Diagonal Terms Research Articles

The effect of twisting motion dependent diagonal hopping on the I-V characteristics of poly(dG)-poly(dC) DNA molecule

The effect of twisting motion dependent diagonal hopping on the I-V characteristic of Poly(dG)-Poly(dC) DNA molecule has been studied. Twisting angle dependent hopping constant is model using semi-empirical Slater-Koster theory. The I-V characteristic of DNA molecule is calculated from transmission probability using Landauer-Buttiker formalism by assuming symmetric voltage drop at the contacts. The transmission probability of charge on the molecule is calculated using transfer and scattering matrix methods, simultaneously. The calculation is carried out on 32 base pairs doubled-stranded DNA molecule model sandwiched in between two metallic electrodes. The results show that at low voltage the magnitude of current is not influenced much by the change of diagonal hopping term caused by base pair twisting motion. Larger influenced is observed at higher voltages, after decreases by increasing the coupling parameter of vibration and diagonal hopping constant up to some value, current increases. This trend is observed in the I-V characteristic of DNA molecule for all frequencies and temperatures used. Lower twisting motion frequency shows larger influences of diagonal hopping term on the current than the one at higher frequencies.

Significance of non-classical damping in seismic qualification of equipment and piping

This paper presents a discussion on the significance of non-classical damping in coupled primary-secondary systems such as building-equipment or building-piping. Closed-form expressions are used to illustrate that the effect of non-classical damping is significant in systems with tuned or nearly tuned uncoupled modes when the mass-interaction is sufficiently small. Further, simple primary-secondary systems are used to illustrate that composite modal damping is another form of classical damping for which the transformed damping matrix, obtained after pre- and post-multiplication of the damping matrix with the modal matrix, contains only diagonal terms. Both the composite and the classical damping give almost identical results that can be much different from the corresponding results for non-classical damping. Finally, it is shown that consideration of classical damping (ignoring the off-diagonal terms) can give excessively conservative results in nearly tuned primary-secondary systems. For perfectly tuned primary-secondary systems, however, classical damping can give responses that are much lower than what they should be.

On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters-Part II: Observability/Estimability Analysis.

This paper presents the second part of a study aiming at the error state selection in Kalman filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). The observability properties of the system are systematically investigated, and the number of unobservable modes is established. Through the analytical manipulation of the full SINS error model, the unobservable modes of the system are determined, and the SSAC error states (except the velocity errors) are proven to be individually unobservable. The estimability of the system is determined through the examination of the major diagonal terms of the covariance matrix and their eigenvalues/eigenvectors. Filter order reduction based on observability analysis is shown to be inadequate, and several misconceptions regarding SSAC observability and estimability deficiencies are removed. As the main contributions of this paper, we demonstrate that, except for the position errors, all error states can be minimally estimated in the SSAC problem and, hence, should not be removed from the filter. Corroborating the conclusions of the first part of this study, a 12-state Kalman filter is found to be the optimal error state selection for SSAC purposes. Results from simulated and experimental tests support the outlined conclusions.

The impact of the diagonals of polynomial forms on limit theorems with long memory

We start with an i.i.d. sequence and consider the product of two polynomial-forms moving averages based on that sequence. The coefficients of the polynomial forms are asymptotically slowly decaying homogeneous functions so that these processes have long memory. The product of these two polynomial forms is a stationary nonlinear process. Our goal is to obtain limit theorems for the normalized sums of this product process in three cases: exclusion of the diagonal terms of the polynomial form, inclusion, or the mixed case (one polynomial form excludes the diagonals while the other one includes them). In any one of these cases, if the product has long memory, then the limits are given by Wiener chaos. But the limits in each of the cases are quite different. If the diagonals are excluded, then the limit is expressed as in the product formula of two Wiener–Itô integrals. When the diagonals are included, the limit stochastic integrals are typically due to a single factor of the product, namely the one with the strongest memory. In the mixed case, the limit stochastic integral is due to the polynomial form without the diagonals irrespective of the strength of the memory.

