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In this paper, we investigate the influence of small disturbance on the statistical behaviors of fluid particles of the three-dimensional divergence-free hexagonal Beltrami flow from a Lagrangian point of view. Due to the butterfly-effect, numerical noise increases exponentially for chaotic dynamic systems. Thus, a powerful strategy, namely, the clean numerical simulation, is used to gain reliable/convergent trajectory in a long enough interval of time. It is found that the statistics of chaotic trajectory of fluid particles are stable in some cases, corresponding to the so-called "normal-chaos," but unstable in some cases, i.e., rather sensitive to small disturbances, corresponding to the so-called "ultra-chaos," which is a new concept proposed currently. Obviously, an ultra-chaotic trajectory of fluid particles is at a higher disorder than a normal chaotic trajectory. In theory, it is impossible to repeat any experimental/numerical results of an ultra-chaotic system even by means of statistics, but reproducibility is a corner-stone of our modern science paradigm. Hence, the wide existence or non-existence of ultra-chaos has a very important meaning. In this paper, we illustrate that the ultra-chaotic trajectories of fluid particles indeed widely exist in a hexagonal Beltrami flow field. This fact is important for deepening our understanding of chaotic dynamic systems and revealing the limitations of our paradigm of modern science. [ABSTRACT FROM AUTHOR]

In this paper, the homotopy renormalization method (HTR) is compared with the homotopy analysis method (HAM), an analytical approximation technique for highly nonlinear problems. Four problems in fluid mechanics, including the Blasius viscous flow, magnetohydrodynamic flow, free-convective boundary-layer flow, and Von Kármán swirling viscous flow, are used for detailed comparison. It is found that the HAM approximations are much more accurate than the HTR approximations at the same order. Furthermore, higher-order approximations with smaller errors can be obtained relatively simply by the HAM, while the HTR struggles in such scenarios. All of these confirm the superiority of the HAM for highly nonlinear problems in fluid mechanics. • The homotopy renormalization method (HTR) is compared with the homotopy analysis method (HAM). • The HAM is more convenient and accurate than the HTR to obtain analytic solution. • Four problems in fluid mechanics are used to illustrate the superiority of the HAM. [ABSTRACT FROM AUTHOR]

Due to its small mass and eccentricity, the motion of a piece of debris in low Earth orbit (LEO) may be chaotic. This paper demonstrates that ultra-chaos widely exists in the case of a square thin plate in LEO with a center of mass (COM) that is initially displaced from the axis of symmetry. Chaotic systems are well-known for their sensitive dependence on initial conditions, though their statistical properties are usually insensitive to small disturbances. However, a recent concept called ultra-chaos has been introduced to describe chaotic systems whose statistics are sensitive to even tiny disturbances. This paper demonstrates that ultra-chaos is widely exists in a square thin plate in LEO with a displaced COM from the axis of symmetry. The results show that an ultra-chaotic plate trajectory exhibits higher disorder than that of a normal plate, with a position deviation that can be two orders of magnitude larger than that of a normal-chaotic subsystem. Distinct from earlier findings concerning ultra-chaotic systems, the present study uncovers the manifestation of ultra-chaos in a physically constrained system devoid of periodic boundaries. Prior investigations of ultra-chaotic systems have featured at least one periodic boundary or lacked a physical boundary. The new concept of ultra chaos provides a plausible explanation as to why space debris can spread to a vast area, as most pieces of debris have a displaced COM. [ABSTRACT FROM AUTHOR]

Understanding the trajectories of passive particles, such as drifters and/or pollutants in geophysical flows, is crucial due to the mostly chaotic nature of such flows. Recently, a novel concept, namely ultra-chaos, has been introduced, which exhibits statistics instability with respect to small disturbances, in contrast to a normal-chaos that has statistics stability. However, quite a few ultra-chaotic systems have been reported to date. This study aims to analyze the trajectories of passive drifters and/or pollutants in a meandering shear flow, with particular emphasis on the prevalence of ultra-chaotic motion. It is found that the ultra-chaotic behavior of passive drifters and/or pollutants is widespread in the ocean jet flow, representing a higher disorder in comparison to the conventional normal-chaos. Obviously, an ultra-chaotic motion of passive drifters and/or pollutants might greatly enhance their dissemination. These findings might deepen our understandings about chaotic motions in geophysical flows, and further confirms the wide existence of ultra-chaos as a new concept. • Ocean drifter motion may be ultra-chaotic, statistically sensitive to disturbances. • Ultra-chaotic motion can enhance dissemination of drifters and pollutants. • Findings deepen geo-flow chaos insights, affirming ultra-chaos presence. [ABSTRACT FROM AUTHOR]

The homotopy analysis method (HAM), a general analytic technique for non-linear problems, is applied to analyze the solute dispersion process in non-Newtonian Carreau-Yasuda and Carreau fluids flow in a straight tube with the effect of wall absorption/reaction. Unlike the other analytical methods such as perturbation method, the HAM provides a simple way to get the convergent series solution. Any assumptions of small or high physical quantities are not required for the HAM. It provides us a great freedom to choose the so-called convergence control parameter which is used to guarantee the convergence of series solution. The convergent series solution is obtained by choosing the optimal value of convergence control parameter for which the series converges fastest. The optimal value of convergence control parameter is obtained by minimizing the square residual which also provides the convergence region for the series solution. The previous analytical studies on solute dispersion fail to justify the convergence of the series solution, whereas in this investigation, our results are convergent and valid for all physical parameters. In addition, present results are validated by the numerical and some existing results. This study explains elaborately about the advantage of the homotopy analysis method over perturbation and eigenfunction expansion methods for nonlinear problems. Owing to the great potential and flexibility of the homotopy analysis method, it is a more suitable analytical approach to solve the different types of non-linear problems in science and engineering. Besides, this study helps to gain some knowledge on the transportation process of drugs in the blood flow. [ABSTRACT FROM AUTHOR]

