Narrow Results

In this study, a spectral analysis method is proposed for a sagged cable with an optimal viscous inertial mass damper (VIMD) under random wind loads based on a generalized state-space formulation. The frequency response functions of the cable responses were evaluated for the wind force vector using complex modes orthogonal to the system matrices, from which the power spectral densities of the cable responses were readily obtained for the spectral matrix of the wind force. The accuracy and efficiency of the proposed method were verified by comparing the root mean square responses with those obtained from the time-domain and covariance analyses. The performance of two VIMDs optimized by the fixed-point method and the maximum damping ratio method was investigated for various cases of cable sag and wind properties. Serviceability failure probability analysis was also conducted using the first-passage problem. The results show that the proposed spectral method is computationally more efficient than the other two analysis methods. The VIMDs optimized for the first original cable mode were found to be highly effective in reducing cable vibration and the probability of serviceability failure.

In this paper, we consider Stark operators perturbed by some bounded potentials. We prove that these operators are purely absolutely continuous (A-C) on some Borel subset S of R. We apply these results when the perturbation is piecewise smooth, in this case we show that the A-C spectrum is the whole real line.

We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both short-range and long-range behaviors of the metric and the perturbation at infinity. For the scattering theory, the existence and asymptotic completeness of the wave operators is proved in a two-Hilbert spaces setting. A stationary formula as well as mapping properties for the scattering operator are derived. The existence of time delay and its equality with the Eisenbud–Wigner time delay is finally presented. Our analysis mainly differs from the existing literature on the choice of a simpler comparison dynamics as well as on the complementary use of time-dependent and stationary scattering theories.

In a semi-classical regime, we study a periodic magnetic Schrödinger operator in ℝ². This is inspired by recent experiments on artificial magnetism with ultra cold atoms in optical lattices, and by the new interest for the operator on the hexagonal lattice describing the behavior of an electron in a graphene sheet. We first review some results for the square (Harper), triangular and hexagonal lattices. Then, we study the case when the periodicity is given by the kagome lattice considered by Hou. Following the techniques introduced by Helffer–Sjöstrand and Carlsson, we reduce this problem to the study of a discrete operator on ℓ²(ℤ²;ℂ³) and a pseudo-differential operator on L²(ℝ;ℂ³), which keep the symmetries of the kagome lattice. We estimate the coefficients of these operators in the case of a weak constant magnetic field. Plotting the spectrum for rational values of the magnetic flux divided by 2πh where h is the semi-classical parameter, we obtain a picture similar to Hofstadter's butterfly. We study the properties of this picture and prove the symmetries of the spectrum and the existence of flat bands, which do not occur in the case of the three previous models.

The electron method spectroscopy consists in the detection of very low energy electrons formed in electron–molecule collisions. The advantage of this method over the method of optical spectroscopy lies in the possibility to study optically forbidden states, so the complexity of spectrum rises steeply, which makes its analysis more difficult. Besides electron states, there are also a vibrational states in threshold spectra analysis, and those had to be identified and classified. This paper presents an expert system developed to automate, speed up and improve the N₂ threshold spectra analysis.

In this paper an expert system is presented that was developed with the aim to analyze electron spectra on the threshold energies in collision with triatomic and polyatomic molecules. This expert system was made by updating the expert system for the analysis of the threshold spectra of two-atomic molecules. In contrast to the threshold spectra of two-atomic molecules, where were exist more or less defined structures of excited states, as well as vibrational levels, in the threshold spectra of triatomic molecules clearly defined structures almost do not exist. The application of the expert system in the process of triatomic and polyatomic molecules spectra analysis has an important role because it enables analysis of larger number of excited states, vibrational levels, and resonances, which can be missed in the analysis by classical methods, either because of low intensity or because of insufficiently defined separation of peaks in spectrum, which arise from the overlapping of a large number of peaks.

We report the spectral analysis of current-noise data obtained under voltage clamp condition in bilayer lipid membrane, using Lomb Scargle Periodogram. Such spectral analysis shows evidence of crossover from an uncorrelated phenomenon towards a state of long range correlation in time and space with the increase of applied bias. Based on these observations a probable mechanism of transmembrane charge conduction has been outlined in the light of self-organized criticality.

