Abstract:The starting point for this paper lies in the results obtained by Sedov (1944) for isotropic turbulence with the self-preserving hypothesis. A careful consideration of the mathematical structure of the Karman-Howarth equation leads to an exact analysis of all possible cases and to all admissible solutions of the problem. This kind of appropriate manipulation escaped the attention of a number of scientists who developed the theory of turbulence and processed the experimental data for a long time. This paper revisits this interesting problem from a new point of view. Firstly, a new complete set of solutions are obtained, and Sedov’s solution is one special case of this set of solutions. Based on these exact solutions, some physically significant consequences of recent advances in the theory of self-preserved homogenous statistical solution of the Navier-Stokes equations are presented. New results could be obtained for the analysis on turbulence features, such as the scaling behavior, the spectrum, and also the large scale dynamics. Integral turbulence length scales based on the exact solutions are discussed, and used to derive rigorously a new recursion equation, which would be helpful in understanding the dynamical process of turbulence, especially for the Markov property and turbulence cascade. The general energy spectra and their behavior in the lowest wave number range are investigated. According to the present theory, the Loitsiansky integral is not an invariant in general cases.

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	1. Large-Scale Dynamics of Isotropic Turbulence
	Ran Zheng
	Mechanics 17 May 2006
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	Abstract:The starting point for this paper lies in the results obtained by Sedov (1944) for isotropic turbulence with the self-preserving hypothesis. A careful consideration of the mathematical structure of the Karman-Howarth equation leads to an exact analysis of all possible cases and to all admissible solutions of the problem. This kind of appropriate manipulation escaped the attention of a number of scientists who developed the theory of turbulence and processed the experimental data for a long time. This paper revisits this interesting problem from a new point of view. Firstly, a new complete set of solutions are obtained, and Sedov’s solution is one special case of this set of solutions. Based on these exact solutions, some physically significant consequences of recent advances in the theory of self-preserved homogenous statistical solution of the Navier-Stokes equations are presented. New results could be obtained for the analysis on turbulence features, such as the scaling behavior, the spectrum, and also the large scale dynamics. Integral turbulence length scales based on the exact solutions are discussed, and used to derive rigorously a new recursion equation, which would be helpful in understanding the dynamical process of turbulence, especially for the Markov property and turbulence cascade. The general energy spectra and their behavior in the lowest wave number range are investigated. According to the present theory, the Loitsiansky integral is not an invariant in general cases.
	TO cite this article:Ran Zheng. Large-Scale Dynamics of Isotropic Turbulence[OL].[17 May 2006] http://en.paper.edu.cn/en_releasepaper/content/6657


	2. Similarity Solutions of Velocity Distributions in Homogeneous Isotropic Turbulence
	Ran Zheng
	Mechanics 05 May 2006
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	Abstract:The starting point for this paper lies in the results obtained by Tatsumi (2004) for isotropic turbulence with the self-preserving hypothesis. A careful consideration of the mathematical structure of the one-point velocity distribution function equation obtained by Tatsumi (2004) leads to an exact analysis of all possible cases and to all admissible solutions of the problem. This paper revisits this interesting problem from a new point of view. Firstly, a new complete set of solutions are obtained. Based on these exact solutions, some physically significant consequences of recent advances in the theory of homogenous statistical solution of the Navier-Stokes equations are presented. The comparison with former theory was also made. The origin of non-gaussian character could be deduced from the above exact solutions.
	TO cite this article:Ran Zheng. Similarity Solutions of Velocity Distributions in Homogeneous Isotropic Turbulence[OL].[ 5 May 2006] http://en.paper.edu.cn/en_releasepaper/content/6505

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	3. An extended stochastic response surface method for random field problems
	Shuping Huang
	Mechanics 26 April 2006
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	Abstract:An efficient and accurate uncertainty propagation methodology for mechanics problems with random fields is developed in this paper. This methodology is based on the stochastic response surface method (SRSM) which has been previously proposed for problems dealing only with random variables. This paper extends SRSM to problems involving random fields or random processes fields. The favourable property of SRSM lies in that the deterministic computational model can be treated as a black box, as in the case of commercial finite element codes. Numerical examples are used to highlight the features of this technique and to demonstrate the accuracy and efficiency of the proposed method. A comparison with Monte Carlo simulation shows that the proposed method can achieve numerical results close to those from Monte Carlo simulation while dramatically reducing the number of deterministic finite element runs.
	TO cite this article:Shuping Huang. An extended stochastic response surface method for random field problems[OL].[26 April 2006] http://en.paper.edu.cn/en_releasepaper/content/6410