Highlights • The 313 new families of periodic orbits of free-fall three-body problem are gained. • A new numerical strategy, namely the "clean numerical simulation" (CNS), is used. • The generalized Kepler's third law is confirmed. Abstract Although the free-fall triple system has been numerically studied for more than one century, however, only four collisionless periodic orbits have been found. In this paper, using a supercomputer and a new strategy for chaotic dynamic systems, called "clean numerical simulation" (CNS), we successfully gained 316 collisionless periodic orbits of the free-fall triple system with a few chosen values of mass ratios, including three collisionless periodic orbits which were found before. Especially, 313 collisionless free-fall periodic orbits are entirely new. What's more, we can gain periodic free-fall three-body orbits in a random ratio of mass. Thus, this is a good example to prove that there exist an infinite number of periodic solutions for the triple system. In addition, it is found that, for a given ratio of mass, there exists a generalized Kepler's third law for the periodic three-body system. All of these would enrich our knowledge and deepen our understanding about the famous three-body problem as a whole. [ABSTRACT FROM AUTHOR]

It is well-known that chaotic dynamic systems, e.g., three-body system and turbulent flow, have sensitive dependence on the initial conditions (SDIC). Unfortunately, numerical noises, i.e., truncation error and round-off error, always exist in practice. Thus, due to the SDIC, the long-term accurate prediction of chaotic dynamic systems is practically impossible. In this paper, a new strategy for chaotic dynamic systems, i.e., the clean numerical simulation (CNS), is briefly described, and applied to a few Hamiltonian chaotic systems. With negligible numerical noises, the CNS can provide convergent (reliable) chaotic trajectories in a long enough interval of time. This is very important for Hamiltonian systems, and thus should have many applications in various fields. It is found that the traditional numerical methods in double precision cannot give not only reliable trajectories but also reliable Fourier power spectra and autocorrelation functions (ACFs). In addition, even the statistic properties of chaotic systems cannot be correctly obtained by means of traditional numerical algorithms in double precision, as long as these statistics are time-dependent. The CNS results strongly suggest that one had better to be very careful on the direct numerical simulation (DNS) results of statistically unsteady turbulent flows, although DNS results often agree well with experimental data when the turbulent flow is in a statistical stationary state. [ABSTRACT FROM AUTHOR]

A liquid bath vibrating vertically can lead to the emergence of a self-propelled walking droplet on its free surface, which can exhibit chaotic motion. It is well-known that trajectories of a chaotic system are sensitive to its initial condition, known as the "butterfly-effect", while its statistics normally remain stable to small disturbances: this type of chaos is called "normal-chaos". However, a concept called "ultra-chaos" has been recently introduced, whose statistical features are unstable, i.e. extremely sensitive to small disturbances. Up to now, a few examples of ultra-chaos have been reported. In this paper, the influence of tiny disturbances on the motion of walking droplet is investigated. It is found that both normal-chaos and ultra-chaos exist in the motion of the walking droplet. Different from the normal-chaotic motion, even the statistical properties of the droplet's ultra-chaotic motion are sensitive to tiny disturbances. Therefore, this illustrates once again that ultra-chaos indeed exists widely and represents a higher disorder compared with normal-chaos. The ultra-chaos as a new concept can widen our knowledge about chaos and provide us with a new point of view to study chaotic properties. It should be emphasized that, for an ultra-chaos, it is impossible to repeat any results of its physical experiments or numerical simulations even in the meaning of statistics! Unfortunately, reproducibility is a corner stone of modern science. Thus, the paradigm of modern scientific research might be invalid for an ultra-chaotic system. [ABSTRACT FROM AUTHOR]

• We obtain accurate solutions for arbitrarily large uniform loading. • The bending stress is non-negligible at edges, even at a large loading. • The perturbation method fails for the large deflection of the plate. The large deflection of a thin rectangular plate under uniform loading is a classic problem in solid mechanics. However, the equations are challenging to solve due to their strong nonlinearity. To the author's best knowledge, existing studies have only reported solutions for rectangular plates with immovable clamped edges within the range of loadings a 4 q / (D h) < 500. In this study, we employ the homotopy analysis method (HAM) to address this problem and obtain accurate solutions even when the loading a 4 q / (D h) reaches as high as 10 5. Additionally, we discover that the central deflection w (0 , 0) / h follows a scaling law of [ a 4 q / (D h) ] 1 / 3 for loadings a 4 q / (D h) > 10 4 , which agrees with the scaling law for extremely large deflections. Consequently, we can utilize this scaling law to extrapolate our homotopy series solution from a 4 q / (D h) = 10 4 to even larger loadings. Our investigation also reveals that the bending and membrane stresses increase with the loading. The maximum bending stress is located at the edge, while the location of the maximum membrane stress shifts from the plate center towards the edge as the loading increases. Moreover, we find that even for large deflections, the bending stress remains significant at the edge, challenging the assumption of negligible bending stress adopted by the membrane equations. Thus, the membrane equation may over-predict the plate deflection even under large loadings. These findings advance our understanding of the large deflection of a thin rectangular plate with clamped edges, which has important applications in aerospace, ocean, chemical, and microelectronic engineering. The results presented in this paper can also be used to verify other algorithms designed for highly nonlinear problems. [ABSTRACT FROM AUTHOR]

