quantitative accuracy only under the expected condition that alpha is large, that is, for very stiff chains. Stiff chains can also be simulated with small alpha and small theta and compared to an OSF approximation suitably generalized to chains with finite rather than vanishing theta, and increasing agreement with OSF is found the smaller is theta. The two approximations, one becoming exact as alpha --> infinity with fixed theta, the other as theta --> 0 with fixed alpha, are quantitatively similar in behavior, both giving a persistence length P = P0 + aD2 for stiff chains, where D is the Debye length. However, the coefficient apq is about twice the value of aOSF. Under other conditions the simulations show that P may or not be linear in D2 at small or moderate D, depending on the magnitudes of alpha, beta, theta, and the charge density but always becomes linear at large D. Even at a moderately low charge density, corresponding to fewer than 20% of the beads being charged, and with strong crumpling induced by large beta, increasing D dissolves blobs and recovers a linear dependence of P on D2, although a lower power of D gives an adequate fit at moderate D. For the class of models considered, it is concluded that the only universal feature is the asymptotic linearity of P in D2, regardless of flexibility or stiffness.

Nonmetallic electronegativity equalization and point-dipole interaction model including exchange interactions for molecular dipole moments and polarizabilities.

PubMed

Smalø, Hans S; Astrand, Per-Olof; Jensen, Lasse

2009-07-28

The electronegativity equalization model (EEM) has been combined with a point-dipole interaction model to obtain a molecular mechanics model consisting of atomic charges, atomic dipole moments, and two-atom relay tensors to describe molecular dipole moments and molecular dipole-dipole polarizabilities. The EEM has been phrased as an atom-atom charge-transfer model allowing for a modification of the charge-transfer terms to avoid that the polarizability approaches infinity for two particles at infinite distance and for long chains. In the present work, these shortcomings have been resolved by adding an energy term for transporting charges through individual atoms. A Gaussian distribution is adopted for the atomic charge distributions, resulting in a damping of the electrostatic interactions at short distances. Assuming that an interatomic exchange term may be described as the overlap between two electronic charge distributions, the EEM has also been extended by a short-range exchange term. The result is a molecular mechanics model where the difference of charge transfer in insulating and metallic systems is modeled regarding the difference in bond length between different types of system. For example, the model is capable of modeling charge transfer in both alkanes and alkenes with alternating double bonds with the same set of carbon parameters only relying on the difference in bond length between carbon sigma- and pi-bonds. Analytical results have been obtained for the polarizability of a long linear chain. These results show that the model is capable of describing the polarizability scaling both linearly and nonlinearly with the size of the system. Similarly, a linear chain with an end atom with a high electronegativity has been analyzed analytically. The dipole moment of this model system can either be independent of the length or increase linearly with the length of the chain. In addition, the model has been parametrized for alkane and alkene chains with data from density functional theory calculations, where the polarizability behaves differently with the chain length. For the molecular dipole moment, the same two systems have been studied with an aldehyde end group. Both the molecular polarizability and the dipole moment are well described as a function of the chain length for both alkane and alkene chains demonstrating the power of the presented model.

Entangled state teleportation through a couple of quantum channels composed of XXZ dimers in an Ising- XXZ diamond chain

NASA Astrophysics Data System (ADS)

Rojas, M.; de Souza, S. M.; Rojas, Onofre

2017-02-01

The quantum teleportation plays an important role in quantum information process, in this sense, the quantum entanglement properties involving an infinite chain structure is quite remarkable because real materials could be well represented by an infinite chain. We study the teleportation of an entangled state through a couple of quantum channels, composed by Heisenberg dimers in an infinite Ising-Heisenberg diamond chain, the couple of chains are considered sufficiently far away from each other to be ignored the any interaction between them. To teleporting a couple of qubits through the quantum channel, we need to find the average density operator for Heisenberg spin dimers, which will be used as quantum channels. Assuming the input state as a pure state, we can apply the concept of fidelity as a useful measurement of teleportation performance of a quantum channel. Using the standard teleportation protocol, we have derived an analytical expression for the output concurrence, fidelity, and average fidelity. We study in detail the effects of coupling parameters, external magnetic field and temperature dependence of quantum teleportation. Finally, we explore the relations between entanglement of the quantum channel, the output entanglement and the average fidelity of the system. Through a kind of phase diagram as a function of Ising-Heisenberg diamond chain model parameters, we illustrate where the quantum teleportation will succeed and a region where the quantum teleportation could fail.

Renormalized charge in a two-dimensional model of colloidal suspension from hypernetted chain approach.

PubMed

Camargo, Manuel; Téllez, Gabriel

2008-04-07

The renormalized charge of a simple two-dimensional model of colloidal suspension was determined by solving the hypernetted chain approximation and Ornstein-Zernike equations. At the infinite dilution limit, the asymptotic behavior of the correlation functions is used to define the effective interactions between the components of the system and these effective interactions were compared to those derived from the Poisson-Boltzmann theory. The results we obtained show that, in contrast to the mean-field theory, the renormalized charge does not saturate, but exhibits a maximum value and then decays monotonically as the bare charge increases. The results also suggest that beyond the counterion layer near to the macroion surface, the ionic cloud is not a diffuse layer which can be handled by means of the linearized theory, as the two-state model claims, but a more complex structure is settled by the correlations between microions.

Synthesis, crystal structure, and electrical and magnetic properties of BaMo{sub 6}Te{sub 6}: A novel reduced molybdenum telluride containing infinite chains of trans-face shared Mo{sub 6} octahedra

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

Gall, Philippe; Guizouarn, Thierry; Potel, Michel

Powder samples and single crystals of the new ternary compound BaMo{sub 6}Te{sub 6} were obtained by solid state reaction. The structure was determined by single-crystal X-ray diffraction. BaMo{sub 6}Te{sub 6} crystallizes in the hexagonal space group P6{sub 3}/m (No. 176) with unit-cell parameters a=9.3941(2) Å, c=4.5848(1) Å and Z=1. Full-matrix least-squares refinement on F{sup 2} using 452 independent reflections for 17 refinable parameters resulted in R1=0.0208 and wR2=0.0539. The structure consists of one-dimensional infinite chains of trans-face shared Mo{sub 6} octahedra capped by Se atoms. These chains that are running along the c axis are separated from each other bymore » nine-coordinate Ba atoms. Resistivity measurements on a single crystal indicated that the BaMo{sub 6}Te{sub 6} compound is metallic down to 160 K and semiconductor below. Magnetic susceptibility measurements showed that BaMo{sub 6}Te{sub 6} is weakly diamagnetic with no anomaly at the metal–semiconductor transition. - Graphical abstract: We present here the synthesis, the crystal structure, and the electrical and magnetic properties of the new compound BaMo{sub 6}Te{sub 6} containing infinite chains of trans-face shared Mo{sub 6} octahedra. - Highlights: • BaMo{sub 6}Te{sub 6} contains infinite chains of trans-face-sharing Mo{sub 6} octahedra |Mo{sub 6/2}|{sub ∞}{sup 1}. • Synthesis by solid state reaction. • Single-crystal X-ray study. • Continuous metal–nonmetal transition. • Anderson localization.« less

Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c = m/2

NASA Astrophysics Data System (ADS)

Minami, Kazuhiko

2017-12-01

An infinite number of spin chains are solved and it is derived that the ground-state phase transitions belong to the universality classes with central charge c = m / 2, where m is an integer. The models are diagonalized by automatically obtained transformations, many of which are different from the Jordan-Wigner transformation. The free energies, correlation functions, string order parameters, exponents, central charges, and the phase diagram are obtained. Most of the examples consist of the stabilizers of the cluster state. A unified structure of the one-dimensional XY and cluster-type spin chains is revealed, and other series of solvable models can be obtained through this formula.

Valence-bond theory of linear Hubbard and Pariser-Parr-Pople models

NASA Astrophysics Data System (ADS)

Soos, Z. G.; Ramasesha, S.

1984-05-01

The ground and low-lying states of finite quantum-cell models with one state per site are obtained exactly through a real-space basis of valence-bond (VB) diagrams that explicitly conserve the total spin. Regular and alternating Hubbard and Pariser-Parr-Pople (PPP) chains and rings with Ne electrons on N(<=12) sites are extrapolated to infinite arrays. The ground-state energy and optical gap of regular U=4|t| Hubbard chains agree with exact results, suggesting comparable accuracy for alternating Hubbard and PPP models, but differ from mean-field results. Molecular PPP parameters describe well the excitations of finite polyenes, odd polyene ions, linear cyanine dyes, and slightly overestimate the absorption peaks in polyacetylene (CH)x. Molecular correlations contrast sharply with uncorrelated descriptions of topological solitons, which are modeled by regular polyene radicals and their ions for both wide and narrow alternation crossovers. Neutral solitons have no midgap absorption and negative spin densities, while the intensity of the in-gap excitation of charged solitons is not enhanced. The properties of correlated states in quantum-cell models with one valence state per site are discussed in the adiabatic limit for excited-state geometries and instabilities to dimerization.

Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

NASA Technical Reports Server (NTRS)

Balas, M. J.; Kaufman, H.; Wen, J.

1985-01-01

A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

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 \

Aerodynamic stiffness of an unbound eccentric whirling centrifugal impeller with an infinite number of blades

NASA Technical Reports Server (NTRS)

Allaire, P. E.; Branagan, L. A.; Kocur, J. A.

1982-01-01

An unbounded eccentric centrifugal impeller with an infinite number of log spiral blades undergoing synchronous whirling in an incompressible fluid is considered. The forces acting on it due to coriolis forces, centripetal forces, changes in linear momentum, changes in pressure due to rotating and changes in pressure due to changes in linear momentum are evaluated.

Quantum transverse-field Ising model on an infinite tree from matrix product states

NASA Astrophysics Data System (ADS)

Nagaj, Daniel; Farhi, Edward; Goldstone, Jeffrey; Shor, Peter; Sylvester, Igor

2008-06-01

We give a generalization to an infinite tree geometry of Vidal’s infinite time-evolving block decimation (iTEBD) algorithm [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)] for simulating an infinite line of quantum spins. We numerically investigate the quantum Ising model in a transverse field on the Bethe lattice using the matrix product state ansatz. We observe a second order phase transition, with certain key differences from the transverse field Ising model on an infinite spin chain. We also investigate a transverse field Ising model with a specific longitudinal field. When the transverse field is turned off, this model has a highly degenerate ground state as opposed to the pure Ising model whose ground state is only doubly degenerate.

A motif for infinite metal atom wires.

PubMed

Yin, Xi; Warren, Steven A; Pan, Yung-Tin; Tsao, Kai-Chieh; Gray, Danielle L; Bertke, Jeffery; Yang, Hong

2014-12-15

A new motif for infinite metal atom wires with tunable compositions and properties is developed based on the connection between metal paddlewheel and square planar complex moieties. Two infinite Pd chain compounds, [Pd4(CO)4(OAc)4Pd(acac)2] 1 and [Pd4(CO)4(TFA)4Pd(acac)2] 2, and an infinite Pd-Pt heterometallic chain compound, [Pd4(CO)4(OAc)4Pt(acac)2] 3, are identified by single-crystal X-ray diffraction analysis. In these new structures, the paddlewheel moiety is a Pd four-membered ring coordinated by bridging carboxylic ligands and μ2 carbonyl ligands. The planar moiety is either Pd(acac)2 or Pt(acac)2 (acac = acetylacetonate). These moieties are connected by metallophilic interactions. The results showed that these one-dimensional metal wire compounds have photoluminescent properties that are tunable by changing ligands and metal ions. 3 can also serve as a single source precursor for making Pd4Pt bimetallic nanostructures with precise control of metal composition. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Infinite coherence time of edge spins in finite-length chains

NASA Astrophysics Data System (ADS)

Maceira, Ivo A.; Mila, Frédéric

2018-02-01

Motivated by the recent observation that exponentially long coherence times can be achieved for edge spins in models with strong zero modes, we study the impact of level crossings in finite-length spin chains on the dynamics of the edge spins. Focusing on the X Y spin-1 /2 chain with a transverse or longitudinal magnetic field, two models relevant to understanding recent experimental results on cobalt adatoms, we show that the edge spins can remain coherent for an infinite time even for a finite-length chain if the magnetic field is tuned to a value at which there is a level crossing. Furthermore, we show that the edge spins remain coherent for any initial state for the integrable case of a transverse field because all states have level crossings at the same value of the field, while the coherence time is increasingly large for lower temperatures in the case of a longitudinal field, which is nonintegrable.

Maximally reliable Markov chains under energy constraints.

PubMed

Escola, Sean; Eisele, Michael; Miller, Kenneth; Paninski, Liam

2009-07-01

Signal-to-noise ratios in physical systems can be significantly degraded if the outputs of the systems are highly variable. Biological processes for which highly stereotyped signal generations are necessary features appear to have reduced their signal variabilities by employing multiple processing steps. To better understand why this multistep cascade structure might be desirable, we prove that the reliability of a signal generated by a multistate system with no memory (i.e., a Markov chain) is maximal if and only if the system topology is such that the process steps irreversibly through each state, with transition rates chosen such that an equal fraction of the total signal is generated in each state. Furthermore, our result indicates that by increasing the number of states, it is possible to arbitrarily increase the reliability of the system. In a physical system, however, an energy cost is associated with maintaining irreversible transitions, and this cost increases with the number of such transitions (i.e., the number of states). Thus, an infinite-length chain, which would be perfectly reliable, is infeasible. To model the effects of energy demands on the maximally reliable solution, we numerically optimize the topology under two distinct energy functions that penalize either irreversible transitions or incommunicability between states, respectively. In both cases, the solutions are essentially irreversible linear chains, but with upper bounds on the number of states set by the amount of available energy. We therefore conclude that a physical system for which signal reliability is important should employ a linear architecture, with the number of states (and thus the reliability) determined by the intrinsic energy constraints of the system.

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Local conformation and intermolecular interaction of rigid ring polymers are not always the same as the linear analogue: cyclic amylose tris(phenylcarbamate) in Θ solvents.

PubMed

Asano, Natsuki; Kitamura, Shinichi; Terao, Ken

2013-08-15

Small-angle X-ray scattering and static and dynamic light scattering measurements were made for cyclic amylose tris(phenylcarbamate) (cATPC) of which weight-average molar mass M(w) ranges from 1.3 × 10(4) to 1.5 × 10(5) to determine their z-average mean square radius of gyration z, particle scattering function P(q), hydrodynamic radius R(H), and second virial coefficient A2 in methyl acetate (MEA), ethyl acetate (EA), and 4-methyl-2-pentanone (MIBK). The obtained z, P(q), and R(H) data were analyzed in terms of the wormlike ring to estimate the helix pitch per residue h and the Kuhn segment length λ(-1) (the stiffness parameter, twice the persistence length). Both h and λ(-1) for cATPC in MEA, EA, and MIBK are smaller than those for linear amylose tris(phenylcarbamate) (ATPC) in the corresponding solvent and the discrepancy becomes more significant with increasing the molar volume of the solvent. This indicates that not every rigid ring has the same local helical structure and chain stiffness as that for the linear polymer in the M(w) range investigated while infinitely long ring chains should have the same local conformation. This conformational difference also affects A2. In actuality, negative A2 was observed for cATPC in MIBK at the Θ temperature of linear ATPC whereas intermolecular topological interaction of ring polymers increases A2.

Propagation of acoustic waves in a stratified atmosphere, 1

NASA Technical Reports Server (NTRS)

Kalkofen, W.; Rossi, P.; Bodo, G.; Massaglia, S.

1994-01-01

This work is motivated by the chromospheric 3 minute oscillations observed in the K(sub 2v) bright points. We study acoustic gravity waves in a one-dimensional, gravitationally stratified, isothermal atmosphere. The oscillations are excited either by a velocity pulse imparted to a layer in an atmosphere of infinite vertical extent, or by a piston forming the lower boundary of a semi-infinite medium. We consider both linear and non-linear waves.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts.

PubMed

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts

NASA Astrophysics Data System (ADS)

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Graph determined symbolic dynamics and hybrid systems

NASA Astrophysics Data System (ADS)

Ayers, Kimberly Danielle

In this paper we explore the concept of symbolic dynamical systems whose structure is determined by a directed graph, and then discrete-continuous hybrid systems that arise from such dynamical systems. Typically, symbolic dynamics involve the study of a left shift of a bi-infinite sequence. We examine the case when the bi-infinite system is dictated by a graph; that is, the sequence is a bi-infinite path of a directed graph. We then use the concept to study a system of dynamical systems all on the same compact space M, where "switching" between the systems occurs as given by the bi-infinite sequence in question. The concepts of limit sets, chain recurrent sets, chaos, and Morse sets for these systems are explored.

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

NASA Technical Reports Server (NTRS)

Banks, H. T.; Wang, C.

1989-01-01

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

An improved technique for determining reflection from semi-infinite atmospheres with linearly anisotropic phase functions. [radiative transfer

NASA Technical Reports Server (NTRS)

Fricke, C. L.

1975-01-01

A solution to the problem of reflection from a semi-infinite atmosphere is presented, based upon Chandrasekhar's H-function method for linearly anisotropic phase functions. A modification to the Gauss quadrature formula which gives about the same accuracy with 10 points as the conventional Gauss quadrature does with 100 points was developed. A computer program achieving this solution is described and results are presented for several illustrative cases.

Crystal structure of cis-tetra-aqua-dichlorido-cobalt(II) sulfolane disolvate.

PubMed

Boudraa, Mhamed; Bouacida, Sofiane; Bouchareb, Hasna; Merazig, Hocine; Chtoun, El Hossain

2015-02-01

In the title compound, [CoCl2(H2O)4]·2C4H8SO2, the Co(II) cation is located on the twofold rotation axis and is coordinated by four water mol-ecules and two adjacent chloride ligands in a slightly distorted octa-hedral coordination environment. The cisoid angles are in the range 83.27 (5)-99.66 (2)°. The three transoid angles deviate significantly from the ideal linear angle. The crystal packing can be described as a linear arrangement of complex units along c formed by bifurcated O-H⋯Cl hydrogen bonds between two water mol-ecules from one complex unit towards one chloride ligand of the neighbouring complex. Two solvent mol-ecules per complex are attached to this infinite chain via O-H⋯O hydrogen bonds in which water mol-ecules act as the hydrogen-bond donor and sulfolane O atoms as the hydrogen-bond acceptor sites.

Extraction of diffuse correlation spectroscopy flow index by integration of Nth-order linear model with Monte Carlo simulation

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

Shang, Yu; Lin, Yu; Yu, Guoqiang, E-mail: guoqiang.yu@uky.edu

2014-05-12

Conventional semi-infinite solution for extracting blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements may cause errors in estimation of BFI (αD{sub B}) in tissues with small volume and large curvature. We proposed an algorithm integrating Nth-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in tissue for the extraction of αD{sub B}. The volume and geometry of the measured tissue were incorporated in the Monte Carlo simulation, which overcome the semi-infinite restrictions. The algorithm was tested using computer simulations on four tissue models with varied volumes/geometries and applied on an in vivo strokemore » model of mouse. Computer simulations shows that the high-order (N ≥ 5) linear algorithm was more accurate in extracting αD{sub B} (errors < ±2%) from the noise-free DCS data than the semi-infinite solution (errors: −5.3% to −18.0%) for different tissue models. Although adding random noises to DCS data resulted in αD{sub B} variations, the mean values of errors in extracting αD{sub B} were similar to those reconstructed from the noise-free DCS data. In addition, the errors in extracting the relative changes of αD{sub B} using both linear algorithm and semi-infinite solution were fairly small (errors < ±2.0%) and did not rely on the tissue volume/geometry. The experimental results from the in vivo stroke mice agreed with those in simulations, demonstrating the robustness of the linear algorithm. DCS with the high-order linear algorithm shows the potential for the inter-subject comparison and longitudinal monitoring of absolute BFI in a variety of tissues/organs with different volumes/geometries.« less

Syntheses, structures, and properties of two new zinc(II) metal-organic frameworks based on flexible 1,6-bis(2-methyl-imidazole-1-yl)hexane ligand

NASA Astrophysics Data System (ADS)

Jin, Jun-Cheng; Fu, Ai-Yun; Li, Dian; Chang, Wen-Gui; Wu, Ju; Yang, Mei; Xie, Cheng-Gen; Xu, Guang-Nian; Cai, An-Xing; Wu, Ai-Hua

2014-11-01

Two new zinc(II) metal-organic compounds of [Zn(ADC)(bimh)]n (1) and [Zn(ADA)(bimh)]n (2) (H2ADC = 1,3-adamantanedicarboxylic acid, H2ADA = 1,3-adamantanediacetic acid, bimh = 1,6-bis(2-methyl-imidazole-1-yl)-hexane, have been structurally characterized by X-ray diffraction analysis. In compound 1, the zinc(II) ions are bridged by ADC and bimh ligands to form a 1D looped chain. In compound 2, the ADA molecules alternately bridge Zn(II) atoms to form infinite chains, and then the 1D chain is connected through the bimh ligand resulting in an undulating infinite two-dimensional (2D) polymeric network. Additionally, TG analysis, XRPD and fluorescent properties for compounds 1 and 2 are also measured and discussed.

A Novel Coordination Polymer Based on Trinuclear Cobalt Building Blocks Cluster: Synthesis, Crystal Structure, and Properties

NASA Astrophysics Data System (ADS)

Lu, J. F.; Tang, Z. H.; Shi, J.; Ge, H. G.; Jiang, M.; Song, J.; Jin, L. X.

2017-12-01

The title compound {[Co3(μ3-OH)(μ2-H2O)2(H2O)5(BTC)2] · 6H2O} n (H3BTC is a 1,3,5-benzenetricarboxylic acid) was prepared and characterized by single crystal and powder X-ray diffraction, Fourier transform infrared spectroscopy, thermogravimetric and elemental analyses. The single crystal X-ray diffraction reveals that the title compound consists of 1D infinite zigzag chains which were constructed by trinuclear cobalt cluster and BTC3- ligand. Neighbouring above-mentioned 1D infinite zigzag chains are further linked by intermolecular hydrogen bonding to form a 3D supermolecular structure. In addition, the luminescent properties of the title compound were investigated.

A control theory approach to the analysis and synthesis of the experimentally observed motion primitives.

PubMed

Nori, Francesco; Frezza, Ruggero

2005-11-01

Recent experiments on frogs and rats, have led to the hypothesis that sensory-motor systems are organized into a finite number of linearly combinable modules; each module generates a motor command that drives the system to a predefined equilibrium. Surprisingly, in spite of the infiniteness of different movements that can be realized, there seems to be only a handful of these modules. The structure can be thought of as a vocabulary of "elementary control actions". Admissible controls, which in principle belong to an infinite dimensional space, are reduced to the linear vector space spanned by these elementary controls. In the present paper we address some theoretical questions that arise naturally once a similar structure is applied to the control of nonlinear kinematic chains. First of all, we show how to choose the modules so that the system does not loose its capability of generating a "complete" set of movements. Secondly, we realize a "complete" vocabulary with a minimal number of elementary control actions. Subsequently, we show how to modify the control scheme so as to compensate for parametric changes in the system to be controlled. Remarkably, we construct a set of modules with the property of being invariant with respect to the parameters that model the growth of an individual. Robustness against uncertainties is also considered showing how to optimally choose the modules equilibria so as to compensate for errors affecting the system. Finally, the motion primitive paradigm is extended to locomotion and a related formalization of internal (proprioceptive) and external (exteroceptive) variables is given.

Rotating metric in nonsingular infinite derivative theories of gravity

NASA Astrophysics Data System (ADS)

Cornell, Alan S.; Harmsen, Gerhard; Lambiase, Gaetano; Mazumdar, Anupam

2018-05-01

In this paper, we will provide a nonsingular rotating spacetime metric for a ghost-free infinite derivative theory of gravity in a linearized limit. We will provide the predictions for the Lense-Thirring effect for a slowly rotating system, and how it is compared with that from general relativity.

Direct Connection between the RII Chain and the Nonautonomous Discrete Modified KdV Lattice

NASA Astrophysics Data System (ADS)

Maeda, Kazuki; Tsujimoto, Satoshi

2013-11-01

The spectral transformation technique for symmetric RII polynomials is developed. Use of this technique reveals that the nonautonomous discrete modified KdV (nd-mKdV) lattice is directly connected with the RII chain. Hankel determinant solutions to the semi-infinite nd-mKdV lattice are also presented.

Concentrated Solutions of Single-Chain Nanoparticles: A Simple Model for Intrinsically Disordered Proteins under Crowding Conditions.

PubMed

Moreno, Angel J; Lo Verso, Federica; Arbe, Arantxa; Pomposo, José A; Colmenero, Juan

2016-03-03

By means of large-scale computer simulations and small-angle neutron scattering (SANS), we investigate solutions of single-chain nanoparticles (SCNPs), covering the whole concentration range from infinite dilution to melt density. The analysis of the conformational properties of the SCNPs reveals that these synthetic nano-objects share basic ingredients with intrinsically disordered proteins (IDPs), as topological polydispersity, generally sparse conformations, and locally compact domains. We investigate the role of the architecture of the SCNPs in their collapse behavior under macromolecular crowding. Unlike in the case of linear macromolecules, which experience the usual transition from self-avoiding to Gaussian random-walk conformations, crowding leads to collapsed conformations of SCNPs resembling those of crumpled globules. This behavior is already found at volume fractions (about 30%) that are characteristic of crowding in cellular environments. The simulation results are confirmed by the SANS experiments. Our results for SCNPs--a model system free of specific interactions--propose a general scenario for the effect of steric crowding on IDPs: collapse from sparse conformations at high dilution to crumpled globular conformations in cell environments.

A menu-driven software package of Bayesian nonparametric (and parametric) mixed models for regression analysis and density estimation.

PubMed

Karabatsos, George

2017-02-01

Most of applied statistics involves regression analysis of data. In practice, it is important to specify a regression model that has minimal assumptions which are not violated by data, to ensure that statistical inferences from the model are informative and not misleading. This paper presents a stand-alone and menu-driven software package, Bayesian Regression: Nonparametric and Parametric Models, constructed from MATLAB Compiler. Currently, this package gives the user a choice from 83 Bayesian models for data analysis. They include 47 Bayesian nonparametric (BNP) infinite-mixture regression models; 5 BNP infinite-mixture models for density estimation; and 31 normal random effects models (HLMs), including normal linear models. Each of the 78 regression models handles either a continuous, binary, or ordinal dependent variable, and can handle multi-level (grouped) data. All 83 Bayesian models can handle the analysis of weighted observations (e.g., for meta-analysis), and the analysis of left-censored, right-censored, and/or interval-censored data. Each BNP infinite-mixture model has a mixture distribution assigned one of various BNP prior distributions, including priors defined by either the Dirichlet process, Pitman-Yor process (including the normalized stable process), beta (two-parameter) process, normalized inverse-Gaussian process, geometric weights prior, dependent Dirichlet process, or the dependent infinite-probits prior. The software user can mouse-click to select a Bayesian model and perform data analysis via Markov chain Monte Carlo (MCMC) sampling. After the sampling completes, the software automatically opens text output that reports MCMC-based estimates of the model's posterior distribution and model predictive fit to the data. Additional text and/or graphical output can be generated by mouse-clicking other menu options. This includes output of MCMC convergence analyses, and estimates of the model's posterior predictive distribution, for selected functionals and values of covariates. The software is illustrated through the BNP regression analysis of real data.

Spillover, nonlinearity, and flexible structures

NASA Technical Reports Server (NTRS)

Bass, Robert W.; Zes, Dean

1991-01-01

Many systems whose evolution in time is governed by Partial Differential Equations (PDEs) are linearized around a known equilibrium before Computer Aided Control Engineering (CACE) is considered. In this case, there are infinitely many independent vibrational modes, and it is intuitively evident on physical grounds that infinitely many actuators would be needed in order to control all modes. A more precise, general formulation of this grave difficulty (spillover problem) is due to A.V. Balakrishnan. A possible route to circumvention of this difficulty lies in leaving the PDE in its original nonlinear form, and adding the essentially finite dimensional control action prior to linearization. One possibly applicable technique is the Liapunov Schmidt rigorous reduction of singular infinite dimensional implicit function problems to finite dimensional implicit function problems. Omitting details of Banach space rigor, the formalities of this approach are given.

Allele Age Under Non-Classical Assumptions is Clarified by an Exact Computational Markov Chain Approach.

PubMed

De Sanctis, Bianca; Krukov, Ivan; de Koning, A P Jason

2017-09-19

Determination of the age of an allele based on its population frequency is a well-studied problem in population genetics, for which a variety of approximations have been proposed. We present a new result that, surprisingly, allows the expectation and variance of allele age to be computed exactly (within machine precision) for any finite absorbing Markov chain model in a matter of seconds. This approach makes none of the classical assumptions (e.g., weak selection, reversibility, infinite sites), exploits modern sparse linear algebra techniques, integrates over all sample paths, and is rapidly computable for Wright-Fisher populations up to N e  = 100,000. With this approach, we study the joint effect of recurrent mutation, dominance, and selection, and demonstrate new examples of "selective strolls" where the classical symmetry of allele age with respect to selection is violated by weakly selected alleles that are older than neutral alleles at the same frequency. We also show evidence for a strong age imbalance, where rare deleterious alleles are expected to be substantially older than advantageous alleles observed at the same frequency when population-scaled mutation rates are large. These results highlight the under-appreciated utility of computational methods for the direct analysis of Markov chain models in population genetics.

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

Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au; Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au

The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem ofmore » optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.« less

Density functional theory study of the conformational space of an infinitely long polypeptide chain

NASA Astrophysics Data System (ADS)

Ireta, Joel; Scheffler, Matthias

2009-08-01

The backbone conformational space of infinitely long polyalanine is investigated with density-functional theory and mapping the potential energy surface in terms of (L, θ) cylindrical coordinates. A comparison of the obtained (L, θ) Ramachandran-like plot with results from an extended set of protein structures shows excellent conformity, with the exception of the polyproline II region. It is demonstrated the usefulness of infinitely long polypeptide models for investigating the influence of hydrogen bonding and its cooperative effect on the backbone conformations. The results imply that hydrogen bonding together with long-range electrostatics is the main actuator for most of the structures assumed by protein residues.

Limitations of discrete-time quantum walk on a one-dimensional infinite chain

NASA Astrophysics Data System (ADS)

Lin, Jia-Yi; Zhu, Xuanmin; Wu, Shengjun

2018-04-01

How well can we manipulate the state of a particle via a discrete-time quantum walk? We show that the discrete-time quantum walk on a one-dimensional infinite chain with coin operators that are independent of the position can only realize product operators of the form eiξ A ⊗1p, which cannot change the position state of the walker. We present a scheme to construct all possible realizations of all the product operators of the form eiξ A ⊗1p. When the coin operators are dependent on the position, we show that the translation operators on the position can not be realized via a DTQW with coin operators that are either the identity operator 1 or the Pauli operator σx.

A Nth-order linear algorithm for extracting diffuse correlation spectroscopy blood flow indices in heterogeneous tissues.

PubMed

Shang, Yu; Yu, Guoqiang

2014-09-29

Conventional semi-infinite analytical solutions of correlation diffusion equation may lead to errors when calculating blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements in tissues with irregular geometries. Very recently, we created an algorithm integrating a N th-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in homogenous tissues with arbitrary geometries for extraction of BFI (i.e., αD B ). The purpose of this study is to extend the capability of the N th-order linear algorithm for extracting BFI in heterogeneous tissues with arbitrary geometries. The previous linear algorithm was modified to extract BFIs in different types of tissues simultaneously through utilizing DCS data at multiple source-detector separations. We compared the proposed linear algorithm with the semi-infinite homogenous solution in a computer model of adult head with heterogeneous tissue layers of scalp, skull, cerebrospinal fluid, and brain. To test the capability of the linear algorithm for extracting relative changes of cerebral blood flow (rCBF) in deep brain, we assigned ten levels of αD B in the brain layer with a step decrement of 10% while maintaining αD B values constant in other layers. Simulation results demonstrate the accuracy (errors < 3%) of high-order ( N  ≥ 5) linear algorithm in extracting BFIs in different tissue layers and rCBF in deep brain. By contrast, the semi-infinite homogenous solution resulted in substantial errors in rCBF (34.5% ≤ errors ≤ 60.2%) and BFIs in different layers. The N th-order linear model simplifies data analysis, thus allowing for online data processing and displaying. Future study will test this linear algorithm in heterogeneous tissues with different levels of blood flow variations and noises.

A characterization of positive linear maps and criteria of entanglement for quantum states

NASA Astrophysics Data System (ADS)

Hou, Jinchuan

2010-09-01

Let H and K be (finite- or infinite-dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from {\\mathcal B}(H) into {\\mathcal B}(K) is given, which particularly gives a characterization of positive elementary operators including all positive linear maps between matrix algebras. This characterization is then applied to give a representation of quantum channels (operations) between infinite-dimensional systems. A necessary and sufficient criterion of separability is given which shows that a state ρ on HotimesK is separable if and only if (ΦotimesI)ρ >= 0 for all positive finite-rank elementary operators Φ. Examples of NCP and indecomposable positive linear maps are given and are used to recognize some entangled states that cannot be recognized by the PPT criterion and the realignment criterion.

Synthesis, crystal structure and optical properties of a novel sodium lead pentaborate, NaPbB{sub 5}O{sub 9}

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

Zhang, Min; Graduate University of Chinese Academy of Sciences, Beijing 100049; Pan, Shilie, E-mail: slpan@ms.xjb.ac.c

A novel sodium lead pentaborate, NaPbB{sub 5}O{sub 9}, has been successfully synthesized by standard solid-state reaction. The single-crystal X-ray structural analysis showed that NaPbB{sub 5}O{sub 9} crystallizes in the monoclinic space group P2{sub 1}/c with a=6.5324(10) A, b=13.0234(2) A, c=8.5838(10) A, {beta}=104.971(10){sup o}, and Z=4. The crystal structure is composed of double ring [B{sub 5}O{sub 9}]{sup 3-} units, [PbO{sub 7}] and [NaO{sub 7}] polyhedra. [B{sub 5}O{sub 9}]{sup 3-} groups connect with each other forming two-dimensional infinite {sub {infinity}}[B{sub 5}O{sub 9}]{sup 3-} layers, while [PbO{sub 7}] and [NaO{sub 7}] polyhedra are located between the layers. [PbO{sub 7}] polyhedra linked together viamore » corner-sharing O atom forming novel infinite {sub {infinity}}[PbO{sub 6}] chains along the c axis. The thermal behavior, IR spectrum and the optical diffuse reflectance spectrum of NaPbB{sub 5}O{sub 9} were reported. -- Graphical abstract: A new phase, NaPbB{sub 5}O{sub 9}, has been discovered in the ternary M{sub 2}O-PbO-B{sub 2}O{sub 3} (M=alkali-metal) system. The crystal structure consists of a novel infinite {sub {infinity}}[PbO{sub 6}] chains. Display Omitted Research highlights: NaPbB{sub 5}O{sub 9} is the first borate discovered in the ternary M{sub 2}O-PbO-B{sub 2}O{sub 3} (M=alkali-metal) system. NaPbB{sub 5}O{sub 9} crystal structure includes a two-dimensional infinite {sub {infinity}}[B{sub 5}O{sub 9}]{sup 3-} layers and a novel one-dimensional infinite {sub {infinity}}[PbO{sub 6}] chains. [PbO{sub 7}] polyhedron has a highly asymmetric bonding configuration.« less

Time-resolved spectroscopy at surfaces and adsorbate dynamics: Insights from a model-system approach

NASA Astrophysics Data System (ADS)

Boström, Emil; Mikkelsen, Anders; Verdozzi, Claudio

2016-05-01

We introduce a model description of femtosecond laser induced desorption at surfaces. The substrate part of the system is taken into account as a (possibly semi-infinite) linear chain. Here, being especially interested in the early stages of dissociation, we consider a finite-size implementation of the model (i.e., a finite substrate), for which an exact numerical solution is possible. By time-evolving the many-body wave function, and also using results from a time-dependent density functional theory description for electron-nuclear systems, we analyze the competition between several surface-response mechanisms and electronic correlations in the transient and longer time dynamics under the influence of dipole-coupled fields. Our model allows us to explore how coherent multiple-pulse protocols can impact desorption in a variety of prototypical experiments.

On reliable control system designs. Ph.D. Thesis; [actuators

NASA Technical Reports Server (NTRS)

Birdwell, J. D.

1978-01-01

A mathematical model for use in the design of reliable multivariable control systems is discussed with special emphasis on actuator failures and necessary actuator redundancy levels. The model consists of a linear time invariant discrete time dynamical system. Configuration changes in the system dynamics are governed by a Markov chain that includes transition probabilities from one configuration state to another. The performance index is a standard quadratic cost functional, over an infinite time interval. The actual system configuration can be deduced with a one step delay. The calculation of the optimal control law requires the solution of a set of highly coupled Riccati-like matrix difference equations. Results can be used for off-line studies relating the open loop dynamics, required performance, actuator mean time to failure, and functional or identical actuator redundancy, with and without feedback gain reconfiguration strategies.

Effect of capillary forces on the nonstationary fall of a drop in an infinite fluid

NASA Astrophysics Data System (ADS)

Antanovskii, L. K.

1991-12-01

An explicit solution is presented for the linear problem concerning the motion of a drop in an infinite fluid in the presence of any number of surfactants (chemical reactions are not considered in the first approximation). It is shown that the behavior of the system considered is consistent with the Le Chatelier principle. The reactivity of the capillary forces is directly related to the fundamental principles of thermodynamics, which makes it possible to write equations of surfactant thermodiffusion in symmetric form and obtain a relatively simple solution to the linearized problem.

On a new class of completely integrable nonlinear wave equations. I. Infinitely many conservation laws

NASA Astrophysics Data System (ADS)

Nutku, Y.

1985-06-01

We point out a class of nonlinear wave equations which admit infinitely many conserved quantities. These equations are characterized by a pair of exact one-forms. The implication that they are closed gives rise to equations, the characteristics and Riemann invariants of which are readily obtained. The construction of the conservation laws requires the solution of a linear second-order equation which can be reduced to canonical form using the Riemann invariants. The hodograph transformation results in a similar linear equation. We discuss also the symplectic structure and Bäcklund transformations associated with these equations.

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).

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

Shang, Yu; Yu, Guoqiang, E-mail: guoqiang.yu@uky.edu

Conventional semi-infinite analytical solutions of correlation diffusion equation may lead to errors when calculating blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements in tissues with irregular geometries. Very recently, we created an algorithm integrating a Nth-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in homogenous tissues with arbitrary geometries for extraction of BFI (i.e., αD{sub B}). The purpose of this study is to extend the capability of the Nth-order linear algorithm for extracting BFI in heterogeneous tissues with arbitrary geometries. The previous linear algorithm was modified to extract BFIs in different typesmore » of tissues simultaneously through utilizing DCS data at multiple source-detector separations. We compared the proposed linear algorithm with the semi-infinite homogenous solution in a computer model of adult head with heterogeneous tissue layers of scalp, skull, cerebrospinal fluid, and brain. To test the capability of the linear algorithm for extracting relative changes of cerebral blood flow (rCBF) in deep brain, we assigned ten levels of αD{sub B} in the brain layer with a step decrement of 10% while maintaining αD{sub B} values constant in other layers. Simulation results demonstrate the accuracy (errors < 3%) of high-order (N ≥ 5) linear algorithm in extracting BFIs in different tissue layers and rCBF in deep brain. By contrast, the semi-infinite homogenous solution resulted in substantial errors in rCBF (34.5% ≤ errors ≤ 60.2%) and BFIs in different layers. The Nth-order linear model simplifies data analysis, thus allowing for online data processing and displaying. Future study will test this linear algorithm in heterogeneous tissues with different levels of blood flow variations and noises.« less

Patterns of hydrogen bonding involving thiourea in the series of thioureaṡtrans-1,2-bispyridyl ethylene cocrystals - A comparative study

NASA Astrophysics Data System (ADS)

Kole, Goutam Kumar; Kumar, Mukesh

2018-07-01

Thiourea is known to act as a template to preorganise a series of trans-1,2-bispyridyl ethylenes (bpe), where the thiourea molecules present in an infinite zigzag chain with R22(8) graph set (the β-tape) which offers three different types of hydrogen bonding [J. Am. Chem. Soc. 132 (2010) 13434]. This article reports a new cocrystal of thiourea with 3,4‧-bpe and acts as a 'missing link' in the series. In this cocrystal, thiourea present in an infinite corrugated chain with R21(6) graph set, a rarely observed thiourea synthon i.e. α-tape. A comparative study has been discussed which demonstrates various types of hydrogen bonding that exist in the series and their impact on the parallel stacking of the pyridyl based olefins.

On Condensation Properties of Bethe Roots Associated with the XXZ Chain

NASA Astrophysics Data System (ADS)

Kozlowski, Karol K.

2018-02-01

I prove that the Bethe roots describing either the ground state or a certain class of "particle-hole" excited states of the XXZ spin-1/2 chain in any sector with magnetisation m \\in [0;1/2] exist, are uniquely defined, and form, in the infinite volume limit, a dense distribution on a subinterval of R. The results hold for any value of the anisotropy {Δ ≥ -1}. In fact, I establish an even stronger result, namely the existence of an all order asymptotic expansion of the counting function associated with such roots. As a corollary, these results allow one to prove the existence and form of the infinite volume limit of various observables attached to the model -the excitation energy, momentum, the zero temperature correlation functions, so as to name a few- that were argued earlier in the literature.

Non-linear wave interaction in a magnetoplasma column. I - Theory. II Experiment

NASA Technical Reports Server (NTRS)

Larsen, J.-M.; Crawford, F. W.

1979-01-01

The paper presents an analysis of non-linear three-wave interaction for propagation along a cylindrical plasma column surrounded either by a metallic boundary, or by an infinite dielectric, and immersed in an infinite, static, axial magnetic field. An averaged Lagrangian method is used and the results are specialized to parametric amplification and mode conversion, assuming an undepleted pump wave. Computations are presented for a magneto-plasma column surrounded by free space, indicating that parametric growth rates of the order of a fraction of a decibel per centimeter should be obtainable for plausible laboratory plasma parameters. In addition, experiments on non-linear mode conversion in a cylindrical magnetoplasma column are described. The results are compared with the theoretical predictions and good qualitative agreement is demonstrated.

A series of new copper iodobismuthates: structural relationships, optical band gaps affected by dimensionality, and distinct thermal stabilities.

PubMed

Chai, Wen-Xiang; Wu, Li-Ming; Li, Jun-Qian; Chen, Ling

2007-10-15

Three new copper iodobismuthates, red tetranuclear [n-Bu(4)N][Cu(2)(CH(3)CN)(2)Bi(2)I(10)] (1), dark-red infinite linear [Et(4)N](2n)[Cu(2)Bi(2)I(10)](n) (2), and black polymeric ladderlike [Cu(CH(3)CN)(4)](2n)[Cu(2)Bi(2)I(10)](n) (3), crystallize from solutions of BiI3 and CuI in the presence of different cations. A regular structural relationship from 0-D (1) to 1-D linear anion chains (2) to 1-D ladderlike anion chains (3) is observed. The self-assembly of the basic building unit Cu(2)Bi(2)I(10) as altered by different cations is proposed to be the driving force for their formation. The optical band gaps exhibit a structure-related decrease from 1 to 2/3, in agreement with their color changes and the density functional theory (DFT) calculation results. The electronic structures and the relationship with corresponding monobismuth analogues and the Ag-Bi isotypes are discussed on the basis of DFT calculations. In spite of their structural similarities, the compounds are distinctive thermally: 2 is stable to 230 degrees C, 1 undergoes a solvent loss at 85 degrees C to form a new phase that is thermally stable to 230 degrees C, and 3 releases a solvent molecule and decomposes at 80 degrees C into BiI(3) and CuI. The essential reasons for these differences are discussed.

Local unitary transformation method toward practical electron correlation calculations with scalar relativistic effect in large-scale molecules

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

Seino, Junji; Nakai, Hiromi, E-mail: nakai@waseda.jp; Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555

In order to perform practical electron correlation calculations, the local unitary transformation (LUT) scheme at the spin-free infinite-order Douglas–Kroll–Hess (IODKH) level [J. Seino and H. Nakai, J. Chem. Phys.136, 244102 (2012); J. Seino and H. Nakai, J. Chem. Phys.137, 144101 (2012)], which is based on the locality of relativistic effects, has been combined with the linear-scaling divide-and-conquer (DC)-based Hartree–Fock (HF) and electron correlation methods, such as the second-order Møller–Plesset (MP2) and the coupled cluster theories with single and double excitations (CCSD). Numerical applications in hydrogen halide molecules, (HX){sub n} (X = F, Cl, Br, and I), coinage metal chain systems,more » M{sub n} (M = Cu and Ag), and platinum-terminated polyynediyl chain, trans,trans-((p-CH{sub 3}C{sub 6}H{sub 4}){sub 3}P){sub 2}(C{sub 6}H{sub 5})Pt(C≡C){sub 4}Pt(C{sub 6}H{sub 5})((p-CH{sub 3}C{sub 6}H{sub 4}){sub 3}P){sub 2}, clarified that the present methods, namely DC-HF, MP2, and CCSD with the LUT-IODKH Hamiltonian, reproduce the results obtained using conventional methods with small computational costs. The combination of both LUT and DC techniques could be the first approach that achieves overall quasi-linear-scaling with a small prefactor for relativistic electron correlation calculations.« less

New compacton soliton solutions and solitary patterns solutions of nonlinearly dispersive Boussinesq equations

NASA Astrophysics Data System (ADS)

Yan, Zhenya; Bluman, George

2002-11-01

The special exact solutions of nonlinearly dispersive Boussinesq equations (called B( m, n) equations), utt- uxx- a( un) xx+ b( um) xxxx=0, is investigated by using four direct ansatze. As a result, abundant new compactons: solitons with the absence of infinite wings, solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions of these two equations are obtained. The variant is extended to include linear dispersion to support compactons and solitary patterns in the linearly dispersive Boussinesq equations with m=1. Moreover, another new compacton solution of the special case, B(2,2) equation, is also found.

On an adaptive preconditioned Crank-Nicolson MCMC algorithm for infinite dimensional Bayesian inference

NASA Astrophysics Data System (ADS)

Hu, Zixi; Yao, Zhewei; Li, Jinglai

2017-03-01

Many scientific and engineering problems require to perform Bayesian inference for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement, which is referred to as being dimension dependent. To this end, a family of dimensional independent MCMC algorithms, known as the preconditioned Crank-Nicolson (pCN) methods, were proposed to sample the infinite dimensional parameters. In this work we develop an adaptive version of the pCN algorithm, where the covariance operator of the proposal distribution is adjusted based on sampling history to improve the simulation efficiency. We show that the proposed algorithm satisfies an important ergodicity condition under some mild assumptions. Finally we provide numerical examples to demonstrate the performance of the proposed method.

Markov chain sampling of the O(n) loop models on the infinite plane

NASA Astrophysics Data System (ADS)

Herdeiro, Victor

2017-07-01

A numerical method was recently proposed in Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016), 10.1103/PhysRevE.94.043322] showing a precise sampling of the infinite plane two-dimensional critical Ising model for finite lattice subsections. The present note extends the method to a larger class of models, namely the O(n) loop gas models for n ∈(1 ,2 ] . We argue that even though the Gibbs measure is nonlocal, it is factorizable on finite subsections when sufficient information on the loops touching the boundaries is stored. Our results attempt to show that provided an efficient Markov chain mixing algorithm and an improved discrete lattice dilation procedure the planar limit of the O(n) models can be numerically studied with efficiency similar to the Ising case. This confirms that scale invariance is the only requirement for the present numerical method to work.

On the Genealogy of Asexual Diploids

NASA Astrophysics Data System (ADS)

Lam, Fumei; Langley, Charles H.; Song, Yun S.

Given molecular genetic data from diploid individuals that, at present, reproduce mostly or exclusively asexually without recombination, an important problem in evolutionary biology is detecting evidence of past sexual reproduction (i.e., meiosis and mating) and recombination (both meiotic and mitotic). However, currently there is a lack of computational tools for carrying out such a study. In this paper, we formulate a new problem of reconstructing diploid genealogies under the assumption of no sexual reproduction or recombination, with the ultimate goal being to devise genealogy-based tools for testing deviation from these assumptions. We first consider the infinite-sites model of mutation and develop linear-time algorithms to test the existence of an asexual diploid genealogy compatible with the infinite-sites model of mutation, and to construct one if it exists. Then, we relax the infinite-sites assumption and develop an integer linear programming formulation to reconstruct asexual diploid genealogies with the minimum number of homoplasy (back or recurrent mutation) events. We apply our algorithms on simulated data sets with sizes of biological interest.

On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Wang, C.

1990-01-01

The convergence of solutions to the discrete or sampled time linear quadratic regulator problem and associated Riccati equation for infinite dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero (infinity) is established. Both the finite and infinite time horizon problems are studied. In the finite time horizon case, strong continuity of the operators which define the control system and performance index together with a stability and consistency condition on the sampling scheme are required. For the infinite time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary of delay system, and a flexible beam are presented and discussed.

On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter system

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Wang, C.

1992-01-01

The convergence of solutions to the discrete- or sampled-time linear quadratic regulator problem and associated Riccati equation for infinite-dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero(infinity) is established. Both the finite-and infinite-time horizon problems are studied. In the finite-time horizon case, strong continuity of the operators that define the control system and performance index, together with a stability and consistency condition on the sampling scheme are required. For the infinite-time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary or delay system, and a flexible beam are presented and discussed.

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.

Plasmon-Polariton Properties in Metallic Nanosphere Chains

PubMed Central

Jacak, Witold Aleksander; Krasnyj, Jurij; Chepok, Andrej

2015-01-01

The propagation of collective wave type plasmonic excitations along infinite chains of metallic nanospheres has been analyzed, including near-, medium- and far-field contributions to the plasmon dipole interaction with all retardation effects taken into account. It is proven that there exist weakly-damped self-modes of plasmon-polaritons in the chain for which the propagation range is limited by relatively small Ohmic losses only. In this regime, the Lorentz friction irradiation losses on each nanosphere in the chain are ideally compensated by the energy income from the rest of the chain. The completely undamped collective waves were identified in the case of the presence of persistent external excitation of some fragment of the chain. The obtained characteristics of these excitations fit the experimental observations well. PMID:28793415

Chain-reaction crash in traffic flow controlled by taillights

NASA Astrophysics Data System (ADS)

Nagatani, Takashi

2015-02-01

We study the chain-reaction crash (multiple-vehicle collision) in low-visibility condition on a road. In the traffic situation, drivers brake according to taillights of the forward vehicle. The first crash may induce more collisions. We investigate whether or not the first collision induces the chain-reaction crash, numerically and analytically. The dynamic transitions occur from no collisions through a single collision, double collisions and triple collisions, to multiple collisions with decreasing the headway. Also, we find that the dynamic transition occurs from the finite chain reaction to the infinite chain reaction when the headway is less than the critical value. We derive, analytically, the transition points and the region maps for the chain-reaction crash in traffic flow controlled by taillights.

2 + 1 Toda chain. I. Inverse scattering method

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

Lipovskii, V.D.; Shirokov, A.V.

A formal scheme of the inverse scattering method is constructed for the2 + 1 Toda chain in the class of rapidly decreasing Cauchy data. Application of the inverse scattering method to the two-dimensional infinite Toda chain was made difficult by the circumstance that this system is a (2 + 1)-dimensional object, i.e., possesses time and two spatial variables, the role of one of these being played by the chain site number. Because of this, our information about the 2 + 1 Toda chain was limited to a rich set of particular solutions of soliton type obtained in the cycle ofmore » studies by the Darboux transformation method.« less

A problem in non-linear Diophantine approximation

NASA Astrophysics Data System (ADS)

Harrap, Stephen; Hussain, Mumtaz; Kristensen, Simon

2018-05-01

In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.

Infinite time interval backward stochastic differential equations with continuous coefficients.

PubMed

Zong, Zhaojun; Hu, Feng

2016-01-01

In this paper, we study the existence theorem for [Formula: see text] [Formula: see text] solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain the existence of a minimal solution. Furthermore, we study the existence and uniqueness theorem for [Formula: see text] [Formula: see text] solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients. It should be pointed out that the assumptions of this result is weaker than that of Theorem 3.1 in Zong (Turkish J Math 37:704-718, 2013).

High Frequency Magnetic Field Direction Finding Using MGL-S9A B-dot Sensors

DTIC Science & Technology

2013-03-21

relationship for incident plane wave on a linear array . . . . . . . . . . . 26 3.1 B-dot sensor design in CST Microwave Studio...CST Microwave Studio with an infinite PEC ground plane. . . . . . . . . . . . . . . 50 4.2 Radiation pattern of a single B-dot sensor at 32 MHz...simulated in CST Microwave Studio with an infinite PEC ground plane. . . . . . . . . . . . . . . 50 4.3 Radiation efficiency of single loop versus B-dot

Calculation of longitudinal polarizability and second hyperpolarizability of polyacetylene with the coupled perturbed Hartree-Fock/Kohn-Sham scheme: Where it is shown how finite oligomer chains tend to the infinite periodic polymer

NASA Astrophysics Data System (ADS)

Lacivita, Valentina; Rèrat, Michel; Orlando, Roberto; Ferrero, Mauro; Dovesi, Roberto

2012-03-01

The longitudinal polarizability, αxx, and second hyperpolarizability, γxxxx, of polyacetylene are evaluated by using the coupled perturbed Hartree-Fock/Kohn-Sham (HF/KS) scheme as implemented in the periodic CRYSTAL code and a split valence type basis set. Four different density functionals, namely local density approximation (LDA) (pure local), Perdew-Becke-Ernzerhof (PBE) (gradient corrected), PBE0, and B3LYP (hybrid), and the Hartree-Fock Hamiltonian are compared. It is shown that very tight computational conditions must be used to obtain well converged results, especially for γxxxx, that is, very sensitive to the number of k points in reciprocal space when the band gap is small (as for LDA and PBE), and to the extension of summations of the exact exchange series (HF and hybrids). The band gap in LDA is only 0.01 eV: at least 300 k points are required to obtain well converged total energy and equilibrium geometry, and 1200 for well converged optical properties. Also, the exchange series convergence is related to the band gap. The PBE0 band gap is as small as 1.4 eV and the exchange summation must extend to about 130 Å from the origin cell. Total energy, band gap, equilibrium geometry, polarizability, and second hyperpolarizability of oligomers -(C2H2)m-, with m up to 50 (202 atoms), and of the polymer have been compared. It turns out that oligomers of that length provide an extremely poor representation of the infinite chain polarizability and hyperpolarizability when the gap is smaller than 0.2 eV (that is, for LDA and PBE). Huge differences are observed on αxx and γxxxx of the polymer when different functionals are used, that is in connection to the well-known density functional theory (DFT) overshoot, reported in the literature about short oligomers: for the infinite model the ratio between LDA (or PBE) and HF becomes even more dramatic (about 500 for αxx and 1010 for γxxxx). On the basis of previous systematic comparisons of results obtained with various approaches including DFT, HF, Moller-Plesset (MP2) and coupled cluster for finite chains, we can argue that, for the infinite chain, the present HF results are the most reliable.

