High Frequency Vibrations in a Stiff Problem

1997 ◽  
Vol 07 (02) ◽  
pp. 291-311 ◽  
Author(s):  
Miguel Lobo ◽  
Eugenia Pérez
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Problem ◽  
Continuous Spectrum ◽  
High Frequency ◽  
The Other ◽  
Stiff Problem ◽  
Eigenvalues And Eigenfunctions ◽  
High Frequencies ◽  
Stiffness Constant ◽  
High Frequency Vibrations

The stiff problem here considered models the vibrations of a body consisting of two materials, one of them very stiff with respect to the other. We study the asymptotic behavior of the eigenvalues and eigenfunctions of the corresponding spectral problem, when the stiffness constant of only one of the materials tends to 0. We show that the associated operator has a discrete spectrum "converging", in a certain sense, towards a continuous spectrum in [0,∞) corresponding to an operator. We also provide information on the structure of the eigenfunctions associated with the high frequencies.

scholarly journals Effect of pirimicarb application on field ppulations of Myzus persicae (Sulz.) (Homoptera: Aphididae) with different esterase levels

2000 ◽  
Vol 29 (4) ◽  
pp. 739-747
Author(s):  
Rui S. Furiatti ◽  
Sonia M. N. Lázzari
Keyword(s):  
Myzus Persicae ◽  
High Frequency ◽  
The Other ◽  
Biochemical Tests ◽  
Crop Season ◽  
High Frequencies ◽  
Potato Plants ◽  
Before And After ◽  
Potato Crops ◽  
Selection Of

The frequency and intensity of Myzus persicae (Sulz.) resistance were studied using bioassays and biochemical tests in two potato crops in Ibicoara, Bahia. Both areas received several insecticide applications which failed to control M. persicae. By the end of the crop season, one of the areas received two applications of pirimicarb and the other was not sprayed. Six samples of 700 aphids each were randomly collected before and after the pirimicarb applications, with an interval of four days. Specimens of M. persicae were also collected from isolated potato plants. At the laboratory, the samples were characterized by the CL50 based on insecticide bioassays and by total esterase activity using colorimetric assays. After the pirimicarb applications, the susceptible (S), the moderate resistant (R1) and mixed S/R1populations presented decreasing resistance frequencies (from 36.6 to 9.9; 12,0 to 7.5 and 11.4 to 5.9%, respectively). On the other hand, high resistant individuals (R2), extremely resistant (R3), and mixed populations of R1/R2 had increasing frequencies (from 17.7 to 36.7%; 2.3 to 9.1%, and 20.0 to 30.8%, respectively). The survival of S individuals was probably due to their wandering behavior on the plants to avoid sprayed areas. All changes in frequency were reflected in the LC50 and in the resistance ratio (rr). In the pirimicarb untreated area, high frequencies of R2, R3 and R1/R2 were observed. High frequency and resistance intensity of M. persicae in areas under intensive insecticide applications can be related to the selection of resistant populations and due to the entrance of winged migrants from spontaneous plants, where the frequency of R2+R3 was 81.4%.

scholarly journals Review of the Effects of the Influence of External Vibrations on the Freezing Point of Water

2020 ◽  
Vol 320 ◽  
pp. 00032
Author(s):  
Emmanuele Adorni ◽  
Mikhail Ivanov ◽  
Roberto Revetria
Keyword(s):  
Liquid State ◽  
High Frequency ◽  
Low Temperatures ◽  
Freezing Point ◽  
Tap Water ◽  
Distilled Water ◽  
High Frequencies ◽  
High Frequency Vibrations

With this paper we want to provide a first glance at some of those researches that studied how to lower the freezing point of water below the ordinarily point by using external vibrations. All the researches started with experiments on distilled water (obtained with different methodology depending on the experiment) and then moving forward to experiments on tap water (contaminated with a known amount of substances). In all cases, methods to bring the samples to an undercooled state were applied at first. Through high frequency vibrations it has been studied how the formation of ice in a vessel of water can be controlled mainly thanks to the development of the phenomenon of cavitation in the water. By increasing the pressure in certain zones of the samples it was possible to study the phenomena linked to water freezing. Some experiments showed how, even with high frequencies, it is still difficult to obtain reliable results on the topic of keeping the water in a liquid state in conditions of low temperatures and with vibrations applied to the fluid.

scholarly journals Physics Augmented U-Net: A High-Frequency Aware Generative Prior for Microscopy

2021 ◽  
Author(s):  
Jathurshan Pradeepkumar ◽  
Mithunjha Anandakumar ◽  
Vinith Kugathasan ◽  
Andrew Seeber ◽  
Dushan N Wadduwage
Keyword(s):  
High Frequency ◽  
Forward Model ◽  
The Other ◽  
Structured Illumination ◽  
Structured Illumination Microscopy ◽  
Experimental Conditions ◽  
Low Frequencies ◽  
High Frequencies ◽  
Proposed Model ◽  
Microscopy Images