In the frame of the traditional wavelet-Galerkin method based on the compactly supported wavelets, it is important to calculate the so-called connection coefficients that are some integrals whose integrands involve products of wavelets, their derivatives as well as some known coefficients in considered differential equations. However, even for linear differential equations with non-constant coefficient, the computation of connect coefficients becomes rather time-consuming and often even impossible. In this paper, we propose a generalized wavelet-Galerkin method based on the compactly supported wavelets, which is computationally very efficient even for differential equations with non-constant coefficients, no matter linear or nonlinear problems. Some related mathematical theorems are proved, based on which the basic ideas of the generalized wavelet-Galerkin method are described in details. In addition, some examples are used to illustrate its validity and high efficiency. A nonlinear example shows that the generalized wavelet-Galerkin method is not only valid to solve nonlinear problems, but also possesses the ability to find new solutions of multi-solution problems. This method can be widely applied to various types of both linear and nonlinear differential equations in science and engineering. [ABSTRACT FROM AUTHOR]

In this paper, an analytic approximation method for highly nonlinear equations, namely the homotopy analysis method (HAM), is employed to solve some backward stochastic differential equations (BSDEs) and forward-backward stochastic differential equations (FBSDEs), including one with high dimensionality (up to 12 dimensions). By means of the HAM, convergent series solutions can be quickly obtained with high accuracy for a FBSDE in a 6-dimensional case, within less than 1 % CPU time used by a currently reported numerical method for the same case [34]. Especially, as dimensionality enlarges, the increase of computational complexity for the HAM is not as dramatic as this numerical method. All of these demonstrate the validity and high efficiency of the HAM for the backward/forward-backward stochastic differential equations in science, engineering, and finance. [ABSTRACT FROM AUTHOR]

Pt decorated RuFeSe/C catalyst is prepared by reduction of Pt precursor on pre-formed RuFeSe/C for oxygen reduction reaction (ORR). The catalyst is characterized by X-ray diffraction (XRD), energy dispersive spectrometer (EDS), transmission electron microscopy (TEM), and X-ray photoelectron spectroscopy (XPS). The catalyst particles are found to disperse on the carbon support with an average particle size of 2.8 nm. Physical characterizations and electrochemical tests confirm that Pt is deposited on the surfaces of RuFeSe particles and RuFeSe@Pt/C catalyst has a core-shell structure. The as-prepared catalyst has high durability and shows high ORR activity through a four-electron transfer process. RuFeSe@Pt/C exhibits 1.3-fold greater specific activity and 1.4-fold greater mass activity for ORR than Pt/C. More importantly, it has excellent tolerance to methanol. Consequently, RuFeSe@Pt/C may be used as fine cathode catalyst in direct methanol fuel cells (DMFCs). [ABSTRACT FROM AUTHOR]

In scientific computing, it is time-consuming to calculate an inverse operator $\mathcal {A}^{-1}$ of a differential equation $\mathcal {A}\phi = f$ , especially when $\mathcal {A}$ is a highly nonlinear operator. In this paper, based on the homotopy analysis method (HAM), a new approach, namely the method of directly defining inverse mapping (MDDiM), is proposed to gain analytic approximations of nonlinear differential equations. In other words, one can solve a nonlinear differential equation $\mathcal {A}\phi = f$ by means of directly defining an inverse mapping $\mathcal J$ , i.e. without calculating any inverse operators. Here, the inverse mapping $\mathcal {J}$ is even unnecessary to be explicitly expressed in a differential form, since 'mapping' is a more general concept than 'differential operator'. To guide how to directly define an inverse mapping $\mathcal {J}$ , some rules are provided. Besides, a convergence theorem is proved, which guarantees that a convergent series solution given by the MDDiM must be a solution of problems under consideration. In addition, three nonlinear differential equations are used to illustrate the validity and potential of the MDDiM, and especially the great freedom and large flexibility of directly defining inverse mappings for various types of nonlinear problems. The method of directly defining inverse mapping (MDDiM) might open a completely new, more general way to solve nonlinear problems in science and engineering, which is fundamentally different from traditional methods. [ABSTRACT FROM AUTHOR]

The famous three-body problem can be traced back to Newton in 1687, but quite few families of periodic orbits were found in 300 years thereafter. In this paper, we propose an effective approach and roadmap to numerically gain planar periodic orbits of three-body systems with arbitrary masses by means of machine learning based on an artificial neural network (ANN) model. Given any a known periodic orbit as a starting point, this approach can provide more and more periodic orbits (of the same family name) with variable masses, while the mass domain having periodic orbits becomes larger and larger, and the ANN model becomes wiser and wiser. Finally we have an ANN model trained by means of all obtained periodic orbits of the same family, which provides a convenient way to give accurate enough predictions of periodic orbits with arbitrary masses for physicists and astronomers. It suggests that the high-performance computer and artificial intelligence (including machine learning) should be the key to gain periodic orbits of the famous three-body problem. • A machine-learning approach is proposed for massive periodic orbits of three-body systems with arbitrary masses. • A roadmap is given to obtain periodic orbits of three-body problem with arbitrary masses in general cases. • A machine-learning approach is given to classify the different types of orbits of three-body problem. [ABSTRACT FROM AUTHOR]

It is well recognized that pore structure and the hydrophilicity/hydrophobicity balance are key factors for the cathodes of air-breathing proton exchange membrane fuel cells (AB-PEMFCs). In this work, we attempted to adjust the pore structure and hydrophilicity of an air-breathing cathode by using two types of catalysts, Pt/C and Pt/CNT, to prepare the catalyst layer for the air-breathing cathode instead of using a single catalyst. An MEA with the dual-catalyst cathode exhibited significantly improved single-cell performance, which was affected by the ratio of Pt/C to Pt/CNT. Our optimized MEA, which had a ratio of 54:46 in the cathode catalyst layer, achieved a current density of up to 290 mA cm −2 at 0.6 V, which was 14% higher than that of a MEA without Pt/CNT. The Pt/CNT in the catalyst layer played the key role in the overall performance of the AB-PEMFC. We propose that the CNT improved charge transfer and enabled better electrical conductivity than carbon black. In addition, the tubular structure of Pt/CNT made the catalyst layer more porous and permeable to gas. Furthermore, the addition of Pt/CNT may have changed the cathode's hydrophilicity/hydrophobicity balance, giving the cathode better water balance and consequently yielding better performance. [ABSTRACT FROM AUTHOR]

