scholarly journals Asymptotic properties for second-order linear evolution problems with fractional laplacian operators

2021 ◽  
Vol 43 ◽  
pp. e14
Author(s):  
Cleverson Roberto da Luz ◽  
Maíra Fernandes Gauer Palma
Keyword(s):  
Initial Data ◽  
Asymptotic Properties ◽  
Low Frequency ◽  
Frequency Region ◽  
Second Order ◽  
Asymptotic Behavior Of Solutions ◽  
Decay Estimates ◽  
High Frequency Region ◽  
Linear Evolution ◽  
Additional Regularity

In this work we study the asymptotic behavior of solutions for a general linear second-order evolution differential equation in time with fractional Laplace operators in $\mathbb{R}^n$. We obtain improved decay estimates with less demand on the initial data when compared to previous results in the literature. In certain cases, we observe that the dissipative structure of the equation is of regularity-loss type. Due to that special structure, to get decay estimates in high frequency region in the Fourier space it is necessary to impose additional regularity on the initial data to obtain the same decay estimates as in low frequency region. The results obtained in this work can be applied to several initial value problems associated to second-order equations, as for example, wave equation, plate equation, IBq, among others. 

Anderson-Stuart Model to Analyze AC and DC Conductivity of Lithium Zinc-Silicate Glass / Glass-Ceramics

2007 ◽  
Vol 280-283 ◽  
pp. 919-924
Author(s):  
M.S. Jogad ◽  
V.K. Shrikhande ◽  
A.H. Dyama ◽  
L.A. Udachan ◽  
Govind P. Kothiyal
Keyword(s):  
High Frequency ◽  
Glass Ceramics ◽  
Low Frequency ◽  
Frequency Region ◽  
Dc Conductivity ◽  
Frequency Range ◽  
High Frequency Region ◽  
Dc Conductivities ◽  
Conductivity Variation ◽  
Different Temperatures

AC and DC conductivities have been measured by using the real (e¢) and imaginary (e¢¢) parts of the dielectric constant data of glass and glass-ceramics (GC) at different temperatures in the rage 297-642K and in the frequency range 100 Hz to 10 MHz. Using Anderson –Stuart model, we have calculated the activation energy, which is observed to be lower than that of the DC conductivity. The analysis for glass/glass-ceramics indicates that the conductivity variation with frequency exhibits an initial linear region followed by nonlinear region with a maximum in the high-frequency region. The observed frequency dependence of ionic conductivity has been analyzed within the extended Anderson–Stuart model considering both the electrostatic and elastic strain terms. In glass/glassceramic the calculations based on the Anderson-Stuart model agree with the experimental observations in the low frequency region but at higher frequencies there is departure from measured data.

DECAY ESTIMATES OF SOLUTIONS TO A SEMI-LINEAR DISSIPATIVE PLATE EQUATION

2010 ◽  
Vol 07 (03) ◽  
pp. 471-501 ◽  
Author(s):  
YOUSUKE SUGITANI ◽  
SHUICHI KAWASHIMA
Keyword(s):  
Initial Data ◽  
Sobolev Spaces ◽  
Linear Problem ◽  
Dimensional Space ◽  
Weighted Sobolev Spaces ◽  
Decay Estimates ◽  
Plate Equation ◽  
Estimates Of Solutions ◽  
Optimal Decay ◽  
Additional Regularity

We study the initial value problem for a semi-linear dissipative plate equation in n-dimensional space. We observe that the dissipative structure of the linearized equation is of the regularity-loss type. This means that we have the optimal decay estimates of solutions under the additional regularity assumption on the initial data. This regularity-loss property causes the difficulty in solving the nonlinear problem. For our semi-linear problem, this difficulty can be overcome by introducing a set of time-weighted Sobolev spaces, where the time-weights and the regularity of the Sobolev spaces are determined by our regularity-loss property. Consequently, under smallness condition on the initial data, we prove the global existence and optimal decay of the solution in the corresponding Sobolev spaces.

scholarly journals Characterization of Nucleobases in Broadband Terahertz Spectra from 0.5 to 10 THz with the Air-Biased-Coherent-Detection Technique

Sensors ◽  
2019 ◽  
Vol 19 (5) ◽  
pp. 1148 ◽  
Author(s):  
Miao Yu ◽  
Shihan Yan ◽  
Yong-qiang Sun ◽  
Wang Sheng ◽  
Fu Tang ◽  
...  
Keyword(s):  
Low Frequency ◽  
Frequency Region ◽  
Coherent Detection ◽  
Detection Technique ◽  
Terahertz Time Domain Spectroscopy ◽  
High Frequency Region ◽  
Characteristic Absorption ◽  
Thz Range ◽  
Thz Absorption

Terahertz time-domain spectroscopy (THz-TDS) is an effective coherent detection technique for deeply understanding the structures and functions of biomolecules. However, generally not full information in the whole THz range can be obtained due to the limited detection bandwidth (usually less than 5 THz) of the traditional THz-TDS systems. In this paper, effective THz absorption spectra in 0.5–10 THz range of five typical nucleobases of DNA/RNA are characterized with a super broadband THz detection technique, called the air-biased- coherent-detection (THz-ABCD) technique. Few unexpected characteristic absorption peaks appeared in the low-frequency region and meanwhile a series of anticipated characteristic absorption peaks are found in the high-frequency region. The fingerprint spectra of these nucleobases are helpful for further analysis on the vibration and twisting behavior of hydrogen bonds, van der Waals and electrostatic forces etc. between and within DNA/RNA biomolecules.

