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Готові списки джерел за темами / Zero-dispersion limit

Добірка наукової літератури з теми "Zero-dispersion limit"

Автор: Grafiati

Опубліковано: 7 липня 2024

Оновлено: 7 липня 2024

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Статті в журналах з теми "Zero-dispersion limit":

1

David Levermore, C. "The hyperbolic nature of the zero dispersion Kdv limit." Communications in Partial Differential Equations 13, no. 4 (January 1988): 495–514. http://dx.doi.org/10.1080/03605308808820550.

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2

Lax, Peter D. "The zero dispersion limit, a deterministic analogue of turbulence." Communications on Pure and Applied Mathematics 44, no. 8-9 (October 1991): 1047–56. http://dx.doi.org/10.1002/cpa.3160440815.

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3

GLASS, OLIVIER, and SERGIO GUERRERO. "UNIFORM CONTROLLABILITY OF A TRANSPORT EQUATION IN ZERO DIFFUSION–DISPERSION LIMIT." Mathematical Models and Methods in Applied Sciences 19, no. 09 (September 2009): 1567–601. http://dx.doi.org/10.1142/s0218202509003899.

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In this paper, we consider the controllability of a transport equation perturbed by small diffusion and dispersion terms. We prove that for a sufficiently large time, the cost of the null-controllability tends to zero exponentially as the perturbation vanishes. For small times, on the contrary, we prove that this cost grows exponentially.

4

Akhmedova, V. E., and A. V. Zabrodin. "Elliptic parameterization of Pfaff integrable hierarchies in the zero-dispersion limit." Theoretical and Mathematical Physics 185, no. 3 (December 2015): 1718–28. http://dx.doi.org/10.1007/s11232-015-0374-z.

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5

Lin, Chi-Kun, and Yau-Shu Wong. "Zero-dispersion limit of the short-wave–long-wave interaction equations." Journal of Differential Equations 228, no. 1 (September 2006): 87–110. http://dx.doi.org/10.1016/j.jde.2006.03.027.

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6

Holden, H., K. H. Karlsen, and D. Mitrovic. "Zero Diffusion-Dispersion-Smoothing Limits for a Scalar Conservation Law with Discontinuous Flux Function." International Journal of Differential Equations 2009 (2009): 1–33. http://dx.doi.org/10.1155/2009/279818.

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We consider multidimensional conservation laws with discontinuous flux, which are regularized with vanishing diffusion and dispersion terms and with smoothing of the flux discontinuities. We use the approach ofH-measures to investigate the zero diffusion-dispersion-smoothing limit.

7

Berendt-Marchel, M., and A. Wawrzynczak. "Does the Zero Carry Essential Information for Artificial Neural Network learning to simulate the contaminant transport in Urban Areas?" Journal of Physics: Conference Series 2090, no. 1 (November 1, 2021): 012027. http://dx.doi.org/10.1088/1742-6596/2090/1/012027.

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Abstract The release of hazardous materials in urbanized areas is a considerable threat to human health and the environment. Therefore, it is vital to detect the contamination source quickly to limit the damage. In systems localizing the contamination source based on the measured concentrations, the dispersion models are used to compare the simulated and registered point concentrations. These models are run tens of thousands of times to find their parameters, giving the model output’s best fit to the registration. Artificial Neural Networks (ANN) can replace in localization systems the dispersion models, but first, they need to be trained on a large, diverse set of data. However, providing an ANN with a fully informative training data set leads to some computational challenges. For example, a single simulation of airborne toxin dispersion in an urban area might contain over 90% of zero concentration in the positions of the sensors. This leads to the situation when the ANN target includes a few percent positive values and many zeros. As a result, the neural network focuses on the more significant part of the set - zeros, leading to the non-adaptation of the neural network to the studied problem. Furthermore, considering the zero value of concentration in the training data set, we have to face many questions: how to include zero, scale a given interval to hide the zero in the set, and include zero values at all; or limit their number? This paper will try to answer the above questions and investigate to what extend zero carries essential information for the ANN in the contamination dispersion simulation in urban areas. For this purpose, as a testing domain, the center of London is used as in the DAPPLE experiment. Training data is generated by the Quick Urban & Industrial Complex (QUIC) Dispersion Modeling System.

