Asymptotic Models Of Bloch-Floquet Waves In Periodic Waveguides

2008 ◽  
pp. 291-305
Author(s):  
Alexander B. Movchan*
Keyword(s):  
Floquet Waves ◽  
Asymptotic Models

scholarly journals Enhancement factors for grounded ice and ice shelves inferred from an anisotropic ice-flow model

2010 ◽  
Vol 56 (199) ◽  
pp. 805-812 ◽  
Author(s):  
Ying Ma ◽  
Olivier Gagliardini ◽  
Catherine Ritz ◽  
Fabien Gillet-Chaulet ◽  
Gaël Durand ◽  
...  
Keyword(s):  
Ice Sheet ◽  
Actual State ◽  
Polar Ice ◽  
Ice Flow ◽  
Ice Shelves ◽  
State Of Stress ◽  
Asymptotic Models ◽  
Enhancement Factors ◽  
Definition Of ◽  
Stress And Strain Rate

AbstractPolar ice is known to be one of the most anisotropic natural materials. For a given fabric the polycrystal viscous response is strongly dependent on the actual state of stress and strain rate. Within an ice sheet, grounded-ice parts and ice shelves have completely different stress regimes, so one should expect completely different impacts of ice anisotropy on the flow. The aim of this work is to quantify, through the concept of enhancement factors, the influence of ice anisotropy on the flow of grounded ice and ice shelves. For this purpose, a full-Stokes anisotropic marine ice-sheet flowline model is used to compare isotropic and anisotropic diagnostic velocity fields on a fixed geometry. From these full-Stokes results, we propose a definition of enhancement factors for grounded ice and ice shelves, coherent with the asymptotic models used for these regions. We then estimate realistic values for the enhancement factors induced by ice anisotropy for grounded ice and ice shelves.

Permafrost mapping by audiofrequency magnetotellurics

1978 ◽  
Vol 15 (10) ◽  
pp. 1539-1546 ◽  
Author(s):  
A. Koziar ◽  
D. W. Strangway
Keyword(s):  
Mackenzie Delta ◽  
Conductive Layer ◽  
Frequency Range ◽  
Layer Model ◽  
Resistive Layer ◽  
Asymptotic Models ◽  
Two Layer Model ◽  
Electrical Methods ◽  
Permafrost Mapping ◽  
Lateral Variations

The audiofrequency magnetotelluric (AMT) method has been used to study permafrost thickness near Tuktoyaktuk, N.W.T. in the Mackenzie Delta. In the frequency range of 10 Hz–10 kHz the permafrost behaves as a simple resistive layer over a conductive layer. This simple two-layer model can be inverted by asymptotic models to give a unique value for the thickness of the highly resistive frozen layer. In areas of simple layering, these results correlate well with drilling. In areas of sharp lateral variations in resistivity, depths tend to be underestimated. Unlike other electrical methods, AMT is not hampered by the presence of a surface melt layer in the summer if the conductivity–thickness product of this 'active layer' is less than about 0.03 mho (0.03 S).

Two Asymptotic Models for Solid Propellant Combustion

1986 ◽  
Vol 47 (1-2) ◽  
pp. 1-38 ◽  
Author(s):  
Stephen B. Margolis ◽  
Robert C. Armstrong
Keyword(s):  
Solid Propellant ◽  
Propellant Combustion ◽  
Asymptotic Models

scholarly journals Equivalent Robin boundary conditions for acoustic and elastic media

2016 ◽  
Vol 26 (08) ◽  
pp. 1531-1566 ◽  
Author(s):  
Julien Diaz ◽  
Victor Péron
Keyword(s):  
Acoustic Waves ◽  
Mathematical Problem ◽  
Diffraction Problem ◽  
Robin Boundary Condition ◽  
Elastic Displacement ◽  
Fluid Medium ◽  
Asymptotic Models ◽  
Multiscale Expansion ◽  
Robin Boundary ◽  
Equivalent Conditions

We present equivalent conditions and asymptotic models for a diffraction problem of acoustic and elastic waves. The mathematical problem is set with a Robin boundary condition. Elastic and acoustic waves propagate in a solid medium surrounded by a thin layer of fluid medium. Due to the thinness of the layer with respect to the wavelength, this problem is well suited for the notion of equivalent conditions and the effect of the fluid medium on the solid is as a first approximation local. This approach leads to solve only elastic equations. We derive and validate equivalent conditions up to the third order for the elastic displacement. The construction of equivalent conditions is based on a multiscale expansion in power series of the thickness of the layer for the solution of the transmission problem.

scholarly journals Micro-Vibrations and Wave Propagation in Biperiodic Cylindrical Shells