SYNTHESIS, PIEZOELECTRIC, DIELECTRIC AND CONDUCTIVITY STUDIES ON Dy2O3 SUBSTITUTED (Bi0.94Na0.94)0.5Ba0.06TiO3 CERAMICS

2011 ◽  
Vol 01 (04) ◽  
pp. 455-464 ◽  
Author(s):  
K. SAMBASIVA RAO ◽  
HAILEEYESUS WORKINEH ◽  
A. SWATHI ◽  
B. S. KALYANI
Keyword(s):  
Low Frequency ◽  
Charge Carrier Concentration ◽  
Frequency Region ◽  
Relaxor Behavior ◽  
Secondary Phases ◽  
X Ray Diffraction ◽  
High Frequency Region ◽  
Pure Perovskite Structure ◽  
Universal Power Law ◽  
Diffraction Patterns

Polycrystalline ( Bi 0.94-x Dy x Na 0.94)0.5 Ba 0.06 TiO 3 ceramics (x = 0, 0.04, and 0.08, designated as BNBT6, BNBT6: 4Dy and BNBT6: 8Dy, respectively) were prepared by conventional high temperature sintering method. The X-ray diffraction patterns show pure perovskite structure with no secondary phases. Lattice parameters and unit cell volumes have decreased due to Dy2O3 substitution. SEM micrographs revealed denser samples (ρrel > 97%) with uniformly distributed grain sizes. The room temperature piezoelectric properties of Dy2O3 substituted sample at x = 0.04 were relatively higher: d33 = 147 pC/N, k p = 28% and Q m = 128. The samples exhibited infinitesimal change in thickness (≈ 15 nm) to an applied voltage of 100 V, which could be utilized in actuator applications. Relaxor behavior and broad dielectric maxima with diffuse phase transition were observed. The value of RT dielectric constant has increased while dielectric loss was decreased due to Dy2O3 substitution. Conductivity in the materials obeys Jonscher's universal power law. The conductivity in the low frequency region is associated with short range translational hopping while it is associated with the reorientational hopping in the high frequency region. The charge carrier concentration term remained constant over the entire temperature range of (30–500°C).

A Thin Cloud Removal Method for Optical Image Based on Improved Homomorphism Filtering

2014 ◽  
Vol 618 ◽  
pp. 519-522
Author(s):  
Guang Yu ◽  
Wen Bang Sun ◽  
Gang Liu ◽  
Mai Yu Zhou
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Frequency Component ◽  
Frequency Region ◽  
High Frequency Region ◽  
Filtering Method ◽  
Thin Cloud ◽  
Cloud Removal ◽  
Thin Cloud Removal ◽  
Image Definition

Optical remote image is affected by thin cloud inevitably, which debases image definition. Traditional homomorphism filtering frequently used in thin cloud removing has affect on the cloud in low frequency region, but is not effective for those in high frequency region. An improved homomorphism filtering method is proposed on the basis of statistical characters of image information. Instead of the filtering in frequency field, it isolates the low frequency component of the image representing cloud information with calculating neighborhood average in spatial field. Then, the filtered image is enhanced based on rough set. The experiment results show that the proposed method compared to traditional methods can obtain good results and performs faster.

Analysis of Sound Absorption Properties of Three-Leaf Microperforated Panel Absorbers without a Rigid Backing

2014 ◽  
Vol 937 ◽  
pp. 465-471
Author(s):  
Xiao Ling Gai ◽  
Xian Hui Li ◽  
Rui Wu ◽  
Bin Zhang ◽  
Jun Juan Zhao
Keyword(s):  
Sound Absorption ◽  
Low Frequency ◽  
Wide Frequency Range ◽  
Structure Design ◽  
Frequency Region ◽  
Theoretical Development ◽  
Frequency Range ◽  
Absorption Properties ◽  
High Frequency Region ◽  
Energy Dissipated

Microperforated panel (MPP) absorbers have been developed rapidly and used in many fields in recent years. First, based on the Maa’s theory, the theoretical development of MPP is reviewed in this paper. Furthermore, structure design and processing technology of MPP are introduced. Finally, the further development of MPP is discussed. Based on the MPP theory and electro-acoustical equivalent circuit principle, sound absorption properties of three-leaf microperforated panel (TMPP) absorbers without a rigid backing are studied to broaden the sound absorption bandwidth of MPP structure. Simulation results show that TMPP absorbers without a rigid backing have two resonance peaks and the energy dissipated coefficient remains constant in the low frequency range. The resonance frequency moves toward low frequency region with the increasing of the distance, thickness and pore diameter of MPP and moves toward high frequency region with the increasing of the perforation when other parameters keep invariant. The energy dissipated coefficient more than 0.5 over 8 octaves by choosing proper parameters. In conclusion, TMPP absorbers without a rigid backing have good sound absorption properties in a wide frequency range.