8

Tian, Fei Ran. "Oscillations of the zero dispersion limit of the korteweg-de vries equation." Communications on Pure and Applied Mathematics 46, no. 8 (September 1993): 1093–129. http://dx.doi.org/10.1002/cpa.3160460802.

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9

Tovbis, Alexander, Stephanos Venakides, and Xin Zhou. "On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation." Communications on Pure and Applied Mathematics 57, no. 7 (April 16, 2004): 877–985. http://dx.doi.org/10.1002/cpa.20024.

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10

Ercolani, Nicholas M., C. David Levermore, and Taiyan Zhang. "The behavior of the weyl function in the zero-dispersion KdV limit." Communications in Mathematical Physics 183, no. 1 (January 1997): 119–43. http://dx.doi.org/10.1007/bf02509798.

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Більше джерел

Дисертації з теми "Zero-dispersion limit":

1

Tso, Taicheng. "The zero dispersion limits of nonlinear wave equations." Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185840.

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In chapter 2 we use functional analytic methods and conservation laws to solve the initial-value problem for the Korteweg-de Vries equation, the Benjamin-Bona-Mahony equation, and the nonlinear Schrodinger equation for initial data that satisfy some suitable conditions. In chapter 3 we use the energy estimates to show that the strong convergence of the family of the solutions of the KdV equation obtained in chapter 2 in H³(R) as ε → 0; also, we show that the strong L²(R)-limit of the solutions of the BBM equation as ε → 0 before a critical time. In chapter 4 we use the Whitham modulation theory and averaging method to find the 2π-periodic solutions and the modulation equations of the KdV equation, the BBM equation, the Klein-Gordon equation, the NLS equation, the mKdV equation, and the P-system. We show that the modulation equations of the KdV equation, the K-G equation, the NLS equation, and the mKdV equation are hyperbolic but those of the BBM equation and the P-system are not hyperbolic. Also, we study the relations of the KdV equation and the mKdV equation. Finally, we study the complex mKdV equation to compare with the NLS equation, and then study the complex gKdV equation.

2

Badreddine, Rana. "On a DNLS equation related to the Calogero-Sutherland-Moser Hamiltonian system." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM008.

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Il s'agit d'étudier une EDP obtenue par A. Abanov et al (J. Phys. A, 2009) à partir de la limite hydrodynamique du système hamiltonien de Calogero-Sutherland-Moser. On obtient ainsi une équation intégrable de type Schrödinger non linéaire sur l'espace de Hardy qui se trouve posséder une paire de Lax sur la droite et sur le cercle. Le but de cette thèse est d'utiliser la structure d'intégrabilité afin d'établir que l'équation est globalement bien-posée sur le cercle en allant jusqu'à l'espace de régularité critique. En second lieu, on s'intéresse à l'existence de solutions particulières sur le tore. Ainsi, on caractérise les ondes progressives de cette équation, ainsi qu'une classe de solutions s'écrivant sous la forme de fractions rationnelles et qui sont définies spectralement à partir de l'opérateur de Lax. En troisième lieu, on étudie la limite à faible-dispersion (semi-classique) de cette équation sur la droite et on caractérise ses solutions grâce à une formule explicite
This thesis is devoted to a PDE obtained by A. Abanov et al (J. Phys. A, 2009) from the hydrodynamic limit of the Calogero-Sutherland Hamiltonian system. A nonlinear integrable Schrödinger-type equation on the Hardy space is obtained and has a Lax pair structure on the line and on the circle. The goal of this thesis is to establish, by using the integrability structure of this PDE, some global well-posedness results on the circle, extending down to the critical regularity space. Secondly, we investigate the existence of particular solutions. Thus, we characterize the traveling waves and finite gap potentials of this equation on the circle. Thirdly, we study the zero-dispersion (or semiclassical) limit of this equation on the line and characterize its solutions using an explicit formula

Книги з теми "Zero-dispersion limit":

1

Horing, Norman J. Morgenstern. Graphene. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0012.

