scholarly journals Conditions of resonance interaction of acoustic periodic waves interaction

2014 ◽  
Vol 55 ◽  
Author(s):  
Olga Lavcel-Budko ◽  
Aleksandras Krylovas
Keyword(s):  
Equations Of State ◽  
Ideal Gas ◽  
Gas Pressure ◽  
Resonance Interaction ◽  
Initial Time ◽  
Time Interval ◽  
Periodic Waves ◽  
Viscosity Coefficients ◽  
Long Time ◽  
Waves Interaction

We consider differential equations of gas dynamics, when the thermal conductivity and viscosity coefficients equal zero. The system is supplemented with equations of state for the gas pressure and the total energy; these equations do not depend on the properties of gas, i.e. are of a general form. We construct asymptotical approximation for the resonance interaction of acoustic periodic waves, which is uniformly valid in the long time interval. A system coefficient allows determining the resonance occurring condition the relation between gas pressure and temperature at the initial time. We investigate the ideal and non-ideal gas and determine the relationship between the parameters, which causes the of resonanse vanishing in non-ideal gas.

scholarly journals Asymptotical approximation of one dimensional gas dynamics problem

2013 ◽  
Vol 54 ◽  
Author(s):  
Aleksandras Krylovas ◽  
Olga Lavcel-Budko
Keyword(s):  
Asymptotic Approximation ◽  
Gas Dynamics ◽  
Resonant Interaction ◽  
Ideal Gas ◽  
Time Interval ◽  
One Dimensional ◽  
Long Time

We analyze nonlinear one dimensional gas dynamics system. The constructed asymptotic approximation which describes periodic acoustics waves resonant interaction is uniformly valid in the long time interval. The results allow to determine the resonance conditions for the emergence and summarizes the previous analyzed polytropic ideal-gas case.

An Adaptive and Learning System for Feedback-Controlled Evoked Response Studies

1981 ◽  
Vol 20 (03) ◽  
pp. 169-173
Author(s):  
J. Wagner ◽  
G. Pfurtscheixer
Keyword(s):  
Brain Activity ◽  
Evoked Response ◽  
Learning System ◽  
Time Interval ◽  
Electrical Brain Activity ◽  
Long Time ◽  
The Subject ◽  
Eeg Power ◽  
Stimulation System ◽  
Background Eeg

The shape, latency and amplitude of changes in electrical brain activity related to a stimulus (Evoked Potential) depend both on the stimulus parameters and on the background EEG at the time of stimulation. An adaptive, learnable stimulation system is introduced, whereby the subject is stimulated (e.g. with light), whenever the EEG power is subthreshold and minimal. Additionally, the system is conceived in such a way that a certain number of stimuli could be given within a particular time interval. Related to this time criterion, the threshold specific for each subject is calculated at the beginning of the experiment (preprocessing) and adapted to the EEG power during the processing mode because of long-time fluctuations and trends in the EEG. The process of adaptation is directed by a table which contains the necessary correction numbers for the threshold. Experiences of the stimulation system are reflected in an automatic correction of this table. Because the corrected and improved table is stored after each experiment and is used as the starting table for the next experiment, the system >learns<. The system introduced here can be used both for evoked response studies and for alpha-feedback experiments.

scholarly journals Modelling of Pore Collapse during Polymer Sintering: Viscoelastic Model with Enclosed Gas

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2182
Author(s):  
Florian Wohlgemuth ◽  
Dirk Lellinger ◽  
Ingo Alig
Keyword(s):  
Surface Tension ◽  
Gas Transport ◽  
Selective Laser Sintering ◽  
Viscoelastic Model ◽  
Polymer Melt ◽  
Gas Diffusion ◽  
Gas Pressure ◽  
Parameter Study ◽  
Time Interval ◽  
Pore Collapse

Frenkel’s model for the late stage of coalescence of viscous particles has been extended to describe pore collapse in a viscoelastic melt during polymer sintering. The shrinkage of a pore in a polymer melt driven by surface tension is extended by taking into account the effects of trapped gas and gas transport out of the pore. Viscoelasticity has been shown to have a considerable impact on the time scale of the coalescence process. In addition, gas diffusion modifies the coalescence dynamics. Based on a parameter study, different regimes for the pore collapse have been identified. At the beginning of pore collapse, surface tension is considerably stronger than gas pressure within the pore. In this time interval (surface-tension-driven regime), the pore shrinks even in the absence of gas diffusion through the matrix. In the absence of gas transport, the shrinkage dynamic slows down and stops when the surface tension balances the gas pressure in the pore. If gas transport out of the pore is possible, surface tension and gas pressure are balanced while the gas pressure slowly decreases (diffusion-controlled regime). The final phase of pore collapse, which occurs when the gas pressure within the pore decreases sufficiently, is controlled again by surface tension. The limitations of the model are discussed. To analyze the interplay between different mechanisms and process steps during selective laser sintering, the respective time scales are compared using experimental data.