Expansion of the Decoupled Discreet-Time Jacobian Eigenvalue Approximation for Model-Free Analysis of PMU Data

This paper proposes an extension of the algorithm in [1], as well as utilization of the wavelet transform in event detection, including High Impedance Fault (HIF). Techniques to analyze the abundant data of PMUs quickly and effectively are paramount to increasing response time to events and unstable parameters. With the amount of data PMUs output, unstable parameters, tie line oscillations, and HIFs are often overlooked in the bulk of the data. This paper explores model-free techniques to attain stability information and determine events in real-time. When full system connectivity is unknown, many traditional methods requiring other bus measurements can be impossible or computationally extensive to apply. The traditional method of interest is analyzing the power flow Jacobian for singularities and system weak points, attained by applying singular value decomposition. This paper further develops upon the approach in [1] to expand the Discrete-Time Jacobian Eigenvalue Approximation (DDJEA), giving values to significant off-diagonal terms while establishing a generalized connectivity between correlated buses. Statistical linear models are applied over large data sets to prove significance to each term. Then the off diagonal terms are given time-varying weights to account for changes in topology or sensitivity to events using a reduced system model. The results of this novel method are compared to the present errors of the previous publication in order to quantify the degree of improvement that this novel method imposes. The effective bus eigenvalues are briefly compared to Prony analysis to check similarities. An additional application for biorthogonal wavelets is also introduced to detect event types, including the HIF, for PMU data.

A modified version of regularized meshless method for three dimensional potential problem

In this study, three-dimensional potential problem is solved using a novel meshless method. Due to the singularity of the kernel functions, the diagonal terms of the influence matrices in the method of fundamental solutions (MFS) are unobtainable. A proposed approach in the literature of the past decade, namely regularized meshless method (RMM), is proposed to overcome such difficulties by using the proposed desingularization (subtracting and adding-back) technique. The main difficulty for the coincidence of the source and collocation points then disappears. However, the disadvantage of RMM is the order of precision of obtained solution is lower than other numerical methods. In this study, we present a novel technique to promote the order of precision of diagonal term; therefore, we can obtain a more precise solution. Finally, we introduce a typical 3-D numerical example to illustrate the technique. The numerical result is compared with those obtained by the RMM; and a more precise result is obtained.

Anderson localization effect on Mott phase in 1T-TaS2

In the layered dichalcogenide 1T-TaS2, whether there is a disorder-driven transition from insulator to metal is still a matter in dispute. It is predicted that the commensurate charge density wave (CCDW) phase at low temperature behaves as a Mott insulator due to the strong correlation of electrons. Meanwhile, the stacking of TaS layers is found to be dislocated along the c axis, which will introduce considerable effect of disorder. Therefore, further theoretical study is needed to show the cooperative effect of correlation and disorder in 1T-TaS2. The statistical dynamical mean-field theory, which treats interactions and disorder on an equal footing, is used to study the effect of disorder on the Mott insulating phase in 1T-TaS2. Two different kinds of disorder effects are considered in the one-dimensional extended Anderson-Hubbard model, where the stacking dislocation of TaS layers is described by the off-diagonal hopping disorder and the diagonal disorder term represents the effect of disorder introduced by impurities. We find that the off-diagonal disorder by itself could not close the Mott gap at Fermi level, suggesting that Mott mechanism should be more dominant in the CCDW phase of 1T-TaS2 with the stacking dislocation of TaS layers. On the other hand, the diagonal disorder introduced by impurities will close the Mott gap when the strength of disorder (W) is larger than the correlation of electrons (U). Proved by the lattice-size scaling of the generalized inverse participation ratio, both the off-diagonal disorder and diagonal disorder can make all states Anderson-localized. As a result, there is no disorder-induced metal-insulator transition in a correlated system with either off-diagonal disorder or diagonal disorder. In addition, an anomalistic state is introduced by the off-diagonal disorder at the center of the energy band of the non-interacting system, which is a special Anderson-localized state with a very larger localization length. In the correlated cases, the electron-electron interactions have strong effect on splitting the anomalistic state into two individual states, which are located symmetrically in both the upper and lower Hubbard subbands with an energy interval U.

