scholarly journals Perturbative solution to orberβ∈ of the Percus-Yevick equation for triangular well potential forn=2

Pramana ◽  
1981 ◽  
Vol 17 (5) ◽  
pp. 443-443
Author(s):  
K N Swamy ◽  
M Rami Reddy ◽  
P C Wankhede
Keyword(s):  
Perturbative Solution ◽  
Triangular Well Potential

Perturbative solution to order βɛ of the Percus-Yevick equation for triangular well potential forn=2

Pramana ◽  
1981 ◽  
Vol 17 (2) ◽  
pp. 143-158 ◽  
Author(s):  
K N Swamy ◽  
M Rami Reddy ◽  
P C Wankhede
Keyword(s):  
Perturbative Solution ◽  
Triangular Well Potential

scholarly journals Dispersion in doublet-type flows through highly anisotropic porous formations

2021 ◽  
Vol 931 ◽  
Author(s):  
Gerardo Severino
Keyword(s):  
Difficult Problem ◽  
Anisotropy Ratio ◽  
Spatial Moments ◽  
Spatial Moment ◽  
Dispersion Mechanism ◽  
Porous Formation ◽  
Perturbative Solution ◽  
Type Flow ◽  
Simplifying Assumptions ◽  
The Difference

Steady doublet-type flow takes place in a porous formation, where the log-transform $Y = \ln K$ of the spatially variable hydraulic conductivity $K$ is regarded as a stationary random field of two-point autocorrelation $\rho _Y$ . A passive solute is injected at the source in the porous formation and we aim to quantify the resulting dispersion process between the two lines by means of spatial moments. The latter depend on the distance $\ell$ between the lines, the variance $\sigma ^2_Y$ of $Y$ and the (anisotropy) ratio $\lambda$ between the vertical and the horizontal integral scales of $Y$ . A simple (analytical) solution to this difficult problem is obtained by adopting a few simplifying assumptions: (i) a perturbative solution, which regards $\sigma ^2_Y$ as a small parameter, of the velocity field is sought; (ii) pore-scale dispersion is neglected; and (iii) we deal with a highly anisotropic formation ( $\lambda \lesssim 0.1$ ). We focus on the longitudinal spatial moment, as it is of most importance for the dispersion mechanism. A general expression is derived in terms of a single quadrature, which can be straightforwardly carried out once the shape of $\rho _Y$ is specified. Results permit one to grasp the main features of the dispersion processes as well as to assess the difference with similar mechanisms observed in other non-uniform flows. In particular, the dispersion in a doublet-type flow is observed to be larger than that generated by a single line. This effect is explained by noting that the advective velocity in a doublet, unlike that in source/line flows, is rapidly increasing in the far field owing to the presence there of the singularity. From the standpoint of the applications, it is shown that the solution pertaining to $\lambda \to 0$ (stratified formation) provides an upper bound for the dispersion mechanism. Such a bound can be used as a conservative limit when, in a remediation procedure, one has to select the strength as well as the distance $\ell$ of the doublet. Finally, the present study lends itself as a valuable tool for aquifer tests and to validate more involved numerical codes accounting for complex boundary conditions.

scholarly journals Non-Perturbative Solution for Hydromagnetic Flow Over a Linearly Stretching Sheet

2013 ◽  
Vol 18 (3) ◽  
pp. 935-943
Author(s):  
O.D. Makinde ◽  
U.S. Mahabaleswar ◽  
N. Maheshkumar
Keyword(s):  
Power Series ◽  
Stretching Sheet ◽  
Adomian Decomposition Method ◽  
Padé Approximants ◽  
Power Series Solution ◽  
Nonlinear Boundary Value Problems ◽  
Pade Approximants ◽  
Adomian Decomposition ◽  
Wide Range ◽  
Perturbative Solution

Abstract In this paper, the Adomian decomposition method with Padé approximants are integrated to study the boundary layer flow of a conducting fluid past a linearly stretching sheet under the action of a transversely imposed magnetic field. A closed form power series solution based on Adomian polynomials is obtained for the similarity nonlinear ordinary differential equation modelling the problem. In order to satisfy the farfield condition, the Adomian power series is converted to diagonal Padé approximants and evaluated. The results obtained using ADM-Padé are remarkably accurate compared with the numerical results. The proposed technique can be easily employed to solve a wide range of nonlinear boundary value problems

scholarly journals NON-PERTURBATIVE SOLUTION OF THE SUPER-VIRASORO CONSTRAINTS

1993 ◽  
Vol 08 (13) ◽  
pp. 1205-1214 ◽  
Author(s):  
K. BECKER ◽  
M. BECKER
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Scaling Limit ◽  
Virasoro Constraints ◽  
Perturbative Solution ◽  
The One ◽  
Genus Expansion ◽  
Double Scaling Limit

We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also obtain the non-perturbative solution of the super-Virasoro constraints in the double scaling limit but do not find agreement between our flows and the known supersymmetric extensions of KdV.

scholarly journals Toward an Analytic Perturbative Solution for the Abjm Quantum Spectral Curve

2019 ◽  
Vol 198 (2) ◽  
pp. 256-270
Author(s):  
R. N. Lee ◽  
A. I. Onishchenko
Keyword(s):  
Spectral Curve ◽  
Perturbative Solution

Monte Carlo and Perturbation Calculations for a Triangular Well Fluid

1974 ◽  
Vol 52 (1) ◽  
pp. 80-88 ◽  
Author(s):  
Damon N. Card ◽  
John Walkley
Keyword(s):  
Monte Carlo ◽  
Hard Spheres ◽  
Low Density ◽  
Monte Carlo Data ◽  
Density Region ◽  
Wide Range ◽  
Model Fluid ◽  
High Density Region ◽  
Superposition Approximation ◽  
Triangular Well Potential

Monte Carlo data have been generated for a simple model fluid consisting of hard spheres with an attractive triangular well potential. The ranges spanned by the temperature and density are as follows. [Formula: see text] and [Formula: see text]. The machine data have been compared to the modern perturbation theories of (i) Barker, Henderson, and Smith and (ii) Weeks, Chandler, and Andersen. Comparison with the machine data shows that the latter theory is successful in the high density region only, but over a wide range of temperature. The Barker–Henderson approach is best in the low density region but the use of the superposition approximation limits the utility of this theory at high densities.

scholarly journals Pseudo-rapidity distribution from a perturbative solution of viscous hydrodynamics for heavy ion collisions at RHIC and LHC

2018 ◽  
Vol 42 (12) ◽  
pp. 123103 ◽  
Author(s):  
Ze-Fang Jiang ◽  
C. B. Yang ◽  
Chi Ding ◽  
Xiang-Yu Wu
Keyword(s):  
Heavy Ion Collisions ◽  
Heavy Ion ◽  
Rapidity Distribution ◽  
Ion Collisions ◽  
Perturbative Solution ◽  
Viscous Hydrodynamics

Optimised Cluster Theory for the Triangular Well Potential

1980 ◽  
Vol 35 (4) ◽  
pp. 412-414
Author(s):  
K. N. Swamy ◽  
P. C. Wankhede
Keyword(s):  
Monte Carlo ◽  
Radial Distribution ◽  
Hard Sphere ◽  
Distribution Functions ◽  
Radial Distribution Functions ◽  
Sphere Diameter ◽  
Cluster Theory ◽  
Monte Carlo Calculations ◽  
Triangular Well Potential

Abstract The optimised cluster theory of Andersen and Chandler has been applied to calculate the radial distribution functions of a triangular well fluid with the width a the hard sphere diameter The results agree well with Monte Carlo Calculations of Card and Walkley.

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