Reduced graphene oxide co-doped with nitrogen and fluorine (N–F/rGO) was successfully prepared by a simple one-step thermal annealing process using a mixture of graphene oxide and ammonium fluoride in an argon atmosphere. X-ray photoelectron spectroscopy demonstrated that the nitrogen and fluorine atoms were successfully doped into the rGO structure at atomic percentages of 2.51 and 0.74, respectively. Nitrogen adsorption–desorption measurement revealed that the as-prepared N–F/rGO has a high surface area (412 m 2 g −1 ) with numerous slit-shaped pores (1.60 cm 3 g −1 ). The electrocatalytic activity of N–F/rGO for oxygen reduction reaction was found to be higher than that of rGO doped only with nitrogen (N/rGO); in fact, it was comparable to the activity of conventional commercial Pt/C in an alkaline electrolyte. In addition, the catalyst exhibited excellent long-term stability/durability, good methanol tolerance, and high selectivity for the four-electron transfer pathway. A possible mechanism is suggested for the improvement conferred by fluorine. [ABSTRACT FROM AUTHOR]

What is the origin of macroscopic randomness (uncertainty)? This is one of the most fundamental open questions for human beings. In this paper, 10 000 samples of reliable (convergent), multiple-scale (from 10-60 to 102) numerical simulations of a chaotic three-body system indicate that, without any external disturbance, the microscopic inherent uncertainty (in the level of 10-60) due to physical fluctuation of initial positions of the three-body system enlarges exponentially into macroscopic randomness (at the level O(1)) until t = T*, the so-called physical limit time of prediction, but propagates algebraically thereafter when accurate prediction of orbit is impossible. Note that these 10 000 samples use micro-level, inherent physical fluctuations of initial position, which have nothing to do with human beings. Especially, the differences of these 10 000 fluctuations are mathematically so small (in the level of 10-60) that they are physically the same since a distance shorter than a Planck length does not make physical sense according to the string theory. This indicates that the macroscopic randomness of the chaotic three-body system is self-excited, say, without any external force or disturbances, from the inherent micro-level uncertainty. It provides us the new concept "self-excited macroscopic randomness (uncertainty)". The macroscopic randomness is found to be dependent upon microscopic uncertainty, from the statistical viewpoint. In addition, it is found that, without any external disturbance, the chaotic three-body system might randomly disrupt with symmetry-breaking at t = 1000 in about 25% probability, which provides us new concepts "self-excited random disruption", "self-excited random escape" and "self-excited symmetry breaking" of the chaotic three-body system. Hence, it suggests that a chaotic three-body system might randomly evolve by itself, without any external forces or disturbance. Thus, the world is essentially uncertain, since such kind of self-excited macroscopic randomness (uncertainty) is inherent and unavailable. This work also implies that an universe could randomly evolve by itself into complicated structures, without any external forces. To emphasize this point, the so-called "molecule-effect" (or "nonbutterfly effect") of chaos is suggested in this paper. All of these reliable computations could deepen our understandings of chaos from physical viewpoints, and reveal a kind of origin of macroscopic randomness/uncertainty. [ABSTRACT FROM AUTHOR]

In an air-breathing proton exchange membrane fuel cell (ab-PEMFC), large amounts of water are generated and condensed on the cathode at high current densities due to the low operating temperature. Water management for ab-PEMFCs remains a challenge. In this paper, a cathode with a dual catalyst layer structure is designed, and the gas diffusion layer (GDL) and microporous layer (MPL) are optimized to improve the water management of an ab-PEMFC. A thin hydrophilic layer using perfluorosulfonate (Nafion) as the catalyst binder is coated on the electrolyte membrane to form an inner layer that maintains a good proton transfer rate, while a hydrophobic outer layer is prepared using a mixture of Nafion and polytetrafluoroethylene as the binder, preventing the removal of water under low-humidity conditions and expelling the excess water generated in the high current density area. A membrane electrode assembly (MEA) with this dual catalyst layer cathode exhibits excellent air-breathing performance, as the MEA's water management is greatly improved by the dual layer structure. We also find that the thickness of the MPL and the hydrophobicity of the GDL significantly affect the air-breathing performance of the MEA, and we attempt to optimize these parameters. [ABSTRACT FROM AUTHOR]

A high-performance membrane electrode assembly (MEA) with agarose added to the anodic catalyst layer (CL) was successfully prepared. The MEA exhibited excellent performance at low relative humidity (RH) in an air/hydrogen proton exchange membrane fuel cell. The effects of agarose content, RH, cell temperature, and back pressure on the low-humidity performance of this MEA were investigated. The results of water contact angles and water uptake measurements reveal that the hydrophilicity of the anode is significantly improved with the addition of agarose. With a low RH of 20% and a cell temperature of 60 °C, the optimal MEA (MEA-4), containing 4 wt.% agarose in the anode CL, achieves excellent low-humidity performance: the current density reaches 960 mA cm −2 at 0.6 V and 500 mA cm −2 at 0.7 V. After 10 h of continuous operation under the same conditions, the current density decreases just slightly, from 960 to 840 mA cm −2 , whereas the current density of a blank MEA without added agarose degrades sharply. [ABSTRACT FROM AUTHOR]