	4. Evaluating Orthogonal Random Variables in Non-Gaussian Karhunen-Loeve Expansion
	Huang Shuping
	Mechanics 19 April 2006
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	Abstract:A simulation algorithm is developed for generating non-Gaussian processes with a specified marginal distribution function and covariance function, especially for highly skewed non-Gaussian process. It is based on the Karhunen-Loeve (K-L) expansion in terms of deterministic orthogonal functions and uncorrelated K-L random variables. The deterministic functions are obtained from the spectral decomposition of the covariance function. For non-Gaussian processes, the distributions of the K-L variables are however unknown. The strategy for determining these unknown K-L distributions is given below. The validity of the proposed algorithm for simulating highly skewed non-Gaussian process is illustrated using numerical examples.
	TO cite this article:Huang Shuping . Evaluating Orthogonal Random Variables in Non-Gaussian Karhunen-Loeve Expansion[OL].[19 April 2006] http://en.paper.edu.cn/en_releasepaper/content/6315


	5. Nanosolid: Hard Shells Melt Easier
	Sun Changqing
	Mechanics 19 April 2006
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	Abstract:Mechanism is presented for the facscinating facts thatthe surface shell of a nanosolid is harder at temaperature far below the melting point and the hard surface shell melts easier.
	TO cite this article:Sun Changqing. Nanosolid: Hard Shells Melt Easier[OL].[19 April 2006] http://en.paper.edu.cn/en_releasepaper/content/6311


	6. On the Capacity over Spatially Correlated Rayleigh-Fading Channels in the presence of Spatially Correlated Interference
	Yue Dianwu,Zhang T. Q
	Mechanics 13 March 2006
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	Abstract:In this paper, we investigate the capacity of multiple-input/multiple-output (MIMO) systems, which is a general Rayleigh/Rayleigh model including spatially correlated channels as well as spatially correlated interferers. Perfect channel information is assumed to be available to the receiver, but the transmitter has no channel information. Based on the theory of matrix variate distribution, we derive exact closed-form expressions of the moment generating function (MGF) of mutual information of MIMO channels with interference. Then we obtain further exact closed-form expressions of the MIMO ergodic capacity with these MGF formulas of mutual information.
	TO cite this article:Yue Dianwu,Zhang T. Q. On the Capacity over Spatially Correlated Rayleigh-Fading Channels in the presence of Spatially Correlated Interference[OL].[13 March 2006] http://en.paper.edu.cn/en_releasepaper/content/5676


	7. Computing orientation distribution and rheology of turbulent fiber suspensions flowing through a contraction
	Lin Jianzhong
	Mechanics 27 February 2006
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	Abstract:The Reynolds averaged Navier-Stokes equation was solved with the Reynolds stress model to get the mean fluid velocity and the turbulent kinetic energy in the turbulent flow of a contraction with rectangular cross-section. The turbulent velocity fluctuations were represented as a Fourier series with random coefficients. Then the slender-body theory was used to predict the fiber orientation distribution, orientation tensor, additional shear stress and first normal stress difference of suspensions in the flow. Some numerical results are in agreement qualitatively with the experimental ones available in the literature. The results show that the longer fibers tend to align the streamline easily. Increased contraction ratio results in higher fiber alignment in the direction of flow. The fibers are weakly and strongly aligned in the direction of flow in the region near the inlet and the exit, respectively. Fibers are significantly more aligned in the plane of the contraction than they are aligned in the horizontal plane. Contraction ratio and fiber length were shown to strongly and weakly affect the distributions of additional shear stress and first normal stress difference.
	TO cite this article:Lin Jianzhong. Computing orientation distribution and rheology of turbulent fiber suspensions flowing through a contraction[OL].[27 February 2006] http://en.paper.edu.cn/en_releasepaper/content/5398


	8. Intermediate processes, critical phenomena: theory, method, progress of fractional operators and its applications to modern mechanics
	Xu Mingyu,Tan Wenchang
	Mechanics 27 February 2006
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	Abstract:From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equations) used for describing intermediate processes and critical phenomena in physics and mechanics, and their progress in theory and methods, and applications to modern mechanics. Some authors’ researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made.
	TO cite this article:Xu Mingyu,Tan Wenchang. Intermediate processes, critical phenomena: theory, method, progress of fractional operators and its applications to modern mechanics[OL].[27 February 2006] http://en.paper.edu.cn/en_releasepaper/content/5390


	9. Exact statistical theory of isotropic turbulence
	Ran Zheng
	Mechanics 12 January 2006
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	Abstract:Some physically significant consequences of recent advances in the theory of self-preserved homogenous statistical solutions of the Navier-Stokes equations are presented.
	TO cite this article:Ran Zheng. Exact statistical theory of isotropic turbulence[OL].[12 January 2006] http://en.paper.edu.cn/en_releasepaper/content/4988


	10. A Note on Harten’s Entropy Enforcement Condition
	Ran Zheng
	Mechanics 09 January 2006
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	Abstract:The theme of this paper is to understand the nonlinear stability properties of Harten’s TVD scheme from the point views of symmetry inherent in the PDE. Especial attentions are paid to Harten’s entropy enforcement condition. In this paper, we show that Harten’s entropy enforcement condition is consistent with the group invariant conditions.
	TO cite this article:Ran Zheng. A Note on Harten’s Entropy Enforcement Condition[OL].[ 9 January 2006] http://en.paper.edu.cn/en_releasepaper/content/4904

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