Chain-like Systems Research Articles

An experimental investigation of change detection in uncertain chain-like systems

Promising ongoing research on “smart” sensing technologies is offering low-cost alternatives and new opportunities for large-scale SHM. Networks of sensors with wireless communication and computational capabilities can be used to increase the spatial resolution of data collection while providing a distributed computing framework for implementing structural health monitoring algorithms. Robust and practical SHM methodologies being able to rapidly and accurately detect and assess changes in the monitored system are required to be at the core of these “smart” structures. A data-driven non-parametric identification technique is used to implement a robust change detection methodology for uncertain MDOF chain-like systems that can be implemented in densely distributed smart-sensor networks. Experimental data from a test-bed structure tested at Los Alamos National Laboratory are used to evaluate the effectiveness and reliability of the proposed SHM methodology. The results of this study showed that the proposed approach was able, in a rigorous statistical framework, to confidently detect the presence of structural changes, accurately locate the structural section where the change occurred, and provide an accurate estimate of the actual level of “change”. Additionally, a full-order finite element model of the test structure, as well as the results from the experimental modal identification using the ERA algorithm were employed to validate the results obtained in this change-detection study.

A novel approach for the structural identification and monitoring of a full-scale 17-storybuilding based on ambient vibration measurements

For reliable and practical application of structural health monitoring approaches inconjunction with dense sensor arrays deployed on ‘smart’ systems, there is a need todevelop and evaluate alternate strategies for efficient problem decomposition to rapidlyand accurately determine the occurrence, location and level of small changesin the underlying structural characteristics of a monitored system based on itsvibrational signature. Furthermore, there is also a need to quantify the level ofuncertainties in the identified system characteristics so as to have a measurablelevel of confidence in the parameters to be relied on for the detection of genuinechanges (damage) in the monitored system. This study presents the results of twotime-domain identification techniques applied to a full-scale 17-story building, based onambient vibration measurements. The Factor building is a steel frame structurelocated on the UCLA campus. This building was instrumented permanently with adense array of 72-channel accelerometers, and the acceleration data are beingcontinuously recorded. The first identification method used in this study is theNExT/ERA, which is regarded as a global (or centralized) approach, since it dealswith the global dynamic properties of the structure. The second method is atime-domain identification technique for chain-like MDOF systems. Since in thismethod the identification of each link of the chain is performed independently,it is regarded as a local (or decentralized) identification methodology. For thesame reason, this method can be easily adopted for large-scale sensor networkarchitectures in which the centralized approaches are not feasible due to massivestorage, power, bandwidth and computational requirements. To have a statisticallymeaningful results, 50 days of recorded data are considered in this study. Themodal parameter and chain identification procedures are performed over timewindows of 2 h each and with 50% overlap. Using the NExT/ERA method, 12dominant modes of the building were identified. It was observed that variations in thefrequency estimation are relatively small; the coefficient of variation is about 1–2%for most of the estimated modal frequencies. Chain system identification wassuccessfully implemented using the output-only data acquired from the Factorbuilding. Probability distributions of the estimated coefficients of displacement andvelocity terms in the interstory restoring functions (which are the mass-normalizedlocal stiffness and damping values) that were found based on the chain systemidentification are presented. The variability of the estimated parameters due totemperature fluctuations is investigated. It is shown that there is a strong correlationbetween the modal frequency variations and the temperature variations in a 24 hperiod.

Theory of phase equilibria for model mixtures of n-alkanes, perfluoroalkanes and perfluoroalkylalkane diblock surfactants