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Chapter 12 introduces Graphene, which is a two-dimensional “Dirac-like” material in the sense that its energy spectrum resembles that of a relativistic electron/positron (hole) described by the Dirac equation (having zero mass in this case). Its device-friendly properties of high electron mobility and excellent sensitivity as a sensor have attracted a huge world-wide research effort since its discovery about ten years ago. Here, the associated retarded Graphene Green’s function is treated and the dynamic, non-local dielectric function is discussed in the degenerate limit. The effects of a quantizing magnetic field on the Green’s function of a Graphene sheet and on its energy spectrum are derived in detail: Also the magnetic-field Green’s function and energy spectrum of a Graphene sheet with a quantum dot (modelled by a 2D Dirac delta-function potential) are thoroughly examined. Furthermore, Chapter 12 similarly addresses the problem of a Graphene anti-dot lattice in a magnetic field, discussing the Green’s function for propagation along the lattice axis, with a formulation of the associated eigen-energy dispersion relation. Finally, magnetic Landau quantization effects on the statistical thermodynamics of Graphene, including its Free Energy and magnetic moment, are also treated in Chapter 12 and are seen to exhibit magnetic oscillatory features.

Частини книг з теми "Zero-dispersion limit":

1

Correia, Joaquim M. C. "Zero Limit for Multi-D Conservation Laws with Nonlinear Dissipation and Dispersion." In Modeling, Dynamics, Optimization and Bioeconomics II, 147–63. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55236-1_9.

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2

Wright, Otis C. "Explicit Construction of The Lax-Levermore Minimizer for the KdV Zero Dispersion Limit." In Singular Limits of Dispersive Waves, 157–64. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4615-2474-8_12.

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3

Dbebria, Hajer, and Ali Salem. "Exact Controllability For Korteweg-De Vries Equation and its Cost in the Zero-Dispersion Limit." In Applied Mathematics in Tunisia, 293–306. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-18041-0_19.

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4

"The zero dispersion limit, a deterministic analogue of turbulence." In Nonlinear Evolutionary Partial Differential Equations, 53–64. Providence, Rhode Island: American Mathematical Society, 1996. http://dx.doi.org/10.1090/amsip/003/05.

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5

Mussardo, Giuseppe. "Fermionic Formulation of the Ising Model." In Statistical Field Theory, 290–309. Oxford University PressOxford, 2009. http://dx.doi.org/10.1093/oso/9780199547586.003.0009.

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Abstract In this chapter we will study the continuum limit formulation of the two-dimensional Ising model, starting from the hamiltonian limit of its transfer matrix. We will first derive the quantum hamiltonian of the model and then we will study its most important properties, such as the duality transformation. This symmetry involves the order and disorder operators and we will clarify their physical interpretation. Afterwards, we will see how to diagonalize the quantum hamiltonian by means of particular fermionic fields. The operator mapping between the order/disorder operators and the fermionic fields is realized by the so-called Wigner–Jordan transformation: this brings the original hamiltonian to a quadratic form in the creation and annihilation operators of the fermions. The determination of the spectrum is then obtained by a Bogoliubov transformation, a technique extremely useful also in other contexts, such as superconductivity phenomena. In the limit in which the lattice spacing goes to zero, the Ising model becomes a theory of free Majorana fermions. They satisfy a relativistic dispersion relation and their mass is a direct measurement of the displacement of the temperature from the critical value.

6

Müller, J., and T. K. Fanneløp. "Experimental Study of Heavy-Gas Dispersion on Sloping Surf aces." In Mixing and Dispersion in Stably Stratified Flows, 39–56. Oxford University PressOxford, 1999. http://dx.doi.org/10.1093/oso/9780198500155.003.0003.