2020 ◽  
Vol 22 (3) ◽  
pp. 789-808
Author(s):  
Barbara Tomczyk ◽  
Anna Litawska
Keyword(s):  
Wave Propagation ◽  
Periodic Structures ◽  
Cylindrical Shells ◽  
Combined Model ◽  
Asymptotic Models ◽  
Wave Propagation Problem ◽  
Modelling Procedure ◽  
Constant Coefficients ◽  
A Cell ◽  
Averaged Model

AbstractThe objects of consideration are thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to study a certain long wave propagation problem related to micro-fluctuations of displacement field caused by a periodic structure of the shells. This micro-dynamic problem will be analysed in the framework of a certain mathematical averaged model derived by means of the combined modelling procedure. The combined modelling applied here includes two techniques: the asymptotic modelling procedure and a certain extended version of the known tolerance non-asymptotic modelling technique based on a new notion of weakly slowly-varying function. Both these procedures are conjugated with themselves under special conditions. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, governing equations of the averaged combined model have constant coefficients depending also on a cell size. It will be shown that the micro-periodic heterogeneity of the shells leads to exponential micro-vibrations and to exponential waves as well as to dispersion effects, which cannot be analysed in the framework of the asymptotic models commonly used for investigations of vibrations and wave propagation in the periodic structures.

Asymptotic Models of the Blood Flow in Arteries and Veins

2013 ◽  
Vol 194 (1) ◽  
pp. 44-57 ◽  
Author(s):  
V. A. Kozlov ◽  
S. A. Nazarov
Keyword(s):  
Blood Flow ◽  
Asymptotic Models ◽  
Arteries And Veins

scholarly journals Modelling Methionine Requirements of Fast- and Slow-Growing Chinese Yellow-Feathered Chickens during the Starter Phase

Animals ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 443 ◽  
Author(s):  
Long Li ◽  
K.F.M. Abouelezz ◽  
Zhonggang Cheng ◽  
A.E.G. Gad-Elkareem ◽  
Qiuli Fan ◽  
...  
Keyword(s):  
Regression Models ◽  
Polynomial Regression ◽  
Conversion Ratio ◽  
Quadratic Polynomial ◽  
Maximal Growth ◽  
Feed Conversion ◽  
Asymptotic Models ◽  
Males And Females ◽  
Slow Growing ◽  
Daily Gain

Two experiments were carried out to investigate the dietary methionine requirement for fast and slow-growing Chinese yellow-feathered breeds during the starter phase, based on growth variables and regression models. In Experiment 1, a total of 2880 one-day-old Lingnan chicks (fast growing breed) were used to test the methionine requirement from 1 to 21 days of age for males and females separately. Of each gender, 1440 birds were allocated into 6 dietary methionine levels (0.28%, 0.32%, 0.37%, 0.43%, 0.50% and 0.63%), each with 6 pen replicates of 40 chicks. Experiment 2 had the same design with Guangxi chicks (slow growing breed) from 1 to 30 d of age. Results indicated that significant nonlinear or quadratic responses to increasing dietary methionine levels were observed in body weight, daily gain, feed intake and feed conversion ratio of both breeds. In summary, the quadratic polynomial regression showed that the optimal methionine requirements for maximal growth performance of Lingnan chickens were 0.52–0.58% in males, 0.51% in females, and 0.53% in mixed genders. The corresponding values for Guangxi breed were 0.53% in males by quadratic polynomial regression and 0.43% in females, and 0.48% to 0.49% in mixed sexes by exponential asymptotic models.

scholarly journals The Landau-Zener Transition and the Surface Hopping Method for the 2D Dirac Equation for Graphene

2017 ◽  
Vol 21 (2) ◽  
pp. 313-357 ◽  
Author(s):  
Ali Faraj ◽  
Shi Jin
Keyword(s):  
Dirac Equation ◽  
Electrostatic Potential ◽  
Numerical Experiments ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Two Dimensional ◽  
Lagrangian Surface ◽  
Surface Hopping ◽  
Asymptotic Models ◽  
Semiclassical Regime

AbstractA Lagrangian surface hopping algorithm is implemented to study the two dimensional massless Dirac equation for Graphene with an electrostatic potential, in the semiclassical regime. In this problem, the crossing of the energy levels of the system at Dirac points requires a particular treatment in the algorithm in order to describe the quantum transition—characterized by the Landau-Zener probability— between different energy levels. We first derive the Landau-Zener probability for the underlying problem, then incorporate it into the surface hopping algorithm. We also show that different asymptotic models for this problem derived in [O. Morandi, F. Schurrer, J. Phys. A:Math. Theor. 44 (2011) 265301]may give different transition probabilities. We conduct numerical experiments to compare the solutions to the Dirac equation, the surface hopping algorithm, and the asymptotic models of [O. Morandi, F. Schurrer, J. Phys. A: Math. Theor. 44 (2011) 265301].

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