@article {2271,
	title = {Behavior of interacting species in vacancy affinity capillary electrophoresis described by mass balance equation},
	journal = {Electrophoresis},
	volume = {29},
	number = {16},
	year = {2008},
	note = {ISI Document Delivery No.: 343MCTimes Cited: 0Cited Reference Count: 42Sun, Ying Fang, Ning Chen, David D. Y.},
	month = {Aug},
	pages = {3333-3341},
	type = {Article},
	abstract = {Vacancy ACE (VACE) is one of the ACE methods, and has been used to study binding interactions between different biomolecules. Thermodynamic binding constants can be estimated with nonlinear regression methods. With a highly efficient computer simulation program (SimDCCE), it is possible to demonstrate the detailed behaviors of each species during the interaction process under different conditions. In this work, thirteen scenarios in four different combinations of migration orders of the free protein, free drug, and complex formed are studied. The detailed interaction process between protein and ligand is discussed and illustrated based on the mass balance equation, also called mass transfer equation. By properly setting the parameters in the simulation model, the influence of different factors during the interaction process can be well understood.},
	keywords = {affinity capillary electrophoresis, binding constant, COMPUTER-SIMULATION, CONSTANTS, DRUG-PROTEIN-BINDING, equation, EXPERIMENTAL VALIDATION, FRONTAL ANALYSIS, HUMAN-SERUM-ALBUMIN, HUMMEL-DREYER, mass balance, method, PERFORMANCE LIQUID-CHROMATOGRAPHY, vacancy affinity capillary electrophoresis, WALL ADSORPTION, ZONE-ELECTROPHORESIS},
	isbn = {0173-0835},
	url = {<Go to ISI>://000258856900008},
	author = {Sun, Y. and Fang, N. and Chen, D. D. Y.}
}
@article {685,
	title = {An analytical formulation of CPMAS},
	journal = {Solid State Nuclear Magnetic Resonance},
	volume = {23},
	number = {1-2},
	year = {2003},
	note = {ISI Document Delivery No.: 662PWTimes Cited: 4Cited Reference Count: 21},
	month = {Feb-Mar},
	pages = {28-49},
	type = {Article},
	abstract = {An exact expression for the cross polarization between two spin1/2 particles is derived from the quantum Liouville equation. This is given in the form of two integrodifferential equations. These can be solved exactly in the static case (no sample spinning) and a powder average easily performed numerically. With magic-angle spinning, the neglect of certain interference terms simplifies the numerical calculation. A further assumption decoupling the calculation of the sidebands gives a very simple formula that is capable of giving a qualitative interpretation of all experimental observations. Examples are given illustrating typical buildup curves and CPMAS matching profiles. (C) 2002 Elsevier Science (USA). All rights reserved.},
	keywords = {CPMAS, cross polarization, CROSS-POLARIZATION EXPERIMENTS, DYNAMICS, equation, generalized master equation, magic-angle spinning, MAGNETIC-RESONANCE, NMR, quantum Liouville, SOLIDS, TRANSIENT OSCILLATIONS},
	isbn = {0926-2040},
	url = {<Go to ISI>://000181957200003},
	author = {Marica, F. and Snider, R. F.}
}
@article {737,
	title = {Towards the resolution of the Gibbs phenomena},
	journal = {Journal of Computational and Applied Mathematics},
	volume = {161},
	number = {1},
	year = {2003},
	note = {ISI Document Delivery No.: 742YDTimes Cited: 27Cited Reference Count: 25},
	month = {Dec},
	pages = {41-65},
	type = {Article},
	abstract = {It is well known that the expansion of an analytic nonperiodic function on a finite interval in a Fourier series leads to spurious oscillations at the interval boundaries. This result is known as the Gibbs phenomenon. The present paper introduces a new method for the resolution of the Gibbs phenomenon which follows on the reconstruction method of Gottlieb and coworkers (SIAM Rev. 39 (1997) 644) based on Gegenbauer polynomials orthogonal with respect to weight function (1-x(2))(lambda-1/2). We refer to their approach as the direct method and to the new methodology as the inverse method. Both methods use the finite set of Fourier coefficients of some given function as input data in the re-expansion of the function in Gegenbauer polynomials or in other orthogonal basis sets. The finite partial sum of the new expansion provides a spectrally accurate approximation to the function. In the direct method, this requires that certain conditions are met concerning the parameter lambda in the weight function, the number of Fourier coefficients, N and the number of Gegenbauer polynomials, m. We show that the new inverse method can give exact results for polynomials independent of lambda and with m=N. The paper presents several numerical examples applied to a single domain or to subdomains of the main domain so as to illustrate the superiority of the inverse method in comparison with the direct method. (C) 2003 Elsevier B.V. All rights reserved.},
