scholarly journals Energy characteristics of a nonlinear layer at resonant frequencies of wave scattering and generation

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 222-232 ◽  
Author(s):  
Lutz Angermann ◽  
Vasyl V. Yatsyk ◽  
Mykola V. Yatsyk
Keyword(s):  
Eigenvalue Problems ◽  
Coupled System ◽  
Wave Radiation ◽  
Homogeneous Field ◽  
Nonlinear Boundary Value Problems ◽  
Intense Fields ◽  
Nonlinear Object ◽  
Computational Errors ◽  
Layered Dielectric ◽  
Plane Oscillations

Abstract This work presents a mathematical model, a computational scheme and experimental results describing the electrodynamic characteristics of a nonmagnetic, isotropic, E-polarized, nonlinear layered dielectric object with a cubically polarizable medium. The nonlinear object is irradiated by a quasi-homogeneous field, where the incident field constitutes of a packet of phase-synchronized plane oscillations. In the case under consideration the excitation may consist both of a highly intense electromagnetic field at a basic (fundamental) frequency, which results in the generation of the third harmonic, as well as of weakly intense fields at multiples of the basic frequency which produce no harmonics, but only have an influencing effect on the processes of wave radiation. The investigations were carried out within the setting of a coupled system approach at resonant excitation frequencies determined by the eigenvalues of the induced eigenvalue problems. A verification of the energy balance law is carried out. By means of estimations for the conditionalities of the occuring matrices, the level of degeneration of the induced non-self-adjoint spectral problems as well as the sensitivity of the coupled system of nonlinear boundary value problems with respect to computational errors are verified.

scholarly journals WRF-CMAQ two-way coupled system with aerosol feedback: software development and preliminary results

2012 ◽  
Vol 5 (2) ◽  
pp. 299-312 ◽  
Author(s):  
D. C. Wong ◽  
J. Pleim ◽  
R. Mathur ◽  
F. Binkowski ◽  
T. Otte ◽  
...  
Keyword(s):  
Air Quality ◽  
Meteorological Data ◽  
Coupled System ◽  
Feedback Mechanism ◽  
Wave Radiation ◽  
Computational Time ◽  
Transfer Model ◽  
Radiative Feedback ◽  
Coupling System ◽  
Tropospheric Aerosol

Abstract. Air quality models such as the EPA Community Multiscale Air Quality (CMAQ) require meteorological data as part of the input to drive the chemistry and transport simulation. The Meteorology-Chemistry Interface Processor (MCIP) is used to convert meteorological data into CMAQ-ready input. Key shortcoming of such one-way coupling include: excessive temporal interpolation of coarsely saved meteorological input and lack of feedback of atmospheric pollutant loading on simulated dynamics. We have developed a two-way coupled system to address these issues. A single source code principle was used to construct this two-way coupling system so that CMAQ can be consistently executed as a stand-alone model or part of the coupled system without any code changes; this approach eliminates maintenance of separate code versions for the coupled and uncoupled systems. The design also provides the flexibility to permit users: (1) to adjust the call frequency of WRF and CMAQ to balance the accuracy of the simulation versus computational intensity of the system, and (2) to execute the two-way coupling system with feedbacks to study the effect of gases and aerosols on short wave radiation and subsequent simulated dynamics. Details on the development and implementation of this two-way coupled system are provided. When the coupled system is executed without radiative feedback, computational time is virtually identical when using the Community Atmospheric Model (CAM) radiation option and a slightly increased (~8.5%) when using the Rapid Radiative Transfer Model for GCMs (RRTMG) radiation option in the coupled system compared to the offline WRF-CMAQ system. Once the feedback mechanism is turned on, the execution time increases only slightly with CAM but increases about 60% with RRTMG due to the use of a more detailed Mie calculation in this implementation of feedback mechanism. This two-way model with radiative feedback shows noticeably reduced bias in simulated surface shortwave radiation and 2-m temperatures as well improved correlation of simulated ambient ozone and PM2.5 relative to observed values for a test case with significant tropospheric aerosol loading from California wildfires.