New infinite-dimensional hidden symmetries for heterotic string theory

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

Gao Yajun

The symmetry structures of two-dimensional heterotic string theory are studied further. A (2d+n)x(2d+n) matrix complex H-potential is constructed and the field equations are extended into a complex matrix formulation. A pair of Hauser-Ernst-type linear systems are established. Based on these linear systems, explicit formulations of new hidden symmetry transformations for the considered theory are given and then these symmetry transformations are verified to constitute infinite-dimensional Lie algebras: the semidirect product of the Kac-Moody o(d,d+n-circumflex) and Virasoro algebras (without center charges). These results demonstrate that the heterotic string theory under consideration possesses more and richer symmetry structures than previously expected.

Gauge invariance of excitonic linear and nonlinear optical response

NASA Astrophysics Data System (ADS)

Taghizadeh, Alireza; Pedersen, T. G.

2018-05-01

We study the equivalence of four different approaches to calculate the excitonic linear and nonlinear optical response of multiband semiconductors. These four methods derive from two choices of gauge, i.e., length and velocity gauges, and two ways of computing the current density, i.e., direct evaluation and evaluation via the time-derivative of the polarization density. The linear and quadratic response functions are obtained for all methods by employing a perturbative density-matrix approach within the mean-field approximation. The equivalence of all four methods is shown rigorously, when a correct interaction Hamiltonian is employed for the velocity gauge approaches. The correct interaction is written as a series of commutators containing the unperturbed Hamiltonian and position operators, which becomes equivalent to the conventional velocity gauge interaction in the limit of infinite Coulomb screening and infinitely many bands. As a case study, the theory is applied to hexagonal boron nitride monolayers, and the linear and nonlinear optical response found in different approaches are compared.

Nature of bonding and cooperativity in linear DMSO clusters: A DFT, AIM and NCI analysis.

PubMed

Venkataramanan, Natarajan Sathiyamoorthy; Suvitha, Ambigapathy

2018-05-01

This study aims to cast light on the nature of interactions and cooperativity that exists in linear dimethyl sulfoxide (DMSO) clusters using dispersion corrected density functional theory. In the linear DMSO, DMSO molecules in the middle of the clusters are bound strongly than at the terminal. The plot of the total binding energy of the clusters vs the cluster size and mean polarizabilities vs cluster size shows an excellent linearity demonstrating the presence of cooperativity effect. The computed incremental binding energy of the clusters remains nearly constant, implying that DMSO addition at the terminal site can happen to form an infinite chain. In the linear clusters, two σ-hole at the terminal DMSO molecules were found and the value on it was found to increase with the increase in cluster size. The quantum theory of atoms in molecules topography shows the existence of hydrogen and SO⋯S type in linear tetramer and larger clusters. In the dimer and trimer SO⋯OS type of interaction exists. In 2D non-covalent interactions plot, additional peaks in the regions which contribute to the stabilization of the clusters were observed and it splits in the trimer and intensifies in the larger clusters. In the trimer and larger clusters in addition to the blue patches due to hydrogen bonds, additional, light blue patches were seen between the hydrogen atom of the methyl groups and the sulphur atom of the nearby DMSO molecule. Thus, in addition to the strong H-bonds, strong electrostatic interactions between the sulphur atom and methyl hydrogens exists in the linear clusters. Copyright © 2018 Elsevier Inc. All rights reserved.

Cooperativity of halogen, chalcogen, and pnictogen bonds in infinite molecular chains by electronic structure theory.

PubMed

George, Janine; Deringer, Volker L; Dronskowski, Richard

2014-05-01

Halogen bonds (XBs) are intriguing noncovalent interactions that are frequently being exploited for crystal engineering. Recently, similar bonding mechanisms have been proposed for adjacent main-group elements, and noncovalent "chalcogen bonds" and "pnictogen bonds" have been identified in crystal structures. A fundamental question, largely unresolved thus far, is how XBs and related contacts interact with each other in crystals; similar to hydrogen bonding, one might expect "cooperativity" (bonds amplifying each other), but evidence has been sparse. Here, we explore the crucial step from gas-phase oligomers to truly infinite chains by means of quantum chemical computations. A periodic density functional theory (DFT) framework allows us to address polymeric chains of molecules avoiding the dreaded "cluster effects" as well as the arbitrariness of defining a "large enough" cluster. We focus on three types of molecular chains that we cut from crystal structures; furthermore, we explore reasonable substitutional variants in silico. We find evidence of cooperativity in chains of halogen cyanides and also in similar chalcogen- and pnictogen-bonded systems; the bonds, in the most extreme cases, are amplified through cooperative effects by 79% (I···N), 90% (Te···N), and 103% (Sb···N). Two experimentally known organic crystals, albeit with similar atomic connectivity and XB characteristics, show signs of cooperativity in one case but not in another. Finally, no cooperativity is observed in alternating halogen/acetone and halogen/1,4-dioxane chains; in fact, these XBs weaken each other by up to 26% compared to the respective gas-phase dimers.

Density matrix renormalization group for a highly degenerate quantum system: Sliding environment block approach

NASA Astrophysics Data System (ADS)

Schmitteckert, Peter

2018-04-01

We present an infinite lattice density matrix renormalization group sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct representation of commensurability issues and the treatment of degenerate systems. As an example we apply the method to a spin chain featuring a highly degenerate ground-state space where the new sweeping scheme provides an increase in performance as well as accuracy by many orders of magnitude compared to a recently published work.

Nonlinear distortion of thin liquid sheets

NASA Astrophysics Data System (ADS)

Mehring, Carsten Ralf

Thin planar, annular and conical liquid sheets or films are analyzed, in a unified manner, by means of a reduced- dimension approach providing governing equations for the nonlinear motion of planar and swirling annular thin inviscid and incompressible liquid sheets in zero gravity and with axial disturbances only. Temporal analyses of periodically disturbed infinite sheets are considered, as well as spatial analyses of semi-infinite sheets modulated at the nozzle exit. Results on planar and swirling annular or conical sheets are presented for a zero density ambient gas. Here, conical sheets are obtained in the nearfield of the nozzle exit by considering sheets or films with swirl in excess of that needed to stabilize the discharging stream in its annular configuration. For nonswirling annular sheets a spatially and/or temporally constant gas-core pressure is assumed. A model extension considering the influence of aerodynamic effects on planar sheets is proposed. For planar and annular sheets, linear analyses of the pure initial- and pure boundary-value problem provide insight into the propagation characteristics of dilational and sinuous waves, the (linear) coupling between both wave modes, the stability limits for the annular configuration, as well as the appearance of particular waves on semi-infinite modulated sheets downstream from the nozzle exit. Nonlinear steady-state solutions for the conical configuration (without modulation) are illustrated. Comparison between nonlinear and linear numerical and linear analytical solutions for temporally or spatially developing sheets provides detailed information on the nonlinear distortion characteristics including nonlinear wave propagation and mode-coupling for all the considered geometric configurations and for a variety of parameter configurations. Sensitivity studies on the influence of Weber number, modulation frequency, annular radius, forcing amplitude and sheet divergence on breakup or collapse length and times are reported for modulated semi-infinite annular and conical sheets. Comparisons between the different geometric configurations are made. For periodically disturbed planar sheets, accuracy of the employed reduced-dimension approach is demonstrated by comparison with more accurate two-dimensional vortex dynamics simulations.

Anomalous dynamical phase in quantum spin chains with long-range interactions

NASA Astrophysics Data System (ADS)

Homrighausen, Ingo; Abeling, Nils O.; Zauner-Stauber, Valentin; Halimeh, Jad C.

2017-09-01

The existence or absence of nonanalytic cusps in the Loschmidt-echo return rate is traditionally employed to distinguish between a regular dynamical phase (regular cusps) and a trivial phase (no cusps) in quantum spin chains after a global quench. However, numerical evidence in a recent study (J. C. Halimeh and V. Zauner-Stauber, arXiv:1610.02019) suggests that instead of the trivial phase, a distinct anomalous dynamical phase characterized by a novel type of nonanalytic cusps occurs in the one-dimensional transverse-field Ising model when interactions are sufficiently long range. Using an analytic semiclassical approach and exact diagonalization, we show that this anomalous phase also arises in the fully connected case of infinite-range interactions, and we discuss its defining signature. Our results show that the transition from the regular to the anomalous dynamical phase coincides with Z2-symmetry breaking in the infinite-time limit, thereby showing a connection between two different concepts of dynamical criticality. Our work further expands the dynamical phase diagram of long-range interacting quantum spin chains, and can be tested experimentally in ion-trap setups and ultracold atoms in optical cavities, where interactions are inherently long range.

Magneto-elastic modeling of composites containing chain-structured magnetostrictive particles

NASA Astrophysics Data System (ADS)

Yin, H. M.; Sun, L. Z.; Chen, J. S.

2006-05-01

Magneto-elastic behavior is investigated for two-phase composites containing chain-structured magnetostrictive particles under both magnetic and mechanical loading. To derive the local magnetic and elastic fields, three modified Green's functions are derived and explicitly integrated for the infinite domain containing a spherical inclusion with a prescribed magnetization, body force, and eigenstrain. A representative volume element containing a chain of infinite particles is introduced to solve averaged magnetic and elastic fields in the particles and the matrix. Effective magnetostriction of composites is derived by considering the particle's magnetostriction and the magnetic interaction force. It is shown that there exists an optimal choice of the Young's modulus of the matrix and the volume fraction of the particles to achieve the maximum effective magnetostriction. A transversely isotropic effective elasticity is derived at the infinitesimal deformation. Disregarding the interaction term, this model provides the same effective elasticity as Mori-Tanaka's model. Comparisons of model results with the experimental data and other models show the efficacy of the model and suggest that the particle interactions have a considerable effect on the effective magneto-elastic properties of composites even for a low particle volume fraction.

Matrix Transformations between Certain Sequence Spaces over the Non-Newtonian Complex Field

PubMed Central

Efe, Hakan

2014-01-01

In some cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So the theory of matrix transformations has always been of great interest in the study of sequence spaces. In the present paper, we introduce the matrix transformations in sequence spaces over the field ℂ* and characterize some classes of infinite matrices with respect to the non-Newtonian calculus. Also we give the necessary and sufficient conditions on an infinite matrix transforming one of the classical sets over ℂ* to another one. Furthermore, the concept for sequence-to-sequence and series-to-series methods of summability is given with some illustrated examples. PMID:25110740

On improvement of the series convergence in the problem of the vibrations of orhotropic rectangular prism

NASA Astrophysics Data System (ADS)

Lyashko, A. D.

2017-11-01

A new analytical presentation of the solution for steady-state oscillations of orthotopic rectangular prism is found. The corresponding infinite system of linear algebraic equations has been deduced by the superposition method. A countable set of precise eigenfrequencies and elementary eigenforms is found. The identities are found which make it possible to improve the convergence of all the infinite series in the solution of the problem. All the infinite series in presentation of solution are analytically summed up. Numerical calculations of stresses in the rectangular orthotropic prism with a uniform along the border and harmonic in time load on two opposite faces have been performed.

Finding Optimal Gains In Linear-Quadratic Control Problems

NASA Technical Reports Server (NTRS)

Milman, Mark H.; Scheid, Robert E., Jr.

1990-01-01

Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

Private algebras in quantum information and infinite-dimensional complementarity

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

Crann, Jason, E-mail: jason-crann@carleton.ca; Laboratoire de Mathématiques Paul Painlevé–UMR CNRS 8524, UFR de Mathématiques, Université Lille 1–Sciences et Technologies, 59655 Villeneuve d’Ascq Cédex; Kribs, David W., E-mail: dkribs@uoguelph.ca

We introduce a generalized framework for private quantum codes using von Neumann algebras and the structure of commutants. This leads naturally to a more general notion of complementary channel, which we use to establish a generalized complementarity theorem between private and correctable subalgebras that applies to both the finite and infinite-dimensional settings. Linear bosonic channels are considered and specific examples of Gaussian quantum channels are given to illustrate the new framework together with the complementarity theorem.

Self-dual gravity is completely integrable

NASA Astrophysics Data System (ADS)

Nutku, Y.; Sheftel, M. B.; Kalayci, J.; Yazıcı, D.

2008-10-01

We discover a multi-Hamiltonian structure of a complex Monge-Ampère equation (CMA) set in a real first-order 2-component form. Therefore, by Magri's theorem this is a completely integrable system in four real dimensions. We start with Lagrangian and Hamiltonian densities and obtain a symplectic form and the Hamiltonian operator that determines the Dirac bracket. We have calculated all point symmetries of the 2-component CMA system and Hamiltonians of the symmetry flows. We have found two new real recursion operators for symmetries which commute with the operator of a symmetry condition on solutions of the CMA system. These operators form two Lax pairs for the 2-component system. The recursion operators, applied to the first Hamiltonian operator, generate infinitely many real Hamiltonian structures. We show how to construct an infinite hierarchy of higher commuting flows together with the corresponding infinite chain of their Hamiltonians.

Surface segregation and surface tension of polydisperse polymer melts.

PubMed

Minnikanti, Venkatachala S; Qian, Zhenyu; Archer, Lynden A

2007-04-14

The effect of polydispersity on surface segregation of a lower molecular weight polymer component in a higher molecular weight linear polymer melt host is investigated theoretically. We show that the integrated surface excess zM of a polymer component of molecular weight M satisfies a simple relation zM=2Ue(M/Mw-1)phiM, where Mw is the weight averaged molecular weight, phiM is the polymer volume fraction, and Ue is the attraction of polymer chain ends to the surface. Ue is principally of entropic origin, but also reflects any energetic preference of chain ends to the surface. We further show that the surface tension gammaM of a polydisperse melt of high molar mass components depends on the number average degree of polymerization Mn as, gammaM=gammainfinity+2UerhobRT/Mn. The parameter gammainfinity is the asymptotic surface tension of an infinitely long polymer of the same chemistry, rhob is the bulk density of the polymer, R is the universal gas constant, and T is the temperature. The predicted gammaM compare favorably with surface tension values obtained from self-consistent field theory simulations that include equation of state effects, which account for changes in polymer density with molecular weight. We also compare the predicted surface tension with available experimental data.

Chain-reaction crash on a highway in high visibility

NASA Astrophysics Data System (ADS)

Nagatani, Takashi

2016-05-01

We study the chain-reaction crash (multiple-vehicle collision) in high-visibility condition on a highway. In the traffic situation, drivers control their vehicles by both gear-changing and braking. Drivers change the gears according to the headway and brake according to taillights of the forward vehicle. We investigate whether or not the first collision induces the chain-reaction crash numerically. It is shown that dynamic transitions occur from no collisions, through a single collision, to multiple collisions with decreasing the headway. Also, we find that the dynamic transition occurs from the finite chain reaction to the infinite chain reaction when the headway is less than the critical value. We compare the multiple-vehicle collisions in high-visibility with that in low-visibility. We derive the transition points and the region maps for the chain-reaction crash in high visibility.

Grid-free density functional calculations on periodic systems.

PubMed

Varga, Stefan

2007-09-21

Density fitting scheme is applied to the exchange part of the Kohn-Sham potential matrix in a grid-free local density approximation for infinite systems with translational periodicity. It is shown that within this approach the computational demands for the exchange part scale in the same way as for the Coulomb part. The efficiency of the scheme is demonstrated on a model infinite polymer chain. For simplicity, the implementation with Dirac-Slater Xalpha exchange functional is presented only. Several choices of auxiliary basis set expansion coefficients were tested with both Coulomb and overlap metric. Their effectiveness is discussed also in terms of robustness and norm preservation.

Grid-free density functional calculations on periodic systems

NASA Astrophysics Data System (ADS)

Varga, Štefan

2007-09-01

Density fitting scheme is applied to the exchange part of the Kohn-Sham potential matrix in a grid-free local density approximation for infinite systems with translational periodicity. It is shown that within this approach the computational demands for the exchange part scale in the same way as for the Coulomb part. The efficiency of the scheme is demonstrated on a model infinite polymer chain. For simplicity, the implementation with Dirac-Slater Xα exchange functional is presented only. Several choices of auxiliary basis set expansion coefficients were tested with both Coulomb and overlap metric. Their effectiveness is discussed also in terms of robustness and norm preservation.

Calculation of longitudinal polarizability and second hyperpolarizability of polyacetylene with the coupled perturbed Hartree-Fock/Kohn-Sham scheme: where it is shown how finite oligomer chains tend to the infinite periodic polymer.

PubMed

Lacivita, Valentina; Rèrat, Michel; Orlando, Roberto; Ferrero, Mauro; Dovesi, Roberto

2012-03-21

The longitudinal polarizability, α(xx), and second hyperpolarizability, γ(xxxx), of polyacetylene are evaluated by using the coupled perturbed Hartree-Fock/Kohn-Sham (HF/KS) scheme as implemented in the periodic CRYSTAL code and a split valence type basis set. Four different density functionals, namely local density approximation (LDA) (pure local), Perdew-Becke-Ernzerhof (PBE) (gradient corrected), PBE0, and B3LYP (hybrid), and the Hartree-Fock Hamiltonian are compared. It is shown that very tight computational conditions must be used to obtain well converged results, especially for γ(xxxx), that is, very sensitive to the number of k(->) points in reciprocal space when the band gap is small (as for LDA and PBE), and to the extension of summations of the exact exchange series (HF and hybrids). The band gap in LDA is only 0.01 eV: at least 300 k(->) points are required to obtain well converged total energy and equilibrium geometry, and 1200 for well converged optical properties. Also, the exchange series convergence is related to the band gap. The PBE0 band gap is as small as 1.4 eV and the exchange summation must extend to about 130 Å from the origin cell. Total energy, band gap, equilibrium geometry, polarizability, and second hyperpolarizability of oligomers -(C(2)H(2))(m)-, with m up to 50 (202 atoms), and of the polymer have been compared. It turns out that oligomers of that length provide an extremely poor representation of the infinite chain polarizability and hyperpolarizability when the gap is smaller than 0.2 eV (that is, for LDA and PBE). Huge differences are observed on α(xx) and γ(xxxx) of the polymer when different functionals are used, that is in connection to the well-known density functional theory (DFT) overshoot, reported in the literature about short oligomers: for the infinite model the ratio between LDA (or PBE) and HF becomes even more dramatic (about 500 for α(xx) and 10(10) for γ(xxxx)). On the basis of previous systematic comparisons of results obtained with various approaches including DFT, HF, Moller-Plesset (MP2) and coupled cluster for finite chains, we can argue that, for the infinite chain, the present HF results are the most reliable. © 2012 American Institute of Physics

On the stability of an infinite swept attachment line boundary layer

NASA Technical Reports Server (NTRS)

Hall, P.; Mallik, M. R.; Poll, D. I. A.

1984-01-01

The instability of an infinite swept attachment line boundary layer is considered in the linear regime. The basic three dimensional flow is shown to be susceptible to travelling wave disturbances which propagate along the attachment line. The effect of suction on the instability is discussed and the results suggest that the attachment line boundary layer on a swept wing can be significantly stabilized by extremely small amounts of suction. The results obtained are in excellent agreement with the available experimental observations.

Revealing infinite derivative gravity's true potential: The weak-field limit around de Sitter backgrounds

NASA Astrophysics Data System (ADS)

Edholm, James

2018-03-01

General Relativity is known to produce singularities in the potential generated by a point source. Our universe can be modeled as a de Sitter (dS) metric and we show that ghost-free infinite derivative gravity (IDG) produces a nonsingular potential around a dS background, while returning to the GR prediction at large distances. We also show that although there are an apparently infinite number of coefficients in the theory, only a finite number actually affect the predictions. By writing the linearized equations of motion in a simplified form, we find that at distances below the Hubble length scale, the difference between the IDG potential around a flat background and around a de Sitter background is negligible.

Asymptotically Exact Solution of the Problem of Harmonic Vibrations of an Elastic Parallelepiped

NASA Astrophysics Data System (ADS)

Papkov, S. O.

2017-11-01

An asymptotically exact solution of the classical problem of elasticity about the steadystate forced vibrations of an elastic rectangular parallelepiped is constructed. The general solution of the vibration equations is constructed in the form of double Fourier series with undetermined coefficients, and an infinite system of linear algebraic equations is obtained for determining these coefficients. An analysis of the infinite system permits determining the asymptotics of the unknowns which are used to convolve the double series in both equations of the infinite systems and the displacement and stress components. The efficiency of this approach is illustrated by numerical examples and comparison with known solutions. The spectrum of the parallelepiped symmetric vibrations is studied for various ratios of its sides.

Phylogenetic mixtures and linear invariants for equal input models.

PubMed

Casanellas, Marta; Steel, Mike

2017-04-01

The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).

Yb5Ga2Sb6: a mixed valent and narrow-band gap material in the RE5M2X6 family.

PubMed

Subbarao, Udumula; Sarkar, Sumanta; Gudelli, Vijay Kumar; Kanchana, V; Vaitheeswaran, G; Peter, Sebastian C

2013-12-02

A new compound Yb5Ga2Sb6 was synthesized by the metal flux technique as well as high frequency induction heating. Yb5Ga2Sb6 crystallizes in the orthorhombic space group Pbam (no. 55), in the Ba5Al2Bi6 structure type, with a unit cell of a = 7.2769(2) Å, b = 22.9102(5) Å, c = 4.3984(14) Å, and Z = 2. Yb5Ga2Sb6 has an anisotropic structure with infinite anionic double chains (Ga2Sb6)(10-) cross-linked by Yb(2+) and Yb(3+) ions. Each single chain is made of corner-sharing GaSb4 tetrahedra. Two such chains are bridged by Sb2 groups to form double chains of 1/∞ [Ga2Sb6(10-)]. The compound satisfies the classical Zintl-Klemm concept and is a narrow band gap semiconductor with an energy gap of around 0.36 eV calculated from the electrical resistivity data corroborating with the experimental absorption studies in the IR region (0.3 eV). Magnetic measurements suggest Yb atoms in Yb5Ga2Sb6 exist in the mixed valent state. Temperature dependent magnetic susceptibility data follows the Curie-Weiss behavior above 100 K and no magnetic ordering was observed down to 2 K. Experiments are accompanied by all electron full-potential linear augmented plane wave (FP-LAPW) calculations based on density functional theory to calculate the electronic structure and density of states. The calculated band structure shows a weak overlap of valence band and conduction band resulting in a pseudo gap in the density of states revealing semimetallic character.

Linear Rayleigh-Taylor instability in an accelerated Newtonian fluid with finite width

NASA Astrophysics Data System (ADS)

Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

2018-04-01

The linear theory of Rayleigh-Taylor instability is developed for the case of a viscous fluid layer accelerated by a semi-infinite viscous fluid, considering that the top interface is a free surface. Effects of the surface tensions at both interfaces are taken into account. When viscous effects dominate on surface tensions, an interplay of two mechanisms determines opposite behaviors of the instability growth rate with the thickness of the heavy layer for an Atwood number AT=1 and for sufficiently small values of AT. In the former case, viscosity is a less effective stabilizing mechanism for the thinnest layers. However, the finite thickness of the heavy layer enhances its viscous effects that, in general, prevail on the viscous effects of the semi-infinite medium.

Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing.

PubMed

Xu, Jason; Minin, Vladimir N

2015-07-01

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes.

Efficient Transition Probability Computation for Continuous-Time Branching Processes via Compressed Sensing

PubMed Central

Xu, Jason; Minin, Vladimir N.

2016-01-01

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the discrete state space is large or uncountable. Classical methods such as matrix exponentiation are infeasible for large or countably infinite state spaces, and sampling-based alternatives are computationally intensive, requiring integration over all possible hidden events. Recent work has successfully applied generating function techniques to computing transition probabilities for linear multi-type branching processes. While these techniques often require significantly fewer computations than matrix exponentiation, they also become prohibitive in applications with large populations. We propose a compressed sensing framework that significantly accelerates the generating function method, decreasing computational cost up to a logarithmic factor by only assuming the probability mass of transitions is sparse. We demonstrate accurate and efficient transition probability computations in branching process models for blood cell formation and evolution of self-replicating transposable elements in bacterial genomes. PMID:26949377

Structure of the BBGKY hierarchy near phase transition

NASA Astrophysics Data System (ADS)

Ramanathan, G. V.; Jedrzejek, C.

1980-06-01

A nonperturbative method, as opposed to diagrammatic expansions, is used to study critical phenomena in a fluid with a small hard core and a weak, long-ranged attractive potential. Using the natural small parameter related to the inverse of the range of the attractive potential, spatially uniformly valid asymptotic estimates are made for the magnitudes of all correlations (which are defined as the excess from the generalized superposition approximation) in a region near phase transition in arbitrary number of dimensions. It is shown that if the dimension of the space is larger than four, the correlation hierarchy truncates at the three-body level. The pair correlation satisfies a linear equation. The solution is precisely of Ornstein-Zernike form. For dimensions smaller than four, the hierarchy is still an infinite chain, but considerably simpler than the BBGKY hierarchy. In this case, at the critical point, the correlations are shown to satisfy a scaling law which is the same as that for S4 spin systems.

Flux quench in a system of interacting spinless fermions in one dimension

NASA Astrophysics Data System (ADS)

Nakagawa, Yuya O.; Misguich, Grégoire; Oshikawa, Masaki

2016-05-01

We study a quantum quench in a one-dimensional spinless fermion model (equivalent to the XXZ spin chain), where a magnetic flux is suddenly switched off. This quench is equivalent to imposing a pulse of electric field and therefore generates an initial particle current. This current is not a conserved quantity in the presence of a lattice and interactions, and we investigate numerically its time evolution after the quench, using the infinite time-evolving block decimation method. For repulsive interactions or large initial flux, we find oscillations that are governed by excitations deep inside the Fermi sea. At long times we observe that the current remains nonvanishing in the gapless cases, whereas it decays to zero in the gapped cases. Although the linear response theory (valid for a weak flux) predicts the same long-time limit of the current for repulsive and attractive interactions (relation with the zero-temperature Drude weight), larger nonlinearities are observed in the case of repulsive interactions compared with that of the attractive case.

Towards Stability Analysis of Jump Linear Systems with State-Dependent and Stochastic Switching

NASA Technical Reports Server (NTRS)

Tejada, Arturo; Gonzalez, Oscar R.; Gray, W. Steven

2004-01-01

This paper analyzes the stability of hierarchical jump linear systems where the supervisor is driven by a Markovian stochastic process and by the values of the supervised jump linear system s states. The stability framework for this class of systems is developed over infinite and finite time horizons. The framework is then used to derive sufficient stability conditions for a specific class of hybrid jump linear systems with performance supervision. New sufficient stochastic stability conditions for discrete-time jump linear systems are also presented.

A time scheduling model of logistics service supply chain based on the customer order decoupling point: a perspective from the constant service operation time.

PubMed

Liu, Weihua; Yang, Yi; Xu, Haitao; Liu, Xiaoyan; Wang, Yijia; Liang, Zhicheng

2014-01-01

In mass customization logistics service, reasonable scheduling of the logistics service supply chain (LSSC), especially time scheduling, is benefit to increase its competitiveness. Therefore, the effect of a customer order decoupling point (CODP) on the time scheduling performance should be considered. To minimize the total order operation cost of the LSSC, minimize the difference between the expected and actual time of completing the service orders, and maximize the satisfaction of functional logistics service providers, this study establishes an LSSC time scheduling model based on the CODP. Matlab 7.8 software is used in the numerical analysis for a specific example. Results show that the order completion time of the LSSC can be delayed or be ahead of schedule but cannot be infinitely advanced or infinitely delayed. Obtaining the optimal comprehensive performance can be effective if the expected order completion time is appropriately delayed. The increase in supply chain comprehensive performance caused by the increase in the relationship coefficient of logistics service integrator (LSI) is limited. The relative concern degree of LSI on cost and service delivery punctuality leads to not only changes in CODP but also to those in the scheduling performance of the LSSC.

A Time Scheduling Model of Logistics Service Supply Chain Based on the Customer Order Decoupling Point: A Perspective from the Constant Service Operation Time

PubMed Central

Yang, Yi; Xu, Haitao; Liu, Xiaoyan; Wang, Yijia; Liang, Zhicheng

2014-01-01

In mass customization logistics service, reasonable scheduling of the logistics service supply chain (LSSC), especially time scheduling, is benefit to increase its competitiveness. Therefore, the effect of a customer order decoupling point (CODP) on the time scheduling performance should be considered. To minimize the total order operation cost of the LSSC, minimize the difference between the expected and actual time of completing the service orders, and maximize the satisfaction of functional logistics service providers, this study establishes an LSSC time scheduling model based on the CODP. Matlab 7.8 software is used in the numerical analysis for a specific example. Results show that the order completion time of the LSSC can be delayed or be ahead of schedule but cannot be infinitely advanced or infinitely delayed. Obtaining the optimal comprehensive performance can be effective if the expected order completion time is appropriately delayed. The increase in supply chain comprehensive performance caused by the increase in the relationship coefficient of logistics service integrator (LSI) is limited. The relative concern degree of LSI on cost and service delivery punctuality leads to not only changes in CODP but also to those in the scheduling performance of the LSSC. PMID:24715818

Many-body localization in Ising models with random long-range interactions

NASA Astrophysics Data System (ADS)

Li, Haoyuan; Wang, Jia; Liu, Xia-Ji; Hu, Hui

2016-12-01

We theoretically investigate the many-body localization phase transition in a one-dimensional Ising spin chain with random long-range spin-spin interactions, Vi j∝|i-j |-α , where the exponent of the interaction range α can be tuned from zero to infinitely large. By using exact diagonalization, we calculate the half-chain entanglement entropy and the energy spectral statistics and use them to characterize the phase transition towards the many-body localization phase at infinite temperature and at sufficiently large disorder strength. We perform finite-size scaling to extract the critical disorder strength and the critical exponent of the divergent localization length. With increasing α , the critical exponent experiences a sharp increase at about αc≃1.2 and then gradually decreases to a value found earlier in a disordered short-ranged interacting spin chain. For α <αc , we find that the system is mostly localized and the increase in the disorder strength may drive a transition between two many-body localized phases. In contrast, for α >αc , the transition is from a thermalized phase to the many-body localization phase. Our predictions could be experimentally tested with an ion-trap quantum emulator with programmable random long-range interactions, or with randomly distributed Rydberg atoms or polar molecules in lattices.

Sampled-Data Kalman Filtering and Multiple Model Adaptive Estimation for Infinite-Dimensional Continuous-Time Systems

DTIC Science & Technology

2007-03-01

mathematical frame- 1-6 work of linear algebra and functional analysis [122, 33], while Kalman-Bucy filtering [96, 32] is an especially important...Engineering, Air Force Institute of Technology (AU), Wright- Patterson AFB, Ohio, March 2002. 85. Hoffman, Kenneth and Ray Kunze. Linear Algebra (Second Edition...Engineering, Air Force Institute of Technology (AU), Wright- Patterson AFB, Ohio, December 1989. 189. Strang, Gilbert. Linear Algebra and Its Applications

Effect of debond growth on stress-intensity factors in a cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

NASA Technical Reports Server (NTRS)

Bigelow, C. A.

1986-01-01

Stress-intensity factors are determined for a cracked infinite sheet adhesively bonded to a stringer, and debonding of the adhesive layer is predicted. The stringer is modeled as a semi-infinite sheet. Adhesive nonlinearity is also included. Both the sheet and stringer are treated as homogeneous, orthotropic materials. A set of integral equations is formulated and solved to obtain the adhesive shear stresses and crack-tip stress-intensity factors. Adhesive debonding is predicted using a rupture criterion based on the combined adhesive stresses. When the crack is not under the stringer, the debond extends along the edge of the stringer. When the crack tip is beneath the stringer, the debond grows to the end of the crack, then along the edge of the stringer. Stress levels required for debond initiation decrease as the crack tip is moved beneath the stringer. With a nonlinear adhesive, the debond initiates at higher applied stress levels than in linear adhesive cases. Compared with the linear adhesive solution, modeling a nonlinear adhesive causes the stress-intensity factor to increase when the bond is assumed to remain intact but causes the stress-intensity factor to decrease when debonding is included.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

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.

Acoustic plane wave diffraction from a truncated semi-infinite cone in axial irradiation

NASA Astrophysics Data System (ADS)

Kuryliak, Dozyslav; Lysechko, Victor

2017-11-01

The diffraction problem of the plane acoustic wave on the semi-infinite truncated soft and rigid cones in the case of axial incidence is solved. The problem is formulated as a boundary-value problem in terms of Helmholtz equation, with Dirichlet and Neumann boundary conditions, for scattered velocity potential. The incident field is taken to be the total field of semi-infinite cone, the expression of which is obtained by solving the auxiliary diffraction problem by the use of Kontorovich-Lebedev integral transformation. The diffracted field is sought via the expansion in series of the eigenfunctions for subdomains of the Helmholtz equation taking into account the edge condition. The corresponding diffraction problem is reduced to infinite system of linear algebraic equations (ISLAE) making use of mode matching technique and orthogonality properties of the Legendre functions. The method of analytical regularization is applied in order to extract the singular part in ISLAE, invert it exactly and reduce the problem to ISLAE of the second kind, which is readily amenable to calculation. The numerical solution of this system relies on the reduction method; and its accuracy depends on the truncation order. The case of degeneration of the truncated semi-infinite cone into an aperture in infinite plane is considered. Characteristic features of diffracted field in near and far fields as functions of cone's parameters are examined.

3-Benzyl­sulfanyl-1H-1,2,4-triazol-5-amine

PubMed Central

Zhang, Shuai; Liu, Pei-Jiang; Ma, Dong-Sheng; Hou, Guang-Feng

2012-01-01

In the title mol­ecule, C9H10N4S, the dihedral angle between the benzene and triazole rings is 81.05 (5)°. In the crystal, N—H⋯N hydrogen bonds link the mol­ecules into infinite zigzag chains along [010]. PMID:22259582

Eigenenergies of a Relativistic Particle in an Infinite Range Linear Potential Using WKB Method

ERIC Educational Resources Information Center

Shivalingaswamy, T.; Kagali, B. A.

2011-01-01

Energy eigenvalues for a non-relativistic particle in a linear potential well are available. In this paper we obtain the eigenenergies for a relativistic spin less particle in a similar potential using an extension of the well-known WKB method treating the potential as the time component of a four-vector potential. Since genuine bound states do…

Chandrasekhar equations for infinite dimensional systems

NASA Technical Reports Server (NTRS)

Ito, K.; Powers, R.

1985-01-01

The existence of Chandrasekhar equations for linear time-invariant systems defined on Hilbert spaces is investigated. An important consequence is that the solution to the evolutional Riccati equation is strongly differentiable in time, and that a strong solution of the Riccati differential equation can be defined. A discussion of the linear-quadratic optimal-control problem for hereditary differential systems is also included.

Tunnel current across linear homocatenated germanium chains

NASA Astrophysics Data System (ADS)

Matsuura, Yukihito

2014-01-01

The electronic transport properties of germanium oligomers catenating into linear chains (linear Ge chains) have been theoretically studied using first principle methods. The conduction mechanism of a Ge chain sandwiched between gold electrodes was analyzed based on the density of states and the eigenstates of the molecule in a two-probe environment. Like that of silicon chains (Si chains), the highest occupied molecular orbital of Ge chains contains the extended σ-conjugation of Ge 4p orbitals at energy levels close to the Fermi level; this is in contrast to the electronic properties of linear carbon chains. Furthermore, the conductance of a Ge chain is expected to decrease exponentially with molecular length L. The decay constant β, which is defined as e-βL, of a Ge chain is similar to that of a Si chain, whereas the conductance of the Ge chains is higher than that of Si chains even though the Ge-Ge bond length is longer than the Si-Si bond length.

Mechanism Underlying IκB Kinase Activation Mediated by the Linear Ubiquitin Chain Assembly Complex

PubMed Central

Fujita, Hiroaki; Akita, Mariko; Kato, Ryuichi; Sasaki, Yoshiteru; Wakatsuki, Soichi

2014-01-01

The linear ubiquitin chain assembly complex (LUBAC) ligase, consisting of HOIL-1L, HOIP, and SHARPIN, specifically generates linear polyubiquitin chains. LUBAC-mediated linear polyubiquitination has been implicated in NF-κB activation. NEMO, a component of the IκB kinase (IKK) complex, is a substrate of LUBAC, but the precise molecular mechanism underlying linear chain-mediated NF-κB activation has not been fully elucidated. Here, we demonstrate that linearly polyubiquitinated NEMO activates IKK more potently than unanchored linear chains. In mutational analyses based on the crystal structure of the complex between the HOIP NZF1 and NEMO CC2-LZ domains, which are involved in the HOIP-NEMO interaction, NEMO mutations that impaired linear ubiquitin recognition activity and prevented recognition by LUBAC synergistically suppressed signal-induced NF-κB activation. HOIP NZF1 bound to NEMO and ubiquitin simultaneously, and HOIP NZF1 mutants defective in interaction with either NEMO or ubiquitin could not restore signal-induced NF-κB activation. Furthermore, linear chain-mediated activation of IKK2 involved homotypic interaction of the IKK2 kinase domain. Collectively, these results demonstrate that linear polyubiquitination of NEMO plays crucial roles in IKK activation and that this modification involves the HOIP NZF1 domain and recognition of NEMO-conjugated linear ubiquitin chains by NEMO on another IKK complex. PMID:24469399

Monte Carlo simulation of star/linear and star/star blends with chemically identical monomers

NASA Astrophysics Data System (ADS)

Theodorakis, P. E.; Avgeropoulos, A.; Freire, J. J.; Kosmas, M.; Vlahos, C.

2007-11-01

The effects of chain size and architectural asymmetry on the miscibility of blends with chemically identical monomers, differing only in their molecular weight and architecture, are studied via Monte Carlo simulation by using the bond fluctuation model. Namely, we consider blends composed of linear/linear, star/linear and star/star chains. We found that linear/linear blends are more miscible than the corresponding star/star mixtures. In star/linear blends, the increase in the volume fraction of the star chains increases the miscibility. For both star/linear and star/star blends, the miscibility decreases with the increase in star functionality. When we increase the molecular weight of linear chains of star/linear mixtures the miscibility decreases. Our findings are compared with recent analytical and experimental results.

Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries

NASA Astrophysics Data System (ADS)

Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

2018-05-01

A recent article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs, which have infinite-dimensional Lie point symmetry groups due to the linear superposition principle. Their symmetry algebra always contains a two-dimensional subalgebra realized by linearly connected vector fields. We identify all classes of linear first-order DODSs that have additional symmetries, not due to linearity alone, and we present representatives of each class. These additional symmetries are then used to construct exact analytical particular solutions using symmetry reduction.

Micromechanics-based magneto-elastic constitutive modeling of particulate composites

NASA Astrophysics Data System (ADS)

Yin, Huiming

Modified Green's functions are derived for three situations: a magnetic field caused by a local magnetization, a displacement field caused by a local body force and a displacement field caused by a local prescribed eigenstrain. Based on these functions, an explicit solution is derived for two magnetic particles embedded in the infinite medium under external magnetic and mechanical loading. A general solution for numerable magnetic particles embedded in an infinite domain is then provided in integral form. Two-phase composites containing spherical magnetic particles of the same size are considered for three kinds of microstructures. With chain-structured composites, particle interactions in the same chain are considered and a transversely isotropic effective elasticity is obtained. For periodic composites, an eight-particle interaction model is developed and provides a cubic symmetric effective elasticity. In the random composite, pair-wise particle interactions are integrated from all possible positions and an isotropic effective property is reached. This method is further extended to functionally graded composites. Magneto-mechanical behavior is studied for the chain-structured composite and the random composite. Effective magnetic permeability, effective magnetostriction and field-dependent effective elasticity are investigated. It is seen that the chain-structured composite is more sensitive to the magnetic field than the random composite; a composite consisting of only 5% of chain-structured particles can provide a larger magnetostriction and a larger change of effective elasticity than an equivalent composite consisting of 30% of random dispersed particles. Moreover, the effective shear modulus of the chain-structured composite rapidly increases with the magnetic field, while that for the random composite decreases. An effective hyperelastic constitutive model is further developed for a magnetostrictive particle-filled elastomer, which is sampled by using a network of body-centered cubic lattices of particles connected by macromolecular chains. The proposed hyperelastic model is able to characterize overall nonlinear elastic stress-stretch relations of the composites under general three-dimensional loading. It is seen that the effective strain energy density is proportional to the length of stretched chains in unit volume and volume fraction of particles.

Existence of Hartree-Fock excited states for atoms and molecules

NASA Astrophysics Data System (ADS)

Lewin, Mathieu

2018-04-01

For neutral and positively charged atoms and molecules, we prove the existence of infinitely many Hartree-Fock critical points below the first energy threshold (that is, the lowest energy of the same system with one electron removed). This is the equivalent, in Hartree-Fock theory, of the famous Zhislin-Sigalov theorem which states the existence of infinitely many eigenvalues below the bottom of the essential spectrum of the N-particle linear Schrödinger operator. Our result improves a theorem of Lions in 1987 who already constructed infinitely many Hartree-Fock critical points, but with much higher energy. Our main contribution is the proof that the Hartree-Fock functional satisfies the Palais-Smale property below the first energy threshold. We then use minimax methods in the N-particle space, instead of working in the one-particle space.

Complete devil's staircase and crystal-superfluid transitions in a dipolar XXZ spin chain: a trapped ion quantum simulation

NASA Astrophysics Data System (ADS)

Hauke, Philipp; Cucchietti, Fernando M.; Müller-Hermes, Alexander; Bañuls, Mari-Carmen; Cirac, J. Ignacio; Lewenstein, Maciej

2010-11-01

Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many metastable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional (1D) model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization and quasi-exact numerical techniques (density-matrix renormalization group and infinite time-evolving block decimation). We find that the complete devil's staircase—an infinite sequence of crystal states existing at vanishing tunneling—spreads to a succession of lobes similar to the Mott lobes found in Bose-Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar 2D models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long-range (algebraic) correlations, as opposed to models with nearest-neighbor tunneling, that show exponential decay of correlations.

Crystal structures of 4-meth-oxy-N-(4-methyl-phenyl)benzene-sulfonamide and N-(4-fluoro-phenyl)-4-meth-oxy-benzene-sulfonamide.

PubMed

Rodrigues, Vinola Z; Preema, C P; Naveen, S; Lokanath, N K; Suchetan, P A

2015-11-01

Crystal structures of two N-(ar-yl)aryl-sulfonamides, namely, 4-meth-oxy-N-(4-methyl-phen-yl)benzene-sulfonamide, C14H15NO3S, (I), and N-(4-fluoro-phen-yl)-4-meth-oxy-benzene-sulfonamide, C13H12FNO3S, (II), were determined and analyzed. In (I), the benzene-sulfonamide ring is disordered over two orientations, in a 0.516 (7):0.484 (7) ratio, which are inclined to each other at 28.0 (1)°. In (I), the major component of the sulfonyl benzene ring and the aniline ring form a dihedral angle of 63.36 (19)°, while in (II), the planes of the two benzene rings form a dihedral angle of 44.26 (13)°. In the crystal structure of (I), N-H⋯O hydrogen bonds form infinite C(4) chains extended in [010], and inter-molecular C-H⋯πar-yl inter-actions link these chains into layers parallel to the ab plane. The crystal structure of (II) features N-H⋯O hydrogen bonds forming infinite one dimensional C(4) chains along [001]. Further, a pair of C-H⋯O inter-molecular inter-actions consolidate the crystal packing of (II) into a three-dimensional supra-molecular architecture.

On Discontinuous Piecewise Linear Models for Memristor Oscillators

NASA Astrophysics Data System (ADS)

Amador, Andrés; Freire, Emilio; Ponce, Enrique; Ros, Javier

2017-06-01

In this paper, we provide for the first time rigorous mathematical results regarding the rich dynamics of piecewise linear memristor oscillators. In particular, for each nonlinear oscillator given in [Itoh & Chua, 2008], we show the existence of an infinite family of invariant manifolds and that the dynamics on such manifolds can be modeled without resorting to discontinuous models. Our approach provides topologically equivalent continuous models with one dimension less but with one extra parameter associated to the initial conditions. It is possible to justify the periodic behavior exhibited by three-dimensional memristor oscillators, by taking advantage of known results for planar continuous piecewise linear systems. The analysis developed not only confirms the numerical results contained in previous works [Messias et al., 2010; Scarabello & Messias, 2014] but also goes much further by showing the existence of closed surfaces in the state space which are foliated by periodic orbits. The important role of initial conditions that justify the infinite number of periodic orbits exhibited by these models, is stressed. The possibility of unsuspected bistable regimes under specific configurations of parameters is also emphasized.

Wronskian solutions of the T-, Q- and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl (M | N)

NASA Astrophysics Data System (ADS)

Tsuboi, Zengo

2013-05-01

In [1] (Z. Tsuboi, Nucl. Phys. B 826 (2010) 399, arxiv:arXiv:0906.2039), we proposed Wronskian-like solutions of the T-system for [ M , N ]-hook of the general linear superalgebra gl (M | N). We have generalized these Wronskian-like solutions to the ones for the general T-hook, which is a union of [M1 ,N1 ]-hook and [M2 ,N2 ]-hook (M =M1 +M2, N =N1 +N2). These solutions are related to Weyl-type supercharacter formulas of infinite dimensional unitarizable modules of gl (M | N). Our solutions also include a Wronskian-like solution discussed in [2] (N. Gromov, V. Kazakov, S. Leurent, Z. Tsuboi, JHEP 1101 (2011) 155, arxiv:arXiv:1010.2720) in relation to the AdS5 /CFT4 spectral problem.

From Newton's Law to the Linear Boltzmann Equation Without Cut-Off

NASA Astrophysics Data System (ADS)

Ayi, Nathalie

2017-03-01

We provide a rigorous derivation of the linear Boltzmann equation without cut-off starting from a system of particles interacting via a potential with infinite range as the number of particles N goes to infinity under the Boltzmann-Grad scaling. More particularly, we will describe the motion of a tagged particle in a gas close to global equilibrium. The main difficulty in our context is that, due to the infinite range of the potential, a non-integrable singularity appears in the angular collision kernel, making no longer valid the single-use of Lanford's strategy. Our proof relies then on a combination of Lanford's strategy, of tools developed recently by Bodineau, Gallagher and Saint-Raymond to study the collision process, and of new duality arguments to study the additional terms associated with the long-range interaction, leading to some explicit weak estimates.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

Intertwining solutions for magnetic relativistic Hartree type equations

NASA Astrophysics Data System (ADS)

Cingolani, Silvia; Secchi, Simone

2018-05-01

We consider the magnetic pseudo-relativistic Schrödinger equation where , m  >  0, is an external continuous scalar potential, is a continuous vector potential and is a convolution kernel, is a constant, , . We assume that A and V are symmetric with respect to a closed subgroup G of the group of orthogonal linear transformations of . If for any , the cardinality of the G-orbit of x is infinite, then we prove the existence of infinitely many intertwining solutions assuming that is either linear in x or uniformly bounded. The results are proved by means of a new local realization of the square root of the magnetic laplacian to a local elliptic operator with Neumann boundary condition on a half-space. Moreover we derive an existence result of a ground state intertwining solution for bounded vector potentials, if G admits a finite orbit.

Linear regulator design for stochastic systems by a multiple time scales method

NASA Technical Reports Server (NTRS)

Teneketzis, D.; Sandell, N. R., Jr.

1976-01-01

A hierarchically-structured, suboptimal controller for a linear stochastic system composed of fast and slow subsystems is considered. The controller is optimal in the limit as the separation of time scales of the subsystems becomes infinite. The methodology is illustrated by design of a controller to suppress the phugoid and short period modes of the longitudinal dynamics of the F-8 aircraft.

Chandrasekhar equations for infinite dimensional systems

NASA Technical Reports Server (NTRS)

Ito, K.; Powers, R. K.

1985-01-01

Chandrasekhar equations are derived for linear time invariant systems defined on Hilbert spaces using a functional analytic technique. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a strong solution of the Riccati differential equation. A detailed discussion on the linear quadratic optimal control problem for hereditary differential systems is also included.

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

Suhara, Tadahiro; Kanada-En'yo, Yoshiko

We investigate the linear-chain structures in highly excited states of {sup 14}C using a generalized molecular-orbital model, by which we incorporate an asymmetric configuration of three {alpha} clusters in the linear-chain states. By applying this model to the {sup 14}C system, we study the {sup 10}Be+{alpha} correlation in the linear-chain state of {sup 14}C. To clarify the origin of the {sup 10}Be+{alpha} correlation in the {sup 14}C linear-chain state, we analyze linear 3 {alpha} and 3{alpha} + n systems in a similar way. We find that a linear 3{alpha} system prefers the asymmetric 2{alpha} + {alpha} configuration, whose origin ismore » the many-body correlation incorporated by the parity projection. This configuration causes an asymmetric mean field for two valence neutrons, which induces the concentration of valence neutron wave functions around the correlating 2{alpha}. A linear-chain structure of {sup 16}C is also discussed.« less

Teaching Wave Propagation and the Emergence of Viete's Formula

ERIC Educational Resources Information Center

Cullerne, J. P.; Goekjian, M. C. Dunn

2012-01-01

The well-known result for the frequency of a simple spring-mass system may be combined with elementary concepts like speed = wavelength x frequency to obtain wave propagation speeds for an infinite chain of springs and masses (masses "m" held apart at equilibrium distance "a" by springs of stiffness "gamma"). These propagation speeds are dependent…

1-Benzyl-2-(1H-indol-3-yl)-5-oxo-pyrrolidine-2-carbonitrile.

PubMed

Tamazyan, Rafael; Armen, Ayvazyan; Ashot, Martirosyan; Sahak, Gasparyan; Schinazi, Raymond

2008-01-04

In the title compound, C(20)H(17)N(3)O, a potential anti-human immunodeficiency virus type 1 (HIV-1) non-nucleoside reverse-transcriptase inhibitor, the pyrrolidine ring has an envelope conformation. In the crystal structure, adjacent mol-ecules are connected into infinite chains via an N-H⋯O hydrogen bond.

A mechanical comparison of linear and double-looped hung supplemental heavy chain resistance to the back squat: a case study.

PubMed

Neelly, Kurt R; Terry, Joseph G; Morris, Martin J

2010-01-01

A relatively new and scarcely researched technique to increase strength is the use of supplemental heavy chain resistance (SHCR) in conjunction with plate weights to provide variable resistance to free weight exercises. The purpose of this case study was to determine the actual resistance being provided by a double-looped versus a linear hung SHCR to the back squat exercise. The linear technique simply hangs the chain directly from the bar, whereas the double-looped technique uses a smaller chain to adjust the height of the looped chain. In both techniques, as the squat descends, chain weight is unloaded onto the floor, and as the squat ascends, chain weight is progressively loaded back as resistance. One experienced and trained male weight lifter (age = 33 yr; height = 1.83 m; weight = 111.4 kg) served as the subject. Plate weight was set at 84.1 kg, approximately 50% of the subject's 1 repetition maximum. The SHCR was affixed to load cells, sampling at a frequency of 500 Hz, which were affixed to the Olympic bar. Data were collected as the subject completed the back squat under the following conditions: double-looped 1 chain (9.6 kg), double-looped 2 chains (19.2 kg), linear 1 chain, and linear 2 chains. The double-looped SHCR resulted in a 78-89% unloading of the chain weight at the bottom of the squat, whereas the linear hanging SHCR resulted in only a 36-42% unloading. The double-looped technique provided nearly 2 times the variable resistance at the top of the squat compared with the linear hanging technique, showing that attention must be given to the technique used to hang SHCR.

Catena-poly[[bis(1H-benzotriazole-kappaN3)cobalt(II)]-di-mu-tricyanomethanido-kappa2N:N'] and catena-poly[[bis(3,5-dimethyl-1H-pyrazole-kappaN2)manganese(II)]-di-mu-tricyanomethanido-kappa2N:N'].

PubMed

Shao, Ze-Huai; Luo, Jun; Cai, Rui-Fang; Zhou, Xi-Geng; Weng, Lin-Hong; Chen, Zhen-Xia

2004-06-01

Two new one-dimensional coordination polymers, viz. the title compounds, [Co[C(CN)(3)](2)(C(6)H(5)N(3))(2)](n), (I), and [Mn[C(CN)(3)](2)(C(5)H(8)N(2))(2)](n), (II), have been synthesized and characterized by X-ray diffraction. Both complexes consist of linear chains with double 1,5-tricyanomethanide bridges between neighbouring divalent metal ions. The Co and Mn atoms are located on centres of inversion. In (I), the coordination environment of the Co(II) atom is that of an elongated octahedron. The Co(II) atom is coordinated in the equatorial plane by four nitrile N atoms of four bridging tricyanomethanide ions, with Co-N distances of 2.106 (2) and 2.110 (2) A, and in the apical positions by two N atoms from the benzotriazole ligands, with a Co-N distance of 2.149 (2) A. The [Co[C(CN)(3)](2)(C(6)H(5)N(3))(2)] units form infinite chains extending along the a axis. These chains are crosslinked via a hydrogen bond between the uncoordinated nitrile N atom of a tricyanomethanide anion and the H atom on the uncoordinated N atom of a benzotriazole ligand from an adjacent chain, thus forming a three-dimensional network structure. In (II), the Mn(II) atom also adopts a slightly distorted octahedral geometry, with four nitrile N atoms of tricyanomethanide ligands [Mn-N = 2.226 (2) and 2.227 (2) A] in equatorial positions and two N atoms of the monodentate 3,5-dimethylpyrazole ligands [Mn-N = 2.231 (2) A] in the axial sites. In (II), one-dimensional polymeric chains extending along the b axis are formed, with tricyanomethanide anions acting as bidentate bridging ligands. A hydrogen bond between the uncoordinated nitrile N atom of the tricyanomethanide ligand and the H atom on the uncoordinated N atom of a 3,5-dimethylpyrazole group from a neighbouring chain links the molecule into a two-dimensional layered structure.

