Application of Similarity Theory to the Characterization of Non-Transferred Laminar Plasma Jet Generation

Laminar-flow non-transferred DC plasma jets were generated by a torch with an inter-electrode insert by which the arc column was limited to a length of about 20 mm. Current–voltage characteristics, thermal efficiency and jet length, a parameter which changes greatly with the generating parameters in contrast with the almost unchangeable jet length of the turbulent plasma, were investigated systematically, by using the similarity theory combined with the corresponding experimental examination. Formulae in non-dimensional forms were derived for predicting the characteristics of the laminar plasma jet generation, within the parameter ranges where no transfer to turbulent flow occurs. Mean arc temperature in the torch channel and mean jet-flow temperature at the torch exit were obtained, and the results indicate that the thermal conductivity feature of the working gas seems to be an important factor affecting thermal efficiency of laminar plasma generation.

Novel Investigation on Principle of Similarity for Microgravity Two-Phase Flow

根据两流体同心环状流线性稳定性分析的结果 ,对微重力气 /液两相流地面模拟实验所应遵循的相似准则进行了探讨 ,得到了一个新的重力无关性准则 ,即Bond数和环形区流体相的毛细数之比的绝对值不大于 1 .此外 ,微重力气 /液两相流模拟实验还必须满足两个条件 ,即流量比和气相表观Weber数应与所模拟的流动中对应数值相等 . In the present paper, the principle of similarity for two phase flows at microgravity is studied based on the results of the linear stability analysis of the two fluid concentric annular flow configuration. A new criterion of gravity independence, namely the absolute value of the ratio between the Bond number and the capillary number of the phase flowing in the annulus is no more than one, is achieved. It is also pointed out that the flowrate ratio and the gas superficial Weber number must have the same ...

Similarity consideration of structural bifurcation buckling

Many structural bifurcation buckling problems exhibit a scaling or power law property. Dimensional analysis is used to analyze the general scaling property. The concept of a new dimensionless number, the response number-Rn, suggested by the present author for the dynamic plastic response and failure of beams, plates and so on, subjected to large dynamic loading, is generalized in this paper to study the elastic, plastic, dynamic elastic as well as dynamic plastic buckling problems of columns, plates as well as shells. Structural bifurcation buckling can be considered when Rn(n) reaches a critical value.

Designing Of Partial Similarity Models And Evaluation Method In Polymer Flooding Experiment

Based on the scaling criteria of polymer flooding reservoir obtained in our previous work in which the gravity and capillary forces, compressibility, non-Newtonian behavior, absorption, dispersion, and diffusion are considered, eight partial similarity models are designed. A new numerical approach of sensitivity analysis is suggested to quantify the dominance degree of relaxed dimensionless parameters for partial similarity model. The sensitivity factor quantifying the dominance degree of relaxed dimensionless parameter is defined. By solving the dimensionless governing equations including all dimensionless parameters, the sensitivity factor of each relaxed dimensionless parameter is calculated for each partial similarity model; thus, the dominance degree of the relaxed one is quantitatively determined. Based on the sensitivity analysis, the effect coefficient of partial similarity model is defined as the summation of product of sensitivity factor of relaxed dimensionless parameter and its relative relaxation quantity. The effect coefficient is used as a criterion to evaluate each partial similarity model. Then the partial similarity model with the smallest effect coefficient can be singled out to approximate to the prototype. Results show that the precision of partial similarity model is not only determined by the number of satisfied dimensionless parameters but also the relative relaxation quantity of the relaxed ones.

Self-similarity limits of genomic signatures

It is shown that metric representation of DNA sequences is one-to-one. By using the metric representation method, suppression of nucleotide strings in the DNA sequences is determined. For a DNA sequence, an optimal string length to display genomic signature in chaos game representation is obtained by eliminating effects of the finite sequence. The optimal string length is further shown as a self-similarity limit in computing information dimension. By using the method, self-similarity limits of bacteria complete genomic signatures are further determined.

