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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]

This paper investigates the mechanical behaviour of a bi-layered panel containing many particles in one layer and demonstrates the size effect of particles on the deflection. The inclusion-based boundary element method (iBEM) considers a fully bounded bi-material system. The fundamental solution for two-jointed half spaces has been used to acquire elastic fields resulting from source fields over inclusions and boundary-avoiding multi-domain integral along the interface. Eshelby's equivalent inclusion method is used to simulate the material mismatch with a continuously distributed eigenstrain field over the equivalent inclusion. The eigenstrain is expanded at the centre of the inclusion, which provides tailorable accuracy based on the order of the polynomial of the eigenstrain. As a single-domain approach, the iBEM algorithm is particularly suitable for conducting virtual experiments of bi-layered composites with many defects or reinforcements for both local analysis and homogenization purposes. The maximum deflection of solar panel coupons is studied under uniform vertical loading merged with inhomogeneities of different material properties, dimensions and volume fractions. The size of defects or reinforcements plays a significant role in the deflection of the panel, even with the same volume fraction, as the substrate is relatively thin. [ABSTRACT FROM AUTHOR]

Modulation instability, breather formation, and the Fermi–Pasta–Ulam–Tsingou recurrence (FPUT) phenomena are studied in this article. Physically, such nonlinear systems arise when the medium is slightly anisotropic, e.g., optical fibers with weak birefringence where the slowly varying pulse envelopes are governed by these coherently coupled Schrödinger equations. The Darboux transformation is used to calculate a class of breathers where the carrier envelope depends on the transverse coordinate of the Schrödinger equations. A "cascading mechanism" is utilized to elucidate the initial stages of FPUT. More precisely, higher order nonlinear terms that are exponentially small initially can grow rapidly. A breather is formed when the linear mode and higher order ones attain roughly the same magnitude. The conditions for generating various breathers and connections with modulation instability are elucidated. The growth phase then subsides and the cycle is repeated, leading to FPUT. Unequal initial conditions for the two waveguides produce symmetry breaking, with "eye-shaped" breathers in one waveguide and "four-petal" modes in the other. An analytical formula for the time or distance of breather formation for a two-waveguide system is proposed, based on the disturbance amplitude and instability growth rate. Excellent agreement with numerical simulations is achieved. Furthermore, the roles of modulation instability for FPUT are elucidated with illustrative case studies. In particular, depending on whether the second harmonic falls within the unstable band, FPUT patterns with one single or two distinct wavelength(s) are observed. For applications to temporal optical waveguides, the present formulation can predict the distance along a weakly birefringent fiber needed to observe FPUT. [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]

This paper investigates the stress concentration of an adhesive material containing a micro air void subjected to a harmonic dynamic surface load. The elastodynamic Green's function was used to derive the elastic field and take into account the boundary effect. Using the equivalent inclusion method, the micro air void was replaced by the matrix but an eigenstrain and fictitious force were introduced to simulate the material mismatch. Coupling with the boundary element method, one can assemble a linear equation system from which the microvoid and boundary effect are fully taken into account and the eigenstrain, fictitious force, and unknown boundary responses can be calculated. Therefore, the elastodynamic field can be obtained from the equivalent inclusion problem with the prescribed boundary conditions for any bounded domain. The results have been verified and compared with the finite-element simulation for a static case, the classic Eshelby solution for a low-frequency case, and the traditional boundary element method for a full time-harmonic case. A parametric study of stress concentration factors in the adhesive for one void with various depths and frequencies was performed. This method can be extended to general cases of many particles embedded in a matrix with arbitrary boundary conditions. [ABSTRACT FROM AUTHOR]

