Contact Value Formulae for the Density Profiles of the Electric Double Layer

2008 ◽  
Vol 73 (4) ◽  
pp. 558-574 ◽  
Author(s):  
Douglas J. Henderson ◽  
Lutful B. Bhuiyan
Keyword(s):  
Computer Simulations ◽  
Density Profile ◽  
Physical Interpretation ◽  
Electric Double Layer ◽  
Reasonable Agreement ◽  
Hard Wall ◽  
Density Profiles ◽  
Sum Rule ◽  
Recent Computer ◽  
Local Expression

An exact sum rule, due to Henderson, Blum, and Lebowitz, for the contact value of the density profile of ions in a primitive model electrolyte next to a planar, nonpolarizable charged hard wall, has been known for some years. This result has a pleasing physical interpretation and is local. It has been useful in assessing the accuracy of theoretical approximations. However, a sum rule for the contact value of the charge profile for the same system has, until recently, not been known. A few years ago, Boda and Henderson proposed what they thought might be a useful, but approximate, local expression for the contact value of the charge profile at a weakly charged electrode. Very recent computer simulations indicate that this expression may well be exact at low electrode charge. Recently, Holovko, Badiali, and di Caprio have obtained a more general, but nonlocal, sum rule for the contact value of the charge profile that is valid for all electrode charge. In this paper, we develop an alternative, nonlocal, but nonrigorous expression for this quantity. Both the expression of Holovko et al. and our new expression are examined by means of computer simulations. The Holovko et al. expression is exact and, within numerical uncertainties, seems supported by our simulations. Although admittedly nonrigorous, our simpler expression is in seemingly reasonable agreement with simulation and thus appears to be useful. The relation between the two expressions has not been established.

Structure of chemically reacting particles near a hard wall from integral equations and computer simulations

1996 ◽  
Vol 74 (1-2) ◽  
pp. 65-76 ◽  
Author(s):  
A. Trokhymchuk ◽  
D. Henderson ◽  
S. Sokołowski
Keyword(s):  
Monte Carlo ◽  
Computer Simulations ◽  
Hard Spheres ◽  
Total Density ◽  
Hard Wall ◽  
Monte Carlo Data ◽  
Density Profiles ◽  
Interparticle Potential ◽  
Theoretical Predictions ◽  
Chemically Reacting

We performed Monte-Carlo computer simulations of a fluid of chemically reacting, or overlapping, hard spheres near a hard wall. The model of the interparticle potential is that introduced by Cummings and Stell. This investigation is directed to the determination of the structure of the fluid at the wall, and the orientation of the dimers in particular. In addition, we applied the singlet Percus–Yevick, hypernetted chain and Born–Green–Yvon equations to calculate the total density profiles of the particles. A comparison with the Monte-Carlo data indicates that the singlet Percus–Yevick theory is superior and leads to results that are in reasonable agreement with simulations for all the parameters investigated. We also calculated the average numbers of dimers formed in the bulk part of the system and the results are compared with different theoretical predictions.

scholarly journals A numerical fit of analytical to simulated density profiles in dark matter haloes

2005 ◽  
pp. 13-32 ◽  
Author(s):  
R. Caimmi ◽  
C. Marmo ◽  
T. Valentinuzzi
Keyword(s):  
High Resolution ◽  
Density Profile ◽  
Geometrical Parameters ◽  
Density Profiles ◽  
Mean Values ◽  
Geometrical Properties ◽  
Best Fitting ◽  
Definition Of ◽  
Additional Support ◽  
Open Question

Analytical and geometrical properties of generalized power-law (GPL) density profiles are investigated in detail. In particular, a one-to-one correspondence is found between mathematical parameters (a scaling radius, r0, a scaling density, ?0, and three exponents, ?, ?, ?), and geometrical parameters (the coordinates of the intersection of the asymptotes, xC, yC, and three vertical intercepts, b, b?, b?, related to the curve and the asymptotes, respectively): (r0,?0,?,?,?) ? (xC,yC,b,b?,b?). Then GPL density profiles are compared with simulated dark haloes (SDH) density profiles, and nonlinear least-absolute values and least-squares fits involving the above mentioned five parameters (RFSM5 method) are prescribed. More specifically, the sum of absolute values or squares of absolute logarithmic residuals, Ri=log?SDH(ri) ? log?GPL(ri), is evaluated on 10 points making a 5dimension hypergrid, through a few iterations. The size is progressively reduced around a fiducial minimum, and superpositions on nodes of earlier hypergrids are avoided. An application is made to a sample of 17 SDHs on the scale of cluster of galaxies, within a flat ?CDM cosmological model (Rasia et al. 2004). In dealing with the mean SDH density profile, a virial radius, Rvir, averaged over the whole sample, is assigned, which allows the calculation of the remaining parameters. Using a RFSM5 method provides a better fit with respect to other methods. The geometrical parameters, averaged over the whole sample of best fitting GPL density profiles, yield (?, ?, ?) ? (0.6,3.1,1.0), to be compared with (?, ?, ?) = (1,3,1), i.e. the NFW density profile (Navarro et al. 1995, 1996, 1997), (?, ?, ?) = (1.5,3, 1.5) (Moore et al. 1998, 1999), (?, ?, ?) = (1,2.5,1) (Rasia et al. 2004); and, in addition, ? ? 1.5 (Hiotelis 2003), deduced from the application of a RFSM5 method, but using a different definition of scaled radius, or concentration; and ? ? 1.21.3 deduced from more recent high-resolution simulations (Diemand et al. 2004, Reed et al. 2005). No evident correlation is found between SDH dynamical state (relaxed or merging) and asymptotic inner slope of the fitting logarithmic density profile or (for SDH comparable virial masses) scaled radius. Mean values and standard deviations of some parameters are calculated, and in particular the decimal logarithm of the scaled radius, ?vir, reads < log?vir >= 0.74 and ?slog?vir = 0.150.17, consistent with previous results related to NFW density profiles. It provides additional support to the idea, that NFW density profiles may be considered as a convenient way to parametrize SDH density profiles, without implying that it necessarily produces the best possible fit (Bullock et al. 2001). A certain degree of degeneracy is found in fitting GPL to SDH density profiles. If it is intrinsic to the RFSM5 method or it could be reduced by the next generation of high-resolution simulations, still remains an open question. .