Analysis of Nuclear Factor-κB (NF-κB) Essential Modulator (NEMO) Binding to Linear and Lysine-linked Ubiquitin Chains and Its Role in the Activation of NF-κB*

PubMed Central

Kensche, Tobias; Tokunaga, Fuminori; Ikeda, Fumiyo; Goto, Eiji; Iwai, Kazuhiro; Dikic, Ivan

2012-01-01

Nuclear factor-κB (NF-κB) essential modulator (NEMO), a component of the inhibitor of κB kinase (IKK) complex, controls NF-κB signaling by binding to ubiquitin chains. Structural studies of NEMO provided a rationale for the specific binding between the UBAN (ubiquitin binding in ABIN and NEMO) domain of NEMO and linear (Met-1-linked) di-ubiquitin chains. Full-length NEMO can also interact with Lys-11-, Lys-48-, and Lys-63-linked ubiquitin chains of varying length in cells. Here, we show that purified full-length NEMO binds preferentially to linear ubiquitin chains in competition with lysine-linked ubiquitin chains of defined length, including long Lys-63-linked deca-ubiquitins. Linear di-ubiquitins were sufficient to activate both the IKK complex in vitro and to trigger maximal NF-κB activation in cells. In TNFα-stimulated cells, NEMO chimeras engineered to bind exclusively to Lys-63-linked ubiquitin chains mediated partial NF-κB activation compared with cells expressing NEMO that binds to linear ubiquitin chains. We propose that NEMO functions as a high affinity receptor for linear ubiquitin chains and a low affinity receptor for long lysine-linked ubiquitin chains. This phenomenon could explain quantitatively distinct NF-κB activation patterns in response to numerous cell stimuli. PMID:22605335

Translational Dielectric Friction on a Chain of Charged Spheres

PubMed Central

Boughammoura, Sondès; M'halla, Jalel

2014-01-01

We have proved in details that the dielectric friction remains the principal frictional effect for a stretched polyion modeled as a chain of charged spheres, whereas, in the case of Manning's model (infinite thread with a continuous distribution of charge), this friction effect is nonexistent. According to this chain model, it is therefore possible to detect by conductivity measurements any transition from a coiled configuration (ellipsoidal model) to a stretched configuration during dilution process. We have also underlined the important interdependence between the dielectric friction and the ionic condensation of the counterions, in order to distinguish between the Ostwald regime and the Manning regime for which the degree of condensation is practically constant in a large range of concentrations. PMID:24672333

The consistency of positive fully fuzzy linear system

NASA Astrophysics Data System (ADS)

Malkawi, Ghassan O.; Alfifi, Hassan Y.

2017-11-01

In this paper, the consistency of fuzziness of positive solution of the n × n fully fuzzy linear system (P - FFLS) is studied based on its associated linear system (P - ALS). That can consist of the whole entries of triangular fuzzy numbers in a linear system without fuzzy operations. The nature of solution is differentiated in case of fuzzy solution, non-fuzzy solution and fuzzy non-positive solution. Moreover, the analysis reveals that the P - ALS is applicable to provide the set of infinite number of solutions. Numerical examples are presented to illustrate the proposed analysis.

Representing Lumped Markov Chains by Minimal Polynomials over Field GF(q)

NASA Astrophysics Data System (ADS)

Zakharov, V. M.; Shalagin, S. V.; Eminov, B. F.

2018-05-01

A method has been proposed to represent lumped Markov chains by minimal polynomials over a finite field. The accuracy of representing lumped stochastic matrices, the law of lumped Markov chains depends linearly on the minimum degree of polynomials over field GF(q). The method allows constructing the realizations of lumped Markov chains on linear shift registers with a pre-defined “linear complexity”.

Hypercyclic subspaces for Frechet space operators

NASA Astrophysics Data System (ADS)

Petersson, Henrik

2006-07-01

A continuous linear operator is hypercyclic if there is an such that the orbit {Tnx} is dense, and such a vector x is said to be hypercyclic for T. Recent progress show that it is possible to characterize Banach space operators that have a hypercyclic subspace, i.e., an infinite dimensional closed subspace of, except for zero, hypercyclic vectors. The following is known to hold: A Banach space operator T has a hypercyclic subspace if there is a sequence (ni) and an infinite dimensional closed subspace such that T is hereditarily hypercyclic for (ni) and Tni->0 pointwise on E. In this note we extend this result to the setting of Frechet spaces that admit a continuous norm, and study some applications for important function spaces. As an application we also prove that any infinite dimensional separable Frechet space with a continuous norm admits an operator with a hypercyclic subspace.

On optimal infinite impulse response edge detection filters

NASA Technical Reports Server (NTRS)

Sarkar, Sudeep; Boyer, Kim L.

1991-01-01

The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient, has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

Chandrasekhar equations for infinite dimensional systems. Part 2: Unbounded input and output case

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Powers, Robert K.

1987-01-01

A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and the existence, uniqueness, and regularity of the results of their solutions established.

Molecular Dynamics Simulation Studies of Fracture in Two Dimensions

DTIC Science & Technology

1980-05-01

reversibility of trajectories. The microscopic elastic constants, dispersion relation and phonon spectrum of the system were determined by lattice dynamics. These... linear elasticity theory of a two-dimensional crack embedded in an infinite medium. System con- sists of 436 particles arranged in a tri- angular lattice ...satisfying these demands. In evaluating the mechanical energy of his model, Griffith used a result from linear elasticity theory, namely that for any body

Probability distributions for Markov chain based quantum walks

NASA Astrophysics Data System (ADS)

Balu, Radhakrishnan; Liu, Chaobin; Venegas-Andraca, Salvador E.

2018-01-01

We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the probability distribution on the states of the underlying Markov chain is always convergent in the Cesaro sense. In particular, we deduce that the limiting distribution is uniform if the transition matrix is symmetric. In the case of a non-symmetric Markov chain, we exemplify that the limiting distribution of the quantum walk is not necessarily identical with the stationary distribution of the underlying irreducible Markov chain. The Szegedy scheme can be extended to infinite state Markov chains (random walks). In the second part, we formulate the quantum walk induced from a lazy random walk on the line. We then obtain the weak limit of the quantum walk. It is noted that the current quantum walk appears to spread faster than its counterpart-quantum walk on the line driven by the Grover coin discussed in literature. The paper closes with an outlook on possible future directions.

The E3 ligase HOIP specifies linear ubiquitin chain assembly through its RING-IBR-RING domain and the unique LDD extension

PubMed Central

Smit, Judith J; Monteferrario, Davide; Noordermeer, Sylvie M; van Dijk, Willem J; van der Reijden, Bert A; Sixma, Titia K

2012-01-01

Activation of the NF-κB pathway requires the formation of Met1-linked ‘linear' ubiquitin chains on NEMO, which is catalysed by the Linear Ubiquitin Chain Assembly Complex (LUBAC) E3 consisting of HOIP, HOIL-1L and Sharpin. Here, we show that both LUBAC catalytic activity and LUBAC specificity for linear ubiquitin chain formation are embedded within the RING-IBR-RING (RBR) ubiquitin ligase subunit HOIP. Linear ubiquitin chain formation by HOIP proceeds via a two-step mechanism involving both RING and HECT E3-type activities. RING1-IBR catalyses the transfer of ubiquitin from the E2 onto RING2, to transiently form a HECT-like covalent thioester intermediate. Next, the ubiquitin is transferred from HOIP onto the N-terminus of a target ubiquitin. This transfer is facilitated by a unique region in the C-terminus of HOIP that we termed ‘Linear ubiquitin chain Determining Domain' (LDD), which may coordinate the acceptor ubiquitin. Consistent with this mechanism, the RING2-LDD region was found to be important for NF-κB activation in cellular assays. These data show how HOIP combines a general RBR ubiquitin ligase mechanism with unique, LDD-dependent specificity for producing linear ubiquitin chains. PMID:22863777

Localization and elasticity in entangled polymer liquids as a mesoscopic glass transition

NASA Astrophysics Data System (ADS)

Schweizer, Kenneth

2010-03-01

The reptation-tube model is widely viewed as the correct zeroth order model for entangled linear polymer dynamics under quiescent conditions. Its key ansatz is the existence of a mesoscopic dynamical length scale that prohibits transverse chain motion beyond a tube diameter of order 3-10 nm. However, the theory is phenomenological and lacks a microscopic foundation, and many fundamental questions remain unanswered. These include: (i) where does the confining tube field come from and can it be derived from statistical mechanics? (ii) what is the microscopic origin of the magnitude, and power law scaling with concentration and packing length, of the plateau shear modulus? (iii) is the tube diameter time-dependent? (iv) does the confinement field contribute to elasticity ? (v) do entanglement constraints have a finite strength? Building on our new force-level theories for the dynamical crossover and activated barrier hopping in glassy colloidal suspensions and polymer melts, a first principles self-consistent theory has been developed for entangled polymers. Its basic physical elements, and initial results that address the questions posed above, will be presented. The key idea is that beyond a critical degree of polymerization, the chain connectivity and excluded volume induced intermolecular correlation hole drives temporary localization on an intermediate length scale resulting in a mesoscopic ``ideal kinetic glass transition.'' Large scale isotropic motion is effectively quenched due to the emergence of chain length dependent entropic barriers. However, the barrier height is not infinite, resulting in softening of harmonic localization at large displacements, temporal increase of the confining length scale, and a finite strength of entanglement constraints which can be destroyed by applied stress.

Linear ubiquitin chains: enzymes, mechanisms and biology

PubMed Central

2017-01-01

Ubiquitination is a versatile post-translational modification that regulates a multitude of cellular processes. Its versatility is based on the ability of ubiquitin to form multiple types of polyubiquitin chains, which are recognized by specific ubiquitin receptors to induce the required cellular response. Linear ubiquitin chains are linked through Met 1 and have been established as important players of inflammatory signalling and apoptotic cell death. These chains are generated by a ubiquitin E3 ligase complex called the linear ubiquitin chain assembly complex (LUBAC) that is thus far the only E3 ligase capable of forming linear ubiquitin chains. The complex consists of three subunits, HOIP, HOIL-1L and SHARPIN, each of which have specific roles in the observed biological functions of LUBAC. Furthermore, LUBAC has been found to be associated with OTULIN and CYLD, deubiquitinases that disassemble linear chains and counterbalance the E3 ligase activity of LUBAC. Gene mutations in HOIP, HOIL-1L and OTULIN are found in human patients who suffer from autoimmune diseases, and HOIL-1L mutations are also found in myopathy patients. In this paper, we discuss the mechanisms of linear ubiquitin chain generation and disassembly by their respective enzymes and review our current understanding of their biological functions and association with human diseases. PMID:28446710

Linear ubiquitin chains: enzymes, mechanisms and biology.

PubMed

Rittinger, Katrin; Ikeda, Fumiyo

2017-04-01

Ubiquitination is a versatile post-translational modification that regulates a multitude of cellular processes. Its versatility is based on the ability of ubiquitin to form multiple types of polyubiquitin chains, which are recognized by specific ubiquitin receptors to induce the required cellular response. Linear ubiquitin chains are linked through Met 1 and have been established as important players of inflammatory signalling and apoptotic cell death. These chains are generated by a ubiquitin E3 ligase complex called the linear ubiquitin chain assembly complex (LUBAC) that is thus far the only E3 ligase capable of forming linear ubiquitin chains. The complex consists of three subunits, HOIP, HOIL-1L and SHARPIN, each of which have specific roles in the observed biological functions of LUBAC. Furthermore, LUBAC has been found to be associated with OTULIN and CYLD, deubiquitinases that disassemble linear chains and counterbalance the E3 ligase activity of LUBAC. Gene mutations in HOIP, HOIL-1L and OTULIN are found in human patients who suffer from autoimmune diseases, and HOIL-1L mutations are also found in myopathy patients. In this paper, we discuss the mechanisms of linear ubiquitin chain generation and disassembly by their respective enzymes and review our current understanding of their biological functions and association with human diseases. © 2017 The Authors.

1-Benzyl-2-(1H-indol-3-yl)-5-oxo­pyrrolidine-2-carbonitrile

PubMed Central

Tamazyan, Rafael; Armen, Ayvazyan; Ashot, Martirosyan; Sahak, Gasparyan; Schinazi, Raymond

2008-01-01

In the title compound, C20H17N3O, a potential anti-human immunodeficiency virus type 1 (HIV-1) non-nucleoside reverse-transcriptase inhibitor, the pyrrolidine ring has an envelope conformation. In the crystal structure, adjacent mol­ecules are connected into infinite chains via an N—H⋯O hydrogen bond. PMID:21201400

Structure and magnetism of a new hydrogen-bonded layered cobalt(II) network, constructed by the unprecedented carboxylate-phosphinate ligand [O2(C6H5)PCH2CO2]2-.

PubMed

Midollini, Stefano; Orlandini, Annabella; Rosa, Patrick; Sorace, Lorenzo

2005-03-21

By hydrothermal reaction of CoCl2 x 6H2O with K2pcc (H2pcc = phenyl(carboxymethyl) phosphinic acid) at 423 K, a novel hybrid material of formula [Co2(pcc)2 (H2O)2] x H2O has been obtained. The compound, which is the first pcc/metal complex reported, exhibits a polymeric arrangement, where cobalt metal ions, linked together by bridging carboxylate and phosphinate oxygens, form infinite chains of edge-shared CoO6 octahedra. The cobalt chains are in turn linked together through important hydrogen-bonding interactions, which create an infinite 2D architecture. The two crystallographically independent cobalt centers, both displaying distorted octahedral coordination, present different environments as one is surrounded by six ligand oxygens and the other by four ligand oxygens and by two water oxygens. Careful magnetic studies performed by a home-built alternating current susceptometer reveal that the system undergoes an antiferromagnetic transition below 2.0 K leading to a canted structure. Field-dependent studies further indicate the occurrence of a metamagnetic transition at a critical field of 650 +/- 50 G.

Almost-dispersionless pulse transport in long quasiuniform spring-mass chains: A different kind of Newton's cradle

NASA Astrophysics Data System (ADS)

Vaia, Ruggero

2018-04-01

Almost-dispersionless pulse transfer between the extremal masses of a uniform harmonic spring-mass chain of arbitrary length can be induced by suitably modifying two masses and their spring's elastic constant at both extrema of the chain. It is shown that a deviation (or a pulse) imposed to the first mass gives rise to a wave packet that, after a time of the order of the chain length, almost perfectly reproduces the same deviation (pulse) at the opposite end, with an amplitude loss that is as small as 1.3% in the infinite-length limit; such a dynamics can continue back and forth again for several times before dispersion cleared the effect. The underlying coherence mechanism is that the initial condition excites a bunch of normal modes with almost equal frequency spacing. This constitutes a possible mechanism for efficient energy transfer, e.g., in nanofabricated structures.

Linear and nonlinear dynamics of isospectral granular chains

NASA Astrophysics Data System (ADS)

Chaunsali, R.; Xu, H.; Yang, J.; Kevrekidis, P. G.

2017-04-01

We study the dynamics of isospectral granular chains that are highly tunable due to the nonlinear Hertz contact law interaction between the granular particles. The system dynamics can thus be tuned easily from being linear to strongly nonlinear by adjusting the initial compression applied to the chain. In particular, we introduce both discrete and continuous spectral transformation schemes to generate a family of granular chains that are isospectral in their linear limit. Inspired by the principle of supersymmetry in quantum systems, we also introduce a methodology to add or remove certain eigenfrequencies, and we demonstrate numerically that the corresponding physical system can be constructed in the setting of one-dimensional granular crystals. In the linear regime, we highlight the similarities in the elastic wave transmission characteristics of such isospectral systems, and emphasize that the presented mathematical framework allows one to suitably tailor the wave transmission through a general class of granular chains, both ordered and disordered. Moreover, we show how the dynamic response of these structures deviates from its linear limit as we introduce Hertzian nonlinearity in the chain and how nonlinearity breaks the notion of linear isospectrality.

B and F Projection Methods for Nearly Incompressible Linear and Nonlinear Elasticity and Plasticity using Higher-order NURBS Elements

DTIC Science & Technology

2007-08-01

Infinite plate with a hole: sequence of meshes produced by h-refinement. The geometry of the coarsest mesh...recalled with an emphasis on k -refinement. In Section 3, the use of high-order NURBS within a projection technique is studied in the geometri - cally linear...case with a B̄ method to investigate the choice of approximation and projection spaces with NURBS.

Rigorous Model Reduction for a Damped-Forced Nonlinear Beam Model: An Infinite-Dimensional Analysis

NASA Astrophysics Data System (ADS)

Kogelbauer, Florian; Haller, George

2018-06-01

We use invariant manifold results on Banach spaces to conclude the existence of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces of the linearized beam equation. Reduction in the governing PDE to SSMs provides an explicit low-dimensional model which captures the correct asymptotics of the full, infinite-dimensional dynamics. Our approach is general enough to admit extensions to other types of continuum vibrations. The model-reduction procedure we employ also gives guidelines for a mathematically self-consistent modeling of damping in PDEs describing structural vibrations.

Acquisition of Inertia by a Moving Crack

NASA Astrophysics Data System (ADS)

Goldman, Tamar; Livne, Ariel; Fineberg, Jay

2010-03-01

We experimentally investigate the dynamics of “simple” tensile cracks. Within an effectively infinite medium, a crack’s dynamics perfectly correspond to inertialess behavior predicted by linear elastic fracture mechanics. Once a crack interacts with waves that it generated at earlier times, this description breaks down. Cracks then acquire inertia and sluggishly accelerate. Crack inertia increases with crack speed v and diverges as v approaches its limiting value. We show that these dynamics are in excellent accord with an equation of motion derived in the limit of an infinite strip [M. Marder, Phys. Rev. Lett. 66, 2484 (1991)PRLTAO0031-900710.1103/PhysRevLett.66.2484].

Finite-size Scaling of the Density of States in Photonic Band Gap Crystals

NASA Astrophysics Data System (ADS)

Hasan, Shakeeb Bin; Mosk, Allard P.; Vos, Willem L.; Lagendijk, Ad

2018-06-01

The famous vanishing of the density of states (DOS) in a band gap, be it photonic or electronic, pertains to the infinite-crystal limit. In contrast, all experiments and device applications refer to finite crystals, which raises the question: Upon increasing the linear size L of a crystal, how fast does the DOS approach the infinite-crystal limit? We present a theory for finite crystals that includes Bloch-mode broadening due to the presence of crystal boundaries. Our results demonstrate that the DOS for frequencies inside a band gap has a 1 /L scale dependence for crystals in one, two and three dimensions.

Perfect commuting-operator strategies for linear system games

NASA Astrophysics Data System (ADS)

Cleve, Richard; Liu, Li; Slofstra, William

2017-01-01

Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.

Design and analysis of linear cascade DNA hybridization chain reactions using DNA hairpins

NASA Astrophysics Data System (ADS)

Bui, Hieu; Garg, Sudhanshu; Miao, Vincent; Song, Tianqi; Mokhtar, Reem; Reif, John

2017-01-01

DNA self-assembly has been employed non-conventionally to construct nanoscale structures and dynamic nanoscale machines. The technique of hybridization chain reactions by triggered self-assembly has been shown to form various interesting nanoscale structures ranging from simple linear DNA oligomers to dendritic DNA structures. Inspired by earlier triggered self-assembly works, we present a system for controlled self-assembly of linear cascade DNA hybridization chain reactions using nine distinct DNA hairpins. NUPACK is employed to assist in designing DNA sequences and Matlab has been used to simulate DNA hairpin interactions. Gel electrophoresis and ensemble fluorescence reaction kinetics data indicate strong evidence of linear cascade DNA hybridization chain reactions. The half-time completion of the proposed linear cascade reactions indicates a linear dependency on the number of hairpins.

Localized Single Frequency Lasing States in a Finite Parity-Time Symmetric Resonator Chain

PubMed Central

Phang, Sendy; Vukovic, Ana; Creagh, Stephen C.; Sewell, Phillip D.; Gradoni, Gabriele; Benson, Trevor M.

2016-01-01

In this paper a practical case of a finite periodic Parity Time chain made of resonant dielectric cylinders is considered. The paper analyzes a more general case where PT symmetry is achieved by modulating both the real and imaginary part of the material refractive index along the resonator chain. The band-structure of the finite periodic PT resonator chains is compared to infinite chains in order to understand the complex interdependence of the Bloch phase and the amount of the gain/loss in the system that causes the PT symmetry to break. The results show that the type of the modulation along the unit cell can significantly affect the position of the threshold point of the PT system. In all cases the lowest threshold is achieved near the end of the Brillouin zone. In the case of finite PT-chains, and for a particular type of modulation, early PT symmetry breaking is observed and shown to be caused by the presence of termination states localized at the edges of the finite chain resulting in localized lasing and dissipative modes at each end of the chain. PMID:26848095

Macromolecular 'size' and 'hardness' drives structure in solvent-swollen blends of linear, cyclic, and star polymers.

PubMed

Gartner, Thomas E; Jayaraman, Arthi

2018-01-17

In this paper, we apply molecular simulation and liquid state theory to uncover the structure and thermodynamics of homopolymer blends of the same chemistry and varying chain architecture in the presence of explicit solvent species. We use hybrid Monte Carlo (MC)/molecular dynamics (MD) simulations in the Gibbs ensemble to study the swelling of ∼12 000 g mol -1 linear, cyclic, and 4-arm star polystyrene chains in toluene. Our simulations show that the macroscopic swelling response is indistinguishable between the various architectures and matches published experimental data for the solvent annealing of linear polystyrene by toluene vapor. We then use standard MD simulations in the NPT ensemble along with polymer reference interaction site model (PRISM) theory to calculate effective polymer-solvent and polymer-polymer Flory-Huggins interaction parameters (χ eff ) in these systems. As seen in the macroscopic swelling results, there are no significant differences in the polymer-solvent and polymer-polymer χ eff between the various architectures. Despite similar macroscopic swelling and effective interaction parameters between various architectures, the pair correlation function between chain centers-of-mass indicates stronger correlations between cyclic or star chains in the linear-cyclic blends and linear-star blends, compared to linear chain-linear chain correlations. Furthermore, we note striking similarities in the chain-level correlations and the radius of gyration of cyclic and 4-arm star architectures of identical molecular weight. Our results indicate that the cyclic and star chains are 'smaller' and 'harder' than their linear counterparts, and through comparison with MD simulations of blends of soft spheres with varying hardness and size we suggest that these macromolecular characteristics are the source of the stronger cyclic-cyclic and star-star correlations.

Analysis of Streamline Separation at Infinity Using Time-Discrete Markov Chains.

PubMed

Reich, W; Scheuermann, G

2012-12-01

Existing methods for analyzing separation of streamlines are often restricted to a finite time or a local area. In our paper we introduce a new method that complements them by allowing an infinite-time-evaluation of steady planar vector fields. Our algorithm unifies combinatorial and probabilistic methods and introduces the concept of separation in time-discrete Markov-Chains. We compute particle distributions instead of the streamlines of single particles. We encode the flow into a map and then into a transition matrix for each time direction. Finally, we compare the results of our grid-independent algorithm to the popular Finite-Time-Lyapunov-Exponents and discuss the discrepancies.

Crystal structure of methyl (4R)-4-(4-meth-oxy-benzo-yl)-4-{[(1R)-1-phenyl-eth-yl]carbamo-yl}butano-ate.

PubMed

Manchado, Alejandro; Salgado, Mateo M; Vicente, Álvaro; Díez, David; Sanz, Francisca; Garrido, Narciso M

2017-04-01

The title compound, C 22 H 25 NO 5 , was prepared by CAN [cerium(IV) ammonium nitrate] oxidation of the corresponding β-lactam. The dihedral angle between the benzene rings is 13.3 (4)° and the C-N-C(=O)-C torsion angle is 176.1 (6)°. In the crystal, amide- C (4) N-H⋯O and reinforcing C-H⋯O hydrogen bonds link the mol-ecules into infinite [010] chains. Further C-H⋯O hydrogen bonds cross-link the chains in the c -axis direction.

Optimal Control for Stochastic Delay Evolution Equations

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

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

Modeling and control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.

1988-01-01

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

On asphericity of convex bodies in linear normed spaces.

PubMed

Faried, Nashat; Morsy, Ahmed; Hussein, Aya M

2018-01-01

In 1960, Dvoretzky proved that in any infinite dimensional Banach space X and for any [Formula: see text] there exists a subspace L of X of arbitrary large dimension ϵ -iometric to Euclidean space. A main tool in proving this deep result was some results concerning asphericity of convex bodies. In this work, we introduce a simple technique and rigorous formulas to facilitate calculating the asphericity for each set that has a nonempty boundary set with respect to the flat space generated by it. We also give a formula to determine the center and the radius of the smallest ball containing a nonempty nonsingleton set K in a linear normed space, and the center and the radius of the largest ball contained in it provided that K has a nonempty boundary set with respect to the flat space generated by it. As an application we give lower and upper estimations for the asphericity of infinite and finite cross products of these sets in certain spaces, respectively.

Unified control/structure design and modeling research

NASA Technical Reports Server (NTRS)

Mingori, D. L.; Gibson, J. S.; Blelloch, P. A.; Adamian, A.

1986-01-01

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

Optimal control of coupled parabolic-hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

NASA Astrophysics Data System (ADS)

Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.

2018-04-01

This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.

Structural and optical properties of self-assembled chains of plasmonic nanocubes

DOE PAGES

Klinkova, Anna; Gang, Oleg; Therien-Aubin, Heloise; ...

2014-10-10

Solution-based linear self-assembly of metal nanoparticles offers a powerful strategy for creating plasmonic polymers, which, so far, have been formed from spherical nanoparticles and nanorods. Here, we report linear solution-based self-assembly of metal nanocubes (NCs), examine the structural characteristics of the NC chains and demonstrate their advanced optical characteristics. Predominant face-to-face assembly of large NCs coated with short polymer ligands led to a larger volume of hot spots in the chains, a nearly uniform E-field enhancement in the gaps between co-linear NCs and a new coupling mode for NC chains, in comparison with chains of nanospheres with similar dimensions, compositionmore » and surface chemistry. The NC chains exhibited a stronger surface enhanced Raman scattering (SERS) signal, in comparison with linear assemblies of nanospheres. The experimental results were in agreement with finite difference time domain (FDTD) simulations.« less

USSR and Eastern Europe Scientific Abstracts, Electronics and Electrical Engineering, Number 33.

DTIC Science & Technology

1977-09-27

reduces to an infinite system of linear homogeneous algebraic equations and leads to Mathieu functions of the k-th order. The solution is convergent in...cylinder walls to be infinitesimally thin ideal conductors. The problem is reduced to a system of Fredholm linear algebraic equations of the second...EXPECTED DEVELOPMENTS OF TRANSISTORIZED LOW-NOISE MICROWAVE AMPLIFIERS Prague SDELOVACI TECHNIKA in Czech Vol 25, No 2, Feb 77 pp 47-49 TALLO, ANTON

Bottlebrush-Guided Polymer Crystallization Resulting in Supersoft and Reversibly Moldable Physical Networks

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

Daniel, William F. M.; Xie, Guojun; Vatankhah Varnoosfaderani, Mohammad

The goal of this study is to use ABA triblock copolymers with central bottlebrush B segments and crystalline linear chain A segments to demonstrate the effect of side chains on the formation and mechanical properties of physical networks cross-linked by crystallites. For this purpose, a series of bottlebrush copolymers was synthesized consisting of central amorphous bottlebrush polymer segments with a varying degree of polymerization (DP) of poly(n-butyl acrylate) (PnBA) side chains and linear tail blocks of crystallizable poly(octadecyl acrylate-stat-docosyl acrylate) (poly(ODA-stat-DA)). The materials were generated by sequential atom transfer radical polymerization (ATRP) steps starting with a series of bifunctional macroinitiatorsmore » followed by the growth of two ODA-stat-DA linear-chain tails and eventually growing poly(nBA) side chains with increasing DPs. Crystallization of the poly(ODA-stat-DA) tails resulted in a series of reversible physical networks with bottlebrush strands bridging crystalline cross-links. They displayed very low moduli of elasticity of the order of 10 3–10 4 Pa. These distinct properties are due to the bottlebrush architecture, wherein densely grafted side chains play a dual role by facilitating disentanglement of the network strands and confining crystallization of the linear-chain tails. This combination leads to physical cross-linking of supersoft networks without percolation of the crystalline phase. The cross-link density was effectively controlled by the DP of the side chains with respect to the DP of the linear tails (n A). Furthermore, shorter side chains allowed for crystallization of the linear tails of neighboring bottlebrushes, while steric repulsion between longer side chains hindered the phase separation and crystallization process and prevented network formation.« less

Bottlebrush-Guided Polymer Crystallization Resulting in Supersoft and Reversibly Moldable Physical Networks

DOE PAGES

Daniel, William F. M.; Xie, Guojun; Vatankhah Varnoosfaderani, Mohammad; ...

2017-02-24

The goal of this study is to use ABA triblock copolymers with central bottlebrush B segments and crystalline linear chain A segments to demonstrate the effect of side chains on the formation and mechanical properties of physical networks cross-linked by crystallites. For this purpose, a series of bottlebrush copolymers was synthesized consisting of central amorphous bottlebrush polymer segments with a varying degree of polymerization (DP) of poly(n-butyl acrylate) (PnBA) side chains and linear tail blocks of crystallizable poly(octadecyl acrylate-stat-docosyl acrylate) (poly(ODA-stat-DA)). The materials were generated by sequential atom transfer radical polymerization (ATRP) steps starting with a series of bifunctional macroinitiatorsmore » followed by the growth of two ODA-stat-DA linear-chain tails and eventually growing poly(nBA) side chains with increasing DPs. Crystallization of the poly(ODA-stat-DA) tails resulted in a series of reversible physical networks with bottlebrush strands bridging crystalline cross-links. They displayed very low moduli of elasticity of the order of 10 3–10 4 Pa. These distinct properties are due to the bottlebrush architecture, wherein densely grafted side chains play a dual role by facilitating disentanglement of the network strands and confining crystallization of the linear-chain tails. This combination leads to physical cross-linking of supersoft networks without percolation of the crystalline phase. The cross-link density was effectively controlled by the DP of the side chains with respect to the DP of the linear tails (n A). Furthermore, shorter side chains allowed for crystallization of the linear tails of neighboring bottlebrushes, while steric repulsion between longer side chains hindered the phase separation and crystallization process and prevented network formation.« less

Thermal mirror spectrometry: An experimental investigation of optical glasses

NASA Astrophysics Data System (ADS)

Zanuto, V. S.; Herculano, L. S.; Baesso, M. L.; Lukasievicz, G. V. B.; Jacinto, C.; Malacarne, L. C.; Astrath, N. G. C.

2013-03-01

The Thermal mirror technique relies on measuring laser-induced nanoscale surface deformation of a solid sample. The amplitude of the effect is directly dependent on the optical absorption and linear thermal expansion coefficients, and the time evolution depends on the heat diffusion properties of the sample. Measurement of transient signals provide direct access to thermal, optical and mechanical properties of the material. The theoretical models describing this effect can be formulated for very low optical absorbing and for absorbing materials. In addition, the theories describing the effect apply for semi-infinite and finite samples. In this work, we apply the Thermal mirror technique to measure physical properties of optical glasses. The semi-infinite and finite models are used to investigate very low optical absorbing glasses. The thickness limit for which the semi-infinite model retrieves the correct values of the thermal diffusivity and amplitude of the transient is obtained using the finite description. This procedure is also employed on absorbing glasses, and the semi-infinite Beer-Lambert law model is used to analyze the experimental data. The experimental data show the need to use the finite model for samples with very low bulk absorption coefficients and thicknesses L < 1.5 mm. This analysis helped to establish limit values of thickness for which the semi-infinite model for absorbing materials could be used, L > 1.0 mm in this case. In addition, the physical properties of the samples were calculated and absolute values derived.

Anomalous critical slowdown at a first order phase transition in single polymer chains.

PubMed

Zhang, Shuangshuang; Qi, Shuanhu; Klushin, Leonid I; Skvortsov, Alexander M; Yan, Dadong; Schmid, Friederike

2017-08-14

Using Brownian dynamics, we study the dynamical behavior of a polymer grafted onto an adhesive surface close to the mechanically induced adsorption-stretching transition. Even though the transition is first order (in the infinite chain length limit, the stretching degree of the chain jumps discontinuously), the characteristic relaxation time is found to grow according to a power law as the transition point is approached. We present a dynamic effective interface model which reproduces these observations and provides an excellent quantitative description of the simulation data. The generic nature of the theoretical model suggests that the unconventional mixing of features that are characteristic for first-order transitions (a jump in an order parameter) and features that are characteristic of critical points (an anomalous slowdown) may be a common phenomenon in force-driven phase transitions of macromolecules.

The study of the behaviour of a disturbed semi-infinite liquid jet using a spatial instability method

NASA Astrophysics Data System (ADS)

Basu (‧nee De), Shukla

2001-11-01

A study has been made of the behaviour of a disturbed semi-infinite liquid jet using a spatial instability method. A sinusoidal disturbance in the axial component of jet velocity at the nozzle is considered which resulted in an elliptic free surface boundary value problem with two non-linear boundary conditions. The system is linearised using perturbation techniques and the first order solution resulted in the dispersion relation. The jet stability is found to depend explicitly on the frequency of the disturbance and the Weber number. The second and third order solutions have been derived analytically which are used to predict on jet break-up and satellite formation.

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.

Thiobarbiturate and barbiturate salts of pefloxacin drug: Growth, structure, thermal stability and IR-spectra

NASA Astrophysics Data System (ADS)

Golovnev, Nicolay N.; Molokeev, Maxim S.; Lesnikov, Maxim K.; Sterkhova, Irina V.; Atuchin, Victor V.

2017-12-01

Three new salts of pefloxacin (PefH) with thiobarbituric (H2tba) and barbituric (H2ba) acids, pefloxacinium 2-thiobarbiturate trihydrate, PefH2(Htba)·3H2O (1), pefloxacinium 2-thiobarbiturate, PefH2(Htba) (2) and bis(pefloxacinium barbiturate) hydrate, (PefH2)2(Hba)2·2.56H2O (3) are synthesized and structurally characterized by the X-ray single-crystal diffraction. The structures of 1-3 contain intramolecular hydrogen bonds Csbnd H⋯F, Osbnd H⋯O. Intermolecular hydrogen bonds Nsbnd H⋯O and Osbnd H⋯O form a 2D plane network in 1. In 2 and 3, intermolecular hydrogen bonds Nsbnd H⋯O form the infinite chains. In 1-3, the Htba- and Hba- ions are connected with PefH2+ only by one intermolecular hydrogen bond Nsbnd H⋯O. In 2 and 3, two Htba- and Hba- ions are connected by two hydrogen bonds Nsbnd H⋯O. These pairs form infinite chains. All three structures are stabilized by the π-π interactions of the head-to-tail type between PefH2+ ions. Compounds 2 and 3 are characterized by powder XRD, TG-DSC and FT-IR.

Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

NASA Technical Reports Server (NTRS)

Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

1989-01-01

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

Estimation for general birth-death processes

PubMed Central

Crawford, Forrest W.; Minin, Vladimir N.; Suchard, Marc A.

2013-01-01

Birth-death processes (BDPs) are continuous-time Markov chains that track the number of “particles” in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle birth and death rates remains largely limited to restrictive linear BDPs in which per-particle birth and death rates are constant. Researchers often observe the number of particles at discrete times, necessitating data augmentation procedures such as expectation-maximization (EM) to find maximum likelihood estimates. For BDPs on finite state-spaces, there are powerful matrix methods for computing the conditional expectations needed for the E-step of the EM algorithm. For BDPs on infinite state-spaces, closed-form solutions for the E-step are available for some linear models, but most previous work has resorted to time-consuming simulation. Remarkably, we show that the E-step conditional expectations can be expressed as convolutions of computable transition probabilities for any general BDP with arbitrary rates. This important observation, along with a convenient continued fraction representation of the Laplace transforms of the transition probabilities, allows for novel and efficient computation of the conditional expectations for all BDPs, eliminating the need for truncation of the state-space or costly simulation. We use this insight to derive EM algorithms that yield maximum likelihood estimation for general BDPs characterized by various rate models, including generalized linear models. We show that our Laplace convolution technique outperforms competing methods when they are available and demonstrate a technique to accelerate EM algorithm convergence. We validate our approach using synthetic data and then apply our methods to cancer cell growth and estimation of mutation parameters in microsatellite evolution. PMID:25328261

Estimation for general birth-death processes.

PubMed

Crawford, Forrest W; Minin, Vladimir N; Suchard, Marc A

2014-04-01

Birth-death processes (BDPs) are continuous-time Markov chains that track the number of "particles" in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle birth and death rates remains largely limited to restrictive linear BDPs in which per-particle birth and death rates are constant. Researchers often observe the number of particles at discrete times, necessitating data augmentation procedures such as expectation-maximization (EM) to find maximum likelihood estimates. For BDPs on finite state-spaces, there are powerful matrix methods for computing the conditional expectations needed for the E-step of the EM algorithm. For BDPs on infinite state-spaces, closed-form solutions for the E-step are available for some linear models, but most previous work has resorted to time-consuming simulation. Remarkably, we show that the E-step conditional expectations can be expressed as convolutions of computable transition probabilities for any general BDP with arbitrary rates. This important observation, along with a convenient continued fraction representation of the Laplace transforms of the transition probabilities, allows for novel and efficient computation of the conditional expectations for all BDPs, eliminating the need for truncation of the state-space or costly simulation. We use this insight to derive EM algorithms that yield maximum likelihood estimation for general BDPs characterized by various rate models, including generalized linear models. We show that our Laplace convolution technique outperforms competing methods when they are available and demonstrate a technique to accelerate EM algorithm convergence. We validate our approach using synthetic data and then apply our methods to cancer cell growth and estimation of mutation parameters in microsatellite evolution.

Stochastic Analysis and Design of Systems

DTIC Science & Technology

2011-09-14

measures is described by the Frobenius - Perron operator corresponding to the map T (qi, ., .). This is the unique operator [Pi] such that∫ A [Pi]µ(x...ξi(k)) are non-linear, the Frobenius - Perron operators are linear operators, but infinite-dimensional. For more details on the theory of these...given by the Frobenius - Perron operator corresponding to the map R(qi, qj , ., .). This is given as ∫ A [Mi,j ]µ(x)dx = Eηj ∫ Rn µ(x).χA(R(qi, qj , x

Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length

NASA Astrophysics Data System (ADS)

Saakian, David B.

2017-08-01

We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.

Discrete-time Markovian-jump linear quadratic optimal control

NASA Technical Reports Server (NTRS)

Chizeck, H. J.; Willsky, A. S.; Castanon, D.

1986-01-01

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.

A Solution to the Fundamental Linear Fractional Order Differential Equation

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

NASA Astrophysics Data System (ADS)

Chakrabarti, Aloknath; Mohapatra, Smrutiranjan

2013-09-01

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Characterizing quantum phase transition by teleportation

NASA Astrophysics Data System (ADS)

Wu, Meng-He; Ling, Yi; Shu, Fu-Wen; Gan, Wen-Cong

2018-04-01

In this paper we provide a novel way to explore the relation between quantum teleportation and quantum phase transition. We construct a quantum channel with a mixed state which is made from one dimensional quantum Ising chain with infinite length, and then consider the teleportation with the use of entangled Werner states as input qubits. The fidelity as a figure of merit to measure how well the quantum state is transferred is studied numerically. Remarkably we find the first-order derivative of the fidelity with respect to the parameter in quantum Ising chain exhibits a logarithmic divergence at the quantum critical point. The implications of this phenomenon and possible applications are also briefly discussed.

Intermolecular hydrogen bonded and self-assembled β-pleated sheet structures of β-sulfidocarbonyls

NASA Astrophysics Data System (ADS)

Hussain, Sahid; Das, Gopal; Chaudhuri, Mihir K.

2007-06-01

The three crystal structures of β-sulfidocarbonyls 1, 2 and 3 synthesized from the reaction of acryl amide with cystiene, 1,2-dithiol and 1,3-dithiols, respectively, in water catalyzed by borax, have been determined at 273 K. The characteristic features of the structures are self-assembly through intermolecular hydrogen bonding leading to infinite chains of molecules in one direction, in addition to the stacking of layers of such molecular chains in the perpendicular direction ultimately giving rise to β-pleated sheets of 3D molecular network involving N-H⋯O, C-H⋯O and C-H⋯S bonding in the crystal lattice.

Influences of the chemical structure of entrainers on the activity coefficients in presence of biodiesel

NASA Astrophysics Data System (ADS)

Mäder, A.; Fleischmann, A.; Fang, Ye; Ruck, W.; Krahl, J.

2012-05-01

In this work we analyzed the strength of the intermolecular forces between biodiesel and the entrainer and their influence on the entrainer's ability to interact with biodiesel. Furthermore we investigated the influence of the chemical structure of an entrainer to the interaction with biodiesel. For this purpose the activity coefficients γ∞ at infinite dilution of acids, aldehydes, ketones and alcohols in biodiesel were measured with the method of headspace gas chromatography (HSGC). Short-chained acids showed the highest interaction of the analyzed entrainers caused by their ability to build hydrogen bonds with biodiesel. Increased chain length of the acids cause reduced interaction with biodiesel, which is mainly due to the higher obstruction of the acid molecule and therefore the reduced ability to build hydrogen bonds with biodiesel. Aldehydes, ketones and alcohols showed lower interaction with biodiesel compared to the acids. Longer-chained alcohols showed increased interaction with biodiesel due to the raised London Forces and an inductive +I effect of the molecule chain.

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.

Half the entanglement in critical systems is distillable from a single specimen

NASA Astrophysics Data System (ADS)

Orús, R.; Latorre, J. I.; Eisert, J.; Cramer, M.

2006-06-01

We establish a quantitative relationship between the entanglement content of a single quantum chain at a critical point and the corresponding entropy of entanglement. We find that, surprisingly, the leading critical scaling of the single-copy entanglement with respect to any bipartitioning is exactly one-half of the entropy of entanglement, in a general setting of conformal field theory and quasifree systems. Conformal symmetry imposes that the single-copy entanglement scales as E1(ρL)=(c/6)lnL-(c/6)(π2/lnL)+O(1/L) , where L is the number of constituents in a block of an infinite chain and c denotes the central charge. This shows that from a single specimen of a critical chain, already half the entanglement can be distilled compared to the rate that is asymptotically available. The result is substantiated by a quantitative analysis for all translationally invariant quantum spin chains corresponding to all isotropic quasifree fermionic models. An example of the XY spin chain shows that away from criticality the above relation is maintained only near the quantum phase transition.

Confined dynamics of grafted polymer chains in solutions of linear polymer

DOE PAGES

Poling-Skutvik, Ryan D.; Olafson, Katy N.; Narayanan, Suresh; ...

2017-09-11

Here, we measure the dynamics of high molecular weight polystyrene grafted to silica nanoparticles dispersed in semidilute solutions of linear polymer. Structurally, the linear free chains do not penetrate the grafted corona but increase the osmotic pressure of the solution, collapsing the grafted polymer and leading to eventual aggregation of the grafted particles at high matrix concentrations. Dynamically, the relaxations of the grafted polymer are controlled by the solvent viscosity according to the Zimm model on short time scales. On longer time scales, the grafted chains are confined by neighboring grafted chains, preventing full relaxation over the experimental time scale.more » Adding free linear polymer to the solution does not affect the initial Zimm relaxations of the grafted polymer but does increase the confinement of the grafted chains. Finally, our results elucidate the physics underlying the slow relaxations of grafted polymer.« less

Confined dynamics of grafted polymer chains in solutions of linear polymer

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

Poling-Skutvik, Ryan D.; Olafson, Katy N.; Narayanan, Suresh

Here, we measure the dynamics of high molecular weight polystyrene grafted to silica nanoparticles dispersed in semidilute solutions of linear polymer. Structurally, the linear free chains do not penetrate the grafted corona but increase the osmotic pressure of the solution, collapsing the grafted polymer and leading to eventual aggregation of the grafted particles at high matrix concentrations. Dynamically, the relaxations of the grafted polymer are controlled by the solvent viscosity according to the Zimm model on short time scales. On longer time scales, the grafted chains are confined by neighboring grafted chains, preventing full relaxation over the experimental time scale.more » Adding free linear polymer to the solution does not affect the initial Zimm relaxations of the grafted polymer but does increase the confinement of the grafted chains. Finally, our results elucidate the physics underlying the slow relaxations of grafted polymer.« less

Lattice model of linear telechelic polymer melts. II. Influence of chain stiffness on basic thermodynamic properties

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

Xu, Wen-Sheng, E-mail: wsxu@uchicago.edu; Freed, Karl F., E-mail: freed@uchicago.edu; Department of Chemistry, The University of Chicago, Chicago, Illinois 60637

2015-07-14

The lattice cluster theory (LCT) for semiflexible linear telechelic melts, developed in Paper I, is applied to examine the influence of chain stiffness on the average degree of self-assembly and the basic thermodynamic properties of linear telechelic polymer melts. Our calculations imply that chain stiffness promotes self-assembly of linear telechelic polymer melts that assemble on cooling when either polymer volume fraction ϕ or temperature T is high, but opposes self-assembly when both ϕ and T are sufficiently low. This allows us to identify a boundary line in the ϕ-T plane that separates two regions of qualitatively different influence of chainmore » stiffness on self-assembly. The enthalpy and entropy of self-assembly are usually treated as adjustable parameters in classical Flory-Huggins type theories for the equilibrium self-assembly of polymers, but they are demonstrated here to strongly depend on chain stiffness. Moreover, illustrative calculations for the dependence of the entropy density of linear telechelic polymer melts on chain stiffness demonstrate the importance of including semiflexibility within the LCT when exploring the nature of glass formation in models of linear telechelic polymer melts.« less

Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Majumdar, Satya N.; Huse, David A.

2017-03-01

We calculate the probability distribution of entanglement entropy S across a cut of a finite one-dimensional spin chain of length L at an infinite-randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form p (S |L ) ˜L-ψ (k ) , where k ≡S /ln[L /L0] , the large deviation function ψ (k ) is found explicitly, and L0 is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix-product-state-based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large L via a mapping to Majorana fermions.

Mixed-order phase transition of the contact process near multiple junctions.

PubMed

Juhász, Róbert; Iglói, Ferenc

2017-02-01

We have studied the phase transition of the contact process near a multiple junction of M semi-infinite chains by Monte Carlo simulations. As opposed to the continuous transitions of the translationally invariant (M=2) and semi-infinite (M=1) system, the local order parameter is found to be discontinuous for M>2. Furthermore, the temporal correlation length diverges algebraically as the critical point is approached, but with different exponents on the two sides of the transition. In the active phase, the estimate is compatible with the bulk value, while in the inactive phase it exceeds the bulk value and increases with M. The unusual local critical behavior is explained by a scaling theory with an irrelevant variable, which becomes dangerous in the inactive phase. Quenched spatial disorder is found to make the transition continuous in agreement with earlier renormalization group results.

Chiral Luttinger liquids and a generalized Luttinger's theorem in fractional quantum Hall edges via finite-entanglement scaling

NASA Astrophysics Data System (ADS)

Varjas, Daniel; Zaletel, Michael; Moore, Joel

2014-03-01

We use bosonic field theories and the infinite system density matrix renormalization group (iDMRG) method to study infinite strips of fractional quantum Hall (FQH) states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge mode exponents and momenta without finite-size errors. We analyze states in the first and second level of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid (χLL) theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the non-chiral case. We prove a generalized Luttinger's theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in 1D.

Chiral Luttinger liquids and a generalized Luttinger theorem in fractional quantum Hall edges via finite-entanglement scaling

NASA Astrophysics Data System (ADS)

Varjas, Dániel; Zaletel, Michael P.; Moore, Joel E.

2013-10-01

We use bosonic field theories and the infinite system density matrix renormalization group method to study infinite strips of fractional quantum Hall states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge-mode exponents, and momenta without finite-size errors. We analyze states in the first and second levels of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the nonchiral case. We prove a generalized Luttinger theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in one dimension.

The effect of magnetic nanoparticle concentration on the structure organisation of a microferrogel

NASA Astrophysics Data System (ADS)

Ryzhkov, A. V.; Melenev, P. V.; Balasoiu, M.; Raikher, Yu L.

2018-03-01

Coarse-grained molecular dynamics simulation is applied to study the structural response of micro-sized magnetopolymer objects – microferrogels (MFG). The results for MFGs with different magnetic properties and concentrations of magnetic filler nanoparticles are analysed to detect the transition between non-aggregated configurations and the states with pronounced chains. The nanoparticles are assumed to be either magnetically isotropic or to possess infinite magnetic anisotropy. It is shown that, depending on the type of the particle anisotropy, an applied field in rather different ways affects the MFG structure and shape. Diagrams describing the degree of aggregation as a function of the parameter of the interparticle magnetodipolar interaction and concentration are presented. In particular, it is found that in the case of infinitely anisotropic nanoparticles the aggregation transitions undergoes via a non-trivial scenario. The effect of the structure transformations on the volume change of the MFG objects is studied as well.

Infinite charge mobility in muscovite at 300 K

NASA Astrophysics Data System (ADS)

Russell, F. Michael; Archilla, Juan F. R.; Frutos, Fabian; Medina-Carrasco, Santiago

2017-11-01

Evidence is presented for infinite charge mobility in natural crystals of muscovite mica at room temperature. Muscovite has a basic layered structure containing a flat monatomic sheet of potassium sandwiched between mirror silicate layers. It is an excellent electrical insulator. Studies of defects in muscovite crystals indicated that positive charge could propagate over great distances along atomic chains in the potassium sheets in the absence of an applied electric potential. The charge moved in association with anharmonic lattice excitations that moved at about sonic speed and created by nuclear recoil of the radioactive isotope 40K. This was verified by measuring currents passing through crystals when irradiated with energetic alpha particles at room temperature. The charge propagated more than 1000 times the range of the alpha particles of average energy and 250 times the range of channelling particles of maximum energy. The range is limited only by size of the crystal.

Data-driven discovery of Koopman eigenfunctions using deep learning

NASA Astrophysics Data System (ADS)

Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan

2017-11-01

Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems.

Piecewise linear approximation for hereditary control problems

NASA Technical Reports Server (NTRS)

Propst, Georg

1987-01-01

Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

Blind Deconvolution for Distributed Parameter Systems with Unbounded Input and Output and Determining Blood Alcohol Concentration from Transdermal Biosensor Data.

PubMed

Rosen, I G; Luczak, Susan E; Weiss, Jordan

2014-03-15

We develop a blind deconvolution scheme for input-output systems described by distributed parameter systems with boundary input and output. An abstract functional analytic theory based on results for the linear quadratic control of infinite dimensional systems with unbounded input and output operators is presented. The blind deconvolution problem is then reformulated as a series of constrained linear and nonlinear optimization problems involving infinite dimensional dynamical systems. A finite dimensional approximation and convergence theory is developed. The theory is applied to the problem of estimating blood or breath alcohol concentration (respectively, BAC or BrAC) from biosensor-measured transdermal alcohol concentration (TAC) in the field. A distributed parameter model with boundary input and output is proposed for the transdermal transport of ethanol from the blood through the skin to the sensor. The problem of estimating BAC or BrAC from the TAC data is formulated as a blind deconvolution problem. A scheme to identify distinct drinking episodes in TAC data based on a Hodrick Prescott filter is discussed. Numerical results involving actual patient data are presented.

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

Isotropic probability measures in infinite-dimensional spaces

NASA Technical Reports Server (NTRS)

Backus, George

1987-01-01

Let R be the real numbers, R(n) the linear space of all real n-tuples, and R(infinity) the linear space of all infinite real sequences x = (x sub 1, x sub 2,...). Let P sub in :R(infinity) approaches R(n) be the projection operator with P sub n (x) = (x sub 1,...,x sub n). Let p(infinity) be a probability measure on the smallest sigma-ring of subsets of R(infinity) which includes all of the cylinder sets P sub n(-1) (B sub n), where B sub n is an arbitrary Borel subset of R(n). Let p sub n be the marginal distribution of p(infinity) on R(n), so p sub n(B sub n) = p(infinity) (P sub n to the -1 (B sub n)) for each B sub n. A measure on R(n) is isotropic if it is invariant under all orthogonal transformations of R(n). All members of the set of all isotropic probability distributions on R(n) are described. The result calls into question both stochastic inversion and Bayesian inference, as currently used in many geophysical inverse problems.

Decay of a linear pendulum in a collisional gas: Spatially one-dimensional case

NASA Astrophysics Data System (ADS)

Tsuji, Tetsuro; Aoki, Kazuo

2014-05-01

An infinitely wide plate, subject to an external force in its normal direction obeying Hooke's law, is placed in an infinite expanse of a rarefied gas. When the plate is displaced from its equilibrium position and released, it starts in general an oscillatory motion in its normal direction. This is the one-dimensional setting of a linear pendulum considered previously for a collisionless gas and a special Lorentz gas by the present authors [T. Tsuji and K. Aoki, J. Stat. Phys. 146, 620 (2012), 10.1007/s10955-011-0412-7]. The motion decays as time proceeds because of the drag force on the plate exerted by the surrounding gas. The long-time behavior of the unsteady motion of the gas caused by the motion of the plate is investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation with special interest in the rate of the decay of the oscillatory motion of the plate. The result provides numerical evidence that the displacement of the plate decays in proportion to an inverse power of time for large time.

