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Dynamics and properties of breathers for the modified Korteweg–de Vries equations with negative cubic nonlinearities are studied. While breathers and rogue waves are absent in a single component waveguide for the negative nonlinearity case, coupling can induce regimes of modulation instabilities. Such instabilities are correlated with the existence of rogue waves and breathers. Similar scenarios have been demonstrated previously for coupled systems of nonlinear Schrödinger and Hirota equations. Both real- and complex-valued modified Korteweg–de Vries equations will be treated, which are applicable to stratified fluids and optical waveguides, respectively. One special family of breathers for coupled, complex-valued equations is derived analytically. Robustness and stability of breathers are studied computationally. Knowledge of the growth rates of modulation instability of plane waves provides an instructive prelude on the robustness of breathers to deterministic perturbations. A theoretical formulation of the linear instability of breathers will involve differential equations with periodic coefficient, i.e., a Floquet analysis. Breathers associated with larger eigenvalues of the monodromy matrix tend to suffer greater instability and increased tendency of distortion. Predictions based on modulation instability and Floquet analysis show excellent agreements. The same trend is obtained for simulations conducted with random noise disturbances. Linear approaches like modulation instabilities and Floquet analysis, thus, generate a very illuminating picture of the nonlinear dynamics. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation possesses doubly periodic solutions expressible in terms of the Jacobi elliptic functions. Such solutions can be realized through doubly periodic patterns observed in experiments in fluid mechanics and optics. Stability and robustness of these doubly periodic wave profiles in the focusing regime are studied computationally by using two approaches. First, linear stability is considered by Floquet theory. Growth will occur if the eigenvalues of the monodromy matrix are of a modulus larger than unity. This is verified by numerical simulations with input patterns of different periods. Initial patterns associated with larger eigenvalues will disintegrate faster due to instability. Second, formation of these doubly periodic patterns from a tranquil background is scrutinized. Doubly periodic profiles are generated by perturbing a continuous wave with one Fourier mode, with or without the additional presence of random noise. Effects of varying phase difference, perturbation amplitude, and randomness are studied. Varying the phase angle has a dramatic influence. Periodic patterns will only emerge if the perturbation amplitude is not too weak. The growth of higher-order harmonics, as well as the formation of breathers and repeating patterns, serve as a manifestation of the classical problem of Fermi–Pasta–Ulam–Tsingou recurrence. [ABSTRACT FROM AUTHOR]

It is widely acknowledged that greenhouse gases (GHG) like carbon dioxide (CO2), nitrous oxide (N2O), and methane (CH4) play a key role in the development of global climate change. 17% of China's GHG came from the agricultural industry. For China's future development, it is essential to investigate low-carbon emission paths in planting fields, as one of the key components of agriculture. In this study, the IPCC method was used to estimate the total carbon emission from cultivation in Eastern China. The Tapio decoupling model was used to study the relationship between economic growth and carbon emission. An extended STIRPAT stimulus model was established to predict the carbon emission of the planting industry in East China with three development paths. The results show that carbon emission in East China has shown a fluctuating downward trend with a peak in 1999, which has strong decoupling characteristics with economic growth. Adjusting agricultural structure and raising the mechanization rate can remarkably reduce agricultural carbon emission. Compared to 2020, carbon emission in 2035 will decrease by 12.50%, 13.68%, and 14.32% with Baseline, Low-carbon, and Enhanced Low-carbon scenarios, respectively. Effective measures such as optimizing planting structure by adjusting rice area, promoting intensive mechanization, and improving fertilizer use efficiency can reduce carbon emission actively. [ABSTRACT FROM AUTHOR]

A multiscale modeling method is proposed to derive effective thermal conductivity in two-phase graded particulate composites. In the particle-matrix zone, a graded representative volume element is constructed to represent the random microstructure at the neighborhood of a material point. At the steady state, the particle’s averaged heat flux is solved by integrating the pairwise thermal interactions from all other particles. The homogenized heat flux and temperature gradient are further derived, through which the effective thermal conductivity of the graded medium is calculated. In the transition zone, a transition function is introduced to make the homogenized thermal fields continuous and differentiable. By means of temperature boundary conditions, the temperature profile in the gradation direction is solved. When the material gradient is zero, the proposed model can also predict the effective thermal conductivity of uniform composites with the particle interactions. Parametric analyses and comparisons with other models and available experimental data are presented to demonstrate the capability of the proposed method. [ABSTRACT FROM AUTHOR]