A strain sensor using chain-structured ferromagnetic particles (FPs) in a multi-walled carbon nanotube (MWCNT)/polydimethylsiloxane (PDMS) nanocomposite was fabricated under a magnetic field and its strain sensitivity was evaluated at different material proportions. When the proportion of MWCNTs that are well dispersed in PDMS is higher than the percolation threshold, the strain sensitivity reduces with the increase of MWCNTs, in general; whereas a higher volume fraction of FPs produces a higher strain sensitivity when the chain-structure of FPs sustains. The mechanisms causing this interesting phenomenon have been demonstrated through the microstructural evolution and micromechanics-based modeling. These findings indicate that an optimal design of the volume fraction of FPs and MWCNTs exists to achieve the best strain sensitivity of this type of sensors. It is demonstrated that the nanocomposites containing 20 vol.% of nickel particles and 0.35 wt.% MWCNTs exhibit a high strain sensitivity of ~80. [ABSTRACT FROM AUTHOR]

The equivalent inclusion method is presented to derive the Stokes flow of multiple drops moving in a viscous fluid at a small Reynolds number. The drops are replaced by inclusions with the same viscosity as the fluid, but an eigenstrain rate field that is a fictitious nonmechanical strain rate field is introduced to represent the viscosity mismatch between each drop and the matrix fluid. The velocity and pressure fields can be solved by considering the body force and eigenstrain rate on the inclusions with the Green's function technique. When one spherical drop is considered, the solution recovers the closed-form classic solution. This method is versatile and can be used in the simulation of a many-body system with different drop size, elongation ratio, and viscosity. Numerical examples demonstrate the capability and accuracy of the proposed formulation and illustrate particles' rotation and motion caused by particle interactions. [ABSTRACT FROM AUTHOR]

By means of a fundamental solution for a single inhomogeneity embedded in a function- ally graded material matrix, a self-consistent model is proposed to investigate the effective thermal conductivity distribution in a functionally graded particulate nanocomposite. The "Kapitza thermal resistance" along the interface between a particle and the matrix is simulated with a perfect interface but a lower thermal conductivity of the particle. The results indicate that the effective thermal conductivity distribution greatly depends on Kapitza thermal resistance, particle size, and degree of material gradient. [ABSTRACT FROM AUTHOR]

This work investigates the elastic fields which develop in an overlay bonded to a rigid substrate when the system is subjected to thermally induced stress. A two-dimensional solution of the displacement field is derived for periodic discontinuities distributed in a hot mix asphalt overlay bonded to a rigid pavement, where the length of the pavement before cracking develops is much larger than its layer thickness. A series form solution is obtained, requiring calibration due to the limitation of the basis functions used. The formulation allows thermal cracks of variable depth to be considered, and its accuracy is verified through comparisons with numerical solutions obtained with ABAQUS. Energy release rates are calculated from the model for top-down plane strain cracking and three-dimensional channeling. By comparing the energy release rates with the fracture toughness of the overlay, conditions for crack initiation and an estimation of crack depth for a given temperature change can be estimated. Although several simplifying assumptions are made in the current approach, it is shown to be more general and therefore more widely applicable as compared to existing closed-form solutions. The solutions are valuable to the pavement analyst who seeks to understand the general mechanisms of thermally induced pavement deterioration and for the researcher wishing to perform early stage verification of more complex pavement models. [ABSTRACT FROM AUTHOR]

Coupled magnetoelastic behaviour is investigated for two-phase composites containing randomly dispersed ferromagnetic particles under both magnetic and mechanical loading. The pair-wise particle interactions for magnetic field and elastic field are first defined by the solution for two particles embedded in the infinite domain, which is explicitly solved by the Green's function technique. By integrating the interactions from all other particles in the representative volume element, the homogenized magnetic and elastic fields are then obtained. Effective magnetostriction due to the magnetic interaction force is further derived. Without consideration of magnetic loading, this micromechanical model provides an effective elasticity with the pair-wise particle interactions. By dropping the interaction term, this model is reduced into Mori–Tanaka's model. Finally, magnetoelasticity is numerically solved by considering the magnetomechanical coupling effect. It is predicted that the effective Young's modulus and shear modulus decrease along with the increase of magnetic loading for random composites. [ABSTRACT FROM AUTHOR]

