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At least 1,513 records · Page 84

Accelerating the Global Arrays ComEx Runtime using Multiple Progress Ranks

Partitioned Global Address Space (PGAS) models are part of system software that are being designed to support communication runtime for exascale applications. Suitability of using MPI as a scalable PGAS communication subsystem has been shown as a viable option due to its standardization and higher performance. We used MPI two-sided semantics with a combination of automatic and user defined splitting of MPI communicators to achieve asynchronous progress. Our implementation can make use of multiple asynchronous progress ranks (PR) per node that can be mapped to the computing architecture of a node in a distributed cluster. We are able to show significant speed up of over 2.0X and scaling of communication bound computational chemistry application over 1024 nodes of state- of-the-art HPC clusters. Our results show that while running a communication bound application workload on a certain number of cluster nodes, a use of optimum number of ranks dedicated for communication may be used to achieve asynchronous communication progress and obtain highest performance.

PGAS, global-arrays, NWCHEM, NWChemEx, HPC, GPGPU↗

Distributed Solution Approach for a Stackelberg Pricing Game of Aggregated Demand Response

Demand-side management is a fundamental up-to-date strategy that transforms the traditional power grid to a modern smart grid where the flexible pricing mechanisms play a critical role in its successful implementation. In this paper, the pricing-demand response between a distribution system operator (DSO) and load aggregators (LAs) is modeled as a Stackelberg game, where the DSO is the price maker that adjusts its strategy based on observed responses from LAs. With the concerns of computational cost and privacy protection, two distributed solution approaches, particle swarm optimization and pattern search algorithm, are conducted and compared with the classical centralized backward induction approach. Numerical results on a small case study demonstrate the effectiveness of the proposed distributed solution approaches in leveraging flexible demand response potential.

Chen, Yang↗

The History of Monte Carlo and MCNP at Los Alamos [Slides]

The Monte Carlo method for radiation particle transport has its origins at LANL dating back to the 1940’s. The creators of these methods were Drs. Stanislaw Ulam, John von Neumann, Robert Richtmyer, and Nicholas Metropolis. Monte Carlo methods for particle transport have been driving computational developments since the beginning of modern computers; this continues today. In the 1950’s and 1960’s, these new methods were organized into a series of special-purpose Monte Carlo codes, including MCS, MCN, MCP, and MCG. These codes were able to transport neutrons and photons for specialized LANL applications. In 1977, these separate codes were combined to create the LANL Monte Carlo N-Particle (MCNP) radiation particle transport code. In 1983, MCNP3 was released for public distribution to the Radiation Safety Information Computational Center (RSICC). MCNP6.3 will be released late in 2021. Each year, LANL has ~100 MCNP new users and RSICC ~1250 new licenses distributed. This talk will review the Los Alamos history of the development of the modern Monte Carlo method and MCNP.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Thermal-Fluid and Thermal-Structural Response of the T-Tube Modular Divertor to Spatiotemporally Varying Heat Loads

Tungsten (W) is the leading candidate for divertor target plates because of its high melting point (>3000°C), thermal conductivity, and ultimate tensile stress. While W and its alloys are the only solid materials that can survive the high heat fluxes incident on the divertor, W’s low-ductility high ductile-to-brittle transition temperature of ~600°C and relatively low recrystallization temperature (RT) of ~1300°C pose structural (among other) challenges. The objective of this work is to estimate the thermal-fluid and thermal-structural performance of the helium (He)-cooled T-tube divertor, which was originally developed by the Advanced Reactor Innovation and Evaluation Study (ARIES) using numerical simulations. Here, predictions of temperature distributions across the plasma-facing structural component and surface pressures from computational fluid dynamics simulations are used to determine stress distributions using commercial structural finite element modeling software over a range of fusion-relevant conditions. The maximum allowable incident heat fluxes are determined based on the temperature limits imposed by the ITER elastic Structural Design Criteria for In-vessel Components (SDC-IC) and the maximum RT over a range of He mass flow rates and presented in the form of performance design charts. Our recent work found that thermal- structural criteria accounting for the low ductility of W in a finger-type modular divertor constrain the maximum incident heat fluxes to values well below the ITER specifications, and those based on considering only the RT demonstrate that integrated thermal-fluid and elastic structural performance evaluation are required for accurate assessment of divertor performance. This novel analysis of the T-tube considers how nonuniform and transient incident heat fluxes affect its thermal-fluid and thermal-structural performance, as well as the effect of volumetric heating, which can be as great as 27% of the power incident on the divertor surface. The W tile of the T-tube, with its relatively large plasma-facing area of ~15 cm 2 , will likely experience significant spatial variations in incident heat flux. This work therefore assesses whether steady-state incident heat flux profiles with a peak of 10 MW/m 2 and maximum heat flux gradients of 200 MW/m 2 per m exceed the structural limits imposed by the ITER elastic SDC-IC and the maximum RT over a range of fusion-relevant conditions. The effect of transient heat fluxes typical of plasma detachment and reattachment from the target plate due, for example, to gas injection are also evaluated