Non-diagonal multivariable fractional prefilter in motion control

A novel approach for robust Commande Robuste d'Ordre Non Entier (CRONE) control of multi input multi output (MIMO) systems using quantitative feedback theory (QFT) design is discussed through fractional prefilters with off-diagonal elements. More design flexibility is guaranteed when using the non-diagonal prefilter. For a given system, the CRONE control approach is combined with QFT design to get the controller matrix. After that, the classic diagonal fractional prefilter expression is extended to a fully populated prefilter matrix. The Davidson-Cole fractional prefilter optimisation is used to determine the diagonal terms of prefilter. The role of the off-diagonal elements of prefilter is to eliminate loop interactions in the case of reference tracking. So a sequential design procedure is proposed in order to get the fully populated prefilter matrix elements. The performance of the novel methodology is finally verified by adopting the designed prefilter and controller to govern the MIMO SCARA robot model.

Non-diagonal multivariable fractional prefilter in motion control

A novel approach for robust Commande Robuste d'Ordre Non Entier (CRONE) control of multi input multi output (MIMO) systems using quantitative feedback theory (QFT) design is discussed through fractional prefilters with off-diagonal elements. More design flexibility is guaranteed when using the non-diagonal prefilter. For a given system, the CRONE control approach is combined with QFT design to get the controller matrix. After that, the classic diagonal fractional prefilter expression is extended to a fully populated prefilter matrix. The Davidson-Cole fractional prefilter optimisation is used to determine the diagonal terms of prefilter. The role of the off-diagonal elements of prefilter is to eliminate loop interactions in the case of reference tracking. So a sequential design procedure is proposed in order to get the fully populated prefilter matrix elements. The performance of the novel methodology is finally verified by adopting the designed prefilter and controller to govern the MIMO SCARA robot model.

Open and ducted propeller virtual mass and damping coefficients by URANS-method in straight and oblique flow

The virtual mass and damping coefficients of an open and ducted propeller are determined using URANS computations. Time-accurate simulations are carried out for an open propeller forced to harmonic motion in two separate directions, translational x1- and rotational x4- directions. The analysis produces the diagonal coefficients of the virtual mass m11, m44 together with the diagonal damping terms c11, c44. The cross-terms m14, m41 and c14, c41 are also evaluated. A range of advance numbers is considered in the simulations. Several excitation frequencies and amplitudes are applied in order to determine the impact of viscosity on the vibrational coefficients. Oblique flow cases are also considered and the related virtual mass and damping coefficients are analyzed. The computed cases are compared to potential flow simulations and to published semi-empirical results. The average magnitudes of the coefficients correspond quite reasonably to those computed by the CFD method. However, the viscous effects are found to have a certain impact on some coefficients.

Algebraic diagonals and walks: Algorithms, bounds, complexity

The diagonal of a multivariate power series F is the univariate power series DiagF generated by the diagonal terms of F. Diagonals form an important class of power series; they occur frequently in number theory, theoretical physics and enumerative combinatorics. We study algorithmic questions related to diagonals in the case where F is the Taylor expansion of a bivariate rational function. It is classical that in this case DiagF is an algebraic function. We propose an algorithm that computes an annihilating polynomial for DiagF. We give a precise bound on the size of this polynomial and show that, generically, this polynomial is the minimal polynomial and that its size reaches the bound. The algorithm runs in time quasi-linear in this bound, which grows exponentially with the degree of the input rational function. We then address the related problem of enumerating directed lattice walks. The insight given by our study leads to a new method for expanding the generating power series of bridges, excursions and meanders. We show that their first N terms can be computed in quasi-linear complexity in N, without first computing a very large polynomial equation.

Three-state interactions determine the second-order nonlinear optical response

Using the sum-rules, the sum-over-states expression for the diagonal term of first hyperpolarizability can be expressed as the sum of three-state interaction terms. We study the behavior of a generic three-state term to show that is possible to tune the contribution of resonant terms by tuning the spectrum of the molecule. When extrapolated to the off-resonance regime, the three-state interaction terms are shown to behave in a similar manner as the three-level model used to derive the fundamental limits. We finally show that most results derived using the three-level ansatz are general, and apply to molecules where more than three levels contribute to the second-order nonlinear response or/and far from optimization.