A micromechanical damage model is developed for two-phase functionally graded materials (FGMs) considering the interracial debonding of particles and pair-wise interactions between particles. Given an applied mechanical loading on the upper and lower boundaries of an FGM, in the particle matrix zones, interactions from all other particles over the representative volume element (RVE) are integrated to calculate the homogenized elastic fields. A transition function is constructed to solve the elastic field in the transition zone. The progressive damage process is dependent on the applied loading and is represented by the debonding angles which are obtained from the relation between particle stress and interracial strength. In terms of the elastic equivalency, debonded, isotropic particles are replaced by perfectly bonded, orthotropic particles. Correspondingly, the effective elasticity distribution in the gradation direction is solved. The computational implementation is discussed and numerical simulations are provided to illustrate the capability of the proposed model. [ABSTRACT FROM AUTHOR]

The mechanical properties of periodic composites containing identical spherical particles are investigated using the principles of micromechanics and homogenization procedures. The averaged strain and stress fields are derived in terms of an eight-particle interaction. The effective elasticity with the cubic symmetry tensor is explicitly obtained. If the interaction term is dropped, then one recovers the conventional Mori–Tanaka model. With further approximations, the dilute model and the self-consistent model can also be obtained within the proposed framework. It is observed that the particle interactions make no contribution to the effective bulk modulus, a result that is consistent with other models and experiments for composites with cubic lattices. [ABSTRACT FROM AUTHOR]

Background: The finite element method (FEM) is a powerful mathematical tool to simulate and visualize the mechanical deformation of tissues and organs during medical examinations or interventions. It is yet a challenge to build up an FEM mesh directly from a volumetric image partially because the regions (or structures) of interest (ROIs) may be irregular and fuzzy. Methods: A software package, ImageParser, is developed to generate an FEM mesh from 3-D tomographic medical images. This software uses a semi-automatic method to detect ROIs from the context of image including neighboring tissues and organs, completes segmentation of different tissues, and meshes the organ into elements. Results: The ImageParser is shown to build up an FEM model for simulating the mechanical responses of the breast based on 3-D CT images. The breast is compressed by two plate paddles under an overall displacement as large as 20% of the initial distance between the paddles. The strain and tangential Young's modulus distributions are specified for the biomechanical analysis of breast tissues. Conclusion: The ImageParser can successfully exact the geometry of ROIs from a complex medical image and generate the FEM mesh with customer-defined segmentation information. [ABSTRACT FROM AUTHOR]

A micromechanics-based model with particle interaction has been developed to study the effective elastic properties of chain-structured ferromagnetic composites subject to both magnetic and mechanical loading. Magnetomechanical coupled behavior is numerically simulated and magnetic-field-dependent elasticity is calculated using the Green’s function technique in a manner such that microstructure evolution is considered. Due to the magnetic angular momentum, the effective shear modulus of the composites increases much faster than the effective Young’s modulus as the magnetic field increases. Two mechanisms resulting in magnetic-field-dependent elasticity are demonstrated. [ABSTRACT FROM AUTHOR]

A micromechanics-based composite model is developed for the elastic behavior and its modulus evolution of cirrhotic human liver correlated with different pathological stages. Microstructurally, the cirrhotic liver is hypothesized to be pathologically elastic nodules embedded in the soft tissue matrix whose hyperelastic behavior is controlled by the Veronda-Westmann model. Under finite deformation, the total strain energy of the liver is collected through the combination of that in nodule particles and that in the tissue matrix. The overall constitutive relation of the pathological liver can further be established through the nonlinear hyperelasticity theory. Predictions of the elastic modulus and its pathological evolution are compared with available experimental data. [ABSTRACT FROM AUTHOR]