A crossed laser and molecular beam photofragmentation apparatus is described. The apparatus is equipped with a rotatable molecular beam source and a translationally movable ultrahigh vacuum mass spectrometer for time-of-flight (TOF) measurements. Using this apparatus we have measured the TOF spectra of S and CS resulting from the photofragmentation processes, CS2+hν(193 nm)→CS(X,v)+S(1D or 3P). The translational energy distributions of photofragments derived from the S and CS TOF spectra are in good agreement. This observation, together with the finding that the TOF spectra of S and CS are independent of laser power in the 25–150 mJ range, shows that the further absorption of a laser photon by CS to form C(3P)+S(3P) within the laser pulse is insignificant. The TOF spectra of S obtained at electron ionization energies of 20 and 50 eV are indiscernible, indicating that the contribution to the TOF spectrum of S from dissociative ionization of CS is negligible at electron impact energies ≤50 eV. The thermochemical thresholds for the S(1D) and S(3P) channels are determined to be 18.7 and 45.0±0.4 kcal/mol, respectively, consistent with literature values. Structures found in the translational energy distribution can be correlated with vibrational structures of CS(X,v=0–5) associated with the S(1D) channel. The translational energy distribution supports the previous observation that the vibrational state distribution of CS(X,v) is peaked at v=3. The TOF experiment is also consistent with the S(3P)/S(1D) ratio of 2.8±0.3 determined in a recent vacuum ultraviolet laser induced fluorescence measurement on the S photofragment. Photofragments from CS2 clusters are observed at small laboratory angles with respect to the CS2 beam direction and are found to have velocity distributions peaked at the CS2 cluster beam velocity. [ABSTRACT FROM AUTHOR]

We have measured the translational energy releases of the laser photodissociation processes CH3SCH3+hν (193 nm)→CH3+CH3S [process (1)] and CH3SCH2+H [process (2)]; and CH3S+hν (193 nm)→S+CH3 [process (3)]. The onsets of the translational energy distributions for photofragments of processes (1) and (2) allow the direct determination of 74.9±1.5 and 91±2.5 kcal/mol for the dissociation energies of the CH3–SCH3 and H–CH2SCH3 bonds at 0 K, respectively. The threshold observed for S formed by process (3) is consistent with the conclusion that the production of S(3P) is small compared to S(1D). The photoelectron–photoion coincidence (PEPICO) spectra for CH3SCH+3, CH3SCH+2, CH3S+ (or CH2SH+ ), and CH2S+ resulting from photoionization of CH3SCH3 have been measured in the wavelength region of 900–1475 Å. The PEPICO study allows the construction of a detailed breakdown diagram for the formation of CH3SCH+2, CH3S+ (or CH2SH+ ), and CH2S+ from energy-selected CH3SCH+3 ions. [ABSTRACT FROM AUTHOR]

The kinetic energy releases of the photodissociation processes, CH3SH+hν (193 nm)→CH3+SH, CH3S+H, and CH2S+H2, have been measured using the time-of-flight mass spectrometric method. These measurements allow the direct determination of the dissociation energies for the CH3–SH and CH3S–H bonds at 0 K as 72.4±1.5 and 90±2 kcal/mol, respectively. The further dissociation of SH according to the process SH+hν (193 nm)→S+H has also been observed. The appearance energy (AE) of S produced in the latter process is consistent with the formation of S(3P)+H. The photoelectron–photoion coincidence (PEPICO) spectra for CH3SH+, CH3S+ (or CH2SH+), and CH2S+ from CH3SH have been measured in the wavelength range of 925–1460 Å. The PEPICO measurements make possible the construction of the breakdown diagram for the unimolecular decomposition of internal-energy-selected CH3SH+ in the range of 0–83 kcal/mol. The AE measured for CH2S+ is consistent with the conclusion that the activation energy is negligible for 1,2-H2 elimination from CH3SH+. [ABSTRACT FROM AUTHOR]