	keywords = {equation, Gibbs phenomenon, spectral methods},
	isbn = {0377-0427},
	url = {<Go to ISI>://000186545000003},
	author = {Shizgal, B. D. and Jung, J. H.}
}
@article {5213,
	title = {Nonhydrodynamic aspects of electron transport near a boundary: The Milne problem},
	journal = {Physical Review E},
	volume = {63},
	number = {1},
	year = {2001},
	note = {ISI Document Delivery No.: 392HFTimes Cited: 2Cited Reference Count: 40Part 2},
	month = {Jan},
	pages = {11},
	type = {Article},
	abstract = {The nonhydrodynamic behavior of electrons near a boundary is studied with the Milne problem of transport theory. A system of electrons dilutely dispersed in a hear bath of atomic moderators is considered in the positive one-dimensional spatial half-space with an absorbing boundary at the origin which mimics an electrode. A flux of electrons is assumed to originate at an infinite distance Rom the boundary. The Fokker-Planck equation for the electron distribution function in space and velocity is considered. The density and temperature profiles are determined, and the departure from hydrodynamic behavior near the boundary is studied. Argon and helium are chosen as the moderators, and results with different cross sections are obtained. The Fokker-Planck equation is solved with an expansion in Legendre and Speed polynomials, and compared wherever possible with results obtained with a Monte Carlo simulation. The behavior near the boundary is shown to be strongly influenced by the Ramsauer-Townsend minimum in the electron-Ar momentum transfer cross section.},
	keywords = {ARGON PLASMA, DEPENDENCE, equation, MODEL, MONTE-CARLO, RAREFIED-GAS FLOWS},
	isbn = {1063-651X},
	url = {<Go to ISI>://000166405100057},
	author = {Vasenkov, A. V. and Shizgal, B. D.}
}
@article {2995,
	title = {RELAXATION DYNAMICS OF HOT PROTONS IN A THERMAL BATH OF ATOMIC-HYDROGEN},
	journal = {Physical Review E},
	volume = {49},
	number = {1},
	year = {1994},
	note = {ISI Document Delivery No.: MV514Times Cited: 10Cited Reference Count: 58},
	month = {Jan},
	pages = {347-358},
	type = {Article},
	abstract = {We present a rigorous kinetic theory formulation of the relaxation of hot protons (H+) in a bath of thermal atomic hydrogen (H). We apply the (well-known) quantum-mechanical scattering theory to (H+,H) collisions and calculate the differential elastic cross section as a function of collision energy and scattering angle. This calculation includes the effects Of both direct and charge-exchange scattering. We then solve the time-dependent Boltzmann equation numerically for the H+ distribution function with an initial delta-function distribution. We also consider two approximate models for the collision dynamics, each based on the assumption that charge exchange dominates the relaxation and that no momentum is transferred in a collision (the linear-trajectory approximation). The first model uses the Rapp-Francis [J. Chem. Phys. 37, 2631 (1962)] energy-dependent cross section in the exact kernel which defines the Boltzmann collision operator. The second model uses a hard-sphere cross section in an approximate collision kernel. We compare the relaxation behavior calculated with the approximate formulations with the exact solution. We also calculate the mobility of H+ in H and compare the exact and-approximate; formulations. This study has applications to processes in astrophysics and aeronomy such as the non-thermal escape of H from planetary atmospheres.},
	keywords = {CHARGE-EXCHANGE, COLLISION KERNELS, EIGENVALUES, ENERGIES, equation, ESCAPE, EXOSPHERE, TRANSPORT, VENUS},
	isbn = {1063-651X},
	url = {<Go to ISI>://A1994MV51400048},
	author = {Clarke, A. S. and Shizgal, B.}
}
@article {3184,