Modeling of Perforated Screens or Membrane Using Rigid Frame Porous Models Combined with Thin Membrane Resonance Sound Absorbing Theory

2013 ◽  
Vol 357-360 ◽  
pp. 1206-1211
Author(s):  
Xiao Ling Gai ◽  
Xian Hui Li ◽  
Bin Zhang ◽  
Peng Xie ◽  
Zhi Hui Ma
Keyword(s):  
High Frequency ◽  
Sound Absorption ◽  
Mass Density ◽  
Low Frequency ◽  
Frequency Region ◽  
Thin Membrane ◽  
High Frequency Region ◽  
Rigid Frame ◽  
Membrane Resonance

The sound absorption ability of screen or perforated membrane is studied based on rigid frame porous models combined with thin membrane resonance sound absorbing theory in this paper. Results show that the sound absorption of screen or perforated membrane is better considering the role of membrane than using the rigid frame porous models when the mass density of screen or perforated membrane is smaller. The rigid frame porous model is very accuracy to model the sound absorption ability of screen or perforated membrane when the mass density of membrane is greater. The parameter studies present that the sound absorption peaks move toward low frequency region with the increasing of the depth of air-back cavity, mass density and thickness of screens or perforated membrane and moves toward high frequency region with the increasing of the perforation and perforated radius of screens or perforated membrane when other parameters keep invariant.

scholarly journals Asymptotic behavior of solutions to an evolution equation for bidirectional surface waves in a convecting fluid

2020 ◽  
Vol 72 (10) ◽  
pp. 1386-1399
Author(s):  
H. Mahmoudi ◽  
A. Esfahani
Keyword(s):  
Evolution Equation ◽  
Surface Waves ◽  
Asymptotic Properties ◽  
Global Solutions ◽  
Polynomial Decay ◽  
Equation Modeling ◽  
Asymptotic Behavior Of Solutions ◽  
Decay Estimates ◽  
Initial Value ◽  
The Cauchy Problem

UDC 517.9 We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. We study the existence, uniqueness, and asymptotic properties of global solutions to the initial value problem associated withthis equation in . We obtain some polynomial decay estimates of the energy.

scholarly journals Image Fusion Algorithm at Pixel Level Based on Edge Detection

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Jiming Chen ◽  
Liping Chen ◽  
Mohammad Shabaz
Keyword(s):  
Edge Detection ◽  
Image Fusion ◽  
High Frequency ◽  
Low Frequency ◽  
Frequency Region ◽  
Experimental Comparison ◽  
Fusion Algorithm ◽  
High Frequency Region ◽  
Running Time ◽  
Low Efficiency

In the present scenario, image fusion is utilized at a large level for various applications. But, the techniques and algorithms are cumbersome and time-consuming. So, aiming at the problems of low efficiency, long running time, missing image detail information, and poor image fusion, the image fusion algorithm at pixel level based on edge detection is proposed. The improved ROEWA (Ratio of Exponentially Weighted Averages) operator is used to detect the edge of the image. The variable precision fitting algorithm and edge curvature change are used to extract the feature line of the image edge and edge angle point of the feature to improve the stability of image fusion. According to the information and characteristics of the high-frequency region and low-frequency region, different image fusion rules are set. To cope with the high-frequency area, the local energy weighted fusion approach based on edge information is utilized. The low-frequency region is processed by merging the region energy with the weighting factor, and the fusion results of the high findings demonstrate that the image fusion technique presented in this work increases the resolution by 1.23 and 1.01, respectively, when compared to the two standard approaches. When compared to the two standard approaches, the experimental results show that the proposed algorithm can effectively reduce the lack of image information. The sharpness and information entropy of the fused image are higher than the experimental comparison method, and the running time is shorter and has better robustness.

On the Assignment and Directional Dispersion of Polar Phonon Modes in K3Cu(CN)4 and K3Ag(CN)4

1974 ◽  
Vol 29 (7) ◽  
pp. 1011-1016
Author(s):  
W. Nitsch ◽  
H. J. Falge ◽  
R. Claus
Keyword(s):  
Light Scattering ◽  
High Frequency ◽  
Low Frequency ◽  
Frequency Region ◽  
Longitudinal Vibrations ◽  
Phonon Modes ◽  
High Frequency Region ◽  
Single Crystalline ◽  
Scattering Measurements ◽  
Stretching Vibrations

Polar phonon modes in single crystalline K3Cu(CN)4 and K3Ag(CN)4 have been experimentally studied by light scattering. Measurements at 293, 82 and 6 K made possible assignments in the low frequency region from 0 to about 700 cm-1 and the high frequency region from 2030 to about 2100 cm-1 originating from the C≡N stretching vibrations. Directional dispersion due to the anisotropy of K3Cu(CN)4 has been studied and allowed the identification of the transversal and longitudinal vibrations in the high frequency region. IR-reflectivity measurements, partly on the basis of the ATR-method, have been used in order to support the assignments in this region.

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