Hierarchically structured spherical mesoporous nanoflowers (HSMNF) with well-defined morphology and uniform size were synthesized by a hydrothermal method, in which a mixture of cyclohexane and water was used as the solvent, with cetylpyridinium bromide (CPB) as the template, tetraethyl orthosilicate as the source of inorganic silica, and urea as the hydrolysis additive. The flower size ranged from 200 nm to 500 nm, and the thickness of a “petal” was about 10 nm. We investigated the effects of solvent composition ( V cyclohexane / V water ), hydrothermal temperature, and molar ratio of Si to CPB on morphology and structure. The presence of cyclohexane was found to be crucial for the nanoflowers to form, and a solvent with high cyclohexane content was beneficial for the formation of smaller and more uniform nanoflowers, whereas low cyclohexane content resulted in the collapse of the nanoflower structure. The optimal ratio of cyclohexane to water was 1:1 by volume. The hydrothermal temperature and molar ratio of Si to CPB strongly affected nanoflower size and structure, as well as petal thickness. The optimal hydrothermal temperature was 120 °C, and the optimal molar ratio of Si to CPB was 4.37. The sample synthesized under optimal conditions exhibited well-defined morphology and uniform flower size. Its BET surface area reached 502 m 2 /g. The nanoflowers were under 200 nm in diameter, and their average mesopore size was ca. 4 nm, as measured by N 2 adsorption–desorption. Using synthesized nanoflowers as the support, we prepared a supported PdAu bimetallic catalyst for the hydrogenation of phenol. This catalyst exhibited high activity (with a conversion rate of up to 90%) and high selectivity for cyclohexanone (up to 92%). This nanoflower's morphology, high surface area, and large pore size may make it a valuable and promising material for applications in the catalysis, adsorption and controlled release of drugs fields. [ABSTRACT FROM AUTHOR]

Pd@Pt nanoparticles with a three-dimensional (3D) nanospherical shape have been prepared using a two-step approach in which the Pd nanospheres are synthesized controllably by a solvothermal method, and then a Pt monolayer is deposited on the Pd nanospheres using an underpotential deposition process. We systematically investigate (i) the influences of temperature and additive on the morphology of the Pd nanoparticles and (ii) the electrochemical activity of Pd@Pt for the oxygen reduction reaction (ORR). The Pd@Pt nanoparticles exhibit enhanced activity towards the ORR. The mass activity of Pt in the Pd@Pt nanospheres (1.03 A mgPt −1 ) is 3.3 times higher than that of commercial Pt/C (0.24 A mgPt −1 ). The catalyst enhanced activity may result from the 3D structure of the Pd nanospheres and the monolayer dispersion of Pt on the surface of the nanoparticles. [ABSTRACT FROM AUTHOR]

Abstract: Ultra-low Pt loading membrane electrode assemblies (ULP MEAs) are prepared through in situ construction of core–shell Ir@Pt nanoparticles (Ir/Vulcan XC-72R as the core) on the surface of an electrode via a pulse electrochemical deposition (PED) approach. The core material is coated on a membrane with a conventional catalyst-coated membrane process prior to the deposition of the shell metal (Pt in this case). The ULP MEAs are characterized by X-ray Diffraction (XRD), Transmission Electron Microscopy (TEM) and X-ray Photoelectron Spectroscopy (XPS). The effects of a number of preparation parameters on cell performance are investigated in detail. The performance of the ULP MEA, in which the anode loadings of Pt and metals are ∼0.012 mg cm−2 and 0.044 mg cm−2(0.012 mg cm−2 Pt + 0.032 mg cm−2 Ir) respectively, is found to be competitive with that of an MEA prepared with an anode Pt loading of 0.1 mg cm−2 (commercial Pt/C catalyst from Johnson Matthey), manifesting the solid advantage of this in situ PED method. [Copyright &y& Elsevier]

Abstract: Uniform nitrogen and sulfur co-doped carbon nanospheres with an average diameter of approximately 200nm were prepared using sulfur and polyacrylonitrile as precursors. The materials were characterized using scanning electron microscopy, transmission electron microscopy, elemental analysis, and X-ray photoelectron spectroscopy. The characterization results suggest the as-prepared materials had uniform, porous, nanospherical morphologies and high surface areas. For the typical sample containing 9.5% sulfur, the surface area is up to 653m2 g−1. The catalysts exhibited enhanced catalytic activity, outstanding long-term stability, and excellent methanol tolerance in an alkaline medium. Significantly, the sulfur addition was found to be vital in improving materials’ catalytic performance through preventing aggregation of the nanospheres, constructing porous structures, increasing the surface area, and participating in the formation of active sites. [Copyright &y& Elsevier]

Abstract: Nitrogen-doped carbon nanotube (N-CNT) arrays were prepared by chemical vapor deposition, using ferrocene as the catalyst precursor and imidazole as the carbon and nitrogen precursor. For the reduction of oxygen, the N-CNTs showed excellent electrocatalytic activity in both acidic and alkaline media. The N-CNTs were characterized by scanning and transmission electron microscopy, X-ray diffraction, X-ray photoelectron spectroscopy, and elemental analysis. The samples had a high nitrogen content (8.54at.%) and a bamboo-like structure, and their activity varied according to the amount of pyridinic nitrogen they contained. [Copyright &y& Elsevier]

Abstract: The direct ethanol fuel cell has been attracting increased attention due to its safety and the wider availability of ethanol as compared with methanol. The present work investigates the anodic oxidation of ethanol on a core-shell structured Ru@PtPd/C catalyst in alkaline media. The catalyst shows high activity toward the anodic oxidation of ethanol; with 18wt.% ruthenium as the core and 12wt.% PtPd (Pt:Pd=1:0.2) as the active shell, its activity in terms of PtPd loading is 1.3, 3, 1.4, and 2.0 times as high as that of PtPd/C, PtRu/C, Pd/C, and Pt/C, respectively, indicating high utilization of Pt and Pd. The ratio of forward peak current density to backward peak current density (I f/I b) reaches 1.5, which is 1.9 times that of PtPd/C catalyst, revealing high poisoning tolerance to the intermediates in ethanol electrooxidation. In addition, the stability of Ru@PtPd/C is higher than that of Pt/C and PtPd/C, as evidenced by chronoamperometric evaluations. The catalyst is extensively characterized by transmission electron microscopy (TEM), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy. The core-shell structure of the catalyst is revealed by XRD and TEM. [Copyright &y& Elsevier]