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Abstract The motion of a dense-gas cloud is known to be strongly influenced by slopes. Various theoretical models have been proposed but the scarcity of experimental data makes their validation difficult. An extensive experimental study of heavy-gas clouds suddenly released on uniform sloping surfaces was therefore undertaken. Both, cylindrical releases on an unobstructed surface and 2-d releases in a channel were investigated. The parameters varied include the gas density, the release volume and aspect ratio, and the slope. A new model combining the slumping motion of the cloud, calculated using a modified box-model, with the slope-dependent motion of its center of gravity, is proposed herein. Good agreement with experimental data is obtained in general as well as in the limit of zero slope and in the early spreading phase.

Тези доповідей конференцій з теми "Zero-dispersion limit":

1

Kodama, Y. "Analytical Theory of NRZ Signal Transmission." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: Optica Publishing Group, 1996. http://dx.doi.org/10.1364/nlgw.1996.sab.2.

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Several recent experiments demonstrated the feasibility of high-bit-rate, long-haul optical telecommunications using IMDD nonreturn-to-zero (NRZ) signals in periodically amplified fiber links operating close to the zero group-velocity-dispersion (GVD) wavelength [1,2]. Both experiments [1, 2] and numerical simulations [3] show that distortion of the NRZ signal results from spectral broadening due to amplifier noise induced-four-wave mixing (FWM), and from fiber self-phase modulation (SPM) in combination with the small residual GVD. While noise-seeded FWM may be suppressed by means of dispersion management [4], the signal distortion due to SPM and GVD sets a stringent upper limit to the transmitted signal power.

2

Agrawal, Govind P., and M. J. Potasek. "Nonlinear pulse propagation at the zerodispersion wavelength of single-mode fibers." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/oam.1985.wn3.

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Nonlinear pulse propagation in single-mode fibers is studied numerically using the beam-propagation method. In particular, we consider wave propagation at the zero-dispersion wavelength. Depending on the relative importance of the nonlinear and the higher-order dispersive effects, both the pulse shape and the pulse spectrum show qualitatively different behavior and new features arise when the two effects are comparable. For typical system parameters, the nonlinear and dispersive contributions are comparable for a specific pulse width τ c ~ 1 ps. When the pulses are broader than τc, nonlinearity dominates and leads to significant pulse broadening that would limit the performance of high-data-rate optical communication systems operating at the zero-dispersion wavelength.1 For pulses shorter than τc, dispersion dominates and is responsible for the pulse broadening. Interestingly enough, the nonlinearity can reduce the amount of broadening relative to that occurring in a linear dispersive medium.

3

Wabnitz, S., and J. M. Soto-Crespo. "Conjugate solitons in optical fibers." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: Optica Publishing Group, 1998. http://dx.doi.org/10.1364/nlgw.1998.nwe.2.

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As well-known, optical phase conjugation undoes optical signal distortions upon propagation in dispersive and nonlinear medium [1]. By generating the conjugate replica of a signal at the middle of fiber-optic transmission link, dispersive and nonlinear broadenings may be compensated for [2]. When applied to soliton systems, mid-span spectral inversion also removes other important transmission capacity-limiting effects such as pulse interactions [3]. Four-wave mixing in fibers may also be exploited for wavelength-shifting and time-demultiplexing of high-bit-rate signals. For efficient and broadband frequency conversion, pumping near the zero-dispersion wavelength of a dispersion-shifted fiber (DSF) is required [4,5]. As a result, the fiber group-velocity dispersion (GVD) has opposite signs at the signal and conjugate wavelengths. In the conjugation of ultrashort solitons, that is for DSF lengths equal or longer than the dispersion distance, the effect of finite GVD at the signal and conjugate wavelengths sets a fundamental limit to the conversion efficiency.

4

Sunak, Harish R. D., and Hatem A. H. Abdelkader. "Soliton-based lightwave system using single-mode fluoride fibers." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.tht8.

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We report a theoretical study of an all- optical long-distance soliton-based lightwave system using single-mode heavy metal fluoride (HMF) fibers at 2.55 μm, where the minimum loss is projected to be ~0.03 dB/km. Mollenauer has experimentally demonstrated soliton transmission over more than 6000 km in single-mode silica fibers at ~1.6 μm, with loss periodically compensated by Raman gain by using a pump at ~1.47 μm. Our motivation was to investigate what can be possible in future when single-mode HMF fibers become a practical reality. Since the peak Raman gain shift in HMF fibers is 580 cm-1, the pump will be at 2.22 μm, with 0.06-dB/km loss. A simple step-index HMF fiber with good dispersion flattening was used in this study and its properties are as follows: core diameter 6 μm; relative index difference 0.95%; zero dispersion wavelength is 2.48 μm, with a slope of 0.008 ps/nm2/km; dispersion at 2.55 μm is 0.6 ps/nm/km, with negative group velocity dispersion as required and small manufacturing tolerances will still preserve this. The band width length (Gordon-Haus) limit was calculated to be ~120,000 GHz·km.

5

Fontana, F., G. Bordogna, G. Grasso, M. Romagnoli, M. Midrio, and P. Franco. "Method for the Determination of the Resonant Group Velocity Dispersion in Erbium Doped Fiber Lasers." In Nonlinear Guided-Wave Phenomena. Washington, D.C.: Optica Publishing Group, 1993. http://dx.doi.org/10.1364/nlgwp.1993.md.1.

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Whenever an optical signal is tuned into a resonance such as a band pass filter or a laser transition, a dispersion arising from the resonance starts playing a role on the propagation of the signal. The effect of the dispersion on the signal depends on few parameters such as the dispersion spectral width, the amplitude or the strength of the interaction of the signal with the resonance. In long haul optical telecommunication systems, a certain number of optical ampifiers are required to restore the depletion of the optical, signal caused by the filer losses. Neverthless the effect of the resonant group velocity dispersion (GVD) provided by the amplifiers plays a minor role as long as non zero GVD for the link is chosen. More critical is the effect of the resonant GVD in erbium doped fiber lasers (EDFL's) where the length of the active medium may, in principle, coincide with the the length of the cavity. The effect of a spectrally varying GVD profile is that of distorting the temporal profile of a pulse during the propagation [1]. In the soliton fiber lasers the temporal asymmetry provided by the resonant dispersion is partially compensated by the restoration of the nonlinear gain, and eventually the ultimate pulse duration differs from the natural limit imposed by the gain bandwidth.

6

Shelby, R. M., M. Rosenbluh, P. D. Drummond, and S. J. Carte. "Squeezed solitons: quantum and thermal noise effects." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.mf2.

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Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary distortion-free propagation only requires the proper choice of pulse width and shape for a given pulse energy. However, quantum fluctuations do not undergo stationary propagation but rather evolve due to dispersion and self-phase modulation. As a soliton pulse propagates, zero-point or vacuum noise associated with the pulse evolves into squeezed noise. Vacuum fluctuations are responsible for the fundamental detector noise floor known as the shot noise limit. Reduction of the noise in the detection of squeezed soliton pulses has achieved a noise level 34% below this limit. In optical fibers, thermal fluctuation of the refractive index limit the noise reduction that can be achieved by adding phase fluctuations in excess of the vacuum noise. At low frequencies thermal noise originates from local structural dynamics of fused silica which produces a 1/f power spectrum and from guided acoustic wage Brillouin scattering which modulates the refractive index at frequencies characteristic of the fiber structure. The bandwidth of these fluctuations is ~2 GHz; and for soliton pulses with spectral bandwidth much >2 GHz, we have shown that this noise can be made insignificant. For very short pulses, however, noise from Raman scattering must be considered. Recent calculations incorporating this noise mechanism are compared with experiment.

7

De Rossi, Alfredo, Claudio Conti, and Stefano Trillo. "Stability criterion and multistability of Kerr-like gap solitons." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: Optica Publishing Group, 1998. http://dx.doi.org/10.1364/nlgw.1998.ntha.5.

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It is well-known that periodic Bragg structures induce gaps in the linear dispersion relation where the propagation is forbidden. Thanks to the nonlinearity, the e.m. energy can be localized at these frequencies in the form of gap solitons [1-5]. Their most intriguiging feature is the possibility to travel with velocities much slower than the light velocity, or remarkably even at zero velocity (stationary trapping) in the limit case. Propagation of slow solitonic envelopes was recently demonstrated experimentally operating near Bragg wavelength of a fiber grating [5]. However no experimental data in the region of zero (or extremely small) velocities has been reported to date. To address the observability of stationary localization, a fundamental prerequesite to be fullfilled is the stability of the gap solitons. In spite of its importance the stability problem for gap solitons was left practically unaddressed, except for few numerical simulations. Here our purpose is to derive an analytical stability criterion, starting from the usual coupled-mode formulation of the propagation [1]. This involves derivatives of the invariants similarly to a well-known criterion for equations with second-order dispersion (i.e., nonlinear Schrödinger type [6]), recently extended to quadratic solitons [7,8]. Specifically, we consider the Lorentz-invariant Hamiltonian equations which rule the propagation of forward (+) and backward (−) envelopes u ± at Bragg or gap-center carrier frequency with cubic nonlinearity [1,2] where H is the conserved Hamiltonian of Eqs. (1).

8

Li, Guoyi, Rajesh Kumar Neerukatti, and Aditi Chattopadhyay. "Fully Coupled Numerical Simulation for Wave Propagation in Composite Materials." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-66159.

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Composite materials are used in many advanced engineering applications because of their high specific strength and specific stiffness. However, the complex damage mechanisms and failure modes are still not well-understood and limit their wide-spread applications. It is critical to monitor the structural heath for improved understanding of damage evolution and accurate life estimation. Ultrasonic wave based structure health monitoring (SHM) technique is a promising approach and has been investigated by many researchers. However, for the techniques to be reliable, it is necessary to understand the wave propagation behavior in composites. A fully coupled numerical simulation model has been developed to understand wave propagation and dissipation in composites under different excitation frequencies. The model is based on the local interaction simulation approaches/sharp interface model (LISA/SIM), and is computationally efficient compared to traditional finite element methods. This model is used to emulate wave behavior in composites in the current work. The output sensor signals are processed using matching pursuit decomposition algorithm to study the zero-order anti-symmetric and symmetric Lamb wave modes, including attenuation effects and dispersion. The results show good agreement with published experiments. Sensitivity studies show that wave velocities and amplitudes vary significantly with changes in the material properties and stiffness.

9

Spaulding, Kevin E., and G. Michael Morris. "Hybrid mode-index/diffractive achromatic waveguide lenses." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/oam.1990.mll8.

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Conventional waveguide lenses suffer from a large amount of chromatic aberration, which limits their usable wavelength range to a relatively small interval around the design wavelength. If unstable or broadband light sources are used in the system, this chromatic dispersion can significantly affect the performance of an integrated optical device. It is shown that an achromatic waveguide lens can be made with a hybrid mode-index/diffractive doublet. With this approach it is possible to cancel the longitudinal chromatic aberration of the refractive (mode-index) lens by an appropriately chosen diffractive lens element. With typical waveguide materials, a 10 mm focal length, f/5 hybrid lens can be made to have a usable wavelength range of approximately 80 nm; this is a more than order-of-magnitude improvement over conventional mode-index and diffractive lens elements. The magnitude of the wavelength range for a hybrid achromatic lens is approximately proportional to the f/number of the lens, so it is possible to get even larger wavelength ranges with correspondingly larger f/numbers. Under certain circumstances, the power of the diffractive element in the hybrid achromatic doublet can be shown to go to zero, producing an achromatic mode-index singlet.