	title = {STABILITY OF BINARY-MIXTURES - SUPERSATURATION LIMITS OF AQUEOUS ALKALI-HALIDE SOLUTIONS},
	journal = {Journal of Chemical Physics},
	volume = {100},
	number = {5},
	year = {1994},
	note = {ISI Document Delivery No.: MY349Times Cited: 20Cited Reference Count: 38},
	month = {Mar},
	pages = {3827-3842},
	type = {Article},
	abstract = {The stability of ionic binary mixtures is investigated by an integral equation method. In presenting the theory a distinction is made between primary and secondary stability criteria, and this distinction is used to clarify some misconceptions in the literature. The derived stability criteria are then applied to electrolyte solutions as well as to a simple binary mixture. In a simple mixture of hard spheres in wafer, both mechanical and material instabilities are found near the spinodal line along with evidence of long-range hydrophobic forces. Results for the electrolyte solutions indicate that salts with only large ions, such as CsI, and those with a smaller ion, such as Na+ or K+, behave differently near the spinodal line. CsI acts hydrophobicly, and appears to undergo demixing from the solvent, whereas NaCl and KCl, which bind the solvent more tightly, do not show clear signs of any such demixing, but do appear to become mechanically unstable. Finally, some recent results of Chen and Forstmann [J. Chem; Phys. 97, 3696 (1992)] are discussed and applied to the present systems.},
	keywords = {DIPOLAR, ELECTROLYTE-SOLUTIONS, equation, FLUID MIXTURES, HYPERNETTED-CHAIN APPROXIMATION, INSTABILITY, NEUTRAL HARD-SPHERES, PHASE, SEPARATION, SPINODAL CURVE},
	isbn = {0021-9606},
	url = {<Go to ISI>://A1994MY34900047},
	author = {Ursenbach, C. P. and Patey, G. N.}
}
@article {2748,
	title = {DIELECTRIC-RELAXATION OF DIPOLAR LIQUIDS},
	journal = {Journal of Chemical Physics},
	volume = {99},
	number = {3},
	year = {1993},
	note = {ISI Document Delivery No.: LN782Times Cited: 19Cited Reference Count: 33},
	month = {Aug},
	pages = {2068-2073},
	type = {Article},
	abstract = {An approximate expression is derived for the dielectric function epsilon(k, omega). The theory includes inertial and non-Markovian effects and is free of adjustable parameters. For the k = 0 case, detailed comparisons are made with computer simulation results for dipolar soft-sphere and Stockmayer fluids, and the theory is shown to be qualitatively sound at both low and high frequencies. The present approximation should be very useful in developing a theory of solvation dynamics which properly includes important inertial effects.},
	keywords = {COMPUTER-SIMULATION, electrostatic, equation, INVARIANT EXPANSION, ION SOLVATION, LIQUIDS, MEAN SPHERICAL MODEL, MOLECULAR LIQUIDS, ORNSTEIN-ZERNIKE, PERIODIC BOUNDARY-CONDITIONS, POLAR, SOLVATION DYNAMICS, SYSTEMS},
	isbn = {0021-9606},
	url = {<Go to ISI>://A1993LN78200067},
	author = {Chandra, A. and Wei, D. Q. and Patey, G. N.}
}
@article {2930,
	title = {ORIENTATIONAL ORDER IN SIMPLE DIPOLAR FLUIDS - DENSITY-FUNCTIONAL THEORY AND ABSOLUTE-STABILITY CONDITIONS},
	journal = {Physical Review E},
	volume = {47},
	number = {1},
	year = {1993},
	note = {ISI Document Delivery No.: KY134Times Cited: 59Cited Reference Count: 29},
	month = {Jan},
	pages = {506-512},
	type = {Article},
	abstract = {The formation of ferroelectric liquid crystals by simple dipolar models is investigated using density-functional theory and absolute-stability analysis. It is emphasized that for such systems well defined results can only be found by specifying exactly how the long-range dipolar interactions are treated. Explicit formal expressions are derived for mean-reaction-field boundary conditions and these are combined with integral-equation approximations in order to obtain numerical results for fluids of dipolar hard and soft spheres. The calculations predict isotropic-to-ferroelectric-nematic transitions in qualitative agreement with computer simulations. The quantitative agreement, however, is rather poor.},
	keywords = {COMPUTER-SIMULATION, ELECTROSTATIC SYSTEMS, equation, HARD-SPHERES, INVARIANT EXPANSION, MEAN SPHERICAL MODEL, ORNSTEIN-ZERNIKE, PERIODIC BOUNDARY-CONDITIONS, POLAR SYSTEMS, TRANSITION},
	isbn = {1063-651X},
	url = {<Go to ISI>://A1993KY13400062},
	author = {Wei, D. Q. and Patey, G. N. and Perera, A.}
}
@article {2873,
