Investigations on nonlinear optics are active, with the applications in the modulators, fiber lasers, optical sensors, etc. In this paper, we focus our attention on a system for the ultra-short ...pulses in an inhomogeneous multi-component nonlinear optical medium. Starting from the existing Lax pair and one-fold Darboux transformation (DT), we construct the N-fold DT of that system, which involves N distinct spectral parameters, where N is a positive integer. The N-fold generalized DT with one spectral parameter is obtained through resorting to the Taylor-series-expansion coefficients of a special solution to that Lax pair. Double-pole soliton solutions of that system are derived via that N-fold generalized DT with N=2. With the aid of the N-fold DT, an N-fold Darboux matrix is constructed, based on which the multi-pole soliton solutions in the determinant form with respect to the electromagnetic field E are determined. Graphically, we find that those double-pole soliton solutions are a kind of the bound-state soliton solutions which represent the elastic interactions between the two solitons. Effects of the coefficients in that system on the double-pole soliton are shown via choosing the trigonometric, linear and quadratic functions. Furthermore, we present the triple-pole soliton and quadruple-pole soliton with respect to E. Our results might be useful in understanding the ultra-short pulses in the nonlinear optical media.
It is very important to create novel topologies and improve structural complexity for covalent organic frameworks (COFs) that might lead to unprecedented properties and applications. Despite the ...progress achieved over the past decade, the structural diversity and complexity of COFs are quite limited. In this Communication, we report the construction of COFs bearing three different kinds of pores through the heterostructural mixed linker strategy involving the condensation of a D 2h -symmetric tetraamine and two C 2-symmetric dialdehydes of different lengths. The complicated structures of the triple-pore COFs have been confirmed by powder X-ray diffraction and pore size distribution analyses.
Nonlinear evolution equations (NLEEs) are seen in such fields as fluid dynamics, plasma physics and optics. A (3+1)-dimensional time-dependent-coefficient Boiti-Leon-Manna-Pempinelli equation is ...investigated in this paper. Via the logarithmic transformation on non-zero background, a bilinear form is derived. Via the bilinear form, a bilinear-Bäcklund transformation with some solutions is acquired, while the one-soliton, two-soliton and multiple soliton solutions with two different nonlinear dispersion relations are worked out. On some non-zero backgrounds, multi-kink solutions are derived. Via the complex conjugation, half-periodic kink solutions are obtained.
•A (3+1)-dimensional time-dependent-coefficient Boiti-Leon-Manna-Pempinelli equation is investigated in this paper.•Via the Hirota method, a bilinear form of that equation is derived.•A set of bilinear Bäcklund transformations have been obtained.•Soliton solutions on non-zero backgrounds with two cases of nonlinear dispersion relations are derived.•With some backgrounds, multi-kink and half-periodic kink solutions are derived.
Nonlinear differential-difference equations appear in optics, condensed matter physics, plasma physics and other fields. In this paper, we investigate a nonlinear differential-difference hierarchy ...relevant, in the case of θ=0, to the Ablowitz-Ladik equation, where θ=0,1. That hierarchy is obtained via a discrete spectral problem and the associated discrete spectral problem. When θ=1, Lax pair of the first nonlinear differential-difference system in that hierarchy is obtained. When θ=1, conservation laws and N-fold Darboux transformation of the first nonlinear differential-difference system in that hierarchy are derived with the aid of that Lax pair, where N is a positive integer. When θ=1, explicit exact solutions of that system are determined via that N-fold Darboux transformation. Discrete one soliton and interaction between the discrete one soliton and one breather-like wave are graphically depicted.
•A new nonlinear differential-difference hierarchy is constructed.•Conservation laws and N-fold Darboux transformation of the first system in that hierarchy are derived.•Certain explicit exact solutions of that system are obtained.•Discrete one soliton and interaction between the discrete one soliton and one breatherlike wave are graphically depicted.
•Novel fin structures are proposed for heat transfer enhancement of PCM.•Visualization of the melting process of PCM within the BTMS is presented.•Thermal management performance of PCM-Fin based BTMS ...is evaluated.
Phase change materials (PCM) based battery thermal management system (BTMS) usually suffers from the low thermal conductivity of PCM. In this paper, novel fin structures which consist of longitudinal fins and cylindrical rings are proposed for heat transfer enhancement. Experiments are firstly designed to compare the thermal performance of different BTMSs. Results demonstrate that the PCM-Fin system shows superior performance over the pure battery system and the PCM system. Numerical simulations are also conducted based on the model validation with the experimental data to reveal the underlying mechanisms. It is found that fin structures not only increase the heat transfer area but also introduce a thermal conductive network within the PCM, which contributes positively to the improvement of thermal performance of the battery. Moreover, the effects of the position of rings, the number of rings and fins, and the heat generation rate on the thermal management performance are evaluated. Results show that the optimal numbers for rings and fins are 1 and 8, respectively, and the recommended dimensionless distance between ring and battery is 0.2. It is also found that the PCM-Fin system can control the temperature rise of the battery even under the heat generation rate of 20 W.
