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Shiqi Zhou - One of the best experts on this subject based on the ideXlab platform.
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approximate Analytic Expression of surface charge density surface potential relationship for a spherical colloidal particle immersed in a general electrolyte solution
Journal of Dispersion Science and Technology, 2015Co-Authors: Shiqi Zhou, Qinghao ZhongAbstract:We implement a variational iteration method for solving a Poisson–Boltzmann equation (PBE) describing a spherical colloid immersed in a general electrolyte solution. In this method, a general Lagrange multiplier is introduced to construct correction functional for the problem, and the multiplier is identified optimally via a variational method; a linearization solution of the original PBE is chosen as an initial approximation for the iteration. To proceed with the iteration Analytically, we approximate the highly nonlinear term of the PBE by a polynomial of proper order. Due to presence of an exponent integral function in the first-order iteration solution, higher-order iteration solutions are Analytically unavailable currently. Based on the first-order iteration solution, Analytic Expression for surface charge density/surface potential relationship is acquired. The present Analytic solution contrasts sharply with previous ones by two striking features: (1) the present one surpasses well beyond previous a...
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an approximate Analytic Expression for the surface charge density surface potential relationship for a spherical colloidal particle
Journal of Colloid and Interface Science, 1998Co-Authors: Shiqi ZhouAbstract:An approximate Analytic Expression for the surface charge density/surface potential relationship (final sigma/psi0) for a spherical colloidal particle in a solution of mixed and nonsymmetrical electrolytes is obtained by solving a nonlinear Poisson-Boltzmann equation using a linearization approximation. The approximate Analytic Expression is fit for the case of large kappaa(kappa = Debye-Huckel inverse parameter, a = colloidal particle radius), but for the case of small kappaa, the approximate Analytic Expression is applicable only when kappaa >/= 0.03, with a maximal percent relative error of 5.0, even for surface potentials up to 334 mV (25 degreesC). The approximate Analytic Expressions reported in the literature have a low limit of kappaa, 0.5 or even 2.0. The present approximate Analytic Expression has a simple structure and is characterized by the ease with which it is adapted for analysis. Copyright 1998 Academic Press.
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An Approximate Analytic Expression for the Surface Charge Density/Surface Potential Relationship for a Spherical Colloidal Particle
Journal of colloid and interface science, 1998Co-Authors: Shiqi ZhouAbstract:An approximate Analytic Expression for the surface charge density/surface potential relationship (final sigma/psi0) for a spherical colloidal particle in a solution of mixed and nonsymmetrical electrolytes is obtained by solving a nonlinear Poisson-Boltzmann equation using a linearization approximation. The approximate Analytic Expression is fit for the case of large kappaa(kappa = Debye-Huckel inverse parameter, a = colloidal particle radius), but for the case of small kappaa, the approximate Analytic Expression is applicable only when kappaa >/= 0.03, with a maximal percent relative error of 5.0, even for surface potentials up to 334 mV (25 degreesC). The approximate Analytic Expressions reported in the literature have a low limit of kappaa, 0.5 or even 2.0. The present approximate Analytic Expression has a simple structure and is characterized by the ease with which it is adapted for analysis. Copyright 1998 Academic Press.
K C Shaing - One of the best experts on this subject based on the ideXlab platform.
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an approximate Analytic Expression for neoclassical toroidal plasma viscosity in tokamaks
Nuclear Fusion, 2010Co-Authors: K C Shaing, S A Sabbagh, M S ChuAbstract:An approximate Analytic Expression for neoclassical toroidal plasma viscosity in tokamaks that have error fields or magnetohydrodynamic activities is presented. The Expression smoothly joins transport fluxes or plasma viscosity in all the known collisionality regimes derived from the solution of the bounce averaged drift kinetic equation and should be useful in modelling results of existing and future tokamak experiments. It also incorporates some of the extensions of the known Expressions to include the effects of finite ∇B drift in the non-resonant transport processes. Here, B is the magnitude of the magnetic field. The toroidal momentum balance equation is a nonlinear function of the radial electric field when the neoclassical plasma viscosity is dominant. It can have bifurcated solutions for the radial electric field and may lead to better plasma confinement as a result.