A key challenge in optical microscopy is to image fast at high-resolution. To address this problem, we propose "Physics Augmented U-Net", which combines deep learning and structured illumination microscopy (SIM). In SIM, the structured illumination aliases out-of-band high-frequencies to the passband of the microscope; thus SIM captures some high-frequencies even when the image is sampled at low-resolution. To utilize these features, we propose a three-element method: 1) a modified U-Net model, 2) a physics-based forward model of SIM 3) an inference algorithm combining the two models. The modified U-Net architecture is similar to the seminal work, but the bottleneck is modified by concatenating two latent vectors, one encoding low-frequencies (LFLV), and the other encoding high-frequencies (HFLV). LFLV is learned by U-Net contracting path, and HFLV is learned by a second encoding path. In the inference mode, the high-frequency encoder is removed; HFLV is then optimized to fit the measured microscopy images to the output of the forward model for the generated image by the U-Net. We validated our method on two different datasets under different experimental conditions. Since a latent vector is optimized instead of a 2D image, the inference mode is less computationally complex. The proposed model is also more stable compared to other generative prior-based methods. Finally, as the forward model is independent of the U-Net, Physics Augmented U-Net can enhance resolution on any variation of SIM without further retraining.

High frequency asymptotic analysis of a string with rapidly oscillating density

2000 ◽  
Vol 11 (6) ◽  
pp. 595-622 ◽  
Author(s):  
C. CASTRO ◽  
E. ZUAZUA
Keyword(s):  
Asymptotic Expansion ◽  
Eigenvalue Problem ◽  
Asymptotic Analysis ◽  
Explicit Formula ◽  
High Frequency ◽  
Critical Size ◽  
The Other ◽  
Full Description ◽  
Eigenvalues And Eigenfunctions ◽  
Asymptotic Formulae

We consider the eigenvalue problem associated with the vibrations of a string with rapidly oscillating periodic density. In a previous paper we stated asymptotic formulae for the eigenvalues and eigenfunctions when the size of the microstructure ε is shorter than the wavelength of the eigenfunctions 1/√λε. On the other hand, it has been observed that when the size of the microstructure is of the order of the wavelength of the eigenfunctions (ε ∼ 1/√λε) singular phenomena may occur. In this paper we study the behaviour of the eigenvalues and eigenfunctions when 1/√λε is larger than the critical size ε. We use the WKB approximation which allows us to find an explicit formula for eigenvalues and eigenfunctions with respect to ε. Our analysis provides all order correction formulae for the limit eigenvalues and eigenfunctions above the critical size. Each term of the asymptotic expansion requires one more derivative of the density. Thus, a full description requires the density to be C∞ smooth.

scholarly journals Asymptotic approximations for eigenvalues and eigenfunctions of a spectral problem in a thin graph-like junction with a concentrated mass in the node

2020 ◽  
pp. 1-65
Author(s):  
Taras Mel’nyk
Keyword(s):  
Asymptotic Behavior ◽  
Small Parameter ◽  
Spectral Problem ◽  
Asymptotic Expansions ◽  
Multiscale Analysis ◽  
Asymptotic Approximations ◽  
Concentrated Mass ◽  
Eigenvalues And Eigenfunctions

A spectral problem is considered in a thin 3D graph-like junction that consists of three thin curvilinear cylinders that are joined through a domain (node) of the diameter [Formula: see text] where [Formula: see text] is a small parameter. A concentrated mass with the density [Formula: see text] [Formula: see text] is located in the node. The asymptotic behavior of the eigenvalues and eigenfunctions is studied as [Formula: see text] i.e. when the thin junction is shrunk into a graph. There are five qualitatively different cases in the asymptotic behavior [Formula: see text] of the eigenelements depending on the value of the parameter [Formula: see text] In this paper three cases are considered, namely, [Formula: see text] [Formula: see text] and [Formula: see text] Using multiscale analysis, asymptotic approximations for eigenvalues and eigenfunctions are constructed and justified with a predetermined accuracy with respect to the degree of [Formula: see text] For irrational [Formula: see text] a new kind of asymptotic expansions is introduced. These approximations show how to account the influence of local geometric and physical inhomogeneity of the node in the corresponding limit spectral problem on the graph for different values of the parameter [Formula: see text]

ON VIBRATING MEMBRANES WITH VERY HEAVY THIN INCLUSIONS

2004 ◽  
Vol 14 (07) ◽  
pp. 987-1034 ◽  
Author(s):  
YU. D. GOLOVATY ◽  
D. GÓMEZ ◽  
M. LOBO ◽  
E. PÉREZ
Keyword(s):  
Asymptotic Behavior ◽  
High Frequency ◽  
Concentrated Mass ◽  
High Frequency Vibrations

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 ωε of width 2ε and it has a density of order O(ε-m). The density is of order O(1) outside this inclusion ωε, 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.