Three-wave (triad) resonance in a uniformly stratified fluid is investigated as a case study of energy transfer among oscillatory modes. The existence of a degenerate triad is demonstrated explicitly, where two components have identical group velocity. An illuminating example is a resonance involving waves from modes 1, 3, 5 families, but many other combinations are possible. The physical applications and nonlinear dynamics of rogue waves derived analytically in the literature are examined. Exact solutions with four free parameters (two related to the amplitudes of the background plane waves, two related to the frequencies of slowly varying envelopes) describe motions localized in both space and time. The differences between rogue waves of the degenerate versus the nondegenerate cases are highlighted. The phase and profile of the degenerate case rogue waves are correlated. The volume or energy of the rogue wave (defined as the total extent or energy contents of the fluid set in motion for the duration of the rogue wave) may change drastically, if the wave envelope parameters vary. Pulsating modes (breathers) have been studied previously by layered-fluid and modified Korteweg-de Vries models. Here we extend the consideration to stratified fluids but for the simpler case of nondegenerate triads. Instabilities of fission and fusion of breathers are confirmed computationally with Floquet analysis. This knowledge should prove useful for energy transfer processes in the oceans.

Evolution of resonant three-wave interaction is governed by quadratic nonlinearities. While propagating localized modes and inverse scattering mechanisms have been studied, transient states such as rogue waves and breathers are not fully understood. Modulation instability modes can trigger growth of disturbances and the eventual development of breathers. Here we study computationally the dynamics beyond the first formation of breathers, and demonstrate repeating patterns of breathers as a manifestation of the Fermi-Pasta-Ulam-Tsingou recurrence (FPUT). While nonlinearity governs the actual dynamics, the range of wave numbers for modulation instability remains a useful indicator. Depending on the stability characteristics of the fundamental mode and the higher-order harmonics ("sidebands"), "regular" and "staggered" FPUT patterns can arise. A "cascading mechanism" provides analytical verification, as the fundamental and sideband modes attain the same magnitude at one particular instant, signifying the first occurrence of a breather. A triangular spectrum is also computed, similar to experimental observations of optical pulses. Such spectra can elucidate the spreading of energy among the sidebands and components of the triad resonance. The concept of "effective energy" is examined and the eigenvalues of the inverse scattering mechanism are computed. Both approaches are utilized to correlate with the occurrence of regular or staggered FPUT. These numerical and analytical studies can enhance our understanding of wave interactions in fluid mechanics and optics.

The understanding of hematopoietic stem cell (HSC) emergence is important to generate HSCs from pluripotent precursors. However, integrated signaling network that regulates the niche of nascent HSCs remains unclear. Herein, we uncovered a novel role of TGF-β1 in the metabolic niche of HSC emergence using the tgf-β1b -/- zebrafish. Our findings first showed that Tgf-β1 transcripts were enriched in the nascent HSCs. Loss of tgf-β1b caused a decrease of nascent HSCs within the aorta-gonad-mesonephros. Moreover, tgf-β1b + cells were runx1 + HSCs and underwent an endothelial-to-hematopoietic-transition process. Although the autocrine of Tgf-β1 in HSCs rather than endothelial cells was highly demanded to regulate HSC generation, we found that tgf-β1b promoted HSC emergence through the endothelial c-Jun N-terminal kinase/c-Jun signaling. Chromatin immunoprecipitation (ChIP)-sequencing data showed that tgf-β1b/c-Jun targeted g6pc3 of FoxO signaling to promote gluconeogenesis and maintain a high glucose level in the niche. Furthermore, loss of tgf-β1b increased the endoplasmic-reticulum stress and oxidative stress by disturbing metabolic homeostasis. Adding a low dose of TGF-β1 protein could promote the differentiation of mouse embryonic stem cells towards HSCs in vitro. Altogether, our study provided insights into a new feature of TGF-β1 in the regulation of glucose metabolism and nascent HSC niche, which may contribute to therapies of hematological malignancies.

Various types of stressors were given to different groups of animals to examine their effects on the mesostriatal and mesolimbic serotonergic pathways. Results indicate that shock-induced fighting experience preferentially decreased serotonin (5-HT) levels in the dorsal raphe and striatum, while air puff stimulation selectively lowered 5-HT and 5-hydroxyindoleacetic acid (5-HIAA) contents in the median raphe and hippocampus. Both immobilization and light footshock stress have a more consistent effect on both serotonergic systems. These results suggest that different stressors have differential influences upon central 5-HT neurons and, other than anatomical differentiation, these serotonergic neurons are not homogeneous with respect to their responses to stress either.