Cosmic muon flux is recorded by two plastic scintillator detectors: one located at ground level and the other located in the Belgrade underground laboratory (25 m w.e.). Power spectral analysis of the raw detector data for the period from January 1^st 2002 to December 31^st 2002 is performed. Similar periodicities are found in both data sets (ground and underground), but with different amplitudes. Main periodicity in the underground detector data has a 26.5 days period, while the highest amplitude signal in the ground detector data has a 243 ± 45 days period. Other signals present in the time series correspond to higher harmonics of the solar rotation period. There is also a wave with a 34.4 days period, whose significance is confirmed by different methods of spectral analysis. The same periodicity is recently found in some processes on the Sun.

We show numerically that the orthogonal transformation corresponding to the eigenvectors of (random) left circulant matrices, has similar performance in signal/image processing like the discrete cosine transform.

The classification of life should be based on the intrinsic mechanism in the evolution of life. We found new methods to classify life into Archaea, Bacteria and Eucarya based on the correlation analysis and spectral analysis of protein length distributions. We show that there is rich evolutionary information stored in the fluctuations of protein length distributions. The intrinsic mechanism of diversification of life is revealed by the properties of protein length distributions.

The integrable Lakshmanan–Porsezian–Daniel (LPD) equation originating in nonlinear fiber is studied in this work via the Riemann–Hilbert (RH) approach. First, we give the spectral analysis of the Lax pair, from which an RH problem is formulated. Afterwards, by solving the special RH problem with reflectionless under the conditions of irregularity, the formula of general $N$-soliton solutions can be obtained. In addition, the localized structures and dynamic behaviors of the breathers and solitons corresponding to the real part, imaginary part and modulus of the resulting solution $r(x,t)$ are shown graphically and discussed in detail. Unlike 1- or 2-order breathers and solitons, 3-order breathers and soliton solutions rapidly collapse when they interact with each other. This phenomenon results in unbounded amplitudes which imply that higher-order solitons are not a simple nonlinear superposition of basic soliton solutions.

In remote sensing image classification, distance measurements and classification criteria are equally important; and less accuracy of either would affect classification accuracy. Remote sensing image classification was performed by combining support vector machine (SVM) and $k$-nearest neighbor (KNN). This was based on the separability of classes using SVM and the spatial and spectral characteristics of remote sensing data. Moreover, a distance formula is proposed as the measure criterion that considers both luminance and direction of the vectors. First, the SVM is trained and the support vectors (SVs) are obtained for each class. In the testing phase, newly tested samples were entered, and average distance between the test samples and SVs for each class are calculated using the distance formula. Finally, decisions are made to classify the test samples into the class with minimal average distance. This procedure is repeated until all test samples are classified. In the combinatorial algorithm, the nearest neighbor classifier is used to classify a testing sample, i.e. the average Euclidean distance between the testing data point to each set of SVs from different categories is calculated and the nearest neighbor classifier identifies the category with minimum distance. The proposed combinatorial algorithm has advantages over the conventional KNN for eliminating the $k$ parameter selection problem and reducing heavy learning time. A comparison is carried out with SVM, KNN and Spectral Angle Mapper (SAM) classification using ALOS/PALSAR and PSM images, and the effectiveness of the proposed algorithm is demonstrated.

Motivated by the growing popularity of time-variant evolutionary algorithms (EAs) in solving practical problems, this paper uses spectral analyses to study convergence in probability for a general class of time-variant EAs which can be asymptotically described by reducible Markov chains with multiple aperiodic recurrent classes, covering many existing concrete case studies as specific instantiations. We provide a universal yet easily checkable characteristic for time-variant EAs satisfying global convergence, by introducing the asymptotical elitism and asymptotical monotonicity. To illustrate the effectiveness of our result, we consider four specific EAs with distinct asymptotical behavior, and recover, under even mild conditions, the state-of-the-art result as simple applications of our general theorem. Besides, simulation experiments further verify these results.

This paper considers higher-dimensional generalizations of the classical one-dimensional two-automatic Thue–Morse sequence on ℕ. This is done by taking the same automaton-structure as in the one-dimensional case, but using binary number systems in ℤ^m instead of in ℕ. It is shown that the corresponding ±1-valued Thue–Morse sequences are either periodic or have a singular continuous spectrum, dependent on the binary number system. Specific results are given for dimensions up to six, with extensive illustrations for the one-, two- and three-dimensional case.