C. The Continuous Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 177-206
Author(s):  
J. B. Oke ◽  
C. A. Whitney
Keyword(s):  
Continuous Spectrum ◽  
Variable Stars ◽  
Velocity Fields ◽  
The Other ◽  
Line Spectrum ◽  
Direct Information ◽  
Thermodynamic Structure ◽  
Diagnostic Interpretation ◽  
Pulsating Variable Stars ◽  
The Continuum

Pecker:The topic to be considered today is the continuous spectrum of certain stars, whose variability we attribute to a pulsation of some part of their structure. Obviously, this continuous spectrum provides a test of the pulsation theory to the extent that the continuum is completely and accurately observed and that we can analyse it to infer the structure of the star producing it. The continuum is one of the two possible spectral observations; the other is the line spectrum. It is obvious that from studies of the continuum alone, we obtain no direct information on the velocity fields in the star. We obtain information only on the thermodynamic structure of the photospheric layers of these stars–the photospheric layers being defined as those from which the observed continuum directly arises. So the problems arising in a study of the continuum are of two general kinds: completeness of observation, and adequacy of diagnostic interpretation. I will make a few comments on these, then turn the meeting over to Oke and Whitney.

Simulation of vibration piercing of pipe blank at press

2020 ◽  
Vol 76 (11) ◽  
pp. 1128-1138
Author(s):  
S. R. Rakhmanov
Keyword(s):  
High Frequency ◽  
Deformation Zone ◽  
Pipe Blank ◽  
Equipment Operation ◽  
Metal Deformation ◽  
Technological Tool ◽  
High Frequency Vibrations ◽  
Pipe Blanks ◽  
Wave Phenomena

In some cases, the processes of piercing or expanding pipe blanks involve the use of high-frequency active vibrations. However, due to insufficient knowledge, these processes are not widely used in the practice of seamless pipes production. In particular, the problems of increasing the efficiency of the processes of piercing or expanding a pipe blank at a piercing press using high-frequency vibrations are being solved without proper research and, as a rule, by experiments. The elaboration of modern technological processes for the production of seamless pipes using high-frequency vibrations is directly related to the choice of rational modes of metal deformation and the prediction resistance indicators of technological tools and the reliability of equipment operation. The creation of a mathematical model of the process of vibrating piercing (expansion) of an axisymmetric pipe blank at a piercing press of a pipe press facility is an actual task. A calculation scheme for the process of piercing a pipe plank has been elaborated. A dependence was obtained characterizing the speed of front of plastic deformation propagation on the speed of penetration of a vibrated axisymmetric mandrel into the pipe workpiece being pierced. The dynamic characteristics of the occurrence of wave phenomena in the metal being pierced under the influence of a vibrated tool have been determined, which significantly complements the previously known ideas about the stress-strain state of the metal in the deformation zone. The deformation fields in the zones of the disturbed region of the deformation zone were established, taking into account the high-frequency vibrations of the technological tool. It has been established that the choice of rational parameters (amplitude-frequency characteristics) of the vibration piercing process of a pipe blank results in significant increase in the efficiency of the process, the durability of the technological tool and the quality of the pierced blanks.

scholarly journals Rheology of rounded mammalian cells over continuous high-frequencies

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Gotthold Fläschner ◽  
Cosmin I. Roman ◽  
Nico Strohmeyer ◽  
David Martinez-Martin ◽  
Daniel J. Müller
Keyword(s):  
High Frequency ◽  
Mammalian Cells ◽  
Mechanical Response ◽  
Cell Mass ◽  
Low Frequency ◽  
Mass Measurements ◽  
High Frequencies ◽  
Polymer Relaxation ◽  
Continuous Frequency ◽  
Rheological Experiments

AbstractUnderstanding the viscoelastic properties of living cells and their relation to cell state and morphology remains challenging. Low-frequency mechanical perturbations have contributed considerably to the understanding, yet higher frequencies promise to elucidate the link between cellular and molecular properties, such as polymer relaxation and monomer reaction kinetics. Here, we introduce an assay, that uses an actuated microcantilever to confine a single, rounded cell on a second microcantilever, which measures the cell mechanical response across a continuous frequency range ≈ 1–40 kHz. Cell mass measurements and optical microscopy are co-implemented. The fast, high-frequency measurements are applied to rheologically monitor cellular stiffening. We find that the rheology of rounded HeLa cells obeys a cytoskeleton-dependent power-law, similar to spread cells. Cell size and viscoelasticity are uncorrelated, which contrasts an assumption based on the Laplace law. Together with the presented theory of mechanical de-embedding, our assay is generally applicable to other rheological experiments.

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