scholarly journals Optimal Perturbations of an Oceanic Vortex Lens

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 63 ◽  
Author(s):  
Thomas Meunier ◽  
Claire Ménesguen ◽  
Xavier Carton ◽  
Sylvie Le Gentil ◽  
Richard Schopp
Keyword(s):  
Normal Mode ◽  
Growth Rates ◽  
Time Interval ◽  
Time Intervals ◽  
Horizontal Structure ◽  
Azimuthal Wave ◽  
Wave Numbers ◽  
Non Linear ◽  
Long Time ◽  
Short Time

The stability properties of a vortex lens are studied in the quasi geostrophic (QG) framework using the generalized stability theory. Optimal perturbations are obtained using a tangent linear QG model and its adjoint. Their fine-scale spatial structures are studied in details. Growth rates of optimal perturbations are shown to be extremely sensitive to the time interval of optimization: The most unstable perturbations are found for time intervals of about 3 days, while the growth rates continuously decrease towards the most unstable normal mode, which is reached after about 170 days. The horizontal structure of the optimal perturbations consists of an intense counter-shear spiralling. It is also extremely sensitive to time interval: for short time intervals, the optimal perturbations are made of a broad spectrum of high azimuthal wave numbers. As the time interval increases, only low azimuthal wave numbers are found. The vertical structures of optimal perturbations exhibit strong layering associated with high vertical wave numbers whatever the time interval. However, the latter parameter plays an important role in the width of the vertical spectrum of the perturbation: short time interval perturbations have a narrow vertical spectrum while long time interval perturbations show a broad range of vertical scales. Optimal perturbations were set as initial perturbations of the vortex lens in a fully non linear QG model. It appears that for short time intervals, the perturbations decay after an initial transient growth, while for longer time intervals, the optimal perturbation keeps on growing, quickly leading to a non-linear regime or exciting lower azimuthal modes, consistent with normal mode instability. Very long time intervals simply behave like the most unstable normal mode. The possible impact of optimal perturbations on layering is also discussed.

scholarly journals Radiomorphology of the Habib Sealer-Induced Resection Plane during Long-Time Followup:A Longitudinal Single Center Experience after 64 Radiofrequency-AssistedLiver Resections

HPB Surgery ◽  
2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Robert Kleinert ◽  
Roger Wahba ◽  
Christoph Bangard ◽  
Klaus Prenzel ◽  
Arnulf H. Hölscher ◽  
...  
Keyword(s):  
Liver Resection ◽  
Morphological Characteristics ◽  
Postoperative Mortality ◽  
Coagulation Necrosis ◽  
Time Interval ◽  
Safe Alternative ◽  
Time Points ◽  
Single Center Experience ◽  
Long Time

Background. Radiofrequency (RF-) assisted liver resection devices like the Habib sealer induce a necrotic resection plane from which a small margin of necrotic liver tissue remains in situ. The aim of the present paper was to report our long-time experience with the new resection method and the morphological characteristics of the remaining necrotic resection plane. Methods. 64 RF-assisted liver resections were performed using the Habib sealer. Followup was assessed at defined time points. Results. The postoperative mortality was 3,6% and morbidity was 18%. The followup revealed that the necrotic zone was detectable in all analyzed CT and MRI images as a hypodense structure without any contrast enhancement at all time points, irrespectively of the time interval between resection and examination. Conclusion. Liver resection utilizing radiofrequency-induced resection plane coagulation is a safe alternative to the established resection techniques. The residual zone of coagulation necrosis remains basically unchanged during a followup of three years. This has to be kept in mind when evaluating the follow up imaging of these patients.

LONG‐TIME RESPONSE PREDICTED BY EXACT ELASTIC RAY THEORY

Geophysics ◽  
1965 ◽  
Vol 30 (3) ◽  
pp. 363-368 ◽  
Author(s):  
T. W. Spencer
Keyword(s):  
Formal Solution ◽  
Intermediate Stage ◽  
Time Limit ◽  
Time Interval ◽  
Individual Response ◽  
Axially Symmetric ◽  
Long Time ◽  
The Difference ◽  
The Individual ◽  
Significant Figures

The formal solution for an axially symmetric radiation field in a multilayered, elastic system can be expanded in an infinite series. Each term in the series is associated with a particular raypath. It is shown that in the long‐time limit the individual response functions produced by a step input in particle velocity are given by polynomials in odd powers of the time. For rays which suffer m reflections, the degree of the polynomials is 2m+1. The total response is obtained by summing all rays which contribute in a specified time interval. When the rays are selected indiscriminately, the difference between the magnitude of the partial sum at an intermediate stage of computation and the magnitude of the correct total sum may be greater than the number of significant figures carried by the computer. A prescription is stated for arranging the rays into groups. Each group response function varies linearly in the long‐time limit and goes to zero when convolved with a physically realizable source function.

scholarly journals On Jensen-type Inequalities for Nonsmooth Radial Scattering Solutions of a Loglog Energy-Supercritical Schrödinger Equation