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

MaNGA DynPop – I. Quality-assessed stellar dynamical modelling from integral-field spectroscopy of 10K nearby galaxies: a catalogue of masses, mass-to-light ratios, density profiles, and dark matter

ABSTRACT This is the first paper in our series on the combined analysis of the Dynamics and stellar Population (DynPop) for the MaNGA survey in the final SDSS Data Release 17 (DR17). Here, we present a catalogue of dynamically determined quantities for over 10 000 nearby galaxies based on integral-field stellar kinematics from the MaNGA survey. The dynamical properties are extracted using the axisymmetric Jeans Anisotropic Modelling (JAM) method, which was previously shown to be the most accurate for this kind of study. We assess systematic uncertainties using eight dynamical models with different assumptions. We use two orientations of the velocity ellipsoid: either cylindrically aligned JAMcyl or spherically aligned JAMsph. We also make four assumptions for the models’ dark versus luminous matter distributions: (1) mass-follows-light, (2) free NFW dark halo, (3) cosmologically constrained NFW halo, (4) generalized NFW dark halo, i.e. with free inner slope. In this catalogue, we provide the quantities related to the mass distributions (e.g. the density slopes and enclosed mass within a sphere of a given radius for total mass, stellar mass, and dark matter mass components). We also provide the complete models which can be used to compute the full luminous and mass distribution of each galaxy. Additionally, we visually assess the qualities of the models to help with model selections. We estimate the observed scatter in the measured quantities which decreases as expected with improvements in quality. For the best data quality, we find a remarkable consistency of measured quantities between different models, highlighting the robustness of the results.

Astronomy & Astrophysics↗

A virtual source model for Kilo-voltage cone beam CT: Source characteristics and model validation

Purpose: The purpose of this investigation was to study the source characteristics of a clinical kilo-voltage cone beam CT unit and to develop and validate a virtual source model that could be used for treatment planning purposes. Methods: We used a previously commissioned full Monte Carlo model and new bespoke software to study the source characteristics of a clinical kilo-voltage cone beam CT (CBCT) unit. We identified the main particle sources, their spatial, energy and angular distribution for all the image acquisition presets currently used in our clinical practice. This includes a combination of two energies (100 and 120 kVp), two filters (neutral and bowtie), and eight different x-ray beam apertures. We subsequently built a virtual source model which we validated against full Monte Carlo calculations. Results: We found that the radiation output of the clinical kilo-voltage cone beam CT unit investigated in this study could be reproduced with a virtual model comprising of two sources (target and filtration cone) or three sources (target, filtration cone and bowtie filter) when additional filtration was used. With this model, we accounted for more than 97% of the photons exiting the unit. Each source in our model was characterised by a origin distribution in both X and Y directions, a fluence map, a single energy spectrum for unfiltered beams and a two dimensional energy spectrum for bowtie filtered beams. The percentage dose difference between full Monte Carlo and virtual source model based dose distributions was well within the statistical uncertainty associated with the calculations ( {+-} 2%, one standard deviation) in all cases studied. Conclusions: The virtual source that we developed is accurate in calculating the dose delivered from a commercial kilo-voltage cone beam CT unit operating with routine clinical image acquisition settings. Our data have also shown that target, filtration cone, and bowtie filter sources needed to be all included in the model in order to accurately replicate the dose distribution from the clinical radiation beam.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

TU-AB-BRB-00: New Methods to Ensure Target Coverage

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. The treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.

60 APPLIED LIFE SCIENCES↗

TU-AB-BRB-01: Coverage Evaluation and Probabilistic Treatment Planning as a Margin Alternative

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. The treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.

60 APPLIED LIFE SCIENCES↗

TU-AB-BRB-02: Stochastic Programming Methods for Handling Uncertainty and Motion in IMRT Planning

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. The treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.

60 APPLIED LIFE SCIENCES↗

TU-AB-BRB-03: Coverage-Based Treatment Planning to Accommodate Organ Deformable Motions and Contouring Uncertainties for Prostate Treatment

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. The treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.