	title = {PROPERTIES OF COLLOCATION 3RD-DERIVATIVE OPERATORS},
	journal = {Journal of Computational Physics},
	volume = {105},
	number = {1},
	year = {1993},
	note = {ISI Document Delivery No.: KT822Times Cited: 14Cited Reference Count: 9},
	month = {Mar},
	pages = {182-185},
	type = {Note},
	keywords = {equation},
	isbn = {0021-9991},
	url = {<Go to ISI>://A1993KT82200018},
	author = {Merryfield, W. J. and Shizgal, B.}
}
@article {7288,
	title = {ELECTRON DEGRADATION AND THERMALIZATION IN CH4 GAS},
	journal = {Journal of Chemical Physics},
	volume = {97},
	number = {3},
	year = {1992},
	note = {ISI Document Delivery No.: JE891Times Cited: 17Cited Reference Count: 44},
	month = {Aug},
	pages = {2061-2074},
	type = {Article},
	abstract = {The relaxation to equilibrium of an ensemble of electrons dilutely dispersed in a large excess of CH4 is studied with solutions of the Boltzmann equation. Elastic and vibrationally inelastic collision processes are included in the analysis. The relaxation time for the approach to equilibrium defined for the relaxation of the average electron energy is determined for two different cross section sets. The kinetic theory formalism, based on the Boltzmann equation, is compared with the formalism used in radiation chemistry and physics and based on the Spencer-Fano equation.},
	keywords = {APPROXIMATION, equation, INITIAL PRODUCTS, NEUTRAL GASES, SPENCER-FANO, SUBEXCITATION ELECTRONS, SWARMS, TIME-DEPENDENT ASPECTS, TRANSPORT-COEFFICIENTS, VELOCITY DISTRIBUTION FUNCTION, YIELDS},
	isbn = {0021-9606},
	url = {<Go to ISI>://A1992JE89100051},
	author = {Kowari, K. and Demeio, L. and Shizgal, B.}
}
@article {6958,
	title = {INTERACTION FREE-ENERGY BETWEEN PLANAR WALLS IN DENSE FLUIDS - AN ORNSTEIN-ZERNIKE APPROACH WITH RESULTS FOR HARD-SPHERE, LENNARD-JONES, AND DIPOLAR SYSTEMS},
	journal = {Physical Review A},
	volume = {44},
	number = {12},
	year = {1991},
	note = {ISI Document Delivery No.: GW604Times Cited: 63Cited Reference Count: 43},
	month = {Dec},
	pages = {8224-8234},
	type = {Article},
	abstract = {The interaction free energy per unit area between planar walls is given as a convolution of wall-solvent pair-correlation functions. This result, derived from the large radius limit of the macrosphere-solvent Ornstein-Zernike equations, and from the hypernetted-chain closure, provides a statistical-mechanical basis for the Derjaguin approximation, and is both generally applicable and computationally tractable. It is found that the interaction between hard walls in a hard-sphere fluid is oscillatory, and in good agreement with simulations. The van der Waals attraction emerges from asymptotic analyses of Lennard-Jones and dipolar fluids, and the full expression allows calculation of this quantity down to molecular separations. This is demonstrated by numerical results for dipolar fluids.},
	keywords = {APPROXIMATION, ELECTRICAL DOUBLE-LAYERS, ELECTROLYTES, equation, HYPERNETTED-CHAIN, INHOMOGENEOUS FLUIDS, INVARIANT EXPANSION, MODEL, MONTE-CARLO, SURFACES},
	isbn = {1050-2947},
	url = {<Go to ISI>://A1991GW60400049},
	author = {Attard, P. and Berard, D. R. and Ursenbach, C. P. and Patey, G. N.}
}
@article {7113,
	title = {A REINTERPRETATION OF DENSE GAS KINETIC-THEORY},
	journal = {Journal of Statistical Physics},
	volume = {63},
	number = {3-4},
	year = {1991},
	note = {ISI Document Delivery No.: FP349Times Cited: 10Cited Reference Count: 33},
	month = {May},
	pages = {707-718},
	type = {Article},
	abstract = {In dense gas kinetic theory it is standard to express all reduced distribution functions as functionals of the singlet distribution function. Since the singlet distribution function includes aspects of correlated particles as well as describing the properties of freely moving particles, it is here argued that these aspects should more clearly be distinguished and that it is the distribution function for free particles that is the prime object in terms of which dense gas kinetic theory should be expressed. The standard equations of dense gas kinetic theory are rewritten from this point of view and the advantages of doing so are discussed.},
	keywords = {equation, GAS KINETIC THEORY, GENERALIZED BOLTZMANN EQUATION},
	isbn = {0022-4715},
	url = {<Go to ISI>://A1991FP34900014},
	author = {Snider, R. F.}
}