Decay of a linear pendulum in a collisional gas: spatially one-dimensional case.

PubMed

Tsuji, Tetsuro; Aoki, Kazuo

2014-05-01

An infinitely wide plate, subject to an external force in its normal direction obeying Hooke's law, is placed in an infinite expanse of a rarefied gas. When the plate is displaced from its equilibrium position and released, it starts in general an oscillatory motion in its normal direction. This is the one-dimensional setting of a linear pendulum considered previously for a collisionless gas and a special Lorentz gas by the present authors [T. Tsuji and K. Aoki, J. Stat. Phys. 146, 620 (2012)]. The motion decays as time proceeds because of the drag force on the plate exerted by the surrounding gas. The long-time behavior of the unsteady motion of the gas caused by the motion of the plate is investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation with special interest in the rate of the decay of the oscillatory motion of the plate. The result provides numerical evidence that the displacement of the plate decays in proportion to an inverse power of time for large time.

Feedback linearizing control of a MIMO power system

NASA Astrophysics Data System (ADS)

Ilyes, Laszlo

Prior research has demonstrated that either the mechanical or electrical subsystem of a synchronous electric generator may be controlled using single-input single-output (SISO) nonlinear feedback linearization. This research suggests a new approach which applies nonlinear feedback linearization to a multi-input multi-output (MIMO) model of the synchronous electric generator connected to an infinite bus load model. In this way, the electrical and mechanical subsystems may be linearized and simultaneously decoupled through the introduction of a pair of auxiliary inputs. This allows well known, linear, SISO control methods to be effectively applied to the resulting systems. The derivation of the feedback linearizing control law is presented in detail, including a discussion on the use of symbolic math processing as a development tool. The linearizing and decoupling properties of the control law are validated through simulation. And finally, the robustness of the control law is demonstrated.

Characteristic α and 6He decays of linear-chain structures in 16C

NASA Astrophysics Data System (ADS)

Baba, T.; Kimura, M.

2018-05-01

The linear-chain states of 16C and their decay modes are theoretically investigated by using the antisymmetrized molecular dynamics. It is found that the positive-parity linear-chain states have the (3/2π-) 2(1/2σ-) 2 configuration and primary decay to 12Be(21+) as well as to 12Be(g.s.) by α -particle emission. Moreover, we show that they also decay via the 6He+10Be channel. In the negative-parity states, it is found that two types of linear chains exist. One has the valence neutrons occupying the molecular orbits (3/2π-) 2(1 /2σ-) (3 /2π+) , while the other's configuration cannot be explained in terms of the molecular orbits because of the strong parity mixing. Both configurations constitute the rotational bands with a large moment of inertia and intraband E 2 transitions. Their α and 6He reduced widths are sufficiently large to be distinguished from other noncluster states although they are smaller than those of the positive-parity linear chain.

High-pressure synthesis and characterization of the first cerium fluoride borate CeB{sub 2}O{sub 4}F

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

Hinteregger, Ernst; Wurst, Klaus; Tribus, Martina

2013-08-15

CeB{sub 2}O{sub 4}F is the first cerium fluoride borate, which is exclusively built up of one-dimensional, infinite chains of condensed trigonal-planar [BO{sub 3}]{sup 3−} groups. This new cerium fluoride borate was synthesized under high-pressure/high-temperature conditions of 0.9 GPa and 1450 °C in a Walker-type multianvil apparatus. The compound crystallizes in the orthorhombic space group Pbca (No. 61) with eight formula units and the lattice parameters a=821.63(5), b=1257.50(9), c=726.71(6) pm, V=750.84(9) Å{sup 3}, R{sub 1}=0.0698, and wR{sub 2}=0.0682 (all data). The structure exhibits a 9+1 coordinated cerium ion, one three-fold coordinated fluoride ion and a one-dimensional chain of [BO{sub 3}]{sup 3−}more » groups. Furthermore, IR spectroscopy, Electron Micro Probe Analysis and temperature-dependent X-ray powder diffraction measurements were performed. - Graphical abstract: A new rare-earth fluoride borate CeB{sub 2}O{sub 4}F could be synthesized under high-pressure/high-temperature conditions of 0.9 °GPa and 1450 °Cin a Walker-type multianvil apparatus. The crystal structure represents a new structure type in the class of rare-earth fluoride borates. The structure exhibits a 9+1 coordinated cerium ion, one three-fold coordinated fluoride ion and a one-dimensional chain of [BO{sub 3}]{sup 3−} groups. A closer view on the ac-plane shows an interesting wave-like modulation of the borate chains. Highlights: • CeB{sub 2}O{sub 4}F is the first fluoride borate exclusively built up of one-dimensional, infinite chains of condensed trigonal-planar [BO{sub 3}]{sup 3−} groups. • CeB{sub 2}O{sub 4}F is the first cerium fluoride borate. • High-pressure conditions were necessary to synthesize CeB{sub 2}O{sub 4}F.« less

Computation of output feedback gains for linear stochastic systems using the Zangwill-Powell method

NASA Technical Reports Server (NTRS)

Kaufman, H.

1977-01-01

Because conventional optimal linear regulator theory results in a controller which requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. To this effect a stochastic linear model has been developed that accounts for process parameter and initial uncertainty, measurement noise, and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was then performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell.

Flexible polyelectrolyte chain in a strong electrolyte solution: Insight into equilibrium properties and force-extension behavior from mesoscale simulation

NASA Astrophysics Data System (ADS)

Malekzadeh Moghani, Mahdy; Khomami, Bamin

2016-01-01

Macromolecules with ionizable groups are ubiquitous in biological and synthetic systems. Due to the complex interaction between chain and electrostatic decorrelation lengths, both equilibrium properties and micro-mechanical response of dilute solutions of polyelectrolytes (PEs) are more complex than their neutral counterparts. In this work, the bead-rod micromechanical description of a chain is used to perform hi-fidelity Brownian dynamics simulation of dilute PE solutions to ascertain the self-similar equilibrium behavior of PE chains with various linear charge densities, scaling of the Kuhn step length (lE) with salt concentration cs and the force-extension behavior of the PE chain. In accord with earlier theoretical predictions, our results indicate that for a chain with n Kuhn segments, lE ˜ cs-0.5 as linear charge density approaches 1/n. Moreover, the constant force ensemble simulation results accurately predict the initial non-linear force-extension region of PE chain recently measured via single chain experiments. Finally, inspired by Cohen's extraction of Warner's force law from the inverse Langevin force law, a novel numerical scheme is developed to extract a new elastic force law for real chains from our discrete set of force-extension data similar to Padè expansion, which accurately depicts the initial non-linear region where the total Kuhn length is less than the thermal screening length.

Flexible polyelectrolyte chain in a strong electrolyte solution: Insight into equilibrium properties and force-extension behavior from mesoscale simulation.

PubMed

Malekzadeh Moghani, Mahdy; Khomami, Bamin

2016-01-14

Macromolecules with ionizable groups are ubiquitous in biological and synthetic systems. Due to the complex interaction between chain and electrostatic decorrelation lengths, both equilibrium properties and micro-mechanical response of dilute solutions of polyelectrolytes (PEs) are more complex than their neutral counterparts. In this work, the bead-rod micromechanical description of a chain is used to perform hi-fidelity Brownian dynamics simulation of dilute PE solutions to ascertain the self-similar equilibrium behavior of PE chains with various linear charge densities, scaling of the Kuhn step length (lE) with salt concentration cs and the force-extension behavior of the PE chain. In accord with earlier theoretical predictions, our results indicate that for a chain with n Kuhn segments, lE ∼ cs (-0.5) as linear charge density approaches 1/n. Moreover, the constant force ensemble simulation results accurately predict the initial non-linear force-extension region of PE chain recently measured via single chain experiments. Finally, inspired by Cohen's extraction of Warner's force law from the inverse Langevin force law, a novel numerical scheme is developed to extract a new elastic force law for real chains from our discrete set of force-extension data similar to Padè expansion, which accurately depicts the initial non-linear region where the total Kuhn length is less than the thermal screening length.

Quasi-integrable non-linear Schrödinger models, infinite towers of exactly conserved charges and bright solitons

NASA Astrophysics Data System (ADS)

Blas, H.; do Bonfim, A. C. R.; Vilela, A. M.

2017-05-01

Deformations of the focusing non-linear Schrödinger model (NLS) are considered in the context of the quasi-integrability concept. We strengthen the results of JHEP 09 (2012) 103 for bright soliton collisions. We addressed the focusing NLS as a complement to the one in JHEP 03 (2016) 005 , in which the modified defocusing NLS models with dark solitons were shown to exhibit an infinite tower of exactly conserved charges. We show, by means of analytical and numerical methods, that for certain two-bright-soliton solutions, in which the modulus and phase of the complex modified NLS field exhibit even parities under a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved during the scattering process of the solitons. We perform extensive numerical simulations and consider the bright solitons with deformed potential V=2η /2+\\upepsilon{({|ψ |}^2)}^{2+\\upepsilon},\\upepsilon \\in \\mathbb{R},η <0 . However, for two-soliton field components without definite parity we also show numerically the vanishing of the first non-trivial anomaly and the exact conservation of the relevant charge. So, the parity symmetry seems to be a sufficient but not a necessary condition for the existence of the infinite tower of conserved charges. The model supports elastic scattering of solitons for a wide range of values of the amplitudes and velocities and the set { η, ɛ}. Since the NLS equation is ubiquitous, our results may find potential applications in several areas of non-linear science.

The role of nanoparticle rigidity on the diffusion of linear polystyrene in a polymer nanocomposite

DOE PAGES

Miller, Brad; Imel, Adam E.; Holley, Wade; ...

2015-11-12

The impact of the inclusion of a nanoparticle in a polymer matrix on the dynamics of the polymer chains is an area of recent interest. In this article, we describe the role of nanoparticle rigidity or softness on the impact of the presence of that nanoparticle on the diffusive behavior of linear polymer chains. The neutron reflectivity results clearly show that the inclusion of 10 nm soft nanoparticles in a polymer matrix (R g ~ 20 nm) increases the diffusion coefficient of the linear polymer chain. Surprisingly, thermal analysis shows that these nanocomposites exhibit an increase in their glass transitionmore » temperature, which is incommensurate with an increase in free volume. Therefore, it appears that this effect is more complex than a simple plasticizing effect. Results from small-angle neutron scattering of the nanoparticles in solution show a structure that consists of a gel like core with a corona of free chain ends and loops. Furthermore, the increase in linear polymer diffusion may be related to an increase in constraint release mechanisms in the reptation of the polymer chain, in a similar manner to that which has been reported for the diffusion of linear polymer chains in the presence of star polymers.« less

The role of nanoparticle rigidity on the diffusion of linear polystyrene in a polymer nanocomposite

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

Miller, Brad; Imel, Adam E.; Holley, Wade

The impact of the inclusion of a nanoparticle in a polymer matrix on the dynamics of the polymer chains is an area of recent interest. In this article, we describe the role of nanoparticle rigidity or softness on the impact of the presence of that nanoparticle on the diffusive behavior of linear polymer chains. The neutron reflectivity results clearly show that the inclusion of 10 nm soft nanoparticles in a polymer matrix (R g ~ 20 nm) increases the diffusion coefficient of the linear polymer chain. Surprisingly, thermal analysis shows that these nanocomposites exhibit an increase in their glass transitionmore » temperature, which is incommensurate with an increase in free volume. Therefore, it appears that this effect is more complex than a simple plasticizing effect. Results from small-angle neutron scattering of the nanoparticles in solution show a structure that consists of a gel like core with a corona of free chain ends and loops. Furthermore, the increase in linear polymer diffusion may be related to an increase in constraint release mechanisms in the reptation of the polymer chain, in a similar manner to that which has been reported for the diffusion of linear polymer chains in the presence of star polymers.« less

Geometric MCMC for infinite-dimensional inverse problems

NASA Astrophysics Data System (ADS)

Beskos, Alexandros; Girolami, Mark; Lan, Shiwei; Farrell, Patrick E.; Stuart, Andrew M.

2017-04-01

Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank-Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.

An infinite set of Ward identities for adiabatic modes in cosmology

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

Hinterbichler, Kurt; Hui, Lam; Khoury, Justin, E-mail: khinterbichler@perimeterinstitute.ca, E-mail: lh399@columbia.edu, E-mail: jkhoury@sas.upenn.edu

2014-01-01

We show that the correlation functions of any single-field cosmological model with constant growing-modes are constrained by an infinite number of novel consistency relations, which relate N+1-point correlation functions with a soft-momentum scalar or tensor mode to a symmetry transformation on N-point correlation functions of hard-momentum modes. We derive these consistency relations from Ward identities for an infinite tower of non-linearly realized global symmetries governing scalar and tensor perturbations. These symmetries can be labeled by an integer n. At each order n, the consistency relations constrain — completely for n = 0,1, and partially for n ≥ 2 — themore » q{sup n} behavior of the soft limits. The identities at n = 0 recover Maldacena's original consistency relations for a soft scalar and tensor mode, n = 1 gives the recently-discovered conformal consistency relations, and the identities for n ≥ 2 are new. As a check, we verify directly that the n = 2 identity is satisfied by known correlation functions in slow-roll inflation.« less

Fault-tolerant control of large space structures using the stable factorization approach

NASA Technical Reports Server (NTRS)

Razavi, H. C.; Mehra, R. K.; Vidyasagar, M.

1986-01-01

Large space structures are characterized by the following features: they are in general infinite-dimensional systems, and have large numbers of undamped or lightly damped poles. Any attempt to apply linear control theory to large space structures must therefore take into account these features. Phase I consisted of an attempt to apply the recently developed Stable Factorization (SF) design philosophy to problems of large space structures, with particular attention to the aspects of robustness and fault tolerance. The final report on the Phase I effort consists of four sections, each devoted to one task. The first three sections report theoretical results, while the last consists of a design example. Significant results were obtained in all four tasks of the project. More specifically, an innovative approach to order reduction was obtained, stabilizing controller structures for plants with an infinite number of unstable poles were determined under some conditions, conditions for simultaneous stabilizability of an infinite number of plants were explored, and a fault tolerance controller design that stabilizes a flexible structure model was obtained which is robust against one failure condition.

DOS cones along atomic chains

NASA Astrophysics Data System (ADS)

Kwapiński, Tomasz

2017-03-01

The electron transport properties of a linear atomic chain are studied theoretically within the tight-binding Hamiltonian and the Green’s function method. Variations of the local density of states (DOS) along the chain are investigated. They are crucial in scanning tunnelling experiments and give important insight into the electron transport mechanism and charge distribution inside chains. It is found that depending on the chain parity the local DOS at the Fermi level can form cone-like structures (DOS cones) along the chain. The general condition for the local DOS oscillations is obtained and the linear behaviour of the local density function is confirmed analytically. DOS cones are characterized by a linear decay towards the chain which is in contrast to the propagation properties of charge density waves, end states and Friedel oscillations in one-dimensional systems. We find that DOS cones can appear due to non-resonant electron transport, the spin-orbit scattering or for chains fabricated on a substrate with localized electrons. It is also shown that for imperfect chains (e.g. with a reduced coupling strength between two neighboring sites) a diamond-like structure of the local DOS along the chain appears.

Infinite-disorder critical points of models with stretched exponential interactions

NASA Astrophysics Data System (ADS)

Juhász, Róbert

2014-09-01

We show that an interaction decaying as a stretched exponential function of distance, J(l)˜ e-cl^a , is able to alter the universality class of short-range systems having an infinite-disorder critical point. To do so, we study the low-energy properties of the random transverse-field Ising chain with the above form of interaction by a strong-disorder renormalization group (SDRG) approach. We find that the critical behavior of the model is controlled by infinite-disorder fixed points different from those of the short-range model if 0 < a < 1/2. In this range, the critical exponents calculated analytically by a simplified SDRG scheme are found to vary with a, while, for a > 1/2, the model belongs to the same universality class as its short-range variant. The entanglement entropy of a block of size L increases logarithmically with L at the critical point but, unlike the short-range model, the prefactor is dependent on disorder in the range 0 < a < 1/2. Numerical results obtained by an improved SDRG scheme are found to be in agreement with the analytical predictions. The same fixed points are expected to describe the critical behavior of, among others, the random contact process with stretched exponentially decaying activation rates.

2-(3-Chloro­phen­yl)-4,5-dihydro-1H-imidazole

PubMed Central

Kia, Reza; Fun, Hoong-Kun; Kargar, Hadi

2009-01-01

In the title compound, C9H9ClN2, a substituted imidazoline, the six- and five-membered rings are twisted from each other, making a dihedral angle of 17.07 (5)°. In the crystal structure, a short Cl⋯Cl [3.3540 (3) Å] inter­action is observed. Neighbouring mol­ecules are linked together by inter­molecular N—H⋯N hydrogen bonds into a one-dimensional infinite chain along the [101] direction and short Cl⋯Cl contacts link the chains into a three-dimensional network. There is also a significant π-stacking inter­action between the planar sections of the six- and five-membered rings. PMID:21581940

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

Vourdas, A.

The finite set of subsystems of a finite quantum system with variables in Z(n), is studied as a Heyting algebra. The physical meaning of the logical connectives is discussed. It is shown that disjunction of subsystems is more general concept than superposition. Consequently, the quantum probabilities related to commuting projectors in the subsystems, are incompatible with associativity of the join in the Heyting algebra, unless if the variables belong to the same chain. This leads to contextuality, which in the present formalism has as contexts, the chains in the Heyting algebra. Logical Bell inequalities, which contain “Heyting factors,” are discussed.more » The formalism is also applied to the infinite set of all finite quantum systems, which is appropriately enlarged in order to become a complete Heyting algebra.« less

Ethyl 2-[(carbamothioyl-amino)-imino]-propano-ate.

PubMed

Corrêa, Charlane C; Graúdo, José Eugênio J C; de Oliveira, Luiz Fernando C; de Almeida, Mauro V; Diniz, Renata

2011-08-01

The title compound, C(6)H(11)N(3)O(2)S, consists of a roughly planar mol-ecule (r.m.s deviation from planarity = 0.077 Å for the non-H atoms) and has the S atom in an anti position to the imine N atom. This N atom is the acceptor of a strongly bent inter-nal N-H⋯N hydrogen bond donated by the amino group. In the crystal, mol-ecules are arranged in undulating layers parallel to (010). The mol-ecules are linked via inter-molecular amino-carboxyl N-H⋯O hydrogen bonds, forming chains parallel to [001]. The chains are cross-linked by N(carbazone)-H⋯S and C-H⋯S inter-actions, forming infinite sheets.

A COMPARISON OF TRANSIENT INFINITE ELEMENTS AND TRANSIENT KIRCHHOFF INTEGRAL METHODS FOR FAR FIELD ACOUSTIC ANALYSIS

DOE PAGES

WALSH, TIMOTHY F.; JONES, ANDREA; BHARDWAJ, MANOJ; ...

2013-04-01

Finite element analysis of transient acoustic phenomena on unbounded exterior domains is very common in engineering analysis. In these problems there is a common need to compute the acoustic pressure at points outside of the acoustic mesh, since meshing to points of interest is impractical in many scenarios. In aeroacoustic calculations, for example, the acoustic pressure may be required at tens or hundreds of meters from the structure. In these cases, a method is needed for post-processing the acoustic results to compute the response at far-field points. In this paper, we compare two methods for computing far-field acoustic pressures, onemore » derived directly from the infinite element solution, and the other from the transient version of the Kirchhoff integral. Here, we show that the infinite element approach alleviates the large storage requirements that are typical of Kirchhoff integral and related procedures, and also does not suffer from loss of accuracy that is an inherent part of computing numerical derivatives in the Kirchhoff integral. In order to further speed up and streamline the process of computing the acoustic response at points outside of the mesh, we also address the nonlinear iterative procedure needed for locating parametric coordinates within the host infinite element of far-field points, the parallelization of the overall process, linear solver requirements, and system stability considerations.« less

The crystal structures of iron and cobalt pyridine (py)–sulfates, [Fe(SO4)(py)4]n and [Co3(SO4)3(py)11]n

PubMed Central

Pham, Duyen N. K.; Roy, Mrittika; Kreider-Mueller, Ava; Golen, James A.; Manke, David R.

2018-01-01

The solid-state structures of two metal–pyridine–sulfate compounds, namely catena-poly[[tetra­kis­(pyridine-κN)iron(II)]-μ-sulfato-κ2 O:O′], [Fe(SO4)(C5H5N)4]n, (1), and catena-poly[[tetra­kis­(pyridine-κN)cobalt(II)]-μ-sulfato-κ2 O:O′-[tetra­kis­(pyridine-κN)cobalt(II)]-μ-sulfato-κ3 O,O′:O′′-[tris­(pyridine-κN)cobalt(II)]-μ-sulfato-κ2 O:O′], [Co3(SO4)3(C5H5N)11]n, (2), are reported. The iron compound (1) displays a polymeric structure, with infinite chains of FeII atoms adopting octa­hedral N4O2 coordination environments that involve four pyridine ligands and two bridging sulfate ligands. The cobalt compound (2) displays a polymeric structure, with infinite chains of CoII atoms. Two of the three Co centers have an octa­hedral N4O2 coordination environment that involves four pyridine ligands and two bridging sulfate ligands. The third Co center has an octa­hedral N3O3 coordination environment that involves three pyridine ligands, and two bridging sulfate ligands with one sulfate chelating the cobalt atom.

Structures of nitrato-(2-hydroxybenzaldehydo) (2,2 Prime -bipyridyl)copper and nitrato-(2-hydroxy-5-nitrobenzaldehydo)(2,2 Prime -bipyridyl)copper

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

Chumakov, Yu. M.; Paladi, L. G.; Antosyak, B. Ya.

2011-03-15

Nitrato-(2-hydroxy-5-nitrobenzaldehydo)(2,2 Prime -bipyridyl)copper (I) and nitrato-(2-hydroxybenzaldehydo)(2,2 Prime -bipyridyl)copper (II) were synthesized and characterized by X-ray diffraction. The coordination polyhedron of the central copper atom in complex I can be described as a distorted tetragonal pyramid whose base is formed by the phenol and carbonyl oxygen atoms of the monodeprotonated 2-hydroxy-5nitrobenzaldehyde molecule and the nitrogen atoms of the 2,2 Prime -bipyridyl ligand and whose apex is occupied by the oxygen atom of the nitrato group. In the crystal structure, complexes I are linked by the acido ligands and the NO{sub 2} groups of the aldehyde molecule into infinite chains. In complexmore » II, the central copper atom is coordinated by 2-hydroxybenzaldehyde, 2,2 Prime -bipyridyl, and the nitrato group, resulting in the formation of centrosymmetric dimers. The coordination polyhedron of the central copper atom can be described as a bipyramid (4 + 1 + 1) with the same base as in complex I. The axial vertices of the bipyramid are occupied by the oxygen atom of the nitrato group and the bridging phenol oxygen atom of the adjacent complex related to the initial complex by a center of symmetry. In the crystal structure, complexes II are hydrogen bonded into infinite chains.« less

Emergent universe with wormholes in massive gravity

NASA Astrophysics Data System (ADS)

Paul, B. C.; Majumdar, A. S.

2018-03-01

An emergent universe (EU) scenario is proposed to obtain a universe free from big-bang singularity. In this framework the present universe emerged from a static Einstein universe phase in the infinite past. A flat EU scenario is found to exist in Einstein’s gravity with a non-linear equation of state (EoS). It has been shown subsequently that a physically realistic EU model can be obtained considering cosmic fluid composed of interacting fluids with a non-linear equation of state. It results a viable cosmological model accommodating both early inflation and present accelerating phases. In the present paper, the origin of an initial static Einstein universe needed in the EU model is explored in a massive gravity theory which subsequently emerged to be a dynamically evolving universe. A new gravitational instanton solution in a flat universe is obtained in the massive gravity theory which is a dynamical wormhole that might play an important role in realizing the origin of the initial state of the emergent universe. The emergence of a Lorentzian universe from a Euclidean gravity is understood by a Wick rotation τ = i t . A universe with radiation at the beginning finally transits into the present observed universe with a non-linear EoS as the interactions among the fluids set in. Thus a viable flat EU scenario where the universe stretches back into time infinitely, with no big bang is permitted in a massive gravity.

Growth rate of the linear Richtmyer-Meshkov instability when a shock is reflected

NASA Astrophysics Data System (ADS)

Wouchuk, J. G.

2001-05-01

An analytic model is presented to calculate the growth rate of the linear Richtmyer-Meshkov instability in the shock-reflected case. The model allows us to calculate the asymptotic contact surface perturbation velocity for any value of the incident shock intensity, arbitrary fluids compressibilities, and for any density ratio at the interface. The growth rate comes out as the solution of a system of two coupled functional equations and is expressed formally as an infinite series. The distinguishing feature of the procedure shown here is the high speed of convergence of the intermediate calculations. There is excellent agreement with previous linear simulations and experiments done in shock tubes.

Applications of stochastic mechanics to polyatomic lattices

NASA Astrophysics Data System (ADS)

Beumée, J. G. B.; Vilallonga, E.; Rabitz, H.

1990-03-01

Stochastic quantization in the sense of Nelson provides an alternative interpretation of some aspects of quantum mechanics in the coordinate representation, and it was combined recently with the Ford, Kac, and Mazur (FKM) approximation [J. Math. Phys. 6, 504 (1965)] for large lattices to construct a quantum analog to the Brownian motion process. In this paper a similar approach is applied to model the effect of temperature fluctuations in a one-dimensional ordered chain of atoms with nearest-neighbor linear forces. However, we do not make use of the FKM approximation, and as a consequence the statistical properties of the involved processes are exactly determined by the lattice force field. In particular, we evaluate the covariance matrix for the fluctuations, and we examine its high- and low-temperature behavior. Because of the translation invariance of the interaction potential, the covariance matrix for the fluctuations becomes singular implying that the associated probability density has equal density along the zero eigenvector of the interaction matrix. This behavior is readily interpreted in terms of the motion of the center of mass of the system, which corresponds to a stochastically perturbed translation, while all other modes are bounded with a probability of 1. As is well known, the transformation to internal (bondlength) coordinates leads to a Hamiltonian specified by a nonsingular interaction matrix. We examine the variance of the fluctuations for the internal coordinates, and we show that in the high-temperature limit the result agrees with that of classical statistical mechanics. Both the position and bondlength of the surface atom decrease with time as is expected for a semi-infinite lattice. However, the position of the surface atom is less dependent on substrate-atom positions than is the surface bondlength on substrate bondlengths. Finally, the autocorrelation function of the surface bondlength in the case of a semi-infinite lattice limit is investigated for low- and high-temperature limits.

Rheology modification with ring polymers

NASA Astrophysics Data System (ADS)

Vlassopoulos, Dimitris

It is now established that experimental unconcatenated ring polymers can be purified effectively by means of fractionation at the critical condition. For molecular weights well above the entanglement threshold, purified rings relax stress via power-law (with an exponent of about -0.4), sharply departing from their linear counterparts. Experimental results are in harmony with modeling predictions and simulations. Here, we present results from recent interdisciplinary efforts and discuss two challenges: (i) the nonlinear shear rheology of purified ring melts is also very different from that of unlinked chains. Whereas the latter exhibit features that can be explained, to a first approach, in the framework in the tube model, the former behave akin to unentangled chains with finite extensibility and exhibit much small deformation at steady state. (ii) blends of rings and linear polymers exhibit unique features in different regimes: The addition of minute amounts of linear chains drastically affects ring dynamics. This relates to ring purity and the ability of unlinked linear chains to thread rings. With the help of simulations, it is possible to rationalize the observed surprisingly slow viscoelastic relaxation, which is attributed to ring-linear and ring-ring penetrations. On the other hand, adding small amounts of rings to linear polymers of different molecular weights influences their linear and nonlinear rheology in an unprecedented way. The blend viscosity exceeds that of the slower component (linear) in this non-interacting mixture, and its dependencies on composition and molecular weight ratio are examined, whereas the role of molecular architecture is also addressed. Consequently, closing the ends of a linear chain can serve as a powerful means for molecular manipulation of its rheology. This presentation reflects collaborative efforts with S. Costanzo, Z-C. Yan, R. Pasquino, M. Kaliva, S. Kamble, Y. Jeong, P. Lutz, J. Allgaier, T. Chang, D. Talikis, V. Mavrantzas and M. Rubinstein.

Effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Astrophysics Data System (ADS)

Saunders, B. V.; Murray, B. T.; McFadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1991-10-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress free boundaries is studied using Floquet theory for the linear stability analysis. Situations are considered for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double diffusive convection. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency.

Shear and elongational rheology of photo-oxidative degraded HDPE and LLDPE

NASA Astrophysics Data System (ADS)

Wagner, Manfred Hermann; Zheng, Wang; Wang, Peng; Talamante, Sebastián Ramos; Narimissa, Esmaeil

2017-05-01

The effect of photo-oxidative degradation of high-density polyethylene (HDPE) and linear low-density polyethylene (LLDPE) was investigated by linear and non-linear rheological measurements. The linear-viscoelastic rheological measurements were performed at different temperatures, while the elongational viscosity was measured at 170°C and at different strain rates. The rheological data are indicative of structural changes caused by photo-oxidative degradation including formation of long-chain branches (LCB), cross-linking, and chain scission, and they revealed a cyclic and continuing competition between chain scission and LCB/gel formation. These findings are supported by additional FTIR measurements and direct measurements of the gel content of the degraded samples.

Interaction of CO with an Au monatomic chain at different strains: Electronic structure and ballistic transport

NASA Astrophysics Data System (ADS)

Sclauzero, Gabriele; Dal Corso, Andrea; Smogunov, Alexander

2012-04-01

We study the energetics, the electronic structure, and the ballistic transport of an infinite Au monatomic chain with an adsorbed CO molecule. We find that the bridge adsorption site is energetically favored with respect to the atop site, both at the equilibrium Au-Au spacing of the chain and at larger spacings. Instead, a substitutional configuration requires a very elongated Au-Au bond, well above the rupture distance of the pristine Au chain. The electronic structure properties can be described by the Blyholder model, which involves the formation of bonding/antibonding pairs of 5σ and 2π states through the hybridization between molecular levels of CO and metallic states of the chain. In the atop geometry, we find an almost vanishing conductance due to the 5σ antibonding states giving rise to a Fano-like destructive interference close to the Fermi energy. In the bridge geometry, instead, the same states are shifted to higher energies and the conductance reduction with respect to pristine Au chain is much smaller. We also examine the effects of strain on the ballistic transport, finding opposite behaviors for the atop and bridge conductances. Only the bridge geometry shows a strain dependence compatible with the experimental conductance traces.

An Exactly Soluble Model for Hopping Particles Moving with Correlations Between States due to Exchange Sites

NASA Astrophysics Data System (ADS)

Zhao, Xian-Geng; Jia, Sue-Tang

1992-09-01

The motion of hopping particles on an infinite chain is investigated. The model is characterized by the correlations between states due to exchange sites. The analytic solutions for this system are discussed in general case. For some special cases, exact results are obtained with the help of explicit calculations of propagators and mean square displacement deviation. Both probability propagators for the creation and annihilation of two particles or for the deformation and formation of Frenkel excitons are indicated.

8-Hydr­oxy-5,6,7-trimeth­oxy-2-phenyl-4H-chromen-4-one

PubMed Central

Theodoro, Jahyr E.; Santos, Djalma; Pérez, Hiram; da Silva, Maria Fátima das Graças Fernandes; Ellena, J.

2008-01-01

In the title compound, C18H16O6, the benzopyran group is essentially planar, with the O atoms of the substituent groups lying close to its mean plane. The mol­ecular conformation is governed by intra­molecular inter­actions. The crystal packing is mainly determined by one classical inter­molecular hydrogen bond which gives rise to the formation of an infinite chain along the a axis. PMID:21202382

1-(o-Tol­yl)thio­urea

PubMed Central

Corrêa, Rodrigo S.; Ribeiro, Leandro; Ellena, Javier; Estévez-Hernández, Osvaldo; Duque, Julio

2008-01-01

In the title compound, C8H10N2S, the o-tolyl group and the thio­urea core are planar. The mean planes of the two groups are almost perpendicular [82.19 (8)°]. The thio­urea group is in the thio­amide form, in which resonance is present. In the crystal structure, mol­ecules are linked by inter­molecular N—H⋯S hydrogen bonds, forming two infinite chains parallel to the (110) and (10) planes. PMID:21201662

Chain-Length-Dependent Exciton Dynamics in Linear Oligothiophenes Probed Using Ensemble and Single-Molecule Spectroscopy.

PubMed

Kim, Tae-Woo; Kim, Woojae; Park, Kyu Hyung; Kim, Pyosang; Cho, Jae-Won; Shimizu, Hideyuki; Iyoda, Masahiko; Kim, Dongho

2016-02-04

Exciton dynamics in π-conjugated molecular systems is highly susceptible to conformational disorder. Using time-resolved and single-molecule spectroscopic techniques, the effect of chain length on the exciton dynamics in a series of linear oligothiophenes, for which the conformational disorder increased with increasing chain length, was investigated. As a result, extraordinary features of the exciton dynamics in longer-chain oligothiophene were revealed. Ultrafast fluorescence depolarization processes were observed due to exciton self-trapping in longer and bent chains. Increase in exciton delocalization during dynamic planarization processes was also observed in the linear oligothiophenes via time-resolved fluorescence spectra but was restricted in L-10T because of its considerable conformational disorder. Exciton delocalization was also unexpectedly observed in a bent chain using single-molecule fluorescence spectroscopy. Such delocalization modulates the fluorescence spectral shape by attenuating the 0-0 peak intensity. Collectively, these results provide significant insights into the exciton dynamics in conjugated polymers.

Ionizable side chains at catalytic active sites of enzymes.

PubMed

Jimenez-Morales, David; Liang, Jie; Eisenberg, Bob

2012-05-01

Catalytic active sites of enzymes of known structure can be well defined by a modern program of computational geometry. The CASTp program was used to define and measure the volume of the catalytic active sites of 573 enzymes in the Catalytic Site Atlas database. The active sites are identified as catalytic because the amino acids they contain are known to participate in the chemical reaction catalyzed by the enzyme. Acid and base side chains are reliable markers of catalytic active sites. The catalytic active sites have 4 acid and 5 base side chains, in an average volume of 1,072 Å(3). The number density of acid side chains is 8.3 M (in chemical units); the number density of basic side chains is 10.6 M. The catalytic active site of these enzymes is an unusual electrostatic and steric environment in which side chains and reactants are crowded together in a mixture more like an ionic liquid than an ideal infinitely dilute solution. The electrostatics and crowding of reactants and side chains seems likely to be important for catalytic function. In three types of analogous ion channels, simulation of crowded charges accounts for the main properties of selectivity measured in a wide range of solutions and concentrations. It seems wise to use mathematics designed to study interacting complex fluids when making models of the catalytic active sites of enzymes.

Ionizable Side Chains at Catalytic Active Sites of Enzymes

PubMed Central

Jimenez-Morales, David; Liang, Jie

2012-01-01

Catalytic active sites of enzymes of known structure can be well defined by a modern program of computational geometry. The CASTp program was used to define and measure the volume of the catalytic active sites of 573 enzymes in the Catalytic Site Atlas database. The active sites are identified as catalytic because the amino acids they contain are known to participate in the chemical reaction catalyzed by the enzyme. Acid and base side chains are reliable markers of catalytic active sites. The catalytic active sites have 4 acid and 5 base side chains, in an average volume of 1072 Å3. The number density of acid side chains is 8.3 M (in chemical units); the number density of basic side chains is 10.6 M. The catalytic active site of these enzymes is an unusual electrostatic and steric environment in which side chains and reactants are crowded together in a mixture more like an ionic liquid than an ideal infinitely dilute solution. The electrostatics and crowding of reactants and side chains seems likely to be important for catalytic function. In three types of analogous ion channels, simulation of crowded charges accounts for the main properties of selectivity measured in a wide range of solutions and concentrations. It seems wise to use mathematics designed to study interacting complex fluids when making models of the catalytic active sites of enzymes. PMID:22484856

A Chebyshev matrix method for spatial modes of the Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Danabasoglu, G.; Biringen, S.

1989-01-01

The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blausius boundary layer. The problem is linearized by the companion matrix technique for semi-infinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

A Zero-One Dichotomy Theorem for r-Semi-Stable Laws on Infinite Dimensional Linear Spaces.

DTIC Science & Technology

1978-10-01

SEMISTABLE LAWS - LIKE STABLE ONES - ARE CONTINUOUS: i.e. THEY ASSIGN’ ZERO MASS TO SIIMGLETONS.. DD 172 1 1473 sov’ow as, IMail , 62 i 1 SOee..S $.M 0 102 LfP.Of 4 6601 1ECIuatY CLASSI’PICA1 130N 00 1 100 0449 (W%4 Dma rwer

Collisionless absorption of intense laser radiation in nanoplasma

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

Zaretsky, D F; Korneev, Philipp A; Popruzhenko, Sergei V

The rate of linear collisionless absorption of an electromagnetic radiation in a nanoplasma - classical electron gas localised in a heated ionised nanosystem (thin film or cluster) irradiated by an intense femtosecond laser pulse - is calculated. The absorption is caused by the inelastic electron scattering from the self-consistent potential of the system in the presence of a laser field. The effect proves to be appreciable because of a small size of the systems. General expressions are obtained for the absorption rate as a function of the parameters of the single-particle self-consistent potential and electron distribution function in the regimemore » linear in field. For the simplest cases, where the self-consistent field is created by an infinitely deep well or an infinite charged plane, closed analytic expressions are obtained for the absorption rate. Estimates presented in the paper demonstrate that, over a wide range of the parameters of laser pulses and nanostructures, the collisionless mechanism of heating electron subsystem can be dominant. The possibility of experimental observation of the collisionless absorption of intense laser radiation in nanoplasma is also discussed. (interaction of laser radiation with matter)« less

The surface-induced spatial-temporal structures in confined binary alloys

NASA Astrophysics Data System (ADS)

Krasnyuk, Igor B.; Taranets, Roman M.; Chugunova, Marina

2014-12-01

This paper examines surface-induced ordering in confined binary alloys. The hyperbolic initial boundary value problem (IBVP) is used to describe a scenario of spatiotemporal ordering in a disordered phase for concentration of one component of binary alloy and order parameter with non-linear dynamic boundary conditions. This hyperbolic model consists of two coupled second order differential equations for order parameter and concentration. It also takes into account effects of the “memory” on the ordering of atoms and their densities in the alloy. The boundary conditions characterize surface velocities of order parameter and concentration changing which is due to surface (super)cooling on walls confining the binary alloy. It is shown that for large times there are three classes of dynamic non-linear boundary conditions which lead to three different types of attractor’s elements for the IBVP. Namely, the elements of attractor are the limit periodic simple shock waves with fronts of “discontinuities” Γ. If Γ is finite, then the attractor contains spatiotemporal functions of relaxation type. If Γ is infinite and countable then we observe the functions of pre-turbulent type. If Γ is infinite and uncountable then we obtain the functions of turbulent type.

Models of cylindrical bubble pulsation

PubMed Central

Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hay, Todd A.; Hamilton, Mark F.

2012-01-01

Three models are considered for describing the dynamics of a pulsating cylindrical bubble. A linear solution is derived for a cylindrical bubble in an infinite compressible liquid. The solution accounts for losses due to viscosity, heat conduction, and acoustic radiation. It reveals that radiation is the dominant loss mechanism, and that it is 22 times greater than for a spherical bubble of the same radius. The predicted resonance frequency provides a basis of comparison for limiting forms of other models. The second model considered is a commonly used equation in Rayleigh-Plesset form that requires an incompressible liquid to be finite in extent in order for bubble pulsation to occur. The radial extent of the liquid becomes a fitting parameter, and it is found that considerably different values of the parameter are required for modeling inertial motion versus acoustical oscillations. The third model was developed by V. K. Kedrinskii [Hydrodynamics of Explosion (Springer, New York, 2005), pp. 23–26] in the form of the Gilmore equation for compressible liquids of infinite extent. While the correct resonance frequency and loss factor are not recovered from this model in the linear approximation, it provides reasonable agreement with observations of inertial motion. PMID:22978863

Isotropic probability measures in infinite dimensional spaces: Inverse problems/prior information/stochastic inversion

NASA Technical Reports Server (NTRS)

Backus, George

1987-01-01

Let R be the real numbers, R(n) the linear space of all real n-tuples, and R(infinity) the linear space of all infinite real sequences x = (x sub 1, x sub 2,...). Let P sub n :R(infinity) approaches R(n) be the projection operator with P sub n (x) = (x sub 1,...,x sub n). Let p(infinity) be a probability measure on the smallest sigma-ring of subsets of R(infinity) which includes all of the cylinder sets P sub n(-1) (B sub n), where B sub n is an arbitrary Borel subset of R(n). Let p sub n be the marginal distribution of p(infinity) on R(n), so p sub n(B sub n) = p(infinity)(P sub n to the -1(B sub n)) for each B sub n. A measure on R(n) is isotropic if it is invariant under all orthogonal transformations of R(n). All members of the set of all isotropic probability distributions on R(n) are described. The result calls into question both stochastic inversion and Bayesian inference, as currently used in many geophysical inverse problems.

Generalized analytical solutions to sequentially coupled multi-species advective-dispersive transport equations in a finite domain subject to an arbitrary time-dependent source boundary condition

NASA Astrophysics Data System (ADS)

Chen, Jui-Sheng; Liu, Chen-Wuing; Liang, Ching-Ping; Lai, Keng-Hsin

2012-08-01

SummaryMulti-species advective-dispersive transport equations sequentially coupled with first-order decay reactions are widely used to describe the transport and fate of the decay chain contaminants such as radionuclide, chlorinated solvents, and nitrogen. Although researchers attempted to present various types of methods for analytically solving this transport equation system, the currently available solutions are mostly limited to an infinite or a semi-infinite domain. A generalized analytical solution for the coupled multi-species transport problem in a finite domain associated with an arbitrary time-dependent source boundary is not available in the published literature. In this study, we first derive generalized analytical solutions for this transport problem in a finite domain involving arbitrary number of species subject to an arbitrary time-dependent source boundary. Subsequently, we adopt these derived generalized analytical solutions to obtain explicit analytical solutions for a special-case transport scenario involving an exponentially decaying Bateman type time-dependent source boundary. We test the derived special-case solutions against the previously published coupled 4-species transport solution and the corresponding numerical solution with coupled 10-species transport to conduct the solution verification. Finally, we compare the new analytical solutions derived for a finite domain against the published analytical solutions derived for a semi-infinite domain to illustrate the effect of the exit boundary condition on coupled multi-species transport with an exponential decaying source boundary. The results show noticeable discrepancies between the breakthrough curves of all the species in the immediate vicinity of the exit boundary obtained from the analytical solutions for a finite domain and a semi-infinite domain for the dispersion-dominated condition.

Exotic states of matter with polariton chains

NASA Astrophysics Data System (ADS)

Kalinin, Kirill P.; Lagoudakis, Pavlos G.; Berloff, Natalia G.

2018-04-01

We consider linear periodic chains of exciton-polariton condensates formed by pumping polaritons nonresonantly into a linear network. To the leading order such a sequence of condensates establishes relative phases as to minimize a classical one-dimensional X Y Hamiltonian with nearest and next-to-nearest neighbors. We show that the low-energy states of polaritonic linear chains demonstrate various classical regimes: ferromagnetic, antiferromagnetic, and frustrated spiral phases where quantum or thermal fluctuations are expected to give rise to a spin-liquid state. At the same time nonlinear interactions at higher pumping intensities bring about phase chaos and novel exotic phases.

Non-linear wave interaction in a plasma column

NASA Technical Reports Server (NTRS)

Larsen, J.-M.; Crawford, F. W.

1979-01-01

Non-linear three-wave interaction is analysed for propagation along a cylindrical plasma column surrounded by an infinite dielectric, in the absence of a static magnetic field. An averaged-Lagrangian method is used, and the results are specialized to parametric interaction and mode conversion, assuming an undepleted pump wave. The theory for these two types of interactions is extended to include imperfect synchronism, and the effects of loss. Computations are presented indicating that parametric growth rates of the order of a fraction of a decibel per centimeter should be obtainable for plausible laboratory plasma column parameters.

Ethyl 2-[(carbamothioyl­amino)­imino]­propano­ate

PubMed Central

Corrêa, Charlane C.; Graúdo, José Eugênio J.C.; de Oliveira, Luiz Fernando C.; de Almeida, Mauro V.; Diniz, Renata

2011-01-01

The title compound, C6H11N3O2S, consists of a roughly planar mol­ecule (r.m.s deviation from planarity = 0.077 Å for the non-H atoms) and has the S atom in an anti position to the imine N atom. This N atom is the acceptor of a strongly bent inter­nal N—H⋯N hydrogen bond donated by the amino group. In the crystal, mol­ecules are arranged in undulating layers parallel to (010). The mol­ecules are linked via inter­molecular amino–carboxyl N—H⋯O hydrogen bonds, forming chains parallel to [001]. The chains are cross-linked by Ncarbazone—H⋯S and C—H⋯S inter­actions, forming infinite sheets. PMID:22091006

Infinite hidden conditional random fields for human behavior analysis.

PubMed

Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja

2013-01-01

Hidden conditional random fields (HCRFs) are discriminative latent variable models that have been shown to successfully learn the hidden structure of a given classification problem (provided an appropriate validation of the number of hidden states). In this brief, we present the infinite HCRF (iHCRF), which is a nonparametric model based on hierarchical Dirichlet processes and is capable of automatically learning the optimal number of hidden states for a classification task. We show how we learn the model hyperparameters with an effective Markov-chain Monte Carlo sampling technique, and we explain the process that underlines our iHCRF model with the Restaurant Franchise Rating Agencies analogy. We show that the iHCRF is able to converge to a correct number of represented hidden states, and outperforms the best finite HCRFs--chosen via cross-validation--for the difficult tasks of recognizing instances of agreement, disagreement, and pain. Moreover, the iHCRF manages to achieve this performance in significantly less total training, validation, and testing time.

Synthesis, Structure and bonding Analysis of the Polar Intermetallic Phase Ca2Pt2Cd

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

Samal, Saroj L.; Corbett, John D.

The polar intermetallic phase Ca2Pt2Cd was discovered during explorations of the Ca-Pt-Cd system. The compound was synthesized by high temperature reactions, and its structure refined by single-crystal X-ray diffraction as orthorhombic, Immm, a = 4.4514(5), b = 5.8415(6), c = 8.5976(9) Å, Z = 2. The structure formally contains infinite, planar networks of [Pt2Cd]4– along the ab plane, which can be described as tessellation of six and four-member rings of the anions, with cations stuffed between the anion layers. The infinite condensed platinum chains show a substantial long–short distortion of 0.52 Å, an appreciable difference between Ca2Pt2Cd (26 valence electrons)more » and the isotypic but regular Ca2Cu2Ga (29 VE). The relatively large cation proportion diminishes the usual dominance of polar (Pt–Cd) and 5d–5d (Pt–Pt) contributions to the total Hamilton populations.« less

The effect of polymer architecture on the interdiffusion in thin polymer films

NASA Astrophysics Data System (ADS)

Caglayan, Ayse; Yuan, Guangcui; Satija, Sushil K.; Uhrig, David; Hong, Kunlun; Akgun, Bulent

Branched polymer chains have been traditionally used in industrial applications as additives. Recently they have found applications in electrochromic displays, lithography, biomedical coatings and targeting multidrug resistant bacteria. In some of these applications where they are confined in thin layers, it is important to understand the relation between the mobility and polymer chain architecture to optimize the processing conditions. Earlier interdiffusion measurements on linear and cyclic polymer chains demonstrated the key role of chain architecture on mobility. We have determined the vertical diffusion coefficients of the star polystyrene chains in thin films as a function of number of polymer arms, molecular weight per arm, and film thickness using neutron reflectivity (NR) and compare our results with linear chains of identical total molecular weight. Bilayer samples of 4-arm and 8-arm protonated polystyrenes (hPS) and deuterated polystyrenes (dPS) were used to elucidate the effect of polymer chain architecture on polymer diffusion. NR measurements indicate that the mobility of polymer chains in thin films get faster as the number of polymer arms increases and the arm molecular weight decreases. Both star polymers showed faster interdiffusion compared to their linear analog. Diffusion coefficient of branched PS chains has a weak dependence on the film thickness.

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

Heat conduction in diatomic chains with correlated disorder

NASA Astrophysics Data System (ADS)

Savin, Alexander V.; Zolotarevskiy, Vadim; Gendelman, Oleg V.

2017-01-01

The paper considers heat transport in diatomic one-dimensional lattices, containing equal amounts of particles with different masses. Ordering of the particles in the chain is governed by single correlation parameter - the probability for two neighboring particles to have the same mass. As this parameter grows from zero to unity, the structure of the chain varies from regular staggering chain to completely random configuration, and then - to very long clusters of particles with equal masses. Therefore, this correlation parameter allows a control of typical cluster size in the chain. In order to explore different regimes of the heat transport, two interatomic potentials are considered. The first one is an infinite potential wall, corresponding to instantaneous elastic collisions between the neighboring particles. In homogeneous chains such interaction leads to an anomalous heat transport. The other one is classical Lennard-Jones interatomic potential, which leads to a normal heat transport. The simulations demonstrate that the correlated disorder of the particle arrangement does not change the convergence properties of the heat conduction coefficient, but essentially modifies its value. For the collision potential, one observes essential growth of the coefficient for fixed chain length as the limit of large homogeneous clusters is approached. The thermal transport in these models remains superdiffusive. In the Lennard-Jones chain the effect of correlation appears to be not monotonous in the limit of low temperatures. This behavior stems from the competition between formation of long clusters mentioned above, and Anderson localization close to the staggering ordered state.

Solvothermal syntheses and characterization of three new silver(I)/copper(I)-thioarsenates based on As2+/As3+ ions

NASA Astrophysics Data System (ADS)

Yao, Hua-Gang; Tang, Cheng-Fei; An, Yong-Lin; Ou, Zi-Jian; Wu, Guo-Hao; Lan, Pei; Zheng, Yi-Long

2017-02-01

Three new silver(I)/copper(I)-thioarsenates KAgAsIIS2 (1), RbCu2AsIIIS3 (2) and RbCu4AsIIIS4 (3) have been solvothermally synthesized and structurally characterized. 1 exhibits a two-dimensional anionic network built up by As-As bond connecting the left- and right-handed helical [AgS2]4- chains, and represents the first examples of thioarsenates(II). The structure of 2 consists of two kinds of helical [Cu2S3]4- chains linked by the arsenic atoms to form double layers with rubidium ions between the layers. Compound 3 is built up of infinite [Cu2S2]2- chain and layered [Cu6As2S6] linked to form a three-dimensional anionic framework, [Cu4AsS4]-, and containing channels in which the rubidium cations reside. The optical properties of 1-3 have been investigated by UV-vis spectroscopy.

Large bond-dimension time-evolution block decimation study of the XXZ quantum spin chains of S = 1/2 and 1

NASA Astrophysics Data System (ADS)

Choi, Hwan Bin; Lee, Ji-Woo

2017-09-01

We study quantum phase transitions of a XXZ spin model with spin S = 1/2 and 1 in one dimension. The XXZ spin chain is one of basic models in understanding various one-dimensional magnetic materials. To study this model, we construct infinite-lattice matrix product state (iMPS), which is a tensor product form for a one-dimensional many-body quantum wave function. By using timeevolution- block-decimation method (TEBD) on iMPS, we obtain the ground states of the XXZ model at zero temperature. This method is very delicate in calculating ground states so that we developed a reliable method of finding the ground state with the dimension of entanglement coefficients up to 300, which is beyond the previous works. By analyzing ground-state energies, half-chain entanglement entropies, and entanglement spectrum, we found the signatures of quantum phase transitions between ferromagnetic phase, XY phase, Haldane phase, and antiferromagnetic phase.

Propagating synchrony in feed-forward networks

PubMed Central

Jahnke, Sven; Memmesheimer, Raoul-Martin; Timme, Marc

2013-01-01

Coordinated patterns of precisely timed action potentials (spikes) emerge in a variety of neural circuits but their dynamical origin is still not well understood. One hypothesis states that synchronous activity propagating through feed-forward chains of groups of neurons (synfire chains) may dynamically generate such spike patterns. Additionally, synfire chains offer the possibility to enable reliable signal transmission. So far, mostly densely connected chains, often with all-to-all connectivity between groups, have been theoretically and computationally studied. Yet, such prominent feed-forward structures have not been observed experimentally. Here we analytically and numerically investigate under which conditions diluted feed-forward chains may exhibit synchrony propagation. In addition to conventional linear input summation, we study the impact of non-linear, non-additive summation accounting for the effect of fast dendritic spikes. The non-linearities promote synchronous inputs to generate precisely timed spikes. We identify how non-additive coupling relaxes the conditions on connectivity such that it enables synchrony propagation at connectivities substantially lower than required for linearly coupled chains. Although the analytical treatment is based on a simple leaky integrate-and-fire neuron model, we show how to generalize our methods to biologically more detailed neuron models and verify our results by numerical simulations with, e.g., Hodgkin Huxley type neurons. PMID:24298251

Inhibition of telomerase by linear-chain fatty acids: a structural analysis.

PubMed Central

Oda, Masako; Ueno, Takamasa; Kasai, Nobuyuki; Takahashi, Hirotada; Yoshida, Hiromi; Sugawara, Fumio; Sakaguchi, Kengo; Hayashi, Hideya; Mizushina, Yoshiyuki

2002-01-01

In the present study, we have found that mono-unsaturated linear-chain fatty acids in the cis configuration with C(18) hydrocarbon chains (i.e. oleic acid) strongly inhibited the activity of human telomerase in a cell-free enzymic assay, with an IC(50) value of 8.6 microM. Interestingly, fatty acids with hydrocarbon chain lengths below 16 or above 20 carbons substantially decreased the potency of inhibition of telomerase. Moreover, the cis-mono-unsaturated C(18) linear-chain fatty acid oleic acid was the strongest inhibitor of all the fatty acids tested. A kinetic study revealed that oleic acid competitively inhibited the activity of telomerase ( K (i)=3.06 microM) with respect to the telomerase substrate primer. The energy-minimized three-dimensional structure of the linear-chain fatty acid was calculated and modelled. A molecule width of 11.53-14.26 A (where 1 A=0.1 nm) in the C(16) to C(20) fatty acid structure was suggested to be important for telomerase inhibition. The three-dimensional structure of the telomerase active site (i.e. the substrate primer-binding site) appears to have a pocket that could bind oleic acid, with the pocket being 8.50 A long and 12.80 A wide. PMID:12121150

Quantum networks in divergence-free circuit QED

NASA Astrophysics Data System (ADS)

Parra-Rodriguez, A.; Rico, E.; Solano, E.; Egusquiza, I. L.