60 APPLIED LIFE SCIENCES↗

A Projective Phase Space Generator for Hadronic Vector Boson Plus One Jet Production

In this paper we use our previously developed projective phase space generator for the calculation of the hadronic production of a vector boson with one additional jet at Next-to-Leading Order. The projective phase space generator allows us to make physical predictions in novel ways, speeding up both evaluation time and attainable accuracy. For the numerical evaluation we explore a computational model which combines the use of both multi-threading and distributed resources through the use of grid or cloud computing without depending on local institutional computer availability. The projective phase space method is well suited for this approach and gives through the use of cloud computing instant access to a large pool of resources.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The accurate particle tracer code

The Accurate Particle Tracer (APT) code is designed for systematic large-scale applications of geometric algorithms for particle dynamical simulations. Based on a large variety of advanced geometric algorithms, APT possesses long-term numerical accuracy and stability, which are critical for solving multi-scale and nonlinear problems. To provide a flexible and convenient I/O interface, the libraries of Lua and Hdf5 are used. Following a three-step procedure, users can efficiently extend the libraries of electromagnetic configurations, external non-electromagnetic forces, particle pushers, and initialization approaches by use of the extendible module. APT has been used in simulations of key physical problems, such as runaway electrons in tokamaks and energetic particles in Van Allen belt. As an important realization, the APT-SW version has been successfully distributed on the world’s fastest computer, the Sunway TaihuLight supercomputer, by supporting master–slave architecture of Sunway many-core processors. Here, based on large-scale simulations of a runaway beam under parameters of the ITER tokamak, it is revealed that the magnetic ripple field can disperse the pitch-angle distribution significantly and improve the confinement of energetic runaway beam on the same time.

97 MATHEMATICS AND COMPUTING↗

SBbadger: biochemical reaction networks with definable degree distributions

Abstract Motivation An essential step in developing computational tools for the inference, optimization and simulation of biochemical reaction networks is gauging tool performance against earlier efforts using an appropriate set of benchmarks. General strategies for the assembly of benchmark models include collection from the literature, creation via subnetwork extraction and de novo generation. However, with respect to biochemical reaction networks, these approaches and their associated tools are either poorly suited to generate models that reflect the wide range of properties found in natural biochemical networks or to do so in numbers that enable rigorous statistical analysis. Results In this work, we present SBbadger, a python-based software tool for the generation of synthetic biochemical reaction or metabolic networks with user-defined degree distributions, multiple available kinetic formalisms and a host of other definable properties. SBbadger thus enables the creation of benchmark model sets that reflect properties of biological systems and generate the kinetics and model structures typically targeted by computational analysis and inference software. Here, we detail the computational and algorithmic workflow of SBbadger, demonstrate its performance under various settings, provide sample outputs and compare it to currently available biochemical reaction network generation software. Availability and implementation SBbadger is implemented in Python and is freely available at https://github.com/sys-bio/SBbadger and via PyPI at https://pypi.org/project/SBbadger/. Documentation can be found at https://SBbadger.readthedocs.io. Supplementary information Supplementary data are available at Bioinformatics online.

59 BASIC BIOLOGICAL SCIENCES↗

Correlation function distributions for O ( N ) lattice field theories in the disordered phase

Numerical computations in strongly interacting quantum field theories are often performed using Monte Carlo sampling methods. A key task in these calculations is to estimate the value of a given physical quantity from the distribution of stochastic samples that are generated using the Monte Carlo method. Typically, the sample mean and sample variance are used to define the expectation values and uncertainties of computed quantities. However, the Monte Carlo sample distribution contains more information than these basic properties, and it is useful to investigate it more generally. In this work, the exact form of the probability distributions of two-point correlation functions at zero momentum in O ( N ) lattice field theories in the disordered phase and in infinite volume are determined. These distributions allow for a robust investigation of the efficacy of the Monte Carlo sampling procedure and are shown also to allow for improved estimators of the target physical quantity to be constructed. The theoretical expectations are shown to agree with numerical calculations in the O ( 2 ) model. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

Correlative single-cell hard X-ray computed tomography and X-ray fluorescence imaging

Abstract X-ray computed tomography (XCT) and X-ray fluorescence (XRF) imaging are two non-invasive imaging techniques to study cellular structures and chemical element distributions, respectively. However, correlative X-ray computed tomography and fluorescence imaging for the same cell have yet to be routinely realized due to challenges in sample preparation and X-ray radiation damage. Here we report an integrated experimental and computational workflow for achieving correlative multi-modality X-ray imaging of a single cell. The method consists of the preparation of radiation-resistant single-cell samples using live-cell imaging-assisted chemical fixation and freeze-drying procedures, targeting and labeling cells for correlative XCT and XRF measurement, and computational reconstruction of the correlative and multi-modality images. With XCT, cellular structures including the overall structure and intracellular organelles are visualized, while XRF imaging reveals the distribution of multiple chemical elements within the same cell. Our correlative method demonstrates the feasibility and broad applicability of using X-rays to understand cellular structures and the roles of chemical elements and related proteins in signaling and other biological processes.