Numerical homogenization of the Richards equation for unsaturated water flow through heterogeneous soils

AbstractHomogenized equations and the corresponding effective constitutive relations are generally necessary for numerically modeling large‐scale unsaturated flow processes in soils. Recently, based on the Kirchhoff transformation and the two‐scale convergence theory, a homogenization method for the Richards equation with the Mualem‐van Genuchten model has been proposed, with a constant model parameter α relating to the inverse of the air‐entry pressure and the soil pore size distribution. The homogenized model is computationally efficient and convenient to use because of its explicit expression. In this study, we generalize this method, allowing α to be a spatially distributed random field and proposing a homogenized Richards equation in the mixed form (θ/h) under the condition that the effective hydraulic conductivity tensor is diagonal. This generalization eliminates the limitation of a constant α in practical applications; the proposed homogenized model is meaningful in most situations because the flow problems are influenced mainly by the diagonal terms of conductivity and the off‐diagonal terms are often neglected. Two‐dimensional numerical tests are conducted in soil profiles with different degrees of spatial heterogeneity structure to illustrate that the homogenized model can capture the fine‐scale flow behaviors on coarse grids effectively. Homogenization for the Richards equation with other two commonly used constitutive relations—the Brooks‐Corey model and the Gardner‐Russo model—is also illustrated in this study.

이동하는 소음원 위치 추정을 위한 다양한 빔형성 기법 적용

Capabilities of several beamforming techniques are compared for estimating the position of a moving source. Beamforming has enabled to widen our perspective of aeroacoustics in wind tunnel experiments and has provided useful approach in array measurements. Meanwhile beamforming techniques have been developed in a way to improve estimation accuracy and to save ing effort at the same time. In order to achieve reasonable outcome from aeroacoustic measurement, it is important to identify the spectral characteristics of source and to select an appropriate beamformer. Though aeroacoustic sources normally generates broadband noises, many array signal processing have been focused on narrowband processing which makes calculation numerically efficient. However, calculation in frequency-domain requires selection of single frequency of interest which affects spatial resolution and sidelobe level as a consequence. To be able to localize broadband noise source, it is proposed to use broadband beamforming. The formulas implements the deletion of diagonal term from cross spectral matrix. In this study, trajectory of flying source emitting broadband noise was simulated and several beamformers are applied.

Locally standard torus actions and $h'$-numbers of simplicial posets

We consider the orbit type filtration on a manifold with a locally standard torus action and study the corresponding spectral sequence in homology. When all proper faces of the orbit space are acyclic and the free part of the action is trivial, this spectral sequence can be described in full. The ranks of diagonal terms of its second page are equal to $h'$-numbers of a simplicial poset dual to the orbit space. Betti numbers of a manifold with a locally standard torus action are computed: they depend on the combinatorics and topology of the orbit space but not on the characteristic function. A toric space whose orbit space is the cone over a Buchsbaum simplicial poset is studied by the same homological method. In this case the ranks of the diagonal terms of the spectral sequence at infinity are the $h''$-numbers of the simplicial poset. This fact provides a topological evidence for the nonnegativity of $h''$-numbers of Buchsbaum simplicial posets and links toric topology to some recent developments in enumerative combinatorics.

Comparison of drift force calculation methods in time domain analysis of moored bodies

This paper compares five numerical methods for calculating drift forces in time domain analysis of moored bodies. The first method is the most basic one. It uses all terms of QTF (quadratic transfer function) matrix based on double summation. It is the most correct due to no approximation but needs large memory and cpu time. The second method uses diagonal terms of QTF matrix with Newman approximation. It reduces memory but still uses double summation. When the wave spectrum is narrow banded, the third and fourth methods with more approximated single summation are applicable. Those methods are much approximated but fast due to single summation. One uses fixed local frequency and the other uses time variant local frequency in calculating QTF. The fifth method uses interpolated local frequency of the third and fourth methods. A turret moored FPSO and a spread moored DTV (deck transportation vessel) are analyzed as numerical examples and the accuracy and cpu time are compared for each method.