Abstract: A facile route to synthesize mesoporous hollow silica sphere (MHSS) via TEOS emulsion droplet assisted with dodecyl amine (DDA) was developed in this work. The particle sizes of MHSS are around 400–600nm and the BET surface area is high up to 951m2 g−1 and with a uniform pores diameter of 3.7nm in the silica wall. Thermogravimetric analysis found that the MHSS displayed good thermal stability. The effects of solvent, TEOS amount and DDA addition on the property of MHSS were also investigated. It was found that the solvent composition and the required DDA concentration are the key factors for the determination of hollow structure. Pd loaded MHSS catalyst showed high catalytic activity and good recycling ability in the liquid phenol hydrogenation under mild reaction conditions. [ABSTRACT FROM AUTHOR]

Abstract: The unsteady non-similarity boundary-layer flows caused by an impulsively stretching flat sheet have been investigated. The partial differential equations governing the flows have been solved analytically by means of an analytic technique for strongly non-linear problems, namely the homotopy analysis method (HAM). This analytic approach gives us the convergent series solution uniformly valid for all dimensionless time in the whole spatial region and . To the best of our knowledge, such a kind of series solution has never been obtained. The skin friction coefficient and the boundary-layer thickness are also analyzed for different dimensionless time . [Copyright &y& Elsevier]

Abstract: Carbon-supported core–shell structured Ru@Pt x Pd y /C catalysts with Pt x Pd y as shell and nano-sized Ru as core are prepared by a successive reduction procedure. The catalysts are extensively characterized by transmission electron microscopy (TEM), X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). The formic acid oxidation activity of Ru@Pt x Pd y /C varies with the varying Pt:Pd atomic ratio. The peak oxidation potential on Ru@Pt1Pd2/C shifts negatively for about 200mV compared with that of Pd/C. The higher electro-catalytic activity toward formic acid oxidation on core–shell structured Ru@Pt x Pd y /C catalyst than that on Pt x Pd y /C suggests the high utilization of noble metals. In addition to the enhanced noble metal utilization, Ru@Pt x Pd y /C catalyst also shows improved stability as evidenced by chronoamperometric evaluations. [Copyright &y& Elsevier]

Abstract: Platinum decorated Ru/C catalysts are prepared by successive reduction of a platinum precursor on pre-formed Ru/C. Pt:Ru atomic ratios are varied from 0.13:1 to 0.81:1 to investigate the platinum decoration effects on the catalyst''s structure and electrochemical performance towards the methanol oxidation reaction (MOR) at room temperature. The catalysts are extensively characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), and X-ray photoelectron spectroscopy (XPS). Ru@Pt/C catalysts show enhanced mass-normalized activity and specific activity for the MOR relative to Pt/C. For the anodic oxidation of methanol, the ratio of forward to reverse oxidation peak current R (I f/I b) varies considerably: R decreases from 5.8 to 0.8 when the Pt:Ru ratio increases from 0.13:1 to 0.81:1. When the ratio of Pt:Ru is 0.42:1, R reaches 0.99 (close to that of Pt/C), and further increase of the Pt:Ru ratio leads to almost no decrease in R. Coincidentally, maximum mass-normalized activity is also obtained when Pt:Ru is 0.42:1. [Copyright &y& Elsevier]

Abstract: A miniature air breathing compact direct formic acid fuel cell (DFAFC), with gold covered printed circuit board (PCB) as current collectors and back boards, is designed, fabricated and evaluated. Effects of formic acid concentration and catalyst loading (anodic palladium loading and cathodic platinum loading) on the cell performance are investigated and optimized fuel concentration and catalyst loading are obtained based on experimental results. A maximum power density of 19.6mWcm−2 is achieved at room temperature with passive operational mode when 5.0M formic acid is fed and 1mgcm−2 catalyst at both electrodes is used. The home-made DFAFC also displays good long-term stability at constant current density. [Copyright &y& Elsevier]

Abstract: Electrocatalytic activity for oxygen reduction reaction on magnetically modified PtFe/C catalysts was investigated. X-ray powder diffraction (XRD) revealed that while the as-prepared PtFe/C catalysts were face-centered cubic (f.c.c), the as annealed catalysts at 700° for 3h were face-centered tetragonal (f.c.t). Post-heating transformed the as-prepared catalysts from superparamagnetic into ferromagnetic materials as was measured by vibrating sample magnetometer (VSM). Electrochemical results obtained by rotating disk electrode (RDE) technique showed that oxygen reduction reaction took place by an overall four electron charge transfer process. Polarization curves showed that the electrocatalytic activity on ferromagnetic catalyst for oxygen reduction obviously outperformed the as-prepared paramagnetic catalyst. The values of kinetic parameters for the as-prepared and as-heated catalysts were obtained from linear-line region of mass-transfer-corrected Tafel plots. The catalytic enhancement by the magnetically modified catalyst was explained by the magnetic attractive force toward oxygen thus increasing electrochemical flux at the heterogeneous catalytic interface. [Copyright &y& Elsevier]