2018-04-01

Superconducting circuits are one of the leading quantum platforms for quantum technologies. With growing system complexity, it is of crucial importance to develop scalable circuit models that contain the minimum information required to predict the behaviour of the physical system. Based on microwave engineering methods, divergent and non-divergent Hamiltonian models in circuit quantum electrodynamics have been proposed to explain the dynamics of superconducting quantum networks coupled to infinite-dimensional systems, such as transmission lines and general impedance environments. Here, we study systematically common linear coupling configurations between networks and infinite-dimensional systems. The main result is that the simple Lagrangian models for these configurations present an intrinsic natural length that provides a natural ultraviolet cutoff. This length is due to the unavoidable dressing of the environment modes by the network. In this manner, the coupling parameters between their components correctly manifest their natural decoupling at high frequencies. Furthermore, we show the requirements to correctly separate infinite-dimensional coupled systems in local bases. We also compare our analytical results with other analytical and approximate methods available in the literature. Finally, we propose several applications of these general methods to analogue quantum simulation of multi-spin-boson models in non-perturbative coupling regimes.

First Observations of Laser-Driven Acceleration of Relativistic Electrons in a Semi-Infinite Vacuum Space

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

Plettner, T.; Byer, R.L.; Smith, T.I.

2006-02-17

We have observed acceleration of relativistic electrons in vacuum driven by a linearly polarized visible laser beam incident on a thin gold-coated reflective boundary. The observed energy modulation effect follows all the characteristics expected for linear acceleration caused by a longitudinal electric field. As predicted by the Lawson-Woodward theorem the laser driven modulation only appears in the presence of the boundary. It shows a linear dependence with the strength of the electric field of the laser beam and also it is critically dependent on the laser polarization. Finally, it appears to follow the expected angular dependence of the inverse transitionmore » radiation process. experiment as the Laser Electron Accelerator Project (LEAP).« less

Spectroscopic and structural investigation of 2,5-dicarboxy-1-methylpyridinium inner salt

NASA Astrophysics Data System (ADS)

Barczyński, P.; Komasa, A.; Katrusiak, A.; Dega-Szafran, Z.; Nowaczyk, Ł.; Ratajczak-Sitarz, M.; Szafran, M.

2014-03-01

The structure of 2,5-dicarboxy-1-methylpyridinium inner salt (1), has been studied by X-ray diffraction, B3LYP/6-311G(d,p) calculations, FTIR, Raman and NMR spectroscopy. The molecules are linked by short intermolecular and asymmetric Osbnd H⋯O hydrogen bonds of 2.486(2) Å between carboxyl and carboxylate groups of neighboring molecules into infinite chains. The hydrogen bonds in the molecules optimized by the B3LYP/6-311G(d,p) approach in trimer (2) and dimer (3) are slightly longer than in the crystal. The FTIR spectrum of the investigated inner salt is dominated by a broad and intense absorption in the 1500-800 cm-1 region attributed to the νas(OHO) and γ(OHO) vibrations of the strong hydrogen bond. In the Raman spectrum the broad absorption is absent. Linear correlations, δexp = a + b σcalc between the experimental 1H and 13C NMR chemical shifts (δexp) of the investigated inner salt in D2O and the calculated magnetic isotropic shielding constants (σcalc) for the optimized monomer (4a) solvated in water are reported. The pKa value for 1 of 2.31 ± 0.02 was determined by the potentiometric titration.

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

Li, Hao; Malliakas, Christos D.; Han, Fei

The quaternary compound TlHgInS3 crystallizes in a new structure type of space group, C2/c, with cell parameters a = 13.916(3) angstrom, b = 3.9132(8) angstrom, c = 21.403(4) angstrom, beta = 104.16(3)degrees, V = 1130.1(8) angstrom(3), and rho = 7.241 g/cm(3). The structure is a unique three-dimensional framework with parallel tunnels, which is formed by (1)(infinity)[InS33-] infinite chains bridged by linearly coordinated Hg2+ ions. TlHgInS3 is a semiconductor with a band gap of 1.74 eV and a resistivity of similar to 4.32 G Omega cm. TlHgInS3 single crystals exhibit photocurrent response when exposed to Ag X-rays. The mobility-lifetime product (mumore » tau) of the electrons and holes estimated from the photocurrent measurements are (mu tau)(e) approximate to 3.6 x 10(-4) cm(2)/V and (mu tau)(h) approximate to 2.0 x 10(-4) cm(2)/V. Electronic structure calculations at the density functional theory level indicate an indirect band gap and a relatively small effective mass for both electrons and holes. Based on the photoconductivity data, TlHgInS3 is a potential material for radiation detection applications.« less

Three-dimensional thermocapillary flow regimes with evaporation

NASA Astrophysics Data System (ADS)

Bekezhanova, V. B.; Goncharova, O. N.

2017-10-01

A three-dimensional problem of evaporative convection in a system of the immiscible media with a common thermocapillary interface is studied. New exact solution, which is a generalization of the Ostroumov - Birikh solution of the Navier - Stokes equations in the Oberbeck - Boussinesq approximation, is presented in order to describe the joint flows of the liquid and gas - vapor mixture in an infinite channel with a rectangular cross-section. The motion occurs in the bulk force field under action of a constant longitudinal temperature gradient. The velocity components depend only on the transverse coordinates. The functions of pressure, temperature and concentration of vapor in the gas are characterized by the linear dependence on the longitudinal coordinate. In the framework of the problem statement, which takes into account diffusive mass flux through the interface and zero vapor flux at the upper boundary of the channel, the influence of the gravity and intensity of the thermal action on flow structure is studied. The original three-dimensional problem is reduced to a chain of two-dimensional problems which are solved numerically with help of modification of the method of alternating directions. Arising flows can be characterized as a translational-rotational motion, under that the symmetrical double, quadruple or sextuple vortex structures are formed. Quantity, shape and structure of the vortexes also depend on properties of the working media.

Exact solution of corner-modified banded block-Toeplitz eigensystems

NASA Astrophysics Data System (ADS)

Cobanera, Emilio; Alase, Abhijeet; Ortiz, Gerardo; Viola, Lorenza

2017-05-01

Motivated by the challenge of seeking a rigorous foundation for the bulk-boundary correspondence for free fermions, we introduce an algorithm for determining exactly the spectrum and a generalized-eigenvector basis of a class of banded block quasi-Toeplitz matrices that we call corner-modified. Corner modifications of otherwise arbitrary banded block-Toeplitz matrices capture the effect of boundary conditions and the associated breakdown of translational invariance. Our algorithm leverages the interplay between a non-standard, projector-based method of kernel determination (physically, a bulk-boundary separation) and families of linear representations of the algebra of matrix Laurent polynomials. Thanks to the fact that these representations act on infinite-dimensional carrier spaces in which translation symmetry is restored, it becomes possible to determine the eigensystem of an auxiliary projected block-Laurent matrix. This results in an analytic eigenvector Ansatz, independent of the system size, which we prove is guaranteed to contain the full solution of the original finite-dimensional problem. The actual solution is then obtained by imposing compatibility with a boundary matrix, whose shape is also independent of system size. As an application, we show analytically that eigenvectors of short-ranged fermionic tight-binding models may display power-law corrections to exponential behavior, and demonstrate the phenomenon for the paradigmatic Majorana chain of Kitaev.

Computation of output feedback gains for linear stochastic systems using the Zangnill-Powell Method

NASA Technical Reports Server (NTRS)

Kaufman, H.

1975-01-01

Because conventional optimal linear regulator theory results in a controller which requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. To this effect a stochastic linear model has been developed that accounts for process parameter and initial uncertainty, measurement noise, and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was then performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell. Results using a seventh order process show the proposed procedures to be very effective.

Sinc-Galerkin estimation of diffusivity in parabolic problems

NASA Technical Reports Server (NTRS)

Smith, Ralph C.; Bowers, Kenneth L.

1991-01-01

A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

A selection principle for Benard-type convection

NASA Technical Reports Server (NTRS)

Knightly, G. H.; Sather, D.

1985-01-01

In a Benard-type convection problem, the stationary flows of an infinite layer of fluid lying between two rigid horizontal walls and heated uniformly from below are determined. As the temperature difference across the layer increases beyond a certain value, other convective motions appear. These motions are often cellular in character in that their streamlines are confined to certain well-defined cells having, for example, the shape of rolls or hexagons. A selection principle that explains why hexagonal cells seem to be preferred for certain ranges of the parameters is formulated. An operator-theoretical formulation of one generalized Bernard problem is given. The infinite dimensional problem is reduced to one of solving a finite dimensional system of equations, namely, the selection equations. These equations are solved and a linearized stability analysis of the resultant stationary flows is presented.

Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded Time-Varying Delays

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

Meng, Ziyang; Yang, Tao; Li, Guoqi

We study synchronization of coupled linear systems over networks with weak connectivity and time-varying delays. We focus on the case that the internal dynamics are time-varying but non-expansive. Both uniformly connected and infinitely connected communication topologies are considered. A new concept of P-synchronization is introduced and we first show that global asymptotic P-synchronization can be achieved over directed networks with uniform joint connectivity and arbitrarily bounded delays. We then study the case of the infinitely jointly connected communication topology. In particular, for the undirected communication topologies, it turns out that the existence of a uniform time interval for the communicationmore » topology is not necessary and P-synchronization can be achieved when the time varying delays are arbitrarily bounded. Simulations are given to validate the theoretical results.« less

Nearly bound states in the radiation continuum in a circular array of dielectric rods

NASA Astrophysics Data System (ADS)

Bulgakov, Evgeny N.; Sadreev, Almas F.

2018-03-01

We consider E -polarized bound states in the radiation continuum (BICs) in circular periodical arrays of N infinitely long dielectric rods. We find that each true BIC which occurs in an infinite linear array has its counterpart in the circular array as a near-BIC with extremely large quality factor. We argue analytically as well as numerically that the quality factor of the symmetry-protected near-BICs diverges as eλ N, where λ is a material parameter dependent on the radius and the refraction index of the rods. By tuning of the radius of rods, we also find numerically non-symmetry-protected near-BICs. These near-BICs are localized with exponential accuracy outside the circular array, but fill the whole inner space of the array carrying orbital angular momentum.

Self-similar Relativisitic Disks revisted

NASA Astrophysics Data System (ADS)

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

2001-05-01

We revisit the rotating self-similar disk first studied by Lynden-Bell and Pineault and extend it to include pressure. A two-parameter family of solutions is constructed numerically. These disks are parameterized by the constant linear rotation velocity v, and the isothermal sound speed γ 1/2. For sufficiently high velocities, an ergo region develops in the form of the exterior of a cone. For each value of γ , there is a maximum velocity vc above which there is no equilibrium solutions. For this solution the frame dragging is infinite and the ergo cone closes on the rotation axis. The null geodesic equations are also integrated numerically. Due to the infinite extend and mass of the system, all photon trajectories are focused towards the disk. The behavior of equatorial photons orbits is qualitatively the same as that of cold disks.

A selection principle in Benard-type convection

NASA Technical Reports Server (NTRS)

Knightly, G. H.; Sather, D.

1983-01-01

In a Benard-type convection problem, the stationary flows of an infinite layer of fluid lying between two rigid horizontal walls and heated uniformly from below are determined. As the temperature difference across the layer increases beyond a certain value, other convective motions appear. These motions areoften cellular in character in that their streamlines are confined to certain well-defined cells having, for example, the shape of rolls or hexagons. A selection principle that explains why hexagonal cells seem to be preferred for certain ranges of the parameters is formulated. An operator-theoretical formulation of one generalized Bernard problem is given. The infinite dimensional problem is reduced to one of solving a finite dimensional system of equations, namely, the selection equations. These equations are solved and a linearized stability analysis of the resultant stationary flows is presented.

Pressure-induced stable BeN4 as a high-energy density material

NASA Astrophysics Data System (ADS)

Zhang, Shoutao; Zhao, Ziyuan; Liu, Lulu; Yang, Guochun

2017-10-01

Polynitrogens are the ideal rocket fuels or propellants. Due to strong triple N≡N bond in N2, the direct polymerization of nitrogen is rather difficult (i.e. extreme high temperature and high pressure). However, the use of nitrides as precursors or the reaction of N2 with other elements has been proved to be an effective way to obtain polynitrogens. Here, with assistance of the advanced first-principles swarm-intelligence structure searches, we found that P 1 bar -BeN4, containing infinite zigzag-like polymeric nitrogen chains, can be synthesized by compressing the mixture of Be3N2 and N2 at 25.4 GPa, which is greatly lower than 110 GPa for synthesizing cubic gauche nitrogen and other polynitrogen compounds (e.g. bulk CNO at 52 GPa and SN4 at 49 GPa). Its structural stability can be attributed to the coexistence of ionic Be-N and covalent N-N bonds. Intriguingly, this phase has high kinetic stability and remains metastable at ambient pressure. The exceptional properties, including high energy density (3.60 kJ g-1), high nitrogen content (86.1%), high dynamical stability, and low polymerization pressure, make P 1 bar -structured BeN4 a promising high energy material. Infinite nitrogen chains in P 1 bar -BeN4 transform to N10 rings network in P21/c phase at 115.1 GPa. P 1 bar -BeN4 is metallic, while P21/c-BeN4 is an insulator.

Theoretical and computational studies of excitons in conjugated polymers

NASA Astrophysics Data System (ADS)

Barford, William; Bursill, Robert J.; Smith, Richard W.

2002-09-01

We present a theoretical and computational analysis of excitons in conjugated polymers. We use a tight-binding model of π-conjugated electrons, with 1/r interactions for large r. In both the weak-coupling limit (defined by W>>U) and the strong-coupling limit (defined by W<

Nanoprobe diffusion in entangled polymer solutions: Linear vs. unconcatenated ring chains

NASA Astrophysics Data System (ADS)

Nahali, Negar; Rosa, Angelo

2018-05-01

We employ large-scale molecular dynamics computer simulations to study the problem of nanoprobe diffusion in entangled solutions of linear polymers and unknotted and unconcatenated circular (ring) polymers. By tuning both the diameter of the nanoprobe and the density of the solution, we show that nanoprobes of diameter smaller than the entanglement distance (tube diameter) of the solution display the same (Rouse-like) behavior in solutions of both polymer architectures. Instead, nanoprobes with larger diameters appear to diffuse markedly faster in solutions of rings than in solutions of linear chains. Finally, by analysing the distribution functions of spatial displacements, we find that nanoprobe motion in rings' solutions shows both Gaussian and ergodic behaviors, in all regimes considered, while, in solutions of linear chains, nanoprobes exceeding the size of the tube diameter show a transition to non-Gaussian and non-ergodic motion. Our results emphasize the role of chain architecture in the motion of nanoprobes dispersed in polymer solutions.

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

NASA Astrophysics Data System (ADS)

Antown, Fadi; Dragičević, Davor; Froyland, Gary

2018-03-01

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

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.

Detections of Long Carbon Chains CH_{3}CCCCH, C_{6}H, LINEAR-C_{6}H_{2} and C_{7}H in the Low-Mass Star Forming Region L1527

NASA Astrophysics Data System (ADS)

Araki, Mitsunori; Takano, Shuro; Sakai, Nami; Yamamoto, Satoshi; Oyama, Takahiro; Kuze, Nobuhiko; Tsukiyama, Koichi

2017-06-01

Carbon chains in the warm carbon chain chemistry (WCCC) region has been searched in the 42-44 GHz region by using Green Bank 100 m telescope. Long carbon chains C_{7}H, C_{6}H, CH_{3}CCCCH, and linear-C_{6}H_{2} and cyclic species C_{3}H and C_{3}H_{2}O have been detected in the low-mass star forming region L1527, performing the WCCC. C_{7}H was detected for the first time in molecular clouds. The column density of C_{7}H is derived to be 6.2 × 10^{10} cm^{-2} by using the detected J = 24.5-23.5 and 25.5-24.5 rotational lines. The ^{2}Π_{1/2} electronic state of C_{6}H, locating 21.6 K above the ^{2}Π_{3/2} electronic ground state, and the K_a = 0 line of the para species of linear-C_{6}H_{2} were also detected firstly in molecular clouds. The column densities of the ^{2}Π_{1/2} and ^{2}Π_{3/2} states of C_{6}H in L1527 were derived to be 1.6 × 10^{11} and 1.1 × 10^{12} cm^{-2}, respectively. The total column density of linear-C_{6}H_{2} is obtained to be 1.86 × 10^{11} cm^{-2}. While the abundance ratios of carbon chains in between L1527 and the starless dark cloud Taurus Molecular Cloud-1 Cyanopolyyne Peak (TMC-1 CP) have a trend of decrease by extension of carbon-chain length, column densities of CH_{3}CCCCH and C_{6}H are on the trend. However, the column densities of linear-C_{6}H_{2}, and C_{7}H are as abundant as those of TMC-1 CP in spite of long carbon chain, i.e., they are not on the trend. The abundances of linear-C_{6}H_{2} and C_{7}H show that L1527 is rich for long carbon chains as well as TMC-1 CP.

Asymptotic Eigenstructures

NASA Technical Reports Server (NTRS)

Thompson, P. M.; Stein, G.

1980-01-01

The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain, feedback decouples into single input, single output systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.

Influence of chain topology on polymer crystallization: poly(ethylene oxide) (PEO) rings vs. linear chains.

PubMed

Zardalidis, George; Mars, Julian; Allgaier, Jürgen; Mezger, Markus; Richter, Dieter; Floudas, George

2016-10-04

The absence of entanglements, the more compact structure and the faster diffusion in melts of cyclic poly(ethylene oxide) (PEO) chains have consequences on their crystallization behavior at the lamellar and spherulitic length scales. Rings with molecular weight below the entanglement molecular weight (M < M e ), attain the equilibrium configuration composed from twice-folded chains with a lamellar periodicity that is half of the corresponding linear chains. Rings with M > M e undergo distinct step-like conformational changes to a crystalline lamellar with the equilibrium configuration. Rings melt from this configuration in the absence of crystal thickening in sharp contrast to linear chains. In general, rings more easily attain their extended equilibrium configuration due to strained segments and the absence of entanglements. In addition, rings have a higher equilibrium melting temperature. At the level of the spherulitic superstructure, growth rates are much faster for rings reflecting the faster diffusion and more compact structure. With respect to the segmental dynamics in their semi-crystalline state, ring PEOs with a steepness index of ∼34 form some of the "strongest" glasses.

FAST TRACK PAPER: Non-iterative multiple-attenuation methods: linear inverse solutions to non-linear inverse problems - II. BMG approximation

NASA Astrophysics Data System (ADS)

Ikelle, Luc T.; Osen, Are; Amundsen, Lasse; Shen, Yunqing

2004-12-01

The classical linear solutions to the problem of multiple attenuation, like predictive deconvolution, τ-p filtering, or F-K filtering, are generally fast, stable, and robust compared to non-linear solutions, which are generally either iterative or in the form of a series with an infinite number of terms. These qualities have made the linear solutions more attractive to seismic data-processing practitioners. However, most linear solutions, including predictive deconvolution or F-K filtering, contain severe assumptions about the model of the subsurface and the class of free-surface multiples they can attenuate. These assumptions limit their usefulness. In a recent paper, we described an exception to this assertion for OBS data. We showed in that paper that a linear and non-iterative solution to the problem of attenuating free-surface multiples which is as accurate as iterative non-linear solutions can be constructed for OBS data. We here present a similar linear and non-iterative solution for attenuating free-surface multiples in towed-streamer data. For most practical purposes, this linear solution is as accurate as the non-linear ones.

Redirection and Splitting of Sound Waves by a Periodic Chain of Thin Perforated Cylindrical Shells

NASA Astrophysics Data System (ADS)

Bozhko, Andrey; Sánchez-Dehesa, José; Cervera, Francisco; Krokhin, Arkadii

2017-06-01

The scattering of sound by finite and infinite chains of equally spaced perforated metallic cylindrical shells in an ideal (inviscid) and viscous fluid is theoretically studied using rigorous analytical and numerical approaches. Because of perforations, a chain of thin shells is practically transparent for sound within a wide range of frequencies. It is shown that strong scattering and redirection of sound by 90° may occur only for a discrete set of frequencies (Wood's anomalies) where the leaky eigenmodes are excited. The spectrum of eigenmodes consists of antisymmetric and symmetric branches with normal and anomalous dispersion, respectively. The antisymmetric eigenmode turns out to be a deaf mode, since it cannot be excited at normal incidence. However, at slightly oblique incidence, both modes can be resonantly excited at different but close frequencies. The symmetric mode, due to its anomalous dispersion, scatters sound in the "wrong" direction. This property may find an application for the splitting of the two resonant harmonics of the incoming signal into two beams propagating along the chain in the opposite directions. A chain of perforated cylinders may also be used as a passive antenna that detects the direction to the incoming signal by measuring the frequencies of the waves excited in the chain. Calculations are presented for aluminum shells in viscous air where the effects of anomalous scattering, redirection, and signal splitting are well manifested.

Thermoreversible gelation of poly(vinylidene fluoride) in phthalates: the influence of aliphatic chain length of solvents.

PubMed

Yadav, P Jaya Prakash; Ghosh, Goutam; Maiti, Biswajit; Aswal, Vinod K; Goyal, P S; Maiti, Pralay

2008-04-17

Thermoreversible gelation of poly(vinylidene fluoride) (PVDF) has been studied in a new series of solvents (phthalates), for example, dimethyl phthalate (DMP), diethyl phthalate (DEP), dibutyl phthalate (DBP), and dihexyl phthalate (DHP) as a function of temperature and polymer concentration, both by test tube tilting and dynamic light scattering (DLS) method. The effect of aliphatic chain length (n) of diesters on the gelation kinetics, structure/microstructure and morphology of PVDF gels has been examined. Gelation rate was found to increase with increasing aliphatic chain length of diester. DLS results indicate that the sol-gel transformation proceeds via two-steps: first, microgel domains were formed, and then the infinite three-dimensional (3D) network is established by connecting microgels through polymer chains. The crystallites are responsible for 3D network for gelation in phthalates, and alpha-polymorph is formed during gelation producing higher amount of crystallinity with increasing aliphatic chain length of diester. Morphology of the networks of dried gels in different phthalates showed that fibril thickness and lateral dimensions decrease with higher homologues of phthalates. The scattering intensity is fitted with Debye-Bueche model in small-angle neutron scattering and suggested that both the correlation length and interlamellar spacing increases with n. A model has been proposed, based on electronic structure calculations, to explain the conformation of PVDF chain in presence of various phthalates and their complexes, which offer the cause of higher gelation rate for longer aliphatic chain length.

Entanglement spreading after a geometric quench in quantum spin chains

NASA Astrophysics Data System (ADS)

Alba, Vincenzo; Heidrich-Meisner, Fabian

2014-08-01

We investigate the entanglement spreading in the anisotropic spin-1/2 Heisenberg (XXZ) chain after a geometric quench. This corresponds to a sudden change of the geometry of the chain or, in the equivalent language of interacting fermions confined in a box trap, to a sudden increase of the trap size. The entanglement dynamics after the quench is associated with the ballistic propagation of a magnetization wave front. At the free fermion point (XX chain), the von Neumann entropy SA exhibits several intriguing dynamical regimes. Specifically, at short times a logarithmic increase is observed, similar to local quenches. This is accurately described by an analytic formula that we derive from heuristic arguments. At intermediate times partial revivals of the short-time dynamics are superposed with a power-law increase SA˜tα, with α <1. Finally, at very long times a steady state develops with constant entanglement entropy, apart from oscillations. As expected, since the model is integrable, we find that the steady state is nonthermal, although it exhibits extensive entanglement entropy. We also investigate the entanglement dynamics after the quench from a finite to the infinite chain (sudden expansion). While at long times the entanglement vanishes, we demonstrate that its relaxation dynamics exhibits a number of scaling properties. Finally, we discuss the short-time entanglement dynamics in the XXZ chain in the gapless phase. The same formula that describes the time dependence for the XX chain remains valid in the whole gapless phase.

Effect of short-chain branching on interfacial polymer structure and dynamics under shear flow.

PubMed

Jeong, Sohdam; Kim, Jun Mo; Cho, Soowon; Baig, Chunggi

2017-11-22

We present a detailed analysis on the effect of short-chain branches on the structure and dynamics of interfacial chains using atomistic nonequilibrium molecular dynamics simulations of confined polyethylene melts in a wide range of shear rates. The intrinsically fast random motions of the short branches constantly disturb the overall chain conformation, leading to a more compact and less deformed chain structure of the short-chain branched (SCB) polymer against the imposed flow field in comparison with the corresponding linear polymer. Moreover, such highly mobile short branches along the backbone of the SCB polymer lead to relatively weaker out-of-plane wagging dynamics of interfacial chains, with highly curvy backbone structures in the intermediate flow regime. In conjunction with the contribution of short branches (as opposed to that of the backbone) to the total interfacial friction between the chains and the wall, the SCB polymer shows a nearly constant behavior in the degree of slip (d s ) with respect to shear rate in the weak-to-intermediate flow regimes. On the contrary, in the strong flow regime where irregular chain rotation and tumbling dynamics occur via intensive dynamical collisions between interfacial chains and the wall, an enhancement effect on the chain detachment from the wall, caused by short branches, leads to a steeper increase in d s for the SCB polymer than for the linear polymer. Remarkably, the SCB chains at the interface exhibit two distinct types of rolling mechanisms along the backbone, with a half-dumbbell mesoscopic structure at strong flow fields, in addition to the typical hairpin-like tumbling behavior displayed by the linear chains.

Universal scaling for the quantum Ising chain with a classical impurity

NASA Astrophysics Data System (ADS)

Apollaro, Tony J. G.; Francica, Gianluca; Giuliano, Domenico; Falcone, Giovanni; Palma, G. Massimo; Plastina, Francesco

2017-10-01

We study finite-size scaling for the magnetic observables of an impurity residing at the end point of an open quantum Ising chain with transverse magnetic field, realized by locally rescaling the field by a factor μ ≠1 . In the homogeneous chain limit at μ =1 , we find the expected finite-size scaling for the longitudinal impurity magnetization, with no specific scaling for the transverse magnetization. At variance, in the classical impurity limit μ =0 , we recover finite scaling for the longitudinal magnetization, while the transverse one basically does not scale. We provide both analytic approximate expressions for the magnetization and the susceptibility as well as numerical evidences for the scaling behavior. At intermediate values of μ , finite-size scaling is violated, and we provide a possible explanation of this result in terms of the appearance of a second, impurity-related length scale. Finally, by going along the standard quantum-to-classical mapping between statistical models, we derive the classical counterpart of the quantum Ising chain with an end-point impurity as a classical Ising model on a square lattice wrapped on a half-infinite cylinder, with the links along the first circle modified as a function of μ .

A vast amount of various invariant tori in the Nosé-Hoover oscillator.

PubMed

Wang, Lei; Yang, Xiao-Song

2015-12-01

This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of "chaotic region" and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a "chaotic sea" for the Nosé-Hoover oscillator.

A TBA approach to thermal transport in the XXZ Heisenberg model

NASA Astrophysics Data System (ADS)

Zotos, X.

2017-10-01

We show that the thermal Drude weight and magnetothermal coefficient of the 1D easy-plane Heisenberg model can be evaluated by an extension of the Bethe ansatz thermodynamics formulation by Takahashi and Suzuki (1972 Prog. Theor. Phys. 48 2187). They have earlier been obtained by the quantum transfer matrix method (Klümper 1999 Z. Phys. B 91 507). Furthermore, this approach can be applied to the study of the far-out of equilibrium energy current generated at the interface between two semi-infinite chains held at different temperatures.

Electron-phonon interaction in quantum transport through quantum dots and molecular systems

NASA Astrophysics Data System (ADS)

Ojeda, J. H.; Duque, C. A.; Laroze, D.

2016-12-01

The quantum transport and effects of decoherence properties are studied in quantum dots systems and finite homogeneous chains of aromatic molecules connected to two semi-infinite leads. We study these systems based on the tight-binding approach through Green's function technique within a real space renormalization and polaron transformation schemes. In particular, we calculate the transmission probability following the Landauer-Büttiker formalism, the I - V characteristics and the noise power of current fluctuations taken into account the decoherence. Our results may explain the inelastic effects through nanoscopic systems.

A vast amount of various invariant tori in the Nosé-Hoover oscillator

NASA Astrophysics Data System (ADS)

Wang, Lei; Yang, Xiao-Song

2015-12-01

This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of "chaotic region" and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a "chaotic sea" for the Nosé-Hoover oscillator.

A vast amount of various invariant tori in the Nosé-Hoover oscillator

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

Wang, Lei; Department of Mathematics and Physics, Hefei University, Hefei 230601; Yang, Xiao-Song, E-mail: yangxs@hust.edu.cn

2015-12-15

This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of “chaotic region” and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a “chaotic sea” for the Nosé-Hoover oscillator.

Some efficient methods for obtaining infinite series solutions of n-th order linear ordinary differential equations

NASA Technical Reports Server (NTRS)

Allen, G.

1972-01-01

The use of the theta-operator method and generalized hypergeometric functions in obtaining solutions to nth-order linear ordinary differential equations is explained. For completeness, the analysis of the differential equation to determine whether the point of expansion is an ordinary point or a regular singular point is included. The superiority of the two methods shown over the standard method is demonstrated by using all three of the methods to work out several examples. Also included is a compendium of formulae and properties of the theta operator and generalized hypergeometric functions which is complete enough to make the report self-contained.

Plasma Modes

NASA Astrophysics Data System (ADS)

Dubin, D. H. E.

This chapter explores several aspects of the linear electrostatic normal modes of oscillation for a single-species non-neutral plasma in a Penning trap. Linearized fluid equations of motion are developed, assuming the plasma is cold but collisionless, which allow derivation of the cold plasma dielectric tensor and the electrostatic wave equation. Upper hybrid and magnetized plasma waves in an infinite uniform plasma are described. The effect of the plasma surface in a bounded plasma system is considered, and the properties of surface plasma waves are characterized. The normal modes of a cylindrical plasma column are discussed, and finally, modes of spheroidal plasmas, and finite temperature effects on the modes, are briefly described.

Perturbations of linear delay differential equations at the verge of instability.

PubMed

Lingala, N; Namachchivaya, N Sri

2016-06-01

The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Stabilization of Taylor-Couette flow due to time-periodic outer cylinder oscillation

NASA Technical Reports Server (NTRS)

Murray, B. T.; Mcfadden, G. B.; Coriell, S. R.

1990-01-01

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case when the inner cylinder is rotated at a constant angular velocity and the outer cylinder is driven sinusoidally in time with zero mean rotation. This configuration was studied experimentally by Walsh and Donnelly. The critical Reynolds numbers calculated from linear stability theory agree well with the experimental values, except at large modulation amplitudes and small frequencies. The theoretical values are obtained using Floquet theory implemented in two distinct approaches: a truncated Fourier series representation in time, and a fundamental solution matrix based on a Chebyshev pseudospectral representation in space. For large amplitude, low frequency modulation, the linear eigenfunctions are temporally complex, consisting of a quiescent region followed by rapid change in the perturbed flow velocities.

Controller Synthesis for Periodically Forced Chaotic Systems

NASA Astrophysics Data System (ADS)

Basso, Michele; Genesio, Roberto; Giovanardi, Lorenzo

Delayed feedback controllers are an appealing tool for stabilization of periodic orbits in chaotic systems. Despite their conceptual simplicity, specific and reliable design procedures are difficult to obtain, partly also because of their inherent infinite-dimensional structure. This chapter considers the use of finite dimensional linear time invariant controllers for stabilization of periodic solutions in a general class of sinusoidally forced nonlinear systems. For such controllers — which can be interpreted as rational approximations of the delayed ones — we provide a computationally attractive synthesis technique based on Linear Matrix Inequalities (LMIs), by mixing results concerning absolute stability of nonlinear systems and robustness of uncertain linear systems. The resulting controllers prove to be effective for chaos suppression in electronic circuits and systems, as shown by two different application examples.

Free vibration analysis of elastic structures submerged in an infinite or semi-infinite fluid domain by means of a coupled FE-BE solver

NASA Astrophysics Data System (ADS)

Zheng, Chang-Jun; Bi, Chuan-Xing; Zhang, Chuanzeng; Gao, Hai-Feng; Chen, Hai-Bo

2018-04-01

The vibration behavior of thin elastic structures can be noticeably influenced by the surrounding water, which represents a kind of heavy fluid. Since the feedback of the acoustic pressure onto the structure cannot be neglected in this case, a strong coupled scheme between the structural and fluid domains is usually required. In this work, a coupled finite element and boundary element (FE-BE) solver is developed for the free vibration analysis of structures submerged in an infinite fluid domain or a semi-infinite fluid domain with a free water surface. The structure is modeled by the finite element method (FEM). The compressibility of the fluid is taken into account, and hence the Helmholtz equation serves as the governing equation of the fluid domain. The boundary element method (BEM) is employed to model the fluid domain, and a boundary integral formulation with a half-space fundamental solution is used to satisfy the Dirichlet boundary condition on the free water surface exactly. The resulting nonlinear eigenvalue problem (NEVP) is converted into a small linear one by using a contour integral method. Adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenfrequencies of interest. The Burton-Miller method is used to filter out the fictitious eigenfrequencies of the boundary integral formulations. Numerical examples are given to demonstrate the accuracy and applicability of the developed eigensolver, and also show that the fluid-loading effect strongly depends on both the water depth and the mode shapes.

A new description of Earth's wobble modes using Clairaut coordinates: 1. Theory

NASA Astrophysics Data System (ADS)

Rochester, M. G.; Crossley, D. J.; Zhang, Y. L.

2014-09-01

This paper presents a novel mathematical reformulation of the theory of the free wobble/nutation of an axisymmetric reference earth model in hydrostatic equilibrium, using the linear momentum description. The new features of this work consist in the use of (i) Clairaut coordinates (rather than spherical polars), (ii) standard spherical harmonics (rather than generalized spherical surface harmonics), (iii) linear operators (rather than J-square symbols) to represent the effects of rotational and ellipticity coupling between dependent variables of different harmonic degree and (iv) a set of dependent variables all of which are continuous across material boundaries. The resulting infinite system of coupled ordinary differential equations is given explicitly, for an elastic solid mantle and inner core, an inviscid outer core and no magnetic field. The formulation is done to second order in the Earth's ellipticity. To this order it is shown that for wobble modes (in which the lowest harmonic in the displacement field is degree 1 toroidal, with azimuthal order m = ±1), it is sufficient to truncate the chain of coupled displacement fields at the toroidal harmonic of degree 5 in the solid parts of the earth model. In the liquid core, however, the harmonic expansion of displacement can in principle continue to indefinitely high degree at this order of accuracy. The full equations are shown to yield correct results in three simple cases amenable to analytic solution: a general earth model in rigid rotation, the tiltover mode in a homogeneous solid earth model and the tiltover and Chandler periods for an incompressible homogeneous solid earth model. Numerical results, from programmes based on this formulation, are presented in part II of this paper.

Magnon localization and Bloch oscillations in finite Heisenberg spin chains in an inhomogeneous magnetic field.

PubMed

Kosevich, Yuriy A; Gann, Vladimir V

2013-06-19

We study the localization of magnon states in finite defect-free Heisenberg spin-1/2 ferromagnetic chains placed in an inhomogeneous magnetic field with a constant spatial gradient. Continuous transformation from the extended magnon states to the localized Wannier-Zeeman states in a finite spin chain placed in an inhomogeneous field is described both analytically and numerically. We describe for the first time the non-monotonic dependence of the energy levels of magnons, both long and short wavelength, on the magnetic field gradient, which is a consequence of magnon localization in a finite spin chain. We show that, in contrast to the destruction of the magnon band and the establishment of the Wannier-Stark ladder in a vanishingly small field gradient in an infinite chain, the localization of magnon states at the chain ends preserves the memory of the magnon band. Essentially, the localization at the lower- or higher-field chain end resembles the localization of the positive- or negative-effective-mass band quasiparticles. We also show how the beat dynamics of coherent superposition of extended spin waves in a finite chain in a homogeneous or weakly inhomogeneous field transforms into magnon Bloch oscillations of the superposition of localized Wannier-Zeeman states in a strongly inhomogeneous field. We provide a semiclassical description of the magnon Bloch oscillations and show that the correspondence between the quantum and semiclassical descriptions is most accurate for Bloch oscillations of the magnon coherent states, which are built from a coherent superposition of a large number of the nearest-neighbour Wannier-Zeeman states.

Propagation of high frequency electrostatic surface waves along the planar interface between plasma and dusty plasma

NASA Astrophysics Data System (ADS)

Mishra, Rinku; Dey, M.

2018-04-01

An analytical model is developed that explains the propagation of a high frequency electrostatic surface wave along the interface of a plasma system where semi-infinite electron-ion plasma is interfaced with semi-infinite dusty plasma. The model emphasizes that the source of such high frequency waves is inherent in the presence of ion acoustic and dust ion acoustic/dust acoustic volume waves in electron-ion plasma and dusty plasma region. Wave dispersion relation is obtained for two distinct cases and the role of plasma parameters on wave dispersion is analyzed in short and long wavelength limits. The normalized surface wave frequency is seen to grow linearly for lower wave number but becomes constant for higher wave numbers in both the cases. It is observed that the normalized frequency depends on ion plasma frequencies when dust oscillation frequency is neglected.

Helical vortices: linear stability analysis and nonlinear dynamics

NASA Astrophysics Data System (ADS)

Selçuk, C.; Delbende, I.; Rossi, M.

2018-02-01

We numerically investigate, within the context of helical symmetry, the dynamics of a regular array of two or three helical vortices with or without a straight central hub vortex. The Navier-Stokes equations are linearised to study the instabilities of such basic states. For vortices with low pitches, an unstable mode is extracted which corresponds to a displacement mode and growth rates are found to compare well with results valid for an infinite row of point vortices or an infinite alley of vortex rings. For larger pitches, the system is stable with respect to helically symmetric perturbations. In the nonlinear regime, we follow the time-evolution of the above basic states when initially perturbed by the dominant instability mode. For two vortices, sequences of overtaking events, leapfrogging and eventually merging are observed. The transition between such behaviours occurs at a critical ratio involving the core size and the vortex-separation distance. Cases with three helical vortices are also presented.

Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded Time-Varying Delays

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

Meng, Ziyang; Yang, Tao; Li, Guoqi

Here, we study synchronization of coupled linear systems over networks with weak connectivity and nonuniform time-varying delays. We focus on the case where the internal dynamics are time-varying but non-expansive (stable dynamics with a quadratic Lyapunov function). Both uniformly jointly connected and infinitely jointly connected communication topologies are considered. A new concept of quadratic synchronization is introduced. We first show that global asymptotic quadratic synchronization can be achieved over directed networks with uniform joint connectivity and arbitrarily bounded delays. We then study the case of infinitely jointly connected communication topology. In particular, for the undirected communication topologies, it turns outmore » that the existence of a uniform time interval for the jointly connected communication topology is not necessary and quadratic synchronization can be achieved when the time-varying nonuniform delays are arbitrarily bounded. Finally, simulation results are provided to validate the theoretical results.« less

Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded Time-Varying Delays

DOE PAGES

Meng, Ziyang; Yang, Tao; Li, Guoqi; ...

2017-09-18

Here, we study synchronization of coupled linear systems over networks with weak connectivity and nonuniform time-varying delays. We focus on the case where the internal dynamics are time-varying but non-expansive (stable dynamics with a quadratic Lyapunov function). Both uniformly jointly connected and infinitely jointly connected communication topologies are considered. A new concept of quadratic synchronization is introduced. We first show that global asymptotic quadratic synchronization can be achieved over directed networks with uniform joint connectivity and arbitrarily bounded delays. We then study the case of infinitely jointly connected communication topology. In particular, for the undirected communication topologies, it turns outmore » that the existence of a uniform time interval for the jointly connected communication topology is not necessary and quadratic synchronization can be achieved when the time-varying nonuniform delays are arbitrarily bounded. Finally, simulation results are provided to validate the theoretical results.« less

Stability analysis of unsteady ablation fronts

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

Betti, R.; McCrory, R.L.; Verdon, C.P.

1993-08-01

The linear stability analysis of unsteady ablation fronts, is carried out for a semi-infinite uniform medium. For a laser accelerated target, it is shown that a properly selected modulation of the laser intensity can lead to the dynamic stabilization or growth-rate reduction of a large portion of the unstable spectrum. The theory is in qualitative agreement with the numerical results obtained by using the two-dimensional hydrodynamic code ORCHID.

Stability analysis of unsteady ablation fronts

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

Betti, R.; McCrory, R.L.; Verdon, C.P.

1993-11-08

The linear stability analysis of unsteady ablation fronts is carried out for a semi-infinite uniform medium. For a laser accelerated target, it is shown that a properly selected modulation of the laser intensity can lead to the dynamic stabilization or growth-rate reduction of a large portion of the unstable spectrum. The theory is in qualitative agreement with the numerical results obtained by using the two-dimensional hydrodynamic code ORCHID.

On representations of the filiform Lie superalgebra Lm,n

NASA Astrophysics Data System (ADS)

Wang, Qi; Chen, Hongjia; Liu, Wende

2015-11-01

In this paper, we study the representations for the filiform Lie superalgebras Lm,n, a particular class of nilpotent Lie superalgebras. We determine the minimal dimension of a faithful module over Lm,n using the theory of linear algebra. In addition, using the method of Feingold and Frenkel (1985), we construct some finite and infinite dimensional modules over Lm,n on the Grassmann algebra and the mixed Clifford-Weyl algebra.

Born approximation in linear-time invariant system

NASA Astrophysics Data System (ADS)

Gumjudpai, Burin

2017-09-01

An alternative way of finding the LTI’s solution with the Born approximation, is investigated. We use Born approximation in the LTI and in the transformed LTI in form of Helmholtz equation. General solution are considered as infinite series or Feynman graph. Slow-roll approximation are explored. Transforming the LTI system into Helmholtz equation, approximated general solution can be found for any given forms of force with its initial value.

Zero-determinant strategies in finitely repeated games.

PubMed

Ichinose, Genki; Masuda, Naoki

2018-02-07

Direct reciprocity is a mechanism for sustaining mutual cooperation in repeated social dilemma games, where a player would keep cooperation to avoid being retaliated by a co-player in the future. So-called zero-determinant (ZD) strategies enable a player to unilaterally set a linear relationship between the player's own payoff and the co-player's payoff regardless of the strategy of the co-player. In the present study, we analytically study zero-determinant strategies in finitely repeated (two-person) prisoner's dilemma games with a general payoff matrix. Our results are as follows. First, we present the forms of solutions that extend the known results for infinitely repeated games (with a discount factor w of unity) to the case of finitely repeated games (0 < w < 1). Second, for the three most prominent ZD strategies, the equalizers, extortioners, and generous strategies, we derive the threshold value of w above which the ZD strategies exist. Third, we show that the only strategies that enforce a linear relationship between the two players' payoffs are either the ZD strategies or unconditional strategies, where the latter independently cooperates with a fixed probability in each round of the game, proving a conjecture previously made for infinitely repeated games. Copyright © 2017 Elsevier Ltd. All rights reserved.

Unexpected power-law stress relaxation of entangled ring polymers

PubMed Central

KAPNISTOS, M.; LANG, M.; PYCKHOUT-HINTZEN, W.; RICHTER, D.; CHO, D.; CHANG, T.

2016-01-01

After many years of intense research, most aspects of the motion of entangled polymers have been understood. Long linear and branched polymers have a characteristic entanglement plateau and their stress relaxes by chain reptation or branch retraction, respectively. In both mechanisms, the presence of chain ends is essential. But how do entangled polymers without ends relax their stress? Using properly purified high-molar-mass ring polymers, we demonstrate that these materials exhibit self-similar dynamics, yielding a power-law stress relaxation. However, trace amounts of linear chains at a concentration almost two decades below their overlap cause an enhanced mechanical response. An entanglement plateau is recovered at higher concentrations of linear chains. These results constitute an important step towards solving an outstanding problem of polymer science and are useful for manipulating properties of materials ranging from DNA to polycarbonate. They also provide possible directions for tuning the rheology of entangled polymers. PMID:18953345

Crystal structure and magnetic properties of a unique 3D coordination polymer constructed from flexible aliphatic tricarballylic acid ligands featuring linear trimeric Manganese(II)-based, metal carboxylate chains

NASA Astrophysics Data System (ADS)

Zou, Hua-Hong; Zhang, Shu-Hua; Zeng, Ming-Hua; Zhou, Yan-Ling; Liang, Hong

2008-08-01

A novel linear trimeric-based, Mn(II)-carboxylate chain well separated by long-linking flexible aliphatic tricarballylic acid ligands in a 3D coordination polymer [Mn 3(C 6H 5O 6) 2(H 2O) 4] n ( 1, C 6H 5O 6dbnd CH (COO -)(CH 2COO -) 2, TCA) exhibits low-dimensional antiferromagnetic order at 3.0 K. Such magnetic behavior is arises from the alternate Antiferro-Antiferro-Antiferro' ( J1J1J2) repeating interactions sequence, based on the nature of the binding modes of Mn(II)-carboxylate chain and the effect of interchains arrangement of 1. The reported carboxylate-bridged metal chain systems display a new structurally authenticated example of linear homometallic spin arranged antiferromagnet among metal carboxylates.

Trilithium thio­arsenate octa­hydrate

PubMed Central

Mereiter, Kurt

2013-01-01

The title compound, Li3AsS4·8H2O, is built up from infinite cationic [Li3(H2O)8]3+ chains which extend along [001] and are cross-linked by isolated tetra­hedral AsS4 3− anions via O—H⋯S hydrogen bonds. Two Li and two As atoms lie on special positions with site symmetries -1 (1 × Li) and 2 (1 × Li and 2 × As). The [Li3(H2O)8]3+ chain contains four independent Li atoms of which two are in octa­hedral and two in tetra­hedral coordination by water O atoms. An outstanding feature of this chain is a linear group of three edge-sharing LiO6 octa­hedra to both ends of which two LiO4 tetra­hedra are attached by face-sharing. Such groups of composition Li5O16 are linked into branched chains by means of a further LiO4 tetra­hedron sharing vertices with four adjacent LiO6 octa­hedra. The Li—O bonds range from 1.876 (5) to 2.054 (6) Å for the LiO4 tetra­hedra and from 2.026 (5) to 2.319 (5) Å for the LiO6 octa­hedra. The two independent AsS4 3− anions have As—S bond lengths ranging from 2.1482 (6) to 2.1677 (6) Å [ = 2.161 (10) Å]. The eight independent water mol­ecules of the structure donate 16 relatively straight O—H⋯S hydrogen bonds to all S atoms of the AsS4 tetra­hedra [ = 3.295 (92) Å]. Seven water mol­ecules are in distorted tetra­hedral coordination by two Li and two S; one water mol­ecule has a flat pyramidal coordination by one Li and two S. At variance with related compounds like Schlippe’s salt, Na3SbS4·9H2O, there are neither alkali–sulfur bonds nor O—H⋯O hydrogen bonds in the structure. PMID:23723753

Tuning the thermal conductivity of solar cell polymers through side chain engineering.

PubMed

Guo, Zhi; Lee, Doyun; Liu, Yi; Sun, Fangyuan; Sliwinski, Anna; Gao, Haifeng; Burns, Peter C; Huang, Libai; Luo, Tengfei

2014-05-07

Thermal transport is critical to the performance and reliability of polymer-based energy devices, ranging from solar cells to thermoelectrics. This work shows that the thermal conductivity of a low band gap conjugated polymer, poly(4,8-bis-alkyloxybenzo[1,2-b:4,5-b']dithiophene-2,6-diyl-alt-(alkylthieno[3,4-b]thiophene-2-carboxylate)-2,6-diyl) (PBDTTT), for photovoltaic applications can be actively tuned through side chain engineering. Compared to the original polymer modified with short branched side chains, the engineered polymer using all linear and long side chains shows a 160% increase in thermal conductivity. The thermal conductivity of the polymer exhibits a good correlation with the side chain lengths as well as the crystallinity of the polymer characterized using small-angle X-ray scattering (SAXS) experiments. Molecular dynamics simulations and atomic force microscopy are used to further probe the molecular level local order of different polymers. It is found that the linear side chain modified polymer can facilitate the formation of more ordered structures, as compared to the branched side chain modified ones. The effective medium theory modelling also reveals that the long linear side chain enables a larger heat carrier propagation length and the crystalline phase in the bulk polymer increases the overall thermal conductivity. It is concluded that both the length of the side chains and the induced polymer crystallization are important for thermal transport. These results offer important guidance for actively tuning the thermal conductivity of conjugated polymers through molecular level design.

Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

NASA Astrophysics Data System (ADS)

Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

2018-07-01

The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

Topology of polymer chains under nanoscale confinement.

PubMed

Satarifard, Vahid; Heidari, Maziar; Mashaghi, Samaneh; Tans, Sander J; Ejtehadi, Mohammad Reza; Mashaghi, Alireza

2017-08-24

Spatial confinement limits the conformational space accessible to biomolecules but the implications for bimolecular topology are not yet known. Folded linear biopolymers can be seen as molecular circuits formed by intramolecular contacts. The pairwise arrangement of intra-chain contacts can be categorized as parallel, series or cross, and has been identified as a topological property. Using molecular dynamics simulations, we determine the contact order distributions and topological circuits of short semi-flexible linear and ring polymer chains with a persistence length of l p under a spherical confinement of radius R c . At low values of l p /R c , the entropy of the linear chain leads to the formation of independent contacts along the chain and accordingly, increases the fraction of series topology with respect to other topologies. However, at high l p /R c , the fraction of cross and parallel topologies are enhanced in the chain topological circuits with cross becoming predominant. At an intermediate confining regime, we identify a critical value of l p /R c , at which all topological states have equal probability. Confinement thus equalizes the probability of more complex cross and parallel topologies to the level of the more simple, non-cooperative series topology. Moreover, our topology analysis reveals distinct behaviours for ring- and linear polymers under weak confinement; however, we find no difference between ring- and linear polymers under strong confinement. Under weak confinement, ring polymers adopt parallel and series topologies with equal likelihood, while linear polymers show a higher tendency for series arrangement. The radial distribution analysis of the topology reveals a non-uniform effect of confinement on the topology of polymer chains, thereby imposing more pronounced effects on the core region than on the confinement surface. Additionally, our results reveal that over a wide range of confining radii, loops arranged in parallel and cross topologies have nearly the same contact orders. Such degeneracy implies that the kinetics and transition rates between the topological states cannot be solely explained by contact order. We expect these findings to be of general importance in understanding chaperone assisted protein folding, chromosome architecture, and the evolution of molecular folds.

Long-Chain Perfluoroalkyl acids (PFAAs) Affect the Bioconcentration and Tissue Distribution of Short-Chain PFAAs in Zebrafish (Danio rerio).

PubMed

Wen, Wu; Xia, Xinghui; Hu, Diexuan; Zhou, Dong; Wang, Haotian; Zhai, Yawei; Lin, Hui

2017-11-07

Short- and long-chain perfluoroalkyl acids (PFAAs), ubiquitously coexisting in the environment, can be accumulated in organisms by binding with proteins and their binding affinities generally increase with their chain length. Therefore, we hypothesized that long-chain PFAAs will affect the bioconcentration of short-chain PFAAs in organisms. To testify this hypothesis, the bioconcentration and tissue distribution of five short-chain PFAAs (linear C-F = 3-6) were investigated in zebrafish in the absence and presence of six long-chain PFAAs (linear C-F = 7-11). The results showed that the concentrations of the short-chain PFAAs in zebrafish tissues increased with exposure time until steady states reached in the absence of long-chain PFAAs. However, in the presence of long-chain PFAAs, these short-chain PFAAs in tissues increased until peak values reached and then decreased until steady states, and the uptake and elimination rate constants of short-chain PFAAs declined in all tissues and their BCF ss decreased by 24-89%. The inhibitive effect of long-chain PFAAs may be attributed to their competition for transporters and binding sites of proteins in zebrafish with short-chain PFAAs. These results suggest that the effect of long-chain PFAAs on the bioconcentration of short-chain PFAAs should be taken into account in assessing the ecological and environmental effects of short-chain PFAAs.

Conformation transitions of a single polyelectrolyte chain in a poor solvent: a replica-exchange lattice Monte-Carlo study.

PubMed

Wang, Lang; Wang, Zheng; Jiang, Run; Yin, Yuhua; Li, Baohui

2017-03-15

The thermodynamic behaviors of a strongly charged polyelectrolyte chain in a poor solvent are studied using replica-exchange Monte-Carlo simulations on a lattice model, focusing on the effects of finite chain length and the solvent quality on the chain conformation and conformation transitions. The neutralizing counterions and solvent molecules are considered explicitly. The thermodynamic quantities that vary continuously with temperature over a wide range are computed using the multiple histogram reweighting method. Our results suggest that the strength of the short-range hydrophobic interaction, the chain length, and the temperature of the system, characterized by ε, N, and T, respectively, are important parameters that control the conformations of a charged chain. When ε is moderate, the competition between the electrostatic energy and the short-range hydrophobic interaction leads to rich conformations and conformation transitions for a longer chain with a fixed length. Our results have unambiguously demonstrated the stability of the n-pearl-necklace structures, where n has a maximum value and decreases with decreasing temperature. The maximum n value increases with increasing chain length. Our results have also demonstrated the first-order nature of the conformation transitions between the m-pearl and the (m-1)-pearl necklaces. With the increase of ε, the transition temperature increases and the first-order feature becomes more pronounced. It is deduced that at the thermodynamic limit of infinitely long chain length, the conformational transitions between the m-pearl and the (m-1)-pearl necklaces may remain first order when ε > 0 and m = 2 or 3. Pearl-necklace conformations cannot be observed when either ε is too large or N is too small. To observe a pearl-necklace conformation, the T value needs to be carefully chosen for simulations performed at only a single temperature.