Integral equations for the density profiles of infinitely polydisperse fluids at a hard wall

1999 ◽  
Vol 111 (13) ◽  
pp. 6047-6052 ◽  
Author(s):  
P. Bryk ◽  
A. Patrykiejew ◽  
J. Reszko-Zygmunt ◽  
S. Sokolowski ◽  
D. Henderson
Keyword(s):  
Integral Equations ◽  
Hard Wall ◽  
Density Profiles

Density profiles of a double square-well model of a chemically associating fluid near a hard wall

1995 ◽  
Vol 86 (4) ◽  
pp. 649-664 ◽  
Author(s):  
Orest Pizio ◽  
Andrij Trokhymchuk ◽  
Stefan Sokołowski
Keyword(s):  
Hard Wall ◽  
Density Profiles ◽  
Well Model ◽  
Square Well

The Scattering of Positrons by Helium: Total Cross Sections up to 270 eV

1975 ◽  
Vol 53 (10) ◽  
pp. 962-967 ◽  
Author(s):  
B. Jaduszliwer ◽  
A. Nakashima ◽  
D. A. L. Paul
Keyword(s):  
Energy Range ◽  
Cross Section ◽  
Cross Sections ◽  
Born Approximation ◽  
Reasonable Agreement ◽  
Experimental Results ◽  
Formation Cross Section ◽  
Sum Rule ◽  
Total Cross Sections ◽  
High Energies

The total cross sections for the scattering of positrons by helium have been measured by the method of transmission in the 16 to 270 eV energy range. The experimental results are higher than those of Canter et al. but are in reasonable agreement with recent results of Griffith et al., and at high energies tend towards Born approximation calculations. The integral of the cross section over positron momentum is smaller than the sum rule estimate made by Bransden et al. A tentative value of (0.034 ± 0.017)πa02 is assigned to the positronium formation cross section at threshold.

Non-linear effects in a Rayleigh–Bénard experiment

1970 ◽  
Vol 42 (1) ◽  
pp. 161-175 ◽  
Author(s):  
D. R. Caldwell
Keyword(s):  
Rayleigh Number ◽  
Heat Flow ◽  
Density Profile ◽  
Critical Rayleigh Number ◽  
Temperature Drop ◽  
Density Profiles ◽  
Heating Curve ◽  
Linear Effects ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Observations of temperature drop as a function of heat flow in Rayleigh–Bénard convection with curved density profiles show: (1) reversal of slope in the heating curve, (2) oscillations with time, (3) history dependence, and (4) an increase in critical Rayleigh number as the curvature of the density profile is increased. Some of the results are quite similar to the predictions of Busse.

Density profiles of one-component shielded sticky point fluid near a hard wall

1995 ◽  
Vol 242 (3) ◽  
pp. 297-303 ◽  
Author(s):  
Yu.V Kalyuzhnyi ◽  
O Pizio ◽  
S Sokołowski
Keyword(s):  
Hard Wall ◽  
Density Profiles

Time-dependent density profiles in a filling box

1983 ◽  
Vol 132 ◽  
pp. 457-466 ◽  
Author(s):  
M. Grae Worster ◽  
Herbert E. Huppert
Keyword(s):  
Numerical Integration ◽  
Density Profile ◽  
Approximate Expression ◽  
Time Dependent ◽  
Buoyant Plume ◽  
Governing Equations ◽  
Density Profiles ◽  
Approximate Analytic Expression ◽  
Analytic Expression ◽  
Dependent Density

An approximate analytic expression for the time-dependent density profile formed by a turbulent buoyant plume in a confined region is presented. The analysis is based on the approximation that the density of the fluid behind the first front changes at a rate which is virtually independent of position. The approximate expression is shown to be in excellent agreement with a full numerical integration of the governing equations.

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