Abstract: A new type of CsHSO4–HZSM-5 inorganic composite electrolyte membrane is prepared by mechanically mixing CsHSO4 (CHS) and nanometer-scale HZSM-5 zeolite powders. The effects of HZSM-5 on the crystallite structure, proton conductivity, and thermal stability of the CsHSO4 electrolyte are investigated. Incorporation of HZSM-5 is found to significantly increase the low-temperature proton conductivity of the CsHSO4 electrolyte, extending its operating temperature down to 100°C. The composite electrolyte with 40mol% HZSM-5 shows the highest proton conductivity in the measured temperature range. The low-temperature activation energy of the composite with 40mol% HZSM-5 is lower than that of the CHS–SiO2 composite. The improvement of the proton conductivity can be attributed to the enhanced interfacial interaction between the two phases. And the small HZSM-5 particles lead to a change in the bulk properties of the ionic salts. The melting point of the CHS–HZSM-5 composite electrolyte is lower than that of the pure CHS electrolyte. The CHS–HZSM-5 composite electrolyte is suitable for polymer electrolyte membrane fuel cells operated at 100–200°C. [Copyright &y& Elsevier]

Abstract: We presented a magnetic-field-assisted solvothermal route to prepare hexagonal close-packed (hcp) large Co nanosheets free of any surfactants, complexants or templates. Scanning electron microscope (SEM) images showed that the typical size and thickness of the Co nanosheets were several microns and ca. 50nm, respectively. Magnetic measurement indicated the coercivity of the sample reached 317.3Oe, which was much higher than those of bulk Co metal and previously reported Co nanoplatelets. It was found that the solvents played a crucial role in determining the morphology and the crystal structures of the Co products, and the introduction of ethanol conduced to the formation of pure hcp phase Co microcrystal. The external magnetic field was also found to be indispensable for the formation of sheet-shaped morphology. [Copyright &y& Elsevier]

Abstract: A general analytic approach for nonlinear eigenvalue problems is described. Two physical problems are used as examples to show the validity of this approach for eigenvalue problems with either periodic or non-periodic eigenfunctions. Unlike perturbation techniques, this approach is independent of any small physical parameters. Besides, different from all other analytic techniques, it provides a simple way to ensure the convergence of series of eigenvalues and eigenfunctions so that one can always get accurate enough approximations. Finally, unlike all other analytic techniques, this approach provides great freedom to choose an auxiliary linear operator so as to approximate the eigenfunction more effectively by means of better base functions. This approach provides us a new way to investigate eigenvalue problems with strong nonlinearity. [Copyright &y& Elsevier]

Abstract: By using two non-ionic surfactants, 1,12-diaminododecane and a triblock copolymer surfactant F127, as templates, grape-like solid spheres of super-microporous silica (SMS) with ordered, worm-like pore structures have been successfully synthesized, then characterized by SEM/TEM, XRD, TG/DTA, etc. In a sample synthesized at 70°C, well-formed grape-like spheres with worm-like pores were observed by SEM and TEM. The average pore size is ca. 1.87nm and the specific surface area of the spheres is 865m2/g. The hydrogen storage capacity of the sample Pd/SMS-70-C, prepared by supporting 5wt% palladium on SMS (synthesized at 70°C), is up to 2.56wt% at 1.2MPa hydrogen pressure. [Copyright &y& Elsevier]

Abstract: N doped TiO2 with anatase and rutile mixed crystal were prepared by using tetrabutyl titanate as the precursor via a modified hydrothermal process and calcination at 320°C. The microstructure and morphology of samples were characterized by XRD, UV–vis-DRS, FTIR and XPS. The results showed that N–TiO2 particles were crystallized to anatase and rutile mixed crystal structure; they were presented narrow particle size distribution, and the average particle size was ca. 13.5nm calculated from XRD results. It was found that the N-doped TiO2 particles showed strong visible-light absorption and high photocatalytic activity for the mineralization of Rhodamine B under irradiation by visible light (400–500nm). The high visible-light photocatalytic activity of the obtained N-doped TiO2 might result from the synergetic effect of nitrogen doping and the mixed lattice structure of N–TiO2. Possible mechanism of N–TiO2 mixed crystal formed under hydrothermal conditions was discussed. [Copyright &y& Elsevier]

Abstract: We present here a ‘similar’ solution for the nano boundary layer with nonlinear Navier boundary condition. Three types of flows are considered: (i) the flow past a wedge; (ii) the flow in a convergent channel; (iii) the flow driven by an exponentially-varying outer flows. The resulting differential equations are solved by the homotopy analysis method. Different from the perturbation methods, the present method is independent of small physical parameters so that it is applicable for not only weak but also strong nonlinear flow phenomena. Numerical results are compared with the available exact results to demonstrate the validity of the present solution. The effects of the slip length ℓ, the index parameters n and m on the velocity profile and the tangential stress are investigated and discussed. [Copyright &y& Elsevier]

Abstract: Two novel catalysts for anode oxidation of formic acid, Pd2Co/C and Pd4Co2Ir/C, were prepared by an organic colloid method with sodium citrate as a complexing agent. These two catalysts showed better performance towards the anodic oxidation of formic acid than Pd/C catalyst and commercial Pt/C catalyst. Compared with Pd/C catalyst, potentials of the anodic peak of formic acid at the Pd2Co/C and Pd4Co2Ir/C catalyst electrodes shifted towards negative value by 140 and 50mV, respectively, meanwhile showed higher current densities. At potential of 0.05V (vs. SCE), the current density for Pd4Co2Ir/C catalyst is as high as up to 13.7mAcm−2, which is twice of that for Pd/C catalyst, and six times of that for commercial Pt/C catalyst. The alloy catalysts were nanostructured with a diameter of ca. 3–5nm and well dispersed on carbon according to X-ray diffraction (XRD) and transmission electron microscopy (TEM) measurements. The composition of alloy catalysts was analyzed by energy dispersive X-ray analysis (EDX). Pd4Co2Ir/C catalyst showed the highest activity and best stability making it the best potential candidate for application in a direct formic acid fuel cell (DFAFC). [Copyright &y& Elsevier]