The Ultra-filtration of Macromolecules with Different Conformations and Configurations through Nanopores

NASA Astrophysics Data System (ADS)

Ge, Hui

This Ph. D. thesis presents our study on the ultrafiltration of polymers with different configurations and conformations; namly, theoretically, the passing of polymer chains through a nanopore under an elongational flow filed has been studied for years, but experimental studies are rare because of two following reasons: (1) lacks a precise method to investigate how individual single polymer chain pass through a nanopore; (2) it is difficult, if not impossible, to obtain a set of polymer samples with a narrow molar mass distribution and a uniform structures; except for linear chains. The central question in this study is to find the critical (minimum) flow rate (qc) for each kind of chains, at which the chains can pass through a given nanopore. A comparison of the measured and calculated qc leads to a better understanding how different chains are deformed, stretched and pulled through a nanopore. We have developed a novel method of combinating static and dynamic laser light scattering (LLS) to precisely measure the relative retention concentration ((C0 - C)/C0). Chapter 1 briefly introduces the theoretical background of how applications and lists some of resent research progresses in this area. Polymer with various configurations and conformations pass through nanopores; including polymer linear chains, stars polymer, branched polymers, polymer micelles are introduced. Among them, the de Gennes and Brochard-Wyart's predictions of polymer linear and star chains passing through nanopores are emphasized, in which they predicted that qc of linear chain is qc ≃ kBT/(3pieta), where kB, T and eta are the Boltzmann constant, the absolutely temperature, and the viscosity of solvent, respectively, independent of both the chain length and the pore size; and for star chains passing through nanopores, there exist a optimal entering arm numbers, namely, the star chains passing through nanopores. Chapter 2 details basic theory of static and dynamic laser light scattering (LLS), including its instrumentation and our ultrafiltration setup. Chapter 3 briefly introduces the sample preparation, including the history and mechanism of anionic living polymerization, as well as how we used a novel home-made set-up to prepare linear polystyrene with different chain lengths and star polystyrene with various arm numbers and lengths. Chapter 4 summarizes our measured critical flow rates (qc) of linear polymer chains with different lengths for nanopores with different sizes, since the flow rate is directly related to the hydrodynamic force, we have developed a sensitive method (down to tens fN) to directly assess how much the hydrodynamic force (Fh) is required to overcome the weak entropy elasticity and stretch individual coiled chains in solution. Our method is completely different from the using existing optical tweezers or AFM, because they measure the relatively stronger enthalpy elasticity. Our results confirm that qc is indeed independent of the chain length, but decreases as the pore size increases. The value of qc is ˜10--200 times smaller than kBT/(3pieta). Such a discrepancy has been attributed to the rough assumption made by de Gennes and his coworkers; namely, each chain segment "blob" confined inside the pore is not a hard sphere so that the effective length along the flow direction is much longer than the pore diameter. Finally, using the solution temperature, we varied the chain conformation, our result shows that q c has a minimum which is near, but not exactly located at the theta temperature, might leading to a better way to determine the true ideal state of a polymer solution, at which all viral coefficients, not only the second vanish. Chapter 5 uses polymer solutions made of different mixtures of linear and star chains, we have demonstrated that flushing these solution mixtures through a nanopore with a properly chosen flow rate can effectively and cleanly separate linear and star chains no matter whether linear chains are larger or smaller than star chains. Chapter 6 further investigates how star-like polystyrene pass through a given nanopore under the flow field. Star polystyrene chains with different arm lengths (LA) and numbers (f) passing through a nanopore (20 nm) under an elongational flow field was investigated in terms of the flow-rate dependent relative retention ((C0 - C)/C0), where C 0 and C are the polymer concentrations before and after the ultrafiltration. Our results reveal that for a given arm length (LA), the critical flow rate (qc,star), below which star chains are blocked, dramatically increases with the total arm numbers (f); but for a given f, is nearly independent on LA, contradictory to the previous prediction made by de Gennes and Brochard-Wyart. We have revised their theory in the region fin < fout and also accounted for the effective length of each blob, where fin and fout are the numbers of arms inside and outside the pore, respectively. In the revision, we show that qc,star is indeed independent of LA but related to f and f in in two different ways, depending on whether fin ≤ f/2 or ≥ f/2. A comparison of our experimental and calculated results reveals that most of star chains pass through the nanopores with fin ˜ f/2. Further study of the temperature dependent (C0 - C)/C 0 of polystyrene in cyclohexane reveals that there exists a minimum of qc,star at ˜38 °C, close to its theta temperature (-34.5 °C).

Comparison of the Single Molecule Dynamics of Linear and Circular DNAs in Planar Extensional Flows

NASA Astrophysics Data System (ADS)

Li, Yanfei; Hsiao, Kai-Wen; Brockman, Christopher; Yates, Daniel; McKenna, Gregory; Schroeder, Charles; San Francisco, Michael; Kornfield, Julie; Anderson, Rae

2015-03-01

Chain topology has a profound impact on the flow behaviors of single macromolecules. The absence of free ends separates circular polymers from other chain architectures, i.e., linear, star, and branched. In the present work, we study the single chain dynamics of large circular and linear DNA molecules by comparing the relaxation dynamics, steady state coil-stretch transition, and transient molecular individualism behaviors for the two types of macromolecules. To this end, large circular DNA molecules were biologically synthesized and studied in a microfluidic device that has a cross-slot geometry to develop a stagnation point extensional flow. Although the relaxation time of rings scales in the same way as for the linear analog, the circular polymers show quantitatively different behaviors in the steady state extension and qualitatively different behaviors during a transient stretch. The existence of some commonality between these two topologies is proposed. Texas Tech University John R. Bradford Endowment.

Linear and Nonlinear Elasticity of Networks Made of Comb-like Polymers and Bottle-Brushes

NASA Astrophysics Data System (ADS)

Liang, H.; Dobrynin, A.; Everhart, M.; Daniel, W.; Vatankhah-Varnoosfaderani, M.; Sheiko, S.

We study mechanical properties of networks made of combs and bottle-brushes by computer simulations, theoretical calculations and experimental techniques. The networks are prepared by cross-linking backbones of combs or bottle-brushes with linear chains. This results in ``hybrid'' networks consisting of linear chains and strands of combs or bottle-brushes. In the framework of the phantom network model, the network modulus at small deformations G0 can be represented as a sum of contributions from linear chains, G0 , l, and strands of comb or bottle-brush, G0 , bb. If the length of extended backbone between crosslinks, Rmax, is much longer than the Kuhn length, bk, the modulus scales with the degree of polymerization of the side chains, nsc, and number of monomers between side chains, ng, as G0 , bb (nsc/ng + 1)-1. In the limit when bk becomes of the order of Rmax, the combs and bottle-brushes can be considered as semiflexible chains, resulting in a network modulus to be G0 , bb (nsc/ng + 1)-1(nsc2/2/ng) . In the nonlinear deformation regime, the strain-hardening behavior is described by the nonlinear network deformation model, which predicts that the true stress is a universal function of the structural modulus, G, first strain invariant, I1, and deformation ratio, β. The results of the computer simulations and predictions of the theoretical model are in a good agreement with experimental results. NSF DMR-1409710, DMR-1407645, DMR-1624569, DMR-1436201.

Self-Consistent Field Theories for the Role of Large Length-Scale Architecture in Polymers

NASA Astrophysics Data System (ADS)

Wu, David

At large length-scales, the architecture of polymers can be described by a coarse-grained specification of the distribution of branch points and monomer types within a molecule. This includes molecular topology (e.g., cyclic or branched) as well as distances between branch points or chain ends. Design of large length-scale molecular architecture is appealing because it offers a universal strategy, independent of monomer chemistry, to tune properties. Non-linear analogs of linear chains differ in molecular-scale properties, such as mobility, entanglements, and surface segregation in blends that are well-known to impact rheological, dynamical, thermodynamic and surface properties including adhesion and wetting. We have used Self-Consistent Field (SCF) theories to describe a number of phenomena associated with large length-scale polymer architecture. We have predicted the surface composition profiles of non-linear chains in blends with linear chains. These predictions are in good agreement with experimental results, including from neutron scattering, on a range of well-controlled branched (star, pom-pom and end-branched) and cyclic polymer architectures. Moreover, the theory allows explanation of the segregation and conformations of branched polymers in terms of effective surface potentials acting on the end and branch groups. However, for cyclic chains, which have no end or junction points, a qualitatively different topological mechanism based on conformational entropy drives cyclic chains to a surface, consistent with recent neutron reflectivity experiments. We have also used SCF theory to calculate intramolecular and intermolecular correlations for polymer chains in the bulk, dilute solution, and trapped at a liquid-liquid interface. Predictions of chain swelling in dilute star polymer solutions compare favorably with existing PRISM theory and swelling at an interface helps explain recent measurements of chain mobility at an oil-water interface. In collaboration with: Renfeng Hu, Colorado School of Mines, and Mark Foster, University of Akron. This work was supported by NSF Grants No. CBET- 0730692 and No. CBET-0731319.

The Influence of Preferential Flow on Pressure Propagation and Landslide Triggering of the Rocca Pitigliana Landslide

NASA Astrophysics Data System (ADS)

Shao, W.; Bogaard, T.; Bakker, M.; Berti, M.; Savenije, H. H. G.

2016-12-01

The fast pore water pressure response to rain events is an important triggering factor for slope instability. The fast pressure response may be caused by preferential flow that bypasses the soil matrix. Currently, most of the hydro-mechanical models simulate pore water pressure using a single-permeability model, which cannot quantify the effects of preferential flow on pressure propagation and landslide triggering. Previous studies showed that a model based on the linear-diffusion equation can simulate the fast pressure propagation in near-saturated landslides such as the Rocca Pitigliana landslide. In such a model, the diffusion coefficient depends on the degree of saturation, which makes it difficult to use the model for predictions. In this study, the influence of preferential flow on pressure propagation and slope stability is investigated with a 1D dual-permeability model coupled with an infinite-slope stability approach. The dual-permeability model uses two modified Darcy-Richards equations to simultaneously simulate the matrix flow and preferential flow in hillslopes. The simulated pressure head is used in an infinite-slope stability analysis to identify the influence of preferential flow on the fast pressure response and landslide triggering. The dual-permeability model simulates the height and arrival of the pressure peak reasonably well. Performance of the dual-permeability model is as good as or better than the linear-diffusion model even though the dual-permeability model is calibrated for two single pulse rain events only, while the linear-diffusion model is calibrated for each rain event separately.

Exact analytical modeling of lightwave propagation in planar media with arbitrarily graded index profiles

NASA Astrophysics Data System (ADS)

Krapez, J.-C.

2018-02-01

Applying the Darboux transformation in the optical-depth space allows building infinite chains of exact analytical solutions of the electromagnetic (EM) fields in planar 1D-graded dielectrics. As a matter of fact, infinite chains of solvable admittance profiles (e.g. refractive-index profiles, in the case of non-magnetic materials), together with the related EM fields are simultaneously and recursively obtained. The whole procedure has received the name "PROFIDT method" for PROperty and FIeld Darboux Transformation method. By repeating the Darboux transformations we can find out progressively more complex profiles and their EM solutions. An alternative is to stop after the first step and settle for a particular class of four-parameter admittance profiles that were dubbed of "sech(ξ)-type". These profiles are highly flexible. For this reason, they can be used as elementary bricks for building and modeling profiles of arbitrary shape. In addition, the corresponding transfer matrix involves only elementary functions. The sub-class of "sech(ξ)-type" profiles with horizontal end-slopes (S-shaped function) is particularly interesting: these can be used for high-level modeling of piecewise-sigmoidal refractive-index profiles encountered in various photonic devices such as matchinglayers, antireflection layers, rugate filters, chirped mirrors and photonic crystals. These simple analytical tools also allow exploring the fascinating properties of a new kind of structure, namely smooth quasicrystals. They can also be applied to model propagation of other types of waves in graded media such as acoustic waves and electric waves in tapered transmission lines.

Structure of Irreversibly Adsorbed Star Polymers

NASA Astrophysics Data System (ADS)

Akgun, Bulent; Aykan, Meryem Seyma; Canavar, Seda; Satija, Sushil K.; Uhrig, David; Hong, Kunlun

Formation of irreversibly adsorbed polymer chains on solid substrates have a huge impact on the wetting, glass transition, aging and polymer chain mobility in thin films. In recent years there has been many reports on the formation, kinetics and dynamics of these layers formed by linear homopolymers. Recent studies showed that by varying the number of polymer arms and arm molecular weight one can tune the glass transition temperature of thin polymer films. Using polymer architecture as a tool, the behavior of thin films can be tuned between the behavior of linear chains and soft colloids. We have studied the effect of polymer chain architecture on the structure of dead layer using X-ray reflectivity (XR) and atomic force microscopy. Layer thicknesses and densities of flattened and loosely adsorbed chains has been measured for linear, 4-arm, and 8-arm star polymers with identical total molecular weight as a function of substrate surface energy, annealing temperature and annealing time. Star polymers have been synthesized using anionic polymerization. XR measurements showed that 8-arm star PS molecules form the densest and the thickest dead layers among these three molecules.

Marginally specified priors for non-parametric Bayesian estimation

PubMed Central

Kessler, David C.; Hoff, Peter D.; Dunson, David B.

2014-01-01

Summary Prior specification for non-parametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. A statistician is unlikely to have informed opinions about all aspects of such a parameter but will have real information about functionals of the parameter, such as the population mean or variance. The paper proposes a new framework for non-parametric Bayes inference in which the prior distribution for a possibly infinite dimensional parameter is decomposed into two parts: an informative prior on a finite set of functionals, and a non-parametric conditional prior for the parameter given the functionals. Such priors can be easily constructed from standard non-parametric prior distributions in common use and inherit the large support of the standard priors on which they are based. Additionally, posterior approximations under these informative priors can generally be made via minor adjustments to existing Markov chain approximation algorithms for standard non-parametric prior distributions. We illustrate the use of such priors in the context of multivariate density estimation using Dirichlet process mixture models, and in the modelling of high dimensional sparse contingency tables. PMID:25663813

MD simulation study of the diffusion and local structure of n-alkanes in liquid and supercritical methanol at infinite dilution.

PubMed

Feng, Huajie; Gao, Wei; Su, Li; Sun, Zhenfan; Chen, Liuping

2017-06-01

The diffusion coefficients of 14 n-alkanes (ranging from methane to n-tetradecane) in liquid and supercritical methanol at infinite dilution (at a pressure of 10.5 MPa and at temperatures of 299 K and 515 K) were deduced via molecular dynamics simulations. Values for the radial distribution function, coordination number, and number of hydrogen bonds were then calculated to explore the local structure of each fluid. The flexibility of the n-alkane (as characterized by the computed dihedral distribution, end-to-end distance, and radius of gyration) was found to be a major influence and hydrogen bonding to be a minor influence on the local structure. Hydrogen bonding reduces the flexibility of the n-alkane, whereas increasing the temperature enhances its flexibility, with temperature having a greater effect than hydrogen bonding on flexibility. Graphical abstract The flexibility of the alkane is a major influence and the hydrogen bonding is a minor influence on the first solvation shell; the coordination numbers of long-chain n-alkanes in the first solvation shell are rather low.

Improved numerical methods for infinite spin chains with long-range interactions

NASA Astrophysics Data System (ADS)

Nebendahl, V.; Dür, W.

2013-02-01

We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main ingredient, we introduce the superposed multioptimization method, which allows an efficient optimization of exponentially many MPS of different lengths at different sites all in one step. Here, the algorithm becomes protected against position-dependent effects as caused by spontaneously broken translational invariance. So far, these have been a major obstacle to convergence for the iMPS algorithm if no prior knowledge of the system's translational symmetry was accessible. Further, we investigate some more general methods to speed up calculations and improve convergence, which might be partially interesting in a much broader context, too. As a more special problem, we also look into translational invariant states close to an invariance-breaking phase transition and show how to avoid convergence into wrong local minima for such systems. Finally, we apply these methods to polar bosons with long-range interactions. We calculate several detailed Devil's staircases with the corresponding phase diagrams and investigate some supersolid properties.

Current reversals and metastable states in the infinite Bose-Hubbard chain with local particle loss

NASA Astrophysics Data System (ADS)

Kiefer-Emmanouilidis, M.; Sirker, J.

2017-12-01

We present an algorithm which combines the quantum trajectory approach to open quantum systems with a density-matrix renormalization-group scheme for infinite one-dimensional lattice systems. We apply this method to investigate the long-time dynamics in the Bose-Hubbard model with local particle loss starting from a Mott-insulating initial state with one boson per site. While the short-time dynamics can be described even quantitatively by an equation of motion (EOM) approach at the mean-field level, many-body interactions lead to unexpected effects at intermediate and long times: local particle currents far away from the dissipative site start to reverse direction ultimately leading to a metastable state with a total particle current pointing away from the lossy site. An alternative EOM approach based on an effective fermion model shows that the reversal of currents can be understood qualitatively by the creation of holon-doublon pairs at the edge of the region of reduced particle density. The doublons are then able to escape while the holes move towards the dissipative site, a process reminiscent—in a loose sense—of Hawking radiation.

Life cycle cost optimization of biofuel supply chains under uncertainties based on interval linear programming.

PubMed

Ren, Jingzheng; Dong, Liang; Sun, Lu; Goodsite, Michael Evan; Tan, Shiyu; Dong, Lichun

2015-01-01

The aim of this work was to develop a model for optimizing the life cycle cost of biofuel supply chain under uncertainties. Multiple agriculture zones, multiple transportation modes for the transport of grain and biofuel, multiple biofuel plants, and multiple market centers were considered in this model, and the price of the resources, the yield of grain and the market demands were regarded as interval numbers instead of constants. An interval linear programming was developed, and a method for solving interval linear programming was presented. An illustrative case was studied by the proposed model, and the results showed that the proposed model is feasible for designing biofuel supply chain under uncertainties. Copyright © 2015 Elsevier Ltd. All rights reserved.

Structure and energetics of model amphiphilic molecules at the water liquid-vapor interface - A molecular dynamics study

NASA Technical Reports Server (NTRS)

Pohorille, Andrew; Benjamin, Ilan

1993-01-01

A molecular dynamics study of adsorption of p-n-pentylphenol at infinite dilution at the water liquid-vapor interface is reported. The calculated free energy of adsorption is -8.8 +/- 0.7 kcal/mol, in good agreement with the experimental value of -7.3 kcal/mol. The transition between the interfacial region and the bulk solution is sharp and well-defined by energetic, conformational, and orientational criteria. At the water surface, the phenol head group is mostly immersed in aqueous solvent. The most frequent orientation of the hydrocarbon tail is parallel to the interface, due to dispersion interactions with the water surface. This arrangement of the phenol ring and the alkyl chain requires that the chain exhibits a kink. As the polar head group is being moved into the solvent, the chain length increases and the tail becomes increasingly aligned toward the surface normal, such that the nonpolar part of the molecule exposed to water is minimized. The same effect was achieved when phenol was replaced by a more polar head group, phenolate.

Improved zeolite regeneration processes for preparing saturated branched-chain fatty acids

USDA-ARS?s Scientific Manuscript database

Ferrierite zeolite solid is an excellent catalyst for the skeletal isomerization of unsaturated linear-chain fatty acids (i.e., oleic acid) to unsaturated branched-chain fatty acids (i.e., iso-oleic acid) follow by hydrogenation to give saturated branched-chain fatty acids (i.e., isostearic acid). ...

Quantum conductance oscillation in linear monatomic silicon chains

NASA Astrophysics Data System (ADS)

Liu, Fu-Ti; Cheng, Yan; Yang, Fu-Bin; Chen, Xiang-Rong

2014-02-01

The conductance of linear silicon atomic chains with n=1-8 atoms sandwiched between Au electrodes is investigated by using the density functional theory combined with non-equilibrium Green's function. The results show that the conductance oscillates with a period of two atoms as the number of atoms in the chain is varied. We optimize the geometric structure of nanoscale junctions in different distances, and obtain that the average bond-length of silicon atoms in each chain at equilibrium positions is 2.15±0.03 Å. The oscillation of average Si-Si bond-length can explain the conductance oscillation from the geometric structure of atomic chains. We calculate the transmission spectrum of the chains in the equilibrium positions, and explain the conductance oscillation from the electronic structure. The transport channel is mainly contributed by px and py orbital electrons of silicon atoms. The even-odd oscillation is robust under external voltage up to 1.2 V.

Length-Two Representations of Quantum Affine Superalgebras and Baxter Operators

NASA Astrophysics Data System (ADS)

Zhang, Huafeng

2018-03-01

Associated to quantum affine general linear Lie superalgebras are two families of short exact sequences of representations whose first and third terms are irreducible: the Baxter TQ relations involving infinite-dimensional representations; the extended T-systems of Kirillov-Reshetikhin modules. We make use of these representations over the full quantum affine superalgebra to define Baxter operators as transfer matrices for the quantum integrable model and to deduce Bethe Ansatz Equations, under genericity conditions.

Control optimization, stabilization and computer algorithms for aircraft applications

NASA Technical Reports Server (NTRS)

1975-01-01

Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

Piston flow in a two-dimensional channel

NASA Astrophysics Data System (ADS)

Katopodes, Fotini V.; Davis, A. M. J.; Stone, H. A.

2000-05-01

A solution using biorthogonal eigenfunctions is presented for viscous flow caused by a piston in a two-dimensional channel. The resulting infinite set of linear equations is solved using Spence's optimal weighting function method [IMA J. Appl. Math. 30, 107 (1983)]. The solution is compared to that with a shear-free piston surface; in the latter configuration the fluid more rapidly approaches the Poiseuille flow profile established away from the face of the piston.

Bioinspired Concepts: Unified Theory for Complex Biological and Engineering Systems

DTIC Science & Technology

2006-01-01

i.e., data flows of finite size arrive at the system randomly. For such a system , we propose a modified dual scheduling algorithm that stabilizes ...demon. We compute the efficiency of the controller over finite and infinite time intervals, and since the controller is optimal, this yields hard limits...and highly optimized tolerance. PNAS, 102, 2005. 51. G. N. Nair and R. J. Evans. Stabilizability of stochastic linear systems with finite feedback

Synthesis and antimalarial activity of new chloroquine analogues carrying a multifunctional linear side chain.

PubMed

Iwaniuk, Daniel P; Whetmore, Eric D; Rosa, Nicholas; Ekoue-Kovi, Kekeli; Alumasa, John; de Dios, Angel C; Roepe, Paul D; Wolf, Christian

2009-09-15

We report the synthesis and in vitro antimalarial activity of several new 4-amino- and 4-alkoxy-7-chloroquinolines carrying a linear dibasic side chain. Many of these chloroquine analogues have submicromolar antimalarial activity versus HB3 (chloroquine sensitive) and Dd2 (chloroquine resistant strain of Plasmodium falciparum) and low resistance indices were obtained in most cases. Importantly, compounds 11-15 and 24 proved to be more potent against Dd2 than chloroquine. Branching of the side chain structure proved detrimental to the activity against the CQR strain.

Crystal structure and luminescence properties of silver in AgM(PO{sub 3}){sub 3} (M = Mg, Zn, Ba) polyphosphates

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

Belharouak, I.; Parent, C.; Tanguy, B.

1999-06-01

The relationships between the crystal structures and the luminescent properties of the AgM(PO{sub 3}){sub 3} (M = Mg, Zn, Ba) polyphosphates are reported in comparison with those of AgPO{sub 3}. The structure of the magnesium and zinc phosphates is characterized by long polyphosphates chains connected to infinite chains of [AgO{sub 6}] and [MO{sub 6}] polyhedra sharing faces. The basic structural phosphate unit in AgBa(PO{sub 3}){sub 3} is a P{sub 3}O{sub 9} ring. Silver atoms are located in distorted octahedral sites. Two types of luminescent centers have been observed. The UV emission observed in all these materials is typical of isolatedmore » Ag{sup +} ions. The visible emission observed only in the zinc phosphate is probably the result of a silver-zinc association. 16 refs., 8 figs., 3 tabs.« less

Finite-temperature dynamic structure factor of the spin-1 XXZ chain with single-ion anisotropy

NASA Astrophysics Data System (ADS)

Lange, Florian; Ejima, Satoshi; Fehske, Holger

2018-02-01

Improving matrix-product state techniques based on the purification of the density matrix, we are able to accurately calculate the finite-temperature dynamic response of the infinite spin-1 XXZ chain with single-ion anisotropy in the Haldane, large-D , and antiferromagnetic phases. Distinct thermally activated scattering processes make a significant contribution to the spectral weight in all cases. In the Haldane phase, intraband magnon scattering is prominent, and the on-site anisotropy causes the magnon to split into singlet and doublet branches. In the large-D phase response, the intraband signal is separated from an exciton-antiexciton continuum. In the antiferromagnetic phase, holons are the lowest-lying excitations, with a gap that closes at the transition to the Haldane state. At finite temperatures, scattering between domain-wall excitations becomes especially important and strongly enhances the spectral weight for momentum transfer π .

dl-Asparaginium nitrate

PubMed Central

Moussa Slimane, Nabila; Cherouana, Aouatef; Bendjeddou, Lamia; Dahaoui, Slimane; Lecomte, Claude

2009-01-01

In the title compound, C4H9N2O3 +·NO3 −, alternatively called (1RS)-2-carbamoyl-1-carboxy­ethanaminium nitrate, the asymmetric unit comprises one asparaginium cation and one nitrate anion. The strongest cation–cation O—H⋯O hydrogen bond in the structure, together with other strong cation–cation N—H⋯O hydrogen bonds, generates a succession of infinite chains of R 2 2(8) rings along the b axis. Additional cation–cation C—H⋯O hydrogen bonds link these chains into two-dimensional layers formed by alternating R 4 4(24) and R 4 2(12) rings. Connections between these layers are provided by the strong cation–anion N—H⋯O hydrogen bonds, as well as by one weak C—H⋯O inter­action, thus forming a three-dimensional network. Some of the cation–anion N—H⋯O hydrogen bonds are bifurcated of the type D—H⋯(A 1,A 2). PMID:21577586

Continuous higher-order sliding mode control with time-varying gain for a class of uncertain nonlinear systems.

PubMed

Han, Yaozhen; Liu, Xiangjie

2016-05-01

This paper presents a continuous higher-order sliding mode (HOSM) control scheme with time-varying gain for a class of uncertain nonlinear systems. The proposed controller is derived from the concept of geometric homogeneity and super-twisting algorithm, and includes two parts, the first part of which achieves smooth finite time stabilization of pure integrator chains. The second part conquers the twice differentiable uncertainty and realizes system robustness by employing super-twisting algorithm. Particularly, time-varying switching control gain is constructed to reduce the switching control action magnitude to the minimum possible value while keeping the property of finite time convergence. Examples concerning the perturbed triple integrator chains and excitation control for single-machine infinite bus power system are simulated respectively to demonstrate the effectiveness and applicability of the proposed approach. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Generalized thermalization for integrable system under quantum quench.

PubMed

Muralidharan, Sushruth; Lochan, Kinjalk; Shankaranarayanan, S

2018-01-01

We investigate equilibration and generalized thermalization of the quantum Harmonic chain under local quantum quench. The quench action we consider is connecting two disjoint harmonic chains of different sizes and the system jumps between two integrable settings. We verify the validity of the generalized Gibbs ensemble description for this infinite-dimensional Hilbert space system and also identify equilibration between the subsystems as in classical systems. Using Bogoliubov transformations, we show that the eigenstates of the system prior to the quench evolve toward the Gibbs Generalized Ensemble description. Eigenstates that are more delocalized (in the sense of inverse participation ratio) prior to the quench, tend to equilibrate more rapidly. Further, through the phase space properties of a generalized Gibbs ensemble and the strength of stimulated emission, we identify the necessary criterion on the initial states for such relaxation at late times and also find out the states that would potentially not be described by the generalized Gibbs ensemble description.

Synthesis, structure, and magnetic properties of two 1-D helical coordination polymeric Cu(II) complexes

NASA Astrophysics Data System (ADS)

Bian, He-Dong; Yang, Xiao-E.; Yu, Qing; Chen, Zi-Lu; Liang, Hong; Yan, Shi-Ping; Liao, Dai-Zheng

2008-01-01

Two helical coordination polymeric copper(II) complexes bearing amino acid Schiff bases HL or HL', which are condensed from 2-hydroxy-1-naphthaldehyde with 2-aminobenzoic acid or L-valine, respectively, have been prepared and characterised by X-ray crystallography. In [CuL] n ( 1) the copper(II) atoms are bridged by syn- anti carboxylate groups giving infinite 1-D right-handed helical chains which are further connected by weak C-H⋯Cu interactions to build a 2-D network. While in [CuL'] n ( 2) the carboxylate group acts as a rare monatomic bridge to connect the adjacent copper(II) atoms leading to the formation of a left-handed helical chain. Magnetic susceptibility measurements indicate that 1 exhibits weak ferromagnetic interactions whereas an antiferromagnetic coupling is established for 2. The magnetic behavior can be satisfactorily explained on the basis of the structural data.

Spin-filtering and giant magnetoresistance effects in polyacetylene-based molecular devices

NASA Astrophysics Data System (ADS)

Chen, Tong; Yan, Shenlang; Xu, Liang; Liu, Desheng; Li, Quan; Wang, Lingling; Long, Mengqiu

2017-07-01

Using the non-equilibrium Green's function formalism in combination with density functional theory, we performed ab initio calculations of spin-dependent electron transport in molecular devices consisting of a polyacetylene (CnHn+1) chain vertically attached to a carbon chain sandwiched between two semi-infinite zigzag-edged graphene nanoribbon electrodes. Spin-charge transport in the device could be modulated to different magnetic configurations by an external magnetic field. The results showed that single spin conduction could be obtained. Specifically, the proposed CnHn+1 devices exhibited several interesting effects, including (dual) spin filtering, spin negative differential resistance, odd-even oscillation, and magnetoresistance (MR). Marked spin polarization with a filtering efficiency of up to 100% over a large bias range was found, and the highest MR ratio for the CnHn+1 junctions reached 4.6 × 104. In addition, the physical mechanisms for these phenomena were also revealed.

8-Chloro-6-iodo-2-phenyl­chromeno[4,3-c]pyrazol-4(2H)-one N,N-dimethyl­formamide monosolvate

PubMed Central

Lokhande, Pradeep; Hasanzadeh, Kamal; Khaledi, Hamid; Mohd Ali, Hapipah

2011-01-01

In the title compound, C16H8ClIN2O2·C3H7NO, the fused tricyclic pyrazolo­coumarin ring and the N-phenyl ring are almost coplanar, the dihedral angle between them being 1.86 (9)°. In the crystal, these rings stack on top of each other via π–π inter­actions [centroid–centroid distances = 3.489 (2), 3.637 (2), 3.505 (2) and 3.662 (2) Å], forming infinite chains along the a axis. The chains are connected into layers parallel to ac plane through I⋯O inter­actions [3.0011 (18) Å] between pairs of symmetry-related mol­ecules. The DMF solvent mol­ecules are C—H⋯O bonded to this network. PMID:21837089

A two-dimensional ZnII coordination polymer constructed from benzene-1,2,3-tricarboxylic acid and N,N'-bis[(pyridin-4-yl)methylidene]hydrazine.

PubMed

Wang, Xiangfei; Yang, Fang; Tang, Meng; Yuan, Limin; Liu, Wenlong

2015-07-01

The hydrothermal synthesis of the novel complex poly[aqua(μ4-benzene-1,2,3-tricarboxylato)[μ2-4,4'-(hydrazine-1,2-diylidenedimethanylylidene)dipyridine](μ3-hydroxido)dizinc(II)], [Zn(C9H3O6)(OH)(C12H10N4)(H2O)]n, is described. The benzene-1,2,3-tricarboxylate ligand connects neighbouring Zn4(OH)2 secondary building units (SBUs) producing an infinite one-dimensional chain. Adjacent one-dimensional chains are connected by the N,N'-bis[(pyridin-4-yl)methylidene]hydrazine ligand, forming a two-dimensional layered structure. Adjacent layers are stacked to generate a three-dimensional supramolecular architecture via O-H...O hydrogen-bond interactions. The thermal stability of this complex is described and the complex also appears to have potential for application as a luminescent material.

From Comb-like Polymers to Bottle-Brushes

NASA Astrophysics Data System (ADS)

Liang, Heyi; Cao, Zhen; Dobrynin, Andrey; Sheiko, Sergei

We use a combination of the coarse-grained molecular dynamics simulations and scaling analysis to study conformations of bottle-brushes and comb-like polymers in a melt. Our analysis show that bottle-brushes and comb-like polymers can be in four different conformation regimes depending on the number of monomers between grafted side chains and side chain degree of polymerization. In loosely-grafted comb regime (LC) the degree of polymerization between side chains is longer than side chain degree of polymerization, such that the side chains belonging to the same macromolecule do not overlap. Crossover to a new densely-grafted comb regime (DC) takes place when side chains begin to overlap reducing interpenetration of side chains belonging to different macromolecules. In these two regimes both side-chains and backbone behave as unperturbed linear chains with the effective Kuhn length of the backbone being close to that of linear chain. Further decrease spacer degree of polymerization results in crossover to loosely-grafted bottle-brush regime (LB). In this regime, the bottle-brush backbone is stretched while the side-chains still maintain ideal chain conformation. Finally, for even shorter spacer between grafted side chains, which corresponds to densely-grafted bottle-brush regime (DB), the backbone adopts a fully extended chain conformation, and side-chains begin to stretch to maintain a constant monomer density. NSF DMR-1409710, DMR-1407645, DMR-1624569, DMR-1436201.

Reduced state feedback gain computation. [optimization and control theory for aircraft control

NASA Technical Reports Server (NTRS)

Kaufman, H.

1976-01-01

Because application of conventional optimal linear regulator theory to flight controller design requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. Therefore, a stochastic linear model that was developed is presented which accounts for aircraft parameter and initial uncertainty, measurement noise, turbulence, pilot command and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell. Results using a seventh order process show the proposed procedures to be very effective.

Detector noise statistics in the non-linear regime

NASA Technical Reports Server (NTRS)

Shopbell, P. L.; Bland-Hawthorn, J.

1992-01-01

The statistical behavior of an idealized linear detector in the presence of threshold and saturation levels is examined. It is assumed that the noise is governed by the statistical fluctuations in the number of photons emitted by the source during an exposure. Since physical detectors cannot have infinite dynamic range, our model illustrates that all devices have non-linear regimes, particularly at high count rates. The primary effect is a decrease in the statistical variance about the mean signal due to a portion of the expected noise distribution being removed via clipping. Higher order statistical moments are also examined, in particular, skewness and kurtosis. In principle, the expected distortion in the detector noise characteristics can be calibrated using flatfield observations with count rates matched to the observations. For this purpose, some basic statistical methods that utilize Fourier analysis techniques are described.

Linear rheology and structure of molecular bottlebrushes with short side chains

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

López-Barrón, Carlos R., E-mail: carlos.r.lopez-barron@exxonmobil.com; Brant, Patrick; Crowther, Donna J.

We investigate the microstructure and linear viscoelasticity of model molecular bottlebrushes (BBs) using rheological and small-angle X-ray and neutron scattering measurements. Our polymers have short atactic polypropylene (aPP) side chains of molecular weight ranging from 119 g/mol to 259 g/mol and narrow molecular weight distribution (M{sub w}/M{sub n} 1.02–1.05). The side chain molecular weights are a small fraction of the entanglement molecular weight of the corresponding linear polymer (M{sub e,aPP}= 7.05 kg/mol), and as such, they are unentangled. The morphology of the aPP BBs is characterized as semiflexible thick chains with small side chain interdigitation. Their dynamic master curves, obtained by time-temperature superposition,more » reveal two sequential relaxation processes corresponding to the segmental relaxation and the relaxation of the BB backbone. Due to the short length of the side chains, their fast relaxation could not be distinguished from the glassy relaxation. The fractional free volume is an increasing function of the side chain length (N{sub SC}). Therefore, the glassy behavior of these polymers as well as their molecular friction and dynamic properties are influenced by their N{sub SC} values. The apparent flow activation energies are a decreasing function of N{sub SC}, and their values explain the differences in zero-shear viscosity measured at different temperatures.« less

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.

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Shortcuts to adiabaticity from linear response theory

DOE PAGES

Acconcia, Thiago V.; Bonança, Marcus V. S.; Deffner, Sebastian

2015-10-23

A shortcut to adiabaticity is a finite-time process that produces the same final state as would result from infinitely slow driving. We show that such shortcuts can be found for weak perturbations from linear response theory. Moreover, with the help of phenomenological response functions, a simple expression for the excess work is found—quantifying the nonequilibrium excitations. For two specific examples, i.e., the quantum parametric oscillator and the spin 1/2 in a time-dependent magnetic field, we show that finite-time zeros of the excess work indicate the existence of shortcuts. We finally propose a degenerate family of protocols, which facilitates shortcuts tomore » adiabaticity for specific and very short driving times.« less

Transmogrifying fuzzy vortices

NASA Astrophysics Data System (ADS)

Murugan, Jeff; Millner, Antony

2004-04-01

We show that the construction of vortex solitons of the noncommutative abelian-Higgs model can be extended to a critically coupled gauged linear sigma model with Fayet-Illiopolous D-terms. Like its commutative counterpart, this fuzzy linear sigma model has a rich spectrum of BPS solutions. We offer an explicit construction of the degree-k static semilocal vortex and study in some detail the infinite coupling limit in which it descends to a degree-k Bbb CBbb PkN instanton. This relation between the fuzzy vortex and noncommutative lump is used to suggest an interpretation of the noncommutative sigma model soliton as tilted D-strings stretched between an NS5-brane and a stack of D3-branes in type-IIB superstring theory.

A parametric LQ approach to multiobjective control system design

NASA Technical Reports Server (NTRS)

Kyr, Douglas E.; Buchner, Marc

1988-01-01

The synthesis of a constant parameter output feedback control law of constrained structure is set in a multiple objective linear quadratic regulator (MOLQR) framework. The use of intuitive objective functions such as model-following ability and closed-loop trajectory sensitivity, allow multiple objective decision making techniques, such as the surrogate worth tradeoff method, to be applied. For the continuous-time deterministic problem with an infinite time horizon, dynamic compensators as well as static output feedback controllers can be synthesized using a descent Anderson-Moore algorithm modified to impose linear equality constraints on the feedback gains by moving in feasible directions. Results of three different examples are presented, including a unique reformulation of the sensitivity reduction problem.

Model predictive control of P-time event graphs

NASA Astrophysics Data System (ADS)

Hamri, H.; Kara, R.; Amari, S.

2016-12-01

This paper deals with model predictive control of discrete event systems modelled by P-time event graphs. First, the model is obtained by using the dater evolution model written in the standard algebra. Then, for the control law, we used the finite-horizon model predictive control. For the closed-loop control, we used the infinite-horizon model predictive control (IH-MPC). The latter is an approach that calculates static feedback gains which allows the stability of the closed-loop system while respecting the constraints on the control vector. The problem of IH-MPC is formulated as a linear convex programming subject to a linear matrix inequality problem. Finally, the proposed methodology is applied to a transportation system.

Edge currents in frustrated Josephson junction ladders

NASA Astrophysics Data System (ADS)

Marques, A. M.; Santos, F. D. R.; Dias, R. G.

2016-09-01

We present a numerical study of quasi-1D frustrated Josephson junction ladders with diagonal couplings and open boundary conditions, in the large capacitance limit. We derive a correspondence between the energy of this Josephson junction ladder and the expectation value of the Hamiltonian of an analogous tight-binding model, and show how the overall superconducting state of the chain is equivalent to the minimum energy state of the tight-binding model in the subspace of one-particle states with uniform density. To satisfy the constraint of uniform density, the superconducting state of the ladder is written as a linear combination of the allowed k-states of the tight-binding model with open boundaries. Above a critical value of the parameter t (ratio between the intra-rung and inter-rung Josephson couplings) the ladder spontaneously develops currents at the edges, which spread to the bulk as t is increased until complete coverage is reached. Above a certain value of t, which varies with ladder size (t = 1 for an infinite-sized ladder), the edge currents are destroyed. The value t = 1 corresponds, in the tight-binding model, to the opening of a gap between two bands. We argue that the disappearance of the edge currents with this gap opening is not coincidental, and that this points to a topological origin for these edge current states.

General polytropic self-gravitating cylinder free-fall and accreting mass string with a chain of collapsed objects

NASA Astrophysics Data System (ADS)

Lou, Yu-Qing; Hu, Xu-Yao

2016-06-01

We present a theoretical model framework for general polytropic (GP) hydrodynamic cylinder under self-gravity of infinite length with axial uniformity and axisymmetry. For self-similar dynamic solutions, we derive valuable integrals, analytic asymptotic solutions, sonic critical curves, shock conditions, and global numerical solutions with or without expansion shocks. Among others, we investigate various dynamic solutions featured with central free-fall asymptotic behaviours, corresponding to a collapsed mass string with a sustained dynamic accretion from a surrounding mass reservoir. Depending on the allowed ranges of a scaling index a < -1, such cylindrical dynamic mass accretion rate could be steady, increasing with time and decreasing with time. Physically, such a collapsed mass string or filament would break up into a sequence of sub-clumps and segments as induced by gravitational Jeans instabilities. Depending on the scales involved, such sub-clumps would evolve into collapsed objects or gravitationally bound systems. In diverse astrophysical and cosmological contexts, such a scenario can be adapted on various temporal, spatial and mass scales to form a chain of collapsed clumps and/or compact objects. Examples include the formation of chains of proto-stars, brown dwarfs and gaseous planets along molecular filaments; the formation of luminous massive stars along magnetized spiral arms and circum-nuclear starburst rings in barred spiral galaxies; the formation of chains of compact stellar objects such as white dwarfs, neutron stars, and black holes along a highly condensed mass string. On cosmological scales, one can perceive the formation of chains of galaxies, chains of galaxy clusters or even chains of supermassive and hypermassive black holes in the Universe including the early Universe. All these chains referred to above include possible binaries.

Determination of the pKa of the N-terminal amino group of ubiquitin by NMR

PubMed Central

Oregioni, Alain; Stieglitz, Benjamin; Kelly, Geoffrey; Rittinger, Katrin; Frenkiel, Tom

2017-01-01

Ubiquitination regulates nearly every aspect of cellular life. It is catalysed by a cascade of three enzymes and results in the attachment of the C-terminal carboxylate of ubiquitin to a lysine side chain in the protein substrate. Chain extension occurs via addition of subsequent ubiquitin molecules to either one of the seven lysine residues of ubiquitin, or via its N-terminal α-amino group to build linear ubiquitin chains. The pKa of lysine side chains is around 10.5 and hence E3 ligases require a mechanism to deprotonate the amino group at physiological pH to produce an effective nucleophile. In contrast, the pKa of N-terminal α-amino groups of proteins can vary significantly, with reported values between 6.8 and 9.1, raising the possibility that linear chain synthesis may not require a general base. In this study we use NMR spectroscopy to determine the pKa for the N-terminal α-amino group of methionine1 of ubiquitin for the first time. We show that it is 9.14, one of the highest pKa values ever reported for this amino group, providing a rational for the observed need for a general base in the E3 ligase HOIP, which synthesizes linear ubiquitin chains. PMID:28252051

Tuning conductivity in boron nanowire by edge geometry

NASA Astrophysics Data System (ADS)

Bhuyan, Prabal Dev; Gupta, Sanjeev K.; Sonvane, Yogesh; Gajjar, P. N.

2018-04-01

In present study, we have investigated electronic and temperature dependent transport properties of carbyne like linear chain and ribbon like zigzag structures of Boron (B) nanowire. The linear chain structure showed higher electric and thermal conductivity, as it is sp-hybridized, than its counterpart ribbon (R) structure. However the conductivity of ribbon structure increases with increases in width due to edge geometry effect. The ribbon (3R) structure showed high electric and thermal conductivity of 8.0×1019 1/Ω m s and 0.59×1015 W/ m K respectively. Interestingly we have observed that B linear chain showed higher thermal conductivity of 0.23×1015 W/ m K than its ribbon R and 2R structure above 600K. Because of high Seebeck co-efficient of boron chain and ribbon (R) structures at low temperature, they could find applications in thermoelectric sensors. Our results show that tuning conductivity property of boron nanowire could be of great interest in research for future electric connector in nanodevices.

Target Specificity of the E3 Ligase LUBAC for Ubiquitin and NEMO Relies on Different Minimal Requirements*

PubMed Central

Smit, Judith J.; van Dijk, Willem J.; El Atmioui, Dris; Merkx, Remco; Ovaa, Huib; Sixma, Titia K.

2013-01-01

The ubiquitination of NEMO with linear ubiquitin chains by the E3-ligase LUBAC is important for the activation of the canonical NF-κB pathway. NEMO ubiquitination requires a dual target specificity of LUBAC, priming on a lysine on NEMO and chain elongation on the N terminus of the priming ubiquitin. Here we explore the minimal requirements for these specificities. Effective linear chain formation requires a precise positioning of the ubiquitin N-terminal amine in a negatively charged environment on the top of ubiquitin. Whereas the RBR-LDD region on HOIP is sufficient for targeting the ubiquitin N terminus, the priming lysine modification on NEMO requires catalysis by the RBR domain of HOIL-1L as well as the catalytic machinery of the RBR-LDD domains of HOIP. Consequently, target specificity toward NEMO is determined by multiple LUBAC components, whereas linear ubiquitin chain elongation is realized by a specific interplay between HOIP and ubiquitin. PMID:24030825

Charge Mobility Enhancement for Conjugated DPP-Selenophene Polymer by Simply Replacing One Bulky Branching Alkyl Chain with Linear One at Each DPP Unit

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

Wang, Zhijie; Liu, Zitong; Ning, Lu

Here, we demonstrate a simple, but efficient, approach for improving the semiconducting performances of DPP-based conjugated D-A polymers. This approach involves the replacement of one bulky branching alkyl chain with the linear one at each DPP unit in regular polymer PDPPSe-10 and PDPPSe-12. The UV–vis absorption, Raman spectra, PDS data, and theoretical calculations support that the replacement of bulky branching chains with linear ones can weaken the steric hindrance, and accordingly conjugated backbones become more planar and rigid. GIWAXS data show that the incorporation of linear alkyl chains as in PDPPSe-10 and PDPPSe-12 is beneficial for side-chain interdigitation and interchainmore » dense packing, leading to improvement of interchain packing order and thin film crystallinity by comparing with PDPPSe, which contains branching alkyl chains. On the basis of field-effect transistor (FET) studies, charge mobilities of PDPPSe-10 and PDPPSe-12 are remarkably enhanced. Hole mobilities of PDPPSe-10 and PDPPSe-12 in air are boosted to 8.1 and 9.4 cm 2 V –1 s –1, which are about 6 and 7 times, respectively, than that of PDPPSe (1.35 cm 2 V –1 s –1). Furthermore, both PDPPSe-10 and PDPPSe-12 behave as ambipolar semiconductors under a nitrogen atmosphere with increased hole/electron mobilities up to 6.5/0.48 cm 2 V –1 s –1 and 7.9/0.79 cm 2 V –1 s –1, respectively.« less

Charge Mobility Enhancement for Conjugated DPP-Selenophene Polymer by Simply Replacing One Bulky Branching Alkyl Chain with Linear One at Each DPP Unit

DOE PAGES

Wang, Zhijie; Liu, Zitong; Ning, Lu; ...

2018-04-17

Here, we demonstrate a simple, but efficient, approach for improving the semiconducting performances of DPP-based conjugated D-A polymers. This approach involves the replacement of one bulky branching alkyl chain with the linear one at each DPP unit in regular polymer PDPPSe-10 and PDPPSe-12. The UV–vis absorption, Raman spectra, PDS data, and theoretical calculations support that the replacement of bulky branching chains with linear ones can weaken the steric hindrance, and accordingly conjugated backbones become more planar and rigid. GIWAXS data show that the incorporation of linear alkyl chains as in PDPPSe-10 and PDPPSe-12 is beneficial for side-chain interdigitation and interchainmore » dense packing, leading to improvement of interchain packing order and thin film crystallinity by comparing with PDPPSe, which contains branching alkyl chains. On the basis of field-effect transistor (FET) studies, charge mobilities of PDPPSe-10 and PDPPSe-12 are remarkably enhanced. Hole mobilities of PDPPSe-10 and PDPPSe-12 in air are boosted to 8.1 and 9.4 cm 2 V –1 s –1, which are about 6 and 7 times, respectively, than that of PDPPSe (1.35 cm 2 V –1 s –1). Furthermore, both PDPPSe-10 and PDPPSe-12 behave as ambipolar semiconductors under a nitrogen atmosphere with increased hole/electron mobilities up to 6.5/0.48 cm 2 V –1 s –1 and 7.9/0.79 cm 2 V –1 s –1, respectively.« less

Quantum quenches in two spatial dimensions using chain array matrix product states

DOE PAGES

A. J. A. James; Konik, R.

2015-10-15

We describe a method for simulating the real time evolution of extended quantum systems in two dimensions (2D). The method combines the benefits of integrability and matrix product states in one dimension to avoid several issues that hinder other applications of tensor based methods in 2D. In particular, it can be extended to infinitely long cylinders. As an example application we present results for quantum quenches in the 2D quantum [(2+1)-dimensional] Ising model. As a result, in quenches that cross a phase boundary we find that the return probability shows nonanalyticities in time.

Crystal structure of 1,3-bis-(1H-benzotriazol-1-yl-meth-yl)benzene.

PubMed

Macías, Mario A; Nuñez-Dallos, Nelson; Hurtado, John; Suescun, Leopoldo

2016-06-01

The mol-ecular structure of the title compound, C20H16N6, contains two benzotriazole units bonded to a benzene nucleus in a meta configuration, forming dihedral angles of 88.74 (11) and 85.83 (10)° with the central aromatic ring and 57.08 (9)° with each other. The three-dimensional structure is controlled mainly by weak C-H⋯N and C-H⋯π inter-actions. The mol-ecules are connected in inversion-related pairs, forming the slabs of infinite chains that run along the [-110] and [110] directions.

Computer simulations of polymer chain structure and dynamics on a hypersphere in four-space

NASA Astrophysics Data System (ADS)

Râsmark, Per Johan; Ekholm, Tobias; Elvingson, Christer

2005-05-01

There is a rapidly growing interest in performing computer simulations in a closed space, avoiding periodic boundary conditions. To extend the range of potential systems to include also macromolecules, we describe an algorithm for computer simulations of polymer chain molecules on S3, a hypersphere in four dimensions. In particular, we show how to generate initial conformations with a bond angle distribution given by the persistence length of the chain and how to calculate the bending forces for a molecule moving on S3. Furthermore, we discuss how to describe the shape of a macromolecule on S3, by deriving the radius of gyration tensor in this non-Euclidean space. The results from both Monte Carlo and Brownian dynamics simulations in the infinite dilution limit show that the results on S3 and in R3 coincide, both with respect to the size and shape as well as for the diffusion coefficient. All data on S3 can also be described by master curves by suitable scaling by the corresponding values in R3. We thus show how to extend the use of spherical boundary conditions, which are most effective for calculating electrostatic forces, to polymer chain molecules, making it possible to perform simulations on S3 also for polyelectrolyte systems.

A Linear Regression and Markov Chain Model for the Arabian Horse Registry

DTIC Science & Technology

1993-04-01

as a tax deduction? Yes No T-4367 68 26. Regardless of previous equine tax deductions, do you consider your current horse activities to be... (Mark one...E L T-4367 A Linear Regression and Markov Chain Model For the Arabian Horse Registry Accesion For NTIS CRA&I UT 7 4:iC=D 5 D-IC JA" LI J:13tjlC,3 lO...the Arabian Horse Registry, which needed to forecast its future registration of purebred Arabian horses . A linear regression model was utilized to

A Simulation Study of the Overdetermined Geodetic Boundary Value Problem Using Collocation

DTIC Science & Technology

1989-03-01

9 APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED GEOPHYSICS LABORATORY AIR FORCE SYSTEMS COMMAND UNITED STATES AIR FORCE HANSCOM AIR FORCE BASE...linearized integral equation is obtained through an infinite system of integral equations which is solved step by step by means of Stokes’ function. The...computed. Since 9 and W = W(9) 4 are known on the boundary, then the boundary is known in the new coordinate system . The serious disadvantage of this

Aerodynamics and Hovering Control of LTA Vehicles

DTIC Science & Technology

1977-05-01

not at all the usual terminology for Magnus Force which is usually thought of as arising from viscous effects when cylinder or sphere is rotating and...Number for Circular Cylinders 9 Ratio of the Drag Coefficient of a Circular Cylinder 29 of Finite Length to That of a Cylincer of Infinite Length as...Application of Non-Linear Drag 82 30 Directional Stability Derivative 83 31 Center of Lateral Pressure Location 84 32 Dihedral Effect Derivative 85 v Figures

The Focused Inverse Method for Linear Logic

DTIC Science & Technology

2006-12-04

design and engineering. Furthermore, it is a denouncement of the versatility of the inverse method if one were simply to abandon it for a radically...is technically unavoidable, but the impetus of design for such provers should be to reduce the size of the database. Our answer is to combine the...or “infinitely often P”. Systems such as Lamport’s TLA are not designed with automation as their primary aim; rather, they are intended to engage

Chaos and Robustness in a Single Family of Genetic Oscillatory Networks

PubMed Central

Fu, Daniel; Tan, Patrick; Kuznetsov, Alexey; Molkov, Yaroslav I.