59 BASIC BIOLOGICAL SCIENCES↗

Variable Selection for High Dimensional Bayesian Density Estimation: Application to Human Exposure Simulation

Summary Numerous studies have linked ambient air pollution and adverse health outcomes. Many studies of this nature relate outdoor pollution levels measured at a few monitoring stations with health outcomes. Recently, computational methods have been developed to model the distribution of personal exposures, rather than ambient concentration, and then relate the exposure distribution to the health outcome. Although these methods show great promise, they are limited by the computational demands of the exposure model. We propose a method to alleviate these computational burdens with the eventual goal of implementing a national study of the health effects of air pollution exposure. Our approach is to develop a statistical emulator for the exposure model, i.e. we use Bayesian density estimation to predict the conditional exposure distribution as a function of several variables, such as temperature, human activity and physical characteristics of the pollutant. This poses a challenging statistical problem because there are many predictors of the exposure distribution and density estimation is notoriously difficult in high dimensions. To overcome this challenge, we use stochastic search variable selection to identify a subset of the variables that have more than just additive effects on the mean of the exposure distribution. We apply our method to emulate an ozone exposure model in Philadelphia.

Reich, Brian J.↗

SU-E-I-99: Estimation of Effective Charge Distribution by Dual-Energy CT Reconstruction

Purpose: Computed Tomography (CT) is a method to produce slice image of specific volume from the scanned x-ray projection images. The contrast of CT image is correlated with the attenuation coefficients of the x-ray in the object. The attenuation coefficient is strongly dependent on the x-ray energy and the effective charge of the material. The purpose of this presentation is to show the effective charge distribution predicted by CT images reconstructed with kilovoltage(kV) and megavoltage(MV) x-ray energy. Methods: The attenuation coefficients of x-ray can be characterized by cross section of photoionization and Compton scattering for the specific xray energy. In particular, the photoionization cross section is strongly correlated with the effective charge of the object. Hence we can calculate effective charge by solving the coupled equation between the attenuation coefficient and the theoretical cross section. For this study, we use the megavoltage (MV) and kilovoltage (kV) x-rays of Elekta Synergy as the dual source x-ray, and CT image of the Phantom Laboratory CatPhan is reconstructed by the filtered back projection (FBP) and iterative algorithm for cone-beam CT (CBCT). Results: We report attenuation coefficients of each component of the CatPhan specified by each x-ray source. Also the effective charge distribution is evaluated by the MV and kV dual x-ray sources. The predicted effective charges are comparable with the nominal ones. Conclusion: We developed the MV and kV dual-source CBCT reconstruction to yield the effective charge distribution. For more accuracy, it is critical to remove an effect of the scattering photon in the CBCT reconstruction algorithm. The finding will be fine reference of the effective charge of tissue and lead to the more realistic absorbed-dose calculation. This work was partly supported by the JSPS Core-to-Core Program(No. 23003), and this work was partly supported by JSPS KAKENHI 24234567.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Ionic density distributions near the charged colloids: Spherical electric double layers

We have studied the structure of the spherical electric double layers on charged colloids by a density functional perturbation theory, which is based both on the modified fundamental-measure theory for the hard spheres and on the one-particle direct correlation functional (DCF) for the electronic residual contribution. The contribution of one-particle DCF has been approximated as the functional integration of the second-order correlation function of the ionic fluids in a bulk phase. The calculated result is in very good agreement with the computer simulations for the ionic density distributions and the zeta potentials over a wide range of macroion sizes and electrolyte concentrations, and compares with the results of Yu et al. [J. Chem. Phys. 120, 7223 (2004)] and modified Poisson-Boltzmann approximation [L. B. Bhuiyan and C. W. Outhwaite, Condens. Matter Phys. 8, 287 (2005)]. The present theory is able to provide interesting insights about the charge inversion phenomena occurring at the interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