A High-Resolution Coupled Riverine Flow, Tide, Wind, Wind Wave, and Storm Surge Model for Southern Louisiana and Mississippi. Part I: Model Development and Validation

2010 ◽  
Vol 138 (2) ◽  
pp. 345-377 ◽  
Author(s):  
S. Bunya ◽  
J. C. Dietrich ◽  
J. J. Westerink ◽  
B. A. Ebersole ◽  
J. M. Smith ◽  
...  
Keyword(s):  
High Resolution ◽  
Storm Surge ◽  
Wind Wave ◽  
Wind Waves ◽  
Model Development ◽  
Circulation Model ◽  
Coupled System ◽  
Wave Radiation ◽  
Research Division ◽  
Southern Louisiana

Abstract A coupled system of wind, wind wave, and coastal circulation models has been implemented for southern Louisiana and Mississippi to simulate riverine flows, tides, wind waves, and hurricane storm surge in the region. The system combines the NOAA Hurricane Research Division Wind Analysis System (H*WIND) and the Interactive Objective Kinematic Analysis (IOKA) kinematic wind analyses, the Wave Model (WAM) offshore and Steady-State Irregular Wave (STWAVE) nearshore wind wave models, and the Advanced Circulation (ADCIRC) basin to channel-scale unstructured grid circulation model. The system emphasizes a high-resolution (down to 50 m) representation of the geometry, bathymetry, and topography; nonlinear coupling of all processes including wind wave radiation stress-induced set up; and objective specification of frictional parameters based on land-cover databases and commonly used parameters. Riverine flows and tides are validated for no storm conditions, while winds, wind waves, hydrographs, and high water marks are validated for Hurricanes Katrina and Rita.

scholarly journals The Conversion of Excitation Energy into Generated Energy at the Resonant Frequencies of a Transparent Nonlinear Layer

2019 ◽  
Vol 8 (1) ◽  
pp. 66-74 ◽  
Author(s):  
L. Angermann ◽  
V. V. Yatsyk ◽  
M. V. Yatsyk
Keyword(s):  
Electromagnetic Waves ◽  
Eigenvalue Problems ◽  
Excitation Frequency ◽  
Resonant Frequencies ◽  
Radiation Properties ◽  
Nonlinear Object ◽  
Consistent Solution ◽  
Rigorous Treatment ◽  
Eigen Frequencies ◽  
Resonant Radiation

An iterative algorithm is presented for analyzing the optimal resonant radiation properties of electromagnetic waves by cubically polarized nonlinear layers. The analysis is based on mathematical models for the rigorous treatment of the following problems: Self-consistent solution of both the system of boundary value problems of electrodynamics at resonant frequencies of excitation and generation, as well as the corresponding linearized eigenvalue problems with induced dielectric coefficients. The choice of the resonant excitation frequency of a nonlinear object in dependence on the real parts of the eigen frequencies of the spectral problems is discussed.

Lacunary bifurcation for operator equations and nonlinear boundary value problems on ℝN

1991 ◽  
Vol 118 (3-4) ◽  
pp. 237-270 ◽  
Author(s):  
Hans-Peter Heinz
Keyword(s):  
Nonlinear Boundary ◽  
Eigenvalue Problems ◽  
Real Hilbert Space ◽  
Point Theory ◽  
Elliptic Partial Differential Equations ◽  
Existence Results ◽  
Nonlinear Perturbations ◽  
Nonlinear Boundary Value Problems ◽  
Operator Equations ◽  
Nonlinear Eigenvalue Problems

SynopsisWe consider nonlinear eigenvalue problems of the form Lu + F(u) = λu in a real Hilbert space, where L is a positive self-adjoint linear operator and F is a nonlinearity vanishing to higher order at u = 0. We suppose that there are gaps in the essential spectrum of L and use critical point theory for strongly indefinite functionals to derive conditions for the existence of non-zero solutions for λ belonging to such a gap, and for the bifurcation of such solutions from the line of trivial solutions at the boundary points of a gap. The abstract results are applied to the L2-theory of semilinear elliptic partial differential equations on ℝN. We obtain existence results for the general case and bifurcation results for nonlinear perturbations of the periodic Schrödinger equation.

scholarly journals Coupled System of Boundary Value Problems by Galerkin Method with Cubic B-Splines