2014-01-01

Genetic oscillatory networks can be mathematically modeled with delay differential equations (DDEs). Interpreting genetic networks with DDEs gives a more intuitive understanding from a biological standpoint. However, it presents a problem mathematically, for DDEs are by construction infinitely-dimensional and thus cannot be analyzed using methods common for systems of ordinary differential equations (ODEs). In our study, we address this problem by developing a method for reducing infinitely-dimensional DDEs to two- and three-dimensional systems of ODEs. We find that the three-dimensional reductions provide qualitative improvements over the two-dimensional reductions. We find that the reducibility of a DDE corresponds to its robustness. For non-robust DDEs that exhibit high-dimensional dynamics, we calculate analytic dimension lines to predict the dependence of the DDEs’ correlation dimension on parameters. From these lines, we deduce that the correlation dimension of non-robust DDEs grows linearly with the delay. On the other hand, for robust DDEs, we find that the period of oscillation grows linearly with delay. We find that DDEs with exclusively negative feedback are robust, whereas DDEs with feedback that changes its sign are not robust. We find that non-saturable degradation damps oscillations and narrows the range of parameter values for which oscillations exist. Finally, we deduce that natural genetic oscillators with highly-regular periods likely have solely negative feedback. PMID:24667178

On the Singularity Structure of WKB Solution of the Boosted Whittaker Equation: its Relevance to Resurgent Functions with Essential Singularities

NASA Astrophysics Data System (ADS)

Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya

2016-12-01

Inspired by the symbol calculus of linear differential operators of infinite order applied to the Borel transformed WKB solutions of simple-pole type equation [Kamimoto et al. (RIMS Kôkyûroku Bessatsu B 52:127-146, 2014)], which is summarized in Section 1, we introduce in Section 2 the space of simple resurgent functions depending on a parameter with an infra-exponential type growth order, and then we define the assigning operator A which acts on the space and produces resurgent functions with essential singularities. In Section 3, we apply the operator A to the Borel transforms of the Voros coefficient and its exponentiation for the Whittaker equation with a large parameter so that we may find the Borel transforms of the Voros coefficient and its exponentiation for the boosted Whittaker equation with a large parameter. In Section 4, we use these results to find the explicit form of the alien derivatives of the Borel transformed WKB solutions of the boosted Whittaker equation with a large parameter. The results in this paper manifest the importance of resurgent functions with essential singularities in developing the exact WKB analysis, the WKB analysis based on the resurgent function theory. It is also worth emphasizing that the concrete form of essential singularities we encounter is expressed by the linear differential operators of infinite order.

Stability analysis and stabilization strategies for linear supply chains

NASA Astrophysics Data System (ADS)

Nagatani, Takashi; Helbing, Dirk

2004-04-01

Due to delays in the adaptation of production or delivery rates, supply chains can be dynamically unstable with respect to perturbations in the consumption rate, which is known as “bull-whip effect”. Here, we study several conceivable production strategies to stabilize supply chains, which is expressed by different specifications of the management function controlling the production speed in dependence of the stock levels. In particular, we will investigate, whether the reaction to stock levels of other producers or suppliers has a stabilizing effect. We will also demonstrate that the anticipation of future stock levels can stabilize the supply system, given the forecast horizon τ is long enough. To show this, we derive linear stability conditions and carry out simulations for different control strategies. The results indicate that the linear stability analysis is a helpful tool for the judgement of the stabilization effect, although unexpected deviations can occur in the non-linear regime. There are also signs of phase transitions and chaotic behavior, but this remains to be investigated more thoroughly in the future.

Defects in regular nanosystems and interference spectra at reemission of electromagnetic field attosecond pulses

NASA Astrophysics Data System (ADS)

Matveev, V. I.; Makarov, D. N.

2017-01-01

The effect of defects in nanostructured targets on interference spectra at the reemission of attosecond electromagnetic pulses has been considered. General expressions have been obtained for calculations of spectral distributions for one-, two-, and three-dimensional multiatomic nanosystems consisting of identical complex atoms with defects such as bends, vacancies, and breaks. Changes in interference spectra by a linear chain with several removed atoms (chain with breaks) and by a linear chain with a bend have been calculated as examples allowing a simple analytical representation. Generalization to two- and three-dimensional nanosystems has been developed.

Synthesis and antimalarial activity of new chloroquine analogues carrying a multifunctional linear side chain

PubMed Central

Iwaniuk, Daniel P.; Whetmore, Eric D.; Rosa, Nicholas; Ekoue-Kovi, Kekeli; Alumasa, John; de Dios, Angel C.; Roepe, Paul D.; Wolf, Christian

2009-01-01

We report the synthesis and in vitro antimalarial activity of several new 4-amino-and 4-alkoxy-7-chloroquinolines carrying a linear dibasic side chain. Many of these chloroquine analogues have submicromolar antimalarial activity versus HB3 (chloroquine sensitive) and Dd2 (chloroquine resistant strain of P. falciparum) and low resistance indices were obtained in most cases. Importantly, compounds 11–15 and 24 proved to be more potent against Dd2 than chloroquine. Branching of the side chain structure proved detrimental to the activity against the CQR strain. PMID:19703776

Nanoporous poly(3-hexylthiophene) thin film structures from self-organization of a tunable molecular bottlebrush scaffold

DOE PAGES

Ahn, Suk-kyun; Carrillo, Jan-Michael Y.; Keum, Jong K.; ...

2017-04-07

The ability to widely tune the design of macromolecular bottlebrushes provides access to self-assembled nanostructures formed by microphase segregation in melt, thin film and solution that depart from structures adopted by simple linear copolymers. A series of random bottlebrush copolymers containing poly(3-hexylthiophene) (P3HT) and poly(D,L-lactide) (PLA) side chains grafted on a poly(norbornene) backbone were synthesized via ring-opening metathesis polymerization (ROMP) using the grafting through approach. P3HT side chains induce a physical aggregation of the bottlebrush copolymers upon solvent removal by vacuum drying, primarily driven by attractive π–π interactions; however, the amount of aggregation can be controlled by adjusting side chainmore » composition or by adding linear P3HT chains to the bottlebrush copolymers. Coarse-grained molecular dynamics simulations reveal that linear P3HT chains preferentially associate with P3HT side chains of bottlebrush copolymers, which tends to reduce the aggregation. The nanoscale morphology of microphase segregated thin films created by casting P3HT–PLA random bottlebrush copolymers is highly dependent on the composition of P3HT and PLA side chains, while domain spacing of nanostructures is mainly determined by the length of the side chains. The selective removal of PLA side chains under alkaline conditions generates nanoporous P3HT structures that can be tuned by manipulating molecular design of the bottlebrush scaffold, which is affected by molecular weight and grafting density of the side chains, and their sequence. Furthermore, the ability to exploit the unusual architecture of bottlebrushes to fabricate tunable nanoporous P3HT thin film structures may be a useful way to design templates for optoelectronic applications or membranes for separations.« less

Nanoporous poly(3-hexylthiophene) thin film structures from self-organization of a tunable molecular bottlebrush scaffold

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

Ahn, Suk-kyun; Carrillo, Jan-Michael Y.; Keum, Jong K.

The ability to widely tune the design of macromolecular bottlebrushes provides access to self-assembled nanostructures formed by microphase segregation in melt, thin film and solution that depart from structures adopted by simple linear copolymers. A series of random bottlebrush copolymers containing poly(3-hexylthiophene) (P3HT) and poly(D,L-lactide) (PLA) side chains grafted on a poly(norbornene) backbone were synthesized via ring-opening metathesis polymerization (ROMP) using the grafting through approach. P3HT side chains induce a physical aggregation of the bottlebrush copolymers upon solvent removal by vacuum drying, primarily driven by attractive π–π interactions; however, the amount of aggregation can be controlled by adjusting side chainmore » composition or by adding linear P3HT chains to the bottlebrush copolymers. Coarse-grained molecular dynamics simulations reveal that linear P3HT chains preferentially associate with P3HT side chains of bottlebrush copolymers, which tends to reduce the aggregation. The nanoscale morphology of microphase segregated thin films created by casting P3HT–PLA random bottlebrush copolymers is highly dependent on the composition of P3HT and PLA side chains, while domain spacing of nanostructures is mainly determined by the length of the side chains. The selective removal of PLA side chains under alkaline conditions generates nanoporous P3HT structures that can be tuned by manipulating molecular design of the bottlebrush scaffold, which is affected by molecular weight and grafting density of the side chains, and their sequence. Furthermore, the ability to exploit the unusual architecture of bottlebrushes to fabricate tunable nanoporous P3HT thin film structures may be a useful way to design templates for optoelectronic applications or membranes for separations.« less

Coherent and radiative couplings through two-dimensional structured environments

NASA Astrophysics Data System (ADS)

Galve, F.; Zambrini, R.

2018-03-01

We study coherent and radiative interactions induced among two or more quantum units by coupling them to two-dimensional (2D) lattices acting as structured environments. This model can be representative of atoms trapped near photonic crystal slabs, trapped ions in Coulomb crystals, or to surface acoustic waves on piezoelectric materials, cold atoms on state-dependent optical lattices, or even circuit QED architectures, to name a few. We compare coherent and radiative contributions for the isotropic and directional regimes of emission into the lattice, for infinite and finite lattices, highlighting their differences and existing pitfalls, e.g., related to long-time or large-lattice limits. We relate the phenomenon of directionality of emission with linear-shaped isofrequency manifolds in the dispersion relation, showing a simple way to disrupt it. For finite lattices, we study further details such as the scaling of resonant number of lattice modes for the isotropic and directional regimes, and relate this behavior with known van Hove singularities in the infinite lattice limit. Furthermore, we export the understanding of emission dynamics with the decay of entanglement for two quantum, atomic or bosonic, units coupled to the 2D lattice. We analyze in some detail completely subradiant configurations of more than two atoms, which can occur in the finite lattice scenario, in contrast with the infinite lattice case. Finally, we demonstrate that induced coherent interactions for dark states are zero for the finite lattice.

Conformally-flat, non-singular static metric in infinite derivative gravity

NASA Astrophysics Data System (ADS)

Buoninfante, Luca; Koshelev, Alexey S.; Lambiase, Gaetano; Marto, João; Mazumdar, Anupam

2018-06-01

In Einstein's theory of general relativity the vacuum solution yields a blackhole with a curvature singularity, where there exists a point-like source with a Dirac delta distribution which is introduced as a boundary condition in the static case. It has been known for a while that ghost-free infinite derivative theory of gravity can ameliorate such a singularity at least at the level of linear perturbation around the Minkowski background. In this paper, we will show that the Schwarzschild metric does not satisfy the boundary condition at the origin within infinite derivative theory of gravity, since a Dirac delta source is smeared out by non-local gravitational interaction. We will also show that the spacetime metric becomes conformally-flat and singularity-free within the non-local region, which can be also made devoid of an event horizon. Furthermore, the scale of non-locality ought to be as large as that of the Schwarzschild radius, in such a way that the gravitational potential in any metric has to be always bounded by one, implying that gravity remains weak from the infrared all the way up to the ultraviolet regime, in concurrence with the results obtained in [arXiv:1707.00273]. The singular Schwarzschild blackhole can now be potentially replaced by a non-singular compact object, whose core is governed by the mass and the effective scale of non-locality.

The inviscid pressure field on the tip of a semi-infinite wing and its application to the formation of a tip vortex

NASA Technical Reports Server (NTRS)

Hall, G. F.; Shamroth, S. J.; Mcdonald, H.; Briley, W. R.

1976-01-01

A method was developed for determining the aerodynamic loads on the tip of an infinitely thin, swept, cambered semi-infinite wing at an angle of attack which is operating subsonically in an inviscid medium and is subjected to a sinusoidal gust. Under the assumption of linearized aerodynamics, the loads on the tip are obtained by superposition of the steady aerodynamic results for angle of attack and camber, and the unsteady results for the response to the sinusoidal gust. The near field disturbance pressures in the fluid surrounding the tip are obtained by assuming a dipole representation for the loading on the tip and calculating the pressures accordingly. The near field pressures are used to drive a reduced form of the Navier-Stokes equations which yield the tip vortex formation. The combined viscid-inviscid analysis is applied to determining the pressures and examining the vortex rollup in the vicinity of an unswept, uncambered wing moving steadily at a Mach number of 0.2 at an angle of attack of 0.1 rad. The viscous tip flow calculation shows features expected in the tip flow such as the qualitatively proper development of boundary layers on both the upper and lower airfoil surfaces. In addition, application of the viscous solution leads to the generation of a circular type flow pattern above the airfoil suction surface.

Asymmetrical effects of mesophyll conductance on fundamental photosynthetic parameters and their relationships estimated from leaf gas exchange measurements.

PubMed

Sun, Ying; Gu, Lianhong; Dickinson, Robert E; Pallardy, Stephen G; Baker, John; Cao, Yonghui; DaMatta, Fábio Murilo; Dong, Xuejun; Ellsworth, David; Van Goethem, Davina; Jensen, Anna M; Law, Beverly E; Loos, Rodolfo; Martins, Samuel C Vitor; Norby, Richard J; Warren, Jeffrey; Weston, David; Winter, Klaus

2014-04-01

Worldwide measurements of nearly 130 C3 species covering all major plant functional types are analysed in conjunction with model simulations to determine the effects of mesophyll conductance (g(m)) on photosynthetic parameters and their relationships estimated from A/Ci curves. We find that an assumption of infinite g(m) results in up to 75% underestimation for maximum carboxylation rate V(cmax), 60% for maximum electron transport rate J(max), and 40% for triose phosphate utilization rate T(u) . V(cmax) is most sensitive, J(max) is less sensitive, and T(u) has the least sensitivity to the variation of g(m). Because of this asymmetrical effect of g(m), the ratios of J(max) to V(cmax), T(u) to V(cmax) and T(u) to J(max) are all overestimated. An infinite g(m) assumption also limits the freedom of variation of estimated parameters and artificially constrains parameter relationships to stronger shapes. These findings suggest the importance of quantifying g(m) for understanding in situ photosynthetic machinery functioning. We show that a nonzero resistance to CO2 movement in chloroplasts has small effects on estimated parameters. A non-linear function with gm as input is developed to convert the parameters estimated under an assumption of infinite gm to proper values. This function will facilitate gm representation in global carbon cycle models. © 2013 John Wiley & Sons Ltd.

The influence of preferential flow on pressure propagation and landslide triggering of the Rocca Pitigliana landslide

NASA Astrophysics Data System (ADS)

Shao, Wei; Bogaard, Thom; Bakker, Mark; Berti, Matteo

2016-12-01

The fast pore water pressure response to rain events is an important triggering factor for slope instability. The fast pressure response may be caused by preferential flow that bypasses the soil matrix. Currently, most of the hydro-mechanical models simulate pore water pressure using a single-permeability model, which cannot quantify the effects of preferential flow on pressure propagation and landslide triggering. Previous studies showed that a model based on the linear-diffusion equation can simulate the fast pressure propagation in near-saturated landslides such as the Rocca Pitigliana landslide. In such a model, the diffusion coefficient depends on the degree of saturation, which makes it difficult to use the model for predictions. In this study, the influence of preferential flow on pressure propagation and slope stability is investigated with a 1D dual-permeability model coupled with an infinite-slope stability approach. The dual-permeability model uses two modified Darcy-Richards equations to simultaneously simulate the matrix flow and preferential flow in hillslopes. The simulated pressure head is used in an infinite-slope stability analysis to identify the influence of preferential flow on the fast pressure response and landslide triggering. The dual-permeability model simulates the height and arrival of the pressure peak reasonably well. Performance of the dual-permeability model is as good as or better than the linear-diffusion model even though the dual-permeability model is calibrated for two single pulse rain events only, while the linear-diffusion model is calibrated for each rain event separately. In conclusion, the 1D dual-permeability model is a promising tool for landslides under similar conditions.

Non-Linear Dependence of the Height of a Chain Fountain on Drop Height

ERIC Educational Resources Information Center

Andrew, Y.; Kearns, F.; Mustafa, T.; Salih, R.; Ioratim-Uba, A.; Udall, I.; Usama, M.

2015-01-01

If the end of a long chain, which is contained in an elevated beaker, is dropped over the edge of the beaker and falls, it is observed that as the speed of the chain increases the chain rises to form a loop well above the top of the beaker. The name "chain fountain" has been applied to this phenomenon. In this study the dependence of the…

Synthesis, Crystal Structure, and Magnetic Properties of the Linear-Chain Cobalt Oxide Sr 5Pb 3CoO 12

NASA Astrophysics Data System (ADS)

Yamaura, K.; Huang, Q.; Takayama-Muromachi, E.

2002-02-01

The novel spin-chain cobalt oxide Sr5Pb3CoO12 [Poverline6×2m, a=10.1093(2) Å and c=3.562 51(9) Å at 295 K] is reported. A polycrystalline sample of the compound was studied by neutron diffraction (at 6 and 295 K) and magnetic susceptibility measurements (5 to 390 K). The cobalt oxide was found to be analogous to the copper oxide Sr5Pb3CuO12, which is comprised of magnetic-linear chains at an interchain distance of 10 Å. Although the cobalt oxide chains (μeff of 3.64 μB per Co) are substantially antiferromagnetic (θW=-38.8 K), neither low-dimensional magnetism nor long-range ordering has been found; a local-structure disorder in the chains might have an impact on the magnetism. This compound is highly electrically insulating.

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Astrophysics Data System (ADS)

Saunders, B. V.; Murray, B. T.; McFadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1992-06-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

NASA Technical Reports Server (NTRS)

Saunders, B. V.; Murray, B. T.; Mcfadden, G. B.; Coriell, S. R.; Wheeler, A. A.

1992-01-01

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

On multiple solutions of non-Newtonian Carreau fluid flow over an inclined shrinking sheet

NASA Astrophysics Data System (ADS)

Khan, Masood; Sardar, Humara; Gulzar, M. Mudassar; Alshomrani, Ali Saleh

2018-03-01

This paper presents the multiple solutions of a non-Newtonian Carreau fluid flow over a nonlinear inclined shrinking surface in presence of infinite shear rate viscosity. The governing boundary layer equations are derived for the Carreau fluid with infinite shear rate viscosity. The suitable transformations are employed to alter the leading partial differential equations to a set of ordinary differential equations. The consequential non-linear ODEs are solved numerically by an active numerical approach namely Runge-Kutta Fehlberg fourth-fifth order method accompanied by shooting technique. Multiple solutions are presented graphically and results are shown for various physical parameters. It is important to state that the velocity and momentum boundary layer thickness reduce with increasing viscosity ratio parameter in shear thickening fluid while opposite trend is observed for shear thinning fluid. Another important observation is that the wall shear stress is significantly decreased by the viscosity ratio parameter β∗ for the first solution and opposite trend is observed for the second solution.

The passage of an infinite swept airfoil through an oblique gust. [approximate solution for aerodynamic response

NASA Technical Reports Server (NTRS)

Adamczyk, J. L.

1974-01-01

An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.

On the nonlinear stability of viscous modes within the Rayleigh problem on an infinite flat plate

NASA Technical Reports Server (NTRS)

Webb, J. C.; Otto, S. R.; Lilley, G. M.

1994-01-01

The stability has been investigated of the unsteady flow past an infinite flat plate when it is moved impulsively from rest, in its own plane. For small times the instantaneous stability of the flow depends on the linearized equations of motion which reduce in this problem to the Orr-Sommerfeld equation. It is known that the flow for certain values of Reynolds number, frequency and wave number is unstable to Tollmien-Schlichting waves, as in the case of the Blasius boundary layer flow past a flat plate. With increase in time, the unstable waves only undergo growth for a finite time interval, and this growth rate is itself a function of time. The influence of finite amplitude effects is studied by solving the full Navier-Stokes equations. It is found that the stability characteristics are markedly changed both by the consideration of the time evolution of the flow, and by the introduction of finite amplitude effects.

Investigation and appreciation of optimal output feedback. Volume 1: A convergent algorithm for the stochastic infinite-time discrete optimal output feedback problem

NASA Technical Reports Server (NTRS)

Halyo, N.; Broussard, J. R.

1984-01-01

The stochastic, infinite time, discrete output feedback problem for time invariant linear systems is examined. Two sets of sufficient conditions for the existence of a stable, globally optimal solution are presented. An expression for the total change in the cost function due to a change in the feedback gain is obtained. This expression is used to show that a sequence of gains can be obtained by an algorithm, so that the corresponding cost sequence is monotonically decreasing and the corresponding sequence of the cost gradient converges to zero. The algorithm is guaranteed to obtain a critical point of the cost function. The computational steps necessary to implement the algorithm on a computer are presented. The results are applied to a digital outer loop flight control problem. The numerical results for this 13th order problem indicate a rate of convergence considerably faster than two other algorithms used for comparison.

Investigation, development and application of optimal output feedback theory. Vol. 4: Measures of eigenvalue/eigenvector sensitivity to system parameters and unmodeled dynamics

NASA Technical Reports Server (NTRS)

Halyo, Nesim

1987-01-01

Some measures of eigenvalue and eigenvector sensitivity applicable to both continuous and discrete linear systems are developed and investigated. An infinite series representation is developed for the eigenvalues and eigenvectors of a system. The coefficients of the series are coupled, but can be obtained recursively using a nonlinear coupled vector difference equation. A new sensitivity measure is developed by considering the effects of unmodeled dynamics. It is shown that the sensitivity is high when any unmodeled eigenvalue is near a modeled eigenvalue. Using a simple example where the sensor dynamics have been neglected, it is shown that high feedback gains produce high eigenvalue/eigenvector sensitivity. The smallest singular value of the return difference is shown not to reflect eigenvalue sensitivity since it increases with the feedback gains. Using an upper bound obtained from the infinite series, a procedure to evaluate whether the sensitivity to parameter variations is within given acceptable bounds is developed and demonstrated by an example.

Adaptive and nonadaptive feedback control of global instabilities with application to a heated 2-D jet

NASA Astrophysics Data System (ADS)

Monkewitz, Peter A.; Mingori, D. L.

1992-04-01

Close to the onset of self-excited fluid oscillations the generic complex Ginzburg-Landau is proposed as the lowest order model for the plant. Its linear part which provides the stability boundaries is derived from first principles for both doubly-infinite and semi-infinite flow domains. Concentrating on a single global mode, the model is further simplified to the Stuart-Landau equation. For this latter model, a methodology is developed for the design of single-input single-output controllers. The so designed controllers have been implemented on a self-excited, heated two-dimensional jet with one hot wire as sensor and an acoustic speaker as actuator, and are shown to be effective within their limitations in suppressing or enhancing limit-cycle oscillations. Finally, the effect of of a controller designed to suppress the most unstable global mode on other modes is investigated experimentally in the wake of a cylinder at low Reynolds number, where an encouraging semi-quantitative correspondence to the Ginzburg-Landau model is found.

A path-independent integral for the characterization of solute concentration and flux at biofilm detachments

USGS Publications Warehouse

Moran, B.; Kulkarni, S.S.; Reeves, H.W.

2007-01-01

A path-independent (conservation) integral is developed for the characterization of solute concentration and flux in a biofilm in the vicinity of a detachment or other flux limiting boundary condition. Steady state conditions of solute diffusion are considered and biofilm kinetics are described by an uptake term which can be expressed in terms of a potential (Michaelis-Menten kinetics). An asymptotic solution for solute concentration at the tip of the detachment is obtained and shown to be analogous to that of antiplane crack problems in linear elasticity. It is shown that the amplitude of the asymptotic solution can be calculated by evaluating a path-independent integral. The special case of a semi-infinite detachment in an infinite strip is considered and the amplitude of the asymptotic field is related to the boundary conditions and problem parameters in closed form for zeroth and first order kinetics and numerically for Michaelis-Menten kinetics. ?? Springer Science+Business Media, Inc. 2007.

On the connection coefficients and recurrence relations arising from expansions in series of Laguerre polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.

2003-05-01

A formula expressing the Laguerre coefficients of a general-order derivative of an infinitely differentiable function in terms of its original coefficients is proved, and a formula expressing explicitly the derivatives of Laguerre polynomials of any degree and for any order as a linear combination of suitable Laguerre polynomials is deduced. A formula for the Laguerre coefficients of the moments of one single Laguerre polynomial of certain degree is given. Formulae for the Laguerre coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Laguerre coefficients are also obtained. A simple approach in order to build and solve recursively for the connection coefficients between Jacobi-Laguerre and Hermite-Laguerre polynomials is described. An explicit formula for these coefficients between Jacobi and Laguerre polynomials is given, of which the ultra-spherical polynomials of the first and second kinds and Legendre polynomials are important special cases. An analytical formula for the connection coefficients between Hermite and Laguerre polynomials is also obtained.

An infinite branching hierarchy of time-periodic solutions of the Benjamin-Ono equation

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

Wilkening, Jon

2008-07-01

We present a new representation of solutions of the Benjamin-Ono equation that are periodic in space and time. Up to an additive constant and a Galilean transformation, each of these solutions is a previously known, multi-periodic solution; however, the new representation unifies the subset of such solutions with a fixed spatial period and a continuously varying temporal period into a single network of smooth manifolds connected together by an infinite hierarchy of bifurcations. Our representation explicitly describes the evolution of the Fourier modes of the solution as well as the particle trajectories in a meromorphic representation of these solutions; therefore,more » we have also solved the problem of finding periodic solutions of the ordinary differential equation governing these particles, including a description of a bifurcation mechanism for adding or removing particles without destroying periodicity. We illustrate the types of bifurcation that occur with several examples, including degenerate bifurcations not predicted by linearization about traveling waves.« less

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

DOE PAGES

Steyer, Andrew J.; Van Vleck, Erik S.

2018-04-13

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

Aspect ratio effects on limited scrape-off layer plasma turbulence

NASA Astrophysics Data System (ADS)

Jolliet, Sébastien; Halpern, Federico D.; Loizu, Joaquim; Mosetto, Annamaria; Ricci, Paolo

2014-02-01

The drift-reduced Braginskii model describing turbulence in the tokamak scrape-off layer is written for a general magnetic configuration with a limiter. The equilibrium is then specified for a circular concentric magnetic geometry retaining aspect ratio effects. Simulations are then carried out with the help of the global, flux-driven fluid three-dimensional code GBS [Ricci et al., Plasma Phys. Controlled Fusion 54, 124047 (2012)]. Linearly, both simulations and simplified analytical models reveal a stabilization of ballooning modes. Nonlinearly, flux-driven nonlinear simulations give a pressure characteristic length whose trends are correctly captured by the gradient removal theory [Ricci and Rogers, Phys. Plasmas 20, 010702 (2013)], that assumes the profile flattening from the linear modes as the saturation mechanism. More specifically, the linear stabilization of ballooning modes is reflected by a 15% increase in the steady-state pressure gradient obtained from GBS nonlinear simulations when going from an infinite to a realistic aspect ratio.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

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

Steyer, Andrew J.; Van Vleck, Erik S.

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly,more » exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.« less

Burgers approximation for two-dimensional flow past an ellipse

NASA Technical Reports Server (NTRS)

Dorrepaal, J. M.

1982-01-01

A linearization of the Navier-Stokes equation due to Burgers in which vorticity is transported by the velocity field corresponding to continuous potential flow is examined. The governing equations are solved exactly for the two dimensional steady flow past an ellipse of arbitrary aspect ratio. The requirement of no slip along the surface of the ellipse results in an infinite algebraic system of linear equations for coefficients appearing in the solution. The system is truncated at a point which gives reliable results for Reynolds numbers R in the range 0 R 5. Predictions of the Burgers approximation regarding separation, drag and boundary layer behavior are investigated. In particular, Burgers linearization gives drag coefficients which are closer to observed experimental values than those obtained from Oseen's approximation. In the special case of flow past a circular cylinder, Burgers approximation predicts a boundary layer whose thickness is roughly proportional to R-1/2.

A high-order perturbation of surfaces method for scattering of linear waves by periodic multiply layered gratings in two and three dimensions

NASA Astrophysics Data System (ADS)

Hong, Youngjoon; Nicholls, David P.

2017-09-01

The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.

Posttranslational Modification of HOIP Blocks Toll-Like Receptor 4-Mediated Linear-Ubiquitin-Chain Formation

PubMed Central

Bowman, James; Rodgers, Mary A.; Shi, Mude; Amatya, Rina; Hostager, Bruce; Iwai, Kazuhiro; Gao, Shou-Jiang

2015-01-01

ABSTRACT Linear ubiquitination is an atypical posttranslational modification catalyzed by the linear-ubiquitin-chain assembly complex (LUBAC), containing HOIP, HOIL-1L, and Sharpin. LUBAC facilitates NF-κB activation and inflammation upon receptor stimulation by ligating linear ubiquitin chains to critical signaling molecules. Indeed, linear-ubiquitination-dependent signaling is essential to prevent pyogenic bacterial infections that can lead to death. While linear ubiquitination is essential for intracellular receptor signaling upon microbial infection, this response must be measured and stopped to avoid tissue damage and autoimmunity. While LUBAC is activated upon bacterial stimulation, the mechanisms regulating LUBAC activity in response to bacterial stimuli have remained elusive. We demonstrate that LUBAC activity itself is downregulated through ubiquitination, specifically, ubiquitination of the catalytic subunit HOIP at the carboxyl-terminal lysine 1056. Ubiquitination of Lys1056 dynamically altered HOIP conformation, resulting in the suppression of its catalytic activity. Consequently, HOIP Lys1056-to-Arg mutation led not only to persistent LUBAC activity but also to prolonged NF-κB activation induced by bacterial lipopolysaccharide-mediated Toll-like receptor 4 (TLR4) stimulation, whereas it showed no effect on NF-κB activation induced by CD40 stimulation. This study describes a novel posttranslational regulation of LUBAC-mediated linear ubiquitination that is critical for specifically directing TLR4-mediated NF-κB activation. PMID:26578682

A multichain polymer slip-spring model with fluctuating number of entanglements for linear and nonlinear rheology

DOE PAGES

Ramírez-Hernández, Abelardo; Peters, Brandon L.; Andreev, Marat; ...

2015-12-15

A theoretically informed entangled polymer simulation approach is presented for description of the linear and non-linear rheology of entangled polymer melts. The approach relies on a many-chain representation and introduces the topological effects that arise from the non-crossability of molecules through effective fluctuating interactions, mediated by slip-springs, between neighboring pairs of macromolecules. The total number of slip-springs is not preserved but, instead, it is controlled through a chemical potential that determines the average molecular weight between entanglements. The behavior of the model is discussed in the context of a recent theory for description of homogeneous materials, and its relevance ismore » established by comparing its predictions to experimental linear and non-linear rheology data for a series of well-characterized linear polyisoprene melts. Furthermore, the results are shown to be in quantitative agreement with experiment and suggest that the proposed formalism may also be used to describe the dynamics of inhomogeneous systems, such as composites and copolymers. Importantly, the fundamental connection made here between our many-chain model and the well-established, thermodynamically consistent single-chain mean-field models provides a path to systematic coarse-graining for prediction of polymer rheology in structurally homogeneous and heterogeneous materials.« less

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…

Numerical methods in Markov chain modeling

NASA Technical Reports Server (NTRS)

Philippe, Bernard; Saad, Youcef; Stewart, William J.

1989-01-01

Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

Molecular dynamics simulation study of solvent effects on conformation and dynamics of polyethylene oxide and polypropylene oxide chains in water and in common organic solvents.

PubMed

Hezaveh, Samira; Samanta, Susruta; Milano, Giuseppe; Roccatano, Danilo

2012-03-28

In this paper, the conformation and dynamics properties of polyethylene oxide (PEO) and polypropylene oxide (PPO) polymer chains at 298 K have been studied in the melt and at infinite dilution condition in water, methanol, chloroform, carbon tetrachloride, and n-heptane using molecular dynamics simulations. The calculated density of PEO melt with chain lengths of n = 2, 3, 4, 5 and, for PPO, n = 7 are in good agreement with the available experimental data. The conformational properties of PEO and PPO show an increasing gauche preference for the O-C-C-O dihedral in the following order water>methanol>chloroform>carbon tetrachloride = n-heptane. On the contrary, the preference for trans conformation has a maximum in carbon tetrachloride and n-heptane followed in the order by chloroform, methanol, and water. The PEO conformational preferences are in qualitative agreement with results of NMR studies. PEO chains formed different types of hydrogen bonds with polar solvent molecules. In particular, the occurrence of bifurcated hydrogen bonding in chloroform was also observed. Radii of gyration of PEO chains of length larger than n = 9 monomers showed a good agreement with light scattering data in water and in methanol. For the shorter chains the observed deviations are probably due to the enhanced hydrophobic effects caused by the terminal methyl groups. For PEO the fitting of end-to-end distance distributions with the semi-flexible chain model at 298 K provided persistence lengths of 0.375 and 0.387 nm in water and methanol, respectively. Finally, the radius of gyration of Pluronic P85 turned out to be 2.25 ± 0.4 nm at 293 K in water in agreement with experimental data.

Molecular dynamics simulation study of solvent effects on conformation and dynamics of polyethylene oxide and polypropylene oxide chains in water and in common organic solvents

NASA Astrophysics Data System (ADS)

Hezaveh, Samira; Samanta, Susruta; Milano, Giuseppe; Roccatano, Danilo

2012-03-01

In this paper, the conformation and dynamics properties of polyethylene oxide (PEO) and polypropylene oxide (PPO) polymer chains at 298 K have been studied in the melt and at infinite dilution condition in water, methanol, chloroform, carbon tetrachloride, and n-heptane using molecular dynamics simulations. The calculated density of PEO melt with chain lengths of n = 2, 3, 4, 5 and, for PPO, n = 7 are in good agreement with the available experimental data. The conformational properties of PEO and PPO show an increasing gauche preference for the O-C-C-O dihedral in the following order water>methanol>chloroform>carbon tetrachloride = n-heptane. On the contrary, the preference for trans conformation has a maximum in carbon tetrachloride and n-heptane followed in the order by chloroform, methanol, and water. The PEO conformational preferences are in qualitative agreement with results of NMR studies. PEO chains formed different types of hydrogen bonds with polar solvent molecules. In particular, the occurrence of bifurcated hydrogen bonding in chloroform was also observed. Radii of gyration of PEO chains of length larger than n = 9 monomers showed a good agreement with light scattering data in water and in methanol. For the shorter chains the observed deviations are probably due to the enhanced hydrophobic effects caused by the terminal methyl groups. For PEO the fitting of end-to-end distance distributions with the semi-flexible chain model at 298 K provided persistence lengths of 0.375 and 0.387 nm in water and methanol, respectively. Finally, the radius of gyration of Pluronic P85 turned out to be 2.25 ± 0.4 nm at 293 K in water in agreement with experimental data.

Mechanical desorption of a single chain: unusual aspects of phase coexistence at a first-order transition.

PubMed

Skvortsov, Alexander M; Klushin, Leonid I; Polotsky, Alexey A; Binder, Kurt

2012-03-01

The phase transition occurring when a single polymer chain adsorbed at a planar solid surface is mechanically desorbed is analyzed in two statistical ensembles. In the force ensemble, a constant force applied to the nongrafted end of the chain (that is grafted at its other end) is used as a given external control variable. In the z-ensemble, the displacement z of this nongrafted end from the surface is taken as the externally controlled variable. Basic thermodynamic parameters, such as the adsorption energy, exhibit a very different behavior as a function of these control parameters. In the thermodynamic limit of infinite chain length the desorption transition with the force as a control parameter clearly is discontinuous, while in the z-ensemble continuous variations are found. However, one should not be misled by a too-naive application of the Ehrenfest criterion to consider the transition as a continuous transition: rather, one traverses a two-phase coexistence region, where part of the chain is still adsorbed and the other part desorbed and stretched. Similarities with and differences from two-phase coexistence at vapor-liquid transitions are pointed out. The rounding of the singularities due to finite chain length is illustrated by exact calculations for the nonreversal random walk model on the simple cubic lattice. A new concept of local order parameter profiles for the description of the mechanical desorption of adsorbed polymers is suggested. This concept give evidence for both the existence of two-phase coexistence within single polymer chains for this transition and the anomalous character of this two-phase coexistence. Consequences for the proper interpretation of experiments performed in different ensembles are briefly mentioned.

Optimal design of FIR triplet halfband filter bank and application in image coding.

PubMed

Kha, H H; Tuan, H D; Nguyen, T Q

2011-02-01

This correspondence proposes an efficient semidefinite programming (SDP) method for the design of a class of linear phase finite impulse response triplet halfband filter banks whose filters have optimal frequency selectivity for a prescribed regularity order. The design problem is formulated as the minimization of the least square error subject to peak error constraints and regularity constraints. By using the linear matrix inequality characterization of the trigonometric semi-infinite constraints, it can then be exactly cast as a SDP problem with a small number of variables and, hence, can be solved efficiently. Several design examples of the triplet halfband filter bank are provided for illustration and comparison with previous works. Finally, the image coding performance of the filter bank is presented.

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1991-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

Theoretical studies of optics and charge transport in organic conducting oligomers and polymers: Rational design of improved transparent and conducting polymers

NASA Astrophysics Data System (ADS)

Hutchison, Geoffrey Rogers

Theoretical studies on a variety of oligo- and polyheterocycles elucidate their optical and charge transport properties, suggesting new, improved transparent conductive polymers. First-principles calculations provide accurate methodologies for predicting both optical band gaps of neutral and cationic oligomers and intrinsic charge transfer rates. Multidimensional analysis reveals important motifs in chemical tailorability of oligoheterocycle optical and charge transport properties. The results suggest new directions for design of novel materials. Using both finite oligomer and infinite polymer calculations, the optical band gaps in polyheterocycles follow a modified particle-in-a-box formalism, scaling approximately as 1/N (where N is the number of monomer units) in short chains, saturating for long chains. Calculations demonstrate that band structure changes upon heteroatom substitution, (e.g., from polythiophene to polypyrrole) derive from heteroatom electron affinity. Further investigation of chemical variability in substituted oligoheterocycles using multidimensional statistics reveals the interplay between heteroatom and substituent in correlations between structure and redox/optical properties of neutral and cationic species. A linear correlation between band gaps of neutral and cationic species upon oxidation of conjugated oligomers, shows redshifts of optical absorption for most species and blueshifts for small band gap species. Interstrand charge-transport studies focus on two contributors to hopping-style charge transfer rates: internal reorganization energy and the electronic coupling matrix element. Statistical analysis of chemical variability of reorganization energies in oligoheterocycles proves the importance of reorganization energy in determining intrinsic charge transfer rates (e.g., charge mobility in unsubstituted oligothiophenes). Computed bandwidths across several oligothiophene crystal packing motifs show similar electron and hole bandwidths, and show that well-known tilted and herringbone motifs in oligothiophenes are driven by electrostatic repulsion. Tilted stacks exhibit intrinsic charge-transfer rates smaller than cofacial stacks, but with lower packing energy. Given similar electron and hole bandwidths, a charge injection model explains substitution-modulated majority carrier changes in n- and p-type oligothiophene field-effect transistors.

Modeling of testosterone regulation by pulse-modulated feedback: An experimental data study

NASA Astrophysics Data System (ADS)

Mattsson, Per; Medvedev, Alexander

2013-10-01

The continuous part of a hybrid (pulse-modulated) model of testosterone feedback regulation is extended with infinite-dimensional and nonlinear dynamics, to better explain the testosterone concentration profiles observed in clinical data. A linear least-squares based optimization algorithm is developed for the purpose of detecting impulses of gonadotropin-realsing hormone from measured concentration of luteinizing hormone. The parameters in the model are estimated from hormone concentration measured in human males, and simulation results from the full closed-loop system are provided.

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

Korneeva, Anna; Shaydurov, Vladimir

In the paper, the data analysis is considered for thin-film thermoresistors coated on to a radio-electronic printed circuit board to determine possible zones of its overheating. A mathematical model consists in an underdetermined system of linear algebraic equations with an infinite set of solutions. For computing a more real solution, two additional conditions are used: the smoothness of a solution and the positiveness of an increase of temperature during overheating. Computational experiments demonstrate that an overheating zone is determined exactly with a tolerable accuracy of temperature in it.

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Structural Technology Evaluation and Analysis Program (STEAP) Delivery Order 0042: Development of the Equivalent Overload Model, Demonstration of the Failure of Superposition, and Relaxation/Redistribution Measurement

DTIC Science & Technology

2011-09-01

with the bilinear plasticity relation. We used the bilinear relation, which allowed a full range of hardening from isotropic to kinematic to be...43 Table 12. Verification of the Weight Function Method for Single Corner Crack at a Hole in an Infinite ...determine the “Young’s Modulus,” or the slope of the linear region of the curve, the experimental data is curve fit with

The algebra of supertraces for 2+1 super de Sitter gravity

NASA Technical Reports Server (NTRS)

Urrutia, L. F.; Waelbroeck, H.; Zertuche, F.

1993-01-01

The algebra of the observables for 2+1 super de Sitter gravity, for one genus of the spatial surface is calculated. The algebra turns out to be an infinite Lie algebra subject to non-linear constraints. The constraints are solved explicitly in terms of five independent complex supertraces. These variables are the true degrees of freedom of the system and their quantized algebra generates a new structure which is referred to as a 'central extension' of the quantum algebra SU(2)q.

Effect of Surface Waviness on Transition in Three-Dimensional Boundary-Layer Flow

NASA Technical Reports Server (NTRS)

Masad, Jamal A.

1996-01-01

The effect of a surface wave on transition in three-dimensional boundary-layer flow over an infinite swept wing was studied. The mean flow computed using interacting boundary-layer theory, and transition was predicted using linear stability theory coupled with the empirical eN method. It was found that decreasing the wave height, sweep angle, or freestream unit Reynolds number, and increasing the freestream Mach number or suction level all stabilized the flow and moved transition onset to downstream locations.

Estimation on nonlinear damping in second order distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1989-01-01

An approximation and convergence theory for the identification of nonlinear damping in abstract wave equations is developed. It is assumed that the unknown dissipation mechanism to be identified can be described by a maximal monotone operator acting on the generalized velocity. The stiffness is assumed to be linear and symmetric. Functional analytic techniques are used to establish that solutions to a sequence of finite dimensional (Galerkin) approximating identification problems in some sense approximate a solution to the original infinite dimensional inverse problem.

Infinite Dimensional Linear Systems with Unbounded Control and Observation: A Functional Analytic Approach.

DTIC Science & Technology

1985-02-01

In particular, the optimal control is characterized in terms S of the dual system and conditions are given under which the optimal control is...solution in general and has to be replaced by the differential inclusion x - ex 8 range fi. It is important to note that 0 is boundedly invertible on...above way in terms of operators B, C, T which satisfy the hypotheses (S2-4). -9- L ’- ". * The implications of this hypothesis for the inhomogeneous

Cuticular hydrocarbons as a tool for the identification of insect species: Puparial cases from Sarcophagidae

PubMed Central

Braga, Marina Vianna; Pinto, Zeneida Teixeira; de Carvalho Queiroz, Margareth Maria; Matsumoto, Nana; Blomquist, Gary James

2013-01-01

The external surface of all insects is covered by a species-specific complex mixture of highly stable, very long chain cuticular hydrocarbons (CHCs). Gas chromatography coupled to mass spectrometry was used to identify CHCs from four species of Sarcophagidae, Peckia (Peckia) chrysostoma, Peckia (Pattonella) intermutans, Sarcophaga (Liopygia) ruficornis and Sarcodexia lambens. The identified CHCs were mostly a mixture of n-alkanes, monomethylalkanes and dimethylalkanes with linear chain lengths varying from 23 to 33 carbons. Only two alkenes were found in all four species. S. lambens had a composition of CHCs with linear chain lengths varying from C23 to C33, while the other three species linear chain lengths from 24 to 31 carbons. n-Heptacosane, n-nonacosane and 3-methylnonacosane, n-triacontane and n-hentriacontane occurred in all four species. The results show that these hydrocarbon profiles may be used for the taxonomic differentiation of insect species and are a useful additional tool for taxonomic classification, especially when only parts of the insect specimen are available. PMID:23932943

Biodiesel production from triolein and short chain alcohols through biocatalysis.

PubMed

Salis, Andrea; Pinna, Marcella; Monduzzi, Maura; Solinas, Vincenzo

2005-09-29

Oleic acid alkyl esters (biodiesel) were synthesised by biocatalysis in solvent-free conditions. Different commercial immobilised lipases, namely Candida antarctica B, Rizhomucor miehei, and Pseudomonas cepacia, were tested towards the reaction between triolein and butanol to produce butyl oleate. Pseudomonas cepacia lipase resulted to be the most active enzyme reaching 100% of conversion after 6h. Different operative conditions such as reaction temperature, water activity, and reagent stoichiometric ratio were investigated and optimised. These conditions were then used to investigate the effect of linear and branched short chain alcohols. Methanol and 2-butanol were the worst alcohols: the former, probably, due to its low miscibility with the oil and the latter because secondary alcohols usually are less reactive than primary alcohols. Conversely, linear and branched primary alcohols with short alkyl chains (C(2)--C(4)) showed high reaction rate and conversion. A mixture of linear and branched short chain alcohols that mimics the residual of ethanol distillation (fusel oil) was successfully used for oleic acid ester synthesis. These compounds are important in biodiesel mixtures since they improve low temperature properties.

High sensitivity of positrons to oxygen vacancies and to copper-oxygen chain disorder in YBa2Cu3O(7-x)

NASA Astrophysics Data System (ADS)

von Stetten, E. C.; Berko, S.; Li, X. S.; Lee, R. R.; Brynestad, J.

1988-05-01

Temperature-dependent positron-electron momentum densities have been studied by two-dimensional angular correlation of annihilation radiation from 10 to 320 K in YBa2Cu3O(7-x) samples. The positron ground-state charge density, computed by the linearized augmented-plane-wave method, indicates that in YBa2Cu3O7 delocalized positrons sample preferentially the linear copper-oxygen chains. Positron localization due to disorder in these chains is invoked to explain the striking differences observed between superconducting (x = about 0.02) and nonsuperconducting (x = about 0.70) samples.

Effect of Molecular Architecture on Polymer Melt Surface Dynamics

NASA Astrophysics Data System (ADS)

Foster, Mark

The dynamics of the thermally stimulated surface height fluctuations in a polymer melt dictate wetting, adhesion, and tribology at that surface. These surface fluctuations can be profoundly altered by tethering of the chains. One type of tethering is the tethering of one part of a molecule to another part of the same molecule. This tethering is found in both long chain branched polymers and in macrocycles. We have studied the surface fluctuations with X-ray Photon Correlation Spectroscopy for melts of well-defined, anionically polymerized polystyrenes of various architectures, including linear, 6 arm star, pom-pom, comb and cyclic architectures. For linear chains, the variation of surface relaxation time with in-plane scattering vector can be fit using a hydrodynamic continuum theory (HCT) of thermally stimulated capillary waves that knows nothing of the chain architecture. Assuming the theory is applicable, apparent viscosities of the films may then be inferred from the XPCS data. For unentangled linear chains, the viscosity inferred from XPCS data in this manner is the same as that measured by conventional bulk rheometry. The HCT does a reasonable job of describing the variation of relaxation time with scattering vector for long branched chains also, but only if a viscosity much larger than that of the bulk is assumed. The discrepancy between the viscosity inferred from surface relaxation times using the HCT and that derived from conventional rheometry grows larger as the bulk Tg is approached and is different for each long chain branched architecture. However, for densely branched combs and cyclic chains different behaviors are found. Acknowledgement: Thanks to NSF (CBET 0730692) and the Advanced Photon Source, supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Science, under Contract No. W-31-109-ENG-38.

Energy level alignment of self-assembled linear chains of benzenediamine on Au(111) from first principles

DOE PAGES

Li, Guo; Rangel, Tonatiuh; Liu, Zhen -Fei; ...

2016-03-24

Using density functional theory (DFT) with van der Waals functionals, we calculate the adsorption energetics and geometry of benzenediamine (BDA) molecules on Au(111) surfaces. Our results demonstrate that the reported self-assembled linear chain structure of BDA, stabilized via hydrogen bonds between amine groups, is energetically favored over previously-studied monomeric phases. Moreover, using a model based on many-body perturbation theory within the GW approximation, we obtain approximate self-energy corrections to the DFT highest occupied molecular orbital (HOMO) energy associated with BDA adsorbate phases. As a result, we find that, independent of coverage, the HOMO energy of the linear chain phase ismore » lower relative to the Fermi energy than that of the monomer phase, and in good agreement with values measured with ultraviolet photoelectron spectroscopy and X-ray photoelectron spectroscopy.« less

Energy level alignment of self-assembled linear chains of benzenediamine on Au(111) from first principles

NASA Astrophysics Data System (ADS)

Li, Guo; Rangel, Tonatiuh; Liu, Zhen-Fei; Cooper, Valentino R.; Neaton, Jeffrey B.

2016-03-01

Using density functional theory (DFT) with a van der Waals density functional, we calculate the adsorption energetics and geometry of benzenediamine (BDA) molecules on Au(111) surfaces. Our results demonstrate that the reported self-assembled linear chain structure of BDA, stabilized via hydrogen bonds between amine groups, is energetically favored over previously studied monomeric phases. Moreover, using a model, which includes nonlocal polarization effects from the substrate and the neighboring molecules and incorporates many-body perturbation theory calculations within the GW approximation, we obtain approximate self-energy corrections to the DFT highest occupied molecular orbital (HOMO) energy associated with BDA adsorbate phases. We find that, independent of coverage, the HOMO energy of the linear chain phase is lower relative to the Fermi energy than that of the monomer phase, and in good agreement with values measured with ultraviolet photoelectron spectroscopy and x-ray photoelectron spectroscopy.

Searching for a 4 α linear-chain structure in excited states of 16O with covariant density functional theory

NASA Astrophysics Data System (ADS)

Yao, J. M.; Itagaki, N.; Meng, J.

2014-11-01

A study of the 4 α linear-chain structure in high-lying collective excitation states of 16O with covariant density functional theory is presented. The low-spin states are obtained by configuration mixing of particle-number and angular-momentum projected quadrupole deformed mean-field states with the generator coordinate method. The high-spin states are determined by cranking calculations. These two calculations are based on the same energy density functional PC-PK1. We have found a rotational band at low spin with the dominant intrinsic configuration considered to be the one whereby 4 α clusters stay along a common axis. The strongly deformed rod shape also appears in the high-spin region with the angular momentum 13 ℏ to18 ℏ ; however, whether the state is a pure 4 α linear chain is less obvious than for the low-spin states.

The Linear ubiquitin chain assembly complex acts as a liver tumor suppressor and inhibits hepatocyte apoptosis and hepatitis.

PubMed

Shimizu, Yutaka; Peltzer, Nieves; Sevko, Alexandra; Lafont, Elodie; Sarr, Aida; Draberova, Helena; Walczak, Henning

2017-06-01

Linear ubiquitination is a key posttranslational modification that regulates immune signaling and cell death pathways, notably tumor necrosis factor receptor 1 (TNFR1) signaling. The only known enzyme complex capable of forming linear ubiquitin chains under native conditions to date is the linear ubiquitin chain assembly complex, of which the catalytic core component is heme-oxidized iron regulatory protein 2 ubiquitin ligase-1-interacting protein (HOIP). To understand the underlying mechanisms of maintenance of liver homeostasis and the role of linear ubiquitination specifically in liver parenchymal cells, we investigated the physiological role of HOIP in the liver parenchyma. To do so, we created mice harboring liver parenchymal cell-specific deletion of HOIP (Hoip Δhep mice) by crossing Hoip-floxed mice with albumin-Cre mice. HOIP deficiency in liver parenchymal cells triggered tumorigenesis at 18 months of age preceded by spontaneous hepatocyte apoptosis and liver inflammation within the first month of life. In line with the emergence of inflammation, Hoip Δhep mice displayed enhanced liver regeneration and DNA damage. In addition, consistent with increased apoptosis, HOIP-deficient hepatocytes showed enhanced caspase activation and endogenous formation of a death-inducing signaling complex which activated caspase-8. Unexpectedly, exacerbated caspase activation and apoptosis were not dependent on TNFR1, whereas ensuing liver inflammation and tumorigenesis were promoted by TNFR1 signaling. The linear ubiquitin chain assembly complex serves as a previously undescribed tumor suppressor in the liver, restraining TNFR1-independent apoptosis in hepatocytes which, in its absence, is causative of TNFR1-mediated inflammation, resulting in hepatocarcinogenesis. (Hepatology 2017;65:1963-1978). © 2017 The Authors. Hepatology published by Wiley Periodicals, Inc., on behalf of the American Association for the Study of Liver Diseases.

Crystal structure of 1,3-bis­(1H-benzotriazol-1-yl­meth­yl)benzene

PubMed Central

Macías, Mario A.; Nuñez-Dallos, Nelson; Hurtado, John; Suescun, Leopoldo

2016-01-01

The mol­ecular structure of the title compound, C20H16N6, contains two benzotriazole units bonded to a benzene nucleus in a meta configuration, forming dihedral angles of 88.74 (11) and 85.83 (10)° with the central aromatic ring and 57.08 (9)° with each other. The three-dimensional structure is controlled mainly by weak C—H⋯N and C—H⋯π inter­actions. The mol­ecules are connected in inversion-related pairs, forming the slabs of infinite chains that run along the [-110] and [110] directions. PMID:27308049

Dannie Heineman Prize for Mathematical Physics Prize Lecture: Correlation Functions in Integrable Models II: The Role of Quantum Affine Symmetry

NASA Astrophysics Data System (ADS)

Jimbo, Michio

2013-03-01

Since the beginning of 1980s, hidden infinite dimensional symmetries have emerged as the origin of integrability: first in soliton theory and then in conformal field theory. Quest for symmetries in quantum integrable models has led to the discovery of quantum groups. On one hand this opened up rapid mathematical developments in representation theory, combinatorics and other fields. On the other hand it has advanced understanding of correlation functions of lattice models, leading to multiple integral formulas in integrable spin chains. We shall review these developments which continue up to the present time.

Design of Particulate-Reinforced Composite Materials

PubMed Central

Muc, Aleksander; Barski, Marek

2018-01-01

A microstructure-based model is developed to study the effective anisotropic properties (magnetic, dielectric or thermal) of two-phase particle-filled composites. The Green’s function technique and the effective field method are used to theoretically derive the homogenized (averaged) properties for a representative volume element containing isolated inclusion and infinite, chain-structured particles. Those results are compared with the finite element approximations conducted for the assumed representative volume element. In addition, the Maxwell–Garnett model is retrieved as a special case when particle interactions are not considered. We also give some information on the optimal design of the effective anisotropic properties taking into account the shape of magnetic particles. PMID:29401678

N-(2-Chloro­eth­yl)morpholine-4-carbox­amide

PubMed Central

Ujam, Oguejiofo T.; Asegbeloyin, Jonnie N.; Nicholson, Brian K.; Ukoha, Pius O.; Ukwueze, Nkechi N.