2018 ◽  
Vol 2020 (8) ◽  
pp. 2501-2541
Author(s):  
Tristan Roy
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
A Priori ◽  
Time Interval ◽  
Type Estimate ◽  
A Priori Bound ◽  
Long Time ◽  
Supercritical Nonlinearity ◽  
Gamma S ◽  
Radial Scattering

Abstract We prove scattering of solutions of the loglog energy-supercritical Schrödinger equation $i \partial _{t} u + \triangle u = |u|^{\frac{4}{n-2}} u g(|u|)$ with $g(|u|) := \log ^{\gamma } {( \log{(10+|u|^{2})} )}$, $0 &lt; \gamma &lt; \gamma _{n}$, n ∈ {3, 4, 5}, and with radial data $u(0) := u_{0} \in \tilde{H}^{k}:= \dot{H}^{k} (\mathbb{R}^{n})\,\cap\,\dot{H}^{1} (\mathbb{R}^{n})$, where $\frac{n}{2} \geq k&gt; 1 \left(\text{resp.}\,\frac{4}{3}&gt; k &gt; 1\right)$ if n ∈ {3, 4} (resp. n = 5). The proof uses concentration techniques (see e.g., [ 2, 12]) to prove a long-time Strichartz-type estimate on an arbitrarily long time interval J depending on an a priori bound of some norms of the solution, combined with an induction on time of the Strichartz estimates in order to bound these norms a posteriori (see e.g., [ 8, 10]). We also revisit the scattering theory of solutions with radial data in $\tilde{H}^{k}$, $k&gt; \frac{n}{2}$, and n ∈ {3, 4}; more precisely, we prove scattering for a larger range of $\gamma$ s than in [ 10]. In order to control the barely supercritical nonlinearity for nonsmooth solutions, that is, solutions with data in $\tilde{H}^{k}$, $k \leq \frac{n}{2}$, we prove some Jensen-type inequalities.

scholarly journals ANALYSIS OF THE TIME‐DEPENDENT BEHAVIOUR OF COMPOSITE CROSS‐SECTIONS BY LAPLACE‐TRANSFORM

2005 ◽  
Vol 11 (3) ◽  
pp. 203-209
Author(s):  
Erich Raue ◽  
Thorsten Heidolf
Keyword(s):  
Laplace Transform ◽  
Cross Sections ◽  
Composite Structures ◽  
Time Dependent ◽  
Time Interval ◽  
Final State ◽  
Long Time ◽  
Time Dependent Behaviour ◽  
Linear Differential ◽  
Dependent Behaviour

Composite structures consisting of precast and cast in‐situ concrete elements are increasingly common. These combinations demand a mechanical model which takes into account the time‐dependent behaviour and analysis of the different ages of the connected concrete components. The effect of creep and shrinkage of the different concrete components can be of relevance for the state of serviceability, as well as for the final state. The long‐time behaviour of concrete can be described by the rate‐of‐creep method, combined with a discretisation of time. The internal forces are described for each time interval using a system of linear differential equations, which can be solved by Laplace‐transform.

scholarly journals Induction of Changes in Internal Gas Pressure of Bulky Plant Organs by Temperature Gradients

1990 ◽  
Vol 115 (2) ◽  
pp. 308-312 ◽  
Author(s):  
Kenneth A. Corey ◽  
Zhi-Yi Tan
Keyword(s):  
Bath Temperature ◽  
Ideal Gas ◽  
Gas Pressure ◽  
Temperature Gradients ◽  
Maximum Pressure ◽  
Plant Organs ◽  
Ideal Gas Law ◽  
Increasing Temperature ◽  
Pressure Changes

Water manometers were connected to fruits of tomato (Lycopersicon esculentum Mill.) and pepper (Capsicum annuum L.), and then fruits were submerged in water baths providing initial temperature gradients between fruit and water of 0 to 19C. Apple (Malus domestics Borkh.) fruits, carrot (Daucus carota L.) roots, witloof chicory (Cichorium intybus L.) roots, rhubarb Rheum rhabarbarum L.) petioles, and pokeweed (Phytolacca americana L.) stems were subjected to water bath temperature gradients of 5C. Internal partial vacuums developed in all organs within minutes of imposing the gradients. The maximum partial vacuums in tomato and pepper fruits increased with increasing temperature gradients. Uptake of water accompanied changes in internal pressure reaching maxima of 17% (w/w) and 2% (w/w) of pepper and tomato fruits, respectively, after 22 hours. Maximum pressure changes achieved in bulky organs deviated from those predicted by the ideal gas law, possibly due to concomitant changes in gas pressure upon replacement of intercellular spaces with water and dissolution of CO2. Partial vacuums also developed in pepper fruits, rhubarb petioles, and pokeweed stems following exposure to air 15C cooler than initial organ temperatures. Results point to the role of temperature gradients in the transport of liquids and gases in plant organs.

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