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1.
Tahmineh? Keshavarzi Farideh?Sedaghat G.?Ali?Mansoori 《Microfluidics and nanofluidics》2010,8(1):97-104
The aim of our research is to develop a theory, which can predict the behavior of confined fluids in nanoslit pores. The nanoslit
pores studied in this work consist of two structureless and parallel walls in the xy plane located at z = 0 and z = H, in equilibrium with a bulk homogeneous fluid at the same temperature and at a given uniform bulk density. We have derived
the following general equation for prediction of the normal pressure tensor P
zz
of confined inhomogeneous fluids in nanoslit pores:
$ P_{zz} = kT\rho \left( {r_{1z} } \right)\left[ {1 + \frac{1}{kT}\frac{{\partial \phi_{\text{ext}} }}{{\partial r_{1z} }}{\text{d}}r_{1z} } \right] - \frac{1}{2}\int\limits_{v} {\varphi^{\prime}(\vec{r}_{12} )\rho^{(2)} \left( {\overset{\lower0.5em\hbox{$ P_{zz} = kT\rho \left( {r_{1z} } \right)\left[ {1 + \frac{1}{kT}\frac{{\partial \phi_{\text{ext}} }}{{\partial r_{1z} }}{\text{d}}r_{1z} } \right] - \frac{1}{2}\int\limits_{v} {\varphi^{\prime}(\vec{r}_{12} )\rho^{(2)} \left( {\overset{\lower0.5em\hbox{ 相似文献
2.
We present in this paper an analysis of a semi-Lagrangian second order Backward Difference Formula combined with hp-finite
element method to calculate the numerical solution of convection diffusion equations in ℝ2. Using mesh dependent norms, we prove that the a priori error estimate has two components: one corresponds to the approximation
of the exact solution along the characteristic curves, which is
O(Dt2+hm+1(1+\frac\mathopen|logh|Dt))O(\Delta t^{2}+h^{m+1}(1+\frac{\mathopen{|}\log h|}{\Delta t})); and the second, which is O(Dtp+|| [(u)\vec]-[(u)\vec]h||L¥)O(\Delta t^{p}+\| \vec{u}-\vec{u}_{h}\|_{L^{\infty}}), represents the error committed in the calculation of the characteristic curves. Here, m is the degree of the polynomials in the finite element space, [(u)\vec]\vec{u} is the velocity vector, [(u)\vec]h\vec{u}_{h} is the finite element approximation of [(u)\vec]\vec{u} and p denotes the order of the method employed to calculate the characteristics curves. Numerical examples support the validity
of our estimates. 相似文献
3.
4.
Given a “black box” function to evaluate an unknown rational polynomial
f ? \mathbbQ[x]f \in {\mathbb{Q}}[x] at points modulo a prime p, we exhibit algorithms to compute the representation of the polynomial in the sparsest shifted power basis. That is, we determine
the sparsity $t \in {\mathbb{Z}}_{>0}$t \in {\mathbb{Z}}_{>0}, the shift
a ? \mathbbQ\alpha \in {\mathbb{Q}}, the exponents 0 £ e1 < e2 < ? < et{0 \leq e_{1} < e_{2} < \cdots < e_{t}}, and the coefficients
c1, ?, ct ? \mathbbQ \{0}c_{1}, \ldots , c_{t} \in {\mathbb{Q}} \setminus \{0\} such that
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