2014-01-01

The title compound, C7H13ClN2O2, synthesized by the reaction of 2-chloro­ethyl iso­cyanate and morpholine, crystallizes with four molecules in the asymmetric unit, which have similar conformations and comprise two pairs each related by approximate non-crystallographic inversion centres. Two of them have a modest orientational disorder of the 2-chloro­ethyl fragments [occupancy ratio of 0.778 (4):0.222 (4)]. In the crystal, mol­ecules are linked by N—H⋯O=C hydrogen bonds, forming three crystallographically different kinds of infinite hydrogen-bonded chains extending along [001]. PMID:24826162

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.

Solvation Thermodynamics of Oligoglycine with Respect to Chain Length and Flexibility.

PubMed

Drake, Justin A; Harris, Robert C; Pettitt, B Montgomery

2016-08-23

Oligoglycine is a backbone mimic for all proteins and is prevalent in the sequences of intrinsically disordered proteins. We have computed the absolute chemical potential of glycine oligomers at infinite dilution by simulation with the CHARMM36 and Amber ff12SB force fields. We performed a thermodynamic decomposition of the solvation free energy (ΔG(sol)) of Gly2-5 into enthalpic (ΔH(sol)) and entropic (ΔS(sol)) components as well as their van der Waals and electrostatic contributions. Gly2-5 was either constrained to a rigid/extended conformation or allowed to be completely flexible during simulations to assess the effects of flexibility on these thermodynamic quantities. For both rigid and flexible oligoglycine models, the decrease in ΔG(sol) with chain length is enthalpically driven with only weak entropic compensation. However, the apparent rates of decrease of ΔG(sol), ΔH(sol), ΔS(sol), and their elec and vdw components differ for the rigid and flexible models. Thus, we find solvation entropy does not drive aggregation for this system and may not explain the collapse of long oligoglycines. Additionally, both force fields yield very similar thermodynamic scaling relationships with respect to chain length despite both force fields generating different conformational ensembles of various oligoglycine chains. Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Heat conduction in a chain of colliding particles with a stiff repulsive potential

NASA Astrophysics Data System (ADS)

Gendelman, Oleg V.; Savin, Alexander V.

2016-11-01

One-dimensional billiards, i.e., a chain of colliding particles with equal masses, is a well-known example of a completely integrable system. Billiards with different particle masses is generically not integrable, but it still exhibits divergence of a heat conduction coefficient (HCC) in the thermodynamic limit. Traditional billiards models imply instantaneous (zero-time) collisions between the particles. We relax this condition of instantaneous impact and consider heat transport in a chain of stiff colliding particles with the power-law potential of the nearest-neighbor interaction. The instantaneous collisions correspond to the limit of infinite power in the interaction potential; for finite powers, the interactions take nonzero time. This modification of the model leads to a profound physical consequence—the probability of multiple (in particular triple) -particle collisions becomes nonzero. Contrary to the integrable billiards of equal particles, the modified model exhibits saturation of the heat conduction coefficient for a large system size. Moreover, the identification of scattering events with triple-particle collisions leads to a simple definition of the characteristic mean free path and a kinetic description of heat transport. This approach allows us to predict both the temperature and density dependencies for the HCC limit values. The latter dependence is quite counterintuitive—the HCC is inversely proportional to the particle density in the chain. Both predictions are confirmed by direct numerical simulations.

Degradation of 4-n-nonylphenol under nitrate reducing conditions

PubMed Central

Viñas, Marc; Grotenhuis, Tim; Rijnaarts, Huub H. M.; Langenhoff, Alette A. M.

2010-01-01

Nonylphenol (NP) is an endocrine disruptor present as a pollutant in river sediment. Biodegradation of NP can reduce its toxicological risk. As sediments are mainly anaerobic, degradation of linear (4-n-NP) and branched nonylphenol (tNP) was studied under methanogenic, sulphate reducing and denitrifying conditions in NP polluted river sediment. Anaerobic bioconversion was observed only for linear NP under denitrifying conditions. The microbial population involved herein was further studied by enrichment and molecular characterization. The largest change in diversity was observed between the enrichments of the third and fourth generation, and further enrichment did not affect the diversity. This implies that different microorganisms are involved in the degradation of 4-n-NP in the sediment. The major degrading bacteria were most closely related to denitrifying hexadecane degraders and linear alkyl benzene sulphonate (LAS) degraders. The molecular structures of alkanes and LAS are similar to the linear chain of 4-n-NP, this might indicate that the biodegradation of linear NP under denitrifying conditions starts at the nonyl chain. Initiation of anaerobic NP degradation was further tested using phenol as a structure analogue. Phenol was chosen instead of an aliphatic analogue, because phenol is the common structure present in all NP isomers while the structure of the aliphatic chain differs per isomer. Phenol was degraded in all cases, but did not affect the linear NP degradation under denitrifying conditions and did not initiate the degradation of tNP and linear NP under the other tested conditions. PMID:20640878

Circuit topology of self-interacting chains: implications for folding and unfolding dynamics.

PubMed

Mugler, Andrew; Tans, Sander J; Mashaghi, Alireza

2014-11-07

Understanding the relationship between molecular structure and folding is a central problem in disciplines ranging from biology to polymer physics and DNA origami. Topology can be a powerful tool to address this question. For a folded linear chain, the arrangement of intra-chain contacts is a topological property because rearranging the contacts requires discontinuous deformations. Conversely, the topology is preserved when continuously stretching the chain while maintaining the contact arrangement. Here we investigate how the folding and unfolding of linear chains with binary contacts is guided by the topology of contact arrangements. We formalize the topology by describing the relations between any two contacts in the structure, which for a linear chain can either be in parallel, in series, or crossing each other. We show that even when other determinants of folding rate such as contact order and size are kept constant, this 'circuit' topology determines folding kinetics. In particular, we find that the folding rate increases with the fractions of parallel and crossed relations. Moreover, we show how circuit topology constrains the conformational phase space explored during folding and unfolding: the number of forbidden unfolding transitions is found to increase with the fraction of parallel relations and to decrease with the fraction of series relations. Finally, we find that circuit topology influences whether distinct intermediate states are present, with crossed contacts being the key factor. The approach presented here can be more generally applied to questions on molecular dynamics, evolutionary biology, molecular engineering, and single-molecule biophysics.

Application of Nearly Linear Solvers to Electric Power System Computation

NASA Astrophysics Data System (ADS)

Grant, Lisa L.

To meet the future needs of the electric power system, improvements need to be made in the areas of power system algorithms, simulation, and modeling, specifically to achieve a time frame that is useful to industry. If power system time-domain simulations could run in real-time, then system operators would have situational awareness to implement online control and avoid cascading failures, significantly improving power system reliability. Several power system applications rely on the solution of a very large linear system. As the demands on power systems continue to grow, there is a greater computational complexity involved in solving these large linear systems within reasonable time. This project expands on the current work in fast linear solvers, developed for solving symmetric and diagonally dominant linear systems, in order to produce power system specific methods that can be solved in nearly-linear run times. The work explores a new theoretical method that is based on ideas in graph theory and combinatorics. The technique builds a chain of progressively smaller approximate systems with preconditioners based on the system's low stretch spanning tree. The method is compared to traditional linear solvers and shown to reduce the time and iterations required for an accurate solution, especially as the system size increases. A simulation validation is performed, comparing the solution capabilities of the chain method to LU factorization, which is the standard linear solver for power flow. The chain method was successfully demonstrated to produce accurate solutions for power flow simulation on a number of IEEE test cases, and a discussion on how to further improve the method's speed and accuracy is included.

Elasticity and photoelasticity relationships for polyethylene terephthalate fiber networks by molecular simulation

NASA Astrophysics Data System (ADS)

Nayak, Kapileswar; Das, Sushanta; Nanavati, Hemant

2008-01-01

We present a framework for the development of elasticity and photoelasticity relationships for polyethylene terephthalate fiber networks, incorporating aspects of the primary molecular structure. Semicrystalline polymeric fiber networks are modeled as sequentially arranged crystalline and amorphous regions. Rotational isomeric states-Monte Carlo simulations of amorphous chains of up to 360 bonds (degree of polymerization, DP =60), confined between and bridging infinite impenetrable crystalline walls, have been characterized by Ω, the probability density of the intercrystal separation h, and Δβ, the polarizability anisotropy. lnΩ and Δβ have been modeled as functions of h, yielding the chain deformation relationships. The development has been extended to the fiber network to yield the photoelasticity relationships. We execute our framework by fitting to experimental stress-elongation data and employing the single fitted parameter to directly predict the birefringence-elongation behavior, without any further fitting. Incorporating the effect of strain-induced crystallization into the framework makes it physically more meaningful and yields accurate predictions of the birefringence-elongation behavior.

K0.78Na0.22MoO2AsO4

PubMed Central

Jouini, Raja; Bouzidi, Chahira; Zid, Mohamed Faouzi; Driss, Ahmed

2013-01-01

The title compound, potassium sodium dioxidomolybden­um(VI) arsenate, K0.78Na0.22MoO2AsO4, was synthesized by a solid-state reaction route. The structure is built up from corner-sharing MoO6 octa­hedra and AsO4 tetra­hedra, creating infinite [MoAsO8]∞ chains running along the b-axis direction. As, Mo and all but one O atom are on special positions (4c) with m symmetry and K (occupancy 0.78) is on a position (4a) of -1 in the tunnels. The possible motion of the alkali cations has been investigated by means of the bond-valance sum (BVS) model. The simulation shows that the Na+ motion appears to be easier mainly along the b-axis direction. Structural relationships between the different compounds of the AMoO2AsO4 (A = Ag, Li, Na, K, Rb) series and MXO8 (M = V; X = P, As) chains are discussed. PMID:24109253

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.

Numerical estimation of structure constants in the three-dimensional Ising conformal field theory through Markov chain uv sampler

NASA Astrophysics Data System (ADS)

Herdeiro, Victor

2017-09-01

Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016), 10.1103/PhysRevE.94.043322] introduced a numerical recipe, dubbed uv sampler, offering precise estimations of the conformal field theory (CFT) data of the planar two-dimensional (2D) critical Ising model. It made use of scale invariance emerging at the critical point in order to sample finite sublattice marginals of the infinite plane Gibbs measure of the model by producing holographic boundary distributions. The main ingredient of the Markov chain Monte Carlo sampler is the invariance under dilation. This paper presents a generalization to higher dimensions with the critical 3D Ising model. This leads to numerical estimations of a subset of the CFT data—scaling weights and structure constants—through fitting of measured correlation functions. The results are shown to agree with the recent most precise estimations from numerical bootstrap methods [Kos, Poland, Simmons-Duffin, and Vichi, J. High Energy Phys. 08 (2016) 036, 10.1007/JHEP08(2016)036].

catena-Poly[[bis­(4-carboxy­cyclo­hexane­carboxyl­ato-κ2 O 1,O 1′)cadmium(II)]-μ-1,4-bis­(imidazol-1-ylmeth­yl)benzene-κ2 N 3:N 3′

PubMed Central

Li, Bing-Bing; Xiao, Bo

2009-01-01

In the title coordination polymer, [Cd(C8H11O4)2(C14H14N4)]n, the Cd atom (site symmetry 2) is six-coordin­ated by two O,O′-bidentate 4-carboxy­cyclo­hexa­necarboxyl­ate (Hchdc) ligands and two N atoms from two different 1,4-bis­(imidazol-1-ylmeth­yl)benzene (1,4-bix) mol­ecules in a very distorted cis-CdN2O4 octa­hedral environment. The 1,4-bix mol­ecules act as bridging ligands that bind two CdII atoms, thus forming an infinite chain propagating in [100], which is decorated by the Hchdc anions. The structure is completed by O—H⋯O hydrogen bonds, which link the chains together. PMID:21582692

Probing the statistics of transport in the Hénon Map

NASA Astrophysics Data System (ADS)

Alus, O.; Fishman, S.; Meiss, J. D.

2016-09-01

The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their transport properties. The boundary is composed of invariant "boundary circles." We briefly report recent results of the distribution of rotation numbers of boundary circles for the Hénon quadratic map and show that the probability of occurrence of small integer entries of their continued fraction expansions is larger than would be expected for a number chosen at random. However, large integer entries occur with probabilities distributed proportionally to the random case. The probability distributions of ratios of fluxes through island chains is reported as well. These island chains are neighbours in the sense of the Meiss-Ott Markov-tree model. Two distinct universality families are found. The distributions of the ratio between the flux and orbital period are also presented. All of these results have implications for models of transport in mixed phase space.

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

Koch, D.; Fertitta, E.; Paulus, B.

Due to the importance of both static and dynamical correlation in the bond formation, low-dimensional beryllium systems constitute interesting case studies to test correlation methods. Aiming to describe the whole dissociation curve of extended Be systems we chose to apply the method of increments (MoI) in its multireference (MR) formalism. To gain insight into the main characteristics of the wave function, we started by focusing on the description of small Be chains using standard quantum chemical methods. In a next step we applied the MoI to larger beryllium systems, starting from the Be{sub 6} ring. The complete active space formalismmore » was employed and the results were used as reference for local MR calculations of the whole dissociation curve. Although this is a well-established approach for systems with limited multireference character, its application regarding the description of whole dissociation curves requires further testing. Subsequent to the discussion of the role of the basis set, the method was finally applied to larger rings and extrapolated to an infinite chain.« less

Stick-slip nanofriction in cold-ion traps

NASA Astrophysics Data System (ADS)

Mandelli, Davide; Vanossi, Andrea; Tosatti, Erio

2013-03-01

Trapped cold ions are known to form linear or planar zigzag chains, helices or clusters depending on trapping conditions. They may be forced to slide over a laser induced corrugated potential, a mimick of sliding friction. We present MD simulations of an incommensurate 101 ions chain sliding subject to an external electric field. As expected with increasing corrugation, we observe the transition from a smooth-sliding, highly lubric regime to a strongly dissipative stick-slip regime. Owing to inhomogeneity the dynamics shows features reminiscent of macroscopic frictional behaviors. While the chain extremities are pinned, the incommensurate central part is initially free to slide. The onset of global sliding is preceded by precursor events consisting of partial slips of chain portions further from the center. We also look for frictional anomalies expected for the chain sliding across the linear-zigzag structural phase transition. Although the chain is too short for a proper critical behavior, the sliding friction displays a frank rise near the transition, due to opening of a new dissipative channel via excitations of transverse modes. Research partly sponsored by Sinergia Project CRSII2 136287/1.

Exploring Alkyl Chains in Benzobisthiazole-Naphthobisthiadiazole Polymers: Impact on Solar-Cell Performance, Crystalline Structures, and Optoelectronics.

PubMed

Al-Naamani, Eman; Gopal, Anesh; Ide, Marina; Osaka, Itaru; Saeki, Akinori

2017-11-01

The shapes and lengths of the alkyl chains of conjugated polymers greatly affect the efficiencies of organic photovoltaic devices. This often results in a trade-off between solubility and self-organizing behavior; however, each material has specific optimal chains. Here we report on the effect of alkyl side chains on the film morphologies, crystallinities, and optoelectronic properties of new benzobisthiazole-naphthobisthiadiazole (PBBT-NTz) polymers. The power conversion efficiencies (PCEs) of linear-branched and all-branched polymers range from 2.5% to 6.6%; the variations in these PCEs are investigated by atomic force microscopy, two-dimensional X-ray diffraction (2D-GIXRD), and transient photoconductivity techniques. The best-performing linear-branched polymer, bearing dodecyl and decyltetradecyl chains (C12-DT), exhibits nanometer-scale fibers along with the highest crystallinity, comprising predominant edge-on and partial face-on orientations. This morphology leads to the highest photoconductivity and the longest carrier lifetime. These results highlight the importance of long alkyl chains for inducing intermolecular stacking, which is in contrast to observations made for analogous previously reported polymers.

Ab initio optimization principle for the ground states of translationally invariant strongly correlated quantum lattice models.

PubMed

Ran, Shi-Ju

2016-05-01

In this work, a simple and fundamental numeric scheme dubbed as ab initio optimization principle (AOP) is proposed for the ground states of translational invariant strongly correlated quantum lattice models. The idea is to transform a nondeterministic-polynomial-hard ground-state simulation with infinite degrees of freedom into a single optimization problem of a local function with finite number of physical and ancillary degrees of freedom. This work contributes mainly in the following aspects: (1) AOP provides a simple and efficient scheme to simulate the ground state by solving a local optimization problem. Its solution contains two kinds of boundary states, one of which play the role of the entanglement bath that mimics the interactions between a supercell and the infinite environment, and the other gives the ground state in a tensor network (TN) form. (2) In the sense of TN, a novel decomposition named as tensor ring decomposition (TRD) is proposed to implement AOP. Instead of following the contraction-truncation scheme used by many existing TN-based algorithms, TRD solves the contraction of a uniform TN in an opposite way by encoding the contraction in a set of self-consistent equations that automatically reconstruct the whole TN, making the simulation simple and unified; (3) AOP inherits and develops the ideas of different well-established methods, including the density matrix renormalization group (DMRG), infinite time-evolving block decimation (iTEBD), network contractor dynamics, density matrix embedding theory, etc., providing a unified perspective that is previously missing in this fields. (4) AOP as well as TRD give novel implications to existing TN-based algorithms: A modified iTEBD is suggested and the two-dimensional (2D) AOP is argued to be an intrinsic 2D extension of DMRG that is based on infinite projected entangled pair state. This paper is focused on one-dimensional quantum models to present AOP. The benchmark is given on a transverse Ising chain and 2D classical Ising model, showing the remarkable efficiency and accuracy of the AOP.

Single-polymer dynamics under constraints: scaling theory and computer experiment.

PubMed

Milchev, Andrey

2011-03-16

The relaxation, diffusion and translocation dynamics of single linear polymer chains in confinement is briefly reviewed with emphasis on the comparison between theoretical scaling predictions and observations from experiment or, most frequently, from computer simulations. Besides cylindrical, spherical and slit-like constraints, related problems such as the chain dynamics in a random medium and the translocation dynamics through a nanopore are also considered. Another particular kind of confinement is imposed by polymer adsorption on attractive surfaces or selective interfaces--a short overview of single-chain dynamics is also contained in this survey. While both theory and numerical experiments consider predominantly coarse-grained models of self-avoiding linear chain molecules with typically Rouse dynamics, we also note some recent studies which examine the impact of hydrodynamic interactions on polymer dynamics in confinement. In all of the aforementioned cases we focus mainly on the consequences of imposed geometric restrictions on single-chain dynamics and try to check our degree of understanding by assessing the agreement between theoretical predictions and observations.

Small Angle Neutron Scattering Observation of Chain Retraction after a Large Step Deformation

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

Blanchard, A.; Heinrich, M.; Pyckhout-Hintzen, W.

The process of retraction in entangled linear chains after a fast nonlinear stretch was detected from time-resolved but quenched small angle neutron scattering (SANS) experiments on long, well-entangled polyisoprene chains. The statically obtained SANS data cover the relevant time regime for retraction, and they provide a direct, microscopic verification of this nonlinear process as predicted by the tube model. Clear, quantitative agreement is found with recent theories of contour length fluctuations and convective constraint release, using parameters obtained mainly from linear rheology. The theory captures the full range of scattering vectors once the crossover to fluctuations on length scales belowmore » the tube diameter is accounted for.« less

A correlated ab initio study of linear carbon-chain radicals CnH (n = 2-7)

NASA Technical Reports Server (NTRS)

Woon, D. E.; Loew, G. H. (Principal Investigator)

1995-01-01

Linear carbon-chain radicals CnH for n = 2-7 have been studied with correlation consistent valence and core-valence basis sets and the coupled cluster method RCCSD(T). Equilibrium structures, rotational constants, and dipole moments are reported and compared with available experimental data. The ground state of the even-n series changes from 2 sigma+ to 2 pi as the chain is extended. For C4H, the 2 sigma+ state was found to lie only 72 cm-1 below the 2 pi state in the estimated complete basis set limit for valence correlation. The C2H- and C3H- anions have also been characterized.

How to interpret current-voltage relationships of blocking grain boundaries in oxygen ionic conductors.

PubMed

Kim, Seong K; Khodorov, Sergey; Chen, Chien-Ting; Kim, Sangtae; Lubomirsky, Igor

2013-06-14

A new model based on a linear diffusion equation is proposed to explain the current-voltage characteristics of blocking grain boundaries in Y-doped CeO2 in particular. One can also expect that the model can be applicable to the ionic conductors with blocking grain boundaries, in general. The model considers an infinitely long chain of identical grains separated by grain boundaries, which are treated as regions in which depletion layers of mobile ions are formed due to trapping of immobile charges that do not depend on the applied voltage as well as temperature. The model assumes that (1) the grain boundaries do not represent physical blocking layers, which implies that if there is a second phase at the grain boundaries, then it is too thin to impede ion diffusion and (2) the ions follow Boltzmann distribution throughout the materials. Despite its simplicity, the model successfully reproduces the "power law": current proportional to voltage power n and illustrated with the experimental example of Y-doped ceria. The model also correctly predicts that the product nT, where T is the temperature in K, is constant and is proportional to the grain boundary potential as long as the charge at the grain boundaries remains trapped. The latter allows its direct determination from the current-voltage characteristics and promises considerable simplification in the analysis of the electrical characteristics of the grain boundaries with respect to the models currently in use.

Size-scaling behaviour of the electronic polarizability of one-dimensional interacting systems

NASA Astrophysics Data System (ADS)

Chiappe, G.; Louis, E.; Vergés, J. A.

2018-05-01

Electronic polarizability of finite chains is accurately calculated from the total energy variation of the system produced by small but finite static electric fields applied along the chain direction. Normalized polarizability, that is, polarizability divided by chain length, diverges as the second power of length for metallic systems but approaches a constant value for insulating systems. This behaviour provides a very convenient way to characterize the wave-function malleability of finite systems as it avoids the need of attaching infinite contacts to the chain ends. Hubbard model calculations at half filling show that the method works for a small U  =  1 interaction value that corresponds to a really small spectral gap of 0.005 (hopping t  =  ‑1 is assumed). Once successfully checked, the method has been applied to the long-range hopping model of Gebhard and Ruckenstein showing 1/r hopping decay (Gebhard and Ruckenstein 1992 Phys. Rev. Lett. 68 244; Gebhard et al 1994 Phys. Rev. B 49 10926). Metallicity for U values below the reported metal-insulator transition is obtained but the surprise comes for U values larger than the critical one (when a gap appears in the spectral density of states) because a steady increase of the normalized polarizability with size is obtained. This critical size-scaling behaviour can be understood as corresponding to a molecule which polarizability is unbounded. We have checked that a real transfer of charge from one chain end to the opposite occurs as a response to very small electric fields in spite of the existence of a large gap of the order of U for one-particle excitations. Finally, ab initio quantum chemistry calculations of realistic poly-acetylene chains prove that the occurrence of such critical behaviour in real systems is unlikely.

Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula

NASA Astrophysics Data System (ADS)

Bischoff, Jan-Moritz; Jeckelmann, Eric

2017-11-01

We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems. The dynamical DMRG is used to compute the linear response of a finite system to an applied ac source-drain voltage; then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the dc conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in a homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.

An exact solution of the van der Waals interaction between two ground-state hydrogen atoms

NASA Astrophysics Data System (ADS)

Koga, Toshikatsu; Matsumoto, Shinya

1985-06-01

A momentum space treatment shows that perturbation equations for the H(1s)-H(1s) van der Waals interaction can be exactly solved in their Schrödinger forms without invoking any variational methods. Using the Fock transformation, which projects the momentum vector of an electron from the three-dimensional hyperplane onto the four-dimensional hypersphere, we solve the third order integral-type perturbation equation with respect to the reciprocal of the internuclear distance R. An exact third order wave function is found as a linear combination of infinite number of four-dimensional spherical harmonics. The result allows us to evaluate the exact dispersion energy E6R-6, which is completely determined by the first three coefficients of the above linear combination.

Jeffrey fluid effect on free convective over a vertically inclined plate with magnetic field: A numerical approach

NASA Astrophysics Data System (ADS)

Rao, J. Anand; Raju, R. Srinivasa; Bucchaiah, C. D.

2018-05-01

In this work, the effect of magnetohydrodynamic natural or free convective of an incompressible, viscous and electrically conducting non-newtonian Jeffrey fluid over a semi-infinite vertically inclined permeable moving plate embedded in a porous medium in the presence of heat absorption, heat and mass transfer. By using non-dimensional quantities, the fundamental governing non-linear partial differential equations are transformed into linear partial differential equations and these equations together with associated boundary conditions are solved numerically by using versatile, extensively validated, variational finite element method. The sway of important key parameters on hydrodynamic, thermal and concentration boundary layers are examined in detail and the results are shown graphically. Finally the results are compared with the works published previously and found to be excellent agreement.

Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces

NASA Technical Reports Server (NTRS)

Ito, Kazufumi

1987-01-01

The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.

Effects of the circularly polarized beam of linearized gravitational waves

NASA Astrophysics Data System (ADS)

Barker, W.

2017-08-01

Solutions of the linearized Einstein equations are found that describe a transversely confined beam of circularly polarized gravitational waves on a Minkowski backdrop. By evaluating the cycle-averaged stress-energy-momentum pseudotensor of Landau & Lifshitz it is found that the angular momentum density is concentrated in the ‘skin’ at the edge of the beam where the intensity falls, and that the ratio of angular momentum to energy per unit length of the beam is 2/ω , where ω is the wave frequency, as expected for a beam of spin-2 gravitons. For sharply-defined, uniform, axisymmetric beams, the induced background metric is shown to produce the gravitomagnetic field and frame-dragging effects of a gravitational solenoid, whilst the angular momentum current helically twists the space at infinite radius along the beam axis.

Unconditionally marginal stability of harmonic electron hole equilibria in current-driven plasmas

NASA Astrophysics Data System (ADS)

Schamel, Hans

2018-06-01

Two forms of the linearized eigenvalue problem with respect to linear perturbations of a privileged cnoidal electron hole as a structural nonlinear equilibrium element are established. Whereas its integral form involves integrations along the characteristics or unperturbed particle orbits, the differential form has to cope with a differential operator of infinite order. Both are hence faced with difficulties to obtain a solution. A first successful attempt is, however, made by addressing a single harmonic wave as a nonlinear equilibrium structure. By this microscopic nonlinear approach, its marginal stability against linear perturbations in both linear stability regimes, the sub- and super-critical one, is shown independent of the mobility of ions and in favor with recent observations. Responsible for vanishing damping (growth) is the microscopic distortion of the resonant distribution function. The macroscopic form of the trapping nonlinearity—the 3/2 power term of the electrostatic potential in the density—which disappears in the monochromatic harmonic wave limit is consequently necessary for the occurrence of a nonlinear plasma instability in the sub-critical regime.

Immittance Data Validation by Kramers‐Kronig Relations – Derivation and Implications

PubMed Central

2017-01-01

Abstract Explicitly based on causality, linearity (superposition) and stability (time invariance) and implicit on continuity (consistency), finiteness (convergence) and uniqueness (single valuedness) in the time domain, Kramers‐Kronig (KK) integral transform (KKT) relations for immittances are derived as pure mathematical constructs in the complex frequency domain using the two‐sided (bilateral) Laplace integral transform (LT) reduced to the Fourier domain for sufficiently rapid exponential decaying, bounded immittances. Novel anti KK relations are also derived to distinguish LTI (linear, time invariant) systems from non‐linear, unstable and acausal systems. All relations can be used to test KK transformability on the LTI principles of linearity, stability and causality of measured and model data by Fourier transform (FT) in immittance spectroscopy (IS). Also, integral transform relations are provided to estimate (conjugate) immittances at zero and infinite frequency particularly useful to normalise data and compare data. Also, important implications for IS are presented and suggestions for consistent data analysis are made which generally apply likewise to complex valued quantities in many fields of engineering and natural sciences. PMID:29577007

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.

Three-dimensional earthquake analysis of roller-compacted concrete dams

NASA Astrophysics Data System (ADS)

Kartal, M. E.

2012-07-01

Ground motion effect on a roller-compacted concrete (RCC) dams in the earthquake zone should be taken into account for the most critical conditions. This study presents three-dimensional earthquake response of a RCC dam considering geometrical non-linearity. Besides, material and connection non-linearity are also taken into consideration in the time-history analyses. Bilinear and multilinear kinematic hardening material models are utilized in the materially non-linear analyses for concrete and foundation rock respectively. The contraction joints inside the dam blocks and dam-foundation-reservoir interaction are modeled by the contact elements. The hydrostatic and hydrodynamic pressures of the reservoir water are modeled with the fluid finite elements based on the Lagrangian approach. The gravity and hydrostatic pressure effects are employed as initial condition before the strong ground motion. In the earthquake analyses, viscous dampers are defined in the finite element model to represent infinite boundary conditions. According to numerical solutions, horizontal displacements increase under hydrodynamic pressure. Besides, those also increase in the materially non-linear analyses of the dam. In addition, while the principle stress components by the hydrodynamic pressure effect the reservoir water, those decrease in the materially non-linear time-history analyses.

Activated-Sludge Nitrification in the Presence of Linear and Branched-Chain Alkyl Benzene Sulfonates

PubMed Central

Baillod, Charles R.; Boyle, W. C.

1968-01-01

The effects of biodegradable linear alkyl benzene sulfonate and branched-chain alkyl benzene sulfonate detergents on activated-sludge nitrification were investigated by administering a synthetic waste containing up to 23 mg of each detergent per liter to eight bench-scale, batch, activated-sludge units. It was found that both detergents tended to promote complete oxidation of ammonia to nitrate, whereas control units produced approximately equal amounts of nitrite and nitrate. Various hypotheses are offered to explain the phenomenon. PMID:5636474

Linear viscoelasticity of a single semiflexible polymer with internal friction.

PubMed

Hiraiwa, Tetsuya; Ohta, Takao

2010-07-28

The linear viscoelastic behaviors of single semiflexible chains with internal friction are studied based on the wormlike-chain model. It is shown that the frequency dependence of the complex compliance in the high frequency limit is the same as that of the Voigt model. This asymptotic behavior appears also for the Rouse model with internal friction. We derive the characteristic times for both the high frequency limit and the low frequency limit and compare the results with those obtained by Khatri et al.

Lithium/organosulfur redox cell having protective solid electrolyte barrier formed on anode and method of making same

DOEpatents

De Jonghe, Lutgard C.; Visco, Steven J.; Liu, Meilin; Mailhe, Catherine C.

1990-01-01

A lithium/organosulfur redox cell is disclosed which comprises a solid lium anode, a liquid organosulfur cathode, and a barrier layer formed adjacent a surface of the solid lithium anode facing the liquid organosulfur cathode consisting of a reaction product of the lithium anode with the organosulfur cathode. The organosulfur cathode comprises a material having the formula (R(S).sub.y).sub.N where y=1 to 6, n=2 to 20 and R is one or more different aliphatic or aromatic organic moieties having 1 to 20 carbon atoms, which may include one or more oxygen, sulfur, nitrogen, or fluorine atoms associated with the chain when R comprises an aliphatic chain, wherein the linear chain may be linear or branched, saturated or unsaturated, and wherein either the aliphatic chain or the aromatic ring may have substituted groups thereon.

Chain representations of Open Quantum Systems and Lieb-Robinson like bounds for the dynamics

NASA Astrophysics Data System (ADS)

Woods, Mischa

2013-03-01

This talk is concerned with the mapping of the Hamiltonian of open quantum systems onto chain representations, which forms the basis for a rigorous theory of the interaction of a system with its environment. This mapping progresses as an interaction which gives rise to a sequence of residual spectral densities of the system. The rigorous mathematical properties of this mapping have been unknown so far. Here we develop the theory of secondary measures to derive an analytic, expression for the sequence solely in terms of the initial measure and its associated orthogonal polynomials of the first and second kind. These mappings can be thought of as taking a highly nonlocal Hamiltonian to a local Hamiltonian. In the latter, a Lieb-Robinson like bound for the dynamics of the open quantum system makes sense. We develop analytical bounds on the error to observables of the system as a function of time when the semi-infinite chain in truncated at some finite length. The fact that this is possible shows that there is a finite ``Speed of sound'' in these chain representations. This has many implications of the simulatability of open quantum systems of this type and demonstrates that a truncated chain can faithfully reproduce the dynamics at shorter times. These results make a significant and mathematically rigorous contribution to the understanding of the theory of open quantum systems; and pave the way towards the efficient simulation of these systems, which within the standard methods, is often an intractable problem. EPSRC CDT in Controlled Quantum Dynamics, EU STREP project and Alexander von Humboldt Foundation

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

Wu, Jing-Yun, E-mail: jyunwu@ncnu.edu.tw; Tsai, Chi-Jou; Chang, Ching-Yun

A Zn(II)−salicylaldimine complex [Zn(L{sup salpyca})(H{sub 2}O)]{sub n} (1, where H{sub 2}L{sup salpyca}=4-hydroxy-3-(((pyridin-2-yl)methylimino)methyl)benzoic acid), with a one-dimensional (1D) chain structure, has been successfully converted to a discrete Ni(II)−salicylaldimine complex [Ni(L{sup salpyca})(H{sub 2}O){sub 3}] (2) and an infinite Cu(II)−salicylaldimine complex ([Cu(L{sup salpyca})]·3H{sub 2}O){sub n} (3) through a metal-ion exchange induced structural transformation process. However, such processes do not worked by Mn(II) and Co(II) ions. Solid-state structure analyses reveal that complexes 1–3 form comparable coordinative or supramolecular zigzag chains running along the crystallographic [201] direction. In addition, replacing Zn(II) ion by Ni(II) and Cu(II) ions caused changes in coordination environment and sphere ofmore » metal centers, from a 5-coordinate intermediate geometry of square pyramidal and trigonal bipyramidal in 1 to a 6-coordinate octahedral geometry in 2, and to a 4-coordiante square planar geometry in 3. This study shows that metal-ion exchange serves as a very efficient way of forming new coordination complexes that may not be obtained through direct synthesis. - Graphical abstract: A Zn(II)−salicylaldimine zigzag chain has been successfully converted to a Ni(II)−salicylaldimine supramolecular zigzag chain and a Cu(II)−salicylaldimine coordinative zigzag chain through metal-ion exchange induced structural transformations, which is not achieved by Mn(II) and Co(II) ions.« less

From {sub {infinity}}{sup 1}[(UO{sub 2}){sub 2}O(MoO{sub 4}){sub 4}]{sup 6-} to {sub {infinity}}{sup 1}[(UO{sub 2}){sub 2}(MoO{sub 4}){sub 3}(MoO{sub 5})]{sup 6-} infinite chains in A{sub 6}U{sub 2}Mo{sub 4}O{sub 21} (A=Na, K, Rb, Cs) compounds: Synthesis and crystal structure of Cs{sub 6}[(UO{sub 2}){sub 2}(MoO{sub 4}){sub 3}(MoO{sub 5})

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

Yagoubi, S.; Groupe de Radiochimie, Institut de Physique Nucleaire d'Orsay, Universite Paris-Sud XI, 91406 Orsay Cedex; Obbade, S., E-mail: said.obbade@phelma.grenoble-inp.f

2011-05-15

A new caesium uranyl molybdate belonging to the M{sub 6}U{sub 2}Mo{sub 4}O{sub 21} family has been synthesized by solid-state reaction and its structure determined from single-crystal X-ray diffraction data. Contrary to the other alkali uranyl molybdates of this family (A=Na, K, Rb) where molybdenum atoms adopt only tetrahedral coordination and which can be formulated A{sub 6}[(UO{sub 2}){sub 2}O(MoO{sub 4}){sub 4}], the caesium compound Cs{sub 6}U{sub 2}Mo{sub 4}O{sub 21} should be written Cs{sub 6}[(UO{sub 2}){sub 2}(MoO{sub 4}){sub 3}(MoO{sub 5})] with molybdenum atoms in tetrahedral and square pyramidal environments. Cs{sub 6}[(UO{sub 2}){sub 2}(MoO{sub 4}){sub 3}(MoO{sub 5})] crystallizes in the triclinic symmetry withmore » space group P1-bar and a=10.4275(14) A, b=15.075(2) A, c=17.806(2) A, {alpha}=70.72(1){sup o}, {beta}=80.38(1){sup o} and {gamma}=86.39(1){sup o}, V=2604.7(6) A{sup 3}, Z=4, {rho}{sub mes}=5.02(2) g/cm{sup 3} and {rho}{sub cal}=5.08(3) g/cm{sup 3}. A full-matrix least-squares refinement on the basis of F{sup 2} yielded R{sub 1}=0.0464 and wR{sub 2}=0.0950 for 596 parameters with 6964 independent reflections with I{>=}2{sigma}(I) collected on a BRUKER AXS diffractometer with Mo(K{alpha}) radiation and a CCD detector. The crystal structure of Cs compound is characterized by {sub {infinity}}{sup 1}[(UO{sub 2}){sub 2}(MoO{sub 4}){sub 3}(MoO{sub 5})]{sup 6-} parallels chains built from U{sub 2}O{sub 13} dimeric units, MoO{sub 4} tetrahedra and MoO{sub 5} square pyramids, whereas, Na, K and Rb compounds are characterized by {sub {infinity}}{sup 1}[(UO{sub 2}){sub 2}O(MoO{sub 4}){sub 4}]{sup 6-} parallel chains formulated simply of U{sub 2}O{sub 13} units and MoO{sub 4} tetrahedra. Infrared spectroscopy measurements using powdered samples synthesized by solid-state reaction, confirm the structural results. The thermal stability and the electrical conductivity are also studied. The four compounds decompose at low temperature (between 540 and 610 {sup o}C). -- Graphical abstract: The staking of {sub {infinity}}{sup 1}[(UO{sub 2}){sub 2}(MoO{sub 4}){sub 3}(MoO{sub 5})]{sup 6-} infinite uranyl molybdate ribbons in the Cs{sub 6}[(UO{sub 2}){sub 2}(MoO{sub 4}){sub 3}(MoO{sub 5})] structure. Display Omitted Highlights: {yields} Cs{sub 6}U{sub 2}Mo{sub 4}O{sub 2} a new compound with bidimensional crystal structure, characterized by infinite uranyl molybdate chains. {yields} Crystal structure similar to these of the compounds containing Na, K, Rb. {yields} Molybdenum atoms surrounded by five oxygen atoms to form an original and strongly distorted MoO{sub 5} environment. {yields} The chains arrangement illustrates the key role of the alkaline ionic radius, in the crystal structure distortion for Cs compound.« less

Spherically symmetric analysis on open FLRW solution in non-linear massive gravity

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

Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin, E-mail: chienichiang@berkeley.edu, E-mail: izumi@phys.ntu.edu.tw, E-mail: chen@slac.stanford.edu

2012-12-01

We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity frommore » general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.« less

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

The Finite-Size Scaling Relation for the Order-Parameter Probability Distribution of the Six-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Merdan, Ziya; Karakuş, Özlem

2016-11-01

The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Finite-dimensional compensators for infinite-dimensional systems via Galerkin-type approximation

NASA Technical Reports Server (NTRS)

Ito, Kazufumi

1990-01-01

In this paper existence and construction of stabilizing compensators for linear time-invariant systems defined on Hilbert spaces are discussed. An existence result is established using Galkerin-type approximations in which independent basis elements are used instead of the complete set of eigenvectors. A design procedure based on approximate solutions of the optimal regulator and optimal observer via Galerkin-type approximation is given and the Schumacher approach is used to reduce the dimension of compensators. A detailed discussion for parabolic and hereditary differential systems is included.

Alfven waves associated with long cylindrical satellites

NASA Technical Reports Server (NTRS)

Venkataraman, N. S.; Gustafson, W. A.

1973-01-01

The Alfven wave excited by a long cylindrical satellite moving with a constant velocity at an angle relative to a uniform magnetic field has been calculated. Assuming a plasma with infinite conductivity, the linearized momentum equation and Maxwell's equations are applied to a cylindrical satellite carrying a variable current. The induced magnetic field is determined, and it is shown that the Alfven disturbance zone is of limited extent, depending on the satellite shape. The wave drag coefficient is calculated and shown to be small compared to the induction drag coefficient at all altitudes considered.

Lie group classification of first-order delay ordinary differential equations

NASA Astrophysics Data System (ADS)

Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

2018-05-01

A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs), which consists of linear DODEs and solution-independent delay relations, have infinite-dimensional symmetry algebras—as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension n, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.

The Linear Quadratic Optimal Control Problem for Infinite Dimensional Systems with Unbounded Input and Output Operators.

DTIC Science & Technology

1984-01-01

5.5) respectively (5.3) and (5.8) which means that u(t) - 0 respectively v(t) - 0 for t > o. The evolution of the systems (5.1) and (5.3) in terms ...input/output delays; and b) the general theory is presented in such a way that it applies to both . . ... ..- Lr parabolic and hyperbolic I P9es as...particular emphasis is placed on the development of the duality theory by means of two different state concepts. The resulting evolution equations

On the effect of boundary layer growth on the stability of compressible flows

NASA Technical Reports Server (NTRS)

El-Hady, N. M.

1981-01-01

The method of multiple scales is used to describe a formally correct method based on the nonparallel linear stability theory, that examines the two and three dimensional stability of compressible boundary layer flows. The method is applied to the supersonic flat plate layer at Mach number 4.5. The theoretical growth rates are in good agreement with experimental results. The method is also applied to the infinite-span swept wing transonic boundary layer with suction to evaluate the effect of the nonparallel flow on the development of crossflow disturbances.

Gushing metal chain

NASA Astrophysics Data System (ADS)

Belyaev, Alexander; Sukhanov, Alexander; Tsvetkov, Alexander

2016-03-01

This article addresses the problem in which a chain falls from a glass from some height. This phenomenon demonstrates a paradoxical rise of the chain over the glass. To explain this effect, an initial hypothesis and an appropriate theory are proposed for calculating the steady fall parameters of the chain. For this purpose, the modified Cayley's problem of falling chain given its rise due to the centrifugal force of upward inertia is solved. Results show that the lift caused by an increase in linear density at the part of chain where it is being bent (the upper part) is due to the convergence of the chain balls to one another. The experiments confirm the obtained estimates of the lifting chain.

Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions

NASA Astrophysics Data System (ADS)

Barnett, William A.; Duzhak, Evgeniya Aleksandrovna

2008-06-01

Grandmont [J.M. Grandmont, On endogenous competitive business cycles, Econometrica 53 (1985) 995-1045] found that the parameter space of the most classical dynamic models is stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with many forms of multiperiodic dynamics in between. The econometric implications of Grandmont’s findings are particularly important, if bifurcation boundaries cross the confidence regions surrounding parameter estimates in policy-relevant models. Stratification of a confidence region into bifurcated subsets seriously damages robustness of dynamical inferences. Recently, interest in policy in some circles has moved to New-Keynesian models. As a result, in this paper we explore bifurcation within the class of New-Keynesian models. We develop the econometric theory needed to locate bifurcation boundaries in log-linearized New-Keynesian models with Taylor policy rules or inflation-targeting policy rules. Central results needed in this research are our theorems on the existence and location of Hopf bifurcation boundaries in each of the cases that we consider.

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies.

PubMed

Essa, Khalid S

2014-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values.

Increased electrocatalyzed performance through high content potassium doped graphene matrix and aptamer tri infinite amplification labels strategy: Highly sensitive for matrix metalloproteinases-2 detection.

PubMed

Ren, Xiang; Zhang, Tong; Wu, Dan; Yan, Tao; Pang, Xuehui; Du, Bin; Lou, Wanruo; Wei, Qin

2017-08-15

Herein, a super-labeled immunoassay was fabricated for matrix metalloproteinases-2 detection. A self-corrosion ITO micro circuit board was designed in this sensing platform to reduce the random error in the same testing condition, and the self-constructed sensing platform is portable with a cheap price. The K-modified graphene (K-GS) was utilized as the matrix material, which was synthesized well by phenylate and phenanthrene through the polar bond of nonpolar molecule phenylate and the π-π interaction for the first time. An aptamer-based labels based on Au nanoparticles (AuNPs), thionine (Th) and horseradish peroxidase (HRP) were applied as the signal source for tri infinite amplification. This fabricated super-labeled immunoassay exhibit excellent performance for MMPs-2 detection. It displayed a broad linear range of 10 -4 -10ng/mL with a low detection limit of 35 fg/mL, which may have a potential application in the clinical diagnose. Copyright © 2017 Elsevier B.V. All rights reserved.

Conserved charges of the extended Bondi-Metzner-Sachs algebra

NASA Astrophysics Data System (ADS)

Flanagan, Éanna É.; Nichols, David A.

2017-02-01

Isolated objects in asymptotically flat spacetimes in general relativity are characterized by their conserved charges associated with the Bondi-Metzner-Sachs (BMS) group. These charges include total energy, linear momentum, intrinsic angular momentum and center-of-mass location, and, in addition, an infinite number of supermomentum charges associated with supertranslations. Recently, it has been suggested that the BMS symmetry algebra should be enlarged to include an infinite number of additional symmetries known as super-rotations. We show that the corresponding charges are finite and well defined, and can be divided into electric parity "super center-of-mass" charges and magnetic parity "superspin" charges. The supermomentum charges are associated with ordinary gravitational-wave memory, and the super center-of-mass charges are associated with total (ordinary plus null) gravitational-wave memory, in the terminology of Bieri and Garfinkle. Superspin charges are associated with the ordinary piece of spin memory. Some of these charges can give rise to black hole hair, as described by Strominger and Zhiboedov. We clarify how this hair evades the no-hair theorems.

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies

PubMed Central

Essa, Khalid S.

2013-01-01

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q) = 0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values. PMID:25685472

Multivalency of Sonic hedgehog conjugated to linear polymer chains modulates protein potency.

PubMed

Wall, Samuel T; Saha, Krishanu; Ashton, Randolph S; Kam, Kimberly R; Schaffer, David V; Healy, Kevin E

2008-04-01

A potently active multivalent form of the protein Sonic hedgehog (Shh) was produced by bioconjugation of a modified recombinant form of Shh to the linear polymers poly(acrylic acid) (pAAc) and hyaluronic acid (HyA) via a two-step reaction exploiting carboimiide and maleimide chemistry. Efficiency of the conjugation was approximately 75% even at stoichiometric ratios of 30 Shh molecules per linear HyA chain (i.e., 30:1 Shh/HyA). Bioactivity of the conjugates was tested via a cellular assay across a range of stoichiometric ratios of Shh molecules to HyA linear chains, which was varied from 0.6:1 Shh/HyA to 22:1 Shh/HyA. Results indicate that low conjugation ratios decrease Shh bioactivity and high ratios increase this activity beyond the potency of monomeric Shh, with approximately equal activity between monomeric soluble Shh and conjugated Shh at 7:1 Shh/HyA. In addition, high-ratio constructs increased angiogenesis determined by the in vivo chick chorioallantoic membrane (CAM) assay. These results are captured by a kinetic model of multiple interactions between the Shh/HyA conjugates and cell surface receptors resulting in higher cell signaling at lower bulk Shh concentrations.

Structure of gel phase saturated lecithin bilayers: temperature and chain length dependence.

PubMed Central

Sun, W J; Tristram-Nagle, S; Suter, R M; Nagle, J F

1996-01-01

Systematic low-angle and wide-angle x-ray scattering studies have been performed on fully hydrated unoriented multilamamellar vesicles of saturated lecithins with even chain lengths N = 16, 18, 20, 22, and 24 as a function of temperature T in the normal gel (L beta') phase. For all N, the area per chain Ac increases linearly with T with an average slope dAc/dT = 0.027 A2/degree C, and the lamellar D-spacings also increase linearly with an average slope dD/dT = 0.040 A/degree C. At the same T, longer chain length lecithins have more densely packed chains, i.e., smaller Ac's, than shorter chain lengths. The chain packing of longer chain lengths is found to be more distorted from hexagonal packing than that of smaller N, and the distortion epsilon of all N approaches the same value at the respective transition temperatures. The thermal volume expansion of these lipids is accounted for by the expansion in the hydrocarbon chain region. Electron density profiles are constructed using four orders of low-angle lamellar peaks. These show that most of the increase in D with increasing T is due to thickening of the bilayers that is consistent with a decrease in tilt angle theta and with little change in water spacing with either T or N. Because of the opposing effects of temperature on area per chain Ac and tilt angle 0, the area expansivity alpha A is quite small. A qualitative theoretical model based on competing head and chain interactions accounts for our results. PMID:8842227

Precision measurement of the local bias of dark matter halos

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

Lazeyras, Titouan; Wagner, Christian; Schmidt, Fabian

2016-02-01

We present accurate measurements of the linear, quadratic, and cubic local bias of dark matter halos, using curved 'separate universe' N-body simulations which effectively incorporate an infinite-wavelength overdensity. This can be seen as an exact implementation of the peak-background split argument. We compare the results with the linear and quadratic bias measured from the halo-matter power spectrum and bispectrum, and find good agreement. On the other hand, the standard peak-background split applied to the Sheth and Tormen (1999) and Tinker et al. (2008) halo mass functions matches the measured linear bias parameter only at the level of 10%. The predictionmore » from the excursion set-peaks approach performs much better, which can be attributed to the stochastic moving barrier employed in the excursion set-peaks prediction. We also provide convenient fitting formulas for the nonlinear bias parameters b{sub 2}(b{sub 1}) and b{sub 3}(b{sub 1}), which work well over a range of redshifts.« less

Koopman operator theory: Past, present, and future

NASA Astrophysics Data System (ADS)

Brunton, Steven; Kaiser, Eurika; Kutz, Nathan

2017-11-01

Koopman operator theory has emerged as a dominant method to represent nonlinear dynamics in terms of an infinite-dimensional linear operator. The Koopman operator acts on the space of all possible measurement functions of the system state, advancing these measurements with the flow of the dynamics. A linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. Dynamic mode decomposition has become the leading data-driven method to approximate the Koopman operator, although there are still open questions and challenges around how to obtain accurate approximations for strongly nonlinear systems. This talk will provide an introductory overview of modern Koopman operator theory, reviewing the basics and describing recent theoretical and algorithmic developments. Particular emphasis will be placed on the use of data-driven Koopman theory to characterize and control high-dimensional fluid dynamic systems. This talk will also address key advances in the rapidly growing fields of machine learning and data science that are likely to drive future developments.

Non-modal linear stability analysis of thin film spreading by Marangoni stresses

NASA Astrophysics Data System (ADS)

Fischer, Benjamin John

The spontaneous spreading and stability characteristics of a thin Newtonian liquid film partially coated by an insoluble surfactant monolayer are investigated in this thesis. Thin films sheared by Marangoni stresses ire characterized by film thinning in the upstream region near the terminating edge of the initial monolayer and an advancing ridge further downstream. For sufficiently thin films, experiments have shown there develops dendritic fingering patterns upstream of the ridge. To probe the mechanisms responsible for unstable flow, a non-modal linear stability analysis is required because the base-states describing these flows are space and time-dependent. A new measure of disturbance amplification is introduced, based on the relative kinetic energy of the perturbations to the base-states, to analyze surfactant monolayers spreading either from a finite or infinite source. These studies reveal that disturbance amplification is most significant in highly curved regions of the film characterized by a large: change in the shear stress, which can develop at the advancing ridge and at the edge of the initial monolayer. For spreading from both a finite and infinite source, disturbances that convect through the ridge undergo transient amplification but eventually decay to restore film stability. By contrast, disturbances that localize to the thinned region undergo sustained amplification when surfactant is continuously supplied to the liquid film thereby promoting film instability. By focusing on these susceptible regions, the relevant evolution equations are simplified to extract more information about the mechanism leading to instability. The length-scale controlling these "inner" regions represents the balance of viscous, capillary and Marangoni stresses. Simplification of these equations allows identification of steady travelling wave solutions whose linearized stability behavior shows that a flat film subject to a jump increase in shear stress is asymptotically unstable. This thesis concludes by comparing recent experiments in our laboratory of a droplet of low surface tension liquid (oleic acid) spreading on a thin Newtonian film (glycerol) before the onset of instability with numerical simulations. Similar power law behavior for the ridge advance and qualitatively similar film profiles shapes occur when the simulations utilize a non-linear equation of state for the surfactant monolayer.

Graphite grain-size spectrum and molecules from core-collapse supernovae

NASA Astrophysics Data System (ADS)

Clayton, Donald D.; Meyer, Bradley S.

2018-01-01

Our goal is to compute the abundances of carbon atomic complexes that emerge from the C + O cores of core-collapse supernovae. We utilize our chemical reaction network in which every atomic step of growth employs a quantum-mechanically guided reaction rate. This tool follows step-by-step the growth of linear carbon chain molecules from C atoms in the oxygen-rich C + O cores. We postulate that once linear chain molecules reach a sufficiently large size, they isomerize to ringed molecules, which serve as seeds for graphite grain growth. We demonstrate our technique for merging the molecular reaction network with a parallel program that can follow 1017 steps of C addition onto the rare seed species. Due to radioactivity within the C + O core, abundant ambient oxygen is unable to convert C to CO, except to a limited degree that actually facilitates carbon molecular ejecta. But oxygen severely minimizes the linear-carbon-chain abundances. Despite the tiny abundances of these linear-carbon-chain molecules, they can give rise to a small abundance of ringed-carbon molecules that serve as the nucleations on which graphite grain growth builds. We expand the C + O-core gas adiabatically from 6000 K for 109 s when reactions have essentially stopped. These adiabatic tracks emulate the actual expansions of the supernova cores. Using a standard model of 1056 atoms of C + O core ejecta having O/C = 3, we calculate standard ejection yields of graphite grains of all sizes produced, of the CO molecular abundance, of the abundances of linear-carbon molecules, and of Buckminsterfullerene. None of these except CO was expected from the C + O cores just a few years past.