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an approximate Analytic Expression for plasma viscosity in finite aspect ratio tokamaks and its applications
Physics of Plasmas, 1996Co-Authors: K C Shaing, M Yokoyama, M Wakatani, C T HsuAbstract:An approximate Analytic Expression for plasma viscosity in finite aspect ratio tokamaks is constructed from all the asymptotic limits. The resultant viscosity coefficient is compared with the numerical results of the solution of the linearized drift kinetic equation. Neoclassical fluxes are reformulated in terms of the viscosity and friction coefficients. These fluxes can be employed to study the omnigeneous property of high‐beta small, or large aspect ratio tokamaks.
A. Wilmer - One of the best experts on this subject based on the ideXlab platform.
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Buckling of stiffened plates with bulb flat flanges
International Journal of Solids and Structures, 2004Co-Authors: D.a. Danielson, A. WilmerAbstract:Abstract The subject of this research is the buckling behavior of a rectangular plate, with a bulb flat stiffener attached to one side of the plate. The stiffener cross section has a thin web and a bulb flat flange that extends to one side of the web. The stiffened plate structure is subjected to axial compression that increases to the buckling load. Results of the investigation include planar property formulas for the asymmetric flange geometry, an Analytic Expression for the Saint-Venant torsional constant of the flange cross section, and an Analytic Expression for the buckling stress corresponding to a tripping mode of the structure. The torsional constant for the bulb flat stiffener is 15–23% higher than understood previously. The Analytic Expression for the buckling stress of a bulb flat stiffened plate differs by less than 4% from finite element and experimental results.
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Analytic Expression of the Buckling Loads for Stiffened Plates with Bulb-Flat Flanges
2003Co-Authors: A. WilmerAbstract:Abstract : The subject of this research is the buckling behavior of a simply supported rectangular plate, with a bulb-flat stiffener attached to one side of the plate The plate structure is subjected to axial compression that increases to the buckling load, The stiffener cross-section has a thin web and a bulb-flat flange that extends to one side of the web, Results of the investigation include planar property formulas for the asymmetric flange geometry, an Analytic Expression for the Saint Venant torsional constant of the flange cross-section, and an Analytic Expression for the buckling load corresponding to a tripping mode of the structure, The torsional constant for the bulb-flat stiffener is 15% - 23% higher than understood previously, The Analytic Expression for the buckling load of the bulb-flat stiffened plates considered in this investigation yields values that are 2% - 6% higher than finite element results, It is also shown that the buckling load of a plate with a bulb-flat stiffener is 3% - 4% less than that of a plate with a T-flange stiffener with the same cross-sectional area, At the onset of stiffener tripping, the torsionally superior bulb-flat tends to bend laterally, while the flexurally superior T-flange tends to twist.
A. K. Gautesen - One of the best experts on this subject based on the ideXlab platform.
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Analytic relaxation modulus Expression for a viscoelastic liquid with complex viscosity following a Havriliak–Negami model a)
Journal of Rheology, 2018Co-Authors: Jay Janzen, A. K. GautesenAbstract:From results published by Rudolf Hilfer for the similar problem involving dielectric permittivities, we derive an explicit Analytic Expression for the step-strain relaxation modulus implied by the Havriliak–Negami model for complex viscosities.
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Analytic relaxation modulus Expression for a viscoelastic liquid with complex viscosity following a havriliak negami model a
Journal of Rheology, 2018Co-Authors: Jay Janzen, A. K. GautesenAbstract:From results published by Rudolf Hilfer for the similar problem involving dielectric permittivities, we derive an explicit Analytic Expression for the step-strain relaxation modulus implied by the Havriliak–Negami model for complex viscosities.
C T Hsu - One of the best experts on this subject based on the ideXlab platform.
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an approximate Analytic Expression for plasma viscosity in finite aspect ratio tokamaks and its applications
Physics of Plasmas, 1996Co-Authors: K C Shaing, M Yokoyama, M Wakatani, C T HsuAbstract:An approximate Analytic Expression for plasma viscosity in finite aspect ratio tokamaks is constructed from all the asymptotic limits. The resultant viscosity coefficient is compared with the numerical results of the solution of the linearized drift kinetic equation. Neoclassical fluxes are reformulated in terms of the viscosity and friction coefficients. These fluxes can be employed to study the omnigeneous property of high‐beta small, or large aspect ratio tokamaks.