Diabetic neuropathy may be a result of disturbed vasomotion, the spontaneous rhythmic oscillations of vessel diameter, flow, or pressure in the microcirculation. To examine the differences in vasomotion prior to overt diabetes and with diagnosed diabetes, metabolic and blood flow measurements were obtained from three metabolically distinct groups of nonhuman primates: normoglycemic, metabolic syndrome/prediabetic, and overtly diabetic. Three of these indices characterize spectral properties of microcirculatory vasomotion: (1) the fraction of spectral power in a band around 2.0 Hz, (2) the ratio of spectral power in a band around 1.0 Hz to that around 2.0 Hz, (3) the Hurst exponent. The rest were more traditional measures including (4) fasting plasma Glucose (FPG), (5) glycosylated hemoglobin level (HbA1c), (6) fasting insulin levels (IRI), (7) average systolic blood pressure, and (8) average diastolic blood pressure.

We found that the mean fraction of the spectral power of the vasomotion in the 2 Hz band is significantly greater in the nondiabetic than in the diabetic group. Similarly, the ratio of the spectral power in the 1.0 Hz band to that in the 2.0 Hz band was significantly higher among the diabetic subjects than in the nondiabetic and prediabetic subjects.

Principal component analysis (PCA) of the ensemble of eight measures revealed that values of the first principal component in the diabetic group were highly and significantly different from those of the normal and prediabetic groups, which are also significantly different from each other. Furthermore, the spectral measures of vasomotion offered a distinct advantage over the traditional physiological variables in distinguishing the normal subjects from the prediabetic group, and are likely to reflect very early autonomic dysfunction.

We study elementary cellular automata with memory. The memory is a weighted function averaged over cell states in a time interval, with a varying factor which determines how strongly a cell's previous states contribute to the cell's present state. We classify selected cell-state transition functions based on Lempel–Ziv compressibility of space-time automaton configurations generated by these functions and the spectral analysis of their transitory behavior. We focus on rules 18, 22, and 54 because they exhibit the most intriguing behavior, including computational universality. We show that a complex behavior is observed near the nonmonotonous transition to null behavior (rules 18 and 54) or during the monotonic transition from chaotic to periodic behavior (rule 22).

We consider the evolution problem for the wave equation with nonlinear boundary conditions, modeling the anti-plane shearing on a system of finite faults under a slip-dependent friction in a linear elastic continuum. The associated eigenvalue problem is studied for bounded and unbounded domains. Recent studies showed that this eigenvalue problem plays a key role in earthquake nucleation modeling. We investigate the structure of the positive eigenvalues set and prove the monotone dependence of the first eigenvalue on the friction parameter. For the elastic plane with a collinear system of faults, the eigenvalue problem is reduced to a hyper-singular integral equation. This equation is solved through a semi-analytical technique. Numerical results show a sensible dependence of the first eigenfunction on the geometry and friction heterogeneity.

We consider the vibrations of a membrane that contains a very thin and heavy inclusion around a curve γ. We assume that the membrane occupies a domain Ω of ℝ². The inclusion occupies a layer-like domain ω_ε of width 2ε and it has a density of order O(ε^-m). The density is of order O(1) outside this inclusion ω_ε, the concentrated mass around the curve γ. ε and m are positive parameters, ε∈(0,1) and m>2. We set m=3 and show that low, middle and high frequency vibrations are necessary in order to describe the asymptotic behavior of the vibrations of the whole membrane. We study the asymptotic behavior, as ε→0, of these frequencies and of the corresponding eigenfunctions.

The Self-Organized Hydrodynamics model of collective behavior is studied on an annular domain. A modal analysis of the linearized model around a perfectly polarized steady-state is conducted. It shows that the model has only pure imaginary modes in countable number and is hence stable. Numerical computations of the low-order modes are provided. The fully nonlinear model is numerically solved and nonlinear mode-coupling is then analyzed. Finally, the efficiency of the modal decomposition to analyze the complex features of the nonlinear model is demonstrated.

In this paper, we use spectral methods to introduce Bloch waves for studying the homogenization process in the non-periodic class of generalized Hashin–Shtrikman micro-structures (see Ref. 35), which incorporates both translation and dilation with a family of scales, including one subclass of laminates. We establish the classical homogenization result by providing the spectral representation of the homogenized coefficients. It offers a new lead towards extending the Bloch spectral analysis to general micro-structures, including the class of non-periodic media or the homogenization of Heisenberg operators (see Refs. 8 and 9).