652 publications from this institution
This paper presents a full set of numerical methods for predicting the effective thermal conductivity of natural fibrous materials accurately, which includes a random generation-growth method for generating micro morphology of natural fibrous materials based on existing statistical macroscopic geometrical characteristics and a highly efficient lattice Boltzmann algorithm for solving the energy transport equations through the fibrous material with the multiphase conjugate heat transfer effect considered. Using the present method, the effective thermal conductivity of random fibrous materials is analyzed for different parameters. The simulation results indicate that the fiber orientation angle limit will cause the material effective thermal conductivity to be anisotropic and a smaller orientation angle leads to a stronger anisotropy. The effective thermal conductivity of fibrous material increases with the fiber length and approach a stable value when the fiber tends to be infinite long. The effective thermal conductivity increases with the porosity of material at a super-linear rate and differs for different fiber location distribution functions.
No abstract is provided for this article.
Fractional complex transform is proposed to convert fractional differential equations into ordinary differential equations, so that all analytical methods devoted to advanced calculus can be easily applied to fractional calculus. Two examples are given.
Rubner 1880 surface law reveals that the basal metabolic rate scales with body mass raised to the power of 2/3, which is geometrically correct and biologically relevant. However, Kleiber 1932 scaling law experimentally found that the scaling index was 3/4 instead of 2/3. There is no theory that can explain the Kleiber's data, explanations in Science in 1997 and later in Nature in 2002 for 3/4 scaling law for all life were apparently wrong. Here we show that Rubner's surface law was approximately correct, and it requires modification due to the fact that a cell is porous. Using fractal theory, the scaling index is about 0.7, 0.73, and 0.83, respectively, for inactive, active and motion statuses, and Kleiber's exponent can be fully explained by Rubner's law.
No abstract is provided for this article.
A variational principle is established for the differential–difference system arising in stratified hydrostatic flows by the semi-inverse method. An insight into its physical understanding is given.
A convection-diffusion equation for E reaction arising in rotating disk electrodes is discussed and solved by Taylor series method and Pade approximation. A fractional modification is suggested to deal with the porous property of the electrodes, the effect of the porous structure on the convection-diffusion process is elucidated.
In this paper, we consider the time-fractional two-mode coupled Burgers equation with the Caputo fractional derivative. A modified homotopy perturbation method coupled with Laplace transform (He-Laplace method) is applied to find its approximate analytical solution. The method is to decompose the equation into a series of linear equations, which can be effectively and easily solved by the Laplace transform. The solution process is illustrated step by step, and the results show that the present method is extremely powerful for fractional differential equations.
This paper obtains an explicit analytical solution for nonlinear Poisson‐Boltzmann equation by the homotopy perturbation method, which does not require a small parameter in the equation under study, so it can be applied to both the weakly and strongly nonlinear problems. The obtained results show the evidence of the usefulness of the homotopy perturbation method for obtaining approximate analytical solutions for nonlinear equations.
The fractal harmonic law admits that the friction between the pure water and the moving surface is the minimum when fractal dimensions of water in Angstrom scale are equal to fractal dimensions of the moving surface in micro scale. In the paper, the fractal harmonic law is applied to demonstrate the mechanism of waterproof/ dustproof. The waterproof phenomenon of goose feathers and lotus leaves is illustrated to verify our results and experimental results agree well with our theoretical analysis.
A description of stable working conditions for spinning two-strand yarn is given. A theoretical model underlying Sirospun yarn spinning is also given. Based on the variational formulation established for the coupled oscillators arising in two-strand yarn spinning, a simple analytical model for the forces that determine the nonlinear oscillation during the yarn spinning, as a function of inlet velocities, strand-spacing, and forces acting on the strands is proposed, which reveals that resonance occurs when the convergence angle is near 127 degrees.
Any physical laws are scale-dependent, the same phenomenon might lead to debating theories if observed using different scales. The two-scale thermodynamics observes the same phenomenon using two different scales, one scale is generally used in the conventional continuum mechanics, and the other scale can reveal the hidden truth beyond the continuum assumption, and fractal calculus has to be adopted to establish governing equations. Here basic properties of fractal calculus are elucidated, and the relationship between the fractal calculus and traditional calculus is revealed using the two-scale transform, fractal variational principles are discussed for 1-D fluid mechanics. Additionally planet distribution in the fractal solar system, dark energy in the fractal space, and a fractal ageing model are also discussed.
Snail powders have many medicine functions. This paper uses the powders as additives for fabrication of nanofibers by the electrospinning and the bubble electrospinning, such work has never been studied before in any open literature. Unsmooth nanofiber is observed, and small fibers have higher acid-proof and alkali-proof properties, and their main reasons are revealed. Snail’s slime involved in the powder has a fast immobilization property, and the immobilization process will blocks surface motion of the spun jets during the spinning process. Potential applications of the unsmooth nanofibers are predicted.
This paper proposes three standard variational iteration algorithms for solving differential equations, integro-differential equations, fractional differential equations, fractal differential equations, differential-difference equations and fractional/fractal differential-difference equations. The physical interpretations of the fractional calculus and the fractal derivative are given and an application to discrete lattice equations is discussed. The paper then examines the acceleration of some iteration formulae with particular emphasis being placed on the exponential Pade approximant that is suggested for solitary solutions and the sinusoidal Pade approximant that is usually used for periodic and compacton solutions. The paper points out that there may not be any physical meaning to the exact solutions of many nonlinear equations and stresses the importance of searching for approximate solutions that satisfy both the equations and the appropriate initial/boundary conditions. The variational iteration method is particularly suitable for solving this kind of problems. Approximate initial/boundary conditions and point boundary initial/conditions are also discussed, with the variational iteration method being capable of recovering the correct initial/boundary conditions and finding the solutions simultaneously.
In this paper, a nonlinear algebraic equation f(x)=0, by applying Taylor's theorem, is converted into a coupled iteration system L(xn+1)+g(xn)=0 and g(xn)=f(xn)−L(xn), where L(x)=Ax2+Bx+C. The formula is of high convergence. Some examples are given.
Thermal science becomes a main tool to the search for hidden pearls in various phenomena from geoscience to nuclear energy. This article elucidates the absolute temperature in view of the geometric potential theory, which sheds a new light on many mysteries in our world, including unification of Newton?s gravity and Coulomb's electronic force, quantized trajectories of planets, the Earth?s inner core, prediction of the speed of light and two-scale thermodynamics. Some conjectures are suggested to elucidate relativity in view of thermodynamics.