An extension of the SAFT-VR equation of state, the so-called hetero-SAFT approach [Y. Peng, H. Zhao, and C. McCabe, Molec. Phys. 104, 571 (2006)], is used to examine the phase equilibria exhibited by a number of model binary mixtures of n-alkanes, perfluoroalkanes and perfluoroalkylalkane diblock surfactants. Despite the increasing recent interest in semifluorinated alkanes (or perfluoroalkylalkane diblock molecules), the phase behaviour of mixtures involving these molecules with n-alkanes or perfluoroalkanes is practically unknown from the experimental point of view. In this work, we use simple molecular models for n-alkanes, perfluoroalkanes and perfluoroalkylalkane diblock molecules to predict, from a molecular perspective, the phase behaviour of selected model mixtures of perfluoroalkylalkanes with n-alkanes and perfluoroalkanes. In particular, we focus our interest on the understanding of the microscopic conditions that control the liquid–liquid separation and the stabilization of these mixtures. n-Alkanes and perfluoroalkanes are modelled as tangentially bonded monomer segments with molecular parameters taken from the literature. The perfluoroalkylalkane diblock molecules are modelled as heterosegmented diblock chains, with parameters for the alkyl and perfluoroalkyl segments developed in earlier work. This simple approach, which was proposed in previous work [P. Morgado, H. Zhao, F. J. Blas, C. McCabe, L. P. N. Rebelo, and E. J. M. Filipe, J. Phys. Chem. B, 111, 2856], is now extended to describe model n-alkane (or perfluoroalkane) + perfluroalkylalkane binary mixtures. We have obtained the phase behaviour of different mixtures and studied the effect of the molecular weight of n-alkanes and perfluoroalkanes on the type of phase behaviour observed in these mixtures. We have also analysed the effect of the number of alkyl and perfluoroalkyl chemical groups in the surfactant molecule on the phase behaviour. In addition to the usual vapour–liquid phase separation, liquid–liquid, positive azeotropes, and Bancroft points are found for different mixtures. This rich phase behaviour is a consequence of a delicate balance between the alkyl–alkyl, perfluoroalkyl–perfluoroalkyl, and alkyl–perfluoroalkyl interactions in different molecules. We used the SAFT-VR microscopic description of chain-like systems to analyse the conditions that n-alkane (or perfluoroalkane) + perfluoroalkyalkane mixtures should posses in order to exhibit complete liquid miscibility. Although the model proposed here is chosen to reproduce most of the quantitative features of the phase equilibria of some pure perfluoroalkylalkane diblock surfactants and their mixtures with n-alkanes, this is the first time the SAFT approach has been used to predict the phase behaviour of the mixtures considered here. The lack of experimental data for these systems does not allow us to test the accuracy of our theoretical predictions directly. However, since SAFT has proven to be an excellent approach for the prediction of the phase behaviour of complex mixtures, we expect that the theory will reproduce the most important qualitative trends exhibited by real mixtures.

Electronic and optical properties of functionalized carbon chains with the localized Hartree–Fock and conventional Kohn–Sham methods

Abstract The electronic and optical properties of extended functionalized carbyne chains, polyynes and cumulenes, are investigated with the localized Hartree–Fock method, with conventional Kohn–Sham methods, and with the Hartree–Fock method. It is found that even for very long polyynes the carbon–carbon bond lengths within a polyyne alternate while for long cumulenes no carbon–carbon bond length alternation occurs. Polyynes exhibit a finite HOMO–LUMO gap even if they become very long while cumulenes are found to become metallic in the limit of long chain lengths. The geometry and the electro-optical properties of polyynes cannot be influenced significantly by simple sp-σ-bonded end groups. The optically active 1 Σ u + ←X 1 Σ g + electronic transition in polyynes is investigated by time-dependent density-functional theory (TDDFT). The known systematic underestimation of excitation energies in large chain-like systems by TDDFT methods is also found for the systems considered here. Deficiencies in the commonly used exchange-correlation kernels are identified as the main source of this shortcoming of TDDFT methods. Unphysical Coulomb self-interactions present in conventional Kohn–Sham potentials seem to not contribute significantly to the problem.

Fluid solid equilibrium for two dimensional tangent hard disk chains from Wertheim’s perturbation theory

Wertheim’s first order thermodynamic perturbation theory [M. S. Wertheim, J. Chem. Phys. 87, 7323 (1987)] has been extended to the two-dimensional tangent hard disk dimer for both the solid and the fluid phases. This extension utilizes pre-existing equations of state for the fluid [C. F. Tejero and J. A. Cuesta, Phys. Rev. E 47, 490 (1993)] and for the solid phases [B. J. Alder, W. G. Hoover, and D. A. Young, J. Chem. Phys. 49, 3688 (1968)], of the two-dimensional hard disk monomer system. The theory has been compared to simulation results and a good agreement has been found between them. Results are also presented for the fluid–solid tie line for m=2 up to m=30. The results of this work may be of interest to those involved in the study of chainlike systems adsorbed on a two-dimensional surface.

