Search results for "PEAK"

Analytic solutions and Singularity formation for the Peakon b--Family equations

2012

This paper deals with the well-posedness of the b-family equation in analytic function spaces. Using the Abstract Cauchy-Kowalewski theorem we prove that the b-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to H s with s>3/2, and the momentum density u 0-u 0, xx does not change sign, we prove that the solution stays analytic globally in time, for b≥1. Using pseudospectral numerical methods, we study, also, the singularity formation for the b-family equations with the singularity tracking method. This method allows us to follow the process of the singularity formation in the complex plane as the singularity a…

Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"

1998

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega)/\omega^2$ as a precursor of the instability. We argue that this peak is the anal…

Theory of vibrational anomalies in glasses

2015

Abstract The theory of elasticity with spatially fluctuating elastic constants (heterogeneous-elasticity theory) is reviewed. It is shown that the vibrational anomalies associated with the boson peak can be qualitatively and quantitatively explained in terms of this theory. Two versions of a mean-field theory for solving the stochastic equation of motion are presented: the coherent-potential approximation (CPA) and the self-consistent Born approximation (SCBA). It is shown that the latter is included in the former in the Gaussian and weak-disorder limit. We are able to discuss and explain cases in which the change of the vibrational spectrum by varying an external parameter can be accounted…

Fractional Tajimi–Kanai model for simulating earthquake ground motion

2014

The ground acceleration is usually modeled as a filtered Gaussian process. The most common model is a Tajimi–Kanai (TK) filter that is a viscoelastic Kelvin–Voigt unit (a spring in parallel with a dashpot) carrying a mass excited by a white noise (acceleration at the bedrock). Based upon the observation that every real material exhibits a power law trend in the creep test, in this paper it is proposed the substitution of the purely viscous element in the Kelvin Voigt element with the so called springpot that is an element having an intermediate behavior between purely elastic (spring) and purely viscous (dashpot) behavior ruled by fractional operator. With this choice two main goals are rea…

The Dynamics of Supercooled Silica: Acoustic modes and Boson peak

1997

Using molecular dynamics computer simulations we investigate the dynamics of supercooled silica in the frequency range 0.5-20~THz and the wave-vector range 0.13-1.1\AA^{-1}. We find that for small wave-vectors the dispersion relations are in very good agreement with the ones found in experiments and that the frequency at which the boson-peak is observed shows a maximum at around 0.39\AA^{-1}.

Über eine bestimmung der peaklage von reinen und komplexen photopeaks

1966

Abstract To determine the center of photopeaks normally occuring in γ-spectra in complex form, some modified methods are developed for most typical cases: a. single peak and constant background; b. single peak and exponentially decreasing background; c. two overlapping peaks at different distances of energy and varying peak intensities. The statistical fluctuations can be widely eliminated by use of a simple averaging method, so that peak center locations can be evaluated even in the case of relatively small peak intensities. Applying the methods proposed to some cases of strongly overlapping photopeaks, excellent agreement between the theoretical and experimentally obtained values could be…

Scaling laws in the distribution of galaxies

2004

Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale distribution of galaxies in the Universe is far from random: it is highly structured over a vast range of scales. To describe cosmic structures, we need to build mathematically quantifiable descriptions of structure. Identifying where scaling laws apply and the nature of those scaling laws is an important part of understanding which physical mechanisms have been responsible for the organization of clusters, superclusters of galaxies and the voids between them. Find…

Detection of ventricular fibrillation using the autocorrelation function analysis of the ECG

2003

A method is developed for the detection of ventricular fibrillation (VF) and life-threatening arrhythmias. The method is based on direct and simple peak analysis of the autocorrelation function (ACF). It can differentiate between VF (coarse and fine) and non-VH rhythms. ECG records during ventricular tachycardia (VT) and VF were obtained, and 4-s-long segments were digitized at 200 Hz and then split in three groups (VT, VF regular, and VF irregular). ACFs were computed, and positive peak P(j) (j=1, 2, . . .), RPL(j)=P(j)/2SE(1), TR(1)=P(1) width/lag P(1), and D(j)=P(j)-P(j+1) were measured and calculated for each sample. Results show that: (a) RPL(j)(j=1, 2, 3) together with D(j) present hi…

Sound attenuation and anharmonic damping in solids with correlated disorder

2010

We study via self-consistent Born approximation a model for sound waves in a disordered environment, in which the local fluctuations of the shear modulus G are spatially correlated with a certain correlation length The theory predicts an enhancement of the density of states over Debye's omega(2) law (boson peak) whose intensity increases for increasing correlation length, and whose frequency position is shifted downwards as lg. Moreover, the predicted disorder-induced sound attenuation coefficient r(k) obeys a universal scaling law F(k) = f (ke) for a given variance of G. Finally, the inclusion of the lowest-order contribution to the anharmonic sound damping into the theory allows us to rec…

2021

Abstract We propose a signal deconvolution procedure for imaging spectrometer data, where a measured point spread function (PSF) is deconvolved itself before being used for deconvolution of the signal. We evaluate the effectiveness of our procedure for improvement of the spatio-spectral signal, as well as our target application, i.e. estimation of sun-induced fluorescence (SIF). Imaging spectrometers are well established instruments for remote sensing. When used for scientific purposes these instruments are usually calibrated on a regular basis. In our case the point spread function of the optics is measured in an elaborate procedure with a tunable monochromator point light source. PSFs are…