Abstract: Novel ternary palladium based alloy catalysts, PdFeIr/C, for oxygen reduction reaction (ORR) have been successfully prepared via an organic colloid method with ethylene glycol as solvent and sodium citrate as complexing agent. The catalysts were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM) and energy dispersive X-ray analysis (EDX). Electrochemical activity of the catalysts for ORR was evaluated by steady state polarization measurements, which were carried out on an ultra thin layer rotating disk electrode (RDE). Compared to pure Pd/C and Pd3Fe/C, results showed that the ORR activity of PdFeIr/C was highest, and its methanol tolerance was better than Pt/C catalyst. [Copyright &y& Elsevier]

Abstract: Ultrafine Co nanoparticles with the size of ca. 2 nm were prepared by an organic colloid method, in which sodium formate acted as reducing agent, ethylene glycol acted as solvent, sodium citrate acted as both complexing agent and stabilizing agent, respectively. X-ray diffraction (XRD) analysis indicated that the as-prepared Co nanoparticles were in hexagonal close-packed phase, and transmission electron microscope (TEM) images revealed that the size of the well-dispersed Co nanoparticles was as small as 2 nm, and the sizes were distributed in a very narrow region. The hysteresis loop of the as-prepared Co sample measured at room temperature showed a superparamagnetic behavior due to the extremely small size of the products. It was revealed that sodium citrate played a crucial role in decreasing the particle size and narrowing the size distribution. [Copyright &y& Elsevier]

Two composites LaNi4.8Sn0.2/CNTs and NdNi4.8Sn0.2/CNTs were prepared by an impregnation-reduction method. Their hydrogen storage capacity could reach up to 2.96 wt% and 2.88 wt% respectively at room temperature and 1.0 MPa pressure. These values, which might result from the synergetic effect between the alloy nanoparticles and the pretreated CNTs, were three times higher than those of the unsupported MNi4.8Sn0.2(M=La, Nd) alloys under the same conditions. XRD and TEM revealed that the alloy particles were uniformly dispersed on the CNTs and the average particle size was Ca. 30 nm. The composites also showed good stability and the hydrogen storage capacity decreased by less than 6% after 100 adsorption-desorption cycles. Moreover, no noticeable change in crystalline structure was observed for the composites. [ABSTRACT FROM AUTHOR]

A type of novel material with a high hydrogen storage capacity was prepared by supporting PdNi18 alloy nanoparticles, which were synthesized by using a new colloid method, on the surface of pretreated multiwal led carbon nanotubes (MWCNTs). The average PdNi18 alloy particle sizes calculated from XRD patterns were ca. 3 nm, and the high dispersion of these particles on MWCNTs was confirmed by TEM image. Hydrogen storage performance of the composite was investigated under moderate pressure (0.1-1.5 MPa) at room temperature, and a maximum storage capacity of ca. 2.3 wt% was achieved under 1.5 MPa at room temperature, which was much higher than that reported previously under the same conditions. [ABSTRACT FROM AUTHOR]

Abstract: An analytic approach based on the homotopy analysis method is proposed to solve a nonlinear model of combined convective and radiative cooling of a spherical body. An explicit series solution is given, which agrees well with the exact or numerical solutions. Our series solutions indicate that, for the nonlinear model of combined convective and radiative cooling of a spherical body, the temperature on the surface of the body decays more quickly for larger values of the Biot number Bi and/or the radiation–conduction parameter N rc. Different from traditional analytic techniques based on eigenfunctions and eigenvalues for linear problems, our approach is independent of the concepts of eigenfunctions and eigenvalues, and besides is valid for nonlinear problems in general. This analytic method provides us with a new way to obtain series solutions of unsteady nonlinear heat conduction problems, which are valid for all dimensionless times 0⩽ τ <+∞. [Copyright &y& Elsevier]

Abstract: In this paper, we show that the so-called “homotopy perturbation method” is only a special case of the homotopy analysis method. Both methods are in principle based on Taylor series with respect to an embedding parameter. Besides, both can give very good approximations by means of a few terms, if initial guess and auxiliary linear operator are good enough. The difference is that, “the homotopy perturbation method” had to use a good enough initial guess, but this is not absolutely necessary for the homotopy analysis method. This is mainly because the homotopy analysis method contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region and rate of solution series. So, the homotopy analysis method is more general. Besides, the update of the concept of the “analytical solution” is discussed. [Copyright &y& Elsevier]

Abstract: The boundary-layer flows over a stretched impermeable wall are solved by means of an analytic technique, namely the homotopy analysis method. Two branches of solutions are found. The first agrees well with numerical results given by Banks in 1983. The second branch of solutions can be divided into two parts. One is mathematically equivalent to a branch of solutions of Cheng and Minkowycz’s equation reported by Ingham and Brown in 1986, the other is new and has never been reported. Different from the first branch of solutions, the second branch of solutions shows reversed velocity flows. It is found that the difference of skin frictions of the two branches of solutions is rather small, even when the corresponding profiles of velocity are clearly distinct. Thus, from a practical point of view, we need not worry about large variations of the skin friction on the wall when the profile of the velocity changes from one to the other. [Copyright &y& Elsevier]

A novel binary oxide photocatalyst ZnO/TiO2 was prepared by a new modified sol–gel method using citric acid as a complex reagent and its photocatalytic activity was investigated. The factors, such as the ratio of amount of doped zinc ion, the precursors, and the calcination temperature on the activities of ZnO/TiO2 photocatalyst, were investigated. SO42-/ZnO/TiO2 was prepared by sulfating the dry gels of ZnO/TiO2 with H2SO4 solution. It was showed that the addition of ZnO could enhance the activity significantly, and sulfating ZnO/TiO2 with sulfuric acid resulted to dramatic enhancement, the degradation ratio of methyl orange could be up to 71.9%, compared with 55% of degradation of ZnO/TiO2 catalyst. [Copyright &y& Elsevier]