Scheduling tree-like task systems with non-uniform deadlines subject to unit-length communication delays

We consider the problem of scheduling outforests and inforests with non-uniform deadlines subject to unit-length communication delays. We will prove that minimum-tardiness schedules for outforests on two processors and for chain-like task systems on m processors can be constructed in polynomial time. In addition, we present two polynomial-time approximation algorithms: one with an asymptotic approximation bound of 2−2/ m for scheduling outforests with non-positive deadlines on m processors and one with an asymptotic approximation bound of 2 for scheduling inforests with non-positive deadlines on m processors. Moreover, it is proved that for a special class of inforests, minimum-tardiness schedules on m processors can be constructed in polynomial time.

Molecular thermodynamics for chain-like molecule systems

Recent progress of molecular thermodynamics for chain-like molecule systems in China mainly at East China University of Science and Technology (ECUST) and at Beijing University of Chemical Technology (BUCT) is presented. Molecular simulation results of phase equilibria for chains on both lattice and free space by a configurational-bias vaporization method are summarized. Molecular thermodynamic models based on both cell and lattice approaches and corresponding group-contribution methods are developed that can be successfully used to describe phase behavior. Using cavity correlation function (CCF), an equation of state for chain-like molecule systems is derived that contains three contributions: a hard-sphere-chain reference, a square-well perturbation term and an association term. Numerous illustration examples for practical VLE and LLE calculations are shown. Extension to polyelectrolytes is also presented that shows good results for osmotic pressures in comparison with experimental results.

Fourier space for accurate ab initio RHF band structure calculations on chainlike systems

Fourier space for accurate ab initio RHF band structure calculations on chainlike systems

Fourier space for accurate ab initio RHF band structure calculations on chainlike systems

mMinimal basis-set (STO-3G) direct and Fourier space restricted Hartree-Fock (RHF) calculations on the infinite regular (metallic) and alternating chains of lithium molecules, (-Li2-)x, are reported to illustrate two advantages of the Fourier representation method: accurate calculation of all lattice summations and faithful reproduction of the genuine features of the RHF approach for metallic cases. 0 1996 John Wiley & Sons, Inc.

On the direct energy transfer from donors to acceptors in chainlike polymer systems

In this work we study the direct, incoherent energy transfer from excited donors to acceptors, which are attached to chainlike polymers. We consider both multipolar and exchange-type interactions between the donors and the acceptors. The polymers are modeled through random walks (Gaussian or self-avoiding, depending on the solvent). With the use of the end-to-end distribution function of the walks, we calculate the time dependence of the ensemble averaged decay of the excitation of the donor. For multipolar and exchange-type interactions, we find Kohlrausch–Williams–Watts (KWW) stretched exponential and exponential–logarithmic decay patterns, respectively. The decay forms reflect the quality (good or poor) of the solvent directly and they may be used to test transitions in the polymer conformation.

Exact Solution of Ground State for Uniformly Distributed RVB in One-Dimensional Spin-1/2 Heisenberg Systems with Frustration

The properties of the ground state in chain-like systems, including the competition between ferromagnetic and antiferromagnetic exchange interactions, are discussed. It is, in particular, pointed out that the characteristic singlet state expressed by the combinations of RVB distributed uniformly to spin lattice points is given as the exact solution on some condition of the competition. Besides analytical discussion, the numerical calculation for the spin number N ≦16 is also made so as to make clear the behavior of a multiple degeneracy for the ground state and of low-lying excitation levels.

Convergence of direct space exchange lattice sums in polymer band structure calculations

A study of the convergence properties associated with direct lattice summations of the exchange contributions to the quantities needed in a restricted Hartree–Fock calculation for a polymer, leads to a detailed analysis of the analytic and asymptotic properties of the Fock–Dirac density matrix in the LCAO representation. The results, obtained simply by means of Fourier analysis, provide an important characterization of the restricted Hartree–Fock method as applied to chain-like systems. As a by-product we obtain a general proof in direct space that a partially filled band, which influences drastically the analyticity properties of the density matrix in reciprocal space, leads to a logarithmically diverging derivative of the orbital energy at the Fermi level. This in turn gives a vanishing density of states at that level. This result, well known for the electron gas model, is thus an inherent property of the restricted Hartree–Fock approximation.

