scholarly journals Erratum to “An analytical perturbative solution to the Merton Garman model using symmetries”

2021 ◽  
Vol 41 (4) ◽  
pp. 556-556
Author(s):  
Xavier Calmet ◽  
Nathaniel Wiesendanger Shaw
Keyword(s):  
Perturbative Solution

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

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

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

ON THE LINEARIZATION OF THE BELINSKI-ALEKSEEV EXACT SOLUTION FOR TWO CHARGED MASSES IN EQUILIBRIUM

2008 ◽  
Vol 23 (08) ◽  
pp. 1226-1230 ◽  
Author(s):  
D. BINI ◽  
A. GERALICO ◽  
R. RUFFINI
Keyword(s):  
Exact Solution ◽  
Black Hole ◽  
Massive Particle ◽  
Body System ◽  
Perturbative Solution ◽  
Charged Masses

A perturbative solution describing a two-body system consisting of a Reissner-Nordström black hole and a charged massive particle at rest is presented. The coincidence between such a solution and the linearized form of the recently obtained Belinski-Alekseev exact solution is explicitly shown.

Perturbative solution to the single-mode model of superradiance

1975 ◽  
Vol 11 (4) ◽  
pp. 1354-1357 ◽  
Author(s):  
L. M. Narducci ◽  
V. Bluemel
Keyword(s):  
Single Mode ◽  
Perturbative Solution
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