A generalized model for the effective thermal conductivity of porous media based on self-similarity

A generalized model for the effective thermal conductivity of porous media is derived based on the fact that statistical self-similarity exists in porous media. The proposed model assumes that porous media consist of two portions: randomly distributed non-touching particles and self-similarly distributed particles contacting each other with resistance. The latter are simulated by Sierpinski carpets with side length L = 13 and cutout size C = 3, 5, 7 and 9, respectively, depending upon the porosity concerned. Recursive formulae are presented and expressed as a function of porosity, ratio of areas, ratio of component thermal conductivities and contact resistance, and there is no empirical constant and every parameter has a clear physical meaning. The model predictions are compared with the existing experimental data, and good agreement is found in a wide range of porosity of 0.14-0.80, and this verifies the validity of the proposed model.

Numerical Sensitivity Analysis and Partial Similarity of Porous Media Flows

A numerical optimisation approach to identify dominant dimensionless variables in porous media flows by sensitivity analysis is proposed. We have validated the approach at first by examining a simple oil reservoir theoretically and numerically as well. A more complex water-flooding reservoir is examined based on sensitivity analysis of oil recovery to the similarity parameters, thus demonstrating the feasibility of the proposed approach to identify dominant similarity parameters for water-oil two-phase flows.

Determination of plastic properties by instrumented spherical indentation: Expanding cavity model and similarity solution approach

The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of-piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity Solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed oil three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.

Determination Of Plastic Properties By Instrumented Spherical Indentation: Expanding Cavity Model And Similarity Solution Approach

The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of-piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity Solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed oil three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.

Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence

A scale-similarity model for Lagrangian two-point, two-time velocity correlations LVCs in isotropic turbulence is developed from the Kolmogorov similarity hypothesis. It is a second approximation to the isocontours of LVCs, while the Smith-Hay model is only a first approximation. This model expresses the LVC by its space correlation and a dispersion velocity. We derive the analytical expression for the dispersion velocity from the Navier-Stokes equations using the quasinormality assumption. The dispersion velocity is dependent on enstrophy spectra and shown to be smaller than the sweeping velocity for the Eulerian velocity correlation. Therefore, the Lagrangian decorrelation process is slower than the Eulerian decorrelation process. The data from direct numerical simulation of isotropic turbulence support the scale-similarity model: the LVCs for different space separations collapse into a universal form when plotted against the separation axis defined by the model.

Graphical representation and the similarity of DNA primary sequences

In this article, graphical representations of DNA primary sequences were generated. Topological indices and molecular connectivity indices were calculated and used for the comparison of similarities among eight different DNA segments. The satisfactory results were achieved by this analysis.

Local similarity in organic crystals and the non-uniqueness of X-ray powder patterns

Two new concepts for molecular solids, 'local similarity' and 'boundary-preserving isometry', are defined mathematically and a theorem which relates these concepts is formulated. 'Locally similar' solids possess an identical short-range structure and a 'boundary-preserving isometry' is a new mathematical operation on a finite region of a solid that transforms mathematically a given solid to a locally similar one. It is shown further that the existence of such a 'boundary-preserving isometry' in a given solid has infinitely many 'locally similar' solids as a consequence. Chemical implications, referring to the similarity of X-ray powder patterns and patent registration, are discussed as well. These theoretical concepts, which are first introduced in a schematic manner, are proved to exist in nature by the elucidation of the crystal structure of some diketopyrrolopyrrole (DPP) derivatives with surprisingly similar powder patterns. Although the available powder patterns were not indexable, the underlying crystals could be elucidated by using the new technique of ab initio prediction of possible polymorphs and a subsequent Rietveld refinement. Further ab initio packing calculations on other molecules reveal that 'local crystal similarity' is not restricted to DPP derivatives and should also be exhibited by other molecules such as quinacridones. The 'boundary-preserving isometry' is presented as a predictive tool for crystal engineering purposes and attempts to detect it in crystals of the Cambridge Structural Database (CSD) are reported.

Atom space distance and computing of molecular similarity

A mathematical model on computation of molecular similarity was suggested, The algorithmic techniques for measuring the degree of similarity between pairs of three-dimensional chemical molecules was represented by modified interatomic distance matrices. Current work was carried out on Indigo 2 work station with Sybyl software. Four groups of molecules were used to compute the molecules similarity to testing the mathematical model with satisfactory results.