Covalent organic frameworks (COFs) are crystalline porous materials bearing microporous or mesoporous pores. The type and size of pores play crucial roles in regulating the properties of COFs. In ...this work, a novel COF, which bears two different kinds of ordered pores with controllable sizes: one within microporous range (7.1 Å) and the other in mesoporous range (26.9 Å), has been constructed via one-step synthesis. The structure of the dual-pore COF was confirmed by PXRD investigation, nitrogen adsorption–desorption study, and theoretical calculations.
Robust ceramic color converters withstanding strong laser irradiations have recently drawn great attention for laser‐driven white lighting. However, the local emission within the incident laser spot ...usually expands to the whole surface area of the ceramics, which definitely makes it hard to achieve white light with high luminance and high directionality. Herein, a new strategy is proposed to solve the problem by elaborately introducing uniform spherical pores (diameter of ≈2 µm) into the phosphor ceramics with controlled contents from 8 to 24.6 vol%. The well‐distributed pores, acting as light scattering centers, enable reduction of the luminescent spot size greatly but without any losses in conversion efficiency. By using the high‐scattering ceramic color converters with 15% porosity, the light spot diameter is decreased by 46% and the central illuminance is increased by 156%. Moreover, laser‐driven white light with an enhanced beam directionality and uniformity is also achieved. A superhigh luminous flux of 7199 lm is realized by using this promising color converter in a rotary mode. The designed high‐scattering ceramics with controllable microstructures show great potential for use in extra‐high luminance laser‐driven lighting and projection.
Phosphor ceramics stand out in laser‐driven white lighting. A quite different design strategy is proposed to construct high‐light‐scattering ceramics. The beam expansion ratio is decreased from 3.14 to 1.68 and the center beam illuminance is increased by 156% in the highly scattering sample. Eventually, truly quasi‐point laser‐driven white light with high luminance and high directionality is achieved.
Ethylene-vinyl acetate copolymer (EVA) was added at different contents to the thermoplastic polyurethane (TPU) matrix to form a non-compatible blending system, and foaming materials with high pore ...density were prepared using the supercritical carbon dioxide extrusion method. The influence of the phase morphology and crystal morphology of the TPU/EVA blend on its foaming behavior was studied. The results show that EVA changed the phase morphology and crystal morphology of the blends, leading to the improved melt viscosity and crystallinity of the blend system. At the same time, interfacial nucleation increases the density of cells and decreases the cell thickness and size, which is beneficial for improving the foaming properties of the blends. For the EVA content of 10% (mass fraction), the cell size is small (105.29 μm) and the cell density is the highest (3.74 × 10
cells/cm
). Based on the TPU/EVA phase morphology and crystal morphology, it is found that the sea-island structure of the blend has better foaming properties than the bicontinuous structure.
Investigated in this paper is an extended (3+1)-dimensional Kadomtsev-Petviashvili equation. We determine the
N
-soliton solutions of that equation via an existing bilinear form, and then construct ...the
M
th-order breather and
H
th-order lump solutions from the
N
-soliton solutions using the complex conjugated transformations and long-wave limit method, where
N
,
M
, and
H
are the positive integers. In addition, we develop the hybrid solutions composed of the first-order breather and one soliton, the first-order lump and one soliton, as well as the first-order lump and first-order breather. Through those solutions, we demonstrate the (1) one breather or lump, (2) interaction between the two breathers or lumps, (3) interaction between the one breather and one soliton, (4) interaction between the one lump and one soliton, and (5) interaction between the one lump and one breather. We observe that the amplitude, shape, and velocity of the one breather or lump remain unchanged during the propagation. We also find that the amplitudes, shapes, and velocities of the solitons, breathers, and lumps remain unchanged after the interactions, suggesting that those interactions are elastic.
Systematically tuning the spatial environment around the active sites of synthetic catalysts is a difficult challenge. Here, we show how this can be accomplished in the pores of multicomponent ...metal–organic frameworks. This relies on embedding a catalytic unit in a pore of the MUF-77 framework and then tuning its environment by introducing different functional groups to the surrounding linkers. This approach benefits from the structural regularity of MUF-77, which places each component in a precise location to circumvent disorder. Prolinyl groups, which are catalytically competent toward asymmetric aldol reactions, were selected as the catalytic unit. Since every prolinyl group is positioned in an identical environment, correlations between the pore architecture and the activity of these single-site catalysts can be elucidated. Systematic engineering of the pore structure, which is achieved by installing modulator groups on the framework linkers, impacts on the reaction rate and the enantiomeric excess of the aldol products. Furthermore, the spatial environment around the proline catalyst can override its innate stereochemical preference to dictate the preferred enantiomer of the reaction product. These results offer a new way to design three-dimensional active site environments for synthetic catalysts.