Erratum: Soluble models of rate processes in periodic systems with many degrees of freedom

We show that the parameters of classical many-body rate theory can be evaluated exactly for activated processes in large, chainlike systems. The methods are applied to four simple systems which simulate, in some degree, activated atomic motions in crystals. Each is a linear chain of atoms interacting with near-neighbor forces. One represents evaporation of an adatom from a surface, one an interstitialcy migration, one a vacancy migration, and one the motion of the interface between two phases. Exact analytical calculation of the parameters of many-body rate theory, namely the activation energy and the effective, or attack, frequency are given for each model. The results illustrate the role of cooperative effects in atomic jumps. The commonly made assumption that the attack frequency for such jumps is the characteristic lattice-vibration frequency is shown to be valid in some conditions, but to be a very poor approximation in others. For the evaporating adatom the relative mass of the adatom is allowed to be arbitrary. It is found that the transition rate is proportional to the square root of the relative mass for very light atoms, but otherwise the relative mass enters in a more complicated way, and, in particular, the transition rate remainsmore » finite for an adatom of infinite mass.« less

Soluble models of rate processes in periodic systems with many degrees of freedom.

We show that the parameters of classical many-body rate theory can be evaluated exactly for activated processes in large, chainlike systems. The methods are applied to four simple systems which simulate, in some degree, activated atomic motions in crystals. Each is a linear chain of atoms interacting with near-neighbor forces. One represents evaporation of an adatom from a surface, one an interstitialcy migration, one a vacancy migration, and one the motion of the interface between two phases. Exact analytical calculation of the parameters of many-body rate theory, namely the activation energy and the effective, or attack, frequency are given for each model. The results illustrate the role of cooperative effects in atomic jumps. The commonly made assumption that the attack frequency for such jumps is the characteristic lattice-vibration frequency is shown to be valid in some conditions, but to be a very poor approximation in others. For the evaporating adatom the relative mass of the adatom is allowed to be arbitrary. It is found that the transition rate is proportional to the square root of the relative mass for very light atoms, but otherwise the relative mass enters in a more complicated way, and, in particular, the transition rate remainsmore » finite for an adatom of infinite mass.« less

Possible band-structure shapes of quasi-one-dimensional solids

The well-known restrictions on the possible shapes of electron energy bands arising from one-dimensional (1D) periodic potentials do not apply to chainlike physical systems such as polymers or molecular stacks, which are three dimensional objects periodic along a line. For such quasi-one-dimensional (Q1D) crystals, bands can be nondegenerate, but they may also contact one another at the center and/or at the boundaries of the Brillouin zone (BZ), cross at a general $k$ point, or be degenerate throughout the BZ, so that a variety of topologically inequivalent shapes can be formed. These shapes are essentially determined by the spatial symmetry of the Q1D object considered, i.e., by its line group. A complete classification has been worked out, and for every possible Q1D crystal structure the corresponding band shapes are specified. The method focuses on the quantum numbers having clear physical meaning (quasimomentum, quasi angular momentum, etc.); elaborate group-theoretical parlance is avoided. Furthermore, it is studied how this complexity of band shapes which may occur in Q1D crystals affects some predicted physical properties---optical-absorption spectra and vibronic coupling, in particular. First, each singularity of the density-of-states function bears definite symmetry labels, and many direct interband transitions in polymers are forbidden by the line-group selection rules. Next, in the case of electronic degeneracy, many different types of vibronic instabilities are possible. Depending on the line group, the band shapes, and the quantum numbers of the electronic states involved, the active phonons may be longitudinal or transversal, acoustic or optical, single or degenerate, displacive or distortive, etc.; also, various types of symmetry breaking can occur. Finally, applicability to other quasi particles (phonons, etc.) and to solids of higher dimensionality is pointed out.

Evaluation of computational aspects of a modified CS-LCAO-SCF-CO strategy for electronic structure calculations of extended model chains

An analysis is made of the mathematical and computational implications of a recently proposed scheme to calculate the electronic structure of chainlike systems without explicit use of the LCAO density matrix elements. The infinite chain of hydrogen atoms is chosen as a simple test case illustrating the underlying difficulties associated with the scheme. It turns out that the positive features that have motivated the development of this approach do not balance the numerical difficulties. It seems unlikely that, in routine applications, the new strategy will become a real competitor to the existing programs.

An Exact Condensation Procedure for Chain-Like Structures Using a Finite Element-Transfer Matrix Approach

The main objective of this study is to describe a new scheme to carry out the static or dynamic analysis of elastic systems using a combined Finite Element-Transfer Matrix Approach. The proposed scheme offers the advantage of automatic matrix size reduction without having to truncate degrees of freedom, and preserving the strain and kinetic energy throughout the condensation. Although limited to chain-like elastic systems, the method is generalized to non-repetitive configurations with substructures having intermediate active degrees of freedom.