2019 ◽  
Vol 128 ◽  
pp. 09008
Author(s):  
K.N.S Kasi Viswanadham
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Coupled System ◽  
Basis Functions ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Linear And Nonlinear

Coupled system of second order linear and nonlinear boundary value problems occur in various fields of Science and Engineering including heat and mass transfer. In the formulation of the problem, any one of 81 possible types of boundary conditions may occur. These 81 possible boundary conditions are written as a combination of four boundary conditions. To solve a coupled system of boundary value problem with these converted boundary conditions, a Galerkin method with cubic Bsplines as basis functions has been developed. The basis functions have been redefined into a new set of basis functions which vanish on the boundary. The nonlinear boundary value problems are solved with the help of quasilinearization technique. Several linear and nonlinear boundary value problems are presented to test the efficiency of the proposed method and found that numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.

Boundary Element Analysis of Three-Dimensional Water Wave-Structure Dynamic Interaction Problems

1988 ◽  
Vol 110 (2) ◽  
pp. 131-139 ◽  
Author(s):  
N. Tosaka ◽  
K. Kakuda
Keyword(s):  
Boundary Element ◽  
Water Wave ◽  
Eigenvalue Problems ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Wave Structure ◽  
Coupled System ◽  
Dynamic Interaction ◽  
Boundary Integral ◽  
Structure Dynamic

Water wave-structure dynamic interaction problems are treated as eigenvalue problems of the coupled system by means of the boundary element method. The coupled system for a large-sized ocean structure is modelized generally with the three-dimensional continuum mechanics. The boundary integral equations of the coupled system are derived by the weighted residual method and related fundamental solutions. The solving scheme for the discretized equations is discussed in detail. Numerical examples of the three-dimensional problem are given to show the validity of the present method through the comparison with other results.

scholarly journals WRF-CMAQ two-way coupled system with aerosol feedback: software development and preliminary results

2011 ◽  
Vol 4 (3) ◽  
pp. 2417-2450 ◽  
Author(s):  
D. C. Wong ◽  
J. Pleim ◽  
R. Mathur ◽  
F. Binkowski ◽  
T. Otte ◽  
...  
Keyword(s):  
Air Quality ◽  
Meteorological Data ◽  
Coupled System ◽  
Feedback Mechanism ◽  
Wave Radiation ◽  
Computational Time ◽  
Transfer Model ◽  
Radiative Feedback ◽  
Coupling System ◽  
Tropospheric Aerosol

Abstract. Air quality models such as the EPA Community Multiscale Air Quality (CMAQ) require meteorological data as part of the input to drive the chemistry and transport simulation. The Meteorology-Chemistry Interface Processor (MCIP) is used to convert meteorological data into CMAQ-ready input. Key shortcoming of such one-way coupling include: excessive temporal interpolation of coarsely saved meteorological input and lack of feedback of atmospheric pollutant loading on simulated dynamics. We have developed a two-way coupled system to address these issues. A single source code principle was used to construct this two-way coupling system so that CMAQ can be consistently executed as a stand-alone model or part of the coupled system without any code changes; this approach eliminates maintenance of separate code versions for the coupled and uncoupled systems. The design also provides the flexibility to permit users: (1) to adjust the call frequency of WRF and CMAQ to balance the accuracy of the simulation versus computational intensity of the system, and (2) to execute the two-way coupling system with feedbacks to study the effect of gases and aerosols on short wave radiation and subsequent simulated dynamics. Details on the development and implementation of this two-way coupled system are provided. When the coupled system is executed without radiative feedback, computational time is virtually identical when using the Community Atmospheric Model (CAM) radiation option and a slightly increased (~8.5 %) when using the Rapid Radiative Transfer Model for GCMs (RRTMG) radiation option in the coupled system compared to the offline WRF-CMAQ system. Once the feedback mechanism is turned on, the execution time increases only slightly with CAM but increases about 60 % with RRTMG due to the use of a more detailed Mie calculation in this implementation of feedback mechanism. This two-way model with radiative feedback shows noticeably reduced bias in simulated surface shortwave radiation and 2 m temperatures as well improved correlation of simulated ambient ozone and PM2.5 relative to observed values for a test case with significant tropospheric aerosol loading from California wildfires.

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