Decoherence effects in the Stern-Gerlach experiment using matrix Wigner functions

We analyze the Stern-Gerlach experiment in phase space with the help of the matrix Wigner function, which includes the spin degree of freedom. Such analysis allows for an intuitive visualization of the quantum dynamics of the apparatus. We include the interaction with the environment, as described by the Caldeira-Leggett model. The diagonal terms of the matrix provide us with information about the two components of the state, that arise from interaction with the magnetic field gradient. In particular, from the marginals of these components, we obtain an analytical formula for the position and momentum probability distributions in presence of decoherence, that show a diffusive behavior for large values of the decoherence parameter. These features limit the dynamics of the present model. We also observe the decay of the non-diagonal terms with time, and use this fact to quantify the amount of decoherence, from the norm of those terms in phase space. From here, we can define a decoherence time scale, which differs from previous results that make use of the same model.

INFLUENCE OF COMPACTION CONDITION ON THE MICROSTRUCTURE OF A NON-PLASTIC GLACIAL TILL

Optimum design of structures is achieved while the design variables are continuous and discrete. To reduce the computational work involved in the optimization process, all the functions that are expensive to evaluate, are approximated. To approximate these functions, a semi quadratic function is employed. Only the diagonal terms of the Hessian matrix are used and these elements are estimated from the first derivatives that are available from the previous iterations. The second order approximation is obtained for both direct and reciprocal approximations. In addition, a hybrid form of the approximation is introduced. With the help of this approximation, the continuous optimization is obtained. The results are used as the starting point for the discrete optimization. A new penalty function is introduced for discrete optimum design and the discrete variables are obtained in conjunction with the same function approximation. Examples are given and the numerical results are discussed.

Calculation of HVAC inductive coupling using a generalized BEM for Helmholtz equations in unbounded regions

We propose an innovative boundary element method (BEM) finite element method (FEM) model for the calculation of induced voltages on a buried pipeline in close proximity of a high voltage power line.When dealing with unbounded conductive media the BEM requires a specific solving method. The geometry dependent coefficient ci in the general expression is calculated in an indirect way through defining a sphere encompassing the examined domain and extending its radius to infinity. This method is repeatedly discussed by many authors and for the Laplace equations it results into adding −1 to the diagonal terms in the H-matrix. However, calculations show that applying the same technique for a Helmholtz equation leads to a mathematical contradiction.Therefore an innovative method is proposed, based on the skin depth. The radius of the sphere enclosing the domain should not extend to infinity but to a number of times the skin depth. This is for numerical reasons. Hence, a new expression is derived for calculating the factor ci.The simulation results using the BEM–FEM model are compared with the transmission line model (TLM) and a perfect agreement between the two methods is obtained.

Measurement of two-particle pseudorapidity correlations in Pb + Pb collisions at [formula omitted] with the ATLAS detector

Two-particle pseudorapidity correlations, measured using charged particles with pT>0.5 GeV and |η|<2.4, from sNN=2.76 TeV Pb+Pb collisions collected in 2010 by the ATLAS experiment at the LHC are presented. The correlation function CN(η1,η2) is measured for different centrality intervals as a function of the pseudorapidity of the two particles, η1 and η2. The correlation function shows an enhancement along η−≡η1−η2≈0 and a suppression at large η− values. The correlation function also shows a quadratic dependence along the η+≡η1+η2 direction. These structures are consistent with a strong forward-backward asymmetry of the particle multiplicity that fluctuates event to event. The correlation function is expanded in an orthonormal basis of Legendre polynomials, Tn(η1)Tm(η2), and corresponding coefficients an,m are measured. These coefficients are related to mean-square values of the Legendre coefficients, an, of the single particle longitudinal multiplicity fluctuations: an,m=〈anam〉. Significant values are observed for the diagonal terms 〈an2〉 and mixed terms 〈anan+2〉. Magnitude of 〈a12〉 is the largest and the higher order terms decrease quickly with increase in n. The centrality dependence of the leading coefficient 〈a12〉 is compared to that of the mean-square value of the asymmetry of the number of participating nucleons between the two colliding nuclei, and also to the 〈a12〉 calculated from HIJING.