Solution of Travelling Wave for Nonlinear Disturbed Long-Wave System

The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.

Approximate Analytic Solution of Solitary Wave for a Class of Nonlinear Disturbed Long-Wave System

In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.

Comparative investigation of long-wave infrared generation based on ZnGeP_2 and CdSe optical parametric oscillators

Long-wave infrared （IR） generation based on type-Ⅱ （o→e＋o） phase matching ZnGeP2 （ZGP） and CdSe optical parametric oscillators （OPOs） pumped by a 2.05μm Tm,Ho：GdVO4 laser is reported. The comparisons of the birefringent walk-off effect and the oscillation threshold between ZGP and CdSe OPOs are performed theoretically and experimentally. For the ZGP OPO, up to 419 mW output at 8.04 μm is obtained at the 8 kHz pump pulse repetition frequency （PRF） with a slope efficiency of 7.6%. This ZGP OPO can be continuously tuned from 7.8 to 8.5 μm. For the CdSe OPO, we demonstrate a 64 mW output at 8.9μm with a single crystal 28 mm in length.

New Exact Solutions to Dispersive Long-Wave Equations in （2＋1）-Dimensional Space

New exact solutions expressed by the Jacobi elliptic functions are obtained to the （2＋1）-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave solutions and triangular periodic wave solutions are obtained as well.

The axisymmetric long-wave interfacial stability of core-annular flow of power-law fluid with surfactant

The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number. The interface between the two fluids is populated with an insoluble surfactant. The analytic solution for the growth rate of perturbation is obtained with long wave approximation. We are mainly concerned with the effects of shear-thinning/thickening property and interfacial surfactant on the flow stability. The results show that the influence of shear-thinning/thickening property accounts to the change of the capillary number. For a clean interface, the shear-thinning property enhances the capillary instability when the interface is close to the pipe wall. The converse is true when the interface is close to the pipe centerline. For shear-thickening fluids, the situation is reversed. When the interface is close to the pipe centerline, the capillary instability can be restrained due to the influence of surfactant. A parameter set can be found under which the flow is linearly stable.

Solitons and Waves in （2＋l）-Dimensional Dispersive Long-Wave Equation

For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the （2＋l）-dimenslonal dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns.

Research on the Changes of Celestial Tide-generating Force and the Outgoing Long-wave Radiation before the Lushan (China) M_S7.0 Earthquake

Calculation of tidal changes reveals that the MS 7. 0 Lushan County,Sichuan,China,earthquake of April 20,2013 occurred at the minimum phase point of tidal force. It indicates that the seismogenic fault on which the tidal force acts on is of thrust type. The outgoing long-wave radiation( OLR) is the energy radiating from the Earth as infrared radiation at low energy to space. According to the tidal cycle,abnormal OLR change is analyzed based on NOAA satellite data around the whole of China before and after the earthquake. The result shows that the OLR changed evidently with the tide force change.Temporally,the change went through the course: initial OLR rise → s trengthening →reaching abnormal peak → a ttenuation → r eturning to normal; in space,the abnormal area was distributed along the Longmenshan fault and evolved as: scattering→ c onvergent→ s cattering. The process is similar to the change process of rock breaking under stress loading. It indicates that the celestial tidal force can trigger earthquakes when the tectonic stress reaches the critical break point of an active fault and the OLR anomaly is proportional to the seismic tectonic stress change. It is of practical value to combine OLR and tidal force anomaly with earthquake precursor studies.

Kubelka-Munk Revised Theory for High Solar Reflectance and High Long-wave Emissivity Coatings Designing

The Kubelka-Munk revised theory was adopted to derive the mix design theory of high solar reflectance and high emissivity coatings.When the concentration of each colorant is within 20%,and the width of the coating is more than 200 μm,each colorant has enough covering power in visible and near-infrared spectral range.It can be assumed that the addition of colorants in coatings can only change the solar spectral absorption ratio rather than solar spectral scattering coefficient.The spectral scattering coefficient of coatings tends to a constant.The spectral absorption-scattering property of each colorant can be characterized through one parameter.The spectral absorption-scattering coefficient of coatings can be calculated with the multivariate linear relationship of each pigment.Moreover,the results can be expanded for high solar reflectivity and high long-wave emissivity coating preparation.The accuracy of Kubelka-Munk revised theory has been tested and verified through comparison between the calculated value and tested value of coating reflectance.

ON LONG-WAVE BREAKING Ⅰ.CONSIDERING nTH POWER BOTTOM FRICTION

Longwave breaking is the agent for many important upper ocean layer processes including the trans-fer of horizontal momentum. In a previous study on the process of longwave breaking, only linear bot-tom friction was considered.In this paper, we discuss the longwave breaking phenomena in the moregeneral case of nth power bottom friction. Using the theory of blowup of solution,the criterion for thetime and location of the longwave breaking can be obtained.

ON LONG-WAVES BREAKING Ⅱ.IN A HALF INFINITE CHANNEL WITH BOTTOM SLOPE

The propagation of long-waves, such as tidal waves from the coastal oceam into shallow estuarine waters,often produces asymmetries of veolcity and water level in time series resulting in long-wave breaking.Tian (1994) studied the mechanism of long-wave breaking in an infinite channel with constant depth,considering nth power bottom friction. This study is for the case of a half infinite channel with bottomslope, taking linear bottom friction into account. The wave breaking time and wave breaking location areestimated and the criteria for long-wave breaking in this particular case are obtained. The results obtainedcan also be e asily applied to the case considering wind stress.

STUDY OF LONG-WAVE BREAKING

This paper reports study on the mechanism of long-wave breaking in a one-dimensional open chan-nel,without bottom friction,or with linear bottom friction.In general,the wave breaking phenomenon is related to the notion of"blow-up of solution"and can be studied by using the blow-up theory of par-tial differential equations(PDE).A pair of Riemann invariants are introduced to transform the governingequations into ordinary differential equations(ODE)along the characteristic directions of the governingequations.From the properties of the solutions of the ODE,the time and location of wave breakingare estimated and the criterion of long-wave breaking for the case with linear bottom friction is obtained.

ON LONG-WAVE BREAKING Ⅳ. NUMERICAL RESULTS

This paper is a sequel to Tian’s (1994) preceding paper in which the blow-up theory was sug gested for finding an analytical (as opposed to a numerical) description of long-wave breaking. The pre sent long-wave breaking numerical results agree quite well with the author’s previous analytical and theo retical results.

Design of an all-dielectric long-wave infrared wide-angle metalens

Optical metasurfaces are two-dimensional arrays of nano-scatterers that modify optical wavefronts at subwavelength spatial resolution.They achieve the effect of focusing through phase control under a subwavelength scale,and are called metalenses.They are poised to revolutionize optics by enabling complex low-cost systems.However,there are severe monochromatic aberrations in the metasurfaces.In this paper,the coma of the long-wave infrared optical system is eliminated through a single-layer metasurface.By changing the phase function,this metalens has a numerical aperture of 0.89,a focal length of 150μm and a field of view of 120°(0.4@60 line pairs/mm)that enables diffraction-limited monochromatic imaging along the focal plane at a wavelength of 10.6μm.The designed metasurface maintains a favorable value of the modulation transfer function at different angles.This equipment can be widely used in imaging and industrial processing.

Performance Comparison of Long-Wave Infrared Imaging Spectrometer Between Dyson Form and Offner Form

In view of the difficulties in traditional long-wave infrared imaging spectrometer which is hard to realize a high signal-to-noise ratio and miniaturization as well under the weak remote sensing signal,Offner convex grating spectrometer and Dyson concave grating spectrometer,both having concentric structure,are designed and analyzed in the band of 8-12 μm. The diffraction angle expressions of the two spectrometers are obtained and the diffraction characteristics are acquired. Both of the spectrometers are designed in Zemax environment under different F-numbers and different grating constants with the same slit,spatial resolution,spectral resolution and detector. The results show that Dyson grating spectrometer possesses the advantages of higher throughput and smaller volume, and Offner grating spectrometer possesses the advantage of more accessible material and the absence of chromatic aberration. The differences between Dyson form and Offner form show that the former is a better choice in the long-wave infrared imaging spectrometer.

Kac-Moody-Virasoro Symmetry Algebra of (2+1)-Dimensional Dispersive Long-Wave Equation with Arbitrary Order Invariant

By Lie symmetry method, the Lie point symmetries and its Kac-Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given by symmetry group direct method, which can recover Lie point symmetries. Then KMV symmetry algebra of DLWE with arbitrary order invariant is also obtained. On basis of this algebra the group invariant solutions and similarity reductions are also derived.

Numerical Solutions of the Regularized Long-Wave (RLW) Equation Using New Modification of Laplace-Decomposition Method

In this paper the new modification of Laplace Adomian decomposition method (ADM) to obtain numerical solution of the regularized long-wave (RLW) equation is presented. The performance of the method is illustrated by solving two test examples of the problem. To see the accuracy of the method, L2 and L∞ error norms are calculated.

Symmetry Groups and New Exact Solutions of(2+1)-Dimensional Dispersive Long-Wave Equations

Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）- dimensional dispersive long-wave equations are obtained.

Nonlinear air dynamics of a surface effect ship in small-amplitude waves

In many existing works,the seakeeping motions and air dynamics of a surface effect ship(SES)were assumed to be linear under small-amplitude waves(wave amplitude to wave length ratio≤5%)to en-hance the computational efficiency.However,according to SES model test results,it was found that even in small-amplitude waves,the fluctuating air cushion pressure shows significantly nonlinear effects.To precisely reveal this distinctive feature,the origin of nonlinearity was carefully investigated and the air leakage was considered as the main source of nonlinearity based on mathematical analysis in this paper.The reason is that the variance of clearance height under seals is comparable to the clearance height at equilibrium state in small-amplitude waves,which makes the air leakage area intermittently equal to zero without any harmonic variance.Therefore,an efficient partial nonlinear numerical model for the SES dynamics was proposed by combining a linear frequency-domain hydrodynamic model based on the ef-ficient 2.5D methods with a nonlinear time-domain air dynamic model.The nonlinear parts of numerical results from the partial nonlinear model,including the fluctuating air pressure and midship accelerations,agree well with experimental results.The results demonstrate the effectiveness of the partial nonlinear model on the SES seakeeping performance prediction,and confirm that its nonlinearity mainly originates from the air leakage.

Optical facet coatings for high-performance LWIR quantum cascade lasers atλ∼8.5μm

We report on the performance improvement of long-wave infrared quantum cascade lasers(LWIR QCLs)by studying and optimizing the anti-reflection(AR)optical facet coating.Compared to the Al2O3 AR coat⁃ing,the Y_(2)O_(3)AR coating exhibits higher catastrophic optical mirror damage(COMD)level,and the optical facet coatings of both material systems have no beam steering effect.A 3-mm-long,9.5-μm-wide buried-heterostruc⁃ture(BH)LWIR QCL ofλ~8.5μm with Y_(2)O_(3)metallic high-reflection(HR)and AR of~0.2%reflectivity coating demonstrates a maximum pulsed peak power of 2.19 W at 298 K,which is 149%higher than that of the uncoated device.For continuous-wave(CW)operation,by optimizing the reflectivity of the Y_(2)O_(3)AR coating,the maximum output power reaches 0.73 W,which is 91%higher than that of the uncoated device.

Bridging the Fabry–Perot cavity and asymmetric Berreman mode for long-wave infrared nonreciprocal thermal emitters

The long-wave infrared band(8–14μm)is essential for several applications,such as infrared detection,radiative cooling,and near-field heat transfer.However,according to Kirchhoff’s law,the intrinsic balance between thermal absorption and emission limits the further improvement of photon energy conversion and thermal management.Thus,breaking Kirchhoff’s balance and achieving nonreciprocal thermal radiation in the long-wave infrared band are necessary.Most existing designs for nonreciprocal thermal emitters rely on grating or photonic crystal structures to achieve nonreciprocal thermal radiation at narrow peaks,which are relatively complex and typically realize bands larger than 14μm.Here,a sandwich structure consisting of an epsilon-nearzero(ENZ)magneto-optical layer(MOL),a dielectric layer(DL),and a metal layer is proposed to achieve a strong nonreciprocal effect in the long-wave infrared band,which is mainly attributed to the strengthening of the asymmetric Berreman mode by the Fabry–Perot cavity.In addition,the impact of the incident angle,DL thickness,and DL refractive index on the nonreciprocal thermal radiation has been investigated.Moreover,by replacing the ENZ MOL with the gradient ENZ MOL,the existence of the DL can further improve the nonreciprocity of the broadband nonreciprocal thermal radiation.The proposed work promotes the development